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An investigation of ion-bombarded and annealed 〈111〉 surfaces of Ge by spectroscopic ellipsometry
Surface Science 0 North-Holland
96 (1980) 294-306 Publishing Company
AN INVESTIGATION
OF ION-BOMBARDED
AND ANNEALED (111)
SURFACES OF Ge BY SPECTROSCOPIC ELLIPSOMETRY
D.E. ASPNES and A.A. STUDNA Bell Laboratories, Murray Hill, NJ 07974, Received
20 August
USA
1979
_ Ion-bombarded and annealed ( 111) Ge surfaces, maintained in ultrahigh vacuum and characterized by standard LEED and Auger surface analysis techniques, are examined by spectroscopic ellipsometry over the energy range 1.5-6.0 eV. The bombardment and annealing process is found to yield highly reproducible ellipsometric spectra, with run-to-run and sample-tosample variations of the order of 0.2% in the peak value of cz. Accurate dielectric function spectra are obtained for cGe and for the amorphized overlayer formed by ion bombardment. The latter is shown to be 6 f 2% more dense than uhvevaporated material, independent of bombarding species. The damage depth exceeds significantly the projected range parameters of the nuclear limit of the Lindhard-Scharff-Schidtt theory for both Ne and Ar ions, although the E2’3 power law dependence on the ion energy is observed. Finally, the presence of -4 A of amorphous overlayer detected optically on a surface showing a 1 X 1 LEED pattern indicates reconstruction does not proceed uniformly, but by patches.
1. Introduction
In this paper, we discuss spectroscopic ellipsometric measurements on ion-bombarded and annealed Ge single crystals of (111) surface orientation, maintained in ultrahigh vacuum and characterized independently by LEED and Auger surface analysis techniques. The immediate objective is to study the optical response over an extended spectral range of a bulk, thin-film, and surface system whose properties have been established reasonably well be standard uhv methods. The long-term objective is to develop approaches to allow spectroscopic ellipsometry to be applied to the numerous technologically important interfaces involving transparent ambients where, for various reasons such as high ambient pressure or stability, the intrinsically more powerful electron spectroscopies cannot be used. Prerequisites to the successful optical analysis of heterogeneous bulk solids or of thin-film, interface, and surface systems include among others, accurate dielectric function data for the constituents in their pure bulk forms, methods of optically assessing bulk and surface morphology effects if samples are polycrystalline or surfaces are rough, and the development of systematic procedures for objectively determining parameters in simple model representations of complex physical sys294
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and annealed (Ill
)Ge surfaces
295
terns. Despite continuing effort, accurate dielectric function data for pure bulk materials generally are not available. Specifically, the tendency of metal surfaces to contaminate and of metals to form polycrystalline bulk aggregates make their fundamental optical properties exceedingly difficult to determine [ 11. Although a surprisingly large amount of microstructural information can be deduced from the spectral dependence of their pseudodielectric functions, as we have recently shown for Au [2], metals are not materials that are well adapted for the present work. The problem of optically characterizing rough surfaces, which does not directly concern us here, has been discussed elsewhere [3]. The modeling approach that we have developed [3,4] and will use to reduce the pseudodielectric function of the ionbombarded data is based on linear regression analysis [S] , and has also been discussed elsewhere. Briefly, it emphasizes the use of confidence limits to establish which model parameters are being determined by data and which are not, and also to prevent too many parameters from being used. We have chosen single-crystal Ge of (111) surface orientation as the ideal material for this investigation because it is monatomic, highquality material, it is readily available, its optical structure falls in a convenient energy range for spectroscopic ellipsometry, the surface is relatively stable in ultrahigh vacuum, and sharp 2 X 8 LEED patterns can be obtained with a modest amount of effort. The modest-effort characteristic shows that LEED is a useful probe of smd deviations from longrange perfection in this case, and thus is a suitable technique to be used to correlate with ellipsometric spectra.
2. Experimental All data were taken on 10 C2cm n-type Ge single crystals of (111) surface orientation. The samples were polished initially with Syton to provide specular, strainfree surfaces. These were mounted in a Varian ultrahigh vacuum station of base pressure 1 X 10 -lo Torr and with LEED and Auger surface analysis capabilities. A Varian ion-bombardment gun provided a rastered beam of Ne’ or Ar’ ions to achieve uniformity over the 5 X 5 mm2 central region used for ellipsometric measurements. Normal incidence bombardment avoided the possibility of introducing unintentional uniaxial character in the sample surface. The ion beam energy was continuously adjustable from 100-3000 eV. Dielectric function data were taken with a rotating-analyzer ellipsometer described in detail elsewhere [6]. The angle of incidence was 67.08”, and the spectral range was 1.5-6.0 eV. The data were corrected for the effect of optical activity in the quartz Rochon prisms [7].
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and annealed (1 I1 )Ge surfaces
3. Results and discussion 3. I. Production and characterization of reconstructed surfaces For the (111) Ge surface, we find that spectroscopic ellipsometry and LEED are approximately equivalently sensitive for surface characterization, Reproducible ellipsometric spectra for well-ordered surfaces, which corresponded to a peak e2 value of 29.55 + 0.05 at 4.2 eV and at a sample temperature of 36.0 + 0.2”C, were not obtained unless sharp 2 X 8 reconstructed-surface LEED patterns were also obtained. The converse was also observed to be true. Ten minutes of annealing at 620°C was required to obtain a good reconstruction, and the negligible background in the LEED patterns indicated that the major fraction of the surface consisted of large, atomically flat regions. Auger spectroscopy verified that contamination by foreign atoms was negligible. Surprisingly, bombardment and annealing produced reproducible data and sharp 2 X 8 LEED patterns only after a total fluence of the order of 5 X 1018 cm-* of 500 eV ions. With a yield of 0.5-l .O [8], this corresponds to the removal of about 1~ of material. The expected gradual optical deterioration of the sputtered surface and consequent degradation of the ellipsometric data did not occur. In fact, surfaces that had undergone repeated bombardment-annealing cycles and cumulative material removal of over 5 pm yielded the same reconstructed-surface spectra throughout. Although bombardment-annealing cycling resulted in a slow progressive increase in macroscopic scattering as observed qualitatively during alignment with a 6328 a He-Ne laser, optical microscopy showed this to originate from slip planes and thermal etch pits. These defects scatter light out of the specular beam and do not influence the ellipsometric data which originate at the atomically flat, specular regions between the macroscopic defects [9]. The ion-bombardment process itself apparently acts to smoothen these surfaces, as no evidence of the occasional scratches on the original surfaces could be found after long-term treatment. The mandatory removal of 1 pm of initial material fits rather well the thickness of the damage region estimated by the usual rule-of-thumb of 20 X the grit size of the abrasive used in the surface preparation. Once the 1 pm layer had been removed, reconstructed surfaces could be recovered simply by annealing at 620°C for 10 min. 3.2. Dielectric function of crystalline Ge The pseudodielectric function of a single-crystal Ge sample with a clean 2 X 8 reconstructed (111) surface, as calculated from spectroscopic data within the twophase model, is shown in fig. 1. Although the calculated spectra are influenced by modification of the dielectric response of the outer monolayer(s) of Ge due to the termination of the crystal lattice, this effect cannot be separated at present and consequently, we take these data to represent as accurately as currently possible the dielectric function of crystalline Ge (c-Ge) for subsequent data analysis.
