ELLIPSOMETRY APPLIED TO THE STUDY OF SEMICONDUCTOR SURFACES

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ELLIPSOMETRY APPLIED TO THE STUDY OF

SEMICONDUCTOR SURFACES

H. Lüth

To cite this version:

JOURNAL DE PHYSIQUE _{Colloque C5, suppliment au} no 11, Tome 38, Novembre 1977, page C5-115

ELLIPSOMETRY APPLIED TO THE STUDY

OF SEMICONDUCTOR SURFACES

(*)

2. Physikalisches Institut der Rheinisch-Westfalischen Technischen Hochschule Aachen, 5100 Aachen, F. R. Germany

RBsum6.

-

L'ellipsomktrie est une mkthode optique pour ktudier des effets de surface par rkfle- xion. Cet article aborde en bref les questions et les problhmes poses dans une spectroscopie de rkfle- xion des surfaces de semi-conducteurs. La structure kectronique d'une surface de semi-conducteur est caractkrisk par des Btats superficiels klectroniques, des Btats dQivks d'un adsorbat et par des propriktks de couches de charge d'espace. Pour demonter la valeur de la mkthode d'ellipsometrie dans la recherche des effets superficiels &lectroniques, quelques rksultats sont discutks pour les sur- faces (1 11) de Si et (1 10) de GaAs prkparkes en ultravide (UHV). Des mesures ?i une knergie cons-

tante de photons permettent I'ktude de la cinktique d'adsorption. L'ellipsomktrie spectroscopique est appliquk pour I'observation des transitions entre diffBrents Btats klectroniques de surface. Les constantes optiques de la couche de charge d'espace sont changkes par I'adsorption A cause de I'effet Franz-Keldysh. Ces changements donnent des informations au sujet de la courbure des bandes. Abstract. - Ellipsometry is an optical reflection technique which is highly sensitive to surface effects. The present paper briefly lines out the questions and problems arising in optical reflectance measurements on semiconductor surfaces. The electronic structure of a semiconductor surface is characterized by intrinsic electronic surface states, by states due to adsorbate coverages and by space charge layers. The value of ellipsometry in studiing these effects is demonstrated by means of exemplary results obtained on ultrahigh vacuum (UHV) prepared Si (111) and GaAs (110) sur- faces. Measurements at a fixed wavelength allow the investigation of adsorption kinetics. Ellipso- metric spectroscopy is applied to the study of optical transitions between electronic surface states. Furthermore, changes of the optical constants in the space charge layer due to gas adsorption can be used to monitor band bending changes.

1. Introduction.

-

Optical spectroscopy, one of the most powerful tools for solid state investigations in the bulk, has severe limitations for surface studies [I] because of its inherently low surface sensitivity as compared with e. g. electron scattering techniques. In contrast to those methods, however, optical techniques can be applied to interface problems also in cases where vacuum conditions are not given like in catalysis investigations under high pressure or in problems concerning the solid/liquid interface. The problem of low surface sensitivity has been overcome in ellipso- metry, an optical reflection technique in which the change of the state of polarization is determined rather than the change of the light intensity upon reflection.

The change of the state of polarization can be expressed in terms of the ratio of the two complex reflection coefficients R" and

'

R

for light polarized parallel and perpendicular to the plane of incidence,

R

being the ratio of reflected and incident electric field strength. The complex quantity

p = R1l/.RL = tan Y x exp(iA) ₍₁₎ (*) Dedicated to Pr. Dr. G . Heiland on the occasion of his 60th birthday. '

defines the two ellipsometric angles A and Y which are measured in ellipsometry. In applications to surface physics, changes 6A =

K -

A and 6Y =

'Y

-

Y

(2

and F a r e initial values, e. g. for the clean surface) due to a surface treatment give information about changes in the optical properties within a spatial region close to the surface. If performed like usually in the visible spectral range, therefore, ellipsometry probes the electronic structure of the surface.

