Looking up the down staircase: Surface Raman spectroscopy as a probe of adsorbate orientation

JoumzZ of Electron Spectroscopy awl Related Phenomena, 64J65 (1993) 183-191 0368-2048/93/$06.00 @ 1993 - Eleevier Science Publishers B.V. All rights reserved

183

looking Up the Down Staircase: Surface Raman Spectroscopy as a Probe of Adsorbate Orientation Melissa A. Hines, Timothy D. Harris, Alexander L, Harris and Yves J, Chabal AT&T Bell Laboratories, Murray Hill, NJ 07974, USA Unenhanced,

non-resonant

dihydride-terminated

Raman spectra of a H-terminated

vicinal Si(ll1)

surface, Si[G(I I l)-( 11211, with

bilayer steps have been measured. Ail four Si-H stretches (and a 4%

ML kink-defect mode)

can be observed if both the excitation and detection geometries ate f&orable. A method for exttacting the orientation of adsorbates using polarized, angle-resolved Raman scattering is presented. Assuming the C, mode corresponds to a localized Si-H stretch, the step dihydride is found to be rotated 37 f 4” away from the surI&e normal. This value is in agreement with recent izb initio cluster calculations.

1. INTRODUCTION

Their results are illustrated in Fig. 1, The fluorine

Because of the localized nature of semiconductor bonds, reactions at semiconductor surfaces are often constrained more by geometrical factors than by the overall energetics of the reaction. To understand

these

etching

process leads to dihydride

termination of the bilayer steps; however, the bulkterminated geometry is unstable. Because of strong steric interactions between one of the two H’s on the dihydride moiety and the H located on the terrace atom directly

processes, a knowledge of both the nature of the adsorbed species and their relative orientations is necessary.

beneath it, the dihydride

Optical

back away from the terrace by 22’ [4]. Although this distortion relieves some of the steric hindrance, these

vibrational

spectroscopies,

such as Raman

scattering,

infrared absorption and sum-frequency generation, are particularly usefu1 in such systems, because they are sensitive to both the local chemical environment,

as reflected in the resonance frequencies,

and to the orientation of the adsorbate. One reaction in which steric effects predominate

is

the aqueous fluorine etching of flat and vicinal silicon surfaces [l]. These chemical preparations have been

unit is calculated to rotate

cluster calculations indicate that this interaction still affects the Si-H bonds in the equilibrium structure. This leads to the formation

of three non-degenerate

Si-H normal modes (C;, C,, and C,) corresponding to motion of the step atoms (2 dihydride and 1 terrace H). The remaining terrace hydrogens are dynamically coupled to form one normal mode (A) corresponding

shown to produce H-terminated surfaces of unparalleled homogeneity concentrate

and regularity. In this paper, we will on only one of these surfaces, the Si[6( 1 I I)-( ii2)] sur face, which is formed by cutting 7” away from the (111) plane in the (i 12) direction. This results in regularly spaced terraces that are (on average) 6 Si atoms wide separated by single bilayer steps. STM studies [2] have shown that fluorine-etching leads to steps that are atomically straight and kink-free over distances of 100 ,k or more. The microscopic structure of these steps was determined by combining the multiple internal reflection infrared absorption spectra (MIR IRAS) of Jakob and Chabal [3] with the a6 initio cluster calculations of Raghavachari etal.[4].

Figure 1. Schematic of H-terminated

Si[6(11 l)-(ii2)]

surface based on the results of Raghavachari etal. [4] The dihydride unit terminating the biIayer step is rotated away from the terrace to relieve steric interactions, The three H which comprise the step vibrations are lighter in color than the terrace H, and the optical plane is indicated by the broken line.

184 to their in-phase vibration, All four of these modes are infrared-active and observable. The present Raman experiment was motivated by the recent sum-frequency

Raman spectra were obtained

using 600 mW of

514.5 nm light from an Ar’ laser. The incident

generation

(SFG) study of

Morin et A. [5] on this surface. In their study, only

polarization

could be varied using a double Fresnel

Rhomb (Spectra Physics), and the measured extinction ratio after all optics was 225 @ polarization) and ml00

three of the four Si-H stretch modes were observed.

