Gallium Arsenide (GaAs) - Courses

Gallium Arsenide (GaAs)
EDWARD D. PALIK
Naval Research Laboratory
Washington, D.C.
The optical constants of pure (semi-insulating) GaAs are derived from a
number of papers including the far-infrared reststrahlen work of Johnson
et al. [1], Kachare et al. [2], and Holm et at. [3]; the mid-IR work of
Cochran et at. [4]; the near-IR work of Pikhtin and Yas'kov [5]; the calorimetry
work of Christensen et al. [6]; the fundamental band gap work of
Casey et al. [7]; the visible-UV ellipsometry work of Theeten et al. [8]; the
UV reflection work of Philipp and Ehrenreich [9]; and the synchrotron
transmission work of Cardona et al. [10]. A smooth plot of the nand k data,
given in Fig. 2, is obtained from the data of Table II.
The measurements of Johnson et al. [1] to determine nand k were 300-K
transmission measurements of thin samples of resistivity 3.5 x 108 n cm. Slab
thickness was known to ± 1 %. The transmittance was measured to ± 5%
with a Beckmann IR-ll spectrometer system. Surface preparation was described
as optical polish. If this were a mechanical grit polish, then the surfaces
were damaged, as discussed by Holm and Palik [11]. The effect of a
damage layer thousands of angstroms thick can probably be neglected except
at the reststrahlen peak itself. The n data listed were obtained from a graph
of a calculated oscillator fit to the experimental points, the scatter of the
points being ± 0.02 from the fit. The k data listed were read directly off a
smooth-curve graph (no fit in this case). Similar less-detailed measurements
for k have been made by Stolen [12], and his 294-K data (as read from a
graph) are also listed for comparison.
In the reststrahlen region reflectivity data have been fitted by an oscillator
model of the form
'2 [ (n - Ik) = Coo 1 + 2 wl-wiJ
2 .
(1)
W T - W + Irw
used by Kachare et al. [2] and Holm et at. [3]. We averaged these parameters
to obtain W L = 292.1 cm - \ W T = 268.7 cm - \ r = 2.4 cm -1, and Coo = 11.0.
Surfaces were chemically polished to remove saw-cut and grinding damage.
The reference was an aluminum mirror whose reflectivity is given by Bennett
HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS ISBN 0-12·544420-6
429

432 Edward D. Palik
absolute reflectivity is quoted to ± 3%, which could account for much of the
differences between KK analysis, between two laboratories, or between KK
analysis and eIIipsometric measurements.
Except for the spectral regions in which the minimum deviation and interference-fringe
techniques are used, we are hard-pressed to quote n to better
than two significant figures. Things are even worse for k that is generally not
determined better than ± 30%. Physicists, who did most of the measurements
cited, were more interested in positions of peaks to identify vibrational
frequencies and interband transitions, so relative values of k were typically
good but absolute values varied as has been discussed.
The temperature dependence of n in the near IR between 5 and 20 /lm
has been found by Cardona [20] to be
(l/n)(dn/dT) = (4.5 ± 0.2) x 10- 5 (C- 1 ). (3)
Near strong absorption features like band edges and lattice vibrations, the
effects are no doubt even stronger. Data are usually quoted at 297 or 300 K,
which would mean a variation of a few units in the fourth decimal place.
Therefore, we cannot use this decimal place with confidence, although it is
sometimes quoted in Table II.
lt is clear that all samples probably have a native oxide in the form
of Ga 20 3 and AS 20 3 of '" 20-A thickness. This layer presents little or no
problems in the IR region but must be considered in the region above the
band gap of this mixed oxide ('" 5 eV). Theeten et at. [8] and Philipp and
Ehrenreich [9] prepared surfaces by chemical etching and polishing, but the
samples may have been exposed to air before being put into the inert gas
system or the vacuum system. Native oxides typically grow to their final
thickness in a few hours in air but grow rapidly at first exposure. Therefore,
we must assume that an oxide was growing on the samples. This may cause
uncertainties in the determination of k in the UV. Only work with cleaved
or evaporated surfaces in UHV would be free of oxides for a few hours.
REFERENCES
1. C. J. Johnson, G. H. Sherman, and R. Weil, Appl. Opt. 8, 1667 (1969).
2. A. H. Kachare, W. G. Spitzer, F. K. Euler, and A. Kahan, J App/. Phys. 45, 2938 (1974).
3. R. T. Holm, J. W. Gibson, and E. D. Palik, J. Appl. Phys. 48, 212 (1977).
4. W. Cochran, S. J. Fray, F. A. Johnson, J. E. Quarrington, and N. Williams, J. Appl. Phys.
Suppl. 32, 2102 (1961).
5. A. N. Pikhtin and A. D. Yas'koy, Sov. Phys. Semicond. 12,622 (1978); A. N. Pikhtin and
A. D. Yas'koy, Fiz. Tekh. Poluprovodn. 12, 1047 (1978).
6. C. P. Christensen, R. Joiner, S. K. T. Nieh, and W. H. Steier, J. Appl. Phys. 45, 4957 (1974).
7. H. C. Casey, D. D. Sell, and K. W. Wecht, J. App/. Phys. 46,250 (1975).
8. J. B. Theeten, D. E. Aspnes, and R. P. H. Chang, J. Appl. Phys. 49, 6097 (1978); J. B. Theeten,
D. E Aspnes, and R. P. H. Chang, priYate communication (1982).
9. H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).
10. M. Cardona, W. Gudat, B. Sonntag, and P. Y. Yu, in Proc. Int. Con! Phys. Semicond., 10th
Cambridge, 1970, p. 208. u.S. Atomic Energy Commission, Oak Ridge, Tennessee, 1970.

434 Edward D. Palik
eV
TABLE II
Values of nand k for Gallium Arsenide Obtained from Various References·
cm- 1
!lm n k
155 0.007999 0.0181 [10]
150 0.008266 0.0193
145 0.008551 0.0203
144 0.008610 0.0204
143 0.008670 0.0206
142 0.008731 0.0204
141 0.008793 0.0205
140 0.008856 0.0206
135 0.009184 0.0213
130 0.009537 0.0224
125 0.009919 0.0234
120 0.01033 0.0245
115 0.01078 0.0256
113 0.01097 0.0263
111 0.01117 0.0274
110 0.01127 0.0278
109 0.01137 0.0281
108 0.01148 0.0283
107 0.01159 0.0276
106 0.01170 0.0288
105 0.01181 0.0293
104 0.01192 0.0284
103 0.01204 0.0294
102 0.01215 0.0289
100 0.01240 0.0294
95 0.01305 0.0308
90 0.01378 0.0323
85 0.01459 0.0338
80 0.01550 0.0353
75 0.01653 0.0368
70 0.01771 0.0376
65 0.01907 0.0387
60 0.02066 0.0389
55 0.02254 0.0407
50 0.02480 0.0430
48 0.02583 0.0448
• The data of Philipp and 'Ehrenreich [9] given in Seraphin and Bennett [19] are
specified by the wavelength (in micrometers). However, the original data were given in
electron volts, and it is obvious that most of the n, k values were determined for energies
in whole numbers or tenths of a whole number. They were rounded off to three significant
figures and then given the wavelength listed in Seraphin and Bennett [19]. Sometimes
we list these wavelengths and then recalculate energy (in electron volts), thus producing
roundoff error in election volts. The reference is given at the beginning of a tabulation of
nand k, for example, and is understood to refer to all n's and k's below it until a new
reference appears in brackets. The value of k is frequently given as an exponent of 10.
This value of exponent is understood to refer to all k's below it in the table until a new
exponent appears or the number changes from 10- 2 to 10- 1 when a decimal only is used.