On semiconductor surfaces the electronic structure depends on several important factors :

i) Clean ultrahigh vacuum (UHV) prepared sur- faces exhibit intrinsic electronic surface states whose wavefunctions are localized near the surface within a spatial region of 5-10

h;

below the surface [2].

ii) Charge in these states can give rise to band bending within the space charge layer (spatial extension 100-1 000 A) below the surface. This is related to an accumulation or depletion of free carriers with respect to the bulk density.

iii) Adsorbed gases or defects on a surface can chan- ge the density of intrinsic surface states and, therefore, also the band bending within the space charge layer.

These different effects can be investigated by ellip- sometry. The emphasis of the present paper is on the particular type of information which can be derived from ellipsometric measurements on semiconductor surfaces rather than on a description of sophisticated experimental equipment. The examples discussed in this paper are restricted to the semiconductor/vacuum interface but the type of measurement and analysis can be extended to all kinds of semiconductor inter- faces. Similar effects as they have been studied on UHV prepared surfaces are expected for the solid/ liquid interface eventhough problems might be more involved because of the optical effect of the liquid phase adjacent to the solid.

2. Experimental equipment. - Since ellipsometry has become a rather convenient technique in surface physics a number of different experimental set-ups has been developed to measure the ellipsometric angles A and Y .

The conventional experimental arrangement consists of two rotatable polarizers (in the incident and the reflected light beam, respectively) and a fixed quarter- wave plate being used to compensate the change of polarization of a parallel light beam due to reflection (null ellipsometry) [3]. A and Y are calculated from component settings at extinction [3]. For spectroscopy or high-speed measurements automatical ellipsometers are convenient. The extinction settings can be done and read out by means of electronically controlled Faraday rotators in a self-compensating ellipsometer

[4]. Polarization modulators [5] or rotating analyzers [6] are used in other types of automatical ellipsometers . in which the parameter information is contained in the phase and relative amplitude of the ac-component of the transmitted light intensity. A more extensive

discussion of the optical equipment can be found e. g. in ref. 171.

If ellipsometry is used in combination with an UHV chamber containing the reflecting sample, care must be taken in avoiding polarization effects due to windows. Since these effects mostly cannot be ruled out completely absolute values for A and Y generally exhi- bit a systematic error which, however, dces not influence the quantities 6 A and 6Y which are interesting in sur- face studies. Similar problems of course arise in ellip- sometry performed on the liquid/solid interface.

3. Analysis of the data.

-

On an atomic scale, the fundamental reflectance process involves elastic scat- tering and absorption of photons from the array of different atoms that constitute the surface. Hereby, the electronic structure near the surface varies drasti- cally within the outer 1 to 10

A

due to surface states or adsorbed gas molecules. Furthermore within a depth of 100 to 1 000

A,

space charge layers have to be taken into account on semiconductor surfaces. Gas adsorption changes optical transitions due to surface states as well as bulk optical constants within the

space charge layer (Fig. 1). The latter effect arises from the dependence of the optical constants on the electric space charge field (Franz-Keldysh-effect [S, 91). However, this effect induces measurable changes of the optical constants only near critical points of the band structure [9].

i = O VACUUM VACUUM

CLEAN SURFACE SURFACE WITH ADSORBATE

FIG. 1. -Continuum multilayer model for the analysis of ellipsometric s ~ e c t r a of semiconductor surfaces. Surface state

-

transitions within a surface layer (8,) are removed after covering

the clean surface by an adsorbate layer (TAns). Within the space

charge layer the bulk dielectric constant r b ( ~ , ~ ) is modified by the

electric space charge field E s c which is changed to

EL,

due to

adsorption. In contrast to the dimensions shown, the thickness of the space charge layer is actually higher than that of the

surface layer by about two orders of magnitude. The index

i = 0, 1, 2, etc. indicates the particular Iayers.

In spite of this strongly inhomogeneous situation near the surface, most ellipsometric studies intended for surface investigation have been analysed in terms of quasi-macroscopic multilayer models in which adsorbates down to submonolayer coverage, surface states and space charge layers are described by an effective thickness di and complex effective optical

-

N

-

constants zi = E;

-

i~~ (or ni = ni

-

iq), the index i indicating the particular layer. Several approaches have been made to justify this procedure [lo, 11, 121. Even though absolute values for

,

;

G,

d and line shape details should not be taken too serious, it appears that e. g. conclusions concerning spectral structures and transition energies can be obtained quite accura- tely.

