Aspects of inverse photoemission

Journal of Electron Spectroscopy and Related Phenomena, 51 (1990) 55-68 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

55

ASPECTS OF INVERSE PHOTOEMISSION

N. V. SMITH

AT&T Bell Laboratories, Murray Hill, New Jersey 07974, USA

SUMMARY

Ultraviolet inverse photoemission is now established as a viable and valuable spectroscopy for the study of unoccupied electron states in solids and at surfaces. This paper outlines the experimental strategies of the technique, and illustrates its prowess with a selection of highlights: (a) band structure determination; (b) image states, surface states and the surface potential barrier, (c) antibonding states of adsorbates. Connection is made with two-photonphotoemission work and the spectroscopic capabilities of the scanning tunneling microscope.

1. INTRODUCTION This paper is an approximate transcript of a talk intended to convey the capabilities and

accomplishments of ultraviolet inverse photoemission spectroscopy (IPES). A large part of the content of the talk is taken from a recent review article by the author and references therein.’ This material is supplemented with more recent work. In the remainder of this Introduction we describe what IPES is, how it is done, and the current state of the art. The article proceeds with four main topics (Sets. 2-5) which attempt to encapsulate what has heen established and to present also some examples of significant new work which has appeared since Ref. 1 went to press. The emphasis throughout will be on ultraviolet rather than x-ray IPES. 1.1 Phenomenology

IPES consists of bombarding a sample with electrons of known energy E, and detecting emitted photons of energy ho.

Crudely speaking, IPES maps out the unoccupied density of

states, complementary to the way PES replicates the occupied density of states. ‘Ibe unoccupied energy range between the Fermi level EF and vacuum level Ey is of special interest since it is inaccessible in ordinary PES. The complementarity

of IPES and PES is illustrated in Fig. 1 for the case of normal

emission (PES) or normal incidence (IPES) from Cu(OOl).2 The PES data show a feature which moves towards EF with decreasing photon energy (Aw = 15.7, 13.7 and 11.7 ev). Eventually it crosses En and is picked up in the IPES spectrum for Itw = 9.7 eV. This is exactly what one would expect from direct (vertical) transitions along the FAX direction also depicted in Fig. 1.

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56

‘

-4

1

-2

ENERGY

K,

I

0 ABOVE

.

I

‘

2

1

EF (eV)

NORMAL

WAVE

VECTOR

Fig. 1. Comparison between ARPES and KRIPES data for eleetmn p~pagation normal to the Cu(OO1) surface The m&&y d@ersing feature is readily interpreted in terms of direct kconserving transitions with the bulk band stmcmre along the FAX direction in the Brillouin zone. (From Ref. 2.)

1.2 Signal Levels The development of IPES, both in the x-ray and ultraviolet regions, has lagged behind “ordinary”

or “forward”

photoemission spectroscopy @‘ES) by 10 to 20 years. There is a

very good explanation for this dme lag based on the availability of phase space for photon creation as opposed to electron creation. The ratio of cross sections may be expressed3 rs

&p~~/cIpEs)

PI

= 0d+J2,

where 1, and h are the wavelengths of the photoelectron and photon respectively. In the vacuum ultraviolet region (Aw - 10 eV), we have h, - 4 A and &, - 1200 A implying r - 10q5. In the x-ray region (Ao - 1000 eV), we have r - 1C3. Thus the signal level in IPES is 3-to-5 orders of magnitude lower than in PES. 1.3 ExperimentalStrategies

The inherently low signal levels in IPES cannot be overcome simply by raising the incident electron curmnt

to some indefinitely

high value.

Space charge prohibitions

eventually

dominate. The design of electron guns especially adapted for IPES is of paramount concern.4*5 The experimental strategy in ultraviolet lPES is to maximiz detection without compromising energy- and angle-resolution. fronts of attack. The first is the “isochromat”

the solid angle of photon

We can distinguish two broad

mode, using Geiger-Miiller tubes6 solid-state

57 band-pass detectors,7 and refracting monochromators.s

The basic idea of the isochromat

instruments is to hold the photon energy ho constant and to scan the spectrum of unoccupied states by varying E the energy of the incoming electrons. The second front of attack is the grating-spectrograph approach. The basic idea is to put the incident electron beam into a small spot on the sample, which then serves as the virtual entrance aperture for a large-aperture (f/4) grating.