Gal li um Arsenide (GaAs)
TABLE II (Continued )
Gallium Arsenide
eV cm - ! J.lm n k
46 0.02695 0.0476
44 0.02818 0.0518
43 0.02883 0.0546
42 0.02952 0.0470
41 0.03024 0.0426
40 0.03 100 0.0426
38 0.03263 0.0452
35 0.03542 0.0513
30 0.04133 0.0648
29 0.04275 0.0683
28 0.04428 0.0740
27 0.04592 0.0785
26 0.04769 0.0872
25 0.04959 0.0986
24 0.05 166 0.115
23.5 0.05276 0.126
23 0.05391 1.037 [9, 19] 0.141
0.228 [9, 19]
22.5 0.05510 0.1 46 [ 10]
22 0.05636 1.043 0. 148
0.243 [9, 19]
21.5 0.05767 0.147 [ 10]
21 0.05904 1.058 0.162
0.245 [9, 19]
20.5 0.06048 0.164 [10]
20 0.06199 1.025 0.144
0.212 [9, 19]
19.5 0.06358 0.147 [ 10]
19 0.06526 0.981 0. 152
0.234 [9, 19]
18 0.06888 0.936 0.178 [10]
0.267 [9, 19]
17 0.07293 0.889 0.223 [10]
0.324 [9, 19]
16 0.07749 0.850 0.261 [10]
0.411 [9, 19]
15 0.08266 0.836 0.282 [ 10]
0.503 [9, 19]
14 0.08856 0.840 0.602
13 0.09537 0.864 0.709
12.0 0.1033 0.895 0.791
10.8 0.1148 0.923 0.881
10.0 0.1240 0.913 0.974
9.0 0.1378 0.901 1.1 36
8.0 0.1550 0.899 1.435
7.0 0.1771 1.063 1.838
435
(continued)

436 Edward D. Palik
eV
cm- 1
TABLE II (Continued)
Gallium Arsenide
lim n k
6.6 0.1879 1.247 2.047
6.3 0.1968 1.441 1.988
6.2 0.2000 1.424 1.976
6.0 48,390 0.2066 1.264 [8] 2.472 [8]
1.395 [9, 19] 2.048 [9, 19]
5.94 47,910 0.2087 1.287 [8] 2.523 [8]
5.90 47,590 0.2101 1.288 2.556
5.84 47,100 0.2123 1.304 2.592
5.80 46,780 0.2138 1.311 2.625
5.74 46,300 0.2160 1.321 2.673
5.70 45,970 0.2175 1.325 2.710
5.64 45,490 0.2198 1.339 2.772
5.60 45,170 0.2214 1.349 2.815
5.54 44,680 0.2238 1.367 2.885
5.50 44,360 0.2254 1.383 2.936
5.44 43,880 0.2279 1.410 3.019
5.40 43,550 0.2296 1.430 3.079
5.34 43,070 0.2322 1.468 3.181
5.30 42,750 0.2339 1.499 3.255
5.24 42,260 0.2366 1.552 3.384
5.20 41,940 0.2384 1.599 3.484
5.14 41,460 0.2412 1.699 3.660
5.10 41,130 0.2431 1.802 3.795
5.04 40,650 0.2460 2.044 3.992
5.00 40,330 0.2480 2.273 4.084
4.94 39,840 0.2510 2.654 4.106
4.90 39,520 0.2530 2.890 4.047
4.84 39,040 0.2562 3.187 3.898
4.80 38,710 0.2583 3.342 3.770
4.74 38,230 0.2616 3.511 3.574
4.70 37,910 0.2638 3.598 3.452
4.64 37,420 0.2672 3.708 3.280
4.60 37,100 0.2695 3.769 3.169
4.54 36,620 0.2731 3.850 3.018
4.50 36,290 0.2755 3.913 2.919
4.44 35,810 0.2792 4.004 2.715
4.40 35,490 0.2818 4.015 2.563
4.34 35,000 0.2857 3.981 2.368
4.30 34,680 0.2883 3.939 2.260
4.24 34,200 0.2924 3.864 2.132
4.20 33,880 0.2952 3.810 2.069
4.14 33,390 0.2995 3.736 2.001
4.10 33,070 0.3024 3.692 1.969
4.04 32,580 0.3069 3.634 1.935
4.00 32,260 0.3100 3.601 1.920
3.94 31,780 0.3147 3,559 1.907
3.90 31,460 0.3179 3.538 1.904

Gallium Arsenide (GaAs) 437
eV
cm- 1
TABLE II (Continued)
Gallium Arsenide
11m n k
3.84 30,970 0.3229 3.512 1.905
3.80 30,650 0.3263 3.501 1.909
3.74 30,160 0.3315 3.488 1.920
3.70 29,840 0.3351 3.485 1.931
3.64 29,360 0.3406 3.489 1.950
3.60 29,040 0.3444 3.495 1.965
3.54 28,550 0.3502 3.513 1.992
3.50 28,230 0.3542 3.531 2.013
3.48 28,070 0.3563 3.541 2.024
3.46 27,910 0.3583 3.553 2.036
3.44 27,750 0.3604 3.566 2.049
3.42 27,580 0.3625 3.580 2.062
3.40 27,420 0.3647 3.596 2.076
3.38 27,260 0.3668 3.614 2.091
3.36 27,100 0.3690 3.635 2.107
3.34 26,940 0.3712 3.657 2.123
3.32 26,780 0.3734 3.681 2.142
3.30 26,620 0.3757 3.709 2.162
3.28 26,450 0.3780 3.740 2.183
3.26 26,290 0.3803 3.776 2.207
3.24 26,130 0.3827 3.818 2.232
3.22 25,970 0.3850 3.871 2.260
3.20 25,810 0.3875 3.938 2.288
3.18 25,650 0.3899 4.023 2.307
3.16 25,490 0.3924 4.126 2.304
3.14 25,330 0.3949 4.229 2.270
3.12 25,160 0.3974 4.313 2.212
3.10 25,000 0.4000 4.373 2.146
3.08 24,840 0.4025 4.413 2.082
3.06 24,680 0.4052 4.439 2.029
3.04 24,520 0.4078 4.462 1.988
3.02 24,360 0.4105 4.483 1.961
3.00 24,200 0.4133 4.509 1.948
2.98 24,040 0.4161 4.550 1.952
2.96 23,870 0.4189 4.626 1.967
2.94 23,710 0.4217 4.755 1.960
2.92 23,550 0.4246 4.917 1.885
2.90 23,390 0.4275 5.052 1.721
2.88 23,230 0.4305 5.107 1.529
2.86 23,070 0.4335 5.102 1.353
2.84 22,910 0.4366 5.065 1.206
2.82 22,740 0.4397 5.015 1.088
2.80 22,580 0.4428 4.959 0.991
2.78 22,420 0.4460 4.902 0.912
2.76 22,260 0.4492 4.845 0.846
2.74 22,100 0.4525 4.793 0.789
(continued)

438 Edward D. Palik
eV
cm- 1
TABLE II (Continued)
Gallium Arsenide
pID n k
2.72 21,940 0.4558 4.741 0.739
2.70 21,780 0.4592 4.694 0.696
2.68 21,660 0.4626 4.649 0.659
2.66 21,450 0.4661 4.605 0.626
2.64 21,290 0.4696 4.567 0.595
2.62 21,130 0.4732 4.525 0.569
2.60 20,970 0.4769 4.492 0.539
2.58 20,810 0.4806 4.456 0.517
2.56 20,650 0.4843 4.423 0.497
2.54 20,490 0.4881 4.392 0.476
2.52 20,330 0.4920 4.362 0.458
2.50 20,160 0.4959 4.333 0.441
2.48 20,000 0.4999 4.305 0.426
2.46 19,840 0.5040 4.279 0.411
2.44 19,680 0.5081 4.254 0.398
2.42 19,520 0.5123 4.229 0.385
2.40 19,360 0.5166 4.205 0.371
2.38 19,200 0.5209 4.183 0.359
2.36 19,030 0.5254 4.162 0.347
2.34 18,870 0.5299 4.141 0.337
2.32 18,710 0.5344 4.120 0.327
2.30 18,550 0.5391 4.100 0.320
2.28 18,390 0.5438 4.082 0.308
2.26 18,230 0.5486 4.063 0.301
2.24 18,070 0.5535 4.045 0.294
2.22 17,910 0.5585 4.029 0.285
2.20 17,740 0.5636 4.013 0.276
2.18 17,580 0.5687 3.998 0.266
2.16 17,420 0.5740 3.983 0.257
2.14 17,260 0.5794 3.968 0.251
2.12 17,100 0.5848 3.954 0.245
2.10 16,940 0.5904 3.940 0.240
2.08 16,780 0.5961 3.927 0.232
2.06 16,610 0.6019 3.914 0.228
2.04 16,450 0.6078 3.902 0.223
2.02 16,290 0.6138 3.890 0.213
2.00 16,130 0.6199 3.878 0.211
1.98 15,970 0.6262 3.867 0.203
1.96 15,810 0.6326 3.856 0.196
1.94 15,650 0.6391 3.846 0.187
1.92 15,490 0.6458 3.836 0.183
1.90 15,320 0.6526 3.826 0.179
1.88 15,160 0.6595 3.817 0.173
1.86 15,000 0.6666 3.809 0.173
1.84 14,840 0.6738 3.799 0.168
1.82 14,680 0.6812 3.792 0.158
1.80 14,520 6.8888 3.785 0.151