The parameters of a multilayer model as schemati- cally shown in figure 1 are derived via Fresnel's for- mulae [3] from the measured quantities A and Y : eq. (1) relates A and Y with the complex reflection coefficients

R"

and

.

R

'

For a multilayer structure

R"

and R' are effective quantities which must be calcu- lated from reflection coefficients r&, r$ describing transmission and reflection at the ilj interface :

-

n.coscpi

-

iicoscpj r!j = - J ..,

njcos cpi

+

ni cos cpj ni cos cpj

-

nj cos cpi

r$ =

-

..,

ELLIPSOMETRY APPLIED TO THE STUDY O F SEMICONDUCTOR SURFACES C5-117

gi

and

4

are the complex refraction coefficients for the i-th and j-th layer, respectively. q , and qj are the angles the light beam encloses with the interface normal in the i-th and the j-th layer, respectively. Via eqs. (2a, b)

R~'

and

R

are connected with parameters of the layers. For a one-layer model (vacuum (0), layer (I), subs- trate (2)) follows :

= rBi'

+

r l i exp D 1

+

r!?. ry$ exp D with

D = - 4 n i G dl I-l.cos cp,

.

₍₄₎ For mul.tilayer models more involved expressions are derived instead of eqs. (3) and (4).

Since only two measured angles A and Y are avai- lable for the determination of at least three layer para- meters (one-layer model : dl, n,, rc,) reasonable assumptions usually are made for dl and sometimes involved computational work is necessary to fit theore- tical A and Y values to the observed data.

4. Results and discussion. - 4.1 ELECTRONIC SUR-

FACE STATES ON Si(l11) SURFACES.

-

In order to get

information about electronic surface states ellipso- metric spectroscopy has to be performed in which A and Y are measured as a function of photon energy ho. Figure 2 a shows spectra 6 A (ha) and 6Y (ha)

I _. 0 D

St ( I l l )

o .CLEAVED IN UHV

I I I I

FIG. 2. - a) Ellipsometric changes 6 A and 61,u due to oxygen adsorption versus photon energy ; Si (1 11) surfaces prepared in

UHV. b) Spectrum of the imaginary part of the dielectric cons-

tant 1mZs of an assumed surface siate layer (thickness 5 A) as

compared with that of bulk Si : Im Tb 1191 (After Meyer [14]).

(clean minus oxygen covered) as measured by Meyer [4] on Si (111) surfaces. Below the direct bulk transi- tions near 3.4 eV, both 6 A =

-

A and 6Y =

-

Y show considerable structure. For their analysis Meyer used the quasi-macroscopic layer model which has been discussed in section 3 (Fig. 1). 6Y values of the observed magnitude and sign can only be explained within such a model by a decrease of the optical absorption in a surface layer [14, 151 due to oxygen

adsorption. Meyer, therefore, gives the interpretation that a surface state layer

(is,

d,) is present on the clean surface and is removed by the adsorbed oxygen (reasonable for dangling bonds). After formation of the first chemisorbed oxygen monolayer [16, 171 the optical constants of the bulk are valid up to the inter- face with the adsorbate layer, the latter having a real dielectric constant E,,, (Fig. 1). E,,, has been calcu-

lated using a Lorentz-Lorentz relation 117, 181. The contribution of the oxygen layer itself to the ellipso- metric changes (Fig. 2a, dot-dashed line) has been estimated using furthermore results of calibration experiments [IS]. With an assumed thickness of 5

A

(simple scale factor) for the surface state layer Meyer [14] calculated Im s; spectra for the surface state layer

which are compared with bulk data [19] in figure 2b. For both the clean cleaved surface with (2 x 1) and the annealed surface with (7 x 7) superstructure [20] surface state excitations slightly above 2 eV are seen. Since no significant electroreflectance signals are found on Si in this spectral region [21], i. e. since there is no critical point of the bulk band structure near 2 eV, a change of the optical constants within the space charge layer due to Franz-Keldysh effect upon gas adsorption can be ruled out in the analysis. In the

*

scheme of figure 1 one expects &(E,,) % E,,(E~) for

the considered spectral range.