D.E. Aspnes, A.A. Studna / Ion-bombarded
-
-lO-
Ge-
and annealed (111 )Ge surfaces
291
310K
-
THIS WORK
---
PHILIPP DASH-NEWMAN
E (ev)
Fig. 1. Dielectric function data for c-Ge as determined ellipsometrically by the Kramer+Kronig analysis of reflectance data (- - -, ref. [lo]).
(---,
this work)
and
Shown for comparison are dielectric function spectra calculated by Philipp [lo] from a Kramers-Kronig transformation of reflectance data to 21 eV with a suitable extrapolation to higher energy. These data have been corrected for the effect of a GeO* overlayer [lo]. The single datum is an e2 value calculated at 1.5 eV from the absorption measurements of Dash and Newman [ 111. Differences between the reflectance- and ellipsometry-determined spectra for e2 are of the order of 10% of the peak heights. For el, the reflectance data yield a higher peak because the corresponding e2 edge near 2.1 eV is steeper. Some differences, e.g., in the energy position of critical point structures, occur simply because the energy spacing between reflectance points is much larger than the 17 meV spacing between ellipsometric points. Thus the reflectance data cannot be expected to follow fine structure as accurately. Other differences probably relate to the different outer layers of the samples involved. The ellipsometric data were taken on atomically clean 2 X 8 reconstructed surfaces while the reflectance samples were covered by a thin layer of Ge02. The presence of any overlayer of polarizability less than that of the bulk reduces the peak value of e2 at 4.2 eV in both reflectance and ellipsometric calculations; it is possible that the former data were overcorrected for this film, or that the ellipsometric data are influenced to this extent by the 2 X 8 surface layer and associated selvedge region. The differences could be resolved - and the surface polarizability determined - if reflectance measurements were also made on 2 X 8 reconstructed
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D.E. Aspnes, A.A. Studna 1 Ion-bombarded
and annealed (1 II )Ge surfaces
surfaces. We plan ellipsometric measurements on (100) and (110) surfaces as a partial means of resolving these questions. In any case, the differences between data sets shown in fig. 1 are much less than for many previous c-Ge spectra reported in the literature. 3.3. Measurement precision and sample control In thin-film and interface applications, one deals with small differences between spectra that cannot be generated directly by modulation techniques. Thus overall stability and run-to-run reproducibility become important. To demonstrate the short-term stability of the uhv spectroscopic ellipsometer and the importance of sample parameter control, we show in fig. 2 the point-plotter output of the calculated difference between successive er spectra taken with 1 s averaging per data point on a sample with a 2 X 8 reconstructed surface. The spectra differ only in that the sample temperature was 25.2”C in one case and 36.O”C in the other. Thus fig. 2 shows a thermomodulation spectrum (de,/dT) AT for AT= 10.8”C. The structures at 2.1, 2.3, 3.0, and 4.2 eV correspond to the El, El t A,, Eb, and E2 transitions and are well known from previous modulation spectroscopy work [ 121 where T is modulated and the relative reflectance change (R-‘dR/dT) AT is measured directly by phase-sensitive detection. We obtain here the more fundamental change in the dielectric function without need for a Kramers-Kronig analysis, which also requires a knowledge of the dielectric function spectra.
l
-0.4 I 2
Ef I
1 3
I
I 4
I
I 5
I
E (ev) Fig. 2. Thermal modulation spectrum of Ge, calculated by direct subtraction ellipsometric spectra measured for sample temperatures 36.0 and 25.2”C.
of two sets of
D.E. Aspnes, A.A. Studna /Ion-bombarded
and annealed Cl 11 )Ge surfaces
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The scatter in these data over the high-sensitivity 2-5.5 eV range of the source and detector is about *O.OOS, compared to peak E values of about 30. The scatter increases at each end due to a decrease of sensitivity. Thus individual spectra have a short-term relative precision lAe/e 1 of about ?l X 10-4. From the general expression for the standard modulation spectrum AR/R in terms of Ae, the above is equivalent to about +4 X IO-’ in M/R. The peak values in fig. 2 correspond to AR/R values of about 4 X 10d3. The day-to-day precision, which includes also sample preparation variations, is +0.05 in the peak value of e2. To place this reproducibility in other contexts, we note that a change of 0.05 in e2 corresponds here to a change of 3 X 10e4 in the reflectance, or the growth of 0.2 A of a surface oxide, or by fig. 2 a temperature change of 2S”C. Thus the system can be used to determine any of these properties to within the given uncertainties. For submonolayer applications the single most important variable, not surprislingly, is sample preparation. But fig. 2 also shows temperature to be more important than is generally supposed. For this reason, our data are obtained on samples whose temperature is regulated to within +0.2”C, which gives the same order-ofmagnitude uncertainty in this case as an oxide thickness change of kO.01 a. 3.4, Ion bombardment and the amorphized Ge overlayer 3.4.1. Pseudodielectric function data Pseudodielectric function data of once-reconstructed (111) Ge samples for saturation Ar’ bombardment at different energies are shown in fig. 3, together with the reference (111) 2 X 8 spectrum. These data show typical changes due to the presence of an overlayer whose polarizability is generally less than that of the bulk. Similar results are obtained for saturation bombardment with Ne’, although these spectra are not shown explicitly. 3.4.2. Dielectric function and density of amolphized Ge The dielectric function of the amorphized Ge (a-Ge) overlayer can be obtained from the 1000 eV pseudodielectric function spectrum together with that for the (111) 2 X 8 sample within the standard three-phase model by making a suitable estimate for the overlayer thickness, d. In fact, d can be determined quite accurately (+3 A) for the 1000 eV bombardment data by minimizing the residual structure in the overlayer dielectric function near 2.1-2.3 eV. The results for both Ne’ and Ar’ bombardments, for which d values are 90 and 80 A, respectively, are shown in fig. 4. The agreement is excellent, showing that the overlayer dielectric function is well-determined, that the three-phase model is a good approximation, and that the dielectric properties of the amorphized overlayer are independent of the bombarding species. The residual structure near 2.1-2.3 eV is due to small straininduced changes in the dielectric properties of the c-Ge substrate that result from the bombardment process.
