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Ultraviolet Bremsstrahlung spectroscopy
Progress In Surface Science, Vol. 13, pp. 225-284, 1983 Printed in the USA. All rights reserved.
0079-6816/83 $0.00 + .50 Copyright © 1983 Pergamon Press Ltd.
ULTRAVIOLET BREMSSTRAHLUNG SPECTROSCOPY VOLKER DOSE Physikalisches Institut der Universit~t, Am Hubland, D8700 W•rzburg, Germany
Abstract Recent experimental progress has introduced Bremsstrahlung spectroscopy especially in the isochromat mode as a new surface analytical tool. Bremsstrahlung production may be regarded as radiative capture by solids and is therefore the inverse process to the well known photoemission. In contrast to photoemission which probes occupied electronic states at solid surfaces, Bremsstrahlung spectroscopy opens up the possibility to investigate unoccupied electronic states including the important region between Fermi- and vacuum energy. Measurements on polycrystalline materials will be discussed on the basis of an isotropic three step model for Bremsstrahlung emission. More recent experiments on single crystals with electrons of well defined energy and initial momentum ~ have demonstrated that T-resolved spectroscopy provides energy versus momentum dispersion relations for ~noccupied bands. Application of spin polarized electron beams has advanced E-resolved Bremsstrahlung spectroscopy to a state of maturity comparable to spin polarized angle resolved photoemission. This paper attempts to review the development and summarize the present state of ultraviolet Bremsstrahlung isochromat spectroscopy.
Contents I.
Introduction
226
2.
Basic Concepts
227
3.
Experimental Considerations
232
4.
Density of State Measurements
242
5.
Application to more complicated Systems
249
A. Oxidation of nickel B. Surface states at GaAs(ll0) C, UV isochromats from graphite
249 256 259
225
226
Vol ker Dose
6.
Measurements A. B. C. D.
7.
on Single Crystals
264
Direct transitions Electronic surface states Ferromagnetic crystals Chemisorption
264 271 273 277
Concluding Remark
281
References
281 Abbreviations
AES ARUPS BIS DOS EDJDOS IPE LEED PES UV UPS XPS
Auger Electron Spectroscopy Angle resolved ultraviolet Photoelectron Spectroscopy Bremsstrahlung Isochromat Spectroscopy Density of States Energy Distribution of the joint Density of States Inverse Photoemission Low Energy Electron Diffraction Photoelectron Spectroscopy Ultraviolet Ultraviolet Photoelectron Spectroscopy X-ray Photoelectron Spectroscopy
I. Introduction
The first
reliable
strahlung
spectrum
investigation was
bandwidth
monochromator
strahlung
yield
The
x-ray
energy the
frequently Duane
function
conservation
nature
of
found
this
experiment
these
structure
was
~/e
Hunt I
energy
exhibited
carried
early
near
with
a
h~ °
limit of an x-ray bremsin
1915.
they
voltage
Using
recorded
a
narrow
the
brems-
across
the x-ray
U°
corresponding
threshold
was
out
with
investigations
the
given
progressively a
higher
fixed
precision.
monochromator
(= constant colour) measurement
Duane
of the anode material
structure
and
of the accelerating
observed
the first isochromat
characteristic of
Duane
to a q u a n t ~
to determine
Ohlin 2 repeated and
by
tube. to
eU = ~ . Their result was a very important confirmation of o o x-ray bremsstrahlung and their method has subsequently been
the
used
Hunt
constitutes
tuned
as a function
yield
of the short wavelength
reported
in 1946
Hunt
in 1942
limit.
This
the
setting
it
performed.
with much better structure
was
interpreted
resolution shown
of the x-ray tube. A preliminary by Nijboer 3 who
Since
to be
explanation
Ohlin's
data in
terms of unfilled electronic states above the Fermi level of the anode. Research Karlsruhe
in this field came to rest for more than a decade until Kurt Ulmer 4 at in
1958
started
an
experimental
isochromat
program
and
continued
to
U1travi ol et Bremsstrahlung Spectroscopy work
in this
field with
his
group
for nearly
227 The significance
twenty years.
of
Ulmers work with respect to surface science was first recognized by Duke and Park 19725.
Isochromat
laboratories
spectroscopy has been performed
since.
Full appreciation
in a steadily growing number of
of its close
relationship
to photoelectron
spectroscopy has led to the present breathtaking development.
2. Basic Concepts
Though
the expression
"isochromat"
involved in this spectroscopy be most Figure tron
easily understood
a
absorbed
by
a valence
is
thereby
measurement
initially
~o
electron
transfered
of
to the better known photoelectric
at
monochromatic initial
to a
the kind of measurement
final
energy
In ultraviolet
electromagnetic E i of
the
solid
effect.
photoelec-
radiation sample.
is The
state with energy Ef = E i + ~ o "
A
of the rate of emitted electrons as a function of Ef is then taken as
an indicator hand
pretty well
of the elementary radiative process may
of the two spectroscopies.
quantum
electron
right
by reference
I shows a comparison
spectroscopy
describes
the physics
of part
free
the occupation of Fig. electron
probability
I also with
displays
energy
E1
at the
the time
undergoes
initial
state
reverse a
of
radiative
energy
this
E i. The
process.
transition
Photoemission and Bremsstrahlung
EI
Evac i FERMI LEVEL~ / / ~ UPS
IPE
Fig. I: Photoemission and Bremsstrahlung production are related by time reversal. The initial state in photoemlsslon, one electron in the solid and one quantum ~ in the radiation field is the final state in o Bremsstrahlung production. The same correspondence applies to the final state in PES and the initial state in BIS.
An
with
228
Volker Dose
emission
of
electronic can,
a
light
state
quantum
of
the initial
energy ~0 ° constant, function
of
this
nic
states
processes
measure
the final
above
an
state
distribution the
is only
Hamiltonian
and
ends
up
in
a
final
previously
of the solid at energy Ef. Exactly analogous
by variation
ximation
~0 °
state
intensity
energy
Ei,
keeping
distribution
Ef = E i - ~%o"
reflects
Fermi
energy
the available
level.
We
in the interchange
note,
that
to photoemission
the quantum
of light
Within number
unoccupied
quanta ~0 ° as a
the same coarse of empty
the difference
appro-
final electrobetween
of initial and final states.
the
is in both cases
where A denotes
the electromagnetic
e and m are
charge
and mass
tively.
mutual
relationship
The
has been well known in atomic been
rates lar by
extensively
for radiative
atmospheres 6. Pendry 7'8.
first
surface
second
surface
hartree
used
mutual
Consider
two
between
physics to
the
calculate which
surfaces
per photon.
because
the same as in a steradian
the
for
types
of
of light
radiative
experimentally
levels
surfaces
in
properties,
occupied
transitions
hardly
has
respec-
cross sections
in the analysis
solid
identical
accessible
of interstel-
been except
by electrons.
formulated that Let
the
in the
Let Jel be the number of electrons
Conversely
from the second
two
are needed
equivalency
these same levels be empty.
obtained
potential and ~ the momentum operator.
since years. Photolonization
has a given set of energy
Jel and Jph are not equal is not
vector
(2.1)
of the electron and c the velocity
recombination
The
per steradian
lung quanta
two
The interaction
e (~.~ + ~.~) Hint = 2mc
have
we
detection
per
let Jph be the number of bremsstrah-
surface per steradlan per incident electron.
the number
of states
of electrons.
in a steradian
of photons
In a steradian of electrons,
the
number of states is
Le/(2~) 3j I~12cose = [fl/(2~r)3J-2. E-cosO where ~ is the volume of a box containing E the electron
energy in hartrees,
the system,
(2.2)
~ is the electron momentum,
and @ the polar angle of electron emission.
In
a steradlan of photons the number of states is
[fl/(2~)3J I,+,,I2cos@ = [~/(2~)3J.c02/c2cosq~ is
the photon momentum,
c the velocity
the polar angle of photon emission.
of light
It follows that
taken
(2.3) in atomic
units,
and
Ultraviolet Bremsstrahlung Spectroscopy
229
Jph/Jel = [~2/2Ec2].cos@/cosO
photon emission is weaker by c is
prohibitive
surfaces.
2
(2.4)
compared to electron emission. While this factor
in experimental atomic
physics
it
is not
in the case of
solid
For a typical 3d metal Pendry 7 estimates a photon flux of 3xi06 per
second at 0.I
eV band width
for an incident electron current
of I00 ~A. This
estimate has been confirmed experimentally within one order of magnitude. Having discussed the differences between photoemission and bremsstrahlung production we now turn to their common aspects.
From (2.4) it follows that brems-
strahlung production offers the same physical information as angle resolved photoelectron spectroscopy,
but for unoccupied bands.
Its special merit is that it
includes the otherwise hardly accessible region between the Fermi and the vacuum level of the sample. Due to the close relationship between the two spectroscoples theoretical models for bremsstrahlung emission can be derived in a unique manner from
existing
models
for
photoemlsslon.
Though
the
most
rigorous
theoretical
approach treats photoemlsslon as a one step process much more physical insight is gained applying the popular isotroplc three step model 9. The first step involves optical excitation of an electron from an occupied valence band state to an empty conduction band state. surface while
Step two describes the tranport of the hot electron to the
the third step accounts for escape across the surface. Adjustment
of this model appropriate to bremsstrahlung emission leads to the following analogous three steps:
(I) Optical decay of an electron of energy E into an empty final state of energy E - ~ o.
We
conserving Brillouln Ef(~).
We
shall
first
direct zone and shall
assume
that
transition such
this
decay
takes
place
in
a
momentum
that an electron with momentum ~
in the
initial energy Ei(~) decays vertically to a final state
subsequently consider also
complete
relaxation of momentum
conservation. (2) Transport of the photon created in the solid which includes the possibility of absorption. (3) Escape of the photon through the sample surface into the vacuum.
The yield function of emitted bremsstrahlung quanta I(E,~) is in general a sum of a primary contribution Ip(E,~) from electrons that have not suffered an inelastic collision prior to the radiative transition and a background Is(E,~)
I(E,~) = Ip(E,~) + Is(E,~)
(2.5)
230
Volker Dose
A detailed discussion tion
Ip(E,~)
function
is now
D(~),
a
of Is(E,~) will be given in chapter 4. The primary distribufactorized
transport
according
function
to the
T(E,m),
three
and
a
step model
into an escape
bremsstrahlung
distribution
P(E,m)
Ip(E,~) = D(~).T(E,m).P(E,~)
We
first
three
consider
in
step model
electrons these
from
states
more
this
initial
are
detail
the
distribution
bulk
calculation
is given
by
of
final
implies
momentum
crystal
P(E,m).
the bulk
states E i into empty that
(2.6)
states Ef.
which is to be conserved in the reduced zone scheme.
According
optical
to
the
deexcitation
The assumption
~ is a good
quantum
of
that
number
This leads to
i,f = + dir J d' k l 12 6(Ei(k)-Ef (~)-~). 6(El (~)-E)
(2.7)
+
where
p is the momentum
emission. energy
E
The of
delta
the
(2.7)
applies
order
to obtain
all possible
operator
functions
incident
for
one
select
electrons
initial
the total
final
and ~ the vector
state
emission
states
initial
and
states
ensure
per incident
associated
with
the
E corresponding to the i and momentum conservation.
energy
ii> decaying
and average
potential
into
one
electron
final
state
if>. In
at energy E we sum over
over initial states.
The resulting emission
is I ~ i,f dir
i,f Pdir(E,m). =
(2.8) i J d'k ~(Ei(~)-E)
A
small
from on
but
important
the normalizing
~,
the
volume
conditions. from
In
summation final
in runs
energy to
density
be of
approximation
as
(2.8)
of
~
reduces
to
initial
the
density
surfaces.
If we
further
(2.8)
reduces
divided
photoemission
in (2.8) beeing absent I0.
by
the
of
bands
assume to
is
fixed
integrated the
states
by
energy
the
Brillouin at
initial
contributing
experimental
density
of
initial
to
the EDJDOS
as obtained zone
and
energy
the
E.
The
to the initial
and
transition matrix
distribution
is proportional
results
in (2.8) depend
measurements
entire
the radiative
the
photoemission
and denominator
turn
angle
final
constant, states
in
encompasses
and
to ordinary
numerator
which
thoroughly
samples
over all
compared
Both,
integration,
case
polycrystalline
denominator
ment
of
the
difference
denominator.
states. only,
of
the
Within the
the
elejoint same
denominator
Ul travi ol et Bremsstrahl ung Spectroscopy
231
For experiments on single crystals with electrons of well defined energy E and momentum
~
in
vacuo,
the
volame
of
integration
fl is
contracted
around
the
V
electrons momentum ~
in the solid. ~ S
and ~ V
are of course different since only S
the component of momentum parallel to the surface is conserved upon penetration of the surface. The dimension of the volume of integration around ~s depends on the
amount
of
smearing
smearing in turn path at
of
the momentum
component normal
is inversely proportional
to
to the surface.
This
the so called elastic mean free
initial energy E. A detailed discussion of I0 •
this relationship has been
given by Cardona and Ley The
foregoing
from momentum the concept
of
discussion assumed
conserving indirect,
that
transitions.
radiative
Spicer II has
emission
results
exclusively
already quite early
invoked
e.g. ~ non-conserving transitions in order to explain
stationary structure in the energy distribution curves from copper obtained for a variety of photon energies.
If momentum conservation is entirely relaxed,
(2.7)
must be rewritten as
ind = f d'kid'kf ISifl2~(Ei(~i)-E)'6(Ei(ki)-Ef(~f ) - ~ ) +
(2.9)
+
The volume of integration for k i and kf is the entire Brillouin zone. By analogy to (2.8) the total emission Pind(E,~) becomes ~ i,f ind Pind(E,~ ) ~ i,f N(Ei )
(2.10)
where N(Ei) is the density of states at initial energy E i. Assuming further that the momentum matrix element
in (2.9) may be replaced by a constant the double
integration in (2.9) factorizes into
i,f ÷ ÷ ind = f d3ki6(Ei(ki)-E)'f d'kf6(E-~-Ef(kf)) Summation
over
i,f
in
(2.10)
turns
the
two
integrals
into
(2.11) the
densities
of
initial and final states respectively. Since the density of initial states cancels in (2.10), we have that emission via ~ non-conserving transitions is proportional to the density of final states only,
Pind(E,~) ~ N(E-h0)
(2.12)
while ordinary photoemisslon yields within the same approximation the product of initial and final densities of states.
232
Volker Dose
The relative importance of direct and indirect transitions has been continuously discussed
in the photoemissfon
for Bremsstrahlung
literature 12. An attempt to access the problem
emission will
be presented later on in the interpretation of
measurements on polycrystalline nickel. We shall finally briefly comment on the transport and escape factors in (2.6). The transport function T(E,~) is by analogy to photoemlssion given by 9
(XeE ) X (~) T(E,~) = I - Xp(~) in(l + --'-'P--~)e where
Xp
and
Xe are
the photon
Since in the ultraviolet energy
dependent.
The
the sample material if
Bremsstrahlung
constant
and
electron
(2.13)
attenuation
lengths
respectively.
region Xp>>ke' T(E,~) is close to unity and only weakly
escape
under
function D(~)
investigation.
spectroscopy
is
depends
Note,
carried
on the optical
however,
out
in
that D(~)
the
initial energy mode it can, in principle,
isochromat
constants
of
is a constant mode.
In
the
add to the structure observed
in the recorded spectra.
3. Experimental Considerations
Transformation of the schematic arrangement into experimental reality is straightforward. Figure 2 shows in detail the early experimental setup used by the Ulmer 13 . Emitted x-rays are monochromatlzed by a single focusing crystal monochro-
group mator
and
the
Anticoincidence cosmic
transmitted techniques
ray background.
The
radiation
is
detected
by
a
with a ring of surrounding electron source
is heated
Geiger
Geiger
MUller
counters
intermittently
counter. eliminate
in order to
avoid energy smearing by the voltage drop across the filament of the x-ray diode. Energy
resolution
obtained
in this
experiment was
of the order of
1.2 eV at a
pass energy of I keV. Measurements of isochromats of the 4d and 5d metals Mo, W, Nb,
and Ta with a statistical precision of 1.5% required accumulation periods of
about 50 h at emission currents between 5 and 35 mA 14. Note that the electronic power deposited on the sample measure
of
deposited
the overall
in these measurements was between 6 W and 40 W. A
sensitivity
charge which was
of
the apparatus
of the order
of 103 -
is the count rate per unit
I04/C
in this case.
A modern
version of this setup has been reported by Lang and Baer 15 who employ the monochromator band
for an AI K -source
(XPS)
Ulmer's
and
group
techniques
conduction using
in an XPS
band
different
used quantum energies
studies crystals,
spectrometer and nicely combine valence (BIS) partly
in
the
grown
same by
experiment. highly
Though
sophisticated
down to 152 eV this detection energy would not
Ultraviolet Bremsstrahlung Spectroscopy be
considered
to be truely ultraviolet.
233
The first so far reported experimental
setup along the same lines operating in the vacuum ultraviolet was carried out by Baptist
and
Chauvet 16.
graphic
grating
The
dispersive
element
recorded on a toroidal blank.
in
their
experiment
This allows
Is
a holo-
for almost
complete
correction of aberrations especially at low wavelengths. The reported characteristics of the grating are outer dimensions of 30 x 30 mm, with
550 groves
per ~m resulting
focal length of 320 mm
in a dispersion of about 20 A per mm nearly
independent over the whole wavelength range of
I00 A to 500 A corresponding to
energies between 20 and i00 eV. Entrance and exit sllt of the monochromator where chosen to be 0.25 x 4 mm resulting in an optical resolution of I0 A essentially independent of the mean detection energy. The reported sensitivity of the apparatus is 3x105 counts/coulomb deposited charge in the d-band maximum of platinum. Since
space
charge
effects
limit
the
emission
current
to
typically
i mA
the
experiment is still rather slow though it constitutes a considerable improvement over the performance figures reported by Ulmer. A suggestive further improvement of performance may be obtained replacing the combination of
spectrometer
exit
sllt
and
channeltron
by a position sensitive
device made up by a channelplate and a resistive anode. A spectrometer of thls kind has been set up by Fauster and Himpse117. Such a modification enables taking simultaneously isochromat spectra at various monochromator energies if the elec-
HV FIX
TI I VARIABL
I INTE GRAT.
SUPPLY IF-U-
Ic°N' °L I GEN.
I
ANTI -U--U- COINC.
]~-
ICOUNT.
Fig. 2: Schematic of a BlS-spectrometer employed by the Ulmer group.
234
Volker Dose
tron if
energy
the
is varied
electron
by Fauster intensity occupied
or even more
energy
is kept
and Hlmpsel versus
from a polycrystalllne
the density
tion and the resolution ing
of
the
step.
differentiation mentally
A
of states
procedure
of the signal obtained apparatus
initial
energy
gold
target. level
spectra reported
Since Au has a fully resembles
may be simply derived
has
energy
resolution
from the slope of x-ray emission
the Fermi
at
of the apparatus
similar
determined
thls evaluation
constant
The overall
is 0.3 eV as demonstrated
energy
d-band
interesting,
constant.
been
pursued
by
a step func-
from the broaden-
Lang
and
Baer 15.
By
from a silver target they derive an experi-
function.
We
shall
discuss
a
refined
version
of
later on.
/i TRANSMISSION >-
ABSORPTION
u. w O u
REGION
'....:.~:...~.~...
z
z
U.l
om m n, o
I--
z
n,.
( ~o <
Y//////A
// ENERGY
-~
E0
Ema x
Fig. 3: Schematic of an x-ray absorption edge. Near edge absorption acts as a low pass to radiation. The solid curve represents the hlgh energy portion of a Bremsstrahlung spectrum. The hatched area is absorbed by a foll of suitably chosen thickness.
Though up
an
a grating
isochromat
appreciable
monochromator experiment,
investment.
We
shall
the followlng 18. Let us consider A
schematic
edge
of
is given
is the most
offering
therefore first
the x-ray absorption in Fig.
3. Absorption
straightforward
a maximum discuss
the edge and f(E,Eo) Let
coefficient
wlth
be
the
intensity
electrons
of
energy
E •
Suppose
approaches
in
of x-ray absorption.
in the vicinity
of an absorption
of the edge may be regarded
of an absorption
for
an
Let E O be the energetic
distribution a
of
to setting
it involves
two alternative
in the vicinity
the transmission
I(E,E m)
approach
flexibility,
the energy dependence
as a low pass filter to incident x-radiatlon.
E.
of
foll for x-rays
x-rays
moment
position of
from
that
it
a
target were
of energy bombarded
possible
to
m
modulate the
a.c.
the edge position with an amplitude AE o. Then for sufficiently component
of
the
transmitted
radiation
R(E m)
would
be
small AE °
proportional
to
Ultraviolet Bremsstrahlung Spectroscopy l(Eo,Em)-AEo, f(Eo,Eo). This, however,
235
is the isochromat corresponding to a monoch-
romator energy E o. If alternatively we modulate the energy of the incident electrons the recorded photocurrent T(Em)iS
T(Em) = where n(E) denotes
d/dE m f n(E)f(E,Eo)l(E,Em)dE
(3.1)
the spectral sensitivity of the x-ray photon detector cathode.
In order
to proceed with
explicit
functional
the evaluation
form for I(E,Em).
of (3.1)
There
it is necessary
is convincing
that at least near the high energy limit of a bremsstrahlung be written as g(E-Em )19'20
to assume an
experimental
evidence
spectrum I(E,E m) may
A slightly more general assumption would be
l(E,Em) = h(Em)g(E-Em) Within
the
previously
developed
simple
corresponds
to the density of unoccupied
a possible
energy
dependence
of
picture
(3.2)
for
bremsstrahlung
formation
states of the target and h accounts
the radiative
transition
matrix element.
g for
Expe-
rience shows that h is only slowly varying with E . Inserting (3.2) into (3.1) we m obtain T(E m) = dh/dE m f n(E)f(E,Eo)g(E-Em)dE
-
h(Em) ~ ~(E)f(E,Eo) ~/~E g(E-Em)dE
(3.3)
Partial integration of the second term noting that ~(0)f(0,Eo)=0 yields:
T(Em) = J g(E-Em)f(E,Eo)(hdn/dE + ndh/dEm)dE
+ h(Em) ] g(E-Em)n(E) ~/SE f(E,Eo)dE The first
term in (3.4) varies only slowly with energy and will cause a smooth
background ergies
E
simplify
(3.4)
signal B(Em). = E ° since
The second
f(E,E o) varies
term contributes rapidly
in
this
significantly region.
only for en-
We may therefore
the integral further by replacing ~(E) by n(Eo). The remaining integral
is a convolution
of g(E-E m) and ~f/~E which
plays
the role of an apparatus
or
spectrometer function. In particular if f(E,Eo) were a step function
f(E,E o) = i
E,E °
f(E,E o) = 0
E)E °
(3.5)
236
Volker Dose
the derivative would be a Dirac delta function and the second integral in (3.4) would yield
(3.6)
q(Eo)'h(Em)'g(Eo-E m)
I--
AI - foil
m
d = O.&-m
w Z (... (.1
u.
L
<
!
I
72.0
725
73.0
73.5
74.0
ENERGYIW Fig. 4: Effective apparatus function for x-ray absorption at the aluminum LII I edge.
which
is
apart
from
the
factor
q(Eo)
spectrometer energy E . In practice O
by
definition
the
isochromat
taken at
a
~f/BE is given in terms of the mass absorp-
tion coefficient of the foil ~(E,Eo) by
(3.7)
8f(E,Eo)/~E = -pd ~(E,Eo)/~E. exp{-~(E,Eo)Pd }
where p and d denote mass density and thickness of the absorber foll respectively.
(3.7) may
experimentally
be evaluated determined
further
by fitting
a Donlach-Sunji621
x-ray absorption data.
the loll is not critical.
The choice
line
shape to
of the thickness of
It should be chosen such that band stucture effects of
the absorber on the high energy side of the edge do not add further structure to the
apparatus
function.
A transmission
ratio
for x-rays with
energy
just below
and above the edge of 102-103 is sufficient for this purpose. An evaluation 22 of (3.7) an
for aluminum LII I absorption at 73 eV is displayed in Fig. 4. A sketch of
isochromat
spectrometer
employing
the above
discussed
principle
is given in
Fig. 5. Apart from the absorption loll it is identical to an appearance potential spectrometer. tial and
This offers
isochromat
the attractive
spectra with
possibility of taking appearance
the very
same experimental
poten-
setup. Experimental
results for GaAs will be discussed in section 5. We
shall
finally
describe
still
another
alternative
to
the
classical
mono-
Ul travi ol et Bremsstrahl ung Spectroscopy
AI- FOIL
FILAMENT
SAMPLE
237
I
HV SUPPLY
---
Io ,OSCIL- I
II,
i
R,f PLL
LATOR Refj
Out
I 3C-SUPPLY
C PU
ADC
Fig. 5: Schematic of a BIS spectrometer employing x-ray absorption. Apart from the absorption foil the arrangement is identical to a soft x-ray appearance potential spectrometer
chromator. Consider
This a
is
Gelger
al. 24 is made
based ~dller
20 mm
and
a
few
diameter
lowpass
to
an
energy
counter.
The
from a 24 mm diameter
less steel electrode helium
on
the
2 mm
counter
stainless
of 1.5 mm diameter.
crystals
of
thick
incident
iodine.
CaF 2
ultraviolet
first
employed
photoncounter by
23
Dennlnger
steel shell with a central
.
et
stain-
The counter filling consists of 500 mbar The
single
radiation
selective
with
entrance
crystal. a
window
The
cutoff
at
of
entrance about
the
counter
window
i0 eV.
is a
provides
The
yield
a
for
molecular photoionlzatlon of iodine with threshold at 9.23 eV 25
(3.8)
12 + hv + 12 + + e
on
the
The
other
combined
energy
hand
offers
action
dependence
of
a hlghpass
the
entrance
to
the
window
detection
of
ultraviolet
transmission and
provides a bandpass with mean energy of
radiation.
the photoionization
(9.70 ± 0.23)
eV. This
is illustrated in Fig. 6. Photoelectrons tion these
could are
be a
produced
at
possible
source
thermalized
the counterwall,
quickly
also
to deteriorate
by
the
helium
by much less energetic
the counter filling,
energy, captured by dissociative attachment to the iodine.
and
resolution. at
radia-
However,
sufficiently
low
238
Volker Dose
|
•
|
ZO
•
|
;~
Z
/
/
" t--
',
/I
"
"~
O
"
----
.,,--,:..
'tl
•
~""~
•
\,.
........
I
I
9.2
o_,,,
31:
I
9.6 10.0 ENERGY (eV)
lO.Z,
Fig. 6: The ultraviolet transmission of a CaF 2 single crystal (long dashes) represents a low pass to vacuum ultraviolet radiation. The photoionlzation of iodine (short dashes) provides a high pass to the detection of UV radiation. The solid line is the band pass obtained by combination of these properties.
e- + 12 + I + I-
The
cross
maximum
section
for
this
reaction
has
a
of the order of 10 -13 cm 2 at 0.34
fore
very
which
is
efficient strongly
the attachment
and
can be
temperature
further
(3.9)
(0.03
± 0.03)
eV and
eV26 . The attachment
threshold
process
is there-
influenced
dependent.
Slow
process and also by dissociative
of
by the iodine
negative
iodine
vapour ions
pressure
produced
has
provided Gelger ions. ly, lead
a the
counter
lower
threshold 27
central design,
the mean
to multiple
efficiency 28 per cent
of
the
(3.8),
electric
the low energy
drift
velocity
discharges counter
from is
do
is sufficiently
it avoids
This would affect
since
than
electrode
of I
quite
high
(3.10)
not
lead
thick.
counter this
discharges
is unusual
of the negative
in
iodine
of the counter and slmultaneous-
is much
smaller
primary and
to
Though
field detachment
threshold
the same
in
photoionization
12 + hv + I+ + I-
which
a
has
than that of electrons,
ionization been
event.
estimated
to
The
quantum
be
several
Ultraviolet Bremsstrahlung Spectroscopy Some
less
operate
desirable
features
it successfully.
of
the
The vapour
counter
pressure
must
be
239
considered
in
of the iodine is strongly
order
to
tempera-
ture dependent leading to higher primary ionization yield with increasing temperature. by
The attachment
far
the more
rate
important 29
(3.9), one
however,
leading
increases
to a net
also.
decrease
The latter process of
the
counter
is
sensl-
tivity of 8% per degree
Due to the strong energy dependence of the attachment
process,
not
the
counter
does
show
a plateau.