(S polarization).

Because the SFG cross-section is proportional

polarization

to both

the infrared and Raman cross-sections, Morin

cr dl.

measuring

The absolute

was calibrated the reflection

orientation

to better

minimum.

of the

than +2’ by The laser was

suggested that the missing mode, the so-called C, mode,

incident on the sample at an angle of 60” from the

may have a small Raman cross-section; however, this

surface normal and focussed with a 200 mm best form

supposition is problematic. According to the calculations

lens. This illuminated

of Raghavachari er al. [4], this mode corresponds to

region. Scattered light was collected 60” off-normal in

the isolated

a plane perpendicular to the incident beam with a 13 mm FL f/1.8 reflecting objective (Ealing). Stray 514.5 nm

stretching

motion

of the unhindered

dihydride

SCH bond (see Fig. 1). It is difftcult to

understand

how a 22’ rotation of the Si atom could

a roughly 45 x 90 lrm elliptical

light was removed with a holographic filter (Physical Optics). The scattered light was dispersed in a 0.64 m

quench the Raman activity of this bond. In this paper, we will show that all four of the Si-H

single monochromator

stretch modes are indeed Raman active and can be

grating and detected with a LN,-cooled CCD camera

observed if both the excitation and detection geometries are favorable. This orientation dependence explains why

average of three &minute integrations.

the C, mode is missing in the sum-frequency spectra. Because the observed Raman intensities are a very sensitive function

of the relative orientations

of the

electric fields at the surface and the dynamic polarizability of the Si-H bonds, we will show that these spectra can also be used to determine

the tilt

(ISA) with a 2400 groove/mm

(Princeton Instruments).

Reported spectra represent an “Cosmic ray”

events were removed prior to averaging.

3. ORIENTATION DEPENDENCE OF RAMAN SCATTERING Figure 2 shows two unenhanced, non-resonant Raman spectra in the Si-H stretch region of the same

angle of the dihydride unit.

H-terminated

2. EXPERIMENTAL

different

Si[G(11 l)-( i i2)] sample taken with two

detector

orientations

and

ppolarized

excitationalong the step edge. The upper spectrum was taken with the detector pointing “down the stairs”

The H-terminated silicon surfaces were prepared in a manner similar to previous publications [3]. Briefly, 0.6” x 0.5” x 0.020” thermally oxidized silicon samples

prominent

were first degreased

baths of warm

band at 2082 cm-’ corresponds to the in-phase terrace

trichloroethane, room-temperature acetone and methanol. The wafers were then cleaned in a 1:1:4

vibration, A, while the two prominent high frequency modes at 2101 cm-’ and 2135 cm-’ are the C; and C, step vibrations which have been assigned to out-of-phase and in-phase combinations [6] of the interacting

in sequential

solution of 30% H,O,(aq):28% NH ,(aq):H ,O at 80°C for 10 minutes. The thermal oxide was removed by immersion in Buffered Oxide Etch (General Chemical) for 2 minutes, and the exposed silicon surface was etched with 40% NH *F( aq.) for 25 s. The wafer was thoroughly rinsed with deionized water (Millipore) between each step and following the final etch. After etching, the sample was mounted in a high vacuum cell which was then evacuated by a turbomolecular pump. The base pressure of the ceil was estimated to be 1 X lo-'torr.

(position D in Fig. 2). In this orientation,

three

features are observed. The low frequency

dihydride and terrace Si-H bonds. In this configuration, klle C, stepvibration is undetectable. A small feature is also observed at 2087 cm-’ and is due to hydrogen bonded to kink-defect sites [3]. If the cross sections for the A and kink modes are similar, these defects correspond to roughly 3.5% of a monolayer. This may not be a vaild assumption, however, because of the effects of dipole coupling.