Gallium Arsenide (GaAs) 439
eV
CID- 1
TABLE II (Continued)
Gallium Arsenide
/lID n k
1.78 14,360 0.6965 3.779 0.152
1.76 14,200 0.7045 3.772 0.134
1.74 14,030 0.7126 3.762 0.127
1.72 13,870 0.7208 3.752 0.118
1.70 13,710 0.7293 3.742 0.112
1.68 13,550 0.7380 3.734 0.105
1.66 13,390 0.7469 3.725 0.101
1.64 13,230 0.7560 3.716 0.097
1.62 13,070 0.7653 3.707 0.093
1.60 12,900 0.7749 3.700 0.091
1.58 12,740 0.7847 3.693 0.089
1.56 12,580 0.7948 3.685 0.087
1.54 12,420 0.8051 3.679 0.085
1.52 12,260 0.8157 3.672 0.083
1.50 12,100 0.8266 3.666 0.080
7.89 x 10- 2 [7]
1.49 12,020 0.8321 7.28
1.48 11,940 0.8377 6.86
1.47 11,860 0.8434 6.64
1.46 11,780 0.8492 6.28
1.45 11,690 0.8551 6.12
1.44 11,610 0.8610 5.68
1.435 11,570 0.8640 5.57
1.43 11,530 0.8670 5.72
1.425 11,490 0.8700 5.54
1.42 11,450 0.8731 2.71 x 10- 2
1.41 11,370 0.8793 5.95 x 10- 3
1.40 11,290 0.8856 3.6140 [5] 1.69 x 10- 3
1.39 11,210 0.8920 5.68 x 10- 4
1.38 11,130 0.8984 2.50
1.37 11,050 0.9050 1.33 x 10- 4
1.35 10,890 0.9184 3.5690
1.30 10,490 0.9537 3.5388
1.25 10,080 0.9919 3.5138
1.20 9,679 1.033 3.4920
1.15 9,275 1.078 3.4724
1.10 8,872 1.127 3.4546
1.05 8,469 1.181 3.4383
1.00 8,065 1.240 3.4232
0.95 7,662 1.305 3.4094
0.90 7,259 1.378 3.3965
0.85 6,856 1.459 3.3847
0.80 6,452 1.550 3.3737
0.75 6,049 1.653 3.3636
0.70 5,646 1.771 3.3543
0.65 5,243 1.907 3.3457
(continued)

440 Edward D. Palik
eV
cm- 1
TABLE II (Continued)
Gallium Arsenide
Jim n k
0.60 4,839 2.066 3.3378
0.55 4,436 2.254 3.3306
0.50 4,033 2.480 3.3240
0.45 3,629 2.755 3.3180
0.40 3,226 3.100 3.3125
0.35 2,823 3.542 3.3075
0.30 2,420 4.133 3.3027
0.29 2,339 4.275 3.3017
0.28 2,258 4.428 3.3008
0.27 2,178 4.592 3.2998
0.26 2,097 4.768 3.2988
0.25 2,016 4.959 3.2978
0.24 1,936 5.166 3.2968
0.23 1,855 5.391 3.2954
0.22 1,774 5.636 3.2946
0.21 1,694 5.904 3.2934
0.20 1,613 6.199 3.2921
0.19 1,532 6.526 3.2907
0.18 1,452 6.888 3.2891
0.17 1,371 7.293 3.2874
0.16 1,290 7.749 3.2854
0.15 1,210 8.266 3.2831
0.14 1,129 8.856 3.2803
0.1347 1,087 9.2 4.4 x 10- 7 [6]
0.13 1,048 9.537 3.2769
0.1239 1,042 9.6 6.1
0.12 967.9 10.33 3.2727
0.1169 943.4 10.6 7.6 x 10- 7
0.11 887.2 11.27 3.2671
0.100 806.5 12.40 3.2597 4.93 x 10- 6 [4]
0.098 790.4 12.65 1.61 x 10- 5
0.096 774.3 12.91 3.49
0.095 766.2 13.05 3.63
0.094 758.2 13.19 2.72
0.092 742.0 13.48 1.61
0.090 725.9 13.78 3.2493 1.64
0.088 709.8 14.09 2.24
0.086 693.6 14.42 2.40
0.084 677.5 14.76 2.11
0.082 661.4 15.12 2.16
0.080 645.2 15.50 3.2336 2.83
0.Q78 629.1 15.90 4.55
0.076 613.0 16.31 7.66
0.074 596.8 16.75 9.46 x 10- 5
0.073 588.8 16.98 1.00 x 10- 4
0.072 580.7 17.22 1.50
0.071 572.6 17.46 2.05

Gallium Arsenide (GaAs) 441
TABLE II (Continued)
Gallium Arsenide
eV em-I !lID n k
0.Q70 564.6 17.71 3.2081 2.32
0.069 556.5 17.97 6.00 x 10- 4
0.068 548.5 18.23 1.17 x 10- 3
0.067 540.4 18.51 2.59
0.066 532.3 18.79 4.18
0.0655 528.3 18.93 6.10
0.065 524.3 19.07 3.1886 8.27
0.0645 520.2 19.22 3.205 [2, 3] 6.27
0.064 516.2 19.37 4.85
0.0635 512.2 19.53 4.83
0.063 508.1 19.68 4.85
0.0625 504.1 19.84 4.23
0.062 500.1 20.00 4.17
0.0615 496.0 20.16 4.18
0.061 492.0 20.33 4.09
0.060 483.9 20.66 3.1609 [5] 3.45
0.0595 480.0 20.84 3.176 [2, 3] 3.18
0.059 475.9 21.01 3.19
0.058 467.8 21.38 3.57
0.057 459.7 21.75 3.157 4.50
0.0565 455.7 21.94 4.78
0.056 451.7 22.14 4.84
0.0555 447.6 22.34 4.97
0.055 443.6 22.54 5.32
0.054 435.5 22.96 3.126 4.56
0.053 427.5 23.39 3.68
0.0525 423.4 23.62 3.38
0.052 419.4 23.84 3.100 3.43
0.051 411.3 24.31 3.71
0.050 403.3 24.80 2.74
0.0495 399.2 25.05 3.058 2.07
0.049 395.2 25.30 2.07
0.0485 391.2 25.56 2.17
0.048 387.1 25.83 2.10
0.047 379.1 26.38 2.997 2.33
0.046 371.0 26.95 2.91
0.045 362.9 27.55 3.94
0.04463 360 27.78 2.913 6.50 [2, 3]
0.044 354.9 28.18 5.15 [4]
0.04339 350 28.57 2.851 8.40 [2, 3]
0.043 346.8 28.83 8.95 x 10- 3 [4]
0.04215 340 29.41 2.770 1.13 x 10- 2 [2, 3]
0.04092 330 30.30 2.659 1.59
0.03968 320 31.25 2.495 2.43
0.03906 315 31.75 2.380 3.14
(continued)

442 Edward D. Palik
eV
cm- 1
TABLE II (Continued)
Gallium Arsenide
)lm n k
0.03844 310 32.26 2.229 4.21
0.03782 305 32.79 2.020 6.02
0.03720 300 33.33 1.707 9.59 x 10- 2
0.03707 299 33.44 1.623 0.107
0.03695 298 33.56 1.529 0.122
0.03682 297 33.67 1.422 0.141
0.03670 296 33.78 1.298 0.166
0.03658 295 33.90 1.151 0.201
0.03645 294 34.01 0.975 0.257
0.03633 293 34.13 0.761 0.357
0.03620 292 34.25 0.536 0.552
0.03608 291 34.36 0.391 0.826
0.03596 290 34.48 0.323 1.09
0.03583 289 34.60 0.291 1.34
0.03571 288 34.72 0.275 1.57
0.03558 287 34.84 0.267 1.79
0.03546 286 34.96 0.266 2.01
0.03534 285 35.09 0.270 2.23
0.03521 284 35.21 0.278 2.46
0.03509 283 35.33 0.290 2.69
0.03496 282 35.46 0.307 2.94
0.03484 281 35.59 0.329 3.20
0.03472 280 35.71 0.358 3.48
0.03459 279 35.84 0.395 3.79
0.03447 278 35.97 0.443 4.14
0.03434 277 36.10 0.506 4.52
0.03422 276 36.23 0.592 4.97
0.03409 275 36.36 0.713 5.49
0.03397 274 36.50 0.890 6.12
0.03385 273 36.63 1.17 6.91
0.03372 272 36.76 1.64 7.94
0.03360 271 36.90 2.56 9.32
0.03348 270 37.04 4.66 11.0
0.03341 269.5 37.10 6.63 11.6
0.03335 269 37.17 9.30 11.3
0.03329 268.5 37.24 11.6 9.37
0.03323 268 37.31 12.4 6.74
0.03317 267.5 37.38 12.0 4.66
0.03310 267 37.45 11.3 3.30
0.03304 266.5 37.52 10.6 2.43
0.03298 266 37.59 9.90 1.87
0.03286 265 37.74 8.87 1.20
0.03273 264 37.88 8.12 0.844
0.03261 263 38.02 7.55 0.629
0.03248 262 38.17 7.11 0.489
0.03236 261 38.31 6.76 0.393
0.03224 260 38.46 6.47 0.323