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I
I 3
I
2
and annealed (1 II Ge surfaces
I
I
I
4
I
I
5
E (ev) Fig. 3. Pseudodielectric at different energies.
function
spectra
of c-Ge after
saturation
bombardment
with Arf ions
The data for the amorphized overlayer are also compared in fig. 4 with equivalent data for an amorphous Ge film evaporated under ultrahigh vacuum conditions [13]. The spectra are the same, except for an amplitude scaling factor. Recalling that the dielectric function is defined in terms of a polarization per unit volume, it is qualitatively clear from fig. 4 that the amorphized overlayer is more dense and contains fewer voids than the evaporated material. A quantitative value for the density increase, and the density of the amorphized layer, can be obtained using the Bruggeman effective medium approximation (EMA) [ 141 and the measured density [ 13],4.73 + 0.05 g cmm3, of the evaporated material. A linear regression analysis using the volume void fraction, f,, as the single free parameter to relate the two data sets shows that the amorphized layer is 6 + 2% more dense than the evaporated material; that is, it has a density of 5.0 + 0.1 g cmm3. The uncertainties refer to 90% confidence levels calculated in the linear regression analysis. By comparison, the crystalline density is 5.36 g cmm3. Although closer to the ideal amorphous case, the amorphized material still shows a density deficit of 7 + 2% with respect to the crystal. A similar increase of density for amorphized Si relative to evaporated films has also been observed [ 151.
D.E. Aspnes, A.A. Studna /Ion-bombarded
and annealed
-.-EVAF!
20
2
3
4 E (ev)
301
(DON-
5
6
Fig. 4. A comparison between dielectric function spectra of c-Ge amorphized by bombardment with 1000 eV Ne+ and ArC ions. Also shown is a dielectric function spectrum of an amorphous Ge film formed by uhv evaporation (after ref. [ 131).
3.4.3. Damage depth versus bombardment species and energy The penetration depth of light for amorphized Ge is of the order of 100 a at the e2 peak, which is atso the order of magnitude of the thickness of the amorphized overlayers in fig. 3. Thus highly accurate thickness data can be obtained to investigate the dependence on bombardment species and energy. The spectra of fig. 3 were analyzed by linear regression techniques within the three-phase model, using as data the dielectric function spectra for the c-Ge substrate and a-Ge overlayer from figs. I and 4, respectively. The overlayer thickness d was used as the single free parameter. Results for a series of measurements using both Ne’ and Ar* ions are shown in fig. 5. The 90% confidence leveb in d are not shown since they did not exceed 1.5 a in any case. Thus the 90% confidence level values show that the three-phase model is an accurate representation of the actual physical situation, and consequently that the a-Ge-air and c-Ge-a-Ge interfaces are relatively sharp. The data are plotted as a function of the 213 power of the bombarding energy in accordance with the predicted variation in the nuclear (low-energy) limit of the Lindhard-Scharff-S&i&t (LSS) theory [16]. As indicated by the lines on the figure, the data follow rather closely the predicted behavior. For a quantitative comparison, we show also the projected range as determined by computer calculations 1171 based on the LSS theory. We note that the projected range, not total
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0
0.2
1 DAMAGE
(KeV)
I
I
and annealed (I I I Ge surfaces
0.4
0.6
I
’
I
0.0
’
I
’
DEPTH
a-Ge
ON
0.0
EXP
c-Ge
CALC
20
0
L 0
20
40 E2’3
60
80
100
(eVw3)
Pig. 5. Damage depth versus bombarding energy and species as determined from the pseudodielectric function data of fig. 3 and the c- and a-Ge data of figs. 1 and 4. Projected range predictions are also shown.
range, is the relevant quantity to use here. Fig. 5 shows that the calculated projected range falls far short of the observed damage depth, even though the E 2’3 behavior is obeyed rather well and the damage depth for a given energy for Ne exceeds that for Ar. This is not surprising in view of the strong dependence of the optical properties of c-Ge and other semiconductors on disorder, which can be simulated for example by extremely heavy doping. Because the range parameter simply reflects the most likely stopping position for an incident energetic particle, a more complete picture is obtained if the straggling length is also included, where the straggling length is the half-width of an assumed Gaussian distribution of the bombarding species. For Ne in Ge this is approximately 0.9 times the projected range, while for Ar it is 0.7 times the projected range. Taking into account the finite width of the implanted distribution and the sensitivity of the dielectric response of semiconductor crystals of any kind, it is not unreasonable to find the optically determined damage depth exceeding substantially the projected range of the bombarding species. The nature of the damage is most likely to be lattice disorder caused by disloca-
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tions propagating from the directly bombarded region towards the bulk. In combined photoluminescence and chemical etching experiments on similarly bombarded samples of the binary crystal GaAs, Kawabe et al. [18] found that point defects propagated thousands of Angstroms beyond the amorphized layer, whose thickness as estimated by Rutherford backscattering and enhanced chemical etching was similar to that found here for Ge. This type of disorder would be expected to produce more dense material than the void-containing amorphous films produced by sputtering or evaporation onto cold substrates, as we observe here directly from the dielectric function spectrum. The Rutherford backscattering measurements are not able to address this question since they are sensitive only to areal, and not volume, density. A more complete discussion will be given elsewhere. 3.4.4. Partial annealing Fig. 6 shows the dielectric function of an overlayer on a sample for which the annealing was terminated before a 2 X 8 reconstructed-surface LEED pattern was obtained. The sample, however, showed a 1 X 1 ordered LEED pattern from the substrate, indicating from the known sensitivity of LEED to surface condition a surface overlayer on at least part of the surface not more than one monolayer thick. The spectrum shown in fig. 6 was calculated from pseudodielectric function data of the partially annealed sample together with the c-Ge data shown in fig. 1, using the standard three-phase model. The thickness d = 4.4 A was determined by minimizing the amount of critical point structure in the overlayer spectrum.
(PARTIAL ANNEAL) -
-10
I
2
I
I
I
I
3
4
5
I
1
6
E (ev) Fig. 6. Dielectric function of overlayer of incompletely ( 111) surface, shown with that of aCe for comparison.
reconstructed
but atomically
clean
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A.A. Studna /Ion-bombarded
and annealed
cI II Ge surfaces
The dielectric function of the partially annealed overlayer is found to be in good agreement with that of a-Ge as shown in fig. 4. Of particular importance here is the 4.4 A effective thickness, which, if the overlayer were completely amorphous, would suppress the LEED response. Thus we conclude that the reconstruction of the surface region in this case has not progressed uniformly, but in patches. This is perhaps not surprising in view of the logical contradiction inherent in the terminoldamage”. The residual critical point structure in the dielectric ogy “uniform response of the overlayer could result from small shifts in the critical point energies of the substrate, but owing to its well-defined relationship to the c-Ge dielectric response in fig. 1, particularly around 4 eV, a more likely explanation is the composite (patchy) nature of the partially annealed overlayer.