185

Q--l
,Q

D

7;

A

de
TWKK%

C1C2

C3

&!0C2%

\

1 photon/s

2060 2080 2100 2120 2140

Frequency Shift (cm-l) Figure 3. Raman spectra

2060 2080 2100 2120 2140

taken with upstairs

FrequencyShift(cm?> Figure 2. Raman

spectra

taken with two different polarized excitation

different

of H-terminated detector

vi&al

orientations

Si

incident

detector

pointing

the radiating

spectrum.

in Fig. 2 was taken with the

up the stairs (position

orientation

results

The Cs step vibration

the C, step vibration observed

U in Fig. 2).

in a markedly

in the previous

different

is unobservable,

at 2093 cm-‘, which orientation,

orientation

while

was not

is now easily

dependence

qualitatively by examining

understood

the C, mode. To a first approximation, from Si-H

bonds

is dipole

can

radiation

from a source

to the bond

photons

from the C, mode are emitted

oriented

31" (22"+ 7")from the surface normal

axis [7]. Accordingly,

to this bond, it collects other hand, detector

U is oriented C, radiation

D is oriented

of

Ramau scattering

parallel

Fig. 1). Because detector

be

the behavior

Raman

from a dipole (see

perpendicular

efftciently.

dipole-a

poor configuration.

can only be observed

Thus, the

by “looking

up the

down staircase.” A similar effect is observed when the polarization

of

spectra of this surface takenwith light that is linearly polarized upstairs

30” from the surface pointing

spectrum, detecror

E, and E, oriented

the excitation laser is varied. Figure 3 shows two Raman

detected. This

polarizations,

U) and two

f 30’ from the surface normal .

C, mode

This

vicinal Si

(detector

and p-

along the step edge.

The lower spectrum

of H-terminated

detection

On the

more or less along

detector

the incident

normal

(position

and with an

U). In the top

electric field E, points

up the

stairs [S], and the C, modes is relatively intense. When the electric field is rotated in the opposite

direction

[8]

(E, in Fig. 3), C, is not detected. This polarization understood exciting

dependence

the

polarization

Raman

source.

probabilities

Because

the

field

more efficiently

The cj vibration

excites than

is not observed

the

of

induced

lies along the axis of the excited

[7], the E, electric vibration

can be qualitatively

in terms of the relative

bond

C, stretching

the E, electric

field.

in either spectrum,

186

because the detector is in the unfavorable orientation

a polarization

for this mode.

vibration at We Because of this modulation,

When taken together, these two observations explain the sum-frequency

generation

spectra. Because sum-

frequency is a coherent phenomenon,

the signal is

that is modulated

small fraction of the incident

by the molecular a very

light, typically lo”, is

inelastically scattered to a new frequency coR= q + wU. The

orientation

of the

induced

polarization

emitted in a near-specular direction from the excitation

determines the polarization and angular distribution of

laser. In the experiment of Morin et&, the (ppolarized)

the scattered light, which can be regarded as simple

incident and signal beams were oriented 60”

dipole radiation from this source. If the molecule were

from the

surface normal in the plane of the sketches in Figs. 2

equally polatizable

and 3. If the detector were oriented looking up the stairs (position U), the excitation would perforce be

polarization would always coincide with the incident electric field. This type of behavior is found in very

in all directions,

the induced

down the stairs and the electric field would be along

symmetric molecules such as CH,. On the other hand,

E,, In this geometry, C, would be unobservable because the excitation would be inefficient. If the excitation

if the molecule were only polarizable in one direction,

laser and detector

were oriented

in the opposite

orientation, C, would be unobservable detection would be unfavorable.

because the

These arguments do not imply that C, is SFG inactive. If a cross stairs geometry were adopted in which both the excitation laser and detector were oriented parallel to the step edge, this mode should be readily detectable. The explanations presented in this section are only qualitatively correct, as we have neglected the effects of the surface on the applied electric field and have made some rather crude approximations of the Raman effect. In the next section, we will present a quantitative description of Raman scattering at surfaces.

perhaps along a bond axis, the orientation

of the

polarization would be determined solely by molecular orientation.