Gallium Arsenide (GaAs)
eV
cm - 1
TABLE II (Continued)
Gallium Arsenide
/lm n k
0.03 162 255 39.22 5.57 0.t53
0.03100 250 40.00 5.08 9.02 x 10- 2
0.02976 240 41.67 4.57 4.26
0.02852 230 43.48 4.30 2.49
0.02728 220 45.45 4.13 1.63
0.02604 210 47.62 4.02 U S x 10- 2
0.02480 200 SO.OO 3.93
3.87 [1 ]
8.49 x 10 - 3
0.02356 190 52.63 1.09 x 10 - 2 [1 2]
0.02232 180 55.56 1.22
0.02108 170 58.82 1.25 x 10- 2
0.02066 166.7 60 3.77 [2, 3] 3.89 x 10- 3 [2, 3]
3.74 [ 1] 6.92 x 10- 3 [1 ]
0.01984 160 62.S0 US x 10- 2 [12J
0.01860 150 66.67 6.4 x 10- 3
0.0177 1 142.9 70 3.71 [ 2, 3J
3.68 [IJ
3.79 [ 1 J
0.01736 140 71.43 5.0 [12J
0.01612 130 76.92 4.4
0.01550 125 80 3.681 [ 2, 3J 1.84 [2, 3J
3.65 [1 J 3.18 [IJ
0.0 1488 120 83.33 3.9 [ 12J
0.01378 111.1 90 3.662 [2, 3]
3.635 [1 J 2.86 [1 J
0.01364 110 90.91 3.6 [12J
0.01240 100 100 3.650 [2, 3J 3.6
3.625 [ IJ 2.78 [ IJ
0.01116 90 11 1.1 3.8 [1 2J
0.009919 80 125.0 4.2
0.008679 70 142.9 3.5
0.008266 66.67 150 3.623 [ 2, 3J
3.62 [IJ
2.14[IJ
0.007439 60 166.7 2.1 [ 12J
0.006199 50.00 200 3.615 [ 2, 3J
3.61 [ IJ
1.8 [ 12J
0.004959 40 250.0 1.4
0.004133 33.33 300 3.611 [2, 3]
3.60 [1]
0.003720 30 333.3 l.l
0.003 100 25 400 1.2
0.002480 20 500 3.607 [ 2, 3J 1.3
0.001 860 15 667 1.2
0.001240 10 1000 3.606
443

446 A. Borghesi and G. Guizzetti
in concentrated bromine. In the other cases no description of the surface
treatment was given.
The R values in the infrared from various labs agree to within the experimental
uncertainty. It was determined that differences in the free-carrier concentration
had no effect on R. The n values for A :::::: 50 Jim from Parsons and
Coleman [3] and Abagyan et al. [4] present a difference of 0.28% at A =
50 Jim, which lowers to 0.2% at A = 1000 Jim. In Abagyan et al. [4] the error
fln in n, resulting from the measurement of the sample thickness and of wavelength
A, is quoted not exceeding 0.005, while in Parsons and Coleman [3] n
is quoted with four decimal places and its values are those reported in Table
IV for 50 Jim S; A S; 400 Jim.
Parsons and Coleman [3] fit the infrared data and the accurate n data
from Bond [9] and Nelson and Turner [13] in the 0.5-4.0-Jim range by
using for the complex dielectric function g the following form proposed by
Barker [2]:
i.e., a classical-oscillator equation, where Si' vf, and Yi are the osciIIator
strength, restoring force, and linewidth, respectively. The second term in Eq.
(1) represents the electronic contribution and the third one the lattice contribution
with frequency-dependent damping. The fit parameters, given in
Table III, are the same used by Barker [2] to fit IX, R, and Raman data near
the transverse optic mode, except So, which had to be increased from 2.01 to
2.056 for best fit. The net result of this fit is that the refractive index of GaP
can be calculated from Eq. (1) to an accuracy somewhat better than four
figures from microwave to visible frequencies. In particular, in the range
30-200 Jim the fit agrees with the experimental n to a few units in the fourth
decimal place (±0.03%) and yields the precise value eo = 11.147 for the static
relative dielectric constant. In Table IV we have labeled this fit with nf for
the data of Barker [2].
Also, Pikhtin et al. [7] proposed an analytic dispersion relationship for
n in the 0.5-1000-Jim spectral range; it has only six parameters and is simpler
than Eq. (1) but less accurate (±0.8%). However, it is useful to report it,
since by means of a relation in Pikhtin et al. [7] it has been possible also
to fit spectra at 105 K. The fit parameters are from Pikhtin et al. [7].
For frequencies above or below V T == vo, the k spectrum has considerable
structure and values much higher than those predicted from Eq. (1).
Since the same bands are observed in compensated and uncompensated
samples, they are attributed to absorption by the lattice (combination bands)
[1, 2]. However, the IX spectra from different labs are in qualitative but not
in quantitative agreement. In the 12-20-Jim region we have tabulated the

Gallium Phosphide (GaP) 447
data from Pikhtin and Yas'kov [15] because the n-type sample was monocrystalline,
not intentionally doped, with the lowest carrier concentration
(1.15 x 10 17 cm- 3 ). Besides, T spectra were obtained with a double-beam
spectrophotometer, and R was checked against accurate measurements of n.
Near V T the reported values (labeled kr) were obtained from Eq. (1).
As for the 4-23-pm range, Table IV contains experimental values of n
deduced from the positions of interference peaks in T [5,7J. The thickness
of the samples and the interference order were accurately determined by
comparing, in the 0.5-4-pm range, the results obtained with this method and
with the more precise results obtained by using the prism method. The data
from Abagyan et at. [5] and Pikhtin et at. [7] agree to within the 0.1 %, with
an error [7] of ±0.2% at 4 pm and of ±0.47% at 23 pm. The samples were
n type, undoped, and high resistivity (N < 5 x 10 16 cm - 3). Measurements
performed on low-resistivity samples, doped both n- and p-type up to 1.7 X
10 18 cm - 3 have shown that for )" :;::: 3-pm doping reduces n [5, 7]. For this
reason we have disregraded older data for n [22, 23] that are '" 2% lower.
The absorption coefficient between 1 and 12 pm is free-carrier-like; it typically
increases with wavelength and with free-carrier concentration. Besides,
all the n-type samples show a broad absorption band in the 1-4-pm region
that does not occur in p-type material. In this region there are many measurements
of a [8, 12, 15] on crystals doped with different impurities and
with carrier densities ranging from 10 17 to 10 18 cm - 3. We have tabulated
those from Pikhtin and Yas'kov [15] on the basis of the same reasons that
determined the choice in the 12-20-pffi region.
In the 0.53-4-pm range, where GaP is nearly transparent, n measurements
were carried out by the method of prism minimum deviation [7, 9, 13] and
by interference spacing [11] at 2.24 eV (0.5536 pm) and 2.62 eV (0.4733 pm).
The scattering of n data from different authors is within ± 0.0025. In Pikhtin
et at. [7] the absolute values of n were determined to within ±0.0025; in
Bond [9J n was measured to the fourth decimal. In Nelson and Turner [13J
the uncertainty in the individual value was ±0.0002; however, the value
obtained for different prisms differed by substantially more than this. The
differences are believed to be real and to reflect the variation that can be
expected from different samples of GaP. To include the value for all of the
prisms, an uncertainty of ±0.0012 would have to be assigned to the n values
from 0.545 to 0.70 pm in Table IV. These variations were not correlated with
the level of doping, which varied from no intentional doping to 10 18 cm - 3
with the type of dopant (Te, Sn, Zn) or the method of crystal growth (highpressure
boat growth, floating zone, or solution growth).
The intrinsic electronic absorption edge of single crystals was presented
and analyzed by Spitzer et al. [8] at 300 K, by Dean and Thomas [10J between
1.6 and 300 K, and by Pikhtin and Yas'kov [14J between 4.2 and
500 K. The results agree qualitatively, although there is some quantitative
difference. In Table IV we have reported in the 0.54-0.57-pm range the values
from Dean and Thomas [lOJ that are a little lower than those reported