4. Summary In this paper, we report results of an investigation of the dielectric response of c-Ge with clean annealed and amorphized (111) surfaces. The dielectric function of c-Ge with a reconstructed 2 X 8 surface is reproducible to 40.05 in the peak height of e2 for repeated ion bombardment-annealing cycles, showing ion bombardment and annealing to be an effective clean surface preparation technique for optical measurements as well as electron spectroscopic measurements. The importance of sample temperature control, and the run-to-run precision of the uhv scanning ellipsometer, has been demonstrated by obtaining the thermomodulation spectrum for Ge by subtracting dielectric function data measured at two different sample temperatures. Analysis of pseudodielectric function data for ion-bombarded surfaces allows us to obtain the dielectric function and density of amorphized Ge and to investigate quantitatively the nuclear (low-energy) limit of the LSS theory of ion-solid interactions. Finally, we show by analysis of data for partially reconstructed surfaces that the reconstruction takes place nonuniformly over the surface. The results demonstrate the power of the spectroscopic approach to uhv ellipsometry, and provide a necessary step in the link between interface analysis in uhv and more technologically relevant ambients.
Acknowledgment It is a pleasure to thank J.E. Rowe for critical appraisals and advice during the initial phases of the annealing and surface reconstruction part of this work.
References [l] See, for example, P. Rouard and A. Meessen, in: Progress in Optics, Vol. 15, Ed. E. Wolf (North-Holland,
Amsterdam,
1977) p. 77.
D.E. Aspnes, A.A. Studna /Ion-bombarded [2] [3] [4] [5] [6]
[7] [8] [9] [lo]
[II]
[ 121 [ 131 [14] [15]
[ 161 [ 171 [18]
and annealed (111 Ge surfaces
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D.E. Aspnes, E. Kinsbron and D.D. Bacon, Phys. Rev. B21 (1980) 3290. D.E. Aspnes, J.B. Theeten and F. Hottier, Phys. Rev. B20 (1979) 3292. D.E. Aspnes, J.B. Theeten and R.P.H. Chang, J. Vacuum Sci. Technol. 16 (1979) 1374. ES. Keeping, Introduction to Statistical Inference (Van Nostrand, Princeton, 1962) ch. 12. D.E. Aspnes and A.A. Studna, Appl. Opt. 14 (1975) 220; in: Optical Polarimetry Instrumentation and Applications, Vol. 112, Eds. R.M.A. Azzam and D.L. Coffeen (SPIE, Bellingham, WA, 1977) p. 62; Rev. Sci. Instr. 49 (1978) 291. D.E. Aspnes, J. Opt. Sot. Am. 64 (1974) 812. G.K. Wehner, General Mills Report 2309 (1962). M.D. Williams and D.E. Aspnes, Phys. Rev. Letters 41 (1978) 1667. H.R. Philipp, private communication. The original reflectance data are from H.R. Philipp and H. Ehrenreich, in: Semiconductors and Semimetals, Vol. 3, Eds. R.K. Willardson and A.C. Beer (Academic, New York, 1967) p. 93. W.C. Dash and R. Newman, Phys. Rev. 99 (1955) 1151. B. Batz, in: Semiconductors and Semimetals, Vol. 9, Eds. R.K. Willardson and A.C. Beer (Academic, New York, 1972) p. 315. T.M. Donovan, W.E. Spicer, J.M. Bennett and E.J. Ashley, Phys. Rev. B2 (1970) 397. D.A.G. Bruggeman, Ann. Physik (Leipzig) 24 (1934) 636. DE. Aspnes, G.K. Celler, J.M. Poate, G.A. Rozgonyi and T.T. Sheng, in: Proc. Symp. on Laser and Electron Beam Processing of Electronic Materials, Eds. C.L. Anderson, G.K. Celler and G.A. Rozgonyi, Vol. 80-l (Electrochem. Sot., Princeton, NJ, 1980) p. 414. J. Lindhard, M. Scharff and H.E. S&i&t, Mat.-Fys. Medd. Dan. Vid. Selsk. 33 (1963) 14. K. Winterbon, Ion Implantation Range and Energy Deposition Distributions, Vol. 2 (IFI/ Plenum, New York, 1975). M. Kawabe, N. Kanzaki, K. Masuda and S. Namba, Appl. Opt. 17 (1978) 2556.
Discussion A.N. Saxena (Data General Corporation): Now that you have such a nice set up to make dispersion measurements, do you plan to extend your measurements to other semiconductors and materials? For example, InSb? It will be very interesting to make measurements on InSb, because I made ellipsometer measurements of (~1, ~2) on it, and I showed that they were very different from Philipp and Ehrenreich’s numbers obtained from reflectance measurements (cf. A.N. Saxena, Appl. Phys. Letters (1965)). D. Aspnes: Yes, we’ve already looked at Si and plan also to work on III-V’s and metals as well. Thank you for your comment. Of all III-V’s InSb would be most easily cleaned without destroying the stoichiometry of the outer layers. 0. Hunderi (University of Trondheim): You assumed a three phase model with sharp boundaries. Would you not expect a transition region which was partly amorphized and could not this account for the higher polarizability. D.E. Aspnes: Yes, such an irregular boundary could result in an apparently higher polarizability. We checked for this possibility for Si by comparing dielectric function spectra for films amorphized by 100 eV Ar+ and by 40 keV As+ (for which the amorphized layer is effectively infinitely thick) and found the same E spectra in each case, which corresponded again to material more dense than evaporated amorphous Si. The small confidence limits on d values given here suggest that the cGe and a-Ge boundaries are relatively sharp, but the high-energy implantation, which would be conclusive, was not performed on Ge. N.M. Bashara (University of Nebraska): Comment: M.M. Ibrahim reported damage to a depth of 40 A for 400 eV argon ion bombardment. Question: was the sensitivity of ellip-
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sometric measurement to sputtering roughness due to some ellipsometric averaging, which as Azzam pointed out, explained sensitivity of etched and unetched metals? D.E. Aspnes: The absence of a LEED background and the reproducibility of the ellipsometric data for 2 X 8 reconstructed ( 111) surfaces both show that the sputtering roughness is not microscopic, but macroscopic. Macroscopic roughness scatters light out of the ellipsometer optics and does not influence the results for that reason (see ref. [9] above). The same process presumably applies to metals. B. Agius (Ecole Normale Superieure): Why do you say that spectroscopic ellipsometry gives more information than RBS, I mean RBS under channeling conditions? D.E. Aspnes: RBS gives areal densities as opposed to volume densities. That is, the number of scattered projectiles is proportional to the number of targets per unit area and the energy loss likewise. Thus, the dimension normal to the channeling direction does not enter. By contrast, the dielectric function is defined in terms of polarization per unit volume and therefore gives volume densities. The term “more” information is misleading; “complementary” is more appropriate. G.A. Bootsma (Twente University Technology): Did you determine the dependence of bombardment damage on the dose current density? D.E. Aspnes: No. All measurements were performed on surfaces that were bombarded to saturation. To a limited extent, no dependence was observed.