Most molecules lie somewhere between

these two extremes, so the orientation of the polarization is determined by both the incident electric field and the molecular orientation. The (first order) dynamic polarizability of a molecule is a second tank tensor, and the induced polarization, P, is given by lj = C$ Ej, where E is the incident electric field. If the molecule is an isolated diatomic with its bond lying along the z axis, 600 t-X)= OS0 ( 001 i by symmetry [I2]. F is the bond anisotropy and is defined

4. QUANTITATIVE DESCRIPTION OF SURFACE

to be al/a;,

RAMAN SCATTERING

perpendicular and parallel to the bond axis.

In this section, we will first present a brief description of polarized Raman scattering from aligned molecules

A dynamic polarizability of this form can also be used to describe isolated bonds in a molecule. The Raman response of a particular vibration is then given

and

discuss

the

excitation/detection

peculiarities

of an orthogonal

geometry. We then consider the

, the ratio of the molecular polarizabilities

by the sum of the individual (rotated

into their correct

polarizability molecular

tensors

orientation)

distortion of the incident electric field by the surface and a simple model for these effects. Finally, we will combine these two parts and present a quantitative description of surface Raman scattering from isotbd vibrations. Our approach is similar to that of Giergiel et al. [9]. Combination bands and the extraction of

weighted by the composition and phase factors of that normal mode. In out analysis, we assumed that every Si-H bond was described by a polarizability tensor of this form, and that all bonds had the same bond

normal modes will be deferred to a future publication [lo]. The Raman effect is due to the inelastic scattering of light from a molecule by its dynamic polarizability, d [l 11.Briefly, incident light at a frequency 0; induces

Raman signal can be confusing and is best explained by example. Figure 4 shows three identical diatomic molecules (or bonds) being irradiated by electric fields of d&rent orientations. The molecules lie along the z

anisotropy. The relationship between E, P, d, and the detected

axis, the excitation laser propagates along the y axis, and the detector is 60” from the z axis in the = plane. In this example, we will assume tbat the bond anisotropy is 0.25, which is characteristic of an Si-H bond in SM, [13]. The magnitude

and orientation

of the dynamic

polariz;lbility can be calculated from Figure 4. The relationship

between E and P in an

isolated molecule. The laser is incident along the y axis and the detector (D) is oriented 60’ from the z axis. where yis the angle between the electric field and the z axis. If the electric field is parallel or perpendicular to the bond axis, the polarization coincides with the electric field; however, the perpendicular polarization is a factor of 4 smaller than the parallel case. In every other orientation, und the ma~iw

thepokzrkationLiesbetweenthe electricjeki pahrimbility axis ofthe moh-uk (here,

the z axis). In our example, if the electric field is 60” from the z axis (i.e. y= GO”), the induced polarization is 23” from the taxis and half as large as the maximum value. The detected signal can be calculated directly from the induced polarization [ 141. It is given by Idef= J$ P2 sin* (f3, - CJ,,J where &, is the detected intensity, CUEis the radiated frequency, c is the speed of light, and 0, and 0, are the angles the polarization and the detector make with the z axis, respectively. The results of this calculation ate displayed in Fig. 5. The crucial result of this example is that in an orthogonal excitation/detection geometry, the maximum dekrctedintensityhoesnot oa74r when the incident electric jeki is polarized along the bond axis. In this example, the maximum intensity actually occurs at -8.2“. This is quite different than infrared absorption where the maximum intensity occurs when the electric field is aligned with the dynamic dipole. The orientation of a molecule can be calculated from its polarized Raman dependence, but only if the full Raman tensor (with the correct bond anisotropy!) is used. So far, our discussion has neglected the presence of the substrate and the neighboring Si-H bonds. The substrate has a profound effect because it reflects light;

Figure 5. Dependence of the induced polarization

P

and Raman intensity I, on incident polarization angle for isolated molecule shown in Fig. 4. under our operating conditions, 15-60% (depending on polarization) of the incident light is reflected. Both the incident and reflected laser beams can induce Raman scattering, and both the incident and reflected Raman photons can be detected, The effect of the neighboring subtle.