448 A. Borghesi and G. Guizzetti
by Spitzer et al. [8J and Pikhtin and Yas'kov [14J and were obtained with
exceptionally perfect single crystals grown by a modified wet-hydrogen
transport process. All crystals had very high resistivities and three different
thicknesses (0.0212,0.0724, and 0.362 cm).
The 0.8-0.2-/lm region straddling the fundamental band gap has been
measured more recently by ellipsometry on surfaces containing native oxides
that are mathematically "removed" in the analysis, or samples are chemically
polished to remove this oxide and then put into an inert atmosphere while
the measurement of the ellipsometric parameters !/J and d are performed
[24]. We have included these values and at the ends of this spectral region
have overlapped other data for comparison.
The optical properties from the fundamental absorption edge (0.53 /lm)
to about 0.08 pm can be determined by KK analysis of normal-incidence
reflectance data. The R data between 0.53 and 0.21 /lm obtained with a sensitive
double-beam spectrophotometer by Stokowski and Sell [19J provide
a considerable improvement in sensitivity over the older measurements reported
by Philipp and Ehrenreich [16J and Seraphin and Bennett [23]. The
samples used in Stokowski and Sell [19J were grown by the Czochralski
method, were sliced parallel to a {111} face, and a weak ( '" 0.2%) brominemethanol
solution was used as a polishing etch. The absolute-reflectance values
were accurate to within ± 3% of the reflectivity. The data were about
10% higher than those in Philipp and Ehrenreich [16J, in agreement within
1% with those calculated from n at 0.4733 /lm as measured by Dean et al.
[11]. In the 0.21-0.08-/lm range no other R data are available except those
from Philipp and Ehrenreich [16].
Absorption and !"eflection measurements in the 0.08-0.03-/lm range [18,
20J and only absorption measurements in the 0.08-0.008-/lm range [17J
were performed with synchrotron radiation and with a typical resolution of
2 A over the whole spectral range. The crystalline samples for transmission
were obtained by flash evaporation and samples of at least three different
thicknesses between 500 and 1500 A were used. The thicknesses were determined
with a Tolansky interferometer with an accuracy of about 10% and
also during evaporation with a calibrated quartz-crystal monitor. The absolute
values determined for the absorption coefficient were affected by an
error of less than 20%, which arose mainly from uncertainties in the thicknesses.
The R measurements [20J were performed under nearly normal incidence
[15J on polished bulk samples, etched in bromine-methanol solution.
Since the incoming and reflected intensities were not determined simultaneously,
no accurate absolute values of R were obtained (± 50%); therefore
the measured reflectivities were scaled so as to coincide around the first
maximum at 0.059 /lm with the ones calculated by the KK analysis transforms
from II data. Some discrepancies between scaled Rand R from KK
analysis may be due to a structural difference between the thin films used
to measure T and the bulk samples for R. Also, there may be some influence
of the surface treatment and of light scattering. Larger discrepancies be-

Gallium Phosphide (GaP) 449
tween the a experimental data from Cardona et al. [17, 18] and the a values
obtained from KK processing of early R data [16] can be attributed to
R-limited range of R spectra and to the inadequacy of the conventional gasdischarge
spectroscopic sources; in fact, hot-cathode argon lamps have typical
separation of about 1 e V between adjacent lines, equal to the expected
spin-orbit splitting of core levels (0.53 e V for Ga) and to separation between
peaks in the density of conduction states.
In Table IV nand k values in the 0.44-0.08-J-lm range have been obtained
by KK transform on R spectra from Philipp and Ehrenreich [16J and
Stokowski and Sell [19J, extended to shorter wavelengths with the data of
Gudat et al. [20] and longer wavelengths (visible and infrared) with those of
Kleiman and Spitzer [lJ, Giehler and lahne [6J, and Bond [9]. The results
are in fair agreement with the dielectric function ellipsometrically determined
between 0.36 and 0.31 J-lm [21].
REFERENCES
1. D. A. Kleinman and W. G. Spitzer, Phys. Rev. lIS, 110 (1960).
2. A. S. Barker, Jr., Phys. Rev. 165,917 (1968).
3. D. F. Parsons and P. D. Coleman, App/. Opt. 10, 1683 (1971).
4. S. A. Abagyan, G. A. Ivanov, Y. E. Shanurin, and V. I. Amosov, Sov. Phys. Semicond. 5, 889
(1971).
5. S. A. Abagyan, G. A. Ivanov, A. P. Izergin, and Y. E. Shanurin, Sov. Phys. Semicond. 6, 985
(1972).
6. M. Giehler and E. Jahne, Phys. Status Solidi B 73,503 (1976).
7. A. N. Pikhtin, V. T. Prokopenko, and A. D. Yas'kov, Sov. Phys. Semicond. 10, 1224 (1976).
8. W. G . Spitzer, M. Gershenzon, C. 1. Forsch, and D. F. Gibbs, J. Phys. Chem. Sol. 11, 339
(1959).
9. W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
10. P.1. Dean and D. G. Thomas, Phys. Rev. 150,690 (1966).
11. P.1. Dean, G. Kaminsky, and R. B. Zetterstrom, J. Appl. Phys. 3S, 3551 (1967).
12. A. D. Remenyuk, L. G. Zabelina, Yu. 1. Ukhanov, and Y. V. Shmartzev, Sov. Phys. Semicond.
2, 557 (1968).
13. D. F. Nelson and E. H. Turner, J. App/. Phys. 39, 3337 (1968).
14. A. N. Pikhtin and D. A. Yas'kov. Sov. Phys. Solid State 11, 455 (1969).
15. A. N. Pikhtin and D. A. Yas'kov. Phys. Status Solidi 34, 815 (1969).
16. H. R. Philipp and H. Ehrenreich, in "Semiconductors and Semimetals" (R. K. Willardson
and A. C. Beer, eds.), Vol. 3, Chapter 4. Academic, New York, 1967.
17. M. Cardona, W. Gudat, B. Sonntag, and P. Y. Yu, Proc. Int. ConI Phys. Semicond. Cambridge,
1970, p. 208. U.S. Atomic Energy Commission, Oak Ridge, Tennessee, 1970.
18. M. Cardona, W. Gudat, E. E. Koch, M. Skibowski, B. Sonntag, and P. Yu, Phys. Rev.
Lett. 25, 659 (1970).
19. S. E. Stokowski and D. D. Sell, Phys. Rev. B 5, 1636 (1972).
20. W. Gudat, E. E. Koch, P. Y. Yu, M. Cardona, and C. M. Penchina, Phys. Status Solidi
B 52,505 (1972).
21. G. Jungk, Phys. Status Solidi B 67,85 (1975).
22. H. Welker, J. Electron. I, 181 (1955).
23. B. O. Seraphin and H. E. Bennett, in "Semiconductors and Semi metals" (R. K. Willardson
and A. C. Beer, eds.), Vol. 3, p. 219. Academic, New York, 1967.
24. D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983); D. E. Aspnes and A. A. Studna,
private communication (1982).

466 Roy F. Potter
cut as polished prisms having included angles ranging between 5 and 18°.
The angle of minimum deviation was measured to obtain the refractive index.
Data of Icenogle et al. [4] at 297 K and some data of Edwin et al. [5] at
25°C, originally given in tabular form, are listed in Table V. The tabulated
data are plotted in Fig. 4.
The precision of the data of Icenogle et al. [4] was such that Barnes and
Piltch [6] used them as a basis for evaluating the coefficients of a temperaturedependent,
Sellmeier-type equation
n 2 = A + BA 2 /(J.? - C) + DA 2 /(A 2 - E).
Using the temperature-dependent values of n, they found the following
values for the coefficients:
A = -6.040 x 1O- 3 T + 11.05128,
B = 9.295 x 1O- 3 T + 4.00536,
C = -5.392 x 1O- 4 T + 0.5999034,
D = 4.151 x 1O- 4 T + 0.09145,
E = 1.51408T + 3426.5.
We have evaluated this expression for "room temperture" of 18°C (291 K),
over a large infrared wavelength range, and these values are included in
Table V. Some comparison with the results from the several experiments
outlined here can be made in the table. The Sellmeier equation represents
the accurate values for high-grade optical-quality germanium within 0.025%,
or better, over the infrared spectral range 2.5-14 p.m and can be extrapolated
to 2.0 and 40 p.m.
Many more measurements have been reported for this spectral range, but
in most cases the specimens were thin films, amorphous material, or heavily
doped. Evaporated films do not, in general, have properties representative
of bulk material, so such results are applicable only to material evaporated
or sputtered by a given recipe. Li [7] tabulates most such measurements
that have appeared in the literature in the past half-century. Li [7] also gives
a table of recommended values for the infrared at various temperatures.
In the infrared spectral region there are two contributions to the intrinsic
absorption properties of germanium. When the infrared radiation field interacts
with the crystal lattice, it is described as a photon-phonon interaction.
Since selection rules include the conservation of energy and wave vector or
momentum, the spectrum will include features related to the photon excitation
of multiple phonons. Such "phonon" bands have been observed for Ge.
Collins and Fan [8] reported absorption coefficients for phonon bands for
300 K. These have been read from a graph and are listed in Table V. Values
of Lax and Burstein [9] are comparable. More recently, Aronson et al. [10]
have measured the absorption coefficient for high-resistivity Ge ( '" 50 n em)
at 300 K. They used samples of different thickness measuring the transmit-