Signal counting rates may be further

enhanced by parallel detection over Aw by use of microchannel-plate-detectors

in the focal

plane. A number of such advanced instruments are now in routine operation.“” 2. BULK BAND MAPPING JPES in its angle-resolved or k-resolved mode (KRIPES) has the same band-mapping capabilities of angle-resolved PES. The basic algorithm for data reduction expresses the component kll of the electron wave vector parallel to the surface as kll = (2m@)(E-Ev)“*

PI

sin 0,

where fJ is the angle of incidence of the incoming electrons. 2.1 One-Electron Band Structures and Self-Energies Figure 2 shows a comparison between band theory and JPES experiments’2*‘3 for the E(kll) dispersion on Cu(OO1). Similar results have been obtained on other materials. How significant is such agreement, when observed. The band theory predictions shown in Fig. 2 incorporate an X

W

X

U

I-

Fig. 2. Band calculations and JPES data for bulk direct transitions in the two principal azimuths rG and Tx on Cu(OO1). Upper panel shows the Fermi surface and isochromat curves at Ao = 9.7 eV for transitions into band 6. Lower panel shows the corresponding Et(kt,) projections. Computations and filled data circles are from Woodruff et al. (Ref. 12); open data circles are from Jacob et al. (Ref. 13).

58 8% stretch attributed to self-energy corrections to the one-electron band theory.r4 IPBS studies of other metals are not always in such good agreement with bulk band structure calculations. The time is ripe for a detailed study of such discrepancies using a combination of angleresolved IPES and angle-resolved PES. 2.2 High Tc Superconductors There has been considerable

activity using PES and IPES to ascertain the electronic

structure of the new oxide superconductors. The unique feature of these materials is the fact that EF falls within the oxygen 2p-band manifold making 0 an electronically active constituent.

Spectroscopic studies of the valence bands have been directed towards a very basic

question.

Is the appropriate starting point for the ground-state of these systems a bandlike (Permi liquid) or a localized (Hubbard or resonating valence bond) picture? Work was impeded initially by uncertainties associated with sample surface preparation by

scraping or ion ~rnb~~ent

and annealing in vacuum. The oxygen stoichometry tends to be

unstable in such circumstances.

These problems have been removed however with the

discovery I5 of 83K superconductor Bi2SraCaCuaOs.

This material is stable with respect to oxygen stoichometry and can be produced in the form of large single crystals which are readily cleavable. A number of studies have been performed on Bi@~CaCu#s

using IPES.*G20 Figure 3

shows angle-resolved IPES data for this material along the TX azimuth. The general consensus

E-E, kV)

Pig. 3. (a) Sequence of IPBS data for various angles of incidence taken on the high T, superconductor BiaSraCaCuaOs. (b) Emission near Er on a magnified scale. (Prom Ref. 19.)

59

of this and other work is that the unoccupied states extended all the way down to EF, and that (within the limits of experimental resolution) the Fermi edge is well defined. The experimental resolution in IPES (AE 2 0.3 eV) is not yet good enough to search for the opening up of a superconducting band gap, as it is in PES. The features A and B in Fig. 3 correlate with features in the total density of states generated by theoretical band calculations,21822 but do not show the anticipated dispersion with angle. The intriguing feature of the data of Fig. 3 is the intensity increase at EF near 8 = 40’. This constitutes a hint of a band crossing EF somewhere near the %lX position, and is complementary to a similar hint found in angle-resolved PESD 3. IMAGE STATES AND THE SURFACE BARRIER One of the distinctive accomplishments of IPES has been the spectroscopic detection of a Rydberg series of surface states converging on the vacuum level.% These are called imagepotential-induced

surface states (or simply image states) because they arise through the long-

range image-like asymptotic form for the surface barrier. The systematics relating image states to ordinary surface states are now well established,25 and recent attention has turned to using the large IPES data base to put quantitative constraints on acceptable shapes for the surface barrier. The image states arc also detectable using two-photon photoemission (2 PPE). 3.1 Phase Accumulation Model The multiple-reflection approach to surface state formation26 offers a transparent way of viewing the relationship between image states an “ordinary” surface state, and displaying the trends from gap-to-gap, surface-to-surface and metal-to-metal.