Although

both

Si-H bonds is more

the incident

and

Raman

wavelengths are far from any Si-H related resonances, the Si-H bond is still polarizable at these frequencies. As we shall show in the next section, at monolayer coverages this surface polarization contributes signifLntly to the local electric field. We have treated both of these effects in a simple fashion by using a 3-layer dielectric model [ 151.In this model, the substrate is assumed to be a flat, semi-infinite, isotropic dielectric described by its frequencydependent, complex, bulk dielectric constant [ IG]. The adsorbate layer is modeled as a flat, infinitely thin dielectric described by an isotropic, frequencyindependent, real dielectric constant cndrwhich mustbe

188

a&mined

experimentally. The third layer is vacuum.

Given the intensity and polarization of the incident

modes on this surface lie in a plane perpendicular the step edge; this defines the y’z’plane.

to

the surface electric field (Le. the

The mathematical description of this is much more

field inside the adsorbate layer) can be calculated from Maxwell’s equations and the usual boundary conditions

compact. The electric field in vacuum due to the Raman

light (in vacuum),

or

directly [IT].

using

the

appropriate

scattered light is

Green’s

functions [ 181, Following the elegant formulation

of

Reed et d. [18], if the surface electric field Ed due to the J and p components

of an incident (vacuum) field

E “is expressed in the form

=(4F+:;;f;)[:, then the electric field in vacuum ER radiated by a polarization P d m ’ the adsorbate layer with frequency as is given by Once the adsorbate dielectric constant and the bond anisotropy are determined, The functions irelate

the vacuum electric fields to the

surface fields and are functions of the polar angle and frequency (due to dispersion in the substrate dielectric

the orientation

of a bond

on the surface can be extracted from polarized, angleresolved Raman spectra. 5. DETERMINATION OF Ed AND 6

constant) of the vacuum field. Ar is the transpose of A; ek, is the detector polar angle measured with respect

interface, E& affects the relative magnitudes of the in-

to the z axis.

plane and out-of-plane surface electric fields. The bond

At thispoint,

we have all of the necessary physics to

Because of refraction

at the adsorbate-vacuum

anisotropy 6 determines the relative response of a bond

describe surface Raman scattering from isolated bonds;

to electric fields oriented perpendicular

all that remains is geometry. If we state the problem in

the bond axis. Both of these parameters can be extracted

terms of 3 reference

from the polarized, angle-resolved Raman spectra of a

frames (incident,

bond,

and

and parallel to

detector) and the angles between these frames, the geometry is easily handled using rotation matrices [19].

bond of known orientation

In all frames, the .z axis is the surface normal. The excitation laser is incident on the surface at an angle 0, from the z axis in the xz plane. The incident light is linearly polarized an angle yfrom the plane of incidence.

On a vicinal Si(ll1) surface, the in-phase terrace vibration can be used to determine E& and 6 as this vibration is known to lie along the (111) axis (i.e. 9” from the optical plane on our surface). Figure 6 shows

The Raman active bond is at an angle 0 from the i (= z) axis in the y’z’plane, and the y’z’plane is rotated

the incident polarization dependence of the A mode in

away from the ~a plane by an angle x. The detector is at an angle 0, from the d (= z) axis in the y”z”plane, and the ~‘2” plane is rotated away from the y’z’ plane by an angle 4. The infrared absorption experiments of Jakob and Chabal[3] have shown that all vibrational

as long as the band is nor

oriented along the su$ace rwrm.aL

two different detector orientations. The solid lines are the best fit to data taken in three different orientations and relative intensities taken in two orientations assuming the bond tilt, fl, is 9”.

189

80

P%xiiati~~ Angle (3 Figure 7. Polarization

0.2

upstairs detection

0.0

(in upstairs

-so

.