Sensitivity
changes
Volt at mean operating voltages around 650 V have been measured.
of 0.6%
per
Special care has
therefore to be taken if intensity comparisons are made.
i F,, I
[
CaF2
I
INTEGR.
DAC
JIPULSE SHAPE
,, ; ,"500-800V v,,
'J
COMPUTER
Fig. 7: Schematic Geiger counter.
We
finally
discharge. rates.
mention
On
a
of a BIS spectrometer
the
first
This problem,
rather
glance
however,
large
this
dead
would
employing the energy selective
time
of about
seriously
can be circumvented
limit
150 ~s the
following
possible
by experimental
each
counting
precautions
to
be discussed in the following. A block diagram of an Isochromat Geiger
M~ller
counter
is given
spectrometer
is due
to
the energy
employing
the energy selective
in Fig. 7. We have up to now only discussed
optical resolution of the spectrometer. resolution
24
A substantial
distribution
of
contribution to the overall
the electrons
impinging
sample. We use a directly heated tungsten filament as a cathode.
broadening
resulting
from
the
voltage
drop
across
the
on the
Thermal broaden-
ing due to a cathode temperature of about 2200 K seems to be inevitable. nal
the
filament
Additiohas
been
240
Vol ker Dose
eliminated During
by
pulsed
the heating
constant
phase
current
heating
the accelerating
at
a repetition
voltage
is
rate
suppressed.
of
400 c/s.
Bremsstrahlung
measurements are therefore restricted to the interval when the filament is equipotential. The
counter
dead
time problem is solved along the same lines. Every
registered
count is used to switch off the acceleration and to block current integration for a time safely therefore
larger
possible
than the counters
during
the
dead
recovery
time.
No
further
period and counting
primary events
losses
do not
are
occur.
Count rates up to 2000 counts per second are easily possible with this technique. II
I
•
.5
Wo=9.?eV
I
?
1
C
HAFNIUN
•
+.:j 0
0 I
I
I
/+
i
°
i
6
"
°o
8 E/eV
0 o
I
I
-1
0
I
1 E/eV
Fig. 8: The isochromat from polycrystalllne hafnium is nearly a step function and can therefore be used for an experimental determination of the apparatus function of the spectrometer in Fig. 7. Fig. 9: Apparatus function derived from the data in Fig. 8.
The overall the
optical
the
latter
obtain
an
to
behavlour.
resolution of the spectrometer function
Maxwellian
involved
experimental This
be
apparatus
assumptions
ble.
energy
resolution
Such
be a
provided
function
shown
in computing
determination
can
and
of
the
the the as
energy
emission
the
solid
distribution.
current
is
llne
Fig.
in
apparatus
from
an
shape
accidentally
function
isochromat
seems
exhibiting
obtained
at
this
Assuming
in saturation
this curve are quite reasonable,
obtained is
is given by a convolution of
electron
9.
Though
an independent
to be highly a
we the
smeared
detection
desira-
step
like
energy
from
Ultraviolet Bremsstrahlung Spectroscopy polycrystalline function finite
hafnium 30
as
shown
in
Fig. 8.
Simple
does not lead to the desired apparatus
slope
of the "plateau".
241
differentiation
of
this
function because of the small but
We therefore assume
that the data in Fig. 9 result
from a broadening of the function,
f(E') = O(E').(I+~E')
that f(E') the
is,
a
step
has
to be formally
energy
function
scale
is
with
a
superimposed
identified
by
definition
g(E') be the apparatus function.
with of
(3.11)
linear
the density
the
8
energy
dependence.
of empty states
function
at
the
Fermi
Since
the zero of energy.
Let
The measured signal H(E) is then given by
H(E) = ] f(Z')g(Z-E')dE'
(3.12)
h(Z) = dH(E)/dZ
(3.13)
G(E) = ~ g(Z')dE'
(3.14)
Let
and
we then obtain by differentiating
(3.12) the inhomogeneous
differential
equation
h(E) = G'(E) + aG(E)
(3.15)
From the solution of (3.15) we obtain
g(E) = h(E) - aH(E) + a2e-UE ] H(E')exp(uE')dE'
g(E)
as
evaluated
Normalization solid
llne.
from
is The
such
the data that
agreement
the is
in Fig. 8 is displayed area
quite
is
the
good.
same
The
as
as
full
that
abszlssa
(3.16)
dots
in Fig. 9.
the
calculated
under
of
the
curve
in
Fig. 8
denotes the voltage applied between cathode and sample. Compared bilities
to a spectrometer have
transmission of
the
equal the
the
energy.
absorption to that
energy
common
foll
This
very high
are
that
operation
monochromator.
counter,
the last two possi-
is only
possible
the very easy and compact
pseudomonochromator,
per coulomb and is therefore tive.
back
Advantages
of a grating
selective
employing a grating monochromator
draw
however,
the
sensitivity
The ultraviolet
offers
sensitivities
design being
at
in the case approximately
spectrometer of up
a fixed
employing
to 108 counts
by far superior in this respect to any other alterna-
perfomance
order of I0 - 50 ~A. Furthermore,
figure
enables measurements
with currents
the low energy of the electrons
involved
of the in the
242
Volker Dose
measurement species
renders
electronic
in the study
inconvenience valuable
attached
in
the
desorption
of adsorbate to
study
the
of
and
covered
fixed
transient
dissociation
surfaces
quantum
energy
adsorbate
of molecular
unimportant. it
induced
will
adsorbed
In spite
of
therefore
states
be
the most
und measurement
of
adsorption kinetics.
4. Density of State Measurements
Most
of
with
the
the
data
energy
to
be
discussed
selective
in
counter
the
following
spectrometer.
chapters
A diagram
have
relating
been
obtained
accelerating
i 3 / 2 kT
El-I---
.....
°; ll
[
i
eU
. . . . . . . .
Fig. i0: Energy diagram for Bremsstrahlung spectroscopy. Note that the sample work function is irrelevant for the determination of the total electron energy E.
voltage, Fig.
work
functions,
and
mean
The
threshold
for
radiation
I0.
thermal
energy
of
production
the
of
electrons
energy
~o
is given is
from
in
this
diagram
e@ k + 3/2kT + Vac > ~ o
(4.1)
From this relation the Fermi energy is located at
Vac = ~0 ° - e@ k + 3/2kT
Note
that
the sample's
of
considerable
~o
= 9.7 eV,
temperature
work
importance e@ k = 4.5
eV
function in the for
of 2200 K calculated
a
does
study
not
tungsten
from
enter
of adsorbate emitter
the saturation
(4.2)
into
this
covered and
relation. samples.
3/2kT = 0.23
current
This
is
Inserting eV
for
of the filament
a the
Ultraviolet Bremsstrahlung Spectroscopy position mate
of
the Fermi
energy
relies
of course
on a lot of
experimental tally
determined
sonable used not
check
would be at 4.97 V acceleration
agreement
with
g(E).
above
estimate.
the
recallbratlon,
determined
by calculating
function
in all data to be presented require
independently
can be obtained
apparatus
243
The
that will
is
latter
in the following.
a problem
data.
the centroid
result
The
voltage.
This
esti-
An independent
of the experimen-
(4.70 + 0 . 0 4 ) V value,
however,
in reawill
be
Note also that this value does
arise periodically
in experiments
using grating monochromators. I
|
!
!
TANTALUM
20
!
|
/
o=97eV
i
i
!
!
ej
I
,~..
/.
\ ". ° ° o OOOooO oo o e ° °
0
F....-
10 L.L.I F....-
i
i
i
I
i
i
i
i
i
0 2 4 6 8 EXCESS ENERGY (E-~wo)/eV Fig. ii: An experimentally obtained isochromat from polycrystalline tantalum is compared to the density of final unoccupied states in tantalum. Note the discrepancy for excess energies above 5 eV.
Figure Ii tantalum ~ a
shows
target 31.
= 9.7 eV.
o calculation
width
experimentally
was
Full
The solid by
chosen
dots
represent
Petroff
and
Visvanathan 33
to approximate
curve was
normalized
The overall
agreement
is not
also
coincide
predicted with
is slightly
by
1 eV.
theory.
experiment.
In summary,
data, the agreement An entirely
for
measurement
broadened
the experimentally
by
too bad and The
of
the
different
Bolziau
with
a
al. 32
whose
slope.
The
of the experiment the main
maximum
near the Fermi
near the main maximum corresponds
of the model
at
from
of the experiment.
and
of the first maximum
the simplicity
behaviour
et
Lorentzian
threshold
features first
point showing up in the experimental
is quite encouraging
polycrystalllne
density of states
observed
the general
positions
The amplitude
considering
a
to the main emission maximum
too high while the satellite
ly to the inflection
the
isochromats
llne in Fig. Ii is the theoretical
theoretical
are
determined
data displaced used
edge
probabby about
to interprete
the
for excess energies ~ smaller than 5 eV.
is observed
for e ~ 5 eV. The two curves
start
244
Volker Dose
rapidly deviating from each other, the theoretical curve lying below the ultraviolet
isochromat.
far
investigated in our
isochromat from
We have found this behaviour consistently for all materials so
spectrum
electrons
laboratory 31'34.
is expected
that
have
not
As
already mentioned in chapter 2 the
to be composed of a primary component
lost
energy
prior
to
the
radiative
event
Ip(E,~) and a
background Is(E,~) arising from electrons which have suffered one or more energy losses prior to the optical transition. A rough estimate of the probability for radiation
production
using
known
ployed.
the We
the
properties
arrive
sensitive band of processes
in
at
a
ultraviolet of
the
energy
probability
the counter.
of
From
This points
experiment
selective Geiger
10-9
this
are alltogether unimportant
trons entering the sample.
isochromat
per
figure
incident
can
MHller
derived
counter
em-
electron within
the
it is obvious,
in the process
be
that radiative
of thermalizlng the elec-
to an appreciable contribution of I
to S
the overall s i g n a l 31 .
,, ,, o
7//-/j ///////J Fig. 12: Energy level diagramm for Bremsstrahlung emission with and without preceding electron hole pair creation. Electron hole pair production can proceed in two different ways (solid and dashed arrows) leading to the same final state.
Let
P(EI,E 2)
be
the
probability
that
an
electron
of
initial
energy
E1
is
scattered to a final state with energy E 2 creating an electron hole pair and y the probability for radiative transitions with emission of quanta with energy
o (c.f. Fig. 12). Let us assume further, that electron hole pair creation is by far
the dominant energy loss process. With these assumptions we obtain for the rate
Ultraviolet Bremsstrahlung Spectroscopy of
radiation
with
energy
induced
by
electrons
with
245 Initial
energy
El,
O
z(z1,~o) l(Zl,~o) = yN(Zl-~d~o)
+ J e(Ei,E2)dE2{YN(E2-d~o) + J e(E2,E3)dZ31YN(Z3--d~ o) + ... In the first term which represents
the primary component,
placed by X N ( E I - ~ ). The second,
third,
side
the
represent
contributions
to
(4.3)
Ip(E,m) has been re-
and consecutive terms on the right hand
radiative
signal
with
one,
two,
or more
energy losses by electron hole pair creation preceding the radiative event. This model is an extension of that used by Janak et al. 35 for the quantitative explanation of photoelectron energy distributions. I
>
I
I
I
/ " ~
1
I "
' I'
I
' I
I~
I
....
TANTALUM
20
I
h,~= 97eV
o "-
10
~
°
~:'~2 0
-2
,~
--,----~--I
-1
0
I
L--..---,"-',
2
3
~
EXCESS ENERGY
L..n.-.--,---fl
5
6
7
8
9
(E-~.~)IeV
Fig. 13: The heavy dots are an experimental tantalum isochromat spectrum. Small dots represent the direct contribution Id to the total emission. Long dashes, dash dots and small dashes indicate one, two and three electron hole pairs preceding the radiative transition. The solid curve is the sum of the four contributions.
The problem of calculating tion has
been solved
complicated
the function P(EI,E2)
by Kane 36.
An exact
approach
for electron hole pair creaturned out
to be extremely
and computer time consuming. However, Kane was able to prove that a
random ~ approximation originally proposed by Berglund and Spicer 9 yields equally good
results.
With
this
approximation
momentum
conservation
is
relaxed
and
P(EI,E 2) is simply given by the sum of all interband transitions resulting In an
246
Volker Dose
energy loss EI-E 2.
2N(E2) f N(~4)N(e4-EI+E2)dg 4
P(E I,E2) =
(4.4) N(E2)dg2f N(~4)N(e4-El+E2)d~4
The
function
is
normalized
to
two
because
there
are
two
equivalent
types
of
transitions (solid and dashed arrows in Fig. 12) leading to the same final state. Figure 13 shows The heavy the
the
solid dots
direct
results
for
are again
contribution
to
the
previously
the experimental
the
signal
and
discussed data.
The
correspond
to
case of
tantalum 32.
small dots represent the
solid
line
in
Fig. ii. Long dashes indicate the contribution of radiative transitions following the
creation
indicate
of one electron hole
contributions
associated
pair. with
The the
dash dotted curve and short dashes formation
of
two and
three electron
hole pairs respectively. The solid curve is the sum of all contributions. been matched
at
ment
is
finer
details
the intensity maximum.
considerably
improved
The agreement between theory and experi-
especially
are worth mentioning.
It has
The
in
the
region
beyond
first maximum near
5 eV.
the Fermi
But
also
energy is
reproduced perfectly while the second maximum in Fig. 11 has become an inflection point as observed in the experimental data. Similar
results
have
been
obtained
shall not be reproduced here. crystalline pair
nickel 34'37
formations
case.
The
prior
overall
shown to
the
for
the
5d metals
W,
Hf 31,
and
Pt which
Instead we discuss analogous measurements on polyin
Fig. 14.
radiative
quantitative
Up
to
four
transition
agreement
is
again
successive
have
electron
to be included
quite
satisfactory
hole
in this in
this
case. An alternative to adding inelastic contributions to the direct signal I to attempt
is P to remove them from the raw experimental data 34. Assuming that radia-
tive
transitions
used
to calculate
can
be neglected
in
the
thermalization
process,
(4.4)
can
be
the probability W(EI,E 2) for transitions from an initial state
of energy E l to a final state of energy E 2 by a sequence of an arbitrarily high number
of electron hole
convolutions. functions
pairs.
W(EI,E 2)
can be obtained
from
(4.4)
by repeated
The result of such a procedure is shown in Fig. 15. Note that these
exhibit little structure compared suggesting
to the strongly varying densities of
states
used as the input data,
that structure is of secondary
tance.
Only the range of interest in the present context E 2 > ~ o
impor-
is shown. With
the help of these functions the observed radiative signal Ito t may be written as
Itot(El,~o)
= I p ( E l , ~ o) + f W(Ei,E2)Ip(E2,~0o)dE2
(4.5)
Ultraviolet Bremsstrahlung Spectroscopy
1.0
'I
I
I
I
|
l
l
I
l
!
I
I
UV- lsochromat Ni poly
08 >
E 0.6
I
I
247
|
~_........ oeOoe°°°°
0
•
o o o e ° °qb°
--
~ 0./.
contributions / __.
\Theory
. lowicz
m0.2 0
-
=
0 EF
*
=.
2
J-
.
.
L
-'r'-'f"-i-'-i
Z, 6 8 ( E - E F)/eV
t
....
10
12
Fig. 14: Solid dots are the ultraviolet isochromat spectrum from polycrystalline nickel. The lower solid curve is the density of empty states. Dashed and dash-dotted curves represent contributions from electron hole pair production prior to the radiative event. The upper solid curve is the resulting calculated isochromat. Note the small discrepancy at about 2 eV.
10
I
l
~
I
|
I
!
l~uo= 9.?eV E = (E 1 - l ~ w o ) l e V
,
c~
!
I" \
~j ~,
"\ I..\ '-. , ~5
|
.
..:
,-,.
o n
',,
\
¢=3.6 ", '
0
?.2 \ I
&
I
..
,..
10.9\o \
lZ,.5 ~,\
I
8
I
I
I
12
(E2-hUo)/eV Fig. 15: The probability for a transition of an electron with energy E 1 to a state with energy E 2 by electron hole pair production is shown for nickel. The energy range shown is E2 ) ~ o with ~ o = 9.7 eV and c = E l - ~ o "
248
Volker Dose
This for
latter
equation
Ip(El,~o).
comparison
can
The
between
As
solved
result
is
experiment
simple density of states to 3 eV.
be
discussed
by
given and
straightforward
in
interpretation. previously
Flg. 16.
theory.
The
sequential
It provides
dash-dotted
deconvolutlon
a more
line
stringent
represents
the
Thls obviously fails in the region 1 eV
a density
of
states
interpretation
relies
on
indirect
transitions only. A theoretical calculation assuming exclusively direct + transitions with k-averaglng over the entire Brillouin zone with full account of i
w
•
,,;
[~,~.
= E
i' ~,,~.
E 0 "~
'
-
-
•
I
i
" w
I
UV ISOCHR. N"I p01y "
.
I
.
I
0
I
I
2
4
( E -EF )/eV Fig. 16: Data from Fig. 15 have been used to remove the electron hole palr contribution from the nickel spectrum. The resulting experimental data can be explained satisfactorily only if both direct (dashed curve) and T-non conserving transitions are taken into account.
the
dipole
data
are,
transition after
matrix
suitable
element
has
broadening,
been
carried
displayed
as
out by N.V. Smlth 38. His
the
lower
dashed
llne
in
Flg. 16. The sum of the two given as the solid llne approximates the experimental data pretty well.
We may conclude that in isochromats from polycrystalline mate-
rials density of states effects (see also the previous case of tantalum), that is indirect transitions, are prevailing. For a complete understanding, direct
and
indirect
transitions
must
be taken into account.
however, both
This is not at all
surprising. Recalling the phenomenon of band gap emission in photoelectron
spec-
troscopy we expect that Bremssstrahlung spectra wlll contain substantial contributions from initial evanescent an
understanding
of
momentum
states. resolved
This arguement will again be necessary for spectra
to
Obviously nature never presents itself simple minded.
be
presented
in
section
6.
Ultraviolet Bremsstrahlung Spectroscopy 5. Application
to more complicated
249
Systems
A. Oxidation of nickel Transition metal oxides are known to exhibit a wide spectrum of different electronic
properties.
niumoxide haviour and
While
is a perfect
as a function
nlobiumoxide.
tion metal copy
oxides
The
Considerable
oxides
only
tool so
far
due
to
their
impossible
with
its low current
effort
has
insulating
been
spent
insulators
UV
transi-
spectros-
on NiO
isochromat
of 50 ~A/cm 2 on the other hand to allow
of
on the conduction
Measurements
properties.
be-
in vanadium-
on the analysis
information
is NiO 37.
rhe-
to conducting
by H~fner 39. Isochromat
corresponding
insulating
densities
from
as discussed
investigated
nondestructive
and nickel are
and pressure have been observed
to provide
case
cobalt
Transitions
by photoemisslon
are
be sufficiently
conductor.
of temperature
is the suitable
band.
of manganese,
crystals
spectroscopy
has turned out to
the study of nickeloxlde
overlayers
on Ni
substrates. It via
is presently dissociative
ther
exposition
reaction yers
commonly
leads
saturates
of oxide.
accepted
chemisorptlon
to NiO nucleation
at ambient
similar
down
the reaction
behavlour
but
reaction
surfaces
differ
after
reactivity.
of 600 K and oxygen partial pressures
of
Higher
NiO.
surfaces vealed red
favour
partial
production
in such cases
to
NiO.
The
pressures,
binding
Islands.
Increasing
is
The
orientation
temperatures
slow
Ertl et al. 40 suggest
of 10 -3 Pa for the production
oxide.
and markedly
XPS measurements
usually
attributed
to various
degrees
to
damaged have
states with higher binding energies
state
Fur-
three monola-
of different
temperatures,
of nonstoichiometric
oxygen binding
new
lower
of oxide of about
coverages.
a temperature pure
growth
formation
saturation
proceeds
up to 5 - 10.10 -4 Pa.s.
and monocrystals
in
but lead to higher
of oxygen with nickel
exposures
and lateral
temperature
Polycrystalline
show
that
for oxygen
re-
as compa-
lattice
defects
of oxidation
produced
described as Ni203. A series under
the
Fermi
level
of isochromats above
isochromat steep
mentioned
is indicated
of the nickel
corresponding
substrate
conditions
is
by the dashed d-band
is characterized
shown
in
Fig. 17.
line. We observe
emission
with increasing
The
position
a continuous exposure.
a pronounced maximum
the
attenuation
The final oxide
by a very low density of states at the Fermi
rise at 3 eV excess energy,
of
level,
at 4 eV, and another
a
less
pronounced rise at IO eV. The tiny shoulder at I eV will be discussed later. An Pa.s These by
analysis and
of
isochromats
least
the
intermediate
3300.10 -4 Pa.s
squares
have
has been
fitting
been
states
of
oxidation
carried
out
in terms
decomposed
to a linear
into
nickel
combination
and
for
exposure
of
520.10 -4
of a superpositlon nickeloxide
of the clean
model.
contributions
nickel
signal and
250
Volker Dose
UV-lsochromats Ni poly÷Oz T=700K p = 2 10-STorr
o g
0o0
... • •.. •
•~
.4
.."~'~-~....-.
"-
.t
ci,~an,::i
J! ' / • \
:'""%~•""
"
" I k
"
•/001~:
I
"
,
"" %
.:
"1 "1
•
0
2
Fig. 17: Ultraviolet isochromats polyerystalline nickel sample.
for
'1
I
g
I
g
l
g
/, 6 8 ( E -E F) leV various
l
I
10
states
l
I
I
12
of oxidation !
I
I
UV- [sochromat Ni poly 2500L O z
I
of a
I
,,~
T= 700°K
/ /
/ .: 0
Nio ../~
.
|
I
'
0 EF
I
_....'".°"
i
2
Ni
°
,
,
/
~ • .
i
.
.
.
I
.
.
Z, 6 8 ( E -E F) leV
.
.
,
.o--..~__..-
I
10
I
I
_
I
12
Fig. 18: An isoehromat corresponding to an intermediate state of oxidation is decomposed into pure Ni and pure Ni0 contrlbtuions. A indicates the difference between fit and experimental data.
Ul travi ol et Bremsstrahl ung Spectroscopy
251
the oxide isochromat of 26,600-10 -4 Pa.s exposure. The result of such a decomposition is given in Fig. 18. Full dots
represent
structure
obtained after exposure
sample
to
of nickel
and nickeloxlde
3300.10-4pa.s
oxide contributions
oxygen.
Solid
the isochromat
curves
represent
from the composite of the clean nickel
the
nickel
and nickel-
while A is the difference between fit and experiment.
Fits of
similar quality have been obtained for other exposures as well. Repeated isochromat measurements
carried
out after various
oxidation cycles have proved that the
measurement was absolutely nondestructive. The superposition results were used to check the well known logarithmic growth law 41 assumed to be valid in this thickness range.
d
d is the oxide layer thickness partial
pressure,
d o In(l
=
+
L/Lo)
corresponding
to an exposure L at constant oxygen
d o and L ° are free parameters
._.1.0 8 u~ ~co. 8
•
(5.1)
~
which depend sensitively w
Isochromat
Ni 0
T • 700 K p : 2"10"s Torr
~
~
•
on the
/
/ /
"~ .6 r-
7500 L
e~ e-
J
2500 L
"ID
800 L u~ .2
&00 L
0
E
200, L
0
i ,,
,
.
-~
0 .2 .4 .6 .8 1.0 catcutated intensity (S/S..) Fig. 19: The measured intensity of the NiO isochromat signal is compared to values derived from a logarithmic growth law.
oxidation
conditions.
Assuming
an exponential
damping
of
the
incident
due to the finite elastic mean free path in the nickeloxide film,
electrons
the strength of
the nickeloxide signal as a function of film thickness is given by
S(d) = S®{Z - exp(-d/~NiO) }
(5.2)
252
Volker Dose
where
S
indicates
Combining
the
signal
strength
for
an
infinitely
thick
oxide
sample.
(5.1) and (5.2) we obtain
(5.3)
S(d) = S={I - (I + L/Lo)-B }
with
8 = do/%Ni O.
result
Figure 19
shows
of the superposition
derived
from
(5.3).
The
a
comparison
of
S/S=
as
obtained
from
the
model using L ° = 560.10 -4 Pa.s and 8 = 0.4 and values
linear
relationship
between
the
two
sets
of
values
provides an impressive confirmation of (5.1). |
|
l
I
|
Ni p o l y + 0 2 Z
-
/
S" •
15L %
u') '--"
"e/
09 •
0
\
carried
i
I
i
various same
of the oxide
spectroscopy
isochromat
Auger study.
stages
have
studies
I
Some
high
exposure
axis
at
range
as
exposure
sufficiently
oxidation
reported
in order
oxidation
Auger
signal
been
formation
Figure 20 shows
of
sample 43.
> 1
•
-
~OL
i
i
i
i
3 6 AES SIGNAL STRENGTH ( a . u . )
studies
out
:
•
Fig. 20: The measured intensity of the pared to the oxygen AES signal strength.
electron
l
*•
Z
Extensive
!
60L ;
0 I---
.0_
!
but
is expected.
tween these two adsorption
with
function are
the where
Auger
of
also
fitted
linear
transition
analysis
Auger
We have
derived
Auger
signal
relation
relationship
from
obviously
regimes while isochromat
tifies the oxide growth regime.
The
com-
also
from the
of the isochromat
oxygen
given.
is
employing
and Hudson 42. the results
fraction
the
signal
substrates
by Holloway
the nickeloxide a
isochromat
on nickel
to compare
values
exposures
NiO
9
the does
is
from
from
the
linear
for
intersects
chemisorption
the
to
the
not discriminate
be-
spectroscopy
selectively
iden-
U1travi ol et Bremsstrahlung Spectroscopy Though ducible
isochromats in repeated
electron
impact.
influenced
the
characterized exposure
4
force of
origin
from Ni203 may
stimulated either purified
peak
this
the
4 eV
peak
It was
not
in the surface
We
to stoichlometrlc
NiO.
and
be
and
lead
to
a
line
on
the
nickel
to NiO.
therefore
believe
isochromat
A
ion
thls
both occupied and empty electronic
oxygen by electron
3da
Madelung 2p s
3d 8
of
the
result
the result
characterized
to discuss
beeing
by
the
the density of
3d~4s
3d~&s
3d~&s
-2 EF=O 2 ENERGY leV band
structure
models
~
6 for
NiO
8 to UPS
solid
approximation
this work 3d~&s/..,........,..,---
3d e*
in
is a further
states in NiO.