468 Roy F. Potter
[19] are listed in Table V. Room temperature was not stated. Archer [20]
also measured the optical properties over a reduced spectral range with less
spectral detail. Cardona et al. [21] prepared crystalline and amorphous Ge
films on heated and room-temperature KCI substrates, respectively. Samples
were floated off and picked up with a copper mesh. Transmission measurements
were done with synchrotron radiation. The data in Table V were read
from a graph. Room temperature was not stated.
Lukirskii et al. [22] have measured the unpolarized reflectance for Ge as
a function of angle of incidence at four x-ray wavelengths (since e < 1, this
gives a type of external attenuated total reflection). Samples were deposited
on glass substrates. Room temperature was not specified. Note that the angles
as given in Lukirskii et al. [22] are grazing angles, i.e., nl2 -
0.41 flm (1.5-3eV). When the extinction coefficient is low, the agreement in
n between the two sets is quite good (better than 0.25% for 0.83 flm > A >
0.74 flm). As k becomes larger, the discrepancy increases to about 1% at 2 eV
and 4% at 3 eV. At the longer wavelengths Archer's data [20] are about 4%
below those of Aspnes and Studna [19], coming into reasonable agreement
(less than 1% difference) for 0.54 flm > A > 0.36 flm. Thus, the data of Aspnes
and Studna [19] for 0.82 flm > A > 0.2 flm appear to be the best choice for
refractive-index values. Data of Philipp and Taft [17] appear to be too low.
In the spectral region of interband transitions the extinction coefficient
becomes quite large (k > 4), corresponding to absorption coefficients of the
order of 10 6 cm - 1. Reflectance-type measurements must be used. However,
some overlap with transmittance measurements exists for comparison. Measurements
of Dash and Newman [15] extend to 0.69 flm, which permits
comparison with Potter [18J as well as with Aspnes and Studna [19]. The
former appears to be low by about a factor of 2, whilte the agreement with
the latter is within 10-20%, which, given sample treatment and technique
differences, must be considered good. As k becomes larger, Potter's data [18J
come closer to agreeing with those of Aspnes and Studna [19]. For 0.62 flm >
A> 0.4 flm, Potter's data [18J are consistently larger than the data of Aspnes
and Studna [19J by 10-20%. Again, it seems that the data of Aspnes and
Studna [19J would be the choice for values of k.
For values of n overlap regions occur for the data of Briggs [1], Potter
[18J, and the Sellmeier fit. Given that the data of Briggs [lJ and Potter [18]
were taken at 20°C or more, the agreement is good. Below about 2 flm, the
Sellmeier results would increasingly deviate from the measured values. That
the reflectance method agrees with the angle-of-deviation method better than
0.25% in this spectral region establishes the compatibility of the two methods.

Germanium (Ge) 469
Reflectivity-type experiments can presents serious problems to the unwary
for reducing the experimental data to intrinsic material parameters such as
nand k. The condition of the reflecting surface must be well established. Any
damage layer present due to grinding, polishing, etc., must be removed. Chemical
polishes can avoid this problem. Another incipient problem is the likely
presence of a native oxide. A stable oxide grows on germanium to thicknesses
of 50 to 100 A in ambient air. For high-index materials such as Ge,
such a layer must be removed or accounted for. Aspnes et al. [19J stripped
the oxide and took steps to inhibit the oxide growth during the experimental
run. While ellipsometry is very sensitive to the presence of a low-index layer,
reflectance measurements also become quite sensitive to such a layer as k
becomes significant. Both Potter [18J and Archer [20J assumed the presence
of an oxide on their specimens and corrected for it. Archer [20J assumed a
thickness of 10 to 20 A, while Potter [18J assumed a layer with thickness of
50 A and an index of 2.0. (See Aspnes and Stunda [19J for further discussion.)
REFERENCES
1. H. B. Briggs, Phys. Rev. 77, 286 (1950).
2. C. D. Salzberg and J. J. Villa, J. Opt. Soc. Am. 47, 244 (1957).
3. M. Cardona, W. Paul, and H. Brooks, J. Phys. Chem. Solids 8, 204 (1959).
4. H. W. Icenogle, B. C. Platt, and W. L. Wolfe, Appl. Opt. 15, 2348 (1976).
5. R. P. Edwin, M. T. Dudermel, and M. Lamare, Appl. Opt 17, 1066 (1978).
6. N. P. Barnes and M. S. Piltch, J. Opt. Soc. Am. 69,178 (1979).
7. H. H. Li, J. Phys. Chem. Ref Data, 9,561 (1980).
8. R. J. Collins and H. Y. Fan, Phys. Rev. 93, 674 (1954).
9. M. Lax and E. Burstein, Phys. Rev. 97, 39 (1955).
10. 1. R. Aronson, H. G. McLinden, and P.1. Gielisse, Phys, Rev. 135, A 785 (1964).
11. D. L. Stierwalt and Roy F. Potter, Rep. Int. Conf Phys. Semicond., Exter, 1962, p.513.
Institute of Physics and Physical Society, London. 1962.
12. C. M. Randall and R. D. Rawcliffe, Appl. Opt. 6,1889 (1967).
13. M. N. Afsar, D. D. Honijk, W. F. Passchier, and J. Goulon, IEEE Trans. Micro. Theor.
Tech. MTT-25, 505 (1977).
14. G. G. MacFarlane and V. Roberts, Phys. Rev. 98, 1865 (1955).
15. W. C. Dash and R. Newman, Phys. Rev. 99,' 1151 (1955).
16, M, Cardona, in "Optical Properties of Solids" (S, Nudelman and S. S. Mitra, eds,), p, 137,
Plenum, New York, 1969.
17. H. R, Philipp and E. A, Taft, Phys. Rev. 113, 1002 (1959),
18. Roy F. Potter, Phys. Rev, 150, 562 (1966),
19, D, E. Aspnes and A, A. Studna, Phys, Rev, B 27, 985 (1983); D. E. Aspnes, private communication
(1983).
20. R,1. Archer, Phys, Rev, 110, 354 (1958).
21. M. Cardona, W. Gudat, B. Sonntag, and p, y, Yu, Proc. 10th Int. Can! Phys. Semicond.,
Cambridge, 1970, p. 208, U.S, Atomic Energy Commission, Oak Ridge, Tennessee, 1970.
22. A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Y. F. ShepeJov, Opt. Spectrosc. 16, 168
(1964); A. P. Lukirskii, E. P. Savinov, O. A. Ershov, and Y. F. Shepelov, Opt. Spektrosk. 16,
310 (1964).

Germanium (Ge) 471
eV
TABLE V
Values of nand k for Germanium Obtained from Various References·
cm- 1
Jim n k k
525.3 0.00236 0.99741 [22] 9.8 x 10- 4 [22]
394.8 0.00314 0.99590 2.05 x 10- 3
281.8 0.0044 0.99385 4.30
185.1 0.0067 0.99050 9.50 x 10- 3
155 0.007999 1.47 x 10- 2 [21]
150 0.008266 1.55
145 0.008550 1.63
140 0.008856 1.71
135 0.009184 1.77
130 0.009537 1.98
127.5 0.009725 1.94
125 0.009919 1.98
122.5 0.01012 2.02
120 0.01033 1.99
115 0.01078 2.06
110 0.01127 2.21
105 0.01181 2.37
100 0.01240 2.57
97.5 0.01272 2.65
95 0.01305 2.71
90 0.01378 2.79
85 0.01459 3.03
80 0.01550 3.26
75 0.01653 3.39
70 0.01771 3.52
65 0.01907 3.67
60 0.02066 3.94
55 0.02254 4.23
50 0.02480 4.52
45 0.02755 5.04
40 0.03100 6.04
38 0.03263 6.51
36 0.03444 7.40
34 0.03647 8.56
32 0.03875 9.99 x 10- 2
31 0.04000 0.106
30 0.04133 0.102
29 0.04275 7.14 x 10- 2
28 0.04428 7.47 x 10- 2
26 0.04769 0.110
24 0.05166 0.144
22 0.05636 0.179
20 0.06199 0.237
10 0.1240 0.93 [17] 0.86 [17]
9.5 0.1305 1.0
(continued)
• References are indicated in brackets. Data from Stierwalt and Potter [11] obtained at 50 0e
are included because no room-temperature data were available in the 1O-15-Jim region.

