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+
wl-wiJ
2
.
W + Irw
2
WT -
(1)
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
429
HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS
ISBN 0-12·544420-6
430
Edward D. Palik
et at. [13]. A comparison can be made in the longer-wavelength overlap
region with the data of Johnson et al. [1] showing agreement to ~ 0.03 and
better in n. The calculated values of k are almost a factor of 2 smaller than
those measured by Johnson et al. [1] probably because on the low-frequency
side of W T difference bands occur in the 80-200-pm region that would make
the experimental values of k larger than the single-oscillator model, as is
observed. However, k measurements ofIwasa et al. [14] on thin mechanically
polished and epitaxial films are only ~ 10% smaller than those calculated in
the 240-320-cm - 1 region (after a decimal point correction in Fig. 2. of I wasa
et at. [14], so we chose the oscillator-model fit through this region. The
oscillator model can be modified to include a frequency-dependent damping
constant to account for some of the structure away from W T [15]. The static
dielectric constant is found to be 13.00.
The oscillator fit for n is extended up to 480 cm -1. However, several multiphonon bands occur above w L that have been measured directly by Cochran
et at. [4] in the 347-807-cm -1 region. They measured transmission and reflection of thin slabs. Surface preparation was not described. Room temperature varies among the samples and is usually 297 or 300 K, except for these
samples for which it was 292 K (a cold English laboratory or ice water in
the dewar?). Dopant impurities such as Si, Li, and B give rise to local vibration modes that often fall in this spectral region [16].
Calorimetry measurements at CO 2 laser wavelengths [6] produced the
small k values listed in the 1000-cm - 1 region for Czochrolski-grown, undoped, high-resistivity GaAs. No surface preparation was given, although
surely a chemical polish was used. These numbers varied from sample to
sample by a factor of 2 and with other measurements also [17]. Temperaturedependence studies suggest that this absorption is primarily intrinsic due
to multiphonon absorption, although the variation from sample to sample
suggests that residual impurities and surface effects may still be present.
Pikhtin and Yas'kov [5] have measured the index of refraction in the near
IR by using prism (minimum deviation) and interference-fringe techniques.
The authors fitted theirs and Marple's data [18] to an oscillator formula of
the form
2
A
Ei - (hwf
n = 1 + -; In E6 _ (hW)2
+ Ei
G1
_ (hW)2
G2
(hW)2
+ E~ _
+ E~
G3
_ (hW)2'
(2)
with the parameters Eo = 1.428 eY, E1 = 3.0 eY, E2 = 5.1 eY, E3 = 0.0333 eY,
G1 = 39.194 ey2, G2 = 136.08 ey2, G3 = 0.00218 ey2, and A = 0.7/$0 =
0.5858. No damping was assumed. These results for n are listed from 0.1 to
1.4 eY and fit the experimental values to a few units in the third decimal
place. This fit of Eq. (2) agrees with the reststrahlen oscillator fit of Eq. (1)
to within 0.02 at 0.06 eY, but n is smaller primarily due to the fact that in
Eq. (1) Soo = 11.0, while in Eq. (2) the first four terms give 10.9 to three figures
from 5000 to 0 cm -1 when G3 = O. Usually, Soo is the high-frequency back-
Gallium Arsenide (GaAs)
431
ground dielectric constant conveniently defined, where n2 in Eq. (2) is equal
to its low-frequency value when G3 = O. The second term in Eq. (1) could
replace (without GcxJ the last term in Eq. (2) for better description of n over
the entire IR region along with k in the reststrahlen region.
At the fundamental band gap, Casey et al. [7] have measured k for "pure"
and doped thin films by transmission and Kramers-Kronig (KK) analysis
of reflectivity. A I-m Jarrell Ash monochromator was used. The BursteinMoss effect, the change in interband absorption due to free carriers blocking
interband transitions, does change k significantly, but this effect is not discussed here. Transmission samples were bulk samples thinned down to
appropriate thicknesses. Surface preparation was not described. For nearnormal-incidence reflection, epitaxial films of GaAs on Al x Ga 1 - x As were
used. The surfaces in this case would be undamaged. Uncertainty in absorption coefficient IX = 4nk/), was quoted to ± 5% for the transmission data for
3
IX ~ 10 cm - 1, primarily due to uncertainty in thickness measurements.
Theeten et al. [8] have performed continuous wavelength ellipsometry
measurements on chemically polished samples and their results are presented
in the 1.5-6.0-eV region. We have overlapped the Casey et al. [7] and the
Theeten et al. [8] data to demonstrate how these data can differ; at 1.5 eV
the respective k's are 0.079 and 0.041, while are 1.6 eV they are 0.095 and
0.066. The transmission measurements are preferred if the film thickness is
well determined and the surface quality is good. However, in the Casey [7]/
Theeten [3] overlap region the KK analysis was done by Casey et al. [7], so
we prefer the more direct ellipsometric data.
The ellipsometric data [8] are considered better than the KK analyzed
reflection data of Philipp and Ehrenreich [9], since it is a more direct determination with few approximations and assumptions. At 6 eV n is 1.264 compared to 1.395, a difference of 0.1, while k is 2.472 compared to 2.048, a
difference of 0.4. Above 6 eV we list the results of Philipp and Ehrenreich
[9] as tabulated by Seraphin and Bennett [19]. These were near-normalincidence reflection measurements taken over the range 1-25 eV in a vacuum
spectrometer system. Surfaces were chemically prepared.
Transmission of synchrotron radiation was measured by Cardona et al.
[10] in the 15-155-eV region to determine k only. Normal incidence and
grazing incidence vacuum spectrometers were used. Films were flash evaporated on carbon foils or on microscope slides coated with KCl. The films
could be floated on water and picked up on a copper screen. To obtain polycrystalline rather than amorphous samples, the substrate temperature was
~ 250°C. The k data listed were obtained from a graph readable to three
figures. At 15 eV the KK-analyzed reflection data [9] give k = 0.41 while
the transmission data give k = 0.28.
Throughout the visible-UV region we are plagued with values of k from
various laboratories that differ by as much as a factor of 2, although the
usual differences are < 50%. Differences in n are usually less than 10%. Often,
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 2 0 3 and AS 2 0 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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
C. J. Johnson, G. H. Sherman, and R. Weil, Appl. Opt. 8, 1667 (1969).
A. H. Kachare, W. G. Spitzer, F. K. Euler, and A. Kahan, J App/. Phys. 45, 2938 (1974).
R. T. Holm, J. W. Gibson, and E. D. Palik, J. Appl. Phys. 48, 212 (1977).
W. Cochran, S. J. Fray, F. A. Johnson, J. E. Quarrington, and N. Williams, J. Appl. Phys.
Suppl. 32, 2102 (1961).
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).
C. P. Christensen, R. Joiner, S. K. T. Nieh, and W. H. Steier, J. Appl. Phys. 45, 4957 (1974).
H. C. Casey, D. D. Sell, and K. W. Wecht, J. App/. Phys. 46,250 (1975).
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).
H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).
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.
433
Gallium Arsenide (GaAs)
11. R. T. Holm and E. D. Palik, J. Vac. Sci. Techno/. 13,889 (19"16).
12. R. H. Stolen, Phys. Rev. B 11, 767 (1975); R. H. Stolen, Appl. Phys. Lett. 15, 74 (1969).
13. H. E. Bennett, M. Silver, and E. J. Ashley, J. Opt. Soc. Am. 53, 1089 (1963).
14. S. Iwasa, 1. Balslev, and E. Burstein, in lnt. Can! Phys. Semicond., Paris, 1964, p. 1077.
Dunod, Paris, and Academic Press, New York, 1964.
15. A. S. Barker, Jr., Phys. Rev. 165,917 (1968).
16. W. G. Spitzer, in "Semiconductors and Semimetals" (R. K. Willardson and A. C. Beer, eds.),
Vol. 3, p. 17. Academic Press, New York, 1967.
17. L. H. Skolnik, H. G. Lipson, and B. Bendow, Appl. Phys. Lett. 25, 442 (1974).
18. D. T. F. Marple, J. App/. Phys.35, 1241 (1964).
19. B. O. Seraphin and H. E. Bennett, in "Semiconductors and Semimetals" (R. K. Willardson
and A. C. Beer, eds.), Vol. 3, p. 499. Academic Press, New York, 1967.
20. M. Cardona, Proc. Int. Conf. Semicond. Phys., Prague, 1960, p.388. Czech. Acad. Sci.,
Prague, and Academic Press, New York, 1961.
! iijiil
1111111
lol
100~
10- 1
,
~
-
/
2
IU
-""
c-
10-3
,,
:
I
I
I
,I
I
,I
II
I~\I
IG5UL~~~~~-L~~wL~~-U~~:-L-LUU~~~LL~~~
IU2
lUi
10°
WAVELENGTH
10 1
102
103
l)J.m)
Fig. 2. Log-log plot of n (--) and k (----) versus wavelength in micrometers for gallium
arsenide. Data from various references sometimes do not join together in overlap regions.
434
Edward D. Palik
TABLE II
Values of nand k for Gallium Arsenide Obtained from Various References·
eV
155
150
145
144
143
142
141
140
135
130
125
120
115
113
111
110
109
108
107
106
105
104
103
102
100
95
90
85
80
75
70
65
60
55
50
48
cm- 1
!lm
0.007999
0.008266
0.008551
0.008610
0.008670
0.008731
0.008793
0.008856
0.009184
0.009537
0.009919
0.01033
0.01078
0.01097
0.01117
0.01127
0.01137
0.01148
0.01159
0.01170
0.01181
0.01192
0.01204
0.01215
0.01240
0.01305
0.01378
0.01459
0.01550
0.01653
0.01771
0.01907
0.02066
0.02254
0.02480
0.02583
n
k
0.0181 [10]
0.0193
0.0203
0.0204
0.0206
0.0204
0.0205
0.0206
0.0213
0.0224
0.0234
0.0245
0.0256
0.0263
0.0274
0.0278
0.0281
0.0283
0.0276
0.0288
0.0293
0.0284
0.0294
0.0289
0.0294
0.0308
0.0323
0.0338
0.0353
0.0368
0.0376
0.0387
0.0389
0.0407
0.0430
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.