The basic concept is that surface

states are the standing-wave resonances in the effective cavity between the

crystal

and the

surface barrier. The quantization condition for surface state existence is $c + b = 27tn,

Ul

n = 0, 1, 2,...

where QC and $n are the phase changes on electron reflection at the crystal and surface barrier respectively.

The n = 0 solutions are the “ordinary”

or “Shockley”

surface states. For a

surface barrier with an image-potential asymptotic form, $B diverges as (Ev -E)-“*

thereby

generating the Rydberg series of image states.*’ At the boundaries of the surface Brillouin zone (SBZ) the quantization condition is modified to ~$6+ k = 2zn, where we distinguish between odd (-) and even (+) states. Figure 4 shows a comparison between the predictions of the phase accumulation model*s and IPES results13 for Cu( 110). 3.2 Surface Barrier Determination At large distances from a surface the potential must vary as (z-z&

where ~0 is called the

image plane. There is a longstanding and lively debate in the literature concerning the position of zc relative to the outermost atomic plane. The classic jellium calculations of Lang and Kohn29 place ~0 1.2 to 1.6 au. beyond the jellium edge ZJ. For a real metal the jellium edge is

60

0 1.5

I.0

0

0.5

PARALLEL

0.5

WAVE VECTOR

1.0 (A-’

1.5

)

Ei& 4. E(kB) cation of the surface states of clean Cu(ll0) along the two principal ~rnu~s TY and i?%. Largeged circles are the inverse photoemission data of Ref. 13. Photoemission data beIow h$ and Y are also indicated. Open circles labelled l3t and B2 are a~b~~ble to bulk direct transitions. Full curves are the dispersion relations generated by the simple phase ~cumuladon model with an image plane distance se = 1.7 a.u. SQ and S& denote odd and even Shockley states. Sl and St are the first members of an image-state Rydberg series converging on the escape threshold ET indicated by the dashed curves. The toned area represents the projection of the bulk band structure. (From Ref. 28).

conventionally

taken at half an interlayer distance beyond the outermost atomic layer. Some

obvious questions are therefore as follows. What is the value of (z+ - ZJ) for real materials? Is it constant from crystal face to crystal face? What are the trends from metal to metal? The author and colla~mto~ have recently attempted to answer these qu~stions.~ The procedure was to &at assemble the data base for surface states associated with the s,p-gaps of the fee d-band metals. Then, using the phase-adulation

model and a plausible ansatz for the

saturated image barrier, 31 the energies of surface states were generated as a function of ~0. The data base is most extensive and most systematic for the low index faces of Cu. The results are shown in Fig. 5 where hatched areas show the range of ZQ vahaes demanded by experiment. The positions of ZJ are indicated, and it is seen that within the scatter of the data points, the hypothesis of a constant

(zg-zJ)

ValWe

can

be

is that, for a given metal, ~0 is constant irrespective of q. met&s is inconclusive ~~wh~

in between.

on this point, though

sustained. The

CO!Ip?ting

hypothesis

The large scale analysis of the fee

thexz are indications that the truth may lie

61

6 4

6 4 2 0 -2 6 4 2 0 -2

0

1

2

3

4

IMAGE F’LANE DISTANCE (a.~.)

Fig. 5. Dependence of surface-state energies with image-plane distance ~0 for low index Cu surfaces. Full curves labelled S, or Sz are. the surface state energies calculated using the phase accumulation model. Panels on the left pertain to the projections of the bulk L-gap at Cu(l1 l)r, Cu(OO1)~ and Cu(1 lo)?; the edges of the gap Ly and &t are indicated, Panels on the right pertain to the projections of the bulk X-gap at Cu(OOl)F and Cu(llO)X, the lower edge of the gap &, is indicated. Filled circles show the measured surface state energies. Hatched areas indicate the range of qt values consistent with the data. The position ZJ of the ‘ ‘jellium edge*‘, placed at half an atomic layer spacing beyond tire outermost atomic layer is indicated in each case by the heavy vertical arrows. (From Ref. 30).