96 (1980) 294-306 Publishing Company
AN INVESTIGATION
OF ION-BOMBARDED
AND ANNEALED (111)
SURFACES OF Ge BY SPECTROSCOPIC ELLIPSOMETRY
D.E. ASPNES and A.A. STUDNA Bell Laboratories, Murray Hill, NJ 07974, Received
20 August
USA
1979
_ Ion-bombarded and annealed ( 111) Ge surfaces, maintained in ultrahigh vacuum and characterized by standard LEED and Auger surface analysis techniques, are examined by spectroscopic ellipsometry over the energy range 1.5-6.0 eV. The bombardment and annealing process is found to yield highly reproducible ellipsometric spectra, with run-to-run and sample-tosample variations of the order of 0.2% in the peak value of cz. Accurate dielectric function spectra are obtained for cGe and for the amorphized overlayer formed by ion bombardment. The latter is shown to be 6 f 2% more dense than uhvevaporated material, independent of bombarding species. The damage depth exceeds significantly the projected range parameters of the nuclear limit of the Lindhard-Scharff-Schidtt theory for both Ne and Ar ions, although the E2’3 power law dependence on the ion energy is observed. Finally, the presence of -4 A of amorphous overlayer detected optically on a surface showing a 1 X 1 LEED pattern indicates reconstruction does not proceed uniformly, but by patches.
1. Introduction
In this paper, we discuss spectroscopic ellipsometric measurements on ion-bombarded and annealed Ge single crystals of (111) surface orientation, maintained in ultrahigh vacuum and characterized independently by LEED and Auger surface analysis techniques. The immediate objective is to study the optical response over an extended spectral range of a bulk, thin-film, and surface system whose properties have been established reasonably well be standard uhv methods. The long-term objective is to develop approaches to allow spectroscopic ellipsometry to be applied to the numerous technologically important interfaces involving transparent ambients where, for various reasons such as high ambient pressure or stability, the intrinsically more powerful electron spectroscopies cannot be used. Prerequisites to the successful optical analysis of heterogeneous bulk solids or of thin-film, interface, and surface systems include among others, accurate dielectric function data for the constituents in their pure bulk forms, methods of optically assessing bulk and surface morphology effects if samples are polycrystalline or surfaces are rough, and the development of systematic procedures for objectively determining parameters in simple model representations of complex physical sys294
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)Ge surfaces
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terns. Despite continuing effort, accurate dielectric function data for pure bulk materials generally are not available. Specifically, the tendency of metal surfaces to contaminate and of metals to form polycrystalline bulk aggregates make their fundamental optical properties exceedingly difficult to determine [ 11. Although a surprisingly large amount of microstructural information can be deduced from the spectral dependence of their pseudodielectric functions, as we have recently shown for Au [2], metals are not materials that are well adapted for the present work. The problem of optically characterizing rough surfaces, which does not directly concern us here, has been discussed elsewhere [3]. The modeling approach that we have developed [3,4] and will use to reduce the pseudodielectric function of the ionbombarded data is based on linear regression analysis [S] , and has also been discussed elsewhere. Briefly, it emphasizes the use of confidence limits to establish which model parameters are being determined by data and which are not, and also to prevent too many parameters from being used. We have chosen single-crystal Ge of (111) surface orientation as the ideal material for this investigation because it is monatomic, highquality material, it is readily available, its optical structure falls in a convenient energy range for spectroscopic ellipsometry, the surface is relatively stable in ultrahigh vacuum, and sharp 2 X 8 LEED patterns can be obtained with a modest amount of effort. The modest-effort characteristic shows that LEED is a useful probe of smd deviations from longrange perfection in this case, and thus is a suitable technique to be used to correlate with ellipsometric spectra.
2. Experimental All data were taken on 10 C2cm n-type Ge single crystals of (111) surface orientation. The samples were polished initially with Syton to provide specular, strainfree surfaces. These were mounted in a Varian ultrahigh vacuum station of base pressure 1 X 10 -lo Torr and with LEED and Auger surface analysis capabilities. A Varian ion-bombardment gun provided a rastered beam of Ne’ or Ar’ ions to achieve uniformity over the 5 X 5 mm2 central region used for ellipsometric measurements. Normal incidence bombardment avoided the possibility of introducing unintentional uniaxial character in the sample surface. The ion beam energy was continuously adjustable from 100-3000 eV. Dielectric function data were taken with a rotating-analyzer ellipsometer described in detail elsewhere [6]. The angle of incidence was 67.08”, and the spectral range was 1.5-6.0 eV. The data were corrected for the effect of optical activity in the quartz Rochon prisms [7].
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3. Results and discussion 3. I. Production and characterization of reconstructed surfaces For the (111) Ge surface, we find that spectroscopic ellipsometry and LEED are approximately equivalently sensitive for surface characterization, Reproducible ellipsometric spectra for well-ordered surfaces, which corresponded to a peak e2 value of 29.55 + 0.05 at 4.2 eV and at a sample temperature of 36.0 + 0.2”C, were not obtained unless sharp 2 X 8 reconstructed-surface LEED patterns were also obtained. The converse was also observed to be true. Ten minutes of annealing at 620°C was required to obtain a good reconstruction, and the negligible background in the LEED patterns indicated that the major fraction of the surface consisted of large, atomically flat regions. Auger spectroscopy verified that contamination by foreign atoms was negligible. Surprisingly, bombardment and annealing produced reproducible data and sharp 2 X 8 LEED patterns only after a total fluence of the order of 5 X 1018 cm-* of 500 eV ions. With a yield of 0.5-l .O [8], this corresponds to the removal of about 1~ of material. The expected gradual optical deterioration of the sputtered surface and consequent degradation of the ellipsometric data did not occur. In fact, surfaces that had undergone repeated bombardment-annealing cycles and cumulative material removal of over 5 pm yielded the same reconstructed-surface spectra throughout. Although bombardment-annealing cycling resulted in a slow progressive increase in macroscopic scattering as observed qualitatively during alignment with a 6328 a He-Ne laser, optical microscopy showed this to originate from slip planes and thermal etch pits. These defects scatter light out of the specular beam and do not influence the ellipsometric data which originate at the atomically flat, specular regions between the macroscopic defects [9]. The ion-bombardment process itself apparently acts to smoothen these surfaces, as no evidence of the occasional scratches on the original surfaces could be found after long-term treatment. The mandatory removal of 1 pm of initial material fits rather well the thickness of the damage region estimated by the usual rule-of-thumb of 20 X the grit size of the abrasive used in the surface preparation. Once the 1 pm layer had been removed, reconstructed surfaces could be recovered simply by annealing at 620°C for 10 min. 3.2. Dielectric function of crystalline Ge The pseudodielectric function of a single-crystal Ge sample with a clean 2 X 8 reconstructed (111) surface, as calculated from spectroscopic data within the twophase model, is shown in fig. 1. Although the calculated spectra are influenced by modification of the dielectric response of the outer monolayer(s) of Ge due to the termination of the crystal lattice, this effect cannot be separated at present and consequently, we take these data to represent as accurately as currently possible the dielectric function of crystalline Ge (c-Ge) for subsequent data analysis.