435
Gal li um Arsen ide (GaAs)
TABLE II (Continued )
Gallium Arsenide
eV
cm - !
n
J.lm
46
44
43
42
41
40
38
35
30
29
28
27
26
25
24
23.5
23
0.02695
0.02818
0.02883
0.02952
0.03024
0.03 100
0.03263
0.03542
0.04133
0.04275
0.04428
0.04592
0.04769
0.04959
0.05 166
0.05276
0.0539 1
1.037 [9, 19]
22.5
22
0.05510
0.05636
1.043
21.5
21
0.05767
0.05904
1.058
20.5
20
0.06048
0.06199
1.025
19.5
19
0.06358
0.06526
0.981
18
0.06888
0.936
17
0.07293
0.889
16
0.07749
0.850
15
0.08266
0.836
14
13
12.0
10.8
10.0
9.0
8.0
7.0
0.08856
0.09537
0.1033
0.11 48
0.1240
0.1378
0.1550
0.1771
0.840
0.864
0.895
0.923
0.913
0.901
0.899
1.063
k
0.0476
0.0518
0.0546
0.0470
0.0426
0.0426
0.0452
0.0513
0.0648
0.0683
0.0740
0.0785
0.0872
0.0986
0.115
0.126
0.141
0.228 [9, 19]
0.1 46 [ 10]
0. 148
0.243 [ 9, 19]
0.147 [ 10]
0.162
0.245 [9, 19]
0.164 [10]
0.144
0.212 [9, 19]
0.147 [ 10]
0. 152
0.234 [9, 19]
0.178 [10]
0.267 [9, 19]
0.223 [1 0]
0.324 [9, 19]
0.261 [10]
0.411 [9, 19]
0.282 [ 10]
0.503 [9, 19]
0.602
0.709
0.791
0.881
0.974
1.1 36
1.435
1.838
(continued)
436
Edward D. Palik
TABLE II (Continued)
Gallium Arsenide
eV
cm- 1
lim
6.6
6.3
6.2
6.0
48,390
0.1879
0.1968
0.2000
0.2066
5.94
5.90
5.84
5.80
5.74
5.70
5.64
5.60
5.54
5.50
5.44
5.40
5.34
5.30
5.24
5.20
5.14
5.10
5.04
5.00
4.94
4.90
4.84
4.80
4.74
4.70
4.64
4.60
4.54
4.50
4.44
4.40
4.34
4.30
4.24
4.20
4.14
4.10
4.04
4.00
3.94
3.90
47,910
47,590
47,100
46,780
46,300
45,970
45,490
45,170
44,680
44,360
43,880
43,550
43,070
42,750
42,260
41,940
41,460
41,130
40,650
40,330
39,840
39,520
39,040
38,710
38,230
37,910
37,420
37,100
36,620
36,290
35,810
35,490
35,000
34,680
34,200
33,880
33,390
33,070
32,580
32,260
31,780
31,460
0.2087
0.2101
0.2123
0.2138
0.2160
0.2175
0.2198
0.2214
0.2238
0.2254
0.2279
0.2296
0.2322
0.2339
0.2366
0.2384
0.2412
0.2431
0.2460
0.2480
0.2510
0.2530
0.2562
0.2583
0.2616
0.2638
0.2672
0.2695
0.2731
0.2755
0.2792
0.2818
0.2857
0.2883
0.2924
0.2952
0.2995
0.3024
0.3069
0.3100
0.3147
0.3179
n
1.247
1.441
1.424
1.264 [8]
1.395 [9, 19]
1.287 [8]
1.288
1.304
1.311
1.321
1.325
1.339
1.349
1.367
1.383
1.410
1.430
1.468
1.499
1.552
1.599
1.699
1.802
2.044
2.273
2.654
2.890
3.187
3.342
3.511
3.598
3.708
3.769
3.850
3.913
4.004
4.015
3.981
3.939
3.864
3.810
3.736
3.692
3.634
3.601
3,559
3.538
k
2.047
1.988
1.976
2.472 [8]
2.048 [9, 19]
2.523 [8]
2.556
2.592
2.625
2.673
2.710
2.772
2.815
2.885
2.936
3.019
3.079
3.181
3.255
3.384
3.484
3.660
3.795
3.992
4.084
4.106
4.047
3.898
3.770
3.574
3.452
3.280
3.169
3.018
2.919
2.715
2.563
2.368
2.260
2.132
2.069
2.001
1.969
1.935
1.920
1.907
1.904
437
Gallium Arsenide (GaAs)
TABLE II (Continued)
Gallium Arsenide
eV
cm- 1
3.84
3.80
3.74
3.70
3.64
3.60
3.54
3.50
3.48
3.46
3.44
3.42
3.40
3.38
3.36
3.34
3.32
3.30
3.28
3.26
3.24
3.22
3.20
3.18
3.16
3.14
3.12
3.10
3.08
3.06
3.04
3.02
3.00
2.98
2.96
2.94
2.92
2.90
2.88
2.86
2.84
2.82
2.80
2.78
2.76
2.74
30,970
30,650
30,160
29,840
29,360
29,040
28,550
28,230
28,070
27,910
27,750
27,580
27,420
27,260
27,100
26,940
26,780
26,620
26,450
26,290
26,130
25,970
25,810
25,650
25,490
25,330
25,160
25,000
24,840
24,680
24,520
24,360
24,200
24,040
23,870
23,710
23,550
23,390
23,230
23,070
22,910
22,740
22,580
22,420
22,260
22,100
11m
0.3229
0.3263
0.3315
0.3351
0.3406
0.3444
0.3502
0.3542
0.3563
0.3583
0.3604
0.3625
0.3647
0.3668
0.3690
0.3712
0.3734
0.3757
0.3780
0.3803
0.3827
0.3850
0.3875
0.3899
0.3924
0.3949
0.3974
0.4000
0.4025
0.4052
0.4078
0.4105
0.4133
0.4161
0.4189
0.4217
0.4246
0.4275
0.4305
0.4335
0.4366
0.4397
0.4428
0.4460
0.4492
0.4525
n
3.512
3.501
3.488
3.485
3.489
3.495
3.513
3.531
3.541
3.553
3.566
3.580
3.596
3.614
3.635
3.657
3.681
3.709
3.740
3.776
3.818
3.871
3.938
4.023
4.126
4.229
4.313
4.373
4.413
4.439
4.462
4.483
4.509
4.550
4.626
4.755
4.917
5.052
5.107
5.102
5.065
5.015
4.959
4.902
4.845
4.793
k
1.905
1.909
1.920
1.931
1.950
1.965
1.992
2.013
2.024
2.036
2.049
2.062
2.076
2.091
2.107
2.123
2.142
2.162
2.183
2.207
2.232
2.260
2.288
2.307
2.304
2.270
2.212
2.146
2.082
2.029
1.988
1.961
1.948
1.952
1.967
1.960
1.885
1.721
1.529
1.353
1.206
1.088
0.991
0.912
0.846
0.789
(continued)
438
Edward D. Palik
TABLE II (Continued)
Gallium Arsenide
eV
cm- 1
2.72
2.70
2.68
2.66
2.64
2.62
2.60
2.58
2.56
2.54
2.52
2.50
2.48
2.46
2.44
2.42
2.40
2.38
2.36
2.34
2.32
2.30
2.28
2.26
2.24
2.22
2.20
2.18
2.16
2.14
2.12
2.10
2.08
2.06
2.04
2.02
2.00
1.98
1.96
1.94
1.92
1.90
1.88
1.86
1.84
1.82
1.80
21,940
21,780
21,660
21,450
21,290
21,130
20,970
20,810
20,650
20,490
20,330
20,160
20,000
19,840
19,680
19,520
19,360
19,200
19,030
18,870
18,710
18,550
18,390
18,230
18,070
17,910
17,740
17,580
17,420
17,260
17,100
16,940
16,780
16,610
16,450
16,290
16,130
15,970
15,810
15,650
15,490
15,320
15,160
15,000
14,840
14,680
14,520
pID
0.4558
0.4592
0.4626
0.4661
0.4696
0.4732
0.4769
0.4806
0.4843
0.4881
0.4920
0.4959
0.4999
0.5040
0.5081
0.5123
0.5166
0.5209
0.5254
0.5299
0.5344
0.5391
0.5438
0.5486
0.5535
0.5585
0.5636
0.5687
0.5740
0.5794
0.5848
0.5904
0.5961
0.6019
0.6078
0.6138
0.6199
0.6262
0.6326
0.6391
0.6458
0.6526
0.6595
0.6666
0.6738
0.6812
6.8888
n
4.741
4.694
4.649
4.605
4.567
4.525
4.492
4.456
4.423
4.392
4.362
4.333
4.305
4.279
4.254
4.229
4.205
4.183
4.162
4.141
4.120
4.100
4.082
4.063
4.045
4.029
4.013
3.998
3.983
3.968
3.954
3.940
3.927
3.914
3.902
3.890
3.878
3.867
3.856
3.846
3.836
3.826
3.817
3.809
3.799
3.792
3.785
k
0.739
0.696
0.659
0.626
0.595
0.569
0.539
0.517
0.497
0.476
0.458
0.441
0.426
0.411
0.398
0.385
0.371
0.359
0.347
0.337
0.327
0.320
0.308
0.301
0.294
0.285
0.276
0.266
0.257
0.251
0.245
0.240
0.232
0.228
0.223
0.213
0.211
0.203
0.196
0.187
0.183
0.179
0.173
0.173
0.168
0.158
0.151
439
Gallium Arsenide (GaAs)
TABLE II (Continued)
Gallium Arsenide
eV
1.78
1.76
1.74
1.72
1.70
1.68
1.66
1.64
1.62
1.60
1.58
1.56
1.54
1.52
1.50
1.49
1.48
1.47
1.46
1.45
1.44
1.435
1.43
1.425
1.42
1.41
1.40
1.39
1.38
1.37
1.35
1.30
1.25
1.20
1.15
1.10
1.05
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
CID- 1
14,360
14,200
14,030
13,870
13,710
13,550
13,390
13,230
13,070
12,900
12,740
12,580
12,420
12,260
12,100
12,020
11,940
11,860
11,780
11,690
11,610
11,570
11,530
11,490
11,450
11,370
11,290
11,210
11,130
11,050
10,890
10,490
10,080
9,679
9,275
8,872
8,469
8,065
7,662
7,259
6,856
6,452
6,049
5,646
5,243
/lID
0.6965
0.7045
0.7126
0.7208
0.7293
0.7380
0.7469
0.7560
0.7653
0.7749
0.7847
0.7948
0.8051
0.8157
0.8266
0.8321
0.8377
0.8434
0.8492
0.8551
0.8610
0.8640
0.8670
0.8700
0.8731
0.8793
0.8856
0.8920
0.8984
0.9050
0.9184
0.9537
0.9919
1.033
1.078
1.127
1.181
1.240
1.305
1.378
1.459
1.550
1.653
1.771
1.907
k
n
3.779
3.772