The surface state transitions near 2 eV have also been found in electron energy loss spectroscopy (ELS) by Rowe and Ibach [22] and with high resolution by Froitzheim et al. [23]. The maxima of the loss peaks occur at 2.25 eV on the (2 x 1) structure and broade- ned and shifted to 1.7 eV on the (7 x 7) superstructure. On the (2 x 1) structure the transitions are ascribed to the occupied and empty dangling bond surface state bands [20, 231.

4.2 OXYGEN ADSORPTION ON CLEAVED Si (1 11)

SURFACES. - For the investigation of adsorption

kinetics ellipsometry is usually performed at a particu- lar fixed light wavelength. In these studies the optical effect of the gas coverage which is mostly not absor- bing in the considered spectral range is observed in 6A. This common type of measurement has been performed on metal and on semiconductor surfaces and shall not be discussed here in detail. In the context of the present paper another kind of experiment which is particularly characteristic for semiconductor sur- faces is more interesting. On semiconductor surfaces, where surface states mostly are compensated by gas adsorption, this effect showing up as a 6Y change, can also be used to monitor the adsorption kinetics and to give additional information.

OXYGEN DOSAGE (L)

FIG. 3. -Oxygen adsorption on UHV cleaved Si (111) sur-

faces. Ellipsometric changes 6A and 6 y versus oxygen dosage

measured at the fixed wavelength of 546 nm ; 1 Langmuir (L)

is 10-6 torr s.

<

tan a

>

is the mean angle of inclination of the probed surface area with respect to the (111) lattice plane.

Insert : Sticking coefficient S of oxygen in dependence of mean

angle of inclination

<

tan a

>

( N mean step density). Data are

obtained in different apparatus (a, with ion gauge encased ;

b, c with nude ion gauge burning) by different techniques :

ellipsometry (ELLIPS), Auger electron spectroscopy (AES) and

electron energy loss spectroscopy (ELS) (After Dorn et al. [17]).

and subsequent saturation. The dosage regime where

6 Y increases linearly and the saturation kink varies

over one and a half order of magnitude from cleavage to cleavage whereas the 6A changes are essentially the same for all cleaves studied [17]. A relation could be found between the dosage where 6 Y starts saturating and the density of atomic steps measured by LEED (low energy electron diffraction) and an optical method described previously [16].

<

tan a

>

in figure 3, the mean angle of inclination of the considered surface area with respect to the crystal (1 11) lattice plane gives approximately the mean step density because mona- tomic steps are prevailing 1161.

Since the used light wavelength of 546 nm just mat- ches the energy of surface state transitions discussed in section 4.1, the 6 Y changes are interpreted as prefe- rentially caused by the compensation of the dangling bond surface states. This compensation is complete after formation of the first monolayer of oxygen (kink in 6 Y ) . The further increase in 6A is interpreted in agreement with other results as due to the formation of a higher oxidized complex [16, 171. This further oxidation appears to be not dependent on step density whereas the kinetics of the formation of the first adsor- bed oxygen monolayer is strongly influenced by steps. Since it is well known that the first adsorption step builds up monolayer coverage, sticking coefficients S(0) for oxygen can be calculated according to d0/dt = S(8) vp/No where 0 is the fractional coverage, p the pressure, v = 3.48 x

loz0

(cm2 s torr)-I the number of molecules striking the unit area per unit time and unit pressure a t 300 K, and No the number of surface sites for a molecule

As can be seen from figure 3 (insert) S(0) depends exponentially on the mean step density

(--

<

tan a

>)

over at least two orders of magnitude. This result is also obtained by other methods [16] (Fig. 3, insert). Furthermore, a strong influence of an ion gauge during gas inlet has been found which indicates that excited oxygen is more active in oxidizing the surface. The exact mechanism for the step dependence of the sticking coefficient of oxygen on the Si (111) surface is not clear up to now. From recent Auger investigations Kasupke and Henzler [24] suggest that small carbon contaminations, may be preferentially at steps, might partially be responsible.