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310K
-
THIS WORK
---
PHILIPP DASH-NEWMAN
E (ev)
Fig. 1. Dielectric function data for c-Ge as determined ellipsometrically by the Kramer+Kronig analysis of reflectance data (- - -, ref. [lo]).
(---,
this work)
and
Shown for comparison are dielectric function spectra calculated by Philipp [lo] from a Kramers-Kronig transformation of reflectance data to 21 eV with a suitable extrapolation to higher energy. These data have been corrected for the effect of a GeO* overlayer [lo]. The single datum is an e2 value calculated at 1.5 eV from the absorption measurements of Dash and Newman [ 111. Differences between the reflectance- and ellipsometry-determined spectra for e2 are of the order of 10% of the peak heights. For el, the reflectance data yield a higher peak because the corresponding e2 edge near 2.1 eV is steeper. Some differences, e.g., in the energy position of critical point structures, occur simply because the energy spacing between reflectance points is much larger than the 17 meV spacing between ellipsometric points. Thus the reflectance data cannot be expected to follow fine structure as accurately. Other differences probably relate to the different outer layers of the samples involved. The ellipsometric data were taken on atomically clean 2 X 8 reconstructed surfaces while the reflectance samples were covered by a thin layer of Ge02. The presence of any overlayer of polarizability less than that of the bulk reduces the peak value of e2 at 4.2 eV in both reflectance and ellipsometric calculations; it is possible that the former data were overcorrected for this film, or that the ellipsometric data are influenced to this extent by the 2 X 8 surface layer and associated selvedge region. The differences could be resolved - and the surface polarizability determined - if reflectance measurements were also made on 2 X 8 reconstructed
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surfaces. We plan ellipsometric measurements on (100) and (110) surfaces as a partial means of resolving these questions. In any case, the differences between data sets shown in fig. 1 are much less than for many previous c-Ge spectra reported in the literature. 3.3. Measurement precision and sample control In thin-film and interface applications, one deals with small differences between spectra that cannot be generated directly by modulation techniques. Thus overall stability and run-to-run reproducibility become important. To demonstrate the short-term stability of the uhv spectroscopic ellipsometer and the importance of sample parameter control, we show in fig. 2 the point-plotter output of the calculated difference between successive er spectra taken with 1 s averaging per data point on a sample with a 2 X 8 reconstructed surface. The spectra differ only in that the sample temperature was 25.2”C in one case and 36.O”C in the other. Thus fig. 2 shows a thermomodulation spectrum (de,/dT) AT for AT= 10.8”C. The structures at 2.1, 2.3, 3.0, and 4.2 eV correspond to the El, El t A,, Eb, and E2 transitions and are well known from previous modulation spectroscopy work [ 121 where T is modulated and the relative reflectance change (R-‘dR/dT) AT is measured directly by phase-sensitive detection. We obtain here the more fundamental change in the dielectric function without need for a Kramers-Kronig analysis, which also requires a knowledge of the dielectric function spectra.
l
-0.4 I 2
Ef I
1 3
I
I 4
I
I 5
I
E (ev) Fig. 2. Thermal modulation spectrum of Ge, calculated by direct subtraction ellipsometric spectra measured for sample temperatures 36.0 and 25.2”C.
of two sets of
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The scatter in these data over the high-sensitivity 2-5.5 eV range of the source and detector is about *O.OOS, compared to peak E values of about 30. The scatter increases at each end due to a decrease of sensitivity. Thus individual spectra have a short-term relative precision lAe/e 1 of about ?l X 10-4. From the general expression for the standard modulation spectrum AR/R in terms of Ae, the above is equivalent to about +4 X IO-’ in M/R. The peak values in fig. 2 correspond to AR/R values of about 4 X 10d3. The day-to-day precision, which includes also sample preparation variations, is +0.05 in the peak value of e2. To place this reproducibility in other contexts, we note that a change of 0.05 in e2 corresponds here to a change of 3 X 10e4 in the reflectance, or the growth of 0.2 A of a surface oxide, or by fig. 2 a temperature change of 2S”C. Thus the system can be used to determine any of these properties to within the given uncertainties. For submonolayer applications the single most important variable, not surprislingly, is sample preparation. But fig. 2 also shows temperature to be more important than is generally supposed. For this reason, our data are obtained on samples whose temperature is regulated to within +0.2”C, which gives the same order-ofmagnitude uncertainty in this case as an oxide thickness change of kO.01 a. 3.4, Ion bombardment and the amorphized Ge overlayer 3.4.1. Pseudodielectric function data Pseudodielectric function data of once-reconstructed (111) Ge samples for saturation Ar’ bombardment at different energies are shown in fig. 3, together with the reference (111) 2 X 8 spectrum. These data show typical changes due to the presence of an overlayer whose polarizability is generally less than that of the bulk. Similar results are obtained for saturation bombardment with Ne’, although these spectra are not shown explicitly. 3.4.2. Dielectric function and density of amolphized Ge The dielectric function of the amorphized Ge (a-Ge) overlayer can be obtained from the 1000 eV pseudodielectric function spectrum together with that for the (111) 2 X 8 sample within the standard three-phase model by making a suitable estimate for the overlayer thickness, d. In fact, d can be determined quite accurately (+3 A) for the 1000 eV bombardment data by minimizing the residual structure in the overlayer dielectric function near 2.1-2.3 eV. The results for both Ne’ and Ar’ bombardments, for which d values are 90 and 80 A, respectively, are shown in fig. 4. The agreement is excellent, showing that the overlayer dielectric function is well-determined, that the three-phase model is a good approximation, and that the dielectric properties of the amorphized overlayer are independent of the bombarding species. The residual structure near 2.1-2.3 eV is due to small straininduced changes in the dielectric properties of the c-Ge substrate that result from the bombardment process.