Adler 2p s
its
of the high energy
cases
3d 8
the The
is
NiO
Mattheiss 2p 6
Comparison
explanation
in Fig. 17 to be the best
Eastman et al. 2 pS / , ~ 3d s
Flg. 21: data.
was
dissipation.
excess
Experiment
-/~
state
effects
migration,
state
stable
26,600.10 -4 Pa.s
bombardment
power
possible
remove
In both
new
further high energy
electron
thermal
Two possible
It may either
stimulate
that
not
It wlll be used in the following
-6
in the same experiment
solid
clarified.
of Ni203
in the 26,600.10 -4 Pa.s
the
checked
region.
then be considered.
phase.
as
out
state was then stable against
could
or
carried
isochromat
shown
repro-
they were unstable under hlgh energy
studies
transformation
a reduction
NiO
in
isochromat
desorptlon
case
measurements,
potential
bombardment.
in
nature
electrons
the
eV an
states of sample oxidation were absolutely
in Fig. 17. This
(850 eV)
driving
isochromat
Appearance
by
curve
electron
llne
for various
253
and
BIS
254
Volker Dose
A collection of theoretical chromat (b)
results on NiO together with photoemission and iso-
data is given in Fig. 21. Part
(a) shows the Madelung ion energies,
part
the Adler and Feinlelb semiempirical model 44, part (c) an APW calculation by
Mattheis 45 and part the
Fermi
energy
Different spectra
is
symmetry
the experimental
derived
from
characters
were
taken at various
states
in accord
energy
was
EF
with
chosen
energetically Above
(d)
obtained
from
to coincide
from
by
an
Eastman
analysis
An overlap
of
Freeouf 46.
photoelectron
is observed 47.
experiment
The
Fermi
and Fig. 21a to c were
the experimentally
represent NIO
and
below
of oxygen p- and nickel d-
calculations
the UPS
with
the solid dots
The density of states
measurements
selfconslstent
as determined
in Fig. 21d
UPS
photon energies.
new
aligned
data 37'46.
observed
d-band
peak.
isochromat measurements.
They
obviously must be identified with the band like empty 4s states of the Ni 2+ ions predicted
consistently
the energetic lute way.
positions
Remember
of these states
that isochromat
relative
spectroscopy fixes
to the Fermi
level in an abso-
Since Ni 3+ lattice defects which are always present in the experimental-
ly prepared close
by all models.
oxide
layer act as acceptors,
to the valence
band maximum.
The
the Fermi energy of the oxide will be
region with a very low density of states
between the UPS and isochromat data is therefore identical to the full gap width. If
allowance
isochromat valence This
for
band
is
experimental
represents
the
d-maximum
in very
and
good
broadening
s-band the
is made,
threshold. s-band
agreement
The
the
threshold
with
optical
inflection
energetic then
turns
absorption
The optical measurements
the
excited
states
structure of
in
identified as transitions the d 8 configuration measured dence
isochromat
differs
extends
signal. i eV
The
above
emission
empty
in
be
The
suggestive localized
22
is
gives
an
Ni
In their
transitions
into
edge at 3.8 eV is
out
since
identify states
for a broadened
step
that
estimated
function and
emission
this
extrapolation
narrow is a
structure
remainder
energetic
position
this
structure
as
the
type
d8
+
is
resulting d 9.
This
of
in this
the
centered
from
the
of
Its energy depen-
into empty states below the 4s band edge.
the
that
An enlarged view of the
It was concluded
energetically
possibility
to
to
the absorption
is given In Fig. 22.
one expects
from transitions
ruled
is found in the 0-3 eV
is attributed
and
as 3d 8. in Fig. 21b.
than expected.
Fig.
difference E F.
can
therefore into
line
region
energy range
from what
to lower energies
broken
which
into the empty 4s band. The localized excited states of
in this
range near E F results The
J-3 eV
d 8 configuration
are indicated
markedly
to be 4.1 eV.
the NiO one electron density of states.
the
the Ni
the the
were used by Adler and Feinlelb 44 to derive their
semiemplrical model Fig. 21b fr analysis
out
of
between
measurements 48'49
show an absorption edge at 3.8 eV. Further weak structure range.
point
distance
Ni
3d
4s at
about
substrate
different. from
band
It
is
transitions
interpretation
is
U1travi ol et Bremsstrahl ung Spectroscopy supported rently
by SXAPS measurements 37.
emphasizes
contributions
shown
that the density
rance
potential
SXAPS,
from localized
of empty
states
from
is
spectra
beelng
NiO
255
a core level spectroscopy,
empty states~
as derived identical
In fact,
it could be
from a deconvolution
in
shape
to
the
inhe-
of appea-
broken
llne
In
Fig. 22.
NiO ~ .8
•
UV - lsochromat
÷~
g..6 I'--AE2-'I
,
i/
0 0
, 2
1
( E - EFlleV Fig. 22: Enlarged view of the NiO isochromat threshold region. The dashed curve is an extrapolatlon of the 4s band edge. The difference shown as a full line is assumed to result from transitions into localized empty states in NiO.
Following
arguments
interpretation estlmate
of
photoemlsslon distance
of the
given
the
by Baer
structure
coulomb
displayed
correlation
in their
in Fig.
energy
U
in
distance
of
the
NiO.
states
on 4f elements
the
to a straightforward
The
atomic
limit
of
d
Now let AE I be the energetic
peak from the Fermi
localized
work
22 leads
from NIO would be a d8÷ d 7 transition.
of the d photoemlsslon
respective
and Lang 50
energy
observed
in
and similarly isochromat
AE 2 the
spectros-
copy,then
U - AE 1 + dE 2
is
the
net
definition AE I = 1.5 eV U
=
2.5 eV
energy the and in
corresponding
coulomb
to the transition
correlation
AE 2 = 1 eV we splendid
(5.4)
energy.
obtain
agreement
d 8 + d 8 ÷ d 7 + d 9 which
Inserting
as an estimate with
the
value
the
experimental
for the correlation suggested
by
is by numbers energy
H~fner
and
256
Volker Dose
Wertheim 51. 18 eV
and
Arguments
Note the
that
this
value
presented
of by
present
experimental
and NiO
of
Hubbard
model
number
considerably
Adler
and
Feinleib's 44
H~fner
and
Wertheim
value
1 eV would
differs
is
the more
analysis
may
be
reasonable.
lead to expect NiS
from the atomic which
invoked
Similar
yielded
to
show
suggesting
of
13 eV.
that
d-band widths
to be an insulator
the
in NiS
on the basis of the
if the correlation energy was as large as suggested.
exhibits metallic conductivity
limit
NiS, however,
that the couloumb correlation energy in
NiO should also be quite small.
B. Surface states at GaAs([10) The
great
impressive caught The
technical research
similar
larger
faster
by
importance effort.
attention
fundamental one
to
two
of
Though
during gap
the
of
has
silicon has won
the
and
orders
semiconductors
past
magnitude
The
electron as
to
the race up
decade 52.
higher
lead
reason
a
to now, GaAs has is quite
simple.
lead
devices
mobility
compared
to
corresponding
to
silicon.
Electronic
o
-12
-8
-& 0 ENERGY ( E - EvB M )/eV
Fig. 23: Surface density of states at GaAs(ll0) ted surface and two different relaxation models.
surface
states
bonding
on
known
are
special
semiconductor
to exist
the
by Diwan
existence
importance
wafers.
in or near
tial measurements suggesting
of
of
Intrinsic
the fundamental et al. 53 empty
in
(1971)
surface
for an ideally termina-
conjunction
electronic
with
passivation
surface
states
gap of semiconductors. showed states.
band bending
are
Contact
on GaAs
A direct measurement
and well
poten-
surfaces of these
U1traviolet Bremsstrahl ung Spectroscopy surface
states
was
reported
1974
by Eastman
and Freeouf 54 who employed
yield spectroscopy.
In accord with expectation
3d core
empty
level
into
the fundamental
gap.
No
states
also in accord with expectation Ga
dangling
that
the
than
a
bond
is
observed
surface
empty.
since
the bulk conduction
be
Nevertheless
band minimum
e.g.
in
level could be detected,
the As dangling bond is occupied while the and
should
partial
they found transitions from the Ga
from the As 3d core
Lapeyre
structure
state.
below
transition
257
Anderson 55, interpreted
theoretical
one as
year
a
later
surface
calculations
by
pointed
exciton
out
rather
Chelikowsky
and
Cohen 56 in 1975 for an ideally terminated unrelaxed GaAs surface predicted empty surface
states
in
the
gap
thus
supporting
the
conclusion
by
Eastman
and
Freeouf 54 .
12
I
i
|
i
i
i
i
II
i
II
10 GoAs(110) 8
"~Wo = 73eV
y~',l, .... . ..-~..'.~.
E';6-=.,
//: ,"
JQ
o o
-_
o -2
I
I
-4
-2
I
I
0
i
2 Z, ( E - E t a M)/ev
i
i
6
8
Fig. 24: Solid dots represent the measured GaAs isochromat. The full line is the denstiy of states obtained by fitting a linear combination of bulk (dash-dotted) and surface (dashed) density of states,
Earlier in
research
on GaAs
had
been overlooked
1964 Mac Rae and Gobeli 57 had noticed
concluded
that
the
GaAs
some kind of geometric Laar
could
rearrangement
and
Scheer 58
had
GaAs(ll0)
surface.
Their
earlier result 59'60.
surface
reported
this development.
not
be
in LEED
terminated
Already
intensities
and
but must
show
ideally
leaving the surface unit cell unaltered. Van
in
measurements
Moreover
during
irregularities
1967 were
the
absence
repeated
it was demonstrated
in
of
band
1976
bending
and
at
the
confirmed
the
that band bending always reeul-
258
Volker Dose
ted
from
1976
surface
carried
relaxation. the
those
and
layer
layer in
surface
LEED
assumed
affected
first.
eletronic
The
relaxation
the occupied
tion the empty rangement empty
states
and
the
are.
electronic at
in the radiative
ted and surface
states
conduction
band
minimum.
edge
spectrometer
tion
at 24.
72.7 eV was
fitting
The a
contribution (dash-dotted)
calculation resulting
states
mum.
Comparison
mate
of
the
taken
and
line
of
surface
to
the
and
of
spectros-
Since no core levels
The
empirical
is shown
in
emission
by
density
of states.
potential cai63 empirical
Chadi's
(dashed curve).
data.
We
the
LII I absorp-
result
pseudo
from
to the
sensitivity
aluminum
surface
contribution
experimental
rear-
of the density
Isochromat
surface
3 using
for the bond relaxation model fit
surface
into bulk and surface
bulk
Though
on the kind of relaxa-
located with respect
a maximum
from a non-local
the
based on the
respectively 62'63.
measurement 22'64
theoretical
the
binding problem is circumven-
correctly
in section
on
to
by Chelikowsky
with results
this problem.
to achieve
this
consequences
attractive.
data were decomposed
was
tight binding
surface
for
being opposite
between geometric
the excltonic
described
combination
culatlon
the
order
employed
The bulk
is
In
experimental
linear
to approach
process
bond in
makes a measurement
can be energetically
absorption
drastic
modell
particularly
tool
of the GaAs
between 0.08 % and 5 %. The
together
relaxation
structure
GaAs(ll0)
to be the ideal
surface
al. 61
surface
the early calculation
strong dependence
states
are
has
et
of
the displacements
are not that much dependent
This
copy appears
Fig.
bond
states
Lublnsky
existence
of a rotation
relaxation 23 shows
marks. the
of bond lengths
terminated
surface
surface
involved
of
tear
proved
to consist
Figure
and
electronic
and
and
by relaxation,
kind
stucture.
Cohen 56 for an ideally
rotational
scratches studies
by 27 ° and a change
is also
the
as
intensity
It is presently
first
second
imperfections
out
conclude
The solid that
empty
at GaAs(ll0)
ly energetically well above the conduction band mini54 to Eastman's earlier partial yield measurement lead to an esti-
excltonlc
binding
energy
of
1.0 eV
or
1.3 eV
if surface
core
level
shifts are taken into account 65. A recent by
Ludeke
electron the
and
of the valence
Ley 66.
emission
surface
Though
study
the
with
valence
band
splitting,
of
the
valence
to the
structure
leads
valence band
of
XPS
spectra
surface
to the photoemlsslon.
the bond relaxation
is the only one which bottom
comparison
respect
contribution
reconstruction
the
By
band density of surface states has been performed
XPS
is not model
Since
studies
that
various
they were
sensitive
able
angles
to isolate
is shown in Fig.
to the kind
of
25.
of surface
by the isochromat measurements
of the B 3 As derived surface state at
Ludeke
favour
at
Their result
supported
to a splitting band.
normal
taken
the
and bond
Ley's
data
relaxation
do
show
model
such which
a is
Ul travi ol et Bremsstrahl ung Spectroscopy
•
i
i
I
i
•
I
•
•
•
•
I
i
•
G a A s (110)
,
259
I
B1
XPS
U1
~,,
B3
•
i
•
i
-15
I
I
I
S2
I
I
i
•
|
•
i
•
-10 -5 ENERGY (E-Eva M )/eV
•
0
Flg. 25: Surface XPS data for GaAs(ll0)
also compatible with the isochromat data.
C. UV Isochromats from gr_aaphite A
great
graphite
deal of work has using
been carried out
photoemisslon
a
at
Kleser 67
Baer 68 respectively.
and
quantum
in
measurements
energies
wide of
on the valence band
range
1 keV
of
and
Figure 26
quantum
1.5 keV
shows
structure
energles.
have
been
of
Isochromat reported
by
their data together wlth an
ultraviolet isochromat 69. Obviously in this case we flnd a breakdown of the so I
I
!
!
~¢u.=9?eV
"
~/
~'~//
? / °°h"
:3
o o5
I SOCHROMAT ra
(/! C
/~._..~-~/~
= o
. . . .
flWo = tbkeVlyiBaer)
o ...
0
I
0 EF
_ --t------
I
1'~1~, =
I
1 keV
(J.Kieser)
I
5 10 15 excess energy(E-buo)/eV
20
Fig. 26: Graphite isochromat spectra taken at x-ray energies and at 9.7 eV differ considerably because of a symmetry dependent energetic variation of the dipole transition matrix element.
260
Volker Dose
far successfully
employed
interpretation
in terms
of the density of final states.
The UV isochromat is entirely different from those in the x-ray region. Graphite ceeds
is a highly
via
anisotroplc
sp 2 hybridization
Consequently
layered material.
the weak
the band structure
interplane
~ bands
above
and
zone
exhibit
below
leading
between
to
adjacent
a gap
of about
the
Fermi
energy
the
classification
layers
of 1 eV. Photoemlsslon P points
in Flg. in
UPS
dominated
by
s initial
states
dence
begin
to
states
of
respectively.
isochromat
p-states
while
s-states.
This
ments only
near
et
Denley's c-axls
carbon
K
is further which
only
those
obtained
into
final
~
in
graphite are strongly in their
states.
with
presumably
sorption
can,
results
which
Denley's
due
to
apparatus
insufficient
favourable with
spectra
out
quantum
by
with
XPS
from
p
energies
s
results.
the energy
for
s and
connection
The
depen-
p
initial
between
photo-
by
transitions
into
empty
predominantly
transitions
into
empty
due
by x-ray self absorption to dipole
for
is
given
microcrystalllne
comparison. influenced lead
selection
of such measurements
isochromat
absorption
the UV isochromat,
offers more hls
geometry
from
transition
contributions
carbon
dominated
A comparison
for
available
of the isochromats
higher
reversal
supported
ultraviolet
rules
tlme
~
useful
of 0.8 eV at Q and
radiative
equal
born
atomic
interaction of the order
the photoemission
is in accord
of
the
the
are
the
At still
further
data
The
we are then lead to expect that the ultravio-
wlth
tion
agreement
is
both
of the Brlllouin
between 30 eV and 200 eV
of
states,
120 eV.
sections
in mlnd
edge
Pz orbltals.
splitting
a splitting
dependence
= 9.7 eV is o isochromats reflect
x-ray
pro-
find ~ bands
band 70. The results
p initial at
spectroscopy at
to
a semlmetal. a band
quantum energies
trend
cross
conclusion
orientation
causes
gap we
the P point
While at low energies
al. 73
monocrystalllne
ted
This
Bearing
taken
the
as
strong
from
the final p state density.
Denley
ing
a
the photoemission
photolonlzation
electron and isochromat let
graphite
have determined
are observed
dominate.
behaviour of
found
transitions
due
the key to the interpretation
on quantum energy.
and
overall
also
this
at
et al. 71 employing
are
states
of
Within
overlap
zone in the valence
experiment
element
12 eV.
weak and
experiments
provide
26. Bianconl
their
matrix
work
is
bonding
shown in Flg. 27 can be classified in 2 and a bands from sp hybridized states.
which
is rather
of the Brlllouln
photoemlssion
bonding
in plane
of graphite
terms of ~ bands with atomic p character The
While
Their
data,
crystal
graphite
polarization
size.
though
parallel
Kieser's respect. to
the
reflect 72 and
28.
Among
with on
random
poly-
and
polarization selec-
attenuation
however,
in this
Fig.
measurements
do not show any indication
conditions
rules,
by Kieser
in
by additional
to a strong
measure-
of
transitions
in rough
overall
of a w band splitt-
experiment X-radiation graphite
on selfabis detec-
c-axls.
This
Ultraviolet Bremsstrahlung Spectroscopy
261
~
20
20
10 A
-
_~!3E
_'--.. T[
_
_
=
,,, "-.
~ -10
-10
: ~-~-<~ c,A_~ -20
L Q
-20
P H
i
Fig. 27: Cal ulated band structure
I
I
Graphite
of
|
,~
graphite.
°
I
| ssss-
uv-lsochr
° I/
/ ~mat
Absorption /'~,/ ,/" . ~ ~ Spectrum ...~,~ //" / / (Denleye t ~ ~,j Self-Absorption ~j - o ~ Spectrum(Kilser)' 0-
0 I
EF
2 I
/~ I
6 I
8 I
10 12
energy(eV)
Flg. 28: Ultraviolet isochromat compared to graphite Is self absorption spectra.
262
Volker Dose
arrangement rial
was
favours
used
transitions
in his
work,
into
an
final ~ states.
indication
of
the
Since monocrystalline
splitting
observed
in
matethe UV
isochromat is also present in his data.
!
!
|
Graphite
,,
x- ray
, /
'.~
!
,
lsochromat ...~.ll/ '/
.A
7"-.
II
I
" ,
UV -Isochromat
II~'/ 5 10 energy/eV I
0 EF
-"
by Willis et al.
/~~/// I
"--
, \ -.
oo "
/ ~',~~
0j
',
i..,
I
I
15
20
Fig. 29: A properly weighted average of UV and x-ray isochromats exhibits all features predicted by a (smoothed) theoretical density of states calculation.
From
the
and x-ray pied two
foregoing isochromats
electronic sets
discussion
of
provide
states
such
we
conclude
an experimental
in graphite.
data
Figure
reproduces
all
that
a properly
weighted
sum
of UV
estimate to the density of unoccu-
29 shows
structures
that indeed a combination of predicted
by
the
theoretical
density of states calculation 74 in this energy range. From
Fig.
EF~E
27 The
unambiguously final
states
~-band
we
find
that
structure
attributed due
splitting
to is
is
in the UV
to
low
there
the
by
at
one
isochromat
critical
dispersion
reflected
only
points
about
unoccupied in this Q]u Q2g
range with
2-3 eV above
the corresponding
band
in
can a high
the Fermi
double
peak
the
range
therefore
be
density
of
energy.
structure
The
in the
density of states with a 1.3 eV separation. Experimentally we find 1.7 eV. Since adjacent ordered for
the
~
band
layers, graphite
graphite
splitting
occurs
one would expect samples.
grown
on
This
platinum
is
as
a
consequence
of
the
interaction
of
to find the double peak structure only for well indeed
the
substrates.
case. The
Figure carbon
30 was
shows
isochromats
deposited
on
the
Ultraviolet Bremsstrahlung Spectroscopy
i
i
!
i
!
263
!
!
UV - l SOC H ROMAT h ~ o = 9.?eV _.
•
/
o 0
on
~ o
P •
b
Y •
c
0
i
I
i
I
0
2
L,
,
l
i
|
6
8
10
EF
excess energy(E-'h(~o)/eV
i
12
Fig. 30: UV isochromats respond sensitively to the degree of crystallographic perfection of the graphite overlayer. The double peak structure in (c) is due to a ~ band splitting resulting from interlayer interaction in a well ordered sufficiently thick overlayer.
samples
by electron
an isochromat platinum were
substrate
subsequently
polycrystalline the
emission
where Pt(100)
a
well
impact
measurement
emission subject
platinum
spectrum resolved
surface.
for well ordered
decomposition
with peak
graphite 75.
the earlier
isochromat
reflects
was to
no
longer
annealing
substrate
The latter
to support
of adsorbed
from such a carbon layer,
the
sample
for
conclusion
deposited about
of the
to a more an
also
grown
resulting
hour.
For
structure at
a
layers a of
the energy
single
crystal
the LEED pattern characteristic
of the three curves
graphite samples.
point on
such that
carbon
one
pronounced
inflection
sample
that the double
the ~ band splitting
well ordered monocrystalllne
The for
exhibited
Comparison
thick,
1400 K
leads
indication
occurs
Curve a represents
visible.
at
this
benzene.
sufficiently
in Fig.
peak structure from interlayer
30 then leads
of the graphite interaction
in
264
Vol ker Dose 6_~.Measurements on Single Crystals
A. Direct transitions Energy bands in crystalline solids originate from a single particle ground state picture which leads to the concept of Bloch states for a periodic lattice. Though energy bands have been used to calculate electrical, magnetic, and optical properties
of solids,
there has
been little direct
evidence
0 5 Excess energy(E - E F ) / e v
for the existence of
10
Fig. 31: Isochromat spectra for platinum crystals of different orientations clearly demonstrate directional effects.
energy bands,
in particular for the energy versus momentum band dispersion until
the important demonstration of Gobeli et al. 76 of the potential of angular effects in photoemisslon. An enormous activity has been devoted to the field now known as angle as an adult, perspectives directional
resolved photoemlsslon.
Considering angle resolved photoemisslon
the Bremsstrahlung counterpart is still in its baby shoes. However, for
the
effects
future
look
in ultraviolet
quite
promising.
The
Denninger et al. 77
for Bremsstrahlung spectra from the
faces
single
of
platinum
first
demonstration of
£sochromat spectroscopy has been reported by
crystals.
In
their
(I00),
experiment
the
(III), and platinum
(210) single
Ul travi ol et Bremsstrahl ung Spectroscopy crystal was of 0.4 ~ . about pass
sitting
opposite
Electrons
were accelerated
I mA/cm 2. Emitted counter
results
are
incident
within shown
photons
a
solid
in Fig.
electron
to a directly heated
of
31. These
beam,
show
tungsten filament
at a distance
toward the sample with a current density of
were detected
angle
265
with
0.35 sr
spectra,
the previously
normal
to
the
although measured
considerable
dependence
on
described
band
surface.
The
Pt
for a nonparallel
the
crystallographic
Photon detector
Photon detector
I
[olo1 ~w
•+-°°~°-~--Repeltergrid • Fitoment
[lool
v
.
.
.
.
.
Sompte
Fig. 32: Momentum resolved Bremsstrahlung spectroscopy requires an electron beam of well defined energy and direction. A very coarse approach to obtain electrons normally incident on a sample uses a grid behind the filament which, together with the plane sample constitutes a parallel plate capacitor. Negative bias on the grid constricts the angular distribution of the electrons impinging on the sample to angles near normal
orientation strahlung angular
and
emitted for
In
distribution
a negatively negative
therefore
spectra.
biased
potential electrons
the Pt(lll)
llne represents differences tributions
repeller
towards surface
evidence
to gain
of electrons
applied
for
further
incident
grid behind
band
normal shown
to
this
effects
in Brems-
interpretation
15 °
the and
two
the sample
incidence. in Fig.
spectra,
70 ° width
the
on the sample was narrowed by mounting
to the grid with respect
are
structure
support
Sample
(see Fig.
32).
to the cathode data
obtained
33 as the solid
The effect
which
correspond
respectively,
the
band
of
is to bend the with
this setup
llne while
the dashed
the (111) spectrum as given in Fig. 32. In order to interpret
between of
provide
order
to electron structure
angular of
the dis-
platinum 78
266
Vol ker Dose
was
analyzed
initial tion by
and
of
for
direct
final
state
parallel
adding
transitions energies
momentum
reciprocal
at
lattice
with
and
Ei-E f = [~0° = 9.7 eV.
corresponding
the
surface
vectors
to
and
the
E-vectors. allowing
E-values
The
results
Assuming
for
surface
determined
from
were
conservaumklapp
the
band-
Platinum (111) A
I/)
---
2
a 8
<- ? 0 °
A8
<- 3 5 °
>,
Bi
"
c c!
cO Ul I/I W
/ III Ifll I
I
I
I
*
I
0
a
I
a
I
5
10
energy(E EF)/eV
Excess
-
Fig. 33: Isochromat spectra from Pt(lll) with and without negative bias on the repeller grid in Fig. 32. The hatched area represents emission • O O . due to electrons with angles of zncidence between 15 and 70 . Experzmentally observed peaks are indicated by arrows whereas peak positions predicted from a band structure analysis for direct transtions are shown by vertical bars.
structure
experimentally
orientation. vertical predicted above
The
bars
result
at
observable of
the
the
bottom
transitions
should
60 ° • They
of
transitions
search Fig.
occur
for
33. for
The polar
were
the
predicted
(Iii)
surface
interesting angles
for
of
thing the
each
crystal
is
indicated
is
that
incident
all
by the
electrons
should consequently vanish if the polar angles are restricted
to
smaller values as is in fact observed. A similar but more clean cut measurement has been carried out on Ni(lO0) 79. The set
of
data
is
shown
in
Fig.
sample and has been interpreted of
final
various
states. repeller
Emission potentials
34.
The
bottom
curve
is for a polycrystalline
Ni
in section 4 by and large in terms of the density
spectra
from
characterized
the by
Ni
single
crystal
the parameter
were
~ which
taken
for
is the ratio
UI travi ol et Bremsstrahlung Spectroscopy
'
•
• •
•%•°•
°,
~'
°•
267
°
" "'"
• • ° •
°°,•°°
¢=5.6
•
• •-•
• •.e. •"
-
•••,"
a=4.4
==
LL e~ o
==3.3
""
•
>-
"-':
•
• •••e=e•••
•1
a=2.2
•
I
"
UJ
N
•.••'.•,••.,•.
Z
_o
• %
a=0
• "
".....:
I
=E Nil100) w "~e,4.• • • '' • , , ,,, e,,,,.'
I
Ni l s o c h r o m a t s l~u = 9.?eV
0 2 ENERGY ABOVE EF/eV
Fig. 34: circles• repeller sents the
The isochromat from polycrystalline nickel is shown as open Solid dots refer to Ni(100). Parameter ¢ is the ratio of potential to sample potential (see Fig. 30). ¢ = 5.6 reprebest approximation to normal incidence•
of
repeller
to
progressively
voltage
to accelerating
narrowed
angular
calculation
the
effects
shown to confine
turn is for
the ¢=0
the
nickel from
Fermi
transition
bias
to
level in For
voltage•
results
incident
bias
by
the
onset
dictated
to polar angles
has
bulk normal
foil.
is
the electron
well
space
charge
then 15 ° which in
Ni(100)
by
distribution until
of
theoretical
such
a
the above to direct
resolved
interpretation
supported on
angular
diminishes
a single The
Following
is attributed
transitions
incidence,
incidence
of
By
to values smaller than 0.25x2~/a where a II Spectra from the single crystal deviate already
developed. nickel
smaller
corresponds
electrons•
of k
is increased
normal
therefore
the
the difference
direct
¢
of
electrons
constant•
Increasing
distributions
for the polycrystalllne
of accessible
approximation
tions 80.
lattice that
repeller
repeller
to a restriction
the platinum
the number
the
limiting
corresponds
tion of As
was
/.
interpretatransitions. narrows
for ¢=5.6, peak
this
at
peak
1.5 eV above as
bandstructure
transition
should
and
the best
a
direct calcula-
occur
along
268
Vol ker Dose
the
r-A-X
h~
high
symmetry
= 9.7 eV two direct
o are indicated out
by
the
coincides Since
this
line
by down arrows.
experimental
the
in
Brillouin
should
The
data
energetically with emission
of
transitions
transition Fig. 34.
the strong
feature,
however,
is
in
fact
symmetry
forbidden
at
shown
in
Fig.