3.3 Two-Photon Photoemission The image states are accessible not only with IPES but also with two-photon photoemission (2 PPE). The basic idea is to populate the image states with one photon, and then with a second photon to promote an image-state electron into the vacuum where it can be detected using the standard methods of angle-resolved PES. The superior resolution in both energy and angle

permits

definitive

determinations

of image-state

binding

energies

and

effective

masses.s2*33 A very recent development is time-resolved 2 PPE which, by use of pump-probe methodology, is able to measure tire actual lifetimes of image states.34*35

62 4. ADSORBATES IPES offers a valuable way to examine the unoccupied orbitals of atoms and molecules absorbed on surfaces - and to compare the results with expectations based on PES studies and theoretical calculations. 4.1 Fingerprinting A beautiful example of what in PES has become known as “fingerprinting”

is shown for

IPES in Fig. 6. These are IPES data for the sequence benzene, naphthalene, anthracene and tetracene absorbed on Ag(lll),

showing the unoccupied states of x* symmetry.

One is

immediately impressed by the richness of information - the lifting of degeneracies as one proceeds to molecules

of low symmetry, and the good correspondence

.

I

.

I.

I

.I

with theoretical

.,

nw=9.5ev k,,=O

EF=O

2

4

6

6

lo

Energy (eV)

Fig. 6. Isochromat inverse photoemission spectra of epitaxial ordered overlayers of benzene, naphthalene, anthracene, and tetracene on Ag(ll1) taken at normal electron incidence. For comparison the spectrum of a clean Ag(l11) surface is shown. A spectrum of tetracene on Cu(100) is plotted on the top. (From Ref. 36).

63

Schemes for Adsorbed CO

4.2 Hybridization

IPES has contributed

significantly

to our understanding

adsorption of CO on d-band metal surfaces. hybridization

scheme

illustrated

orbitals of d, symmetry of the unoccupied prediction

of the perennial

The conventional

in Fig. 7(a).

There

is covalent

overlap

between

and the 50 lone pair orbital, and this is accompanied

2x’ level of CO with substrate

orbitals of 4

of the substrate

by hybridization

symmetry.

of this scheme is that the stronger the molecule-substrate

the unoccupied

problem

view of bonding is the Blyholder

The qualitative

bond, the higher in energy

2x* level.

co I

METAL 1

2%

CO

METAL

2nen

.-_---

r

--7-----\’

dlr 2=bb

(b)

(a)

4u

Fig. 7. Hybridization schemes for CO adsorbed on a transition metal surface. (a) The basic Blyholder scheme: involving bonding between the molecular 50 orbital and metal orbitals of do-symmetry, with some “back donation” from metal dx-symmetry states into the unoccupied molecular 2x orbital. (b) An “extended Blyholder hybridization scheme” emphasizing additional interaction between the molecular 27~orbital and metal orbitals of px symmetry.

The

actual

expectations. experiments,

results

of

IPES

temperature,

distinguish

main

three

in contradiction

are summarized

with

strong

chemisorption

and physisorption

these

qualitative

in numerous

IPES

in Fig. 8 which plots the 21c* energy The plot of Fig. 8 serves to

that is to say bond strength.

groupings:

(Cu substrates);

am

to the CO 2x* state has been observed

and the compilations37-39

against desorption chemisorption

experiments

A feature attributable

(Pd

(Ag substrate).

and

Ni

substrates);

weak

The trend is for the 2x’ level

to move to lower energies with increasing bond strength. The hydridization orbitals,

as illustrated

the resonance

scheme can be salvaged by invoking in Fig. 7(b).

picture of molecular

This adjustment adsorption.41

strong participation

is supported

of substrate pn

by cluster calculations40

If the substrate(p&dsorbate(2~)

and

interaction

64

Energy of the 277’ Level of CO

-ill4

’

Versus

Substrate

,.?

00)

-0

100

300

200 Desorption

400

Temperature

500

600

(K )

Fig. 8. Correlation between the energy (relative to Ev) of the 27t orbital with adsorption bond strength (as given by the measured desorption temperature) for CO on various metal substrates. (From Ref. 39.)

dominates, the trend of Fig. 8 would then be expected.