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and annealed (1 II Ge surfaces
I
I
I
4
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5
E (ev) Fig. 3. Pseudodielectric at different energies.
function
spectra
of c-Ge after
saturation
bombardment
with Arf ions
The data for the amorphized overlayer are also compared in fig. 4 with equivalent data for an amorphous Ge film evaporated under ultrahigh vacuum conditions [13]. The spectra are the same, except for an amplitude scaling factor. Recalling that the dielectric function is defined in terms of a polarization per unit volume, it is qualitatively clear from fig. 4 that the amorphized overlayer is more dense and contains fewer voids than the evaporated material. A quantitative value for the density increase, and the density of the amorphized layer, can be obtained using the Bruggeman effective medium approximation (EMA) [ 141 and the measured density [ 13],4.73 + 0.05 g cmm3, of the evaporated material. A linear regression analysis using the volume void fraction, f,, as the single free parameter to relate the two data sets shows that the amorphized layer is 6 + 2% more dense than the evaporated material; that is, it has a density of 5.0 + 0.1 g cmm3. The uncertainties refer to 90% confidence levels calculated in the linear regression analysis. By comparison, the crystalline density is 5.36 g cmm3. Although closer to the ideal amorphous case, the amorphized material still shows a density deficit of 7 + 2% with respect to the crystal. A similar increase of density for amorphized Si relative to evaporated films has also been observed [ 151.
D.E. Aspnes, A.A. Studna /Ion-bombarded
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3
4 E (ev)
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(DON-
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Fig. 4. A comparison between dielectric function spectra of c-Ge amorphized by bombardment with 1000 eV Ne+ and ArC ions. Also shown is a dielectric function spectrum of an amorphous Ge film formed by uhv evaporation (after ref. [ 131).
3.4.3. Damage depth versus bombardment species and energy The penetration depth of light for amorphized Ge is of the order of 100 a at the e2 peak, which is atso the order of magnitude of the thickness of the amorphized overlayers in fig. 3. Thus highly accurate thickness data can be obtained to investigate the dependence on bombardment species and energy. The spectra of fig. 3 were analyzed by linear regression techniques within the three-phase model, using as data the dielectric function spectra for the c-Ge substrate and a-Ge overlayer from figs. I and 4, respectively. The overlayer thickness d was used as the single free parameter. Results for a series of measurements using both Ne’ and Ar* ions are shown in fig. 5. The 90% confidence leveb in d are not shown since they did not exceed 1.5 a in any case. Thus the 90% confidence level values show that the three-phase model is an accurate representation of the actual physical situation, and consequently that the a-Ge-air and c-Ge-a-Ge interfaces are relatively sharp. The data are plotted as a function of the 213 power of the bombarding energy in accordance with the predicted variation in the nuclear (low-energy) limit of the Lindhard-Scharff-S&i&t (LSS) theory [16]. As indicated by the lines on the figure, the data follow rather closely the predicted behavior. For a quantitative comparison, we show also the projected range as determined by computer calculations 1171 based on the LSS theory. We note that the projected range, not total
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0
0.2
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0.4
0.6
I
’
I
0.0
’
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’
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a-Ge
ON
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EXP
c-Ge
CALC
20
0
L 0
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40 E2’3
60
80
100
(eVw3)
Pig. 5. Damage depth versus bombarding energy and species as determined from the pseudodielectric function data of fig. 3 and the c- and a-Ge data of figs. 1 and 4. Projected range predictions are also shown.
range, is the relevant quantity to use here. Fig. 5 shows that the calculated projected range falls far short of the observed damage depth, even though the E 2’3 behavior is obeyed rather well and the damage depth for a given energy for Ne exceeds that for Ar. This is not surprising in view of the strong dependence of the optical properties of c-Ge and other semiconductors on disorder, which can be simulated for example by extremely heavy doping. Because the range parameter simply reflects the most likely stopping position for an incident energetic particle, a more complete picture is obtained if the straggling length is also included, where the straggling length is the half-width of an assumed Gaussian distribution of the bombarding species. For Ne in Ge this is approximately 0.9 times the projected range, while for Ar it is 0.7 times the projected range. Taking into account the finite width of the implanted distribution and the sensitivity of the dielectric response of semiconductor crystals of any kind, it is not unreasonable to find the optically determined damage depth exceeding substantially the projected range of the bombarding species. The nature of the damage is most likely to be lattice disorder caused by disloca-
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tions propagating from the directly bombarded region towards the bulk. In combined photoluminescence and chemical etching experiments on similarly bombarded samples of the binary crystal GaAs, Kawabe et al. [18] found that point defects propagated thousands of Angstroms beyond the amorphized layer, whose thickness as estimated by Rutherford backscattering and enhanced chemical etching was similar to that found here for Ge. This type of disorder would be expected to produce more dense material than the void-containing amorphous films produced by sputtering or evaporation onto cold substrates, as we observe here directly from the dielectric function spectrum. The Rutherford backscattering measurements are not able to address this question since they are sensitive only to areal, and not volume, density. A more complete discussion will be given elsewhere. 3.4.4. Partial annealing Fig. 6 shows the dielectric function of an overlayer on a sample for which the annealing was terminated before a 2 X 8 reconstructed-surface LEED pattern was obtained. The sample, however, showed a 1 X 1 ordered LEED pattern from the substrate, indicating from the known sensitivity of LEED to surface condition a surface overlayer on at least part of the surface not more than one monolayer thick. The spectrum shown in fig. 6 was calculated from pseudodielectric function data of the partially annealed sample together with the c-Ge data shown in fig. 1, using the standard three-phase model. The thickness d = 4.4 A was determined by minimizing the amount of critical point structure in the overlayer spectrum.
(PARTIAL ANNEAL) -
-10
I
2
I
I
I
I
3
4
5
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1
6
E (ev) Fig. 6. Dielectric function of overlayer of incompletely ( 111) surface, shown with that of aCe for comparison.
reconstructed
but atomically
clean
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The dielectric function of the partially annealed overlayer is found to be in good agreement with that of a-Ge as shown in fig. 4. Of particular importance here is the 4.4 A effective thickness, which, if the overlayer were completely amorphous, would suppress the LEED response. Thus we conclude that the reconstruction of the surface region in this case has not progressed uniformly, but in patches. This is perhaps not surprising in view of the logical contradiction inherent in the terminoldamage”. The residual critical point structure in the dielectric ogy “uniform response of the overlayer could result from small shifts in the critical point energies of the substrate, but owing to its well-defined relationship to the c-Ge dielectric response in fig. 1, particularly around 4 eV, a more likely explanation is the composite (patchy) nature of the partially annealed overlayer.