3.762
3.752
3.742
3.734
3.725
3.716
3.707
3.700
3.693
3.685
3.679
3.672
3.666
3.6140 [5]
0.152
0.134
0.127
0.118
0.112
0.105
0.101
0.097
0.093
0.091
0.089
0.087
0.085
0.083
0.080
7.89 x
7.28
6.86
6.64
6.28
6.12
5.68
5.57
5.72
5.54
2.71 x
5.95 x
1.69 x
5.68 x
2.50
1.33 x
10- 2 [7]
10- 2
10- 3
10- 3
10- 4
10- 4
3.5690
3.5388
3.5138
3.4920
3.4724
3.4546
3.4383
3.4232
3.4094
3.3965
3.3847
3.3737
3.3636
3.3543
3.3457
(continued)
440
Edward D. Palik
TABLE II (Continued)
Gallium Arsenide
eV
cm- 1
Jim
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.29
0.28
0.27
0.26
0.25
0.24
0.23
0.22
0.21
0.20
0.19
0.18
0.17
0.16
0.15
0.14
0.1347
0.13
0.1239
0.12
0.1169
0.11
0.100
0.098
0.096
0.095
0.094
0.092
0.090
0.088
0.086
0.084
0.082
0.080
0.Q78
0.076
0.074
0.073
0.072
0.071
4,839
4,436
4,033
3,629
3,226
2,823
2,420
2,339
2,258
2,178
2,097
2,016
1,936
1,855
1,774
1,694
1,613
1,532
1,452
1,371
1,290
1,210
1,129
1,087
1,048
1,042
967.9
943.4
887.2
806.5
790.4
774.3
766.2
758.2
742.0
725.9
709.8
693.6
677.5
661.4
645.2
629.1
613.0
596.8
588.8
580.7
572.6
2.066
2.254
2.480
2.755
3.100
3.542
4.133
4.275
4.428
4.592
4.768
4.959
5.166
5.391
5.636
5.904
6.199
6.526
6.888
7.293
7.749
8.266
8.856
9.2
9.537
9.6
10.33
10.6
11.27
12.40
12.65
12.91
13.05
13.19
13.48
13.78
14.09
14.42
14.76
15.12
15.50
15.90
16.31
16.75
16.98
17.22
17.46
k
n
3.3378
3.3306
3.3240
3.3180
3.3125
3.3075
3.3027
3.3017
3.3008
3.2998
3.2988
3.2978
3.2968
3.2954
3.2946
3.2934
3.2921
3.2907
3.2891
3.2874
3.2854
3.2831
3.2803
4.4 x 10- 7 [6]
3.2769
6.1
3.2727
7.6 x 10- 7
3.2671
3.2597
3.2493
3.2336
4.93
1.61
3.49
3.63
2.72
1.61
1.64
2.24
2.40
2.11
2.16
2.83
4.55
7.66
9.46
1.00
1.50
2.05
x 10- 6 [4]
x 10- 5
x 10- 5
x 10- 4
441
Gallium Arsenide (GaAs)
TABLE II (Continued)
Gallium Arsenide
eV
0.Q70
0.069
0.068
0.067
0.066
0.0655
0.065
0.0645
0.064
0.0635
0.063
0.0625
0.062
0.0615
0.061
0.060
0.0595
0.059
0.058
0.057
0.0565
0.056
0.0555
0.055
0.054
0.053
0.0525
0.052
0.051
0.050
0.0495
0.049
0.0485
0.048
0.047
0.046
0.045
0.04463
0.044
0.04339
0.043
0.04215
0.04092
0.03968
0.03906
em-I
564.6
556.5
548.5
540.4
532.3
528.3
524.3
520.2
516.2
512.2
508.1
504.1
500.1
496.0
492.0
483.9
480.0
475.9
467.8
459.7
455.7
451.7
447.6
443.6
435.5
427.5
423.4
419.4
411.3
403.3
399.2
395.2
391.2
387.1
379.1
371.0
362.9
360
354.9
350
346.8
340
330
320
315
!lID
n
17.71
17.97
18.23
18.51
18.79
18.93
19.07
19.22
19.37
19.53
19.68
19.84
20.00
20.16
20.33
20.66
20.84
21.01
21.38
21.75
21.94
22.14
22.34
22.54
22.96
23.39
23.62
23.84
24.31
24.80
25.05
25.30
25.56
25.83
26.38
26.95
27.55
27.78
28.18
28.57
28.83
29.41
30.30
31.25
31.75
3.2081
3.1886
3.205 [2, 3]
3.1609 [5]
3.176 [2, 3]
3.157
3.126
3.100
3.058
2.997
2.913
2.851
2.770
2.659
2.495
2.380
k
2.32
6.00 x 10- 4
1.17 x 10- 3
2.59
4.18
6.10
8.27
6.27
4.85
4.83
4.85
4.23
4.17
4.18
4.09
3.45
3.18
3.19
3.57
4.50
4.78
4.84
4.97
5.32
4.56
3.68
3.38
3.43
3.71
2.74
2.07
2.07
2.17
2.10
2.33
2.91
3.94
6.50 [2, 3]
5.15 [4]
8.40 [2, 3]
8.95 x 10- 3 [4]
1.13 x 10- 2 [2, 3]
1.59
2.43
3.14
(continued)
442
Edward D. Palik
TABLE II (Continued)
Gallium Arsenide
eV
0.03844
0.03782
0.03720
0.03707
0.03695
0.03682
0.03670
0.03658
0.03645
0.03633
0.03620
0.03608
0.03596
0.03583
0.03571
0.03558
0.03546
0.03534
0.03521
0.03509
0.03496
0.03484
0.03472
0.03459
0.03447
0.03434
0.03422
0.03409
0.03397
0.03385
0.03372
0.03360
0.03348
0.03341
0.03335
0.03329
0.03323
0.03317
0.03310
0.03304
0.03298
0.03286
0.03273
0.03261
0.03248
0.03236
0.03224
cm- 1
310
305
300
299
298
297
296
295
294
293
292
291
290
289
288
287
286
285
284
283
282
281
280
279
278
277
276
275
274
273
272
271
270
269.5
269
268.5
268
267.5
267
266.5
266
265
264
263
262
261
260
)lm
32.26
32.79
33.33
33.44
33.56
33.67
33.78
33.90
34.01
34.13
34.25
34.36
34.48
34.60
34.72
34.84
34.96
35.09
35.21
35.33
35.46
35.59
35.71
35.84
35.97
36.10
36.23
36.36
36.50
36.63
36.76
36.90
37.04
37.10
37.17
37.24
37.31
37.38
37.45
37.52
37.59
37.74
37.88
38.02
38.17
38.31
38.46
n
2.229
2.020
1.707
1.623
1.529
1.422
1.298
1.151
0.975
0.761
0.536
0.391
0.323
0.291
0.275
0.267
0.266
0.270
0.278
0.290
0.307
0.329
0.358
0.395
0.443
0.506
0.592
0.713
0.890
1.17
1.64
2.56
4.66
6.63
9.30
11.6
12.4
12.0
11.3
10.6
9.90
8.87
8.12
7.55
7.11
6.76
6.47
k
4.21
6.02
9.59 x 10- 2
0.107
0.122
0.141
0.166
0.201
0.257
0.357
0.552
0.826
1.09
1.34
1.57
1.79
2.01
2.23
2.46
2.69
2.94
3.20
3.48
3.79
4.14
4.52
4.97
5.49
6.12
6.91
7.94
9.32
11.0
11.6
11.3
9.37
6.74
4.66
3.30
2.43
1.87
1.20
0.844
0.629
0.489
0.393
0.323
443
Gall ium Arsenide (GaAs)
TABLE II (Continued)
Gallium Arsenide
eV
cm -
1
0.03 162
0.03 100
0.02976
0.02852
0.02728
0.02604
0.02480
255
250
240
230
220
21 0
200
39.22
40.00
41.67
43.48
45.45
47.62
SO.OO
0.02356
0.02232
0.02108
0.02066
190
180
170
166.7
52.63
55.56
58.82
60
0.01984
0.01860
0.0 177 1
160
150
142.9
62.S0
66.67
70
0.01736
0.01612
0.01550
140
130
125
71.43
76.92
80
0.0 1488
0.0 1378
120
111.1
83.33
90
0.01364
0.01240
110
100
0.0111 6
0.009919
0.008679
0.008266
0.007439
0.006 199
90
80
70
66.67
60
50.00
0.004959
0.00413 3
40
33.33
0.003720
0.003 100
0.002480
0.001 860
0.001240
30
25
20
15
10
n
/lm
90.91
100
11 1.1
125.0
142.9
150
166.7
200
250.0
300
333.3
400
500
667
1000
5.57
5.08
4.57
4.30
4.13
4.02
3.93
3.87 [1 ]
3.77 [2, 3]
3.74 [ 1]
3.7 1 [ 2, 3J
3.68 [IJ
3.681 [ 2, 3J
3.65 [1 J
3.662 [ 2, 3]
3.635 [1 J
3.650 [2, 3J
3.625 [ IJ
3.623 [ 2, 3J
3.62 [I J
3.615 [ 2, 3J
3.61 [ IJ
k
0.t53
9.02 x 10- 2
4.26
2.49
1.63
U S x 10 - 2
8.49 x 10 - 3
1.09 x 10 - 2
1.22
1.25 x 10 - 2
3.89 x 10- 3
6.92 x 10- 3
US x 10- 2
6.4 x 10- 3
3.79 [ 1J
5.0 [12J
4.4
1.84 [ 2, 3J
3.18 [IJ
3.9 [ 12J
2.86 [1 J
3.6 [12J
3.6
2.78 [ IJ
3.8 [1 2J
4.2
3.5
2.14[ IJ
2.1 [ 12J
1.8 [ 12J
1.4
3.6 11 [ 2, 3]
3.60 [1]
l.l
1.2
3.607 [ 2, 3J
1.3
1.2
3.606
[1 2]
[2, 3]
[1 ]
[12J
Gallium Phosphide (GaP)
A. BORGHESI and G. GUIZZETTI
Dipartimento di Fisica "A. Volta" and
Gruppo Nazionale di Struttura della Materia del CNR
Universita di Pavia
Pavia, Italy
The room-temperature values of nand k tabulated here were ·obtained
from the following works and references therein: Kleinman and Spitzer [1],
Barker [2], Parsons and Coleman [3], Abagyan et al. [4, 5], Giehler and
Jahne [6], and Pikhtin et al. [7] for the medium and far infrared; Spitzer et
al. [8], Bond [9], Dean and Thomas [10], Dean et al. [11], Remenyuk et
al. [12], Nelson and Turner [13], and Pikhtin and Yas'kov [7, 14, 15] for
the near infrared and visible; and Philipp and Ehrenreich [16], Cardona et
al. [17, 18], Stokowski and Sell [19], Gudat et ai. [20], and Jungk [21] for
the visible- ultraviolet and the vacuum ultraviolet.