4.3 BAND BENDING AND SURFACE STATES ON GaAs

(1 10) SURFACES. - 4.3.1 j?ranz-Keldysh effect. - A particularly interesting example for the application of ellipsometry is provided by the study of the electronic surface structure of clean and oxygen covered GaAs (110) surfaces [25, 26, 271. The surfaces (-- 5 mm x

10 mm) prepared by cleavage in UHV by means of the double wedge technique are generally free of measu- rable step densities. For both n- and p-type material (carrier concentrations

-

l O I 7 cmT3) a remarkable structure between 1.5 and 3.5 eV is found in the ellipsometric spectra 6A (ha) and GY (ha). The changes

shown in figure 4 are observed after adsorption of

-

IY I- 0 6 n-type L 4 15 2 25 3 35 I

u PHOTON ENERGY h w (eV)

FIG. 4. - Ellipsometric spectra GA(fiw) and Gw(fiw) obtained

by A and measurements on the clean UHV cleaved and oxygen

covered GaAs (110) surface. The dash-dotted curves describe a calculated contribution which remains after subtraction of the changes induced by Franz-Keldysh effect (after Dorn and Liith

[331).

about half a monolayer of oxygen (saturation cove- rage) 1281. In contlast with Si, critical points of the bulk band structure are found just at 2.9 and 3.15 eV where according to section 4.1 ellipsometry would indicate surface state transitions. Further information is obtained from a plot of 6A in dependence of oxygen exposure at the fixed photon energies 2.54 eV (maxi- mum of 6 A (ho) and 2.85 eV (minimum of 6 A (ho)).

ELLIPSOMETRY APPLIED TO THE STUDY OF SEMICONDUCTOR SURFACES C5-119 AFTER CLEAVAGE , , , , I , , , , / I GoAs (110) 02 /w,$;E2 2 S i eV DOSE OF OXYGEN (L)

FIG. 5. - Oxygen adsorption on UHV cleaved GaAs (110)

surfaces : a) Change 6 A versus oxygen dosage measured on

p-type material at the fixed photon energies 2.54 eV (maximum

of 6 A (fiw), Fig. 4a) and 2.85 eV (minimum of 6 A (fiw), Fig. 4a), respectively. (After Liith et al. [27]). (b) Part of 6 A change which

is due to Franz-Keldysh effect in the space charge layer :

{ 6 A (2.54 eV)

-

6 A (2.85 eV) ) versus oxygen dosage. (After

Liith et al. [27]). c ) Energetic position of the Fermi level EF

with respect to the upper edge of the valence band E, at the

surface (After Spicer et al. [26]).

responsible for building up the spectral oscillation at low exposures in the 1-10' L range, and the second one shifting the whole spectral structure to positive values in the one-degree range. Figure 6b (curve 1) shows the relative change of normal

-

incidence reflectivity ARIR calculated from the observed S A and 6Y in figure 4. Maxima and minima found in the ellipso- metry derived spectrum AR/R agree with structure seen in the electroreflectance spectrum (Fig. 6a)

PHOTON ENERGY hw (eV)

FIG. 6.

-

a) Electroreflectance spectrum on n-type GaAs after

Cardona et al. [21]. The sign of ARIR is that observed when the

negative cycle of the modulating voltage (1 V, rms) is applied

to the sample. b) Relative change of reflectivity ARIR as calcu-

lated from the ellipsometric data in figure 4 : curve 1, obtained

from measured 6 A and 6y values ; curve 2, corrected by the

contribution due to the adsorbed oxygen layer ; curve 3, after

subtraction of surface state layer and oxygen contributions

(After Dorn ane Liith [33]).

obtained by Cardona et al. [21]. In those experiments an external electric field applied normal to the reflec- ting surface changes the electric field E,, of the space charge layer within a depth of 100 to 1000

A

below the surface. This modifies the bulk optical constants and the reflectivity near critical points of the bulk band structure [9] due to Franz-Keldysh effect [8, 91 as observed in figure 6a.