4. Summary In this paper, we report results of an investigation of the dielectric response of c-Ge with clean annealed and amorphized (111) surfaces. The dielectric function of c-Ge with a reconstructed 2 X 8 surface is reproducible to 40.05 in the peak height of e2 for repeated ion bombardment-annealing cycles, showing ion bombardment and annealing to be an effective clean surface preparation technique for optical measurements as well as electron spectroscopic measurements. The importance of sample temperature control, and the run-to-run precision of the uhv scanning ellipsometer, has been demonstrated by obtaining the thermomodulation spectrum for Ge by subtracting dielectric function data measured at two different sample temperatures. Analysis of pseudodielectric function data for ion-bombarded surfaces allows us to obtain the dielectric function and density of amorphized Ge and to investigate quantitatively the nuclear (low-energy) limit of the LSS theory of ion-solid interactions. Finally, we show by analysis of data for partially reconstructed surfaces that the reconstruction takes place nonuniformly over the surface. The results demonstrate the power of the spectroscopic approach to uhv ellipsometry, and provide a necessary step in the link between interface analysis in uhv and more technologically relevant ambients.
Acknowledgment It is a pleasure to thank J.E. Rowe for critical appraisals and advice during the initial phases of the annealing and surface reconstruction part of this work.
References [l] See, for example, P. Rouard and A. Meessen, in: Progress in Optics, Vol. 15, Ed. E. Wolf (North-Holland,
Amsterdam,
1977) p. 77.
D.E. Aspnes, A.A. Studna /Ion-bombarded [2] [3] [4] [5] [6]
[7] [8] [9] [lo]
[II]
[ 121 [ 131 [14] [15]
[ 161 [ 171 [18]
and annealed (111 Ge surfaces
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D.E. Aspnes, E. Kinsbron and D.D. Bacon, Phys. Rev. B21 (1980) 3290. D.E. Aspnes, J.B. Theeten and F. Hottier, Phys. Rev. B20 (1979) 3292. D.E. Aspnes, J.B. Theeten and R.P.H. Chang, J. Vacuum Sci. Technol. 16 (1979) 1374. ES. Keeping, Introduction to Statistical Inference (Van Nostrand, Princeton, 1962) ch. 12. D.E. Aspnes and A.A. Studna, Appl. Opt. 14 (1975) 220; in: Optical Polarimetry Instrumentation and Applications, Vol. 112, Eds. R.M.A. Azzam and D.L. Coffeen (SPIE, Bellingham, WA, 1977) p. 62; Rev. Sci. Instr. 49 (1978) 291. D.E. Aspnes, J. Opt. Sot. Am. 64 (1974) 812. G.K. Wehner, General Mills Report 2309 (1962). M.D. Williams and D.E. Aspnes, Phys. Rev. Letters 41 (1978) 1667. H.R. Philipp, private communication. The original reflectance data are from H.R. Philipp and H. Ehrenreich, in: Semiconductors and Semimetals, Vol. 3, Eds. R.K. Willardson and A.C. Beer (Academic, New York, 1967) p. 93. W.C. Dash and R. Newman, Phys. Rev. 99 (1955) 1151. B. Batz, in: Semiconductors and Semimetals, Vol. 9, Eds. R.K. Willardson and A.C. Beer (Academic, New York, 1972) p. 315. T.M. Donovan, W.E. Spicer, J.M. Bennett and E.J. Ashley, Phys. Rev. B2 (1970) 397. D.A.G. Bruggeman, Ann. Physik (Leipzig) 24 (1934) 636. DE. Aspnes, G.K. Celler, J.M. Poate, G.A. Rozgonyi and T.T. Sheng, in: Proc. Symp. on Laser and Electron Beam Processing of Electronic Materials, Eds. C.L. Anderson, G.K. Celler and G.A. Rozgonyi, Vol. 80-l (Electrochem. Sot., Princeton, NJ, 1980) p. 414. J. Lindhard, M. Scharff and H.E. S&i&t, Mat.-Fys. Medd. Dan. Vid. Selsk. 33 (1963) 14. K. Winterbon, Ion Implantation Range and Energy Deposition Distributions, Vol. 2 (IFI/ Plenum, New York, 1975). M. Kawabe, N. Kanzaki, K. Masuda and S. Namba, Appl. Opt. 17 (1978) 2556.
Discussion A.N. Saxena (Data General Corporation): Now that you have such a nice set up to make dispersion measurements, do you plan to extend your measurements to other semiconductors and materials? For example, InSb? It will be very interesting to make measurements on InSb, because I made ellipsometer measurements of (~1, ~2) on it, and I showed that they were very different from Philipp and Ehrenreich’s numbers obtained from reflectance measurements (cf. A.N. Saxena, Appl. Phys. Letters (1965)). D. Aspnes: Yes, we’ve already looked at Si and plan also to work on III-V’s and metals as well. Thank you for your comment. Of all III-V’s InSb would be most easily cleaned without destroying the stoichiometry of the outer layers. 0. Hunderi (University of Trondheim): You assumed a three phase model with sharp boundaries. Would you not expect a transition region which was partly amorphized and could not this account for the higher polarizability. D.E. Aspnes: Yes, such an irregular boundary could result in an apparently higher polarizability. We checked for this possibility for Si by comparing dielectric function spectra for films amorphized by 100 eV Ar+ and by 40 keV As+ (for which the amorphized layer is effectively infinitely thick) and found the same E spectra in each case, which corresponded again to material more dense than evaporated amorphous Si. The small confidence limits on d values given here suggest that the cGe and a-Ge boundaries are relatively sharp, but the high-energy implantation, which would be conclusive, was not performed on Ge. N.M. Bashara (University of Nebraska): Comment: M.M. Ibrahim reported damage to a depth of 40 A for 400 eV argon ion bombardment. Question: was the sensitivity of ellip-
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sometric measurement to sputtering roughness due to some ellipsometric averaging, which as Azzam pointed out, explained sensitivity of etched and unetched metals? D.E. Aspnes: The absence of a LEED background and the reproducibility of the ellipsometric data for 2 X 8 reconstructed ( 111) surfaces both show that the sputtering roughness is not microscopic, but macroscopic. Macroscopic roughness scatters light out of the ellipsometer optics and does not influence the results for that reason (see ref. [9] above). The same process presumably applies to metals. B. Agius (Ecole Normale Superieure): Why do you say that spectroscopic ellipsometry gives more information than RBS, I mean RBS under channeling conditions? D.E. Aspnes: RBS gives areal densities as opposed to volume densities. That is, the number of scattered projectiles is proportional to the number of targets per unit area and the energy loss likewise. Thus, the dimension normal to the channeling direction does not enter. By contrast, the dielectric function is defined in terms of polarization per unit volume and therefore gives volume densities. The term “more” information is misleading; “complementary” is more appropriate. G.A. Bootsma (Twente University Technology): Did you determine the dependence of bombardment damage on the dose current density? D.E. Aspnes: No. All measurements were performed on surfaces that were bombarded to saturation. To a limited extent, no dependence was observed.