A composite smooth-curve plot is given in Fig. 3. Numerical values are
given in Table IV with appropriate references.
In the infrared near the transverse optic mode (VT ~ 27.5 pm), where the
absorption coefficient IY. is too large to allow transmission T measurements
using the thinnest samples available, bulk reflectance R measurements at
near-normal incidence were performed [1,6]' Values for nand k were obtained from a Kramers-Kronig (KK) analysis [2] or by fitting R (from 13 to
42 pm) within the experimental error by classical dispersion theory [1]. As
a by-product of this procedure, the optical constants were calculated and
checked against T measurements in the regions outside the fundamental
band. At longer wavelengths, transmission samples of thicknesses from 30
pm to 1 mm were used; k was derived from T and R, including multiplereflection effects; n was deduced from the interference transmission pattern.
All the samples, except those in Kleinman and Spitzer [1], were single crystals grown by different techniques [floating zone, Czochralski, vapor transport, and liquid encapsulation Czochralski (LEC)], both of n- and p-type
with free-carrier density N ranging from < 5 x 10 15 to 10 18 cm - 3. Some
transmission samples [1,4] were copper compensated to reduce the background absorption, and their surfaces were mechanically polished and etched
445
HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS
Copyright © 1985 by Academic Pr ess, Inc.
All rights of reproduction in any form reserved ,
ISBN 0-12-544420-6
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 VT == 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 VT 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 eV 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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
D. A. Kleinman and W. G. Spitzer, Phys. Rev. lIS, 110 (1960).
A. S. Barker, Jr., Phys. Rev. 165,917 (1968).
D. F. Parsons and P. D. Coleman, App/. Opt. 10, 1683 (1971).
S. A. Abagyan, G. A. Ivanov, Y. E. Shanurin, and V. I. Amosov, Sov. Phys. Semicond. 5, 889
(1971).
S. A. Abagyan, G. A. Ivanov, A. P. Izergin, and Y. E. Shanurin, Sov. Phys. Semicond. 6, 985
(1972).
M. Giehler and E. Jahne, Phys. Status Solidi B 73,503 (1976).
A. N. Pikhtin, V. T. Prokopenko, and A. D. Yas'kov, Sov. Phys. Semicond. 10, 1224 (1976).
W. G . Spitzer, M. Gershenzon, C. 1. Forsch, and D. F. Gibbs, J. Phys. Chem. Sol. 11, 339
(1959).
W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
P.1. Dean and D. G. Thomas, Phys. Rev. 150,690 (1966).
P.1. Dean, G. Kaminsky, and R. B. Zetterstrom, J. Appl. Phys. 3S, 3551 (1967).
A. D. Remenyuk, L. G. Zabelina, Yu. 1. Ukhanov, and Y. V. Shmartzev, Sov. Phys. Semicond.
2, 557 (1968).
D. F. Nelson and E. H. Turner, J. App/. Phys. 39, 3337 (1968).
A. N. Pikhtin and D. A. Yas'kov. Sov. Phys. Solid State 11, 455 (1969).
A. N. Pikhtin and D. A. Yas'kov. Phys. Status Solidi 34, 815 (1969).
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.
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.
M. Cardona, W. Gudat, E. E. Koch, M. Skibowski, B. Sonntag, and P. Yu, Phys. Rev.
Lett. 25, 659 (1970).
S. E. Stokowski and D. D. Sell, Phys. Rev. B 5, 1636 (1972).
W. Gudat, E. E. Koch, P. Y. Yu, M. Cardona, and C. M. Penchina, Phys. Status Solidi
B 52,505 (1972).
G. Jungk, Phys. Status Solidi B 67,85 (1975).
H. Welker, J. Electron. I, 181 (1955).
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.
D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983); D. E. Aspnes and A. A. Studna,
private communication (1982).
450
A. Borghesi and G. Guizzetti
105~ll-~~~~~~~~--~~~~~~~~-L~~~
10- 1
100
WAVELENGTH
102
10 1
10 2
10 3
(}Jm)
Fig 3. Log-log plot of n (---) and k(----) versus wavelength in micrometers for gallium
phosphide.
TABLE III
Dielectric Parameters for
Gallium Phosphide at 300 Ka
Electronic
Sel
Vel
Se2
Ve2
Se3
Ve3
2.570
29,000 em-I
4.131
42,700 em-I
1.390
58,000 em-I
Ionic
Goo
So
Vo
Yo
SI
VI
1'1
S2
v2
1'2
a
9.091
2.056
363.4 em-I
1.1 em-I
7.0 x 10- 4
349.4 em-I
21 em-I
3.5 x 10- 4
358.4 em-I
12.6cm- 1
Data from Parsons and Coleman [3].
TABLE IV
{j)
~
Values of nand k for Gallium Phosphide Obtained from Various References"
eV
em - I
c
JLm
n
n,
k
k,
3
"U
154.0
144.0
134.0
131.2
126.0
122.0
119.0
115.0
110.0
109.2
107.0
106.1
105.0
104.0
100.0
96.0
90.0
80.0
70.0
66.0
60.0
50.0
45.0
40.0
37.0
0.00805
0.00861
0.00925
0.00945
0.00985
0.0102
0.0104
0.0108
0.0113
0.DI14
0.011 6
0.0117
0.011 8
0.0119
0.0124
0.0129
0.0138
0.0155
0.0177
0.01 88
0.0207
0.0248
0.0275
0.0310
0 .0335
::T
1.7 x 10- 2 [17]
1.8
1.7
1.85
1.7
1.8
1.9
2.0
2.15
2.2
2.2
2.25
2.25
2.1
2.15
2.25
2.5
3.0
3.6
3.8
4.15
4.7
5.0
5.5
6. 1
0
(J)
"0
::T
0:
(I)
G3
III
~
(continued)
" References are indicated in brackets. Here n, and k, are fits to experimental data obtained with Eq. (I) and the
parameters of Table III.
.,.
....
C11
~
0'1
TABLE IV (Continued)
l\:)
Gallium Phosphide
eV
35.0
33.0
31.0
29.0
27.0
25.0
24.2
23.5
23.1
22.6
22.2
21.8
21.4
21.2
21.0
20.6
20.5
20.0
19.5
19.0
18.0
17.0
16.0
15.0
14.0
13.0
12.0
cm -
1
Jlm
0.0354
0.0376
0.0400
0.0427
0.0459
0.0496
0.0512
0.0528
0.0537
0.0549
0.0558
0.0569
0.0579
0.0585
0.0590
0.0602
0.0605
0.0620
0.0636
0.0652
0.0689
0.0729
0.0775
0.0826
0.0886
0.0954
0.1033
n
0.730 [16-20]
0.748
0.759
0.780
0.822
nf
k
6.1
6.7
7.3 [20]
8.0
9.3 x 10- 2
0.122
0.141
0.162
0.169
0.167
0.174
0.187
0.193
0.197
0.195
0.190
0.188
0.180
0.192
0.213
0.269
0.323
0.537 [16-20]
0.628
0.718
0.825
0.938
kf
?>
CD
,
0
co
:T
CD
~.
III
::J
0..
G)
G)
c:
N'
N
~
11.0
10.5
9.95
9.5
9.05
8.5
8.05
7.5
7.0
6.75
6.55
6.4
6.0
48,390
0.1127
0.1181
0.1246
0.1305
0.1370
0.1459
0.1540
0.1653
0.1771
0.1837
0.1893
0.1937
0.2066
5.94
5.9
5.84
5.8
47,910
47,590
47,100
46,780
0.2087
0.2101
0.2123
0.2138
5.74
5.7
5.64
5.6
5.54
5.5
5.44
5.4
5.38
5.36
5.34
46,300
45,970
45,490
45,170
44,680
44,360
43,880
43,550
43,390
43,230
43,070
0.2160
0.2175
0.2198
0.2214
0.2238
0.2254
0.2279
0.2296
0.2305
0.2313
0.2322
0.873
0.875
0.998
1.076
1.047
0.943
0.872
0.944
1.054
1.200
1.301
1.207
0.906
1.309 [24]
1.327
1.327
1.342
1.348
0.988 [16-20]
1.368 [24]
1.385
1.418
1.444
1.494
1.543
1.660
1.778
1.851
1.936
2.028
1.040
1.104
1.224
1.183
1.151
1.224
1.401
1.652
1.876
1.968
1.896
1.836
2.281
2.690 [24]
2.766
2.803
2.882
2.934
2.657 [16-20]
3.028 [24]
3.096
3.211
3.297
3.441
3.556
3.752
3.889
3.955
4.019
4.077
G)
~
c:
3
"0
:J'
0
(fl
'0
:J'
0.
([)
Gl
III
~
(continued)
,J:..
(J'1
v:>
.".
0'1
.".
TABLE IV (Continued)
Gallium Phosphide
eV
em-I
5.32
5.30
5.28
5.26
5.24
5.22
5.20
5.18
5.16
5.14
5.12
5.10
5.08
5.06
5.04
5.02
5.00
4.98
4.96
4.94
4.92
4.90
4.88
4.86
4.84
4.82
42,910
42,750
42,590
42,420
42,260
42,100
41,940
41,780
41,620
41,460
41,300
41,130
40,970
40,810
40,650
40,490
40,330
40,170
40,000
39,840
39,680
39,520
39,360
39,200
39,040
38,880
J1.m
0.2331
0.2339
0.2348
0.2357
0.2366
0.2375
0.2384
0.2394
0.2403
0.2412
0.2422
0.2431
0.2441
0.2450
0.2460
0.2470
0.2480
0.2490
0.2500
0.2510
0.2552
0.2530
0.2541
0.2551
0.2562
0.2572
n
2.134
2.248
2.368
2.490
2.607
2.718
2.825
2.930
3.036
3.144
3.248
3.342
3.424
3.498
3.561
3.615
3.661
3.701
3.739
3.774
3.806
3.844
3.880
3.923
3.970
4.018
nr
k
4.128
4.168
4.192
4.201
4.197
4.185
4.170
4.150
4.123
4.086
4.036
3.975
3.909
3.839
3.768
3.698
3.631
3.567
3.509
3.454
3.404
3.358
3.316
3.269
3.218
3.162
kr
~
III
0
...,
to
;;r
CD
~.
Dl
:::J
0..