As has been established meanwhile [29] clean cleaved GaAs (110) surfaces with very low step densi- ties exhibit flat bands both on p- and n-type crystals. Oxygen bends the bands upwards for n- and down- wards for p-typ material, respectively, thereby chang- ing the space charge field E,, (to E;, in fig. 1). Because of Franz-Keldysh effect reflectivity changes are induced near the critical points 2.9 and 3.15 eV. The major oscillating part of the ellipsometric spectra 6A (go) and SY ((ha) in figure 4 is, therefore, attributed to oxy- gen induced band bending changes giving rise to variations of the optical constant

kc

within the space charge layer.

The difference

{

6A (2.54 eV)

-

6A (2.85 eV)} seems to be an appropriate quantity to describe the optical change due to Franz-Keldysh effect. Even- though 6A cannot be expected to be dependent on the space charge field in a simple manner it varies monoto- nically with the absolute amount of the band bending

I

V,

1.

The quantity

{

6A (2.54 eV) - 6A (2.85 eV)

),

plotted in dependence of exposure in figure 5b can therefore be used to monitor band bending changes due to oxygen. For both p- and n-type material similar absolute changes are observed which saturate for dosages higher than 107 L. Band bending changes can already be observed at dosages less than 1 L, far below the range where oxygen is detected in Auger electron spectroscopy 1281. These conclusions are in good agreement with results derived from UPS measure- ments [25, 261 (Fig. Sc), which furthermore indicate that the band bending changes on p- and n-type material have opposite sign.

5 A on the clean cleaved surface (Fig. 1) the optical absorption within this topmost surface layer can be calculated (Fig. 7, curve in full line). A remarkable structure in Im

is

is centered around 3 eV. The corres- ponding optical absorption is attributed to electronic transitions located within the topmost atomic layers (surface states and tails of the bulk band structure).

I I I I I I I I - GaAs (110) 11101

-

EXPERlMENl

-a

-- RELAXED - _{- -,} >THEORY. 101 - after Loure et ol - 1 0 2 4 6 8 10

PHOTON ENERGY ha (eV)

FIG. 7 . - Leff scale (-1 : Imaginary part of the surface dielec-

tric constant ImZs as derived from the ellipsometric data'in figures 4 and 6. is attributed t o a surface layer on the clean cleaved surface containing surface state transitions. Right scale (-

-

and -

..

-) : Spectral dependence of the convolution integral D,"@ Dz between the densities of occupied (D:) and empty ( D 3 electronic states of the topmost atomic layer of a relaxed (insert a) and an idea1 (insert b) GaAs (110) surface. Dz and Dz are taken from calculations of Louie et al. [30].

Local densities of occupied and empty electronic states in the topmost atomic layers of GaAs (110) surfaces have recently been calculated by Louie, Cheli- kowsky, and Cohen using self consistent pseudopoten- tials 1301 and by Pandey, Freeouf and Eastman in a tight-binding model [31]. As a general feature it can be taken from these calculations that on an ideal (110) surface where the atomic configuration of the bulk would be given also in the topmost atomic layer (insert of fig. 7) the density of occupied states derived from the surface atoms has a prominent maximum just below the bulk valence band edge. Empty surface states form a band in the upper half of the forbidden bulk gap. The distribution of surface states is different if the surface is relaxed (1 x 1 reconstruction), i. e, if the topmost Ga atoms are moved into and the As atoms are moved out of the crystal (110) surface without altering any bond lengths from their ideal bulk value (Fig. 7, insert). For this reconstructed surface the empty surface states are moved into the energy range of the bulk conduction band. After the calculation of Pandey et al. [3], the forbidden band on the relaxed surface is nearly free of surface states

whereas in the results of Louie et al. [30] a tail of empty states reaches down into the band gap eventhough the center of the empty states has been shifted upwards into the bulk conduction band.

The densities D,'(E) and D,"(E) of occupied (valence) and empty (conduction) states within the uppermost layer as derived by Louie et al. 1301 have been used to calculate approximately the optical absorption. As a rough approximation for Im

Ls

the convolution integral

Di

@ D," =

!

