Ultraviolet Bremsstrahlung spectroscopy

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 P...

2MB Sizes 19 Downloads 113 Views

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



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.

References I. 2. 3. 4. 5. 6. 7. 8. 9. I0. II. 12. 13. 14. 15. 16.

W. Duane and F.L. Hunt, P_hys. Rev.,6, 166 (1915) P. Ohlin, Ark. Mat. Astro. Fys.,A29, 3 (1942) B.R. Nijboer, physlca (Utrecht),l_~2, 461 (1946) K. Ulmer, Phys. Rev. Lettt,3, 502 (1959) C.B. Duke and R.L. Park, Physics Today, p. 23 (August 1972) D.R. Bates and A. Dalgarno, in Atomic and Molecular Processes, D.R. Bates, ed., Academic Press, New York (1962), p. 608 J.B. Pendry, phys. Rev. Lett.,45, 1356 (1980) J.B. Pendry, J? PhyS. C Solid State Phys.,14, 1381 (1981) C.N. Berglund and W.E. Spicer, Phys. Rev.,136, AI030 (1964) M. Cardona and L. Ley,in Photoemission in Solids I, M. Cardona and L. Ley, eds., Springer Verlag, Berlin-Heidelberg-New York (1978), p. 86 W.E. Spicer, Phys. Rev.,154, 385 (1967) T. Grandke, L. Ley, and M. Cardona, Phys. Rev. Lett.,38, 1033 (1977) H. Claus and K. Ulmer, Z. Physik,173, 462 (1963) H. Merz and K. Ulmer, Z. Physik,197, 409 (1966) J.K. Lang and Y. Baer, Rev. Scl Instrum.,5_O0, 221 (1979) G. Chauvet and R. Baptist, J. Electron Spectrosc. and Relat. Phenom.,24, 255

(1981)

282 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60.

Volker Dose Th. Fauster and F.J. Himpsel, Rev. Sci. Instrum., in course of publication M. Conrad, V. Dose, Th. Fauster, and H. Scheldt, ApplL_Ph~s.,20, 37 (1979) G. B~hm and K° Ulmer, phys. C~lloq. c4,c4, 241 (1971) J. Eggs and K° Ulmer, Z._Physik,213, 293 (1968) S. Doniach and M. Sunji6, J. Phys. C Solid State Physl,3, 285 (1970) V. Dose, H.J. GoSmann, and D. Straub, Surface Sci.,llT, 387 (1982) V. Dose, A_pplt eh_~,14, 117 (1977) G. Denninger, V. Dose, and H. Scheldt, Appl. Phys.,18, 375 (1979) V.H. Dibeler, J.A. Walker, K.E. Mc Culloh, and H.M. Rosenstock, Int. J. Mass Spectrom. Ion Phys.,~, 209 (1971) H. Neuert, private communication J.D. Morrison, H. Hurzeler, M.G. Inghram, and H.E. Stanton, J. Chem. Phys.,33, 821 (1960) V. Dose, Rev. Sci. Instrum.,39, 1055 (1968) V. Dose, V. Meyer, and M. Salzmann, J. Phys. B Atom. Molec. Phys.,3, 1357 (1969) V. Dose and D. Straub, to be published V. Dose and G. Reusing, App !. Phys.,23, 131 (1980) C. Bolzlau, V. Dose, and H. Scheidt, ~_ys. star. sol.(b),93, 197 (1979) J. Petroff and C.R. Viswanathan, Phys t Rev. B,4, 799 (1971) V. Dose, Th. Fauster, and H. Scheidt, J. Phys. F Metal Phys.,ll, 1801 (1981) J.F. Janak, A.R. Williams, and V.L. Moruzzi, Phys. Rev. B,II, 1522 (1975) E.O. Kane, Phys. Rev.,159, 624 (1967) H. Scheidt, M. Gl~bl, and V. Dose, Surface Sci.,ll2, 97 (1981) N.V. Smith and D.P. Woodruff, Phys. Rev. B,25, 3400 (1982) S. H~fner, in Photoemission in Solids II, L. Ley and M. Cardona, eds., Springer Verlag, Berlin-Heidelberg-New York (1979), p. 173 G. Ertl and K. Wandelt, Z. Naturforsch. a,2_99, 768 (1974) K. R~II, H. Zauner, and H. Hoffmann, Vakuum Tech.,4, 102 (1978) P. H. Holloway and J.B, Hudson, Surface Sci.,43, 141 (1974) K. Desinger, Diploma rbeit, W~rzburg (1982) D. Adler and J. Felnleib, Phys. Rev. B,2, 3112 (1970) L.F. Matthelss, Phys. Rev. B,5, 290 (1972) D.E. Eastman and J.L. Freeouf, Phys. Rev. Lett.,3_4, 395 (1975) A.B. Kunz and G.T. Surratt, Solid State Commun.,25, 9 (1978) L. Messick, W.L. Walker, and R. Glosser, Phys. Rev. B,6, 3941 (1972) R.J. Powell and W.E. Splcer, Phys. Rev. B,2, 2182 (1970) J.K. Lang and Y. Baer, Phys~ Rev. Lett~,42, 74 (1978) S. H~fner and G.K. Wertheim, Phys. Rev. B,7, 5086 (1973) H.J. GoBmann, Physik in unserer Zeit,ll, 191 (1980) J.H. Diwan, L.K. Galbraith, and T.E. Fischer, Surface Sci.,26, 587 (1971) D.E. Eastman and J.L. Freeouf, Phys. Rev. Lett.,33, 1601 (1974) G.J. Lapeyre and J. Anderson, Phys. Rev. Lett.,35, 117 (1975) J.R. Chelikowsky and M.L. Cohen, Phys. Rev. B,13, 826 (1976) A.U. Mc Rae and G.W. Gobeli, J_z_.App!. PhZs,35 , 1629 (1964) J. van Laar and J.J. Seheer, Surface Sel.,8, 342 (1967) J. van Laar and A. Huljser, J. Vac. Sci. Technol.,l_3, 769 (1976) J. van Laar, A. Huijser, and T.L. van Rooy, J. Vac. Sci. Technol.,14, 894

(1977) 61. 62. 63. 64. 65. 66.