G)
G)
c:
N'
N
CD
;;
4.80
4.78
4.76
4.74
4.72
4.70
4.68
4.66
4.64
4.62
4.60
4.54
4.50
4.44
4.40
4.34
4.30
4.24
4.20
4.14
4.10
4.04
4.00
3.94
3.90
3.88
3.86
3.84
3.82
3.80
38,710
38,550
38,390
38,230
38,070
37,910
37,750
37,590
37,420
37,260
37,100
36,620
36,290
35,810
35,490
35,000
34,680
34,200
33,880
33,390
33,070
32,580
32,260
31,780
31,460
31,290
31,130
30,970
30,810
30,650
0.2583
0.2594
0.2605
0.2616
0.2627
0.2638
0.2649
0.2661
0.2672
0.2684
0.2695
0.2731
0.2755
0.2792
0.2818
0.2857
0.2883
0.2924
0.2952
0.2995
0.3024
0.3069
0.3100
0.3147
0.3179
0.3195
0.3212
0.3229
0.3246
0.3263
4.062
4.100
4.132
4.157
4.173
4.181
4.181
4.173
4.158
4.137
4.113
4.031
3.978
3.907
3.867
3.817
3.792
3.765
3.754
3.748
3.752
3.769
3.790
3.840
3.890
3.923
3.966
4.021
4.095
4.196
G)
3.096
3.024
2.949
2.871
2.791
2.712
2.634
2.560
2.491
2.427
2.371
2.241
2.180
2.117
2.090
2.066
2.058
2.057
2.063
2.082
2.100
2.137
2.171
2.240
2.303
2.343
2.389
2.443
2.502
2.562
~
c
3
"U
::T
0
(J)
"0
::T
0:
<1l
G)
III
..::g
(continued)
.j:>.
01
01
~
01
0>
TABLE IV (Continued)
Gallium Phosphide
eV
em-I
3.78
3.76
3.74
3.72
3.70
3.68
3.66
3.64
3.62
3.60
3.58
3.56
3.54
3.52
3.50
3.48
3.46
3.44
3.42
3.40
3.38
3.36
3.34
3.32
3.30
3.28
30,490
30,330
30,160
30,000
29,840
29,680
29,520
29,360
29,200
29,040
28,870
28,7 10
28,550
28,390
28,230
28,070
27,910
27,750
27,580
27,420
27,260
27, 100
26,940
26,780
26,620
26,450
pm
0.3280
0.3297
0.3315
0.3333
0.3351
0.3369
0.3388
0.3406
0.3425
0.3444
0.3463
0.3483
0.3502
0.3522
0.3542
0.3563
0.3583
0.3604
0.3625
0.3647
0.3668
0.3690
0.3712
0.3734
0.3757
0.3780
n
4.328
4.497
4.700
4.927
5.149
5.328
5.437
5.472
5.454
5.406
5.339
5.268
5.194
5.121
5.050
4.983
4.920
4.861
4.805
4.751
4.700
4.651
4.604
4.560
4.518
4.479
nr
k
2.615
2.649
2.646
2.585
2.451
2.250
2.010
1.766
1.550
1.368
1.217
1.089
0.982
0.893
0.819
0.752
0.697
0.649
0.605
0.568
0.534
0.503
0.475
0.449
0.426
0.407
kr
?>
OJ
0
..,
co
::T
CD
!!1.
III
:l
a.
G)
G)
c
N'
N
CD
a:.
3.26
3.24
3.22
3.20
3. 18
3. 16
3. 14
3.12
3.1 0
3.08
3.06
3.04
3.02
3.00
2.98
2.96
2.94
2.92
2.90
2.88
2.86
2.84
2.82
2.80
2.78
2.76
2.743
2.74
2.73 1
2.72
26,290
26,130
25,970
25,810
25,650
25,490
25,330
25, 160
25,000
24,840
24,680
24,520
24,360
24,200
24,040
23,870
23,710
23,550
23,390
23,230
23,070
22,9 10
22,740
22,580
22.420
22,260
22,120
22, 100
22,030
21,940
0.3803
0.3827
0.3850
0.3875
0.3899
0.3924
0.3949
0.3974
0.4000
0.4025
0.4052
0.4078
0.4 105
0.4133
0.4161
0.41 89
0.4217
0.4246
0.4275
0.4305
0.4335
0.4366
0.4397
0.4428
0.4460
0.4492
0.452
0.4525
0.454
0.4558
4.442
4.406
4.372
4.339
4.308
4.278
4.249
4.222
4.196
4.171
4.147
4.124
4.102
4.08 1
4.060
4.041
4.023
4.006
3.990
3.976
3.964
3.952
3.936
3.919
3.904
3.896
3.869
3.835
(j)
~
0.388
0.369
0. 353
0.337
0.323
0.310
0.298
0.285
0.275
0.264
0.253
0.244
0.233
0.224
0.218
0.208
0.202
0.194
0.183
0.1 76
0.1 65
0.1 52
0.1 35
0.11 8
0.103
8.5 x 10- 2
3.12 [ 8, 23]
5.7 [24]
2.36 [8, 23J
3.5 [ 24J
c:
3
"U
::T
0
CJ)
1:1
::T
a.
(I)
G)
III
~
(continued)
-""
......
01
01
"""
CO
TABLE IV (Continued)
Gallium Phosphide
eV
2.719
2.713
2.701
2.70
2.678
2.672
2.64
2.638
2.621
2.60
2.599
2.583
2.572
2.541
2.54
2.52
2.500
2.480
2.475
2.460
2.44
2.431
2.412
2.40
2.389
2.380
CID- 1
21,930
21,880
21,780
21,780
21,600
21,550
21,290
21,280
21,140
20,970
20,960
20,830
20,750
20,490
20,490
20,320
20,160
20,000
19,960
19,840
19,680
19,610
19,450
19,360
19,270
19,190
n
!lID
0.456
0.457
0.459
0.4592
0.463
0.464
0.4696
0.470
0.473
0.4769
0.477
0.480
0.432
0.488
0.4881
0.492
0.496
0.500
0.501
0.504
0.5081
0.510
0.514
0.5166
0.519
0.521
3.805
3.730
3.73 [l1J
3.691 [24J
k
nr
kr
1.87 [8, 23J
1.59
1.43
2.7 [24J
1.16 x 10- 2 [8, 23J
9.49 x 10- 3
1.5 x 10- 2 [24J
7.68 x 10- 3 [8,23J
6.37
5.47
4.66
4.29
3.41
3.638 [24J
3.605
3.590
3.4595 [9J
3.06
2.54
2.47
2.18
1.85
~
OJ
0
.....
co
=<I>
!!.!.
I»
:::J
3.561 [24J
a.
1.42
1.19
3.535
1.04 x 10- 3
8.57 x 10- 4
P
G>
c
N'
N
<I>
s:.
2.34
2.339
2.322
2. 322
2.30
2.29
2.28
2.275
2.27
2.26
2.254
2.24
2.23
2.22
2.21 4
2.21
2.20
2.19
2.18
2.175
2.1 4
2.138
2.101
2.1 0
2.066
18,870
18,870
18,730
18,730
18,550
18,470
18,390
18,350
18,310
18,230
18,1 80
18,070
17,990
17,910
17,860
17,820
17,740
17,660
17,580
17,540
17,260
17,240
16,950
16,940
16,670
0.5299
0.530
0.534
0.5 34
0.5 39 1
0.541 4
0.5438
0. 545
0.5462
0.5486
0.55
0.5535
0.5560
0.5585
0.56
0.5610
0.5636
0.566 1
0.5687
0.57
0.5794
0.58
0.59
0.5904
0.60
3.497
2.04
2.033
2.000
16,450
16,390
16,130
0.6078
0.61
0.62
1.968
15,870
0.63
3.350 [ 24]
3.3384 [ 13J
3.3254
3.334 [24]
3.3 132 [ 13]
Gl
3.474
3.463
3.4522 [ 13]
~
5.34
3.34
3.34
2.48 [10]
1.88 [10]
1.3 x 10 - 4
c:
3
"U
::T
0
en
"0
::T
a.
3.449 1
CD
Q
10- 5
3.452 [ 24]
3.4411 [1 3J
3.441 [ 24]
3.430
3.4203 [ 13J
3.421 [2~]
3.411
3.4012 [1 3]
3.393 [ 24]
3.3837 [ 13]
3.3675
3.375 [ 24]
3.3524 [13J
3.4382
9.3 x
6.2
4.2
2.7
1.5 x 10 - 5
3.1 x 10- 6
III
-:g
3.0
1.4 x 10- 6
6.5 x 10- 7
2.8
.",.
(continued)
01
<.0
"'0 "
0)
TABLE IV (Continued)
Gallium Phosphide
eV
em-I
1.94
1.937
1.907
1.90
1.879
1.851
1.84
1.823
1.80
1.797
1.771
1.74
1.70
1.64
1.60
1.550
1.54
1.50
1.378
1.240
1.127
1.033
0.8856
0.8551
0.7749
0.7085
15,650
15,630
15,380
15,320
15,150
14,930
14,840
14,710
14,520
14,490
14,290
14,030
13,710
13,230
12,900
12,500
12,420
12,100
11 ,110
10,000
9,091
8,333
7,143
6,897
6,250
5,714
n
pm
0.639[
0.64
0.65
0.6526
0.66
0.67
0.6738
0.68
0.6888
0.69
0.70
0.7 [26
0.7293
0.7560
0.7749
0.80
0.8051
0.8266
0.90
1.0
l.l
1.2
1.4
3.311 [24]
3.3018 [13]
3.2912
3.295 [24]
3.2811 [13]
3.2716
3.275 [24]
3.2626 [13J
3.262 [ 24]
3.2541 [13]
3.2462
3.245 [ 24]
3.234
3.219
3.209
3.1830 [9J
3.191 [24]
3.178
3.1430 [9]
3.1192
3.0981
3.0844
3.0646
3.0509
kf
3.289[
»
OJ
0
...,
(Q
:::T
<D
!!?
3.1173
III
:J
a.
G)
3.0646
[.45
1.6
1.75
k
nf
G)
1.27 x 10- 5 [15]
c
N'
3.27
~
N
3.0522
0.6888
0.6199
0.5767
0.5636
0.5166
0.4959
0.4769
0.4428
0.4275
0.4133
0.3875
0.3647
0.3444
0.3263
0.3100
0.2952
0.2583
0.2480
0.2254
0.2175
0.2066
0.1907
0.1771
0.1653
0.1590
0.1550
0.1459
0.1378
0.1305
0.1292
0.1240
5,556
5,()()()
4,651
4,545
4,167
4,000
3,846
3,571
3,448
3,333
3,125
2,941
2,778
2,632
2,500
2,381
2,083
2,000
1,818
1,754
1,667
1,538
1,429
1,333
1,282
1,250
1,176
1,111
1,053
1,042
1,000
1.8
2.0
2.15
2.2
2.4
2.5
2.6
2.8
2.9
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.8
5.0
5.5
5.7
6.0
6.5
7.0
7.5
7.8
8.0
8.5
9.0
9.5
9.6
10
3.0439
3.0379
Gl
~
7.70 x 10- 5
3.0331
3.0296
C
3
"U
::r
3.0292
1.71 x 10-
0
4
(J)
"0
::r
3.0271
3.0236
0:
('I)
G3
2.88
3.0215
~
3.0217
.3!