D,"(E 4- ho) x D:(E) dE _{( 5 )} has been calculated. (Dl @ D,") is plotted in figure 7

for the ideal and the relaxed surface in comparison with the imaginary part of the surface dielectric func- tion Im as derived from ellipsometry. Discrepancies between Im

6

and the theoretical curve (a) are pro- bably due to the approximation of the combined den- sity of states by the convolution integral (Eq. (5)). Nevertheless, it can be concluded that the optical absorption within the topmost surface layer Im

gS

as obtained by ellipsometry gives strong evidence for a reconstruction (relaxed surface) being found on the clean cleaved (110) surface of GaAs. This is in good agreement with results obtained by Pandey et al. [31] from a comparison of UPS results with the calculated density of states. Further conclusions like in their paper concerning the degree of relaxation can not be drawn from the present results because of the involved approximations. The same type of reconstruction as described here has also been derived from a LEED (low energy electron diffraction) analysis of the clean GaAs (110) surface [32].

5. Conclusions.

-

The examples presented show that ellipsometry can be applied to semiconductor surfaces to study a variety of problems, like e. g. band bending, surface states, adsorption kinetics. Ellipso- metry is most powerful if it is performed as a spectros- copy with varying photon energies. Moreover, on semiconductor surfaces it appears necessary to per- form spectroscopic measurements prior to studying adsorption processes itself at a fixed wavelength since one has to know the true origin of the observed A and Y changes. In the presence of Franz-Keldysh effect in the space charge layer e. g., the determination of a sticking coefficient S(B) or of a coverage depen- dence on exposure from A changes alone is not possible.

AcknowIedgments.

-

I would like to thank

ELLIPSOMETRY APPLIED TO THE STUDY OF SEMICONDUCTOR SURFACES (25-121

References

[I] L ~ T H , H., AppI. Phys. 8 (1975) 1.

[2] DAVISON, S. G., LEV~NE, J. D., a Surface States >>, in Solid State Physics 25, ed. by F. Seitz, D. Turnbull, and H. Ehrenreich (Academic Press, New York) 1970, p. 1.

[3] MCCRACKIN, F. L., PASSAGLIA, E., STROMBERG, R. R. and STEINBERG, H. L., J. Res. Nut. Bur. Stand. A 67

(1963) 363.

141 MATHIEU, & J., MCCLURE, D. E. and MULLER, R. H., Rev. Sci. Instrum. 45 (1974) 798.

151 JASPERSON, S. N. and SCHNATTERLY, S. E., Rev. Sci. Instrum.

40 (1969) 761.

[6] ASPNES, D. E. and STUDNA, A. A., Appl. Opt. 14 (1975) 220. [7] Proc. 3rd Internatl. Conf. on Ellipsometry, Nebraska,

Sept. 1975, Surf. Sci. 56 (1976) ;

In particular : MULLER, R. H., Surf. Sci. 56 (1976) 19. 181 FRANZ, W., 2. Naturforsch. 13A (1958) 484 ;

KELDYSH, L. V., Zh. Eksp. Teor. Fiz. 34 (1958) 1138 ; [Sov. Phys. JETP 7 (1958) 7881.

[9] CARDONA, M., Modulation Spectroscopy, Solid State Physics, Suppl. 11, ed. by F. Seitz, D. Turnbull and H. Ehrenreich (Acad. Press, New York and London) 1969.

[lo] STRACHAN, C. S., Proc. Cambridge Phil. Soc. 29 (1933) 116.

[Ill BOOTSMA, G. A. and MEYER, F., Surf. Sci. 13 (1969) 110. [I21 AT-, P. W. and WILSON, A. D., Surf. Sci. 22 (1970)

433.

1131 See e. g. : BORN, M., WOLF, E., Principles of Optics (Per- gamon, Oxford) 1965.

1141 MEYER, F., Phys. Rev. (B) 9 (1974) 3622.

[15] BOOTSMA, G. A. and MEYER, F., Surf. Sci. 14 (1969) 52. [16] IBACH, H., HORN, K., DORN, R. and L ~ ~ T H , H., Surf:

Sci. 38 (1973) 433.

1171 DORN, R., LUTH, H. and IBACH, H., Surf: Sci. 42 (1974) 583.

[IS] MEYER, F., DE KLUIZENAAR, E. E. and BOOTSMA, G. A., Surf. Sci. 27 (1971) 88.