A.R. Lubinsky, C.B. Duke, B.W. Lee, and P. Mark, Phys. Rev. Lett.,36, (1976) D.J. Chadi, J. Vac. Sci. Technol.,15, 631 (1978) D.J.Chadl, Phys. Rev. B,18, 1800 (1978) V. Dose, H.J. GoBmann, and D. Straub, Phys. Rev. Lett.,47, 608 (1981) D.E. Eastman, T.C. Chlang, P. Heimann, and F.J° Himpsel, Phys. Lett.,45, 656 (1980) R. Ludeke and L. Ley, J. Vac. Sci. Technol.,16, 1300 (1976)

1058

Rev.

Ultraviolet Bremsstrahlung Spectroscopy 67. 68. 69 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91 92. 93. 94. 95.

96. 97. 98. 99. I00. i01. 102. 103. 104. 105.

283

J. Kieser, in Band Structure Spectroscop_[ of Metals and Alloy_s_, P.J. Fabian and L.M. Watson, eds., Academic Press, New York (1973), p. 557 Y. Baer, J. Electron S2ectrosc. Relat. Phenom.,24, 95 (1981) V. Dose, G. Reusing, and H. Scheldt, Phys. Rev. B,26, 984 (1982) B. Feuerbacher and B. Fitton, P_~_Zs. Rev. Lett.,26, 840 (1971) A. Bianconi, S.B.M. HagstrDm, and R.Z. Bachrach, Phys. Rev. B,I_6, 5543 (1978) J. Kieser, Z. Phzsl k B,26, 1 (1977) D. Denley, P. Perfettl, R.S. Williams, D.A. Shirley, and J. St~hr, Phys. Rev. B,21, 2267 (1980) R.F. Willis, B. Fitton, and G.S. Painter, Phys. Rev. B,9, 1926 (1974) J.W. May, Surface Sci.,17, 267 (1969) G.W. Gobell, F.G. Allen, and E.O. Kane, Phys. Rev. Lett.,12, 94 (1964) G. Dennlnger, V. Dose, and H.P. Bonzel, Phys. Rev. Lett.,48, 279 (1982) N.E. Chrlstensen, private communication G. Denninger, V. Dose, M. Gl~bl, and H. Scheldt, Solid State Commun.,4_22, 583 (1982) F. Szmulowicz and D.M. Pease, Phys. Rev. B,17, 3341 (1978) D.P. Woodruff and N.V. Smith, Phys. Rev. Lett.,48, 283 (1982) D.P. Woodruff N.V. Smith, P.D. Johnson and W.A. Royer, Phys. Rev. B,26, 2943 (1982) G.D. Mahan, Phys. Rev. B,2, 4334 (1970) T. Gustafsson, P.O. Nilsson, and L. Walld~n, Phys. Lett. A,37, 121 (1971) N.V. Smith, private communication M. Gl~bl, private communication P.O. Gartland and B. Slagsvold, Phys. Rev. B,12, 4047 (1975) P.O. Nilsson, J. Kanski, and C.G. Larsson, Solid State Commun.,36 , III (1980) W. Eberhardt, F. Greuter, and E.W. Plummer, Phys. Rev. Lett.,46, 1085 (1981) C.G. Larsson and P.O. Nilsson, Phys. Lett. A,85, 393 (1981) P.D. Johnson and N.V. Smith, Phys. Rev. Lett.,49, 290 (1982) A.M. Turner and J.L. Ersklne, Phys. Rev. B,25, 1983 (1982) F.J. Himpsel and D.E Eastman, P_hys. Rev. B,21, 3207 (1980) F.J. Himpsel and Th. Fauster, Phys. Rev. B,26, 2679 (1982) B. Feuerbacher and B. Fitton, in Electron Spectroscopy for Surface Analysis, H. Ibach, ed., Springer Verlag, Berlin-Heidelberg-New York (1977), p. 151 J. Ungurls, A. Seiler, R.J. Celotta, T.D. Pierce, P.D. Johnson, and N.V. Smith, Phys_t.R e v , Lett.,49, 1047 (1982) E. Kisker, R. Clauberg, and W. Gudat, Rev. Scl. Instrum., in course of publication F.J. Arlinghaus, J.G. Gay, and J.R. Smith, in Theory of Chemlsorptlon, J.R. Smith, ed., Springer Verlag, Berlin-Heldelberg-New York (1980), p. 71 H. Scheidt, M. Gl~bl, and V. Dose, Surface Scl. Lett.,in course of publication Th. Fauster and F.J. Himpsel, submitted for publication V.Dose, M. Gl~bl, and H. Scheidt, J. Vac. Sci. Technol., in course of publication D.T. Ling, J.N. Miller, D.L. Welssman, P. Pianetta, P.M. Stefan, I. Lindau, and W.E. Spicer, Surface Sci.,95, 89 (1980) J.F. van der Veen, F.J. Himpsel, and D.E. Eastman, Solid State Commun.,34, 33 (1980) A. Liebsch, Phys. Rev. B,17,1653 (1978) C.S. Wang and A.J. Freeman, Phys. Rev. B,19, 4930 (1979)