3.18
3.0181
3.0166
3.0159
3.0137
3.0166
3.0137
3.004 [5,7]
3.001
3.007
2.998
2.995
2.992
2.98
3.001
1.69
1.53
1.47
1.91
2.95
4.29
2.993
7.14 x 10- 4
2.984
2.980
2.975
2.970
2.985
2.975
1.3 x 10- 3
2.964
2.964
~
(COlli illued)
01
......
.j:>.
0>
TABLE IV (Continued)
I'\)
Gallium Phosphide
eV
0.1127
0.1033
0.09537
0.08856
0.08266
0.07749
0.07293
0.06888
0.06526
0.06199
0.05904
0.05636
0.05391
0.05166
0.05123
0.05081
0.05040
0.04999
0.04959
0.04881
0.04805
0.04769
0.04696
0.04626
0.04592
0.04575
0.04558
cm -
1
909.1
833.3
769.2
714.3
666.7
625.0
588.2
555.6
526.3
500.0
476.2
454.5
434.8
416.7
413.2
409.8
406.5
403.2
400.0
393.7
387.6
384.6
378.8
373.1
370.4
369.0
367.6
/Jm
11
12
13
14
15
16
17
18
19
20
21
22
23
24.0
24.2
24.4
24.6
24.8
25.0
25.4
25.8
26.0
26.4
26.8
27.0
27.1
27.2
n
2.951
2.936
2.918
2.896
2.871
2.841
2.803
2.755
2.694 [ 7]
2.615
2.511
2.354
k
nr
kr
2.29
2.868
4.49
2.606
2.076
1.585
1.421
1.208
0.908
0.360
0.108
0.086
0.103
0.123
0.208
0.515
1.064
1.740
3.231
7.16 x 10- 3
2.6 x 10- 2
3.3
4.6
7.2 x 10- 2
0.22
0.89
1.74
2.52
2.96
4.05
5.86
7.48
8.69
10.22
}>
III
0
....
(Q
:::T
CD
(/)
III
::::l
0-
(j)
(j)
c:
N'
N
CD
~
0.04541
0.04525
0.04509
0.04492
0.04460
0.04428
0.04366
0.04275
0.04217
0.04133
0.04000
0.03875
0.03815
0.03757
0.03647
0.03542
0.03397
0.03306
0.03163
0.03100
0.02917
0.02755
0.02695
0.02610
0.02480
0.02356
0.02280
0.02244
0.02173
0.02080
366.3
365.0
363.6
362.3
359.7
357.1
352.1
344.8
340.1
333.3
322.6
312.5
307.7
303.0
294.1
285.7
274.0
266.7
255.1
250.0
235.3
222.2
217.4
210.5
200.0
190.0
183.93
181.0
175.29
167.78
27.3
27.4
27.5
27.6
27.8
28.0
28.4
29.0
29.4
30
31
32
32.5
33
34
35
36.5
37.5
39.2
40
42.5
45
46
47.5
50
52.63
54.37
55.25
57.05
59.60
4.732 [4]
4.339
4.115
6.580
10.314
10.483
9.501
8.060
7.348
6.431
5.578
5.182
4.765
11.19
8.62
5.15
3.40
2.10
1.54
0.78
0.31
0.16
6.5 x 10- 2
2.07 x 10·
3.971
3.869
3.793
3.809
3.594
3.606
3.508
3.518
3.461
3.470
3.4440 [3]
3.4435
3.4302
3.4238
2
Q
~
c
3
-U
:::T
0
en
"0
:::T
0:
(!)
G3
III
~
[2]
1.67
1.54
2.24
2.09
1.81
1.15
1.11
1.06
1.17 x 10- 2
5.77 x 10- 3 [3]
4.90
5.18 x 10- 3
2.31
1.46
1.06 x 10- 3
7.03
5.67
4.03
(continued)
oj::.
O"l
(.,)
TABLE IV (Continued)
"'0>"
"'"
Gallium Phosphide
eV
0.02066
0.02009
0.01859
0.01771
0.01727
0.01594
0.01459
0.01363
0.01240
0.01168
0.01090
0.008935
0.008266
0.007360
0.006567
0.006199
0.005724
0.004186
0.004133
0.003387
0.003100
0.002480
0.002066
0.001771
0.001550
0.001378
0.001240
cm- 1
166.7
162.00
149.96
142.9
139.27
128.54
117.70
109.90
100.0
94.21
87.92
72.07
66.67
59.36
52.97
50.00
46.17
33.76
33.33
27.32
25.00
20.00
16.67
14.29
12.50
11.11
10.00
n
!-1m
60
61.73
66.68
70
71.80
77.80
84.96
90.99
100
106.1
113.7
138.8
150
168.5
188.8
200
216.6
296.2
300
366.0
400
500
600
700
800
900
1000
nf
6.9 x 10-4
3.4200
3.4134
3.4010
3.3922
3.3830
3.3754
3.3706
3.3621
3.3584
3.3522
3.3463
3.3450
3.3438
3.3399
3.3407
3.3331 [4]
3.3326
3.3323
3.3321
3.3320
3.33195
3.3319
3.4015
3.3947
3.3915
3.3826
3.3747
3.3697
3.3639
3.3609
3.3579
3.3513
3.3494
3.3472
3.3454
3.3447
3.3438
3.3414
3.3413
3.3405
3.3402
3.3397
3.3394
3.3392
3.3391
3.3390
3.3389
kf
k
3.67
5.31
5.2
4.34
3.84
3.65
3.77
3.0
4.26
3.53
3.81
2.95
3.00
1.3 x 10-4
;:r>
3.19
4.53
3.93
OJ
.,0
7.2
X
10- 5
co
=sCD
~.
III
::J
0.
0
G)
c
N·
N
CD
:;
Germanium (Ge)
ROY F. POTTER
Department of Physics and Astronomy
Western Washington University
Bellingham, Washington
Germanium transistor technology in the 1950s was the basis for extensive
research activity. Good-quality single crystals became available for studies
of the electrical, elastic, and optical properties. Because infrared systems were
also developing, Ge was investigated for its photoelectric characteristics as
well as its optical properties. Much of the work during this period concerned
impurity or doping effects in terms of free-carrier absorption and forbiddengap determinations. Early optical measurements made on evaporated Ge
films had widely scattered results, depending strongly on the conditions of
preparation. However, when quality bulk samples became available, measurement results were obtained that have withstood the passage of time remarkably well. Briggs's tabular data [1] for refractive indices between 1.8 and
2.6 jim are within 0.25% of the present-day accepted values. We include these
values since they have stood the test of time. Salzberg and Villa [2] measured
single-crystal and polycrystalline material almost a decade later for wavelengths between 2 and 16 jim. Their data served as the basis for IR optical
design parameters until present day and are within 0.025% of present-day
measurements. Cardona et ai. [3J published results for Ge for several temperatures between 87 and 197 K. An examination of their figures indicates a
similar degree of agreement with today's values.
In 1976, Icenogle et ai. [4] reported refractive-index values for a series of
temperatures and wavelengths between 2.':> and 13 jim. These authors claimed
a conservative error of approximately 6 x 10- 4 in index n for a percentage
error of ~0.0125%. A few years later, Edwin et al. [5] reported very precise
results for wavelengths between 8 and 14 jim. The value of their results lies
in the fact that two different experimental setups, each in a separate laboratory, were used on the same crystal sample of Ge. The differences between the
two laboratories were between 1 x 10 - 4 and 3 x 10 - 4 (10- 2 and 3 x 10 - 2%).
This represents the apparent level of precision currently available for measuring refractive indices of high-index materials. All the experiments discussed
so far are based on high-quality, single-crystal (in most instances) germanium
465
HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS
Copyright © 1985 by Academic Press. Inc.
All rights of reproduction in any form reserved.
[SBN 0-12-544420-6
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
n2 = 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,
+ 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.
3
B = 9.295 x 1O- T
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-
Germanium (Ge)
467
tance. We have read values from a graph and tabulate these. Their results
overlap the data of Collins and Fan [8]. The band at 300 cm - 1 in the data
of Collins and Fan [8J occurs at 280 cm -1 in the data of Aronsen et al.
[10]. Stierwalt and Potter [11 J measured the spectral emittance of Ge at
50°C from 24.um > A > lO.um. The reader should note that k ~ 10- 5 at
10 .urn and becomes very much smaller at shorter wavelengths corresponding
to three and more phonon interactions.
Randall and Rawcliffe [12J used channel spectra, while Afsar et al. [13J
used asymmetric Fourier-transform spectroscopy to measure nand k for
high-resistivity Ge (l0-50 n cm -1). Their results are in good agreement and
the data of Randall and Rawcliffe [12J are in Table V, although room temperature was not defined. At ,{ > 200-.um free-carrier absorption is beginning
to appear.
As the photon energy is increased, the values of k due to phonon bands
will decrease to insignificant values until the onset of electronic transitions
in the near IR. Absorption increases for frequencies less than the first "edge"
in Ge, again due to phonon or lattice interactions with electrons. Some of
the data of MacFarlane and Roberts [14J obtained on ultrathin bulk samples
by using transmittance at 291 K, as read from a graph, have been tabulated
to show that k has measured values in the 10- 7 range.
At wavelengths shorter than 2 .urn, Ge becomes increasingly absorbing because of the dominance of electronic interband transitions; hence it is no
longer possible to use the angle-of-deviation method for determining n. Transmittance measurements can be used to measure the absorption coefficient rJ.
(or k), but data are not valid for ,{ < 0.6 .urn. Data of Dash and Newman
[15J at 300 K, as read from a graph, are given for 2.um > ,{ > 0.7 .urn. The
agreement in the wavelength overlap with MacFarlane and Roberts [14J is
good, except for the shift of the indirect absorption edge due to the temperature difference.
The optical-measurement methods remaining for shorter wavelengths are
related to aspects of the Fresnel reflectivity coefficients, i.e., ellipsometry and
reflectance. Because the Fresnel reflectivity is a complex quantity obeying
causality laws, it can be expressed as a modulus R1/2 and a phase function.