It should be stressed that the true

situation is much more complex and that final state effects need to be incorporated.1*41 Spinpolarized IPES has been extended to the study of adsorption on a magnetic substrate. The result of two independent experiments42*43 is that the 2x* level of CO adsorbed on Ni shows no detectable exchange splitting. This is in contrast with oxygen adsorbed on Ni, where a distinct exchange splitting due to hydridization

with substrate d orbitals is observed.43 The spin-

polarized IPES work therefore lends further credence to the weakness of the CO (2x)subskate

hybridization.

5. H’ES AND THE STM The scanning-tunneling

microscope (STM) is a new tool used primarily for studying surface

topography on an atomic scale. It also has a spectroscopic dimension which is achieved by setting the microscope tip at some atomic site and then sweeping the current-voltage (I-V) characteristic.

At positive sample bias, electrons tunnel from states just below Ep of the tip

into empty states of the sample surface. In negative bias electrons tunnel from occupied states into the tip. Thus by monitoring changes in the I-V characteristic, we may deduce information on both the occupied and unoccupied density of states of the sample. It is assumed here that the material of the tip does not itself have a highly structured density of states.

65

A

’

I

I

I.

I

I

I

0.0

0.5

1.0

1.5

pq(q -2.0

-1.5

-1.0

4.5

Energy

2.0

relative to EF (evl

Fig. 9. Surface state energies on the (7 x7) reconstructed Si(lll) surface as revealed by I-V spectroscopy in the tunneling microscope and by PES and IPES. The upper panel (A) shows I-V data coded by symbol according to the positions within the 7 x 7 unit cell (see inset) where the spectra were taken. The lower panel shows the filled and empty surface states observed in angle-resolved PES and IPES respectively. (From Ref. 44.)

Examples of STM spectra& are shown in Fig. 9(a) for the well studied case of the 7 x 7 reconstructed surface of Si(ll1). The coded symbols indicate the three inequivalent kinds of atom in the surface unit cell: adatoms (squares) and restatoms (circles and crosses). Each atom has a dangling bond, but it is seen that their spectra are significantly different. For comparison, the correspond IPES and PES data are shown in Fig. 9(b); the latter are of course, spatially integrated. A recent twist introduced by Reihl and Gimxewski and coworkers45*46is to examine photon emission from the vicinity of the microscope tip as a function of bias voltage. This has been done at the conventional

IPES energies4’ and at photon energies in the visible nrgion.46

Figure 10 shows a schematic of the experimental arrangement and examples of data on Si(ll1) 7 x 7. The features At and Bt in the STM-stimulated photon emission spectrum correspond roughly to features AZ and Ba seen in conventional IPES. The feature Ct on the other hand has no counterpart in the IPES data, and is attributed to an image state similar to those discussed in Sec. 3 but Stark shifted47 into the continuum by the strong local electric field.

66

STM

~71

i =const .ECTRON - GUN VOLTAGE IVolt 10

I

15

I 20

*._.. *:. . .:: .*.-..*

B2 *.: . +.-* .._.. -*..*..... s :Si A,

(111) 7x7 hv = 9.5 eV

:.-

I’

..*-

I

I

I

10 TIP-SAMPLE

,,,I

I,,,

15 VOLTAGE (Volt)

20

Fig. 10. The upper part of the figures shows the schematic set up for STM-stimulated photonemission measurements. The lower panels compares an STM stimulated spectrum (a) with a conventional IPES spectrum (b) on Si( 111) 7 x 7 at tie = 9.5 eV. (From Ref. 45).

6.

OMISSIONS The talk on which this paper is based was billed as “Overview of Inverse Photoemission”

Conscious of its many omissions, the author prefers the more modest title “Aspects of Inverse Photoemission”.

The paper is more properly regarded as a partial update of Ref. 1. One large omission is the area of semiconductor band structures, surface states, adsorbates, interfaces, Schottky barrier formation and so on. A large body of IPES work has now been published on these topics, notably by the groups of Reihl, Himpsel and Weaver. May we look forward to a review of this area4s sometime soon?

67

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