The
second
emission remains
the X
35.
one
from band
immediately
constant
For
possible and
from band 7 to band 6 is well
tion of a it was concluded that it is quite weak. it
zone
in fact be energetically
born
7 to band
5
at the Fermi
level.
in intensity upon
varia-
It has been shown later on that
point
and
should
remain
weak 81
upon
moving into the Brillouin zone.
16f 12~" >
Ni
8
w I
W
0
-L,L F"
J X
A
Fig. 35: Section of the nickel band structure along the F-A-X high symmetry line. Expected momentum conserving radiative transitions for a quantum energy h~ = 9.7 eV are indicated by arrows. O
The
experimental
setup
Fig.
33 is of course
ruff
and
operating gies
Smlth 81
between
4 eV
Alternatively, to
the
since
variation
and
final
et
14 eV
by
the Ni
and
calls
al. 82
have
used
were decelerated applying
a
The
latter
approach
the
sample
in
of incidence
elevated Bremsstrahlung
background
of
a
data
in
Fig.
34 and
refinement.
commercial
retarding
a
Pt
electron
to the desired incident
grids was employed
energy.
A disadvantage
and
for an obvious
approach
the angle
in their experiment.
faces
primitive
Woodruff
The electrons
electrons of
to obtain
a pair of parallel
desired the
quite
and
at 40 eV.
employed
is
field
the electrons
voltage
to
to decelerate clearly free on
more
region.
the
Woodgun ener-
sample.
the electrons satisfactory A
systematic
the sample was possible
of the acceleration - deceleration mode is an from high energy electrons
striking metal sur-
other than the sample. Data were obtained for the (001) faces of copper and
nickel.
The nickel
results
taken at angular increments of 5 ° starting from normal
U1travi olet Bremsstrahlung Spectroscopy incidence initial the
are
shown
energy
incident
energetic momentum
in Fig.
results
versus
Variation
in a change
electrons.
position
36.
Since
energy
the angle
of the parallel
kll is
of structure
of
conserved
at
in the spectra
dispersion.
For normal
0 Fig. 36: Variation of of electron incidence.
sion maxima stays the
other
Fig. 34. scans Fig.
0 eV,
A
1.5 eV and
4.5 eV
in energy and intensity
two
show
plot
in the
dispersion.
of
its
final
(I00)
and
(II0)
The
the
previously
these
dispersion
two bands of
tion 82'83'84.
this
state
Within
are apparantly
this
may
quantuza
against
from
energy
While
of
the
relative emls-
angle
feature
analogous
parallel
in the
The solid dots
band
within
7
to
band
like a
state
to
momentum
is shown
final
with
the
is
free electron
estimated the
demonstration
at 0 eV
of the angle of incidence,
1.5 eV
respectively.
approximation
of
in the
r
directions
nearly be
change
6
at
transition
the momentum
any
we observe
respectively.
energy
of
at a given
~No"
upon variation
azimuthal
identified
transition
R=
9.7 eV
feature
37 as solid dots and open circles
course Since
at
constant
of
component
is a direct
2 ~ (E-EF)/eV
isochromats
incidence
the surface
incidence
•
of
269
two
that
for
in
polar
top panel
of
represent
of
6
in
nickel.
(see Fig.
35) the
band
energy
approximaas
a
func-
270
Volker Dose
tion of kll is given by 82
[(EG )24V I
2 2 kll Ef(kll) = ~
+
(6.1)
4E G
E G = ~2G2/2m
is
the
through dashed the
(002)
which curve
reciprocal the
two
in the
lattice
plane
waves
top panel
two band approximation
vector
and V G the pseudopotential
associated
of Fig.
while
(6.2)
37
with
bands
represents
the solid curves
7 and
6
interact.
the dispersion
are from a more
coefficient The
predicted
elaborate
by
band
o
(a)
o
o o
o
o
>4 A
l
LLI ' 2 UJ
1001Fig.
37:
Theory
and
k,,ao/~
experiment
for
-
Ni(lO0)
[110] for
kll
along
LlOOJ
and
[ll0J. Panel a displays the experimental energy dispersion as full dots and open circles. The dashed curve is derived from a two band approximation while the solid curves result from a more elaborate band structure calculation. In panel b experimental peak intensities are compared with calculated dipole matrix elements.
structure position angular Fig.
37.
variation
calculation 82. but
also
the
dependence. Assuming of
proportional
the to
The escape
Inspection intensity estimated and
electrons a
variation
of Fig. of
the
intensities
transport angle in
36 shows
direct
of the
are
functions incidence,
dipole
that not only
transition given
in the
(2.6)
feature
in
the
to stay
intensity
transition
matrix
the energetic exhibits
lower
panel
constant
change element.
an of
with
should
be
This
is
Ul travi ol et Bremsstrahl ung Spectroscopy displayed good. ous
as the solid
curves
The significance
since
obviously
in Fig.
37. The agreement
of this agreement,
an estimate
however,
with experiment
should
of the intensities
271 is quite
not be taken too seri-
from the experimental
data in
Fig. 36 is not easy.
The origin of the second emission feature starting at 4.5 eV
for normal
is not quite clear at present.
incidence
possibility More
of a surface
recently
seems the
Smith 85
initial
state
structure
energy
range.
likely
the possibility
since
momentum.
in
an energy
Gl~b186
measurements
Residual
et al. 82 suggest
the
or emission from a residual surface contamination.
suggested
to be not very
this
state
Woodruff
surface
energy
loss would be expected
moreover
similar
of an electron
to
contamination
did
not
those
in
observe Fig.
any
34
with associated
loss.
This
to randomize indication
over
an
of
enlarged
unoccupied
adsorbate
induced states remains at present the most likely explanation.
B. Electronic It
surface states
is now well
successfully versus
established
employed
parallel
wave
faces of single exhibit band
states Pt.
Larsson
and
using
riers
in
states
calculate
Cu,
to
and
however, bands been
and
there
and
correct
the
located
corresponding
same
They and
the
just
(III)
position
widths
of
the
by Johnson Fig.
38.
Brillouln
zone at polar
Two peaks are clearly
of
these
empty
surface
occupied
parameters
transitions
This will make it difficult from
these
separation
Experimental
and
visible
were
taken
increments
of about
bar-
surface
they
then
spectra
in
the
k u. Their
regarding
the negligible
relative
For
this
Pd(lll),
the bulk
surface
d-
state
has
from their experiment
are
r-K
part
importance
intensity variation
crystals.
azimuth
of
from normal
the
surface
incidence.
Peak A at the Fermi level is again
the unoccupied
into the Pd d-band are permitted.
increasing
For
to separate
2 eV between of
of 2.5 ° starting
in all spectra.
into
two
observation
Smith 91. Emission
angle
transitions
level.
emission
Spectra
bute with
d-
surface
of Ni, Pd, and
the
the
barrier
above
unoccupied
parametrize
surface
energy
and Au have been shown to
the energetic
data.
their
surface states coincide with the high density of d-band the Fermi
state.
in
direct
and
E(klt). Especially Ag,
energetically
positions
Using
an energetic
surface
with
Cu,
arguments
calculated
Bremsstrahlung
displayed
associated
band
photoemlssion
Au.
above
exists
the
relations
states
can be
states on Ni, Pd, and Pt all of which turn out to be empty.
bulk
reported
rigid
obtain
Ag,
immediately
surface
surface
photoemisslon
to exist on the (111) faces of single crystals
Ni and Pt their predicted states
dispersion
Nilsson 90 have
surface
ultraviolet
electronic
states 87'88'89
experimental
order
on
resolved
from the noble metals
simple
are expected
states
vector
surface
Using
angle
investigate
crystals
occupied
complex.
to
that
of the d-band. Direct transitions
remains,
however,
of peak A. Peak B which
For kiL=O no do contriquite
small
is found at
272
Volker Dose
1.7 eV
above
the
Fermi
level
for
normal
incidence
and
which
disperses
rapidly
away from the Fermi level for off normal incidence is suggested to be the surface state
predicted
Johnson
and
chlorine. es
by
theory.
Smith
Exposure
the spectrum
include
Arguments the
in
favour
sensitivity
of the clean Pd(lll)
for a polar angle
of
a
this
surface
structure
state to
given
by
adsorption
of
surface to 3.10 -4 Pa.s of chlorine chang-
of 7.5 ° into
0
of
the dashed
2 & (E-EF}/eV
line.
Peak A is only
6
Fig._38: Experimental isochromats for various angles of incidence along the r-K azimuth on a Pd(lll) surface. Peak A is the Pd d-band emission. The dispersing feature B is a surface state which can be quenched completely by adsorption of 3 L of chlorine.
slightly
attenuated
while
peak
neccessary
but by no means
see
later
on,
the
surface
free
that
the surface
that
states
transitions.
therefore of
layers
electon
direct
gas
and The
is entirely
sufficient
adsorption may
B
volume more
behaviour
leading
seriously
quenched.
alter
convincing
the
projected
thus
argument
bulk
band
rests
on a precision
structure.
a performance state.
to electronic
coupling
states
the dispersion of this structure
the latter argument
of a surface
in general
Bloch
Such
given
between the
by Johnson
lles entirely
As we shall
rearrangement
conditions
influencing
and
the band
of
vacuum
strength Smith
of is
in an absolute gap
It should be mentioned, of
is a
structure
however,
calculation
U1travi ol et Bremsstrahl ung Spectroscopy of
better
than
half
an
structure calculation
C. Ferromagnetic Itinerant and
minority
was
ferromagnetism
and
a
this quantity
indispensable
to
relies
The energetic is
states
and
a
on a splitting difference
quantity
theory of itinerant
to determine
unoccupied
non-relatlvistlc
band
in the case of Pd this appears to be quite optimistic.
spin bands.
splitting
principles
For
crystals
electron
exchange
eV.
273
of
between
considerable
ferromagnetism.
the
polarization
10 i
i
i
I
and
20 e
|
!
i
i
w
i
into majority
the two is called
interest
Considerable
from ARUPS 92. In complicated
exploit
of d-bands
for
the
the
first
effort has been spent
cases such as cobalt 93 it tunability
of
synchrotron
E/eV
, |
I 15
10
ILl
>0 n," W Z ILl
I
It . _
.
.
.
',I
_
: = _ ~ _ _ _ _ I__ - ~-z-: ~ . ~ _ _ _ ~ ~
.
-
As -
As
I
A
A
A
-
Fig. 39: Section of the cobalt band structure. Down arrows indicate Bremsstrahlung and up arrows photoelectron emission used to determine the d-band splitting.
radiation
in
order
to
determine
this
~Eex = (0.85 ± 0.20) eV for the upper range slon
from is
its
0.8
to 4.3 eV.
combination
quantity. d-band
A particularly
with
ordinary
Experiment
in Co while
nice application
photoemisslon
data
resulted
in
theoretical
in order
value
predictions
of inverse
the energetic separation between a pair of exchange split d-bands.
a
photoemls-
to determine
274
Volker Dose
While PES data can be used to locate the occupied majority Fermi
level,
respect
to
Himpsel
and
far,
which
IPE
E F.
be
employed
for
locating
the
empty
band relative minority
to the
band
with
feasibility of the experiment indicated has been shown 94 Fauster in a measurement on cobalt. Unlike the data discussed
The
were
energy I~0° as the
may
constant
obtained
a
function
initial
by recording
the emission
of electron
energy
mode.
!
|
energy,
This
l
their
!
.92eV
|
so
quantum
conducted
of
in
employing
a
!
=
.93eV
c
was
consequence
r L
at a fixed
experiment
is a natural
|
,
intensity
by
CO
::;0 I'rl
_,
-i
z
o
/
U.I
--J 0 0
,
/
U.I
m
-1-
r,
/'//I
C
'
.,J'/
Z 0
_ ~ _ _
212
|
I
I
I
I
I
0
-I
I
1
(E - E F ) / e V Fig. 40: Experimental photoemission (left) and inverse photoemission spectra form Co(0001) showing the ferromagnetic exchange splitting between spin up and unoccupied spin down states. Spectra where recorded in the constant initial energy mode. The dashed curves refer to a photon energy of 16 eV for transition into states at the Fermi level while the solid curve is for Ii eV. Note the band dispersion.
grating monochromator detection sions
from
normally inside
combined
with a position
of several wavelengths. ~
resolved
incident
on
the sample.
pied 3d band the electrons, the photon
Bremsstrahlung Co(O001)
sensitive
The technique data
occupy
a
is
free
device
allowing parallel
for determining
E(~) band disper-
illustrated electron
in Fig.
llke
energy
39.
Electrons
band
(AI,A 2)
From there they undergo a radiative transition into the unoccu-
(A6,A7).
Subtracting
the energy
spectrum
50 meV
replacing
states
approximates
of
the photon energy ~0 from the initial energy of
the 3d band
is at the Fermi
the cobalt a
step
is obtained.
level.
It was
determined
sample by polycrystalline function
at
E F.
The high energy
Assuming
cutoff
of
with an accuracy
of
gold whose density of empty momentum
conservation
the
Ul travi ol et Bremsstrahl ung Spectroscopy wave
vector
normal
of
shown in Fig. from
the
incidence
the
earlier
3d
we
final
have
39. The momentum
dispersion ARUPS 93
of
data.
the
By
energy,
part of the E(kl) Data
points
unoccupied for
for
dispersion
the
two
The
band
to
electron
llke
the electron
states
different
in good
the
the
initial
line
AIA 2 band
energy
state.
F-A-A
For
in ~ space
and
which
was
known
consequently
of the minority
from
the photon
spin AsA 6 band could be
in Fig. 39 are from ARUPS and Bremsstrahenergies
splitting
agreement
of
to
to the surface k± is then calculated
e.g.
by the peak shift
exchange
that
corresponds
band dispersion
indicated
states.
A5A 6
free
for occupied
spectroscopy
d-band
is equal
perpendicular
tuning
mapped. lung
state
k u = 0 which
275
read
with
different
momenta
is 0.15 eV for occupied from
Fig. 40
(0.85 ± 0.25) eV
is
k i.
The
as well as
(0.93 ± 0.I0) eV
obtained
from
photo-
frequently
argued
emission in the region where both bands are occupied. These that
data
band
call
energies
relaxation 95. mination bands
for
of
the final
on the other
exchange state
hand
is a hole
adds
agree quite well with each other,
ferromagnet
opposite
d-bands
of
to
the
of appropriate
tally
Unguris
Fig. 41.
Spin
rents were
again
splitting
exchange
sample
spin
al. 96
Ni
electrons
effects
crystal magnetized crystal
and normal
recorded
with
dependent asymmetry
assembly
as obtained
that relaxation
of PES
by either
is well within
in the present case.
Radiative
transitions
therefore
be
should This
of
has
their
obtained
been
into
the
possible
for
demonstrated
experimental from
only
setup
a GaAsP
spin
experimen-
is
source.
shown Beam
in cur-
of ±2.6 ° . The sample
along the (IT1) direction by a c-shaped electro-
could
to the direction the
both
should therefore
sample
were
for
spectroscopy
magnetization.
sketch
state
the empty 3d states are completely
orientation.
A
since
from a combination
splittings
we conclude
only
final
in the deter-
band and would be expected
of the order of 0.5 ~A with an angular divergence
The
surface
et
polarized
was a Ni(ll0) magnet.
the
such as nickel,
a magnetized
electrons by
that
from
Bremsstrahlung
resolution and therefore altogether unimportant
In a strong
empty
fact
band.
data
sign. Relaxation
the exchange
way
polarized
the
suffer
photoemission
shift of opposite
is
approximately
to the conduction
IPE
It
may
cancel
in the valence
and
experimental
From
should
from
an electron
of
conclusion.
photoemission
shift
splitting
in the determination data.
from
a relaxation
to cause a relaxation add up
interesting
determined
Such the
another
previously
be
rotated
about
of magnetization. described
band
an
axis
in
Bremsstrahlung
pass
photon
the
crystal
emission was
counter.
The
spin
in photon emission A is
1 A =
PoCOSe
n+-n+ •
n++n+
N+-N+ -
N++N+
(6.3)
276 P
o and
Volker Dose is the polarization
n÷,
n+ the
of the
registered
factor P cos= accounts o
incident
counts
electron
beam,
corresponding
to
e the angle of incidence,
either
for the fact that at non-normal
spin
incidence
direction.
The
only a component
PHOTON
e" Beam Ni(110} Fig. 41: Schematic of an apparatus for angle Bremsstrahlung isochromat spectroscopy.
of the incident represent tively
polarization
photon
parallel
fluxes and
is along the magnetization
that would
be expected
antiparallel
check
of any asymmetry
sample
magnetization.
to
the
of non magnetic Experimental
character
data
in
and
the is
strongly
Fermi
level
therefore negative
in
100 %
the N+ spectrum
minority
in the energy
spin
axis. N+ and N+ therefore
spin
of
result
convenient of the
quantities
N
is that the peak seen just absent
The
the d-band
A
by reversal
the corrected
is entirely
of
direction.
was possible
terms
polarized.
region
spin polarized
for a 100 % polarized beam respec-
majority
and N+ are shown in Fig. 42. The most prominent above
resolved
in the N÷ spectrum
asymmetry peak and
A
is
remains
of
course
at a 5 %
level for energies up to 4 eV above E F. Though as stated earlier, ment the
just discussed art
energy, tion
achieved of
the
presents
conventional angle,
of about
and
spin
ultraviolet
resolution
spectroscopy.
experiment monochromator,
the spinpolarized
experi-
the first case where IPE has caught up with state of
photoemisslon.
1 eV and a detection
in isochromat PES
IPE is still in its infancy,
namely
The have
first
just been completed
signal
experiments 97 at an energy
of 50 C/s comparable
Recalling
synchrotron
and Mott
photoemission
the very demanding
radiation,
spin detector
grazing
as compared
nical requirements
for the IPE experiment
zed Bremsstrahlung
excitation for research on ferromagnetism.
to
adds to the attractivity
with
resolu-
to what has been instrumentation incidence the modest
vacuum tech-
of spin polari-
Ultraviolet Bremsstrahlung Spectroscopy
w
g
I
I
I
|
!
z|
|X •
| El l;llil[
z ||If
Z
)'--4
IE
CO One
I
!
0
|
!
!
'
(E-EFI/eV
-31iiiii
"t m
Ni(1101
"-
UJ
!
il|||||
Z
LJJ
|
tttt~tt t]!
I--O3 j--
277
Ni(110)
<-.6 '
2
I
ii
I
0
I
'
(E-EFI/eV
i
2
Fig. 42: Experimental isochromats for normally incident electrons with spin orientation parallel and antlparallel to the majority spin direction (left panel) and asymmetry A in photon production (right panel).
D. Chemlsorptio_n It has been shown already quite early that UV isochromats respond sensitively to gas
adsorption
on metals.
The application of
IPE
to ehemisorptlon problems
is
therefore possible and appears quite promising since relaxation effects are expected to be smaller than in ordinary PES. This relies very much on the fact, that an atomic system gains much less energy upon formation of a negatlv ion than is necessary to positively ionize it. The obvious relevance of chemlsorptlon lies in its on
relation to problems in heterogenous catalysis and corrosion. d-band
metals
is
antlbondlng adsorbate
characterized
in general
by
induced electronic states
the
Chemlsorptlon
formation of bonding and
lying below and above the sub-
strate d-band complex respectively 95'98. Since except for the noble metals the dbands of the transition metals are only partially filled the antlbondlng states appear above
the Fermi
level and are therefore empty.
They have thus far only
been accessible by electron energy loss spectroscopy which does not lend itself to an unambiguous interpretation. IPE is the ideally suited tool for the direct observation of
adsorbate
out were on oxygen Ni(lll) I00,I01
induced unoccupied
adsorption
on
Ni(100) 9Q
states. and
Experiments
so far carried
oxygen and carbon monoxide on
278
Volker Dose
Normal oxygen with
incidence
covered the
energy
surfaces
experimental
in
the
empty d-states ly
Bremsstrahlung
nickel
possible
clean
setup
shown
Ni(100)
in
spectrum
from evanescent
direct
isochromat
spectra
are shown in Fig. Fig. is
32.
transition
from
band
7
clean
The
peak
just
due
band
UV-ISOC HROMAT S
and
results were obtained
to
5
above
transitions
. Contributions to
Ni(100)
These
largely
initial states
from
43.
to
Fermi
into
final
from an energetical-
this
".
the
structure
can
be
(~ ) I
i
I
I
I
I
I
I
incidence
norma[
Ni (100) .,. 02 ~u=, = 9 7 e V .e
•
•
•"
(3
•
I
7
.,..,
t !!
I
I
!
I
l
i
I
i
i
!
I
i"
C: =,
iil
t
i
N i O formation
..D
•
.. =
•e %
0" o"
>.
= .oee'i
o ~9o~"." z
ill
z z
." .
l
"l
O c(2x2)
0
°••°''•'''eJe•
12 ) ..-
_o
I direct transition
oh 03 uJ
•
,'e
•
(a) (b)
: clean
=~
..•"
L--~*
,
-2
i
*
0
2
ENERGY
( E-EF)/eV
from
Ni(100)
Fig. 43: Set of isochromats higher doses of oxygen.
neglected they has
because
become been
tion
they
symmetry
previously
occur
near
forbidden. identified
; /~
I
the X-point
The hatched
of
area
near
i
exposed
the
bulk
under
as a contribution
from band 7 to band 6 in bulk nickel
m
to
progressively
Brillouin
zone where
the peak at about
from a direct
radiative
the X point along
1.7 eV transi-
the r-A-X high
symmmetry line (see Fig. 35). Oxygen adsorption trum.
Exposure
simultaneous
on the surface
to 50.10 -4
attenuation
of
Pa.s
02
causes
prominent
leads
to enhanced
the direct
transition
changes
of the emission spec-
emission
at 1.7 eV. At
just above
E F and
100.10 -4 Pa.s 02
Ultraviolet Bremsstrahlung Spectroscopy emission direct
at
EF
has
transition
again
decreased
feature
has
The
kinetics
of
marked
curve
"a"
oxygen
in
This
adsorption
"a"
Fig.
It exhibits
44.
of
Pa.s
been
43. a
The
With
which
6
followed
nickel
value
and
still higher
recording
corresponding
resonance
like variation |
clean
completely.
has
in Fig.
50.10 -4
resonance
initial
the
exposur-
for NiO emerges.
by arrow
exposure
pattern.
oxygen
the
disappeared
es, a spectrum characteristic
energy
to
279
also
like
emission
produced
the
result
the
emission
at
is displayed
as
enhancement
sharpest
at an
c[2x2J
LEED
of the emission of radiation as a function
|
|
i
|
|
|
a
21 0
/
\
>,.
(bl
~, ..
• 4' C w_
w
o 1.0
J
e. - -
I<,l
".'L.:" •.
I
10 0.1 0
'
"0 &
8'0
'
120 '
'
Exposure
160 '
'
'
(Langmuir)
Fig. 44: Kinetics of oxygen adsorption as monitored by Bermsstrahlung emission. Curves (a), (b) correspond to energies marked "(a), (b)" in Fig. 43.
of oxygen exposure of the tics
is a unique
isochromat
of
oxygen
behaviour.
An
including
adsorption example
shown as curve
property
the direct monitored
ohtalned
"b" in Fig.
at
of the peak at E F, For the other regions transition
by
inverse
an energy
44. Measurements
region around photoemisslon
marked
by arrow
like those
in Fig.
to establish the common intensity scale for the isochromats The
behaviour
of
the
direct
in Fig. 43 upon oxygen exposure ed
photoemission
empty
data
for
transition
Cu(100) I02.
in the case of Ni are occupied
Consequently
the
"extra"
contribution
can be understood
radiative
Part
of
in Fig.
43
is
44 have been used
to the clean
spectrum
(I)
to well establish-
electronic
in Cu. This applies emission
"b"
a monotonic
in Fig. 43.
by reference the
1.7 eV the kineshows
states
in particular
in the Ni isochromat
which
are
to band 6.
at 1.7 eV shows
280 up
Volker Dose as
an
emission chosen.
An
emission mats.
"extra"
photoelectron
photoelectron oxygen
from
c(2x2 1 overlayer
feature
in
the
The conclusion
to a rather
strong
Ni(100)
thereby
and
emission
spectra
Cu
above
Cu(100) leads
electronic
d-band
complex
quantum
energy
spectra
as
quenching
it does
for is
deteriorates
in the surface the coupling
normal
suitably
of the direct
in the Ni isochro-
of the oxygen c[2x2] adsorbate
rearrangement
strongly
the the
to substantial
photoelectron
is that formation
if
layer leads
regions of Cu(100) and
conditions
between
vacuum
free electron and itinerant bulk electronic states of the Cu and Ni samples. The emission of
intensity
at and just above E F behaves o v e r that
cI2x2 j overlayer. source
for
spectra
the
upon
of
Surface
occurance
geometric
umklapp or
near E F were
transitions
with
cal
lattice
to be entirely
vector.
up to polar angles
have of
The
been
of the surface
be responsible,
observed
with
emission
features
layer.
in photoelectron the observed
strong contributions
where ~ denotes
enhancement
This behaviour
as a mechanism
of an oxygen
In case
on
from direct
a surface
the
of the width of the electron
of 70 degrees.
A 40 % enhancement
the advent
shown I03 to be a possible
emission
due to surface umklapp,
independent
improbable
occurs
processes
disappearance
÷ = ~ would kjl
out
quite differently.
sample
rearrangement
enhancement
es highly
the clean
other
recipro-
hand
angular
turned
distribution
in turn renders umklapp process-
for the emission
increase upon oxygen adsorp-
tion. The
only
remaining
ordered
c(2x2)
states.
Current
bonding
electronic
consequence have
is
two
in
d-band
pair is
the intensity
peak
has
prior
course
exposures effect.
the
the
also,
observed adsorbate
formation
emission
induced
on Ni(100)
the filled
portion
within
These
the The
observed
prediction.
Further
and
the
induced
electronic
energetically for
as a
states
d-character
support
well
predict empty anti-
of the Ni d-band
adsorbate
overlayer
for
unoccupied
of O c(2x2]
The been
radiative
structureless shown event.
states would
to
be
to of
exposures NiO
becomes
part
of the
dominated
An adsorbate
within
narrow this
should the
structure
view
may
be
isochromat
by
above
electron
induced
hole
enhancement
of
the pair the
lead us to expect enhanced electron hole
as is in fact observed.
restricted
extra
increase at arrow "b" in Fig. 43 (see also Fig. 44) even
regime.
previously to
on
above
planes.
latter
of empty electronic
formation of
rely
the
interaction.
substrate the
chemisorption
formation density
O(2p)
p-character
with
to
treatments
states I04'I05
Ni(3d)
to three
from
the
must
theoretical
of
accord
drawn in
overlayer
predominantly
first
explanation
of
The validity
less
the
than
of this
~50. i0 -4
prevailing
reason
interpretation
Pa.s. for
For the
higher
observed
28l
Ultraviolet Bremsstrahlung Spectroscopy 7. Concluding Remark
Ultraviolet Bremsstrahlung spectroscopy has already been applied to quite a variety of problems.
An even larger
improvements
experimental
based
on
in
grating
field
of applications
technique.
monochromators
with
The
high
next
is expected with further
generation
acceptance
and
of
spectrometers
multl-detectlon
has
already been set up, The possibility to employ variable quantum energies h~0° will doubtlessly make the technique more popular and eventually lead to a state predicted by Duke and Park 5 already in 1972: "Information on the unoccupied density of states can be obtained by the Bremsstrahlung isochromat technique. This straightforward
approach,
which
consist of energy analyzing
radiative capture of low energy electrons, scientists. My
personal
is that
it will
finally
emitted by the
thus far has been slighted by surface
But, as the fashions of science change, hope
the photons
it will also have its day."
find its place among the other well
established spectroscopies for surface analysis.
Acknowledgments
The author wishes article.
Both,
to acknowledge his coworkers
for their contributions
the scientific and technical assistance
to this
of M. Gl6bl has been an
enormous help for the completion of this paper. Mrs. M. Lucas and D. Straub have done an expert job in preparing the figures.