[I91 PHILLIP, H. R. and EHRENREICH, H., Phys. Rev. 129 (1963) 1550.

[20] See e. g. MONCH, W., In Festkorperprobleme XLII

(Advances in Solid State Physics), ed. by H. J. Queisser (Pergamon Press, Oxford) 1973, p. 241.

[21] CARDONA, M., SHAKLEE, K. L. and POLLACK, F. H., Phvs. Rev. 154 (1967) 696. . ,

[22] ROWE,- J. E. and IBACH, H., Phys. Rev. Lett. 31 (1973) 102.

[23] FROITZHEIM, H., IBACH, H. and MILLS, D. L., Phys. Rev.

B 11 (1975) 4980.

[24] KASUPKE, N. and HENZLER, M., Verh Dtsch. Phys. Ges.

(Vl) 12 (1977) 346.

[25] GUDAT, W. and EASTMAN, D. E., J. Vac. Sci. Technol. 13

(1976) 831.

[26] SPICER, W. E., LINDAU, I., GREGORY, P. E., GARNER, C. M.,

PLANETTA, P. and CHYE, P. W., J. Vac. Sci. Technol.

13 (1976) 780.

[27] LUTH, H., BUCHEL, M., DORN, R., LIEHR, M. and MATZ, R.,

Phys. Rev. (B) 15 (1977) 865.

[28] DORN, R., LUTH, H. and RUSSELL, G. J., Phys. Rev. (B)

10 (1974) 5049.

[29] HCT~TSER, A. and VAN LAAR, J., Surf. Sci. 52 (1975) 202. [30] LOUIE, S. G., CHEL'IKOWSKY, J. R. and COHEN, M. L.,

J. Vac. Sci. Technol. 13 (1976) 790.

[31] PANDEY, K. C., FREEOUF, J. L. and EASTMAN, D. E.,

J. Vac. Sci. Technol. 14 (1977) 904.

[32] DUKE, C. B., LUBINSKY, A. R., LEE, B. W. and MARK, P.,

J. Vac. Sci. Technol. 13 (1976) 761.

6331 DORN, R. and L ~ ~ T H , H., Phys. Rev. Lett. 33 (1974) 1024.

DISCUSSION

F. LUKES. - DO YOU think that the technique you

have just described can be applied even to metals ?

H. LUTH. - I think that it would be very interesting to perform ellipsometric spectroscopy on metal sur- faces : In the near UV (around 5 eV) I would expect surface state transitions in some cases, see e. g. the work which has beendone by G. Rubloff on W surfaces. Taking into account what has been done in the group of Pr. Abeles, one can also expect to get information about deviations from the bulk electronic structure in the topmost atomic layer, e. g. anormalous surface conductivity within a depth of 1-5

A.

The type of expe- riment would be the same as I have described for semi- conductor surfaces, i. e. measurement of changes

6A(ko) and 611/(hw) as induced by some surface treatment.

M. L. THEYE.

-

Comment les maxima observts dans E~ attribuCs & des Ctats de surface sont-ils relits a la

densitt de ces Ctats ? Les rCsultats sont-ils en accord avec ceux des autres mtthodes utilisCes pour mettre en tvidence les ttats de surface ?

H. LUTH.

-

YOU can not, of course from an optical spectroscopy alone derive the absolute positions of surface states with respect to the bulk band structure. Mostly (aslo in the present cases) results from UV photoemission spectroscopy and from optical or elec- tron loss spectroscopy are used in combination. In the particular case of GaAs, 1 only compared a maximum, of the optical surface absorption 1m.& with the convo- lution between occupied and empty states. The ener- getic position of the occupied or empty states with respect to the bulk, bands does not enter here.

The present result are in agreement with quite a number of other data which have been obtained from UV photoemission spectroscopy, electron energy loss spectroscopy, surface photovoltage spectroscopy and measurements of the surface potentiel.

D. LYNCH (a comment).

-

The empty surface states have been seen in UPS by exciting Ga 3d electrons into them. Emitted Auger electrons were detected.

H. LUTH.

-

I agree. They have furthermore been studied by electron energy loss spectroscopy (Ga

3d -+ surface state transitions).