The Kramers-Kronig (KK) relation yields the spectral phase function, given
R over the entire frequency spectrum [16]. Philipp and Taft [17J determined
the reflectance R over a wide spectral region, applying the KK relations to
give nand k. Some of their results as extracted from a graph are tabulated
for ). < 0.25 .urn for 300 K.
Another type of reflectance method is to measure reflectances at nonzero
angles of incidence. Potter [18J measured the ratio Rp/Rs at several angles
of incidence to get the minimum value Rp/Rs and the associated pseudoBrewster angle. Some room-temperature values of nand k for Ge are given
for the spectral range 1.77 .urn > ,{ > 0.6 .urn.
Ellipsometry has been used to measure optical properties from the visible
spectral region to 6 eV (0.207 .urn). The tabulated data of Aspnes and Studna
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 - </J, where </J is
angle of incidence. These data are obtained from a table and are listed as
four points but plotted in Fig. 4 as a continuous line. Note in Fig. 4 that the
k data tend to join the longer-wavelength data of Cardona et al. [21] and
that these data, in turn, tend to join the data of Philipp and Taft [17].
Aspens and Studna's data [19] overlap Potter's [18] for 0.83 flm > A >
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 106 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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16,
17.
18.
19,
20.
21.
22.
H. B. Briggs, Phys. Rev. 77, 286 (1950).
C. D. Salzberg and J. J. Villa, J. Opt. Soc. Am. 47, 244 (1957).
M. Cardona, W. Paul, and H. Brooks, J. Phys. Chem. Solids 8, 204 (1959).
H. W. Icenogle, B. C. Platt, and W. L. Wolfe, Appl. Opt. 15, 2348 (1976).
R. P. Edwin, M. T. Dudermel, and M. Lamare, Appl. Opt 17, 1066 (1978).
N. P. Barnes and M. S. Piltch, J. Opt. Soc. Am. 69,178 (1979).
H. H. Li, J. Phys. Chem. Ref Data, 9,561 (1980).
R. J. Collins and H. Y. Fan, Phys. Rev. 93, 674 (1954).
M. Lax and E. Burstein, Phys. Rev. 97, 39 (1955).
1. R. Aronson, H. G. McLinden, and P.1. Gielisse, Phys, Rev. 135, A785 (1964).
D. L. Stierwalt and Roy F. Potter, Rep. Int. Conf Phys. Semicond., Exter, 1962, p.513.
Institute of Physics and Physical Society, London. 1962.
C. M. Randall and R. D. Rawcliffe, Appl. Opt. 6,1889 (1967).
M. N. Afsar, D. D. Honijk, W. F. Passchier, and J. Goulon, IEEE Trans. Micro. Theor.
Tech. MTT-25, 505 (1977).
G. G. MacFarlane and V. Roberts, Phys. Rev. 98, 1865 (1955).
W. C. Dash and R. Newman, Phys. Rev. 99,' 1151 (1955).
M, Cardona, in "Optical Properties of Solids" (S, Nudelman and S. S. Mitra, eds,), p, 137,
Plenum, New York, 1969.
H. R, Philipp and E. A, Taft, Phys. Rev. 113, 1002 (1959),
Roy F. Potter, Phys. Rev, 150, 562 (1966),
D, E. Aspnes and A, A. Studna, Phys, Rev, B 27, 985 (1983); D. E. Aspnes, private communication (1983).
R,1. Archer, Phys, Rev, 110, 354 (1958).
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.
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).
470
Roy F. Potter
Jl
//
'\
I
\
1\
:~
:1' \
I
\1
I
I
I
I
/
c
I
I
105L-~~~~~~~~~~~~L-~~~~~~
103
10 2
101
WAVELENGTH
100
10 1
102
103
(}J-ml
Fig. 4. Log-log plot of n (--) and k (----) versus wavelength in micrometers for germanium.
Data from various references sometimes do not join together in overlap regions.
471
Germanium (Ge)
TABLE V
Values of nand k for Germanium Obtained from Various References·
eV
525.3
394.8
281.8
185.1
155
150
145
140
135
130
127.5
125
122.5
120
115
110
105
100
97.5
95
90
85
80
75
70
65
60
55
50
45
40
38
36
34
32
31
30
29
28
26
24
22
20
10
9.5
cm- 1
Jim
0.00236
0.00314
0.0044
0.0067
0.007999
0.008266
0.008550
0.008856
0.009184
0.009537
0.009725
0.009919
0.01012
0.01033
0.01078
0.01127
0.01181
0.01240
0.01272
0.01305
0.01378
0.01459
0.01550
0.01653
0.01771
0.01907
0.02066
0.02254
0.02480
0.02755
0.03100
0.03263
0.03444
0.03647
0.03875
0.04000
0.04133
0.04275
0.04428
0.04769
0.05166
0.05636
0.06199
0.1240
0.1305
0.99741 [22]
0.99590
0.99385
0.99050
k
k
n
4
9.8 x 10- [22]
2.05 x 10- 3
4.30
9.50 x 10- 3
1.47 x 10- 2 [21]
1.55
1.63
1.71
0.93 [17]
1.77
1.98
1.94
1.98
2.02
1.99
2.06
2.21
2.37
2.57
2.65
2.71
2.79
3.03
3.26
3.39
3.52
3.67
3.94
4.23
4.52
5.04
6.04
6.51
7.40
8.56
9.99 x 10- 2
0.106
0.102
7.14 x 10- 2
7.47 x 10- 2
0.110
0.144
0.179
0.237
0.86 [17]
1.0
(continued)
• References are indicated in brackets. Data from Stierwalt and Potter [11] obtained at 50 e
are included because no room-temperature data were available in the 1O-15-Jim region.
0
472
Roy F. Potter
TABLE V (Continued)
Germanium
eV
cm-!
n
pm
9
8.5
8
7.5
7
6.5
6
48,390
0.1378
0.1459
0.1550
0.1653
0.1771
0.1907
0.2066
5.94
5.9
5.84
5.8
5.75
5.74
5.7
5.64
5.6
5.54
5.5
47,910
47,590
47,100
46,780
46,380
46,300
45,970
45,490
45,170
44,680
44,360
0.2087
0.2101
0.2123
0.2138
0.2156
0.2160
0.2175
0.2198
0.2214
0.2238
0.2254
5.44
5.4
5.34
5.3
5.25
5.24
5.2
5.14
5.1
5.04
5.0
43,880
43,550
43,070
42,750
42,340
42,260
41,940
41,460
41,130
40,650
40,330
0.2279
0.2296
0.2322
0.2339
0.2362
0.2366
0.2384
0.2412
0.2431
0.2460
0.2480
4.94
4.9
4.84
4.8
4.74
4.7
4.64
4.6
4.54
4.5
4.44
4.4
4.34
4.3
4.24
4.2
4.14
39,840
39,520
39,040
38,710
38,230
37,910
37,420
37,100
36,620
36,290
35,910
35,080
35,000
34,680
34,200
33,880
33,390
0.2510
0.2530
0.2562
0.2583
0.26i6
0.2638
0.2672
0.2695
0.2731
0.2755
0.2792
0.2818
0.2857
0.2883
0.2924
0.2952
0.2995
0.92
0.92
0.92
1.0
1.1
1.3
1.022 [19]
1.073
1.108
1.167
1.209
1.48 [17]
1.273 [19]
1.293
1.345
1.360
1.372
1.380
1.55 [17]
1.387 [19]
1.383
1.377
1.371
1.57 [17]
1.366 [19]
1.364
1.366
1.370
1.382
1.394
1.6 [17]
1.417 [19]
1.435
1.470
1.498
1.546
1.586
1.659
1.720
1.839
1.953
2.226
2.516
3.038
3.338
3.633
3.745
3.837
k
1.14
1.2
1.4
1.6
1.8
2.05
2.34
2.774 [19]
2.801
2.831
2.862
2.873
2.4 [17]
2.874 [19]
2.163
2.852
2.846
2.842
2.842
2.4 [17]
2.849 [19]
2.854
2.877
2.897
2.7 [17]
2.938 [19]
2.973
3.031
3.073
3.146
3.197
2.86 [17]
3.282 [19]
3.342
3.439
3.509
3.624
3.709
3.852
3.960
4.147
4.297
4.543
4.669
4.653
4.507
4.207
4.009
3.756
k
473
Germanium (Ge)
TABLE V (Continued)
Germanium
eV
cm-!