P$hatio~

Figure 6. Polarization in two different represent

the

best

J polarization.

y= 60”, the downstairs

angle

detector

polarization

to

is aligned [8] with

and a bond

0,263 f 0.028. The quoted covariance

matrix

assumption measured

of normally bond

anisotropy

of

to %!G under the

distributed

anisotropy

dielectric

errors are from the formal

and correspond

errors.

is in excellent

Our

agreement

with the 0.25 value reported by Armstrong and Clark [ 131 for the bond anisotropy

the assertion

of the

the electric field at the surf&e,

Our data are completely

inconsistent

with Q, = 1, and

that these effects are negligible

in surface

Raman scattering [2O] must be viewed with suspicion, Jakob and Chabal [3] reported an adsorbate dielectric constant of 2.0 f 0.4 from their infrared investigation of this surface. The discrepancy between these two values is undoubtedly due to dispersion. At frequencies below the characteristic

electronic

layer, the effective with increasing

dielectric

frequency.

absorptions constant

of the surface should

et al. [4] assigned the C, mode to a stretch

of the upper dihydride Si-H bond (see Fig. 1). Assuming this assignment is correct, we can determine the tilt angle of the dihydride unit from Ran-ran spectra of this mode. Figure 7 shows the polarization dependence of the C; mode taken with the detector orientation.

in the upstairs

The grey line is the best fit to data taken

in two orientations using the parameters derived in the

of Si-H in SiH,(g).

This analysis clearly shows that polarization adsorbate kayer a&rts

OF C, TILT ANGLE

On the basis of their 66 initio cluster calculation,

with y= -60”.

From this analysis, we extract an adsorbate of 3.78 + 0.20

of

of the

angles and upstairs detector.

6. DETERMINATION

Raghavachari

constant

and the

of 0’

f 90” corresponds

The upstairs detector

the best fit

orientations),

The solid lines

fit. A polarization

to p polarization;

corresponds

and downstairs

Raghavachari et al. See Fig. 6 for description

of terrace mode (A)

orientations.

of C, mode with

broken line represents the predicted orientation

Angl*?yl

dependence

detector

dependence

The solid lines represent

increase

previous section. From this analysis, we find that the dihydride unit is rotated 37 f 4” from the surface normal. This corresponds to a rotation of 28” from the bulkterminated position and is 6” larger than the 22’ prediction of Raghavachari et al. The lower grey line in Fig. 7 is the predicted intensity in the downstairs detector orientation. At all points,

this curve is below our detection sensitivity. The absence of the C, mode in spectra taken with a downstairs detector (see Fig 2) is thus a purely geometric effect and is quantitatively consistent with the assignment of Raghavachari et al.

190

Our quoted errors correspond

to z!Qa (under the

to use any one model for all experiments,

a serious

assumption of normally distributed errors). A Iittle under

effort, both theoretically and experimentally, to’quant$

half of this error is due to uncertainties in Q, and S.

the a!eficimciaof these models is required.

7. DISCUSSION

8. CONCLUSIONS

This work has explained the origins of the missing C, mode in SFG experiments

We have shown that unenhanced,

non-resonant

and, in doing so, has

Raman spectroscopy is a sensitive and quantitative tool

confirmed the geometry predicted by ab initio cluster

for the determination of adsorbate geometries and bond

calculations.

angles. On the H-terminated

conclusions

It would

be premature

to draw any

i i2)] surface,

Si[G(l 1l)-(

from the 6” (k 4’) discrepancy between

all Si-H stretching modes were observed. Even defect

our measured dihydride tilt angle and the work of Raghavachari et aL; however, a full analysis of all 3 step

percent of a monolayer, were observable. The Raman

modes (to be reported elsewhere[IO]) uncovers some

spectra of tilted adsorbates were shown to be particularly

limitations of the ab inktb calculations. We have been able to quantitatively compare three

sensitive to detector orientation. With judicious choice

predictions

of the simple 3-layer model for surface

Raman scattering with independent (and perhaps most importantly), anisotropy

observations. First the Si-H bond

that we extracted from the terrace mode

Raman spectra is in excellent agreement with literature values. Because Raman spectroscopy is sensitive to all components

of the electric field (see Section 4), this

agreement validates our use of this simple model. Second, the model explains the absence of the C, mode in the downstairs detector geometry. Third, the tilt angle of the C, mode is in good agreement with independent calculations. Taken together, these three predictions

modes, which are present in concentrations

of a few

of detector angle, these modes could be made to disappear entirely. This effect was used to measure the relaxation of the dihydride-terminated step. This dihydride unit was found to rotate 28’ away from its bulk-terminated position in substantial agreement with &%initiucluster calculations.