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0079-6816/83 $0.00 + .50 Copyright © 1983 Pergamon Press Ltd.
ULTRAVIOLET BREMSSTRAHLUNG SPECTROSCOPY VOLKER DOSE Physikalisches Institut der Universit~t, Am Hubland, D8700 W•rzburg, Germany
Abstract Recent experimental progress has introduced Bremsstrahlung spectroscopy especially in the isochromat mode as a new surface analytical tool. Bremsstrahlung production may be regarded as radiative capture by solids and is therefore the inverse process to the well known photoemission. In contrast to photoemission which probes occupied electronic states at solid surfaces, Bremsstrahlung spectroscopy opens up the possibility to investigate unoccupied electronic states including the important region between Fermi- and vacuum energy. Measurements on polycrystalline materials will be discussed on the basis of an isotropic three step model for Bremsstrahlung emission. More recent experiments on single crystals with electrons of well defined energy and initial momentum ~ have demonstrated that T-resolved spectroscopy provides energy versus momentum dispersion relations for ~noccupied bands. Application of spin polarized electron beams has advanced E-resolved Bremsstrahlung spectroscopy to a state of maturity comparable to spin polarized angle resolved photoemission. This paper attempts to review the development and summarize the present state of ultraviolet Bremsstrahlung isochromat spectroscopy.
Contents I.
Introduction
226
2.
Basic Concepts
227
3.
Experimental Considerations
232
4.
Density of State Measurements
242
5.
Application to more complicated Systems
249
A. Oxidation of nickel B. Surface states at GaAs(ll0) C, UV isochromats from graphite
249 256 259
225
226
Vol ker Dose
6.
Measurements A. B. C. D.
7.
on Single Crystals
264
Direct transitions Electronic surface states Ferromagnetic crystals Chemisorption
264 271 273 277
Concluding Remark
281
References
281 Abbreviations
AES ARUPS BIS DOS EDJDOS IPE LEED PES UV UPS XPS
Auger Electron Spectroscopy Angle resolved ultraviolet Photoelectron Spectroscopy Bremsstrahlung Isochromat Spectroscopy Density of States Energy Distribution of the joint Density of States Inverse Photoemission Low Energy Electron Diffraction Photoelectron Spectroscopy Ultraviolet Ultraviolet Photoelectron Spectroscopy X-ray Photoelectron Spectroscopy
I. Introduction
The first
reliable
strahlung
spectrum
investigation was
bandwidth
monochromator
strahlung
yield
The
x-ray
energy the
frequently Duane
function
conservation
nature
of
found
this
experiment
these
structure
was
~/e
Hunt I
energy
exhibited
carried
early
near
with
a
h~ °
limit of an x-ray bremsin
1915.
they
voltage
Using
recorded
a
narrow
the
brems-
across
the x-ray
U°
corresponding
threshold
was
out
with
investigations
the
given
progressively a
higher
fixed
precision.
monochromator
(= constant colour) measurement
Duane
of the anode material
structure
and
of the accelerating
observed
the first isochromat
characteristic of
Duane
to a q u a n t ~
to determine
Ohlin 2 repeated and
by
tube. to
eU = ~ . Their result was a very important confirmation of o o x-ray bremsstrahlung and their method has subsequently been
the
used
Hunt
constitutes
tuned
as a function
yield
of the short wavelength
reported
in 1946
Hunt
in 1942
limit.
This
the
setting
it
performed.
with much better structure
was
interpreted
resolution shown
of the x-ray tube. A preliminary by Nijboer 3 who
Since
to be
explanation
Ohlin's
data in
terms of unfilled electronic states above the Fermi level of the anode. Research Karlsruhe
in this field came to rest for more than a decade until Kurt Ulmer 4 at in
1958
started
an
experimental
isochromat
program
and
continued
to
U1travi ol et Bremsstrahlung Spectroscopy work
in this
field with
his
group
for nearly
227 The significance
twenty years.
of
Ulmers work with respect to surface science was first recognized by Duke and Park 19725.
Isochromat
laboratories
spectroscopy has been performed
since.
Full appreciation
in a steadily growing number of
of its close
relationship
to photoelectron
spectroscopy has led to the present breathtaking development.
2. Basic Concepts
Though
the expression
"isochromat"
involved in this spectroscopy be most Figure tron
easily understood
a
absorbed
by
a valence
is
thereby
measurement
initially
~o
electron
transfered
of
to the better known photoelectric
at
monochromatic initial
to a
the kind of measurement
final
energy
In ultraviolet
electromagnetic E i of
the
solid
effect.
photoelec-
radiation sample.
is The
state with energy Ef = E i + ~ o "
A
of the rate of emitted electrons as a function of Ef is then taken as
an indicator hand
pretty well
of the elementary radiative process may
of the two spectroscopies.
quantum
electron
right
by reference
I shows a comparison
spectroscopy
describes
the physics
of part
free
the occupation of Fig. electron
probability
I also with
displays
energy
E1
at the
the time
undergoes
initial
state
reverse a
of
radiative
energy
this
E i. The
process.
transition
Photoemission and Bremsstrahlung
EI
Evac i FERMI LEVEL~ / / ~ UPS
IPE
Fig. I: Photoemission and Bremsstrahlung production are related by time reversal. The initial state in photoemlsslon, one electron in the solid and one quantum ~ in the radiation field is the final state in o Bremsstrahlung production. The same correspondence applies to the final state in PES and the initial state in BIS.
An
with
228
Volker Dose
emission
of
electronic can,
a
light
state
quantum
of
the initial
energy ~0 ° constant, function
of
this
nic
states
processes
measure
the final
above
an
state
distribution the
is only
Hamiltonian
and
ends
up
in
a
final
previously
of the solid at energy Ef. Exactly analogous
by variation
ximation
~0 °
state
intensity
energy
Ei,
keeping
distribution
Ef = E i - ~%o"
reflects
Fermi
energy
the available
level.
We
in the interchange
note,
that
to photoemission
the quantum
of light
Within number
unoccupied
quanta ~0 ° as a
the same coarse of empty
the difference
appro-
final electrobetween
of initial and final states.
the
is in both cases
where A denotes
the electromagnetic
e and m are
charge
and mass
tively.
mutual
relationship
The
has been well known in atomic been
rates lar by
extensively
for radiative
atmospheres 6. Pendry 7'8.
first
surface
second
surface
hartree
used
mutual
Consider
two
between
physics to
the
calculate which
surfaces
per photon.
because
the same as in a steradian
the
for
types
of
of light
radiative
experimentally
levels
surfaces
in
properties,
occupied
transitions
hardly
has
respec-
cross sections
in the analysis
solid
identical
accessible
of interstel-
been except
by electrons.
formulated that Let
the
in the
Let Jel be the number of electrons
Conversely
from the second
two
are needed
equivalency
these same levels be empty.
obtained
potential and ~ the momentum operator.
since years. Photolonization
has a given set of energy
Jel and Jph are not equal is not
vector
(2.1)
of the electron and c the velocity
recombination
The
per steradian
lung quanta
two
The interaction
e (~.~ + ~.~) Hint = 2mc
have
we
detection
per
let Jph be the number of bremsstrah-
surface per steradlan per incident electron.
the number
of states
of electrons.
in a steradian
of photons
In a steradian of electrons,
the
number of states is
Le/(2~) 3j I~12cose = [fl/(2~r)3J-2. E-cosO where ~ is the volume of a box containing E the electron
energy in hartrees,
the system,
(2.2)
~ is the electron momentum,
and @ the polar angle of electron emission.
In
a steradlan of photons the number of states is
[fl/(2~)3J I,+,,I2cos@ = [~/(2~)3J.c02/c2cosq~ is
the photon momentum,
c the velocity
the polar angle of photon emission.
of light
It follows that
taken
(2.3) in atomic
units,
and
Ultraviolet Bremsstrahlung Spectroscopy
229
Jph/Jel = [~2/2Ec2].cos@/cosO
photon emission is weaker by c is
prohibitive
surfaces.
2
(2.4)
compared to electron emission. While this factor
in experimental atomic
physics
it
is not
in the case of
solid
For a typical 3d metal Pendry 7 estimates a photon flux of 3xi06 per
second at 0.I
eV band width
for an incident electron current
of I00 ~A. This
estimate has been confirmed experimentally within one order of magnitude. Having discussed the differences between photoemission and bremsstrahlung production we now turn to their common aspects.
From (2.4) it follows that brems-
strahlung production offers the same physical information as angle resolved photoelectron spectroscopy,
but for unoccupied bands.
Its special merit is that it
includes the otherwise hardly accessible region between the Fermi and the vacuum level of the sample. Due to the close relationship between the two spectroscoples theoretical models for bremsstrahlung emission can be derived in a unique manner from
existing
models
for
photoemlsslon.
Though
the
most
rigorous
theoretical
approach treats photoemlsslon as a one step process much more physical insight is gained applying the popular isotroplc three step model 9. The first step involves optical excitation of an electron from an occupied valence band state to an empty conduction band state. surface while
Step two describes the tranport of the hot electron to the
the third step accounts for escape across the surface. Adjustment
of this model appropriate to bremsstrahlung emission leads to the following analogous three steps:
(I) Optical decay of an electron of energy E into an empty final state of energy E - ~ o.
We
conserving Brillouln Ef(~).
We
shall
first
direct zone and shall
assume
that
transition such
this
decay
takes
place
in
a
momentum
that an electron with momentum ~
in the
initial energy Ei(~) decays vertically to a final state
subsequently consider also
complete
relaxation of momentum
conservation. (2) Transport of the photon created in the solid which includes the possibility of absorption. (3) Escape of the photon through the sample surface into the vacuum.
The yield function of emitted bremsstrahlung quanta I(E,~) is in general a sum of a primary contribution Ip(E,~) from electrons that have not suffered an inelastic collision prior to the radiative transition and a background Is(E,~)
I(E,~) = Ip(E,~) + Is(E,~)
(2.5)
230
Volker Dose
A detailed discussion tion
Ip(E,~)
function
is now
D(~),
a
of Is(E,~) will be given in chapter 4. The primary distribufactorized
transport
according
function
to the
T(E,m),
three
and
a
step model
into an escape
bremsstrahlung
distribution
P(E,m)
Ip(E,~) = D(~).T(E,m).P(E,~)
We
first
three
consider
in
step model
electrons these
from
states
more
this
initial
are
detail
the
distribution
bulk
calculation
is given
by
of
final
implies
momentum
crystal
P(E,m).
the bulk
states E i into empty that
(2.6)
states Ef.
which is to be conserved in the reduced zone scheme.
According
optical
to
the
deexcitation
The assumption
~ is a good
quantum
of
that
number
This leads to
i,f = + dir J d' k l 12 6(Ei(k)-Ef (~)-~). 6(El (~)-E)
(2.7)
+
where
p is the momentum
emission. energy
E
The of
delta
the
(2.7)
applies
order
to obtain
all possible
operator
functions
incident
for
one
select
electrons
initial
the total
final
and ~ the vector
state
emission
states
initial
and
states
ensure
per incident
associated
with
the
E corresponding to the i and momentum conservation.
energy
ii> decaying
and average
potential
into
one
electron
final
state
if>. In
at energy E we sum over
over initial states.
The resulting emission
is I ~ i,f dir
i,f Pdir(E,m). =
(2.8) i J d'k ~(Ei(~)-E)
A
small
from on
but
important
the normalizing
~,
the
volume
conditions. from
In
summation final
in runs
energy to
density
be of
approximation
as
(2.8)
of
~
reduces
to
initial
the
density
surfaces.
If we
further
(2.8)
reduces
divided
photoemission
in (2.8) beeing absent I0.
by
the
of
bands
assume to
is
fixed
integrated the
states
by
energy
the
Brillouin at
initial
contributing
experimental
density
of
initial
to
the EDJDOS
as obtained zone
and
energy
the
E.
The
to the initial
and
transition matrix
distribution
is proportional
results
in (2.8) depend
measurements
entire
the radiative
the
photoemission
and denominator
turn
angle
final
constant, states
in
encompasses
and
to ordinary
numerator
which
thoroughly
samples
over all
compared
Both,
integration,
case
polycrystalline
denominator
ment
of
the
difference
denominator.
states. only,
of
the
Within the
the
elejoint same
denominator
Ul travi ol et Bremsstrahl ung Spectroscopy
231
For experiments on single crystals with electrons of well defined energy E and momentum
~
in
vacuo,
the
volame
of
integration
fl is
contracted
around
the
V
electrons momentum ~
in the solid. ~ S
and ~ V
are of course different since only S
the component of momentum parallel to the surface is conserved upon penetration of the surface. The dimension of the volume of integration around ~s depends on the
amount
of
smearing
smearing in turn path at
of
the momentum
component normal
is inversely proportional
to
to the surface.
This
the so called elastic mean free
initial energy E. A detailed discussion of I0 •
this relationship has been
given by Cardona and Ley The
foregoing
from momentum the concept
of
discussion assumed
conserving indirect,
that
transitions.
radiative
Spicer II has
emission
results
exclusively
already quite early
invoked
e.g. ~ non-conserving transitions in order to explain
stationary structure in the energy distribution curves from copper obtained for a variety of photon energies.
If momentum conservation is entirely relaxed,
(2.7)
must be rewritten as
ind = f d'kid'kf ISifl2~(Ei(~i)-E)'6(Ei(ki)-Ef(~f ) - ~ ) +
(2.9)
+
The volume of integration for k i and kf is the entire Brillouin zone. By analogy to (2.8) the total emission Pind(E,~) becomes ~ i,f ind Pind(E,~ ) ~ i,f N(Ei )
(2.10)
where N(Ei) is the density of states at initial energy E i. Assuming further that the momentum matrix element
in (2.9) may be replaced by a constant the double
integration in (2.9) factorizes into
i,f ÷ ÷ ind = f d3ki6(Ei(ki)-E)'f d'kf6(E-~-Ef(kf)) Summation
over
i,f
in
(2.10)
turns
the
two
integrals
into
(2.11) the
densities
of
initial and final states respectively. Since the density of initial states cancels in (2.10), we have that emission via ~ non-conserving transitions is proportional to the density of final states only,
Pind(E,~) ~ N(E-h0)
(2.12)
while ordinary photoemisslon yields within the same approximation the product of initial and final densities of states.
232
Volker Dose
The relative importance of direct and indirect transitions has been continuously discussed
in the photoemissfon
for Bremsstrahlung
literature 12. An attempt to access the problem
emission will
be presented later on in the interpretation of
measurements on polycrystalline nickel. We shall finally briefly comment on the transport and escape factors in (2.6). The transport function T(E,~) is by analogy to photoemlssion given by 9
(XeE ) X (~) T(E,~) = I - Xp(~) in(l + --'-'P--~)e where
Xp
and
Xe are
the photon
Since in the ultraviolet energy
dependent.
The
the sample material if
Bremsstrahlung
constant
and
electron
(2.13)
attenuation
lengths
respectively.
region Xp>>ke' T(E,~) is close to unity and only weakly
escape
under
function D(~)
investigation.
spectroscopy
is
depends
Note,
carried
on the optical
however,
out
in
that D(~)
the
initial energy mode it can, in principle,
isochromat
constants
of
is a constant mode.
In
the
add to the structure observed
in the recorded spectra.
3. Experimental Considerations
Transformation of the schematic arrangement into experimental reality is straightforward. Figure 2 shows in detail the early experimental setup used by the Ulmer 13 . Emitted x-rays are monochromatlzed by a single focusing crystal monochro-
group mator
and
the
Anticoincidence cosmic
transmitted techniques
ray background.
The
radiation
is
detected
by
a
with a ring of surrounding electron source
is heated
Geiger
Geiger
MUller
counters
intermittently
counter. eliminate
in order to
avoid energy smearing by the voltage drop across the filament of the x-ray diode. Energy
resolution
obtained
in this
experiment was
of the order of
1.2 eV at a
pass energy of I keV. Measurements of isochromats of the 4d and 5d metals Mo, W, Nb,
and Ta with a statistical precision of 1.5% required accumulation periods of
about 50 h at emission currents between 5 and 35 mA 14. Note that the electronic power deposited on the sample measure
of
deposited
the overall
in these measurements was between 6 W and 40 W. A
sensitivity
charge which was
of
the apparatus
of the order
of 103 -
is the count rate per unit
I04/C
in this case.
A modern
version of this setup has been reported by Lang and Baer 15 who employ the monochromator band
for an AI K -source
(XPS)
Ulmer's
and
group
techniques
conduction using
in an XPS
band
different
used quantum energies
studies crystals,
spectrometer and nicely combine valence (BIS) partly
in
the
grown
same by
experiment. highly
Though
sophisticated
down to 152 eV this detection energy would not
Ultraviolet Bremsstrahlung Spectroscopy be
considered
to be truely ultraviolet.
233
The first so far reported experimental
setup along the same lines operating in the vacuum ultraviolet was carried out by Baptist
and
Chauvet 16.
graphic
grating
The
dispersive
element
recorded on a toroidal blank.
in
their
experiment
This allows
Is
a holo-
for almost
complete
correction of aberrations especially at low wavelengths. The reported characteristics of the grating are outer dimensions of 30 x 30 mm, with
550 groves
per ~m resulting
focal length of 320 mm
in a dispersion of about 20 A per mm nearly
independent over the whole wavelength range of
I00 A to 500 A corresponding to
energies between 20 and i00 eV. Entrance and exit sllt of the monochromator where chosen to be 0.25 x 4 mm resulting in an optical resolution of I0 A essentially independent of the mean detection energy. The reported sensitivity of the apparatus is 3x105 counts/coulomb deposited charge in the d-band maximum of platinum. Since
space
charge
effects
limit
the
emission
current
to
typically
i mA
the
experiment is still rather slow though it constitutes a considerable improvement over the performance figures reported by Ulmer. A suggestive further improvement of performance may be obtained replacing the combination of
spectrometer
exit
sllt
and
channeltron
by a position sensitive
device made up by a channelplate and a resistive anode. A spectrometer of thls kind has been set up by Fauster and Himpse117. Such a modification enables taking simultaneously isochromat spectra at various monochromator energies if the elec-
HV FIX
TI I VARIABL
I INTE GRAT.
SUPPLY IF-U-
Ic°N' °L I GEN.
I
ANTI -U--U- COINC.
]~-
ICOUNT.
Fig. 2: Schematic of a BlS-spectrometer employed by the Ulmer group.
234
Volker Dose
tron if
energy
the
is varied
electron
by Fauster intensity occupied
or even more
energy
is kept
and Hlmpsel versus
from a polycrystalllne
the density
tion and the resolution ing
of
the
step.
differentiation mentally
A
of states
procedure
of the signal obtained apparatus
initial
energy
gold
target. level
spectra reported
Since Au has a fully resembles
may be simply derived
has
energy
resolution
from the slope of x-ray emission
the Fermi
at
of the apparatus
similar
determined
thls evaluation
constant
The overall
is 0.3 eV as demonstrated
energy
d-band
interesting,
constant.
been
pursued
by
a step func-
from the broaden-
Lang
and
Baer 15.
By
from a silver target they derive an experi-
function.
We
shall
discuss
a
refined
version
of
later on.
/i TRANSMISSION >-
ABSORPTION
u. w O u
REGION
'....:.~:...~.~...
z
z
U.l
om m n, o
I--
z
n,.
( ~o <
Y//////A
// ENERGY
-~
E0
Ema x
Fig. 3: Schematic of an x-ray absorption edge. Near edge absorption acts as a low pass to radiation. The solid curve represents the hlgh energy portion of a Bremsstrahlung spectrum. The hatched area is absorbed by a foll of suitably chosen thickness.
Though up
an
a grating
isochromat
appreciable
monochromator experiment,
investment.
We
shall
the followlng 18. Let us consider A
schematic
edge
of
is given
is the most
offering
therefore first
the x-ray absorption in Fig.
3. Absorption
straightforward
a maximum discuss
the edge and f(E,Eo) Let
coefficient
wlth
be
the
intensity
electrons
of
energy
E •
Suppose
approaches
in
of x-ray absorption.
in the vicinity
of an absorption
of the edge may be regarded
of an absorption
for
an
Let E O be the energetic
distribution a
of
to setting
it involves
two alternative
in the vicinity
the transmission
I(E,E m)
approach
flexibility,
the energy dependence
as a low pass filter to incident x-radiatlon.
E.
of
foll for x-rays
x-rays
moment
position of
from
that
it
a
target were
of energy bombarded
possible
to
m
modulate the
a.c.
the edge position with an amplitude AE o. Then for sufficiently component
of
the
transmitted
radiation
R(E m)
would
be
small AE °
proportional
to
Ultraviolet Bremsstrahlung Spectroscopy l(Eo,Em)-AEo, f(Eo,Eo). This, however,
235
is the isochromat corresponding to a monoch-
romator energy E o. If alternatively we modulate the energy of the incident electrons the recorded photocurrent T(Em)iS
T(Em) = where n(E) denotes
d/dE m f n(E)f(E,Eo)l(E,Em)dE
(3.1)
the spectral sensitivity of the x-ray photon detector cathode.
In order
to proceed with
explicit
functional
the evaluation
form for I(E,Em).
of (3.1)
There
it is necessary
is convincing
that at least near the high energy limit of a bremsstrahlung be written as g(E-Em )19'20
to assume an
experimental
evidence
spectrum I(E,E m) may
A slightly more general assumption would be
l(E,Em) = h(Em)g(E-Em) Within
the
previously
developed
simple
corresponds
to the density of unoccupied
a possible
energy
dependence
of
picture
(3.2)
for
bremsstrahlung
formation
states of the target and h accounts
the radiative
transition
matrix element.
g for
Expe-
rience shows that h is only slowly varying with E . Inserting (3.2) into (3.1) we m obtain T(E m) = dh/dE m f n(E)f(E,Eo)g(E-Em)dE
-
h(Em) ~ ~(E)f(E,Eo) ~/~E g(E-Em)dE
(3.3)
Partial integration of the second term noting that ~(0)f(0,Eo)=0 yields:
T(Em) = J g(E-Em)f(E,Eo)(hdn/dE + ndh/dEm)dE
+ h(Em) ] g(E-Em)n(E) ~/SE f(E,Eo)dE The first
term in (3.4) varies only slowly with energy and will cause a smooth
background ergies
E
simplify
(3.4)
signal B(Em). = E ° since
The second
f(E,E o) varies
term contributes rapidly
in
this
significantly region.
only for en-
We may therefore
the integral further by replacing ~(E) by n(Eo). The remaining integral
is a convolution
of g(E-E m) and ~f/~E which
plays
the role of an apparatus
or
spectrometer function. In particular if f(E,Eo) were a step function
f(E,E o) = i
E,E °
f(E,E o) = 0
E)E °
(3.5)
236
Volker Dose
the derivative would be a Dirac delta function and the second integral in (3.4) would yield
(3.6)
q(Eo)'h(Em)'g(Eo-E m)
I--
AI - foil
m
d = O.&-m
w Z (... (.1
u.
L
<
!
I
72.0
725
73.0
73.5
74.0
ENERGYIW Fig. 4: Effective apparatus function for x-ray absorption at the aluminum LII I edge.
which
is
apart
from
the
factor
q(Eo)
spectrometer energy E . In practice O
by
definition
the
isochromat
taken at
a
~f/BE is given in terms of the mass absorp-
tion coefficient of the foil ~(E,Eo) by
(3.7)
8f(E,Eo)/~E = -pd ~(E,Eo)/~E. exp{-~(E,Eo)Pd }
where p and d denote mass density and thickness of the absorber foll respectively.
(3.7) may
experimentally
be evaluated determined
further
by fitting
a Donlach-Sunji621
x-ray absorption data.
the loll is not critical.
The choice
line
shape to
of the thickness of
It should be chosen such that band stucture effects of
the absorber on the high energy side of the edge do not add further structure to the
apparatus
function.
A transmission
ratio
for x-rays with
energy
just below
and above the edge of 102-103 is sufficient for this purpose. An evaluation 22 of (3.7) an
for aluminum LII I absorption at 73 eV is displayed in Fig. 4. A sketch of
isochromat
spectrometer
employing
the above
discussed
principle
is given in
Fig. 5. Apart from the absorption loll it is identical to an appearance potential spectrometer. tial and
This offers
isochromat
the attractive
spectra with
possibility of taking appearance
the very
same experimental
poten-
setup. Experimental
results for GaAs will be discussed in section 5. We
shall
finally
describe
still
another
alternative
to
the
classical
mono-
Ul travi ol et Bremsstrahl ung Spectroscopy
AI- FOIL
FILAMENT
SAMPLE
237
I
HV SUPPLY
---
Io ,OSCIL- I
II,
i
R,f PLL
LATOR Refj
Out
I 3C-SUPPLY
C PU
ADC
Fig. 5: Schematic of a BIS spectrometer employing x-ray absorption. Apart from the absorption foil the arrangement is identical to a soft x-ray appearance potential spectrometer
chromator. Consider
This a
is
Gelger
al. 24 is made
based ~dller
20 mm
and
a
few
diameter
lowpass
to
an
energy
counter.
The
from a 24 mm diameter
less steel electrode helium
on
the
2 mm
counter
stainless
of 1.5 mm diameter.
crystals
of
thick
incident
iodine.
CaF 2
ultraviolet
first
employed
photoncounter by
23
Dennlnger
steel shell with a central
.
et
stain-
The counter filling consists of 500 mbar The
single
radiation
selective
with
entrance
crystal. a
window
The
cutoff
at
of
entrance about
the
counter
window
i0 eV.
is a
provides
The
yield
a
for
molecular photoionlzatlon of iodine with threshold at 9.23 eV 25
(3.8)
12 + hv + 12 + + e
on
the
The
other
combined
energy
hand
offers
action
dependence
of
a hlghpass
the
entrance
to
the
window
detection
of
ultraviolet
transmission and
provides a bandpass with mean energy of
radiation.
the photoionization
(9.70 ± 0.23)
eV. This
is illustrated in Fig. 6. Photoelectrons tion these
could are
be a
produced
at
possible
source
thermalized
the counterwall,
quickly
also
to deteriorate
by
the
helium
by much less energetic
the counter filling,
energy, captured by dissociative attachment to the iodine.
and
resolution. at
radia-
However,
sufficiently
low
238
Volker Dose
|
•
|
ZO
•
|
;~
Z
/
/
" t--
',
/I
"
"~
O
"
----
.,,--,:..
'tl
•
~""~
•
\,.
........
I
I
9.2
o_,,,
31:
I
9.6 10.0 ENERGY (eV)
lO.Z,
Fig. 6: The ultraviolet transmission of a CaF 2 single crystal (long dashes) represents a low pass to vacuum ultraviolet radiation. The photoionlzation of iodine (short dashes) provides a high pass to the detection of UV radiation. The solid line is the band pass obtained by combination of these properties.
e- + 12 + I + I-
The
cross
maximum
section
for
this
reaction
has
a
of the order of 10 -13 cm 2 at 0.34
fore
very
which
is
efficient strongly
the attachment
and
can be
temperature
further
(3.9)
(0.03
± 0.03)
eV and
eV26 . The attachment
threshold
process
is there-
influenced
dependent.
Slow
process and also by dissociative
of
by the iodine
negative
iodine
vapour ions
pressure
produced
has
provided Gelger ions. ly, lead
a the
counter
lower
threshold 27
central design,
the mean
to multiple
efficiency 28 per cent
of
the
(3.8),
electric
the low energy
drift
velocity
discharges counter
from is
do
is sufficiently
it avoids
This would affect
since
than
electrode
of I
quite
high
(3.10)
not
lead
thick.
counter this
discharges
is unusual
of the negative
in
iodine
of the counter and slmultaneous-
is much
smaller
primary and
to
Though
field detachment
threshold
the same
in
photoionization
12 + hv + I+ + I-
which
a
has
than that of electrons,
ionization been
event.
estimated
to
The
quantum
be
several
Ultraviolet Bremsstrahlung Spectroscopy Some
less
operate
desirable
features
it successfully.
of
the
The vapour
counter
pressure
must
be
239
considered
in
of the iodine is strongly
order
to
tempera-
ture dependent leading to higher primary ionization yield with increasing temperature. by
The attachment
far
the more
rate
important 29
(3.9), one
however,
leading
increases
to a net
also.
decrease
The latter process of
the
counter
is
sensl-
tivity of 8% per degree
Due to the strong energy dependence of the attachment
process,
not
the
counter
does
show
a plateau.