472 Roy F. Potter
TABLE V (Continued)
Germanium
eV cm-! pm n k k
9 0.1378 0.92 1.14
8.5 0.1459 0.92 1.2
8 0.1550 0.92 1.4
7.5 0.1653 1.6
7 0.1771 1.0 1.8
6.5 0.1907 1.1 2.05
6 48,390 0.2066 1.3 2.34
1.022 [19] 2.774 [19]
5.94 47,910 0.2087 1.073 2.801
5.9 47,590 0.2101 1.108 2.831
5.84 47,100 0.2123 1.167 2.862
5.8 46,780 0.2138 1.209 2.873
5.75 46,380 0.2156 1.48 [17] 2.4 [17]
5.74 46,300 0.2160 1.273 [19] 2.874 [19]
5.7 45,970 0.2175 1.293 2.163
5.64 45,490 0.2198 1.345 2.852
5.6 45,170 0.2214 1.360 2.846
5.54 44,680 0.2238 1.372 2.842
5.5 44,360 0.2254 1.380 2.842
1.55 [17] 2.4 [17]
5.44 43,880 0.2279 1.387 [19] 2.849 [19]
5.4 43,550 0.2296 1.383 2.854
5.34 43,070 0.2322 1.377 2.877
5.3 42,750 0.2339 1.371 2.897
5.25 42,340 0.2362 1.57 [17] 2.7 [17]
5.24 42,260 0.2366 1.366 [19] 2.938 [19]
5.2 41,940 0.2384 1.364 2.973
5.14 41,460 0.2412 1.366 3.031
5.1 41,130 0.2431 1.370 3.073
5.04 40,650 0.2460 1.382 3.146
5.0 40,330 0.2480 1.394 3.197
1.6 [17] 2.86 [17]
4.94 39,840 0.2510 1.417 [19] 3.282 [19]
4.9 39,520 0.2530 1.435 3.342
4.84 39,040 0.2562 1.470 3.439
4.8 38,710 0.2583 1.498 3.509
4.74 38,230 0.26i6 1.546 3.624
4.7 37,910 0.2638 1.586 3.709
4.64 37,420 0.2672 1.659 3.852
4.6 37,100 0.2695 1.720 3.960
4.54 36,620 0.2731 1.839 4.147
4.5 36,290 0.2755 1.953 4.297
4.44 35,910 0.2792 2.226 4.543
4.4 35,080 0.2818 2.516 4.669
4.34 35,000 0.2857 3.038 4.653
4.3 34,680 0.2883 3.338 4.507
4.24 34,200 0.2924 3.633 4.207
4.2 33,880 0.2952 3.745 4.009
4.14 33,390 0.2995 3.837 3.756

Germanium (Ge) 473
eV
cm-!
TABLE V (Continued)
Germanium
11m n k k
4.1 33,070 0.3024 3.869 3.614
4.04 32,580 0.3069 3.896 3.436
4.0 32,260 0.3100 3.905 3.336
3.94 31,780 0.3147 3.916 3.209
3.9 31,460 0.3179 3.920 3.137
3.84 30,970 0.3229 3.930 3.043
3.8 30,650 0.3263 3.936 2.986
3.74 30,160 0.3315 3.949 2.909
3.7 29,840 0.3351 3.958 2.863
3.64 29,360 0.3406 3.974 2.799
3.6 29,040 0.3444 3.985 2.759
3.54 28,550 0.3502 4.005 2.702
3.5 28,230 0.3542 4.020 2.667
3.44 27,750 0.3604 4.048 2.615
3.4 27,420 0.3647 4.070 2.579
3.34 26,940 0.3712 4.106 2.517
3.3 26,620 0.3757 4.128 2.469
3.24 26,130 0.3827 4.150 2.392
3.2 25,810 0.3875 4.157 2.340
3.14 25,330 0.3949 4.153 2.262
3.1 25,000 0.4000 4.141 2.215
3.04 24,520 0.4078 4.107 2.164
3.0 24,200 0.4133 4.082 2.145
2.94 23,710 0.4217 4.052 2.135
2.9 23,390 0.4275 4.037 2.140
2.84 22,910 0.4366 4.030 2.162
2.8 22,580 0.4428 4.035 2.181
2.74 22,100 0.4525 4.058 2.215
2.7 21,780 0.4592 4.082 2.240
2.64 21,290 0.4696 4.133 2.281
2.6 20,970 0.4769 4.180 2.309
2.54 20,490 0.4881 4.267 2.353
2.5 20,160 0.4959 4.340 2.384
2.44 19,680 0.5081 4.482 2.429
2.4 19,360 0.5166 4.610 2.455
2.34 18,870 0.5299 4.883 2.434
2.3 18,550 0.5391 5.062 2.318
2.24 18,070 0.5535 5,198 2.125
2.2 17,740 0.5636 5.283 2.049
2.14 17,260 0.5794 5.554 1.924
2.1 16,940 0.5904 5.748 1.634
2.05 16,530 0.6048 5.9 [18J 1.1 [18J
2.04 16,450 0.6078 5.708 [19] 1.150 [19]
2.0 16,130 0.6199 5.588 0.933
5.64 [18] 0.8
1.95 15,730 0.6358 5.5 0.66
1.9 15,320 0.6526 5.38 0.54
5.294 [19J 0.638
(continued)

474 Roy F. Potter
eV
cm- 1
TABLE V (Continued)
Germanium
JIm n k k
1.85 14,920 0.6702 5.21 [18] 0.4
1.84 14,840 0.6738 5.152 [19] 0.537
1.8 14,520 0.6888 5.067 0.500
5.08 [18] 0.26
0.466 [15]
1.75 14,110 0.7085 4.99 0.2
1.74 14,030 0.7126 4.961 [19] 0.430 [19]
1.7 13,710 0.7293 4.897 0.401
4.95 [18] 0.18
0.389 [15J
1.64 13,230 0.7560 4.816 [19] 0.364 [19]
1.6 12,900 0.7749 4.763 0.345
4.75 [18] 0.308 [15]
1.54 12,420 0.8051 4.684 [19] 0.316 [19]
1.5 12,100 0.8266 4.653 0.298
4.64 [18] 0.237 [IS]
1.4 11,280 0.8856 4.56 0.190
1.3 10,490 0.9537 4.495 0.167
1.240 10,000 1.0 4.61733 [6]
1.2 9,679 1.033 4.42 [18] 0.123
I.l 8,872 1.127 4.385 0.103
1.033 8,333 1.2 4.35673 [6]
1.0 8,065 1.240 4.325 [18] 8.09 x 10- 2
0.9 7,259 1.378 4.285 7.45
0.8856 7,143 1.4 4.23840 [6]
0.88 7,098 1.409 6.73
0.86 6,936 1.442 6.88
0.84 6,775 1.476 6.58
0.82 6,614 1.512 5.66 x 10- 2
0.8 6,452 1.550 4.275 [16] 5.67 x 10- 3
0.78 6,291 1.590 3.42 x 10- 3
0.775 6,251 1.600 4.17262 [6] 8.15 x 10- 4 [19]
0.76 6,130 1.631 7.79 x 10- 4
0.75 6,049 1.653 5.06
0.74 5,968 1.675 6.67
0.725 5,847 1.710 3.01
0.72 5,807 1.722 4.66
0.7 5,646 1.771 4.18 [18] 2.82 1.27 x 10- 4
0.6888 5,556 1.8 4.13164 [6]
4.143 [I]
0.68 5,485 1.823 1.31 x 10- 4
0.675 5,444 1.837 4.22 x 10- 5
0.6702 5,405 1.85 4.135
0.66 5,323 1.879 6.73 x 10- 5
0.6525 5,263 1.90 4.129
0.65 5,243 1.907 9.71 x 10- 6
0.64 5,162 1.937 7.71 x 10- 6
0.625 5,041 1.984 1.42 x 10- 6
0.6199 5,000 2.0 4.116