REFERENCES AND NOTES [l] Y.

J. Chabal, Mat. Res. Sot. Symp. Proc. 259,

349 (1992). [2] P. Jakob, Y. J. Chabal, K. Raghavachari, R. S. Becker, and A. J. Becker, Surf. Sci. 275, 407 (1992).

strongly suggest that the 3-layer model adequately

[33 P. Jakob and Y, J. Chabal, J, Chem. Phys. 95,

explains the surface electric fields in this system. As pointed out by Feibelman [Zl], the 3-layer model

2897 (1991).

has a number of difficulties at the microscopic level.

Phys. Lett. 206, 156 (1993).

For example, the electric fields at the interfaces between the three layers are discontinuous. Additionally, any

[5] M. Morin, P. Jakob, N. J. Levinos,. Y. J, Chabal, and A. L. Harris, J. Chem. Phys. 96, 6203 (1992).

physical interpretation of the experimentally determined

[G] These modes have unequal contributions the two Si-H bonds. See ref. 4 for more details.

&d (perhaps in terms of the polarizability of the Si-H bond) would be dubious. On the other hand, the magnitude of the error introduced by the 3-layer model, particularly at semiconductor surfaces, is not known at this time. A simple, parameterizable model for the local electric field at a surface is clearly needed. The quantitative interpretation of a wide range of surface spectroscopies, such as infrared absorption, surface Raman scattering and ultraviolet photoemission, hinges on our ability to predict

these fields. Although

it may prove impossible

[4] K. Raghavachari, P. Jakob, and Y. J, Chabal, Chem.

from

[7] This statement is not true for some excitation geometries as discussed in the next section. [8] More correctly, only the component of the field in the plane of the frgure points in this direction. [9] J. Giergiel, C. E. Reed, J. C. Hemminger,

and S.

Ushioda, J. Phys. Chem. 92,5357 (1988). [lo] M. A. Hines, T. D. Harris, A. L. Harris and Y. J. Chabal (in preparation). [ll] The term dynamic

polarizability

refers to the

191

derivative of the molecular polarizability with respect to the

normal

introduction

coordinate

in question.

For an

to surface Raman scattering, see ref. 20.

For the condensed phase picture, see N. W. Ashcroft and N. D. Mermin, Solid State PbysiirJ,(Holt, Rinehart and Winston, Philadelphia, 1976) p. 482486. [12] We have arbitrarily polarizability

throughout

normalized

the dynamic

the paper, as we are not

interested in the absolute Raman cross section. [13] R. S. Armstrong and R. J. H. Clark, J. Chem. Sot. Faraday Trans. 2 72, 11 (1976). [14] See, for example, J. D. Jackson, ClaJsicai Ekctrodynamics, 2nd ed. (Wiley, New York, 1975) p. 394-397.

[15] S. A. Francis and A. H. Ellison, J. Opt. Sot. Am. 49, 131 (1959); R. G. Greenler, J. Chem. Phys. 44, 3 10 (1966); J, D. E. McIntyre and D. E. Aspnes, Surf. Sci. 24, 417 (1971). [ 161D. F. Edwards in Handbook of Optical Constants of SohA, edited by E. D. Palik, (Academic, Orlando, 1985) p. 564-565. [17] Y. J. Chabal in Semicanductor h$zces:

Formation

and Properties, edited by G. LeLay and J. Derrien, Springer Proc. Phys. Vol 22 (Springer, Berlin, 1987)

p. 301-327. [18] C. E. Reed, J. Giergiel, J. C. Hemminger,

and S.

Ushioda, Phys. Rev. B. 36,499O (1987). [191 R N. Zare, Angxhr Momentum, (Wiley, New York, 1988) Ch. 3.

[20] A Campion in Vihational SpectroscopyofMok&s otl .%&es,

edited by J. T. Yates, Jr. and T. E. Madey

(Plenum, New York, 1987) p. 345-415. [21] P. J. Feibelman, Prog. Surf. Sci. 12,287 (1982).