Sensitivity
changes
Volt at mean operating voltages around 650 V have been measured.
of 0.6%
per
Special care has
therefore to be taken if intensity comparisons are made.
i F,, I
[
CaF2
I
INTEGR.
DAC
JIPULSE SHAPE
,, ; ,"500-800V v,,
'J
COMPUTER
Fig. 7: Schematic Geiger counter.
We
finally
discharge. rates.
mention
On
a
of a BIS spectrometer
the
first
This problem,
rather
glance
however,
large
this
dead
would
employing the energy selective
time
of about
seriously
can be circumvented
limit
150 ~s the
following
possible
by experimental
each
counting
precautions
to
be discussed in the following. A block diagram of an Isochromat Geiger
M~ller
counter
is given
spectrometer
is due
to
the energy
employing
the energy selective
in Fig. 7. We have up to now only discussed
optical resolution of the spectrometer. resolution
24
A substantial
distribution
of
contribution to the overall
the electrons
impinging
sample. We use a directly heated tungsten filament as a cathode.
broadening
resulting
from
the
voltage
drop
across
the
on the
Thermal broaden-
ing due to a cathode temperature of about 2200 K seems to be inevitable. nal
the
filament
Additiohas
been
240
Vol ker Dose
eliminated During
by
pulsed
the heating
constant
phase
current
heating
the accelerating
at
a repetition
voltage
is
rate
suppressed.
of
400 c/s.
Bremsstrahlung
measurements are therefore restricted to the interval when the filament is equipotential. The
counter
dead
time problem is solved along the same lines. Every
registered
count is used to switch off the acceleration and to block current integration for a time safely therefore
larger
possible
than the counters
during
the
dead
recovery
time.
No
further
period and counting
primary events
losses
do not
are
occur.
Count rates up to 2000 counts per second are easily possible with this technique. II
I
•
.5
Wo=9.?eV
I
?
1
C
HAFNIUN
•
+.:j 0
0 I
I
I
/+
i
°
i
6
"
°o
8 E/eV
0 o
I
I
-1
0
I
1 E/eV
Fig. 8: The isochromat from polycrystalllne hafnium is nearly a step function and can therefore be used for an experimental determination of the apparatus function of the spectrometer in Fig. 7. Fig. 9: Apparatus function derived from the data in Fig. 8.
The overall the
optical
the
latter
obtain
an
to
behavlour.
resolution of the spectrometer function
Maxwellian
involved
experimental This
be
apparatus
assumptions
ble.
energy
resolution
Such
be a
provided
function
shown
in computing
determination
can
and
of
the
the the as
energy
emission
the
solid
distribution.
current
is
llne
Fig.
in
apparatus
from
an
shape
accidentally
function
isochromat
seems
exhibiting
obtained
at
this
Assuming
in saturation
this curve are quite reasonable,
obtained is
is given by a convolution of
electron
9.
Though
an independent
to be highly a
we the
smeared
detection
desira-
step
like
energy
from
Ultraviolet Bremsstrahlung Spectroscopy polycrystalline function finite
hafnium 30
as
shown
in
Fig. 8.
Simple
does not lead to the desired apparatus
slope
of the "plateau".
241
differentiation
of
this
function because of the small but
We therefore assume
that the data in Fig. 9 result
from a broadening of the function,
f(E') = O(E').(I+~E')
that f(E') the
is,
a
step
has
to be formally
energy
function
scale
is
with
a
superimposed
identified
by
definition
g(E') be the apparatus function.
with of
(3.11)
linear
the density
the
8
energy
dependence.
of empty states
function
at
the
Fermi
Since
the zero of energy.
Let
The measured signal H(E) is then given by
H(E) = ] f(Z')g(Z-E')dE'
(3.12)
h(Z) = dH(E)/dZ
(3.13)
G(E) = ~ g(Z')dE'
(3.14)
Let
and
we then obtain by differentiating
(3.12) the inhomogeneous
differential
equation
h(E) = G'(E) + aG(E)
(3.15)
From the solution of (3.15) we obtain
g(E) = h(E) - aH(E) + a2e-UE ] H(E')exp(uE')dE'
g(E)
as
evaluated
Normalization solid
llne.
from
is The
such
the data that
agreement
the is
in Fig. 8 is displayed area
quite
is
the
good.
same
The
as
as
full
that
abszlssa
(3.16)
dots
in Fig. 9.
the
calculated
under
of
the
curve
in
Fig. 8
denotes the voltage applied between cathode and sample. Compared bilities
to a spectrometer have
transmission of
the
equal the
the
energy.
absorption to that
energy
common
foll
This
very high
are
that
operation
monochromator.
counter,
the last two possi-
is only
possible
the very easy and compact
pseudomonochromator,
per coulomb and is therefore tive.
back
Advantages
of a grating
selective
employing a grating monochromator
draw
however,
the
sensitivity
The ultraviolet
offers
sensitivities
design being
at
in the case approximately
spectrometer of up
a fixed
employing
to 108 counts
by far superior in this respect to any other alterna-
perfomance
order of I0 - 50 ~A. Furthermore,
figure
enables measurements
with currents
the low energy of the electrons
involved
of the in the
242
Volker Dose
measurement species
renders
electronic
in the study
inconvenience valuable
attached
in
the
desorption
of adsorbate to
study
the
of
and
covered
fixed
transient
dissociation
surfaces
quantum
energy
adsorbate
of molecular
unimportant. it
induced
will
adsorbed
In spite
of
therefore
states
be
the most
und measurement
of
adsorption kinetics.
4. Density of State Measurements
Most
of
with
the
the
data
energy
to
be
discussed
selective
in
counter
the
following
spectrometer.
chapters
A diagram
have
relating
been
obtained
accelerating
i 3 / 2 kT
El-I---
.....
°; ll
[
i
eU
. . . . . . . .
Fig. i0: Energy diagram for Bremsstrahlung spectroscopy. Note that the sample work function is irrelevant for the determination of the total electron energy E.
voltage, Fig.
work
functions,
and
mean
The
threshold
for
radiation
I0.
thermal
energy
of
production
the
of
electrons
energy
~o
is given is
from
in
this
diagram
e@ k + 3/2kT + Vac > ~ o
(4.1)
From this relation the Fermi energy is located at
Vac = ~0 ° - e@ k + 3/2kT
Note
that
the sample's
of
considerable
~o
= 9.7 eV,
temperature
work
importance e@ k = 4.5
eV
function in the for
of 2200 K calculated
a
does
study
not
tungsten
from
enter
of adsorbate emitter
the saturation
(4.2)
into
this
covered and
relation. samples.
3/2kT = 0.23
current
This
is
Inserting eV
for
of the filament
a the
Ultraviolet Bremsstrahlung Spectroscopy position mate
of
the Fermi
energy
relies
of course
on a lot of
experimental tally
determined
sonable used not
check
would be at 4.97 V acceleration
agreement
with
g(E).
above
estimate.
the
recallbratlon,
determined
by calculating
function
in all data to be presented require
independently
can be obtained
apparatus
243
The
that will
is
latter
in the following.
a problem
data.
the centroid
result
The
voltage.
This
esti-
An independent
of the experimen-
(4.70 + 0 . 0 4 ) V value,
however,
in reawill
be
Note also that this value does
arise periodically
in experiments
using grating monochromators. I
|
!
!
TANTALUM
20
!
|
/
o=97eV
i
i
!
!
ej
I
,~..
/.
\ ". ° ° o OOOooO oo o e ° °
0
F....-
10 L.L.I F....-
i
i
i
I
i
i
i
i
i
0 2 4 6 8 EXCESS ENERGY (E-~wo)/eV Fig. ii: An experimentally obtained isochromat from polycrystalline tantalum is compared to the density of final unoccupied states in tantalum. Note the discrepancy for excess energies above 5 eV.
Figure Ii tantalum ~ a
shows
target 31.
= 9.7 eV.
o calculation
width
experimentally
was
Full
The solid by
chosen
dots
represent
Petroff
and
Visvanathan 33
to approximate
curve was
normalized
The overall
agreement
is not
also
coincide
predicted with
is slightly
by
1 eV.
theory.
experiment.
In summary,
data, the agreement An entirely
for
measurement
broadened
the experimentally
by
too bad and The
of
the
different
Bolziau
with
a
al. 32
whose
slope.
The
of the experiment the main
maximum
near the Fermi
near the main maximum corresponds
of the model
at
from
of the experiment.
and
of the first maximum
the simplicity
behaviour
et
Lorentzian
threshold
features first
point showing up in the experimental
is quite encouraging
polycrystalllne
density of states
observed
the general
positions
The amplitude
considering
a
to the main emission maximum
too high while the satellite
ly to the inflection
the
isochromats
llne in Fig. Ii is the theoretical
theoretical
are
determined
data displaced used
edge
probabby about
to interprete
the
for excess energies ~ smaller than 5 eV.
is observed
for e ~ 5 eV. The two curves
start
244
Volker Dose
rapidly deviating from each other, the theoretical curve lying below the ultraviolet
isochromat.
far
investigated in our
isochromat from
We have found this behaviour consistently for all materials so
spectrum
electrons
laboratory 31'34.
is expected
that
have
not
As
already mentioned in chapter 2 the
to be composed of a primary component
lost
energy
prior
to
the
radiative
event
Ip(E,~) and a
background Is(E,~) arising from electrons which have suffered one or more energy losses prior to the optical transition. A rough estimate of the probability for radiation
production
using
known
ployed.
the We
the
properties
arrive
sensitive band of processes
in
at
a
ultraviolet of
the
energy
probability
the counter.
of
From
This points
experiment
selective Geiger
10-9
this
are alltogether unimportant
trons entering the sample.
isochromat
per
figure
incident
can
MHller
derived
counter
em-
electron within
the
it is obvious,
in the process
be
that radiative
of thermalizlng the elec-
to an appreciable contribution of I
to S
the overall s i g n a l 31 .
,, ,, o
7//-/j ///////J Fig. 12: Energy level diagramm for Bremsstrahlung emission with and without preceding electron hole pair creation. Electron hole pair production can proceed in two different ways (solid and dashed arrows) leading to the same final state.
Let
P(EI,E 2)
be
the
probability
that
an
electron
of
initial
energy
E1
is
scattered to a final state with energy E 2 creating an electron hole pair and y the probability for radiative transitions with emission of quanta with energy
o (c.f. Fig. 12). Let us assume further, that electron hole pair creation is by far
the dominant energy loss process. With these assumptions we obtain for the rate
Ultraviolet Bremsstrahlung Spectroscopy of
radiation
with
energy
induced
by
electrons
with
245 Initial
energy
El,
O
z(z1,~o) l(Zl,~o) = yN(Zl-~d~o)
+ J e(Ei,E2)dE2{YN(E2-d~o) + J e(E2,E3)dZ31YN(Z3--d~ o) + ... In the first term which represents
the primary component,
placed by X N ( E I - ~ ). The second,
third,
side
the
represent
contributions
to
(4.3)
Ip(E,m) has been re-
and consecutive terms on the right hand
radiative
signal
with
one,
two,
or more
energy losses by electron hole pair creation preceding the radiative event. This model is an extension of that used by Janak et al. 35 for the quantitative explanation of photoelectron energy distributions. I
>
I
I
I
/ " ~
1
I "
' I'
I
' I
I~
I
....
TANTALUM
20
I
h,~= 97eV
o "-
10
~
°
~:'~2 0
-2
,~
--,----~--I
-1
0
I
L--..---,"-',
2
3
~
EXCESS ENERGY
L..n.-.--,---fl
5
6
7
8
9
(E-~.~)IeV
Fig. 13: The heavy dots are an experimental tantalum isochromat spectrum. Small dots represent the direct contribution Id to the total emission. Long dashes, dash dots and small dashes indicate one, two and three electron hole pairs preceding the radiative transition. The solid curve is the sum of the four contributions.
The problem of calculating tion has
been solved
complicated
the function P(EI,E2)
by Kane 36.
An exact
approach
for electron hole pair creaturned out
to be extremely
and computer time consuming. However, Kane was able to prove that a
random ~ approximation originally proposed by Berglund and Spicer 9 yields equally good
results.
With
this
approximation
momentum
conservation
is
relaxed
and
P(EI,E 2) is simply given by the sum of all interband transitions resulting In an
246
Volker Dose
energy loss EI-E 2.
2N(E2) f N(~4)N(e4-EI+E2)dg 4
P(E I,E2) =
(4.4) N(E2)dg2f N(~4)N(e4-El+E2)d~4
The
function
is
normalized
to
two
because
there
are
two
equivalent
types
of
transitions (solid and dashed arrows in Fig. 12) leading to the same final state. Figure 13 shows The heavy the
the
solid dots
direct
results
for
are again
contribution
to
the
previously
the experimental
the
signal
and
discussed data.
The
correspond
to
case of
tantalum 32.
small dots represent the
solid
line
in
Fig. ii. Long dashes indicate the contribution of radiative transitions following the
creation
indicate
of one electron hole
contributions
associated
pair. with
The the
dash dotted curve and short dashes formation
of
two and
three electron
hole pairs respectively. The solid curve is the sum of all contributions. been matched
at
ment
is
finer
details
the intensity maximum.
considerably
improved
The agreement between theory and experi-
especially
are worth mentioning.
It has
The
in
the
region
beyond
first maximum near
5 eV.
the Fermi
But
also
energy is
reproduced perfectly while the second maximum in Fig. 11 has become an inflection point as observed in the experimental data. Similar
results
have
been
obtained
shall not be reproduced here. crystalline pair
nickel 34'37
formations
case.
The
prior
overall
shown to
the
for
the
5d metals
W,
Hf 31,
and
Pt which
Instead we discuss analogous measurements on polyin
Fig. 14.
radiative
quantitative
Up
to
four
transition
agreement
is
again
successive
have
electron
to be included
quite
satisfactory
hole
in this in
this
case. An alternative to adding inelastic contributions to the direct signal I to attempt
is P to remove them from the raw experimental data 34. Assuming that radia-
tive
transitions
used
to calculate
can
be neglected
in
the
thermalization
process,
(4.4)
can
be
the probability W(EI,E 2) for transitions from an initial state
of energy E l to a final state of energy E 2 by a sequence of an arbitrarily high number
of electron hole
convolutions. functions
pairs.
W(EI,E 2)
can be obtained
from
(4.4)
by repeated
The result of such a procedure is shown in Fig. 15. Note that these
exhibit little structure compared suggesting
to the strongly varying densities of
states
used as the input data,
that structure is of secondary
tance.
Only the range of interest in the present context E 2 > ~ o
impor-
is shown. With
the help of these functions the observed radiative signal Ito t may be written as
Itot(El,~o)
= I p ( E l , ~ o) + f W(Ei,E2)Ip(E2,~0o)dE2
(4.5)
Ultraviolet Bremsstrahlung Spectroscopy
1.0
'I
I
I
I
|
l
l
I
l
!
I
I
UV- lsochromat Ni poly
08 >
E 0.6
I
I
247
|
~_........ oeOoe°°°°
0
•
o o o e ° °qb°
--
~ 0./.
contributions / __.
\Theory
. lowicz
m0.2 0
-
=
0 EF
*
=.
2
J-
.
.
L
-'r'-'f"-i-'-i
Z, 6 8 ( E - E F)/eV
t
....
10
12
Fig. 14: Solid dots are the ultraviolet isochromat spectrum from polycrystalline nickel. The lower solid curve is the density of empty states. Dashed and dash-dotted curves represent contributions from electron hole pair production prior to the radiative event. The upper solid curve is the resulting calculated isochromat. Note the small discrepancy at about 2 eV.
10
I
l
~
I
|
I
!
l~uo= 9.?eV E = (E 1 - l ~ w o ) l e V
,
c~
!
I" \
~j ~,
"\ I..\ '-. , ~5
|
.
..:
,-,.
o n
',,
\
¢=3.6 ", '
0
?.2 \ I
&
I
..
,..
10.9\o \
lZ,.5 ~,\
I
8
I
I
I
12
(E2-hUo)/eV Fig. 15: The probability for a transition of an electron with energy E 1 to a state with energy E 2 by electron hole pair production is shown for nickel. The energy range shown is E2 ) ~ o with ~ o = 9.7 eV and c = E l - ~ o "
248
Volker Dose
This for
latter
equation
Ip(El,~o).
comparison
can
The
between
As
solved
result
is
experiment
simple density of states to 3 eV.
be
discussed
by
given and
straightforward
in
interpretation. previously
Flg. 16.
theory.
The
sequential
It provides
dash-dotted
deconvolutlon
a more
line
stringent
represents
the
Thls obviously fails in the region 1 eV
a density
of
states
interpretation
relies
on
indirect
transitions only. A theoretical calculation assuming exclusively direct + transitions with k-averaglng over the entire Brillouin zone with full account of i
w
•
,,;
[~,~.
= E
i' ~,,~.
E 0 "~
'
-
-
•
I
i
" w
I
UV ISOCHR. N"I p01y "
.
I
.
I
0
I
I
2
4
( E -EF )/eV Fig. 16: Data from Fig. 15 have been used to remove the electron hole palr contribution from the nickel spectrum. The resulting experimental data can be explained satisfactorily only if both direct (dashed curve) and T-non conserving transitions are taken into account.
the
dipole
data
are,
transition after
matrix
suitable
element
has
broadening,
been
carried
displayed
as
out by N.V. Smlth 38. His
the
lower
dashed
llne
in
Flg. 16. The sum of the two given as the solid llne approximates the experimental data pretty well.
We may conclude that in isochromats from polycrystalline mate-
rials density of states effects (see also the previous case of tantalum), that is indirect transitions, are prevailing. For a complete understanding, direct
and
indirect
transitions
must
be taken into account.
however, both
This is not at all
surprising. Recalling the phenomenon of band gap emission in photoelectron
spec-
troscopy we expect that Bremssstrahlung spectra wlll contain substantial contributions from initial evanescent an
understanding
of
momentum
states. resolved
This arguement will again be necessary for spectra
to
Obviously nature never presents itself simple minded.
be
presented
in
section
6.
Ultraviolet Bremsstrahlung Spectroscopy 5. Application
to more complicated
249
Systems
A. Oxidation of nickel Transition metal oxides are known to exhibit a wide spectrum of different electronic
properties.
niumoxide haviour and
While
is a perfect
as a function
nlobiumoxide.
tion metal copy
oxides
The
Considerable
oxides
only
tool so
far
due
to
their
impossible
with
its low current
effort
has
insulating
been
spent
insulators
UV
transi-
spectros-
on NiO
isochromat
of 50 ~A/cm 2 on the other hand to allow
of
on the conduction
Measurements
properties.
be-
in vanadium-
on the analysis
information
is NiO 37.
rhe-
to conducting
by H~fner 39. Isochromat
corresponding
insulating
densities
from
as discussed
investigated
nondestructive
and nickel are
and pressure have been observed
to provide
case
cobalt
Transitions
by photoemisslon
are
be sufficiently
conductor.
of temperature
is the suitable
band.
of manganese,
crystals
spectroscopy
has turned out to
the study of nickeloxlde
overlayers
on Ni
substrates. It via
is presently dissociative
ther
exposition
reaction yers
commonly
leads
saturates
of oxide.
accepted
chemisorptlon
to NiO nucleation
at ambient
similar
down
the reaction
behavlour
but
reaction
surfaces
differ
after
reactivity.
of 600 K and oxygen partial pressures
of
Higher
NiO.
surfaces vealed red
favour
partial
production
in such cases
to
NiO.
The
pressures,
binding
Islands.
Increasing
is
The
orientation
temperatures
slow
Ertl et al. 40 suggest
of 10 -3 Pa for the production
oxide.
and markedly
XPS measurements
usually
attributed
to various
degrees
to
damaged have
states with higher binding energies
state
Fur-
three monola-
of different
temperatures,
of nonstoichiometric
oxygen binding
new
lower
of oxide of about
coverages.
a temperature pure
growth
formation
saturation
proceeds
up to 5 - 10.10 -4 Pa.s.
and monocrystals
in
but lead to higher
of oxygen with nickel
exposures
and lateral
temperature
Polycrystalline
show
that
for oxygen
re-
as compa-
lattice
defects
of oxidation
produced
described as Ni203. A series under
the
Fermi
level
of isochromats above
isochromat steep
mentioned
is indicated
of the nickel
corresponding
substrate
conditions
is
by the dashed d-band
is characterized
shown
in
Fig. 17.
line. We observe
emission
with increasing
The
position
a continuous exposure.
a pronounced maximum
the
attenuation
The final oxide
by a very low density of states at the Fermi
rise at 3 eV excess energy,
of
level,
at 4 eV, and another
a
less
pronounced rise at IO eV. The tiny shoulder at I eV will be discussed later. An Pa.s These by
analysis and
of
isochromats
least
the
intermediate
3300.10 -4 Pa.s
squares
have
has been
fitting
been
states
of
oxidation
carried
out
in terms
decomposed
to a linear
into
nickel
combination
and
for
exposure
of
520.10 -4
of a superpositlon nickeloxide
of the clean
model.
contributions
nickel
signal and
250
Volker Dose
UV-lsochromats Ni poly÷Oz T=700K p = 2 10-STorr
o g
0o0
... • •.. •
•~
.4
.."~'~-~....-.
"-
.t
ci,~an,::i
J! ' / • \
:'""%~•""
"
" I k
"
•/001~:
I
"
,
"" %
.:
"1 "1
•
0
2
Fig. 17: Ultraviolet isochromats polyerystalline nickel sample.
for
'1
I
g
I
g
l
g
/, 6 8 ( E -E F) leV various
l
I
10
states
l
I
I
12
of oxidation !
I
I
UV- [sochromat Ni poly 2500L O z
I
of a
I
,,~
T= 700°K
/ /
/ .: 0
Nio ../~
.
|
I
'
0 EF
I
_....'".°"
i
2
Ni
°
,
,
/
~ • .
i
.
.
.
I
.
.
Z, 6 8 ( E -E F) leV
.
.
,
.o--..~__..-
I
10
I
I
_
I
12
Fig. 18: An isoehromat corresponding to an intermediate state of oxidation is decomposed into pure Ni and pure Ni0 contrlbtuions. A indicates the difference between fit and experimental data.
Ul travi ol et Bremsstrahl ung Spectroscopy
251
the oxide isochromat of 26,600-10 -4 Pa.s exposure. The result of such a decomposition is given in Fig. 18. Full dots
represent
structure
obtained after exposure
sample
to
of nickel
and nickeloxlde
3300.10-4pa.s
oxide contributions
oxygen.
Solid
the isochromat
curves
represent
from the composite of the clean nickel
the
nickel
and nickel-
while A is the difference between fit and experiment.
Fits of
similar quality have been obtained for other exposures as well. Repeated isochromat measurements
carried
out after various
oxidation cycles have proved that the
measurement was absolutely nondestructive. The superposition results were used to check the well known logarithmic growth law 41 assumed to be valid in this thickness range.
d
d is the oxide layer thickness partial
pressure,
d o In(l
=
+
L/Lo)
corresponding
to an exposure L at constant oxygen
d o and L ° are free parameters
._.1.0 8 u~ ~co. 8
•
(5.1)
~
which depend sensitively w
Isochromat
Ni 0
T • 700 K p : 2"10"s Torr
~
~
•
on the
/
/ /
"~ .6 r-
7500 L
e~ e-
J
2500 L
"ID
800 L u~ .2
&00 L
0
E
200, L
0
i ,,
,
.
-~
0 .2 .4 .6 .8 1.0 catcutated intensity (S/S..) Fig. 19: The measured intensity of the NiO isochromat signal is compared to values derived from a logarithmic growth law.
oxidation
conditions.
Assuming
an exponential
damping
of
the
incident
due to the finite elastic mean free path in the nickeloxide film,
electrons
the strength of
the nickeloxide signal as a function of film thickness is given by
S(d) = S®{Z - exp(-d/~NiO) }
(5.2)
252
Volker Dose
where
S
indicates
Combining
the
signal
strength
for
an
infinitely
thick
oxide
sample.
(5.1) and (5.2) we obtain
(5.3)
S(d) = S={I - (I + L/Lo)-B }
with
8 = do/%Ni O.
result
Figure 19
shows
of the superposition
derived
from
(5.3).
The
a
comparison
of
S/S=
as
obtained
from
the
model using L ° = 560.10 -4 Pa.s and 8 = 0.4 and values
linear
relationship
between
the
two
sets
of
values
provides an impressive confirmation of (5.1). |
|
l
I
|
Ni p o l y + 0 2 Z
-
/
S" •
15L %
u') '--"
"e/
09 •
0
\
carried
i
I
i
various same
of the oxide
spectroscopy
isochromat
Auger study.
stages
have
studies
I
Some
high
exposure
axis
at
range
as
exposure
sufficiently
oxidation
reported
in order
oxidation
Auger
signal
been
formation
Figure 20 shows
of
sample 43.
> 1
•
-
~OL
i
i
i
i
3 6 AES SIGNAL STRENGTH ( a . u . )
studies
out
:
•
Fig. 20: The measured intensity of the pared to the oxygen AES signal strength.
electron
l
*•
Z
Extensive
!
60L ;
0 I---
.0_
!
but
is expected.
tween these two adsorption
with
function are
the where
Auger
of
also
fitted
linear
transition
analysis
Auger
We have
derived
Auger
signal
relation
relationship
from
obviously
regimes while isochromat
tifies the oxide growth regime.
The
com-
also
from the
of the isochromat
oxygen
given.
is
employing
and Hudson 42. the results
fraction
the
signal
substrates
by Holloway
the nickeloxide a
isochromat
on nickel
to compare
values
exposures
NiO
9
the does
is
from
from
the
linear
for
intersects
chemisorption
the
to
the
not discriminate
be-
spectroscopy
selectively
iden-
U1travi ol et Bremsstrahlung Spectroscopy Though ducible
isochromats in repeated
electron
impact.
influenced
the
characterized exposure
4
force of
origin
from Ni203 may
stimulated either purified
peak
this
the
4 eV
peak
It was
not
in the surface
We
to stoichlometrlc
NiO.
and
be
and
lead
to
a
line
on
the
nickel
to NiO.
therefore
believe
isochromat
A
ion
thls
both occupied and empty electronic
oxygen by electron
3da
Madelung 2p s
3d 8
of
the
result
the result
characterized
to discuss
beeing
by
the
the density of
3d~4s
3d~&s
3d~&s
-2 EF=O 2 ENERGY leV band
structure
models
~
6 for
NiO
8 to UPS
solid
approximation
this work 3d~&s/..,........,..,---
3d e*
in
is a further
states in NiO.