Germanium (Ge)
eV
cm - 1
TABLE V (Continued)
Germanium
Jlm n k k
4.10415 [6]
0.6 4,8 39 2.066 6.58 x 10- 7
0.5904 4,762 2.1 4.104 [1]
0.5636 4,545 2.2 4.092
4.08469 [6]
0.5391 4,348 2.3 4.085 [1]
0.5166 4,167 2.4 4.078
4.07038 [6]
0.4959 4,000 2.5 4.072 [1]
0.4854 3,9 15 2.554 4.06230 [4]
0.4769 3,846 2.6 4.068 [1]
4.05951 [6]
0.4675 3,771 2.652 4.05754 [4]
0.4538 3,660 2.732 4.05310
0.4428 3,571 2.8 4.05105 [6]
0.4341 3,501 2.856 4.04947 [4]
0.4191 3,381 2.958 4.04595
0.4133 3,333 3.0 4.04433 [6]
0.4012 3,236 3.09 4.04292 [4]
0.3874 3,125 3.2 4.03889 [6]
0.3647 2,94 1 3.4 4.03443
0.3444 2,778 3.6 4.03072
0.3263 2,632 3.8 4.02760
0.3100 2,500 4.0 4.02495
0.3009 2,427 4.12 4.02457 [4]
0.2952 2,381 4.2 402268 [6]
0.2818 2,273 4.4 4.02072
0.2695 2,174 4.6 4.01901
0.2583 2,083 4.8 4.01751
0.2480 2,000 5.0 4.01619
0.2389 1,927 5.19 4.01617 [4]
0.2384 1,923 5.2 4.01503 [6]
0.2296 1,852 5.4 4.01399
0.2214 1,786 5.6 4.01305
0.2138 1,724 5.8 4.01222
0.2066 1,667 6.0 4.01146
0.2000 1,613 6.2 4.01078
0.1937 1,563 6.4 4.01015
0.1879 1,515 6.6 4.00958
0.1823 1,471 6.8 4.00906
0.1771 1,429 7.0 4.00858
0.1722 1,389 7.2 4.00814
0.1675 1,351 7.4 4.00773
0.1631 1,316 7.6 4.00736
0.1590 1,282 7.8 4.00701
0.1550 1,250 8.0 4.00668
4.00748 [5]
0.1512 1,220 8.2 4.00637 [6]
475
(continued)

476 Roy F. Potter
eV
cm- 1
TABLE V (Continued)
Germanium
pm n k k
0.1506 1,215 8.23 4.00743 [4]
0.1476 1,190 8.4 4.00609 [6]
0.1442 1,163 8.6 4.00582
0.1409 1,136 8.8 4.00556
0.1378 1,111 9.0 4.00533
4.00620 [5]
0.1348 1,087 9.2 4.00510 [6]
0.1319 1,064 9.4 4.00489
0.1292 1,042 9.6 4.00469
0.1265 1,020 9.8 4.00449
0.1240 1,000 10.0 4.00431
4.00525 [5] 1.43 x 10- 5 [11]
0.1207 973.7 10.27 4.00571 [4]
0.1181 952.4 10.5 4.00389 [6]
0.1137 917.4 10.9 1.30
0.1127 909.1 11.0 4.00351
4.00436 [5]
0.1078 869.6 11.5 4.00316 [6]
0.1033 833.3 12.0 4.00285 3.82
4.00398 [5]
0.1003 809.1 12.36 4.00627 [4]
0.09919 800.0 12.5 4.00255 [6]
0.09840 793.7 12.6 3.51
0.09537 769.2 13.0 4.00228
4.00352 [5]
0.09460 763.4 13.1 4.59
0.09184 740.7 13.5 4.00202 [6]
0.08920 719.4 13.9 3.98
0.08856 714.3 14.0 4.00177
4.00315 [5]
0.08551 689.7 14.5 4.00153 [6] 5.77
0.08431 680 14.71 2.34 x 10- 5 [8]
0.08307 670 14.93 3.56
0.08266 666.7 15.0 4.00130 9.78 x 10- 5
0.08183 660 15.15 5.30
0.08157 657.9 15.2 1.2 x 10- 4
0.08059 650 15.38 6.24
0.07999 645.2 15.5 4.00107 1.71 x 10- 4
0.07935 640 15.63 7.34
0.07811 630 15.87 7.33
0.07749 625.0 16.0 4.00086 9.55 x 10- 5
0.07687 620 16.13 6.54
0.07563 610 16.39 5.61
0.07514 606.1 16.5 1.58 x 10- 4
0.07439 600 16.67 4.91
0.07377 595 16.81 6.02
0.07315 590 16.95 9.44 x 10- 5
0.07293 588.2 17.0 4.00043 2.57
0.07191 580 17.24 1.64 x 10- 4

Germanium (Ge) 477
eV
cm-!
TABLE V (Continued)
Germanium
11m n k k
0.07085 571.4 17.5 3.90
0.07067 570 17.54 2.09
0.06943 560 17.86 2.56
0.06888 555.6 18.0 4.00001 3.01
0.06819 550 18.18 2.68
0.06757 545 18.35 2.63
0.06702 540.5 18.5 4.27
0.06695 540 18.52 2.51
0.06633 535 18.69 2.68
0.06571 530 18.87 3.00
0.06526 526.3 19.0 3.99958 4.53
0.06447 520 19.23 3.21
0.06358 512.8 19.5 4.03
0.06323 510 19.61 3.12
0.06199 500 20.00 3.99915 2.39 3.98
0.06075 490 20.41 1.94
0.06048 487.8 20.5 3.92
0.05951 480 20.83 2.49
0.05904 476.2 21 5.01
0.05827 470 21.28 3.39
0.05767 465.1 21.5 7.70 x 10- 4
0.05703 460 21.74 4.67
0.05636 454.5 22.0 3.99825 1.02 x 10- 3
0.05579 450 22.22 5.84 6.0 x 10- 4 [10]
0.05455 440 22.73 7.24 x 10- 4 8.0 X 10- 4
0.05331 430 23.26 1.11 x 10- 3 1.1 X 10- 3
0.05269 425 23.53 1.27
0.05207 420 23.81 1.10 x 10- 3 1.35
0.05166 416.7 24.0 3.99728
0.05083 410 24.39 7.77 x 10- 4 1.4 x 10- 3
0.05021 405 24.69 9.0 x 10- 4
0.04959 400 25.00 6.17 8.0 x 10- 4
0.04897 395 25.32 8.06 x 10- 4 1.5 X 10- 3
0.04835 390 25.64 1.73 x 10- 3 2.0
0.04769 384.6 26.0 3.99621
0.04711 380 26.32 2.30 2.1
0.04587 370 27.03 2.80 2.5
0.04463 360 27.78 3.76 3.4
0.04428 357.1 28.0 3.99500
0.04401 355 28.17 5.5
0.04370 352.5 28.37 6.7
0.04339 350 28.57 5.23 6.3
0.04308 347.5 28.78 6.7
0.04277 345 28.99 6.92 6.5
0.04215 340 29.41 4.68 3.2
0.04133 333.3 30.0 3.99363
0.04092 330 30.30 3.62 2.95
0.03968 320 31.25 2.98 2.9
(continued)

478 Roy F. Potter
eV
cm- 1
TABLE V (Continued)
Germanium
/Lm n k k
0.03844 310 32.26 2.82 2.7
0.03782 305 32.79 3.00
0.03720 300 33.33 3.18 2.75
0.03658 295 33.90 2.83
0.03596 290 34.48 2.74 3.05
0.03542 285.7 35 3.98925
0.03534 285 35.09 3.45
0.03472 280 35.71 3.55
0.03410 275 36.36 3.3
0.03348 270 37.04 2.75
0.03224 260 38.46 1.55
0.03100 250 40.00 3.98272 0.85
0.02976 240 41.67 0.7
0.02852 230 43.48 0.65
0.02728 220 45.45 0.85
0.02604 210 47.62 1.25
0.02480 200 50.00 1.5
0.02356 190 52.63 1.53
0.02232 180 55.56 1.55
0.02108 170 58.82 1.6
0.01984 160 62.50 1.6
0.1860 150 66.67 1.5
0.01736 140 71.43 4.0060 [12] 1.02 [12] 1.5
0.01643 132.5 75.47 4.0060 1.14
0.01612 130 76.92 1.55
0.01550 125 80.00 4.0060 1.27
0.01488 120 83.33 1.7
0.01457 117.05 85.11 4.0060 1.62
0.01364 110 90.91 4.0063 2.10 2.4
0.01302 105 95.24 2.8
0.01271 102.5 97.56 4.0064 2.41
0.01240 100 100.0 3.0
0.01178 95 105.3 4.0067 2.01 2.5
0.01116 90 111.1 2.1 x 10- 3
0.01085 87.5 114.3 4.0068 1.73
0.009919 80 125.0 4.0067 1.59
0.008989 72.5 137.9 4.0067 1.43
0.008059 65 153.8 4.0065 1.34
0.007129 57.5 173.9 4.0061 1.10
0.006199 50 200.0 4.0059 1.11
0.005269 42.5 235.3 4.0056 1.50
0.004339 35 285.7 4.0052 2.04
0.003410 27.5 363.6 4.0047 2.89
0.002480 20 500.0 4.0043 4.77 x 10- 3