Adler 2p s
its
of the high energy
cases
3d 8
the The
is
NiO
Mattheiss 2p 6
Comparison
explanation
in Fig. 17 to be the best
Eastman et al. 2 pS / , ~ 3d s
Flg. 21: data.
was
dissipation.
excess
Experiment
-/~
state
effects
migration,
state
stable
26,600.10 -4 Pa.s
bombardment
power
possible
remove
In both
new
further high energy
electron
thermal
Two possible
It may either
stimulate
that
not
It wlll be used in the following
-6
in the same experiment
solid
clarified.
of Ni203
in the 26,600.10 -4 Pa.s
the
checked
region.
then be considered.
phase.
as
out
state was then stable against
could
or
carried
isochromat
shown
repro-
they were unstable under hlgh energy
studies
transformation
a reduction
NiO
in
isochromat
desorptlon
case
measurements,
potential
bombardment.
in
nature
electrons
the
eV an
states of sample oxidation were absolutely
in Fig. 17. This
(850 eV)
driving
isochromat
Appearance
by
curve
electron
llne
for various
253
and
BIS
254
Volker Dose
A collection of theoretical chromat (b)
results on NiO together with photoemission and iso-
data is given in Fig. 21. Part
(a) shows the Madelung ion energies,
part
the Adler and Feinlelb semiempirical model 44, part (c) an APW calculation by
Mattheis 45 and part the
Fermi
energy
Different spectra
is
symmetry
the experimental
derived
from
characters
were
taken at various
states
in accord
energy
was
EF
with
chosen
energetically Above
(d)
obtained
from
to coincide
from
by
an
Eastman
analysis
An overlap
of
Freeouf 46.
photoelectron
is observed 47.
experiment
The
Fermi
and Fig. 21a to c were
the experimentally
represent NIO
and
below
of oxygen p- and nickel d-
calculations
the UPS
with
the solid dots
The density of states
measurements
selfconslstent
as determined
in Fig. 21d
UPS
photon energies.
new
aligned
data 37'46.
observed
d-band
peak.
isochromat measurements.
They
obviously must be identified with the band like empty 4s states of the Ni 2+ ions predicted
consistently
the energetic lute way.
positions
Remember
of these states
that isochromat
relative
spectroscopy fixes
to the Fermi
level in an abso-
Since Ni 3+ lattice defects which are always present in the experimental-
ly prepared close
by all models.
oxide
layer act as acceptors,
to the valence
band maximum.
The
the Fermi energy of the oxide will be
region with a very low density of states
between the UPS and isochromat data is therefore identical to the full gap width. If
allowance
isochromat valence This
for
band
is
experimental
represents
the
d-maximum
in very
and
good
broadening
s-band the
is made,
threshold. s-band
agreement
The
the
threshold
with
optical
inflection
energetic then
turns
absorption
The optical measurements
the
excited
states
structure of
in
identified as transitions the d 8 configuration measured dence
isochromat
differs
extends
signal. i eV
The
above
emission
empty
in
be
The
suggestive localized
22
is
gives
an
Ni
In their
transitions
into
edge at 3.8 eV is
out
since
identify states
for a broadened
step
that
estimated
function and
emission
this
extrapolation
narrow is a
structure
remainder
energetic
position
this
structure
as
the
type
d8
+
is
resulting d 9.
This
of
in this
the
centered
from
the
of
Its energy depen-
into empty states below the 4s band edge.
the
that
An enlarged view of the
It was concluded
energetically
possibility
to
to
the absorption
is given In Fig. 22.
one expects
from transitions
ruled
is found in the 0-3 eV
is attributed
and
as 3d 8. in Fig. 21b.
than expected.
Fig.
difference E F.
can
therefore into
line
region
energy range
from what
to lower energies
broken
which
into the empty 4s band. The localized excited states of
in this
range near E F results The
J-3 eV
d 8 configuration
are indicated
markedly
to be 4.1 eV.
the NiO one electron density of states.
the
the Ni
the the
were used by Adler and Feinlelb 44 to derive their
semiemplrical model Fig. 21b fr analysis
out
of
between
measurements 48'49
show an absorption edge at 3.8 eV. Further weak structure range.
point
distance
Ni
3d
4s at
about
substrate
different. from
band
It
is
transitions
interpretation
is
U1travi ol et Bremsstrahl ung Spectroscopy supported rently
by SXAPS measurements 37.
emphasizes
contributions
shown
that the density
rance
potential
SXAPS,
from localized
of empty
states
from
is
spectra
beelng
NiO
255
a core level spectroscopy,
empty states~
as derived identical
In fact,
it could be
from a deconvolution
in
shape
to
the
inhe-
of appea-
broken
llne
In
Fig. 22.
NiO ~ .8
•
UV - lsochromat
÷~
g..6 I'--AE2-'I
,
i/
0 0
, 2
1
( E - EFlleV Fig. 22: Enlarged view of the NiO isochromat threshold region. The dashed curve is an extrapolatlon of the 4s band edge. The difference shown as a full line is assumed to result from transitions into localized empty states in NiO.
Following
arguments
interpretation estlmate
of
photoemlsslon distance
of the
given
the
by Baer
structure
coulomb
displayed
correlation
in their
in Fig.
energy
U
in
distance
of
the
NiO.
states
on 4f elements
the
to a straightforward
The
atomic
limit
of
d
Now let AE I be the energetic
peak from the Fermi
localized
work
22 leads
from NIO would be a d8÷ d 7 transition.
of the d photoemlsslon
respective
and Lang 50
energy
observed
in
and similarly isochromat
AE 2 the
spectros-
copy,then
U - AE 1 + dE 2
is
the
net
definition AE I = 1.5 eV U
=
2.5 eV
energy the and in
corresponding
coulomb
to the transition
correlation
AE 2 = 1 eV we splendid
(5.4)
energy.
obtain
agreement
d 8 + d 8 ÷ d 7 + d 9 which
Inserting
as an estimate with
the
value
the
experimental
for the correlation suggested
by
is by numbers energy
H~fner
and
256
Volker Dose
Wertheim 51. 18 eV
and
Arguments
Note the
that
this
value
presented
of by
present
experimental
and NiO
of
Hubbard
model
number
considerably
Adler
and
Feinleib's 44
H~fner
and
Wertheim
value
1 eV would
differs
is
the more
analysis
may
be
reasonable.
lead to expect NiS
from the atomic which
invoked
Similar
yielded
to
show
suggesting
of
13 eV.
that
d-band widths
to be an insulator
the
in NiS
on the basis of the
if the correlation energy was as large as suggested.
exhibits metallic conductivity
limit
NiS, however,
that the couloumb correlation energy in
NiO should also be quite small.
B. Surface states at GaAs([10) The
great
impressive caught The
technical research
similar
larger
faster
by
importance effort.
attention
fundamental one
to
two
of
Though
during gap
the
of
has
silicon has won
the
and
orders
semiconductors
past
magnitude
The
electron as
to
the race up
decade 52.
higher
lead
reason
a
to now, GaAs has is quite
simple.
lead
devices
mobility
compared
to
corresponding
to
silicon.
Electronic
o
-12
-8
-& 0 ENERGY ( E - EvB M )/eV
Fig. 23: Surface density of states at GaAs(ll0) ted surface and two different relaxation models.
surface
states
bonding
on
known
are
special
semiconductor
to exist
the
by Diwan
existence
importance
wafers.
in or near
tial measurements suggesting
of
of
Intrinsic
the fundamental et al. 53 empty
in
(1971)
surface
for an ideally termina-
conjunction
electronic
with
passivation
surface
states
gap of semiconductors. showed states.
band bending
are
Contact
on GaAs
A direct measurement
and well
poten-
surfaces of these
U1traviolet Bremsstrahl ung Spectroscopy surface
states
was
reported
1974
by Eastman
and Freeouf 54 who employed
yield spectroscopy.
In accord with expectation
3d core
empty
level
into
the fundamental
gap.
No
states
also in accord with expectation Ga
dangling
that
the
than
a
bond
is
observed
surface
empty.
since
the bulk conduction
be
Nevertheless
band minimum
e.g.
in
level could be detected,
the As dangling bond is occupied while the and
should
partial
they found transitions from the Ga
from the As 3d core
Lapeyre
structure
state.
below
transition
257
Anderson 55, interpreted
theoretical
one as
year
a
later
surface
calculations
by
pointed
exciton
out
rather
Chelikowsky
and
Cohen 56 in 1975 for an ideally terminated unrelaxed GaAs surface predicted empty surface
states
in
the
gap
thus
supporting
the
conclusion
by
Eastman
and
Freeouf 54 .
12
I
i
|
i
i
i
i
II
i
II
10 GoAs(110) 8
"~Wo = 73eV
y~',l, .... . ..-~..'.~.
E';6-=.,
//: ,"
JQ
o o
-_
o -2
I
I
-4
-2
I
I
0
i
2 Z, ( E - E t a M)/ev
i
i
6
8
Fig. 24: Solid dots represent the measured GaAs isochromat. The full line is the denstiy of states obtained by fitting a linear combination of bulk (dash-dotted) and surface (dashed) density of states,
Earlier in
research
on GaAs
had
been overlooked
1964 Mac Rae and Gobeli 57 had noticed
concluded
that
the
GaAs
some kind of geometric Laar
could
rearrangement
and
Scheer 58
had
GaAs(ll0)
surface.
Their
earlier result 59'60.
surface
reported
this development.
not
be
in LEED
terminated
Already
intensities
and
but must
show
ideally
leaving the surface unit cell unaltered. Van
in
measurements
Moreover
during
irregularities
1967 were
the
absence
repeated
it was demonstrated
in
of
band
1976
bending
and
at
the
confirmed
the
that band bending always reeul-
258
Volker Dose
ted
from
1976
surface
carried
relaxation. the
those
and
layer
layer in
surface
LEED
assumed
affected
first.
eletronic
The
relaxation
the occupied
tion the empty rangement empty
states
and
the
are.
electronic at
in the radiative
ted and surface
states
conduction
band
minimum.
edge
spectrometer
tion
at 24.
72.7 eV was
fitting
The a
contribution (dash-dotted)
calculation resulting
states
mum.
Comparison
mate
of
the
taken
and
line
of
surface
to
the
and
of
spectros-
Since no core levels
The
empirical
is shown
in
emission
by
density
of states.
potential cai63 empirical
Chadi's
(dashed curve).
data.
We
the
LII I absorp-
result
pseudo
from
to the
sensitivity
aluminum
surface
contribution
experimental
rear-
of the density
Isochromat
surface
3 using
for the bond relaxation model fit
surface
into bulk and surface
bulk
Though
on the kind of relaxa-
located with respect
a maximum
from a non-local
the
based on the
respectively 62'63.
measurement 22'64
theoretical
the
binding problem is circumven-
correctly
in section
on
to
by Chelikowsky
with results
this problem.
to achieve
this
consequences
attractive.
data were decomposed
was
tight binding
surface
for
being opposite
between geometric
the excltonic
described
combination
culatlon
the
order
employed
The bulk
is
In
experimental
linear
to approach
process
bond in
makes a measurement
can be energetically
absorption
drastic
modell
particularly
tool
of the GaAs
between 0.08 % and 5 %. The
together
relaxation
structure
GaAs(ll0)
to be the ideal
surface
al. 61
surface
the early calculation
strong dependence
states
are
has
et
of
the displacements
are not that much dependent
This
copy appears
Fig.
bond
states
Lublnsky
existence
of a rotation
relaxation 23 shows
marks. the
of bond lengths
terminated
surface
surface
involved
of
tear
proved
to consist
Figure
and
electronic
and
and
by relaxation,
kind
stucture.
Cohen 56 for an ideally
rotational
scratches studies
by 27 ° and a change
is also
the
as
intensity
It is presently
first
second
imperfections
out
conclude
The solid that
empty
at GaAs(ll0)
ly energetically well above the conduction band mini54 to Eastman's earlier partial yield measurement lead to an esti-
excltonlc
binding
energy
of
1.0 eV
or
1.3 eV
if surface
core
level
shifts are taken into account 65. A recent by
Ludeke
electron the
and
of the valence
Ley 66.
emission
surface
Though
study
the
with
valence
band
splitting,
of
the
valence
to the
structure
leads
valence band
of
XPS
spectra
surface
to the photoemlsslon.
the bond relaxation
is the only one which bottom
comparison
respect
contribution
reconstruction
the
By
band density of surface states has been performed
XPS
is not model
Since
studies
that
various
they were
sensitive
able
angles
to isolate
is shown in Fig.
to the kind
of
25.
of surface
by the isochromat measurements
of the B 3 As derived surface state at
Ludeke
favour
at
Their result
supported
to a splitting band.
normal
taken
the
and bond
Ley's
data
relaxation
do
show
model
such which
a is
Ul travi ol et Bremsstrahl ung Spectroscopy
•
i
i
I
i
•
I
•
•
•
•
I
i
•
G a A s (110)
,
259
I
B1
XPS
U1
~,,
B3
•
i
•
i
-15
I
I
I
S2
I
I
i
•
|
•
i
•
-10 -5 ENERGY (E-Eva M )/eV
•
0
Flg. 25: Surface XPS data for GaAs(ll0)
also compatible with the isochromat data.
C. UV Isochromats from gr_aaphite A
great
graphite
deal of work has using
been carried out
photoemisslon
a
at
Kleser 67
Baer 68 respectively.
and
quantum
in
measurements
energies
wide of
on the valence band
range
1 keV
of
and
Figure 26
quantum
1.5 keV
shows
structure
energles.
have
been
of
Isochromat reported
by
their data together wlth an
ultraviolet isochromat 69. Obviously in this case we flnd a breakdown of the so I
I
!
!
~¢u.=9?eV
"
~/
~'~//
? / °°h"
:3
o o5
I SOCHROMAT ra
(/! C
/~._..~-~/~
= o
. . . .
flWo = tbkeVlyiBaer)
o ...
0
I
0 EF
_ --t------
I
1'~1~, =
I
1 keV
(J.Kieser)
I
5 10 15 excess energy(E-buo)/eV
20
Fig. 26: Graphite isochromat spectra taken at x-ray energies and at 9.7 eV differ considerably because of a symmetry dependent energetic variation of the dipole transition matrix element.
260
Volker Dose
far successfully
employed
interpretation
in terms
of the density of final states.
The UV isochromat is entirely different from those in the x-ray region. Graphite ceeds
is a highly
via
anisotroplc
sp 2 hybridization
Consequently
layered material.
the weak
the band structure
interplane
~ bands
above
and
zone
exhibit
below
leading
between
to
adjacent
a gap
of about
the
Fermi
energy
the
classification
layers
of 1 eV. Photoemlsslon P points
in Flg. in
UPS
dominated
by
s initial
states
dence
begin
to
states
of
respectively.
isochromat
p-states
while
s-states.
This
ments only
near
et
Denley's c-axls
carbon
K
is further which
only
those
obtained
into
final
~
in
graphite are strongly in their
states.
with
presumably
sorption
can,
results
which
Denley's
due
to
apparatus
insufficient
favourable with
spectra
out
quantum
by
with
XPS
from
p
energies
s
results.
the energy
for
s and
connection
The
depen-
p
initial
between
photo-
by
transitions
into
empty
predominantly
transitions
into
empty
due
by x-ray self absorption to dipole
for
is
given
microcrystalllne
comparison. influenced lead
selection
of such measurements
isochromat
absorption
the UV isochromat,
offers more hls
geometry
from
transition
contributions
carbon
dominated
A comparison
for
available
of the isochromats
higher
reversal
supported
ultraviolet
rules
tlme
~
useful
of 0.8 eV at Q and
radiative
equal
born
atomic
interaction of the order
the photoemission
is in accord
of
the
the
are
the
At still
further
data
The
we are then lead to expect that the ultravio-
wlth
tion
agreement
is
both
of the Brlllouin
between 30 eV and 200 eV
of
states,
120 eV.
sections
in mlnd
edge
Pz orbltals.
splitting
a splitting
dependence
= 9.7 eV is o isochromats reflect
x-ray
pro-
find ~ bands
band 70. The results
p initial at
spectroscopy at
to
a semlmetal. a band
quantum energies
trend
cross
conclusion
orientation
causes
gap we
the P point
While at low energies
al. 73
monocrystalllne
ted
This
Bearing
taken
the
as
strong
from
the final p state density.
Denley
ing
a
the photoemission
photolonlzation
electron and isochromat let
graphite
have determined
are observed
dominate.
behaviour of
found
transitions
due
the key to the interpretation
on quantum energy.
and
overall
also
this
at
et al. 71 employing
are
states
of
Within
overlap
zone in the valence
experiment
element
12 eV.
weak and
experiments
provide
26. Bianconl
their
matrix
work
is
bonding
shown in Flg. 27 can be classified in 2 and a bands from sp hybridized states.
which
is rather
of the Brlllouln
photoemlssion
bonding
in plane
of graphite
terms of ~ bands with atomic p character The
While
Their
data,
crystal
graphite
polarization
size.
though
parallel
Kieser's respect. to
the
reflect 72 and
28.
Among
with on
random
poly-
and
polarization selec-
attenuation
however,
in this
Fig.
measurements
do not show any indication
conditions
rules,
by Kieser
in
by additional
to a strong
measure-
of
transitions
in rough
overall
of a w band splitt-
experiment X-radiation graphite
on selfabis detec-
c-axls.
This
Ultraviolet Bremsstrahlung Spectroscopy
261
~
20
20
10 A
-
_~!3E
_'--.. T[
_
_
=
,,, "-.
~ -10
-10
: ~-~-<~ c,A_~ -20
L Q
-20
P H
i
Fig. 27: Cal ulated band structure
I
I
Graphite
of
|
,~
graphite.
°
I
| ssss-
uv-lsochr
° I/
/ ~mat
Absorption /'~,/ ,/" . ~ ~ Spectrum ...~,~ //" / / (Denleye t ~ ~,j Self-Absorption ~j - o ~ Spectrum(Kilser)' 0-
0 I
EF
2 I
/~ I
6 I
8 I
10 12
energy(eV)
Flg. 28: Ultraviolet isochromat compared to graphite Is self absorption spectra.
262
Volker Dose
arrangement rial
was
favours
used
transitions
in his
work,
into
an
final ~ states.
indication
of
the
Since monocrystalline
splitting
observed
in
matethe UV
isochromat is also present in his data.
!
!
|
Graphite
,,
x- ray
, /
'.~
!
,
lsochromat ...~.ll/ '/
.A
7"-.
II
I
" ,
UV -Isochromat
II~'/ 5 10 energy/eV I
0 EF
-"
by Willis et al.
/~~/// I
"--
, \ -.
oo "
/ ~',~~
0j
',
i..,
I
I
15
20
Fig. 29: A properly weighted average of UV and x-ray isochromats exhibits all features predicted by a (smoothed) theoretical density of states calculation.
From
the
and x-ray pied two
foregoing isochromats
electronic sets
discussion
of
provide
states
such
we
conclude
an experimental
in graphite.
data
Figure
reproduces
all
that
a properly
weighted
sum
of UV
estimate to the density of unoccu-
29 shows
structures
that indeed a combination of predicted
by
the
theoretical
density of states calculation 74 in this energy range. From
Fig.
EF~E
27 The
unambiguously final
states
~-band
we
find
that
structure
attributed due
splitting
to is
is
in the UV
to
low
there
the
by
at
one
isochromat
critical
dispersion
reflected
only
points
about
unoccupied in this Q]u Q2g
range with
2-3 eV above
the corresponding
band
in
can a high
the Fermi
double
peak
the
range
therefore
be
density
of
energy.
structure
The
in the
density of states with a 1.3 eV separation. Experimentally we find 1.7 eV. Since adjacent ordered for
the
~
band
layers, graphite
graphite
splitting
occurs
one would expect samples.
grown
on
This
platinum
is
as
a
consequence
of
the
interaction
of
to find the double peak structure only for well indeed
the
substrates.
case. The
Figure carbon
30 was
shows
isochromats
deposited
on
the
Ultraviolet Bremsstrahlung Spectroscopy
i
i
!
i
!
263
!
!
UV - l SOC H ROMAT h ~ o = 9.?eV _.
•
/
o 0
on
~ o
P •
b
Y •
c
0
i
I
i
I
0
2
L,
,
l
i
|
6
8
10
EF
excess energy(E-'h(~o)/eV
i
12
Fig. 30: UV isochromats respond sensitively to the degree of crystallographic perfection of the graphite overlayer. The double peak structure in (c) is due to a ~ band splitting resulting from interlayer interaction in a well ordered sufficiently thick overlayer.
samples
by electron
an isochromat platinum were
substrate
subsequently
polycrystalline the
emission
where Pt(100)
a
well
impact
measurement
emission subject
platinum
spectrum resolved
surface.
for well ordered
decomposition
with peak
graphite 75.
the earlier
isochromat
reflects
was to
no
longer
annealing
substrate
The latter
to support
of adsorbed
from such a carbon layer,
the
sample
for
conclusion
deposited about
of the
to a more an
also
grown
resulting
hour.
For
structure at
a
layers a of
the energy
single
crystal
the LEED pattern characteristic
of the three curves
graphite samples.
point on
such that
carbon
one
pronounced
inflection
sample
that the double
the ~ band splitting
well ordered monocrystalllne
The for
exhibited
Comparison
thick,
1400 K
leads
indication
occurs
Curve a represents
visible.
at
this
benzene.
sufficiently
in Fig.
peak structure from interlayer
30 then leads
of the graphite interaction
in
264
Vol ker Dose 6_~.Measurements on Single Crystals
A. Direct transitions Energy bands in crystalline solids originate from a single particle ground state picture which leads to the concept of Bloch states for a periodic lattice. Though energy bands have been used to calculate electrical, magnetic, and optical properties
of solids,
there has
been little direct
evidence
0 5 Excess energy(E - E F ) / e v
for the existence of
10
Fig. 31: Isochromat spectra for platinum crystals of different orientations clearly demonstrate directional effects.
energy bands,
in particular for the energy versus momentum band dispersion until
the important demonstration of Gobeli et al. 76 of the potential of angular effects in photoemisslon. An enormous activity has been devoted to the field now known as angle as an adult, perspectives directional
resolved photoemlsslon.
Considering angle resolved photoemisslon
the Bremsstrahlung counterpart is still in its baby shoes. However, for
the
effects
future
look
in ultraviolet
quite
promising.
The
Denninger et al. 77
for Bremsstrahlung spectra from the
faces
single
of
platinum
first
demonstration of
£sochromat spectroscopy has been reported by
crystals.
In
their
(I00),
experiment
the
(III), and platinum
(210) single
Ul travi ol et Bremsstrahl ung Spectroscopy crystal was of 0.4 ~ . about pass
sitting
opposite
Electrons
were accelerated
I mA/cm 2. Emitted counter
results
are
incident
within shown
photons
a
solid
in Fig.
electron
to a directly heated
of
31. These
beam,
show
tungsten filament
at a distance
toward the sample with a current density of
were detected
angle
265
with
0.35 sr
spectra,
the previously
normal
to
the
although measured
considerable
dependence
on
described
band
surface.
The
Pt
for a nonparallel
the
crystallographic
Photon detector
Photon detector
I
[olo1 ~w
•+-°°~°-~--Repeltergrid • Fitoment
[lool
v
.
.
.
.
.
Sompte
Fig. 32: Momentum resolved Bremsstrahlung spectroscopy requires an electron beam of well defined energy and direction. A very coarse approach to obtain electrons normally incident on a sample uses a grid behind the filament which, together with the plane sample constitutes a parallel plate capacitor. Negative bias on the grid constricts the angular distribution of the electrons impinging on the sample to angles near normal
orientation strahlung angular
and
emitted for
In
distribution
a negatively negative
therefore
spectra.
biased
potential electrons
the Pt(lll)
llne represents differences tributions
repeller
towards surface
evidence
to gain
of electrons
applied
for
further
incident
grid behind
band
normal shown
to
this
effects
in Brems-
interpretation
15 °
the and
two
the sample
incidence. in Fig.
spectra,
70 ° width
the
on the sample was narrowed by mounting
to the grid with respect
are
structure
support
Sample
(see Fig.
32).
to the cathode data
obtained
33 as the solid
The effect
which
correspond
respectively,
the
band
of
is to bend the with
this setup
llne while
the dashed
the (111) spectrum as given in Fig. 32. In order to interpret
between of
provide
order
to electron structure
angular of
the dis-
platinum 78
266
Vol ker Dose
was
analyzed
initial tion by
and
of
for
direct
final
state
parallel
adding
transitions energies
momentum
reciprocal
at
lattice
with
and
Ei-E f = [~0° = 9.7 eV.
corresponding
the
surface
vectors
to
and
the
E-vectors. allowing
E-values
The
results
Assuming
for
surface
determined
from
were
conservaumklapp
the
band-
Platinum (111) A
I/)
---
2
a 8
<- ? 0 °
A8
<- 3 5 °
>,
Bi
"
c c!
cO Ul I/I W
/ III Ifll I
I
I
I
*
I
0
a
I
a
I
5
10
energy(E EF)/eV
Excess
-
Fig. 33: Isochromat spectra from Pt(lll) with and without negative bias on the repeller grid in Fig. 32. The hatched area represents emission • O O . due to electrons with angles of zncidence between 15 and 70 . Experzmentally observed peaks are indicated by arrows whereas peak positions predicted from a band structure analysis for direct transtions are shown by vertical bars.
structure
experimentally
orientation. vertical predicted above
The
bars
result
at
observable of
the
the
bottom
transitions
should
60 ° • They
of
transitions
search Fig.
occur
for
33. for
The polar
were
the
predicted
(Iii)
surface
interesting angles
for
of
thing the
each
crystal
is
indicated
is
that
incident
all
by the
electrons
should consequently vanish if the polar angles are restricted
to
smaller values as is in fact observed. A similar but more clean cut measurement has been carried out on Ni(lO0) 79. The set
of
data
is
shown
in
Fig.
sample and has been interpreted of
final
various
states. repeller
Emission potentials
34.
The
bottom
curve
is for a polycrystalline
Ni
in section 4 by and large in terms of the density
spectra
from
characterized
the by
Ni
single
crystal
the parameter
were
~ which
taken
for
is the ratio
UI travi ol et Bremsstrahlung Spectroscopy
'
•
• •
•%•°•
°,
~'
°•
267
°
" "'"
• • ° •
°°,•°°
¢=5.6
•
• •-•
• •.e. •"
-
•••,"
a=4.4
==
LL e~ o
==3.3
""
•
>-
"-':
•
• •••e=e•••
•1
a=2.2
•
I
"
UJ
N
•.••'.•,••.,•.
Z
_o
• %
a=0
• "
".....:
I
=E Nil100) w "~e,4.• • • '' • , , ,,, e,,,,.'
I
Ni l s o c h r o m a t s l~u = 9.?eV
0 2 ENERGY ABOVE EF/eV
Fig. 34: circles• repeller sents the
The isochromat from polycrystalline nickel is shown as open Solid dots refer to Ni(100). Parameter ¢ is the ratio of potential to sample potential (see Fig. 30). ¢ = 5.6 reprebest approximation to normal incidence•
of
repeller
to
progressively
voltage
to accelerating
narrowed
angular
calculation
the
effects
shown to confine
turn is for
the ¢=0
the
nickel from
Fermi
transition
bias
to
level in For
voltage•
results
incident
bias
by
the
onset
dictated
to polar angles
has
bulk normal
foil.
is
the electron
well
space
charge
then 15 ° which in
Ni(100)
by
distribution until
of
theoretical
such
a
the above to direct
resolved
interpretation
supported on
angular
diminishes
a single The
Following
is attributed
transitions
incidence,
incidence
of
By
to values smaller than 0.25x2~/a where a II Spectra from the single crystal deviate already
developed. nickel
smaller
corresponds
electrons•
of k
is increased
normal
therefore
the
the difference
direct
¢
of
electrons
constant•
Increasing
distributions
for the polycrystalllne
of accessible
approximation
tions 80.
lattice that
repeller
repeller
to a restriction
the platinum
the number
the
limiting
corresponds
tion of As
was
/.
interpretatransitions. narrows
for ¢=5.6, peak
this
at
peak
1.5 eV above as
bandstructure
transition
should
and
the best
a
direct calcula-
occur
along
268
Vol ker Dose
the
r-A-X
h~
high
symmetry
= 9.7 eV two direct
o are indicated out
by
the
coincides Since
this
line
by down arrows.
experimental
the
in
Brillouin
should
The
data
energetically with emission
of
transitions
transition Fig. 34.
the strong
feature,
however,
is
in
fact
symmetry
forbidden
at
shown
in
Fig.
The
second
emission remains
the X
35.
one
from band
immediately
constant
For
possible and
from band 7 to band 6 is well
tion of a it was concluded that it is quite weak. it
zone
in fact be energetically
born
7 to band
5
at the Fermi
level.
in intensity upon
varia-
It has been shown later on that
point
and
should
remain
weak 81
upon
moving into the Brillouin zone.
16f 12~" >
Ni
8
w I
W
0
-L,L F"
J X
A
Fig. 35: Section of the nickel band structure along the F-A-X high symmetry line. Expected momentum conserving radiative transitions for a quantum energy h~ = 9.7 eV are indicated by arrows. O
The
experimental
setup
Fig.
33 is of course
ruff
and
operating gies
Smlth 81
between
4 eV
Alternatively, to
the
since
variation
and
final
et
14 eV
by
the Ni
and
calls
al. 82
have
used
were decelerated applying
a
The
latter
approach
the
sample
in
of incidence
elevated Bremsstrahlung
background
of
a
data
in
Fig.
34 and
refinement.
commercial
retarding
a
Pt
electron
to the desired incident
grids was employed
energy.
A disadvantage
and
for an obvious
approach
the angle
in their experiment.
faces
primitive
Woodruff
The electrons
electrons of
to obtain
a pair of parallel
desired the
quite
and
at 40 eV.
employed
is
field
the electrons
voltage
to
to decelerate clearly free on
more
region.
the
Woodgun ener-
sample.
the electrons satisfactory A
systematic
the sample was possible
of the acceleration - deceleration mode is an from high energy electrons
striking metal sur-
other than the sample. Data were obtained for the (001) faces of copper and
nickel.
The nickel
results
taken at angular increments of 5 ° starting from normal
U1travi olet Bremsstrahlung Spectroscopy incidence initial the
are
shown
energy
incident
energetic momentum
in Fig.
results
versus
Variation
in a change
electrons.
position
36.
Since
energy
the angle
of the parallel
kll is
of structure
of
conserved
at
in the spectra
dispersion.
For normal
0 Fig. 36: Variation of of electron incidence.
sion maxima stays the
other
Fig. 34. scans Fig.
0 eV,
A
1.5 eV and
4.5 eV
in energy and intensity
two
show
plot
in the
dispersion.
of
its
final
(I00)
and
(II0)
The
the
previously
these
dispersion
two bands of
tion 82'83'84.
this
state
Within
are apparantly
this
may
quantuza
against
from
energy
While
of
the
relative emls-
angle
feature
analogous
parallel
in the
The solid dots
band
within
7
to
band
like a
state
to
momentum
is shown
final
with
the
is
free electron
estimated the
demonstration
at 0 eV
of the angle of incidence,
1.5 eV
respectively.
approximation
of
in the
r
directions
nearly be
change
6
at
transition
the momentum
any
we observe
respectively.
energy
of
at a given
~No"
upon variation
azimuthal
identified
transition
R=
9.7 eV
feature
37 as solid dots and open circles
course Since
at
constant
of
component
is a direct
2 ~ (E-EF)/eV
isochromats
incidence
the surface
incidence
•
of
269
two
that
for
in
polar
top panel
of
represent
of
6
in
nickel.
(see Fig.
35) the
band
energy
approximaas
a
func-
270
Volker Dose
tion of kll is given by 82
[(EG )24V I
2 2 kll Ef(kll) = ~
+
(6.1)
4E G
E G = ~2G2/2m
is
the
through dashed the
(002)
which curve
reciprocal the
two
in the
lattice
plane
waves
top panel
two band approximation
vector
and V G the pseudopotential
associated
of Fig.
while
(6.2)
37
with
bands
represents
the solid curves
7 and
6
interact.
the dispersion
are from a more
coefficient The
predicted
elaborate
by
band
o
(a)
o
o o
o
o
>4 A
l
LLI ' 2 UJ
1001Fig.
37:
Theory
and
k,,ao/~
experiment
for
-
Ni(lO0)
[110] for
kll
along
LlOOJ
and
[ll0J. Panel a displays the experimental energy dispersion as full dots and open circles. The dashed curve is derived from a two band approximation while the solid curves result from a more elaborate band structure calculation. In panel b experimental peak intensities are compared with calculated dipole matrix elements.
structure position angular Fig.
37.
variation
calculation 82. but
also
the
dependence. Assuming of
proportional
the to
The escape
Inspection intensity estimated and
electrons a
variation
of Fig. of
the
intensities
transport angle in
36 shows
direct
of the
are
functions incidence,
dipole
that not only
transition given
in the
(2.6)
feature
in
the
to stay
intensity
transition
matrix
the energetic exhibits
lower
panel
constant
change element.
an of
with
should
be
This
is
Ul travi ol et Bremsstrahl ung Spectroscopy displayed good. ous
as the solid
curves
The significance
since
obviously
in Fig.
37. The agreement
of this agreement,
an estimate
however,
with experiment
should
of the intensities
271 is quite
not be taken too seri-
from the experimental
data in
Fig. 36 is not easy.
The origin of the second emission feature starting at 4.5 eV
for normal
is not quite clear at present.
incidence
possibility More
of a surface
recently
seems the
Smith 85
initial
state
structure
energy
range.
likely
the possibility
since
momentum.
in
an energy
Gl~b186
measurements
Residual
et al. 82 suggest
the
or emission from a residual surface contamination.
suggested
to be not very
this
state
Woodruff
surface
energy
loss would be expected
moreover
similar
of an electron
to
contamination
did
not
those
in
observe Fig.
any
34
with associated
loss.
This
to randomize indication
over
an
of
enlarged
unoccupied
adsorbate
induced states remains at present the most likely explanation.
B. Electronic It
surface states
is now well
successfully versus
established
employed
parallel
wave
faces of single exhibit band
states Pt.
Larsson
and
using
riers
in
states
calculate
Cu,
to
and
however, bands been
and
there
and
correct
the
located
corresponding
same
They and
the
just
(III)
position
widths
of
the
by Johnson Fig.
38.
Brillouln
zone at polar
Two peaks are clearly
of
these
empty
surface
occupied
parameters
transitions
This will make it difficult from
these
separation
Experimental
and
visible
were
taken
increments
of about
bar-
surface
they
then
spectra
in
the
k u. Their
regarding
the negligible
relative
For
this
Pd(lll),
the bulk
surface
d-
state
has
from their experiment
are
r-K
part
importance
intensity variation
crystals.
azimuth
of
from normal
the
surface
incidence.
Peak A at the Fermi level is again
the unoccupied
into the Pd d-band are permitted.
increasing
For
to separate
2 eV between of
of 2.5 ° starting
in all spectra.
into
two
observation
Smith 91. Emission
angle
transitions
level.
emission
Spectra
bute with
d-
surface
of Ni, Pd, and
the
the
barrier
above
unoccupied
parametrize
surface
energy
and Au have been shown to
the energetic
data.
their
surface states coincide with the high density of d-band the Fermi
state.
in
direct
and
E(klt). Especially Ag,
energetically
positions
Using
an energetic
surface
with
Cu,
arguments
calculated
Bremsstrahlung
displayed
associated
band
photoemlssion
Au.
above
exists
the
relations
states
can be
states on Ni, Pd, and Pt all of which turn out to be empty.
bulk
reported
rigid
obtain
Ag,
immediately
surface
surface
photoemisslon
to exist on the (111) faces of single crystals
Ni and Pt their predicted states
dispersion
Nilsson 90 have
surface
ultraviolet
electronic
states 87'88'89
experimental
order
on
resolved
from the noble metals
simple
are expected
states
vector
surface
Using
angle
investigate
crystals
occupied
complex.
to
that
of the d-band. Direct transitions
remains,
however,
of peak A. Peak B which
For kiL=O no do contriquite
small
is found at
272
Volker Dose
1.7 eV
above
the
Fermi
level
for
normal
incidence
and
which
disperses
rapidly
away from the Fermi level for off normal incidence is suggested to be the surface state
predicted
Johnson
and
chlorine. es
by
theory.
Smith
Exposure
the spectrum
include
Arguments the
in
favour
sensitivity
of the clean Pd(lll)
for a polar angle
of
a
this
surface
structure
state to
given
by
adsorption
of
surface to 3.10 -4 Pa.s of chlorine chang-
of 7.5 ° into
0
of
the dashed
2 & (E-EF}/eV
line.
Peak A is only
6
Fig._38: Experimental isochromats for various angles of incidence along the r-K azimuth on a Pd(lll) surface. Peak A is the Pd d-band emission. The dispersing feature B is a surface state which can be quenched completely by adsorption of 3 L of chlorine.
slightly
attenuated
while
peak
neccessary
but by no means
see
later
on,
the
surface
free
that
the surface
that
states
transitions.
therefore of
layers
electon
direct
gas
and The
is entirely
sufficient
adsorption may
B
volume more
behaviour
leading
seriously
quenched.
alter
convincing
the
projected
thus
argument
bulk
band
rests
on a precision
structure.
a performance state.
to electronic
coupling
states
the dispersion of this structure
the latter argument
of a surface
in general
Bloch
Such
given
between the
by Johnson
lles entirely
As we shall
rearrangement
conditions
influencing
and
the band
of
vacuum
strength Smith
of is
in an absolute gap
It should be mentioned, of
is a
structure
however,
calculation
U1travi ol et Bremsstrahl ung Spectroscopy of
better
than
half
an
structure calculation
C. Ferromagnetic Itinerant and
minority
was
ferromagnetism
and
a
this quantity
indispensable
to
relies
The energetic is
states
and
a
on a splitting difference
quantity
theory of itinerant
to determine
unoccupied
non-relatlvistlc
band
in the case of Pd this appears to be quite optimistic.
spin bands.
splitting
principles
For
crystals
electron
exchange
eV.
273
of
between
considerable
ferromagnetism.
the
polarization
10 i
i
i
I
and
20 e
|
!
i
i
w
i
into majority
the two is called
interest
Considerable
from ARUPS 92. In complicated
exploit
of d-bands
for
the
the
first
effort has been spent
cases such as cobalt 93 it tunability
of
synchrotron
E/eV
, |
I 15
10
ILl
>0 n," W Z ILl
I
It . _
.
.
.
',I
_
: = _ ~ _ _ _ _ I__ - ~-z-: ~ . ~ _ _ _ ~ ~
.
-
As -
As
I
A
A
A
-
Fig. 39: Section of the cobalt band structure. Down arrows indicate Bremsstrahlung and up arrows photoelectron emission used to determine the d-band splitting.
radiation
in
order
to
determine
this
~Eex = (0.85 ± 0.20) eV for the upper range slon
from is
its
0.8
to 4.3 eV.
combination
quantity. d-band
A particularly
with
ordinary
Experiment
in Co while
nice application
photoemisslon
data
resulted
in
theoretical
in order
value
predictions
of inverse
the energetic separation between a pair of exchange split d-bands.
a
photoemls-
to determine
274
Volker Dose
While PES data can be used to locate the occupied majority Fermi
level,
respect
to
Himpsel
and
far,
which
IPE
E F.
be
employed
for
locating
the
empty
band relative minority
to the
band
with
feasibility of the experiment indicated has been shown 94 Fauster in a measurement on cobalt. Unlike the data discussed
The
were
energy I~0° as the
may
constant
obtained
a
function
initial
by recording
the emission
of electron
energy
mode.
!
|
energy,
This
l
their
!
.92eV
|
so
quantum
conducted
of
in
employing
a
!
=
.93eV
c
was
consequence
r L
at a fixed
experiment
is a natural
|
,
intensity
by
CO
::;0 I'rl
_,
-i
z
o
/
U.I
--J 0 0
,
/
U.I
m
-1-
r,
/'//I
C
'
.,J'/
Z 0
_ ~ _ _
212
|
I
I
I
I
I
0
-I
I
1
(E - E F ) / e V Fig. 40: Experimental photoemission (left) and inverse photoemission spectra form Co(0001) showing the ferromagnetic exchange splitting between spin up and unoccupied spin down states. Spectra where recorded in the constant initial energy mode. The dashed curves refer to a photon energy of 16 eV for transition into states at the Fermi level while the solid curve is for Ii eV. Note the band dispersion.
grating monochromator detection sions
from
normally inside
combined
with a position
of several wavelengths. ~
resolved
incident
on
the sample.
pied 3d band the electrons, the photon
Bremsstrahlung Co(O001)
sensitive
The technique data
occupy
a
is
free
device
allowing parallel
for determining
E(~) band disper-
illustrated electron
in Fig.
llke
energy
39.
Electrons
band
(AI,A 2)
From there they undergo a radiative transition into the unoccu-
(A6,A7).
Subtracting
the energy
spectrum
50 meV
replacing
states
approximates
of
the photon energy ~0 from the initial energy of
the 3d band
is at the Fermi
the cobalt a
step
is obtained.
level.
It was
determined
sample by polycrystalline function
at
E F.
The high energy
Assuming
cutoff
of
with an accuracy
of
gold whose density of empty momentum
conservation
the
Ul travi ol et Bremsstrahl ung Spectroscopy wave
vector
normal
of
shown in Fig. from
the
incidence
the
earlier
3d
we
final
have
39. The momentum
dispersion ARUPS 93
of
data.
the
By
energy,
part of the E(kl) Data
points
unoccupied for
for
dispersion
the
two
The
band
to
electron
llke
the electron
states
different
in good
the
the
initial
line
AIA 2 band
energy
state.
F-A-A
For
in ~ space
and
which
was
known
consequently
of the minority
from
the photon
spin AsA 6 band could be
in Fig. 39 are from ARUPS and Bremsstrahenergies
splitting
agreement
of
to
to the surface k± is then calculated
e.g.
by the peak shift
exchange
that
corresponds
band dispersion
indicated
states.
A5A 6
free
for occupied
spectroscopy
d-band
is equal
perpendicular
tuning
mapped. lung
state
k u = 0 which
275
read
with
different
momenta
is 0.15 eV for occupied from
Fig. 40
(0.85 ± 0.25) eV
is
k i.
The
as well as
(0.93 ± 0.I0) eV
obtained
from
photo-
frequently
argued
emission in the region where both bands are occupied. These that
data
band
call
energies
relaxation 95. mination bands
for
of
the final
on the other
exchange state
hand
is a hole
adds
agree quite well with each other,
ferromagnet
opposite
d-bands
of
to
the
of appropriate
tally
Unguris
Fig. 41.
Spin
rents were
again
splitting
exchange
sample
spin
al. 96
Ni
electrons
effects
crystal magnetized crystal
and normal
recorded
with
dependent asymmetry
assembly
as obtained
that relaxation
of PES
by either
is well within
in the present case.
Radiative
transitions
therefore
be
should This
of
has
their
obtained
been
into
the
possible
for
demonstrated
experimental from
only
setup
a GaAsP
spin
experimen-
is
source.
shown Beam
in cur-
of ±2.6 ° . The sample
along the (IT1) direction by a c-shaped electro-
could
to the direction the
both
should therefore
sample
were
for
spectroscopy
magnetization.
sketch
state
the empty 3d states are completely
orientation.
A
since
from a combination
splittings
we conclude
only
final
in the deter-
band and would be expected
of the order of 0.5 ~A with an angular divergence
The
surface
et
polarized
was a Ni(ll0) magnet.
the
such as nickel,
a magnetized
electrons by
that
from
Bremsstrahlung
resolution and therefore altogether unimportant
In a strong
empty
fact
band.
data
sign. Relaxation
the exchange
way
polarized
the
suffer
photoemission
shift of opposite
is
approximately
to the conduction
IPE
It
may
cancel
in the valence
and
experimental
From
should
from
an electron
of
conclusion.
photoemission
shift
splitting
in the determination data.
from
a relaxation
to cause a relaxation add up
interesting
determined
Such the
another
previously
be
rotated
about
of magnetization. described
band
an
axis
in
Bremsstrahlung
pass
photon
the
crystal
emission was
counter.
The
spin
in photon emission A is
1 A =
PoCOSe
n+-n+ •
n++n+
N+-N+ -
N++N+
(6.3)
276 P
o and
Volker Dose is the polarization
n÷,
n+ the
of the
registered
factor P cos= accounts o
incident
counts
electron
beam,
corresponding
to
e the angle of incidence,
either
for the fact that at non-normal
spin
incidence
direction.
The
only a component
PHOTON
e" Beam Ni(110} Fig. 41: Schematic of an apparatus for angle Bremsstrahlung isochromat spectroscopy.
of the incident represent tively
polarization
photon
parallel
fluxes and
is along the magnetization
that would
be expected
antiparallel
check
of any asymmetry
sample
magnetization.
to
the
of non magnetic Experimental
character
data
in
and
the is
strongly
Fermi
level
therefore negative
in
100 %
the N+ spectrum
minority
in the energy
spin
axis. N+ and N+ therefore
spin
of
result
convenient of the
quantities
N
is that the peak seen just absent
The
the d-band
A
by reversal
the corrected
is entirely
of
direction.
was possible
terms
polarized.
region
spin polarized
for a 100 % polarized beam respec-
majority
and N+ are shown in Fig. 42. The most prominent above
resolved
in the N÷ spectrum
asymmetry peak and
A
is
remains
of
course
at a 5 %
level for energies up to 4 eV above E F. Though as stated earlier, ment the
just discussed art
energy, tion
achieved of
the
presents
conventional angle,
of about
and
spin
ultraviolet
resolution
spectroscopy.
experiment monochromator,
the spinpolarized
experi-
the first case where IPE has caught up with state of
photoemisslon.
1 eV and a detection
in isochromat PES
IPE is still in its infancy,
namely
The have
first
just been completed
signal
experiments 97 at an energy
of 50 C/s comparable
Recalling
synchrotron
and Mott
photoemission
the very demanding
radiation,
spin detector
grazing
as compared
nical requirements
for the IPE experiment
zed Bremsstrahlung
excitation for research on ferromagnetism.
to
adds to the attractivity
with
resolu-
to what has been instrumentation incidence the modest
vacuum tech-
of spin polari-
Ultraviolet Bremsstrahlung Spectroscopy
w
g
I
I
I
|
!
z|
|X •
| El l;llil[
z ||If
Z
)'--4
IE
CO One
I
!
0
|
!
!
'
(E-EFI/eV
-31iiiii
"t m
Ni(1101
"-
UJ
!
il|||||
Z
LJJ
|
tttt~tt t]!
I--O3 j--
277
Ni(110)
<-.6 '
2
I
ii
I
0
I
'
(E-EFI/eV
i
2
Fig. 42: Experimental isochromats for normally incident electrons with spin orientation parallel and antlparallel to the majority spin direction (left panel) and asymmetry A in photon production (right panel).
D. Chemlsorptio_n It has been shown already quite early that UV isochromats respond sensitively to gas
adsorption
on metals.
The application of
IPE
to ehemisorptlon problems
is
therefore possible and appears quite promising since relaxation effects are expected to be smaller than in ordinary PES. This relies very much on the fact, that an atomic system gains much less energy upon formation of a negatlv ion than is necessary to positively ionize it. The obvious relevance of chemlsorptlon lies in its on
relation to problems in heterogenous catalysis and corrosion. d-band
metals
is
antlbondlng adsorbate
characterized
in general
by
induced electronic states
the
Chemlsorptlon
formation of bonding and
lying below and above the sub-
strate d-band complex respectively 95'98. Since except for the noble metals the dbands of the transition metals are only partially filled the antlbondlng states appear above
the Fermi
level and are therefore empty.
They have thus far only
been accessible by electron energy loss spectroscopy which does not lend itself to an unambiguous interpretation. IPE is the ideally suited tool for the direct observation of
adsorbate
out were on oxygen Ni(lll) I00,I01
induced unoccupied
adsorption
on
Ni(100) 9Q
states. and
Experiments
so far carried
oxygen and carbon monoxide on
278
Volker Dose
Normal oxygen with
incidence
covered the
energy
surfaces
experimental
in
the
empty d-states ly
Bremsstrahlung
nickel
possible
clean
setup
shown
Ni(100)
in
spectrum
from evanescent
direct
isochromat
spectra
are shown in Fig. Fig. is
32.
transition
from
band
7
clean
The
peak
just
due
band
UV-ISOC HROMAT S
and
results were obtained
to
5
above
transitions
. Contributions to
Ni(100)
These
largely
initial states
from
43.
to
Fermi
into
final
from an energetical-
this
".
the
structure
can
be
(~ ) I
i
I
I
I
I
I
I
incidence
norma[
Ni (100) .,. 02 ~u=, = 9 7 e V .e
•
•
•"
(3
•
I
7
.,..,
t !!
I
I
!
I
l
i
I
i
i
!
I
i"
C: =,
iil
t
i
N i O formation
..D
•
.. =
•e %
0" o"
>.
= .oee'i
o ~9o~"." z
ill
z z
." .
l
"l
O c(2x2)
0
°••°''•'''eJe•
12 ) ..-
_o
I direct transition
oh 03 uJ
•
,'e
•
(a) (b)
: clean
=~
..•"
L--~*
,
-2
i
*
0
2
ENERGY
( E-EF)/eV
from
Ni(100)
Fig. 43: Set of isochromats higher doses of oxygen.
neglected they has
because
become been
tion
they
symmetry
previously
occur
near
forbidden. identified
; /~
I
the X-point
The hatched
of
area
near
i
exposed
the
bulk
under
as a contribution
from band 7 to band 6 in bulk nickel
m
to
progressively
Brillouin
zone where
the peak at about
from a direct
radiative
the X point along
1.7 eV transi-
the r-A-X high
symmmetry line (see Fig. 35). Oxygen adsorption trum.
Exposure
simultaneous
on the surface
to 50.10 -4
attenuation
of
Pa.s
02
causes
prominent
leads
to enhanced
the direct
transition
changes
of the emission spec-
emission
at 1.7 eV. At
just above
E F and
100.10 -4 Pa.s 02
Ultraviolet Bremsstrahlung Spectroscopy emission direct
at
EF
has
transition
again
decreased
feature
has
The
kinetics
of
marked
curve
"a"
oxygen
in
This
adsorption
"a"
Fig.
It exhibits
44.
of
Pa.s
been
43. a
The
With
which
6
followed
nickel
value
and
still higher
recording
corresponding
resonance
like variation |
clean
completely.
has
in Fig.
50.10 -4
resonance
initial
the
exposur-
for NiO emerges.
by arrow
exposure
pattern.
oxygen
the
disappeared
es, a spectrum characteristic
energy
to
279
also
like
emission
produced
the
result
the
emission
at
is displayed
as
enhancement
sharpest
at an
c[2x2J
LEED
of the emission of radiation as a function
|
|
i
|
|
|
a
21 0
/
\
>,.
(bl
~, ..
• 4' C w_
w
o 1.0
J
e. - -
I<,l
".'L.:" •.
I
10 0.1 0
'
"0 &
8'0
'
120 '
'
Exposure
160 '
'
'
(Langmuir)
Fig. 44: Kinetics of oxygen adsorption as monitored by Bermsstrahlung emission. Curves (a), (b) correspond to energies marked "(a), (b)" in Fig. 43.
of oxygen exposure of the tics
is a unique
isochromat
of
oxygen
behaviour.
An
including
adsorption example
shown as curve
property
the direct monitored
ohtalned
"b" in Fig.
at
of the peak at E F, For the other regions transition
by
inverse
an energy
44. Measurements
region around photoemisslon
marked
by arrow
like those
in Fig.
to establish the common intensity scale for the isochromats The
behaviour
of
the
direct
in Fig. 43 upon oxygen exposure ed
photoemission
empty
data
for
transition
Cu(100) I02.
in the case of Ni are occupied
Consequently
the
"extra"
contribution
can be understood
radiative
Part
of
in Fig.
43
is
44 have been used
to the clean
spectrum
(I)
to well establish-
electronic
in Cu. This applies emission
"b"
a monotonic
in Fig. 43.
by reference the
1.7 eV the kineshows
states
in particular
in the Ni isochromat
which
are
to band 6.
at 1.7 eV shows
280 up
Volker Dose as
an
emission chosen.
An
emission mats.
"extra"
photoelectron
photoelectron oxygen
from
c(2x2 1 overlayer
feature
in
the
The conclusion
to a rather
strong
Ni(100)
thereby
and
emission
spectra
Cu
above
Cu(100) leads
electronic
d-band
complex
quantum
energy
spectra
as
quenching
it does
for is
deteriorates
in the surface the coupling
normal
suitably
of the direct
in the Ni isochro-
of the oxygen c[2x2] adsorbate
rearrangement
strongly
the the
to substantial
photoelectron
is that formation
if
layer leads
regions of Cu(100) and
conditions
between
vacuum
free electron and itinerant bulk electronic states of the Cu and Ni samples. The emission of
intensity
at and just above E F behaves o v e r that
cI2x2 j overlayer. source
for
spectra
the
upon
of
Surface
occurance
geometric
umklapp or
near E F were
transitions
with
cal
lattice
to be entirely
vector.
up to polar angles
have of
The
been
of the surface
be responsible,
observed
with
emission
features
layer.
in photoelectron the observed
strong contributions
where ~ denotes
enhancement
This behaviour
as a mechanism
of an oxygen
In case
on
from direct
a surface
the
of the width of the electron
of 70 degrees.
A 40 % enhancement
the advent
shown I03 to be a possible
emission
due to surface umklapp,
independent
improbable
occurs
processes
disappearance
÷ = ~ would kjl
out
quite differently.
sample
rearrangement
enhancement
es highly
the clean
other
recipro-
hand
angular
turned
distribution
in turn renders umklapp process-
for the emission
increase upon oxygen adsorp-
tion. The
only
remaining
ordered
c(2x2)
states.
Current
bonding
electronic
consequence have
is
two
in
d-band
pair is
the intensity
peak
has
prior
course
exposures effect.
the
the
also,
observed adsorbate
formation
emission
induced
on Ni(100)
the filled
portion
within
These
the The
observed
prediction.
Further
and
the
induced
electronic
energetically for
as a
states
d-character
support
well
predict empty anti-
of the Ni d-band
adsorbate
overlayer
for
unoccupied
of O c(2x2]
The been
radiative
structureless shown event.
states would
to
be
to of
exposures NiO
becomes
part
of the
dominated
An adsorbate
within
narrow this
should the
structure
view
may
be
isochromat
by
above
electron
induced
hole
enhancement
of
the pair the
lead us to expect enhanced electron hole
as is in fact observed.
restricted
extra
increase at arrow "b" in Fig. 43 (see also Fig. 44) even
regime.
previously to
on
above
planes.
latter
of empty electronic
formation of
rely
the
interaction.
substrate the
chemisorption
formation density
O(2p)
p-character
with
to
treatments
states I04'I05
Ni(3d)
to three
from
the
must
theoretical
of
accord
drawn in
overlayer
predominantly
first
explanation
of
The validity
less
the
than
of this
~50. i0 -4
prevailing
reason
interpretation
Pa.s. for
For the
higher
observed
28l
Ultraviolet Bremsstrahlung Spectroscopy 7. Concluding Remark
Ultraviolet Bremsstrahlung spectroscopy has already been applied to quite a variety of problems.
An even larger
improvements
experimental
based
on
in
grating
field
of applications
technique.
monochromators
with
The
high
next
is expected with further
generation
acceptance
and
of
spectrometers
multl-detectlon
has
already been set up, The possibility to employ variable quantum energies h~0° will doubtlessly make the technique more popular and eventually lead to a state predicted by Duke and Park 5 already in 1972: "Information on the unoccupied density of states can be obtained by the Bremsstrahlung isochromat technique. This straightforward
approach,
which
consist of energy analyzing
radiative capture of low energy electrons, scientists. My
personal
is that
it will
finally
emitted by the
thus far has been slighted by surface
But, as the fashions of science change, hope
the photons
it will also have its day."
find its place among the other well
established spectroscopies for surface analysis.
Acknowledgments
The author wishes article.
Both,
to acknowledge his coworkers
for their contributions
the scientific and technical assistance
to this
of M. Gl6bl has been an
enormous help for the completion of this paper. Mrs. M. Lucas and D. Straub have done an expert job in preparing the figures.
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