4.1
4.04
4.0
3.94
3.9
3.84
3.8
3.74
3.7
3.64
3.6
3.54
3.5
3.44
3.4
3.34
3.3
3.24
3.2
3.14
3.1
3.04
3.0
2.94
2.9
2.84
2.8
2.74
2.7
2.64
2.6
2.54
2.5
2.44
2.4
2.34
2.3
2.24
2.2
2.14
2.1
2.05
2.04
2.0
33,070
32,580
32,260
31,780
31,460
30,970
30,650
30,160
29,840
29,360
29,040
28,550
28,230
27,750
27,420
26,940
26,620
26,130
25,810
25,330
25,000
24,520
24,200
23,710
23,390
22,910
22,580
22,100
21,780
21,290
20,970
20,490
20,160
19,680
19,360
18,870
18,550
18,070
17,740
17,260
16,940
16,530
16,450
16,130
0.3024
0.3069
0.3100
0.3147
0.3179
0.3229
0.3263
0.3315
0.3351
0.3406
0.3444
0.3502
0.3542
0.3604
0.3647
0.3712
0.3757
0.3827
0.3875
0.3949
0.4000
0.4078
0.4133
0.4217
0.4275
0.4366
0.4428
0.4525
0.4592
0.4696
0.4769
0.4881
0.4959
0.5081
0.5166
0.5299
0.5391
0.5535
0.5636
0.5794
0.5904
0.6048
0.6078
0.6199
1.95
1.9
15,730
15,320
0.6358
0.6526
11 m
n
3.869
3.896
3.905
3.916
3.920
3.930
3.936
3.949
3.958
3.974
3.985
4.005
4.020
4.048
4.070
4.106
4.128
4.150
4.157
4.153
4.141
4.107
4.082
4.052
4.037
4.030
4.035
4.058
4.082
4.133
4.180
4.267
4.340
4.482
4.610
4.883
5.062
5,198
5.283
5.554
5.748
5.9 [18J
5.708 [19]
5.588
5.64 [18]
5.5
5.38
5.294 [19J
k
k
3.614
3.436
3.336
3.209
3.137
3.043
2.986
2.909
2.863
2.799
2.759
2.702
2.667
2.615
2.579
2.517
2.469
2.392
2.340
2.262
2.215
2.164
2.145
2.135
2.140
2.162
2.181
2.215
2.240
2.281
2.309
2.353
2.384
2.429
2.455
2.434
2.318
2.125
2.049
1.924
1.634
1.1 [18J
1.150 [19]
0.933
0.8
0.66
0.54
0.638
(continued)
474
Roy F. Potter
TABLE V (Continued)
Germanium
eV
cm- 1
JIm
1.85
1.84
1.8
14,920
14,840
14,520
0.6702
0.6738
0.6888
n
5.21 [18]
5.152 [19]
5.067
5.08 [18]
k
k
0.4
0.537
0.500
0.26
0.466 [15]
1.75
1.74
1.7
14,110
14,030
13,710
0.7085
0.7126
0.7293
1.64
1.6
13,230
12,900
0.7560
0.7749
1.54
1.5
12,420
12,100
0.8051
0.8266
1.4
1.3
1.240
1.2
I.l
1.033
1.0
0.9
0.8856
0.88
0.86
0.84
0.82
0.8
0.78
0.775
0.76
0.75
0.74
0.725
0.72
0.7
0.6888
11 ,280
10,490
10,000
9,679
8,872
8,333
8,065
7,259
7,143
7,098
6,936
6,775
6,614
6,452
6,291
6,251
6,130
6,049
5,968
5,847
5,807
5,646
5,556
0.8856
0.9537
1.0
1.033
1.127
1.2
1.240
1.378
1.4
1.409
1.442
1.476
1.512
1.550
1.590
1.600
1.631
1.653
1.675
1.710
1.722
1.771
1.8
0.68
0.675
0.6702
0.66
0.6525
0.65
0.64
0.625
0.6199
5,485
5,444
5,405
5,323
5,263
5,243
5,162
5,041
5,000
1.823
1.837
1.85
1.879
1.90
1.907
1.937
1.984
2.0
4.99
4.961 [19]
4.897
4.95 [18]
4.816 [19]
4.763
4.75 [18]
4.684 [19]
4.653
4.64 [18]
4.56
4.495
4.61733 [6]
4.42 [18]
4.385
4.35673 [6]
4.325 [18]
4.285
4.23840 [6]
4.275 [16]
0.2
0.430 [19]
0.401
0.18
0.389 [15J
0.364 [19]
0.345
0.308 [15]
0.316 [19]
0.298
0.237 [IS]
0.190
0.167
0.123
0.103
8.09 x 10- 2
7.45
6.73
6.88
6.58
5.66 x 10- 2
5.67 x 10- 3
3.42 x 10- 3
8.15 x 10- 4 [19]
4.17262 [6]
7.79 x 10- 4
5.06
6.67
3.01
4.18 [18]
4.13164 [6]
4.143 [I]
4.66
2.82
1.27 x 10- 4
1.31 x 10- 4
4.22 x 10- 5
4.135
6.73 x 10- 5
4.129
9.71 x 10- 6
7.71 x
10- 6
1.42 x 10 - 6
4.116
475
Germanium (Ge)
TABLE V (Continued)
Germanium
eV
cm -
1
Jlm
n
k
k
4.10415 [6]
0.6
0.5904
0.5636
4,8 39
4,762
4,545
2.066
2.1
2.2
0.5391
0.5166
4,348
4,167
2.3
2.4
0.4959
0.4854
0.4769
4,000
3,9 15
3,846
2.5
2.554
2.6
0.4675
0.4538
0.4428
0.4341
0.4191
0.4133
0.4012
0.3874
0.3647
0.3444
0.3263
0.3100
0.3009
0.2952
0.2818
0.2695
0.2583
0.2480
0.2389
0.2384
0.2296
0.2214
0.2138
0.2066
0.2000
0.1937
0.1879
0.1823
0.1771
0.1722
0.1675
0.1631
0.1590
0.1550
3,771
3,660
3,571
3,501
3,381
3,333
3,236
3,125
2,94 1
2,778
2,632
2,500
2,427
2,381
2,273
2, 174
2,083
2,000
1,927
1,923
1,852
1,786
1,724
1,667
1,613
1,563
1,515
1,471
1,429
1,389
1,351
1,316
1,282
1,250
2.652
2.732
2.8
2.856
2.958
3.0
3.09
3.2
3.4
3.6
3.8
4.0
4.12
4.2
4.4
4.6
4.8
5.0
5.19
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
0.1512
1,220
8.2
6.58 x 10- 7
4.104 [1]
4.092
4.08469 [6]
4.085 [1]
4.078
4.07038 [6]
4.072 [1]
4.06230 [4]
4.068 [1]
4.05951 [6]
4.05754 [4]
4.05310
4.05105 [6]
4.04947 [4]
4.04595
4.04433 [6]
4.04292 [4]
4.03889 [6]
4.03443
4.03072
4.02760
4.02495
4.02457 [4]
402268 [6]
4.02072
4.01901
4.01751
4.01619
4.01617 [4]
4.01503 [6]
4.01399
4.01305
4.01222
4.01146
4.01078
4.01015
4.00958
4.00906
4.00858
4.00814
4.00773
4.00736
4.00701
4.00668
4.00748 [ 5]
4.00637 [6]
(continu ed)
476
Roy F. Potter
TABLE V (Continued)
Germanium
eV
cm- 1
0.1506
0.1476
0.1442
0.1409
0.1378
1,215
1,190
1,163
1,136
1,111
0.1348
0.1319
0.1292
0.1265
0.1240
1,087
1,064
1,042
1,020
1,000
pm
8.23
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
0.1207
0.1181
0.1137
0.1127
973.7
952.4
917.4
909.1
10.27
10.5
10.9
11.0
0.1078
0.1033
869.6
833.3
11.5
12.0
0.1003
0.09919
0.09840
0.09537
809.1
800.0
793.7
769.2
12.36
12.5
12.6
13.0
0.09460
0.09184
0.08920
0.08856
763.4
740.7
719.4
714.3
13.1
13.5
13.9
14.0
0.08551
0.08431
0.08307
0.08266
0.08183
0.08157
0.08059
0.07999
0.07935
0.07811
0.07749
0.07687
0.07563
0.07514
0.07439
0.07377
0.07315
0.07293
0.07191
689.7
680
670
666.7
660
657.9
650
645.2
640
630
625.0
620
610
606.1
600
595
590
588.2
580
14.5
14.71
14.93
15.0
15.15
15.2
15.38
15.5
15.63
15.87
16.0
16.13
16.39
16.5
16.67
16.81
16.95
17.0
17.24
k
n
4.00743
4.00609
4.00582
4.00556
4.00533
4.00620
4.00510
4.00489
4.00469
4.00449
4.00431
4.00525
4.00571
4.00389
k
[4]
[6]
[5]
[6]
1.43 x 10- 5 [11]
[5]
[4]
[6]
1.30
4.00351
4.00436
4.00316
4.00285
4.00398
4.00627
4.00255
[5]
[6]
3.82
[5]
[4]
[6]
3.51
4.00228
4.00352 [5]
4.59
4.00202 [6]
3.98
4.00177
4.00315 [5]
4.00153 [6]
5.77
2.34 x 10- 5 [8]
3.56
9.78 x 10- 5
4.00130
5.30
1.2 x 10- 4
6.24
1.71 x 10- 4
4.00107
7.34
7.33
9.55 x 10- 5
4.00086
6.54
5.61
1.58 x 10- 4
4.91
6.02
9.44 x 10- 5
4.00043
2.57
1.64 x 10- 4
477
Germanium (Ge)
TABLE V (Continued)
Germanium
eV
0.07085
0.07067
0.06943
0.06888
0.06819
0.06757
0.06702
0.06695
0.06633
0.06571
0.06526
0.06447
0.06358
0.06323
0.06199
0.06075
0.06048
0.05951
0.05904
0.05827
0.05767
0.05703
0.05636
0.05579
0.05455
0.05331
0.05269
0.05207
0.05166
0.05083
0.05021
0.04959
0.04897
0.04835
0.04769
0.04711
0.04587
0.04463
0.04428
0.04401
0.04370
0.04339
0.04308
0.04277
0.04215
0.04133
0.04092
0.03968
cm-!
571.4
570
560
555.6
550
545
540.5
540
535
530
526.3
520
512.8
510
500
490
487.8
480
476.2
470
465.1
460
454.5
450
440
430
425
420
416.7
410
405
400
395
390
384.6
380
370
360
357.1
355
352.5
350
347.5
345
340
333.3
330
320
11 m
17.5
17.54
17.86
18.0
18.18
18.35
18.5
18.52
18.69
18.87
19.0
19.23
19.5
19.61
20.00
20.41
20.5
20.83
21
21.28
21.5
21.74
22.0
22.22
22.73
23.26
23.53
23.81
24.0
24.39
24.69
25.00
25.32
25.64
26.0
26.32
27.03
27.78
28.0
28.17
28.37
28.57
28.78
28.99
29.41
30.0
30.30
31.25
k
n
k
3.90
2.09
2.56
4.00001
3.01
2.68
2.63
4.27
2.51
2.68
3.00
3.99958
4.53
3.21
4.03
3.99915
3.12
2.39
1.94
3.98
3.92
2.49
5.01
3.39
7.70 x 10- 4
4.67
3.99825
5.84
7.24 x 10- 4
1.11 x 10- 3
1.27
1.10 x 10- 3
1.02 x 10- 3
6.0 x 10- 4 [10]
8.0 X 10- 4
1.1 X 10- 3
1.35
3.99728
7.77 x 10- 4
6.17
8.06 x 10- 4
1.73 x 10- 3
1.4 x 10- 3
9.0 x 10- 4
8.0 x 10- 4
1.5 X 10- 3
2.0
2.30
2.80
3.76
2.1
2.5
3.4
3.99621
3.99500
6.92
4.68
5.5
6.7
6.3
6.7
6.5
3.2
3.62
2.98
2.95
2.9
5.23
3.99363
(continued)
478
Roy F. Potter
TABLE V (Continued)
Germanium
eV
0.03844
0.03782
0.03720
0.03658
0.03596
0.03542
0.03534
0.03472
0.03410
0.03348
0.03224
0.03100
0.02976
0.02852
0.02728
0.02604
0.02480
0.02356
0.02232
0.02108
0.01984
0.1860
0.01736
0.01643
0.01612
0.01550
0.01488
0.01457
0.01364
0.01302
0.01271
0.01240
0.01178
0.01116
0.01085
0.009919
0.008989
0.008059
0.007129
0.006199
0.005269
0.004339
0.003410
0.002480
cm- 1
310
305
300
295
290
285.7
285
280
275
270
260
250
240
230
220
210
200
190
180
170
160
150
140
132.5
130
125
120
117.05
110
105
102.5
100
95
90
87.5
80
72.5
65
57.5
50
42.5
35
27.5
20
/Lm
32.26
32.79
33.33
33.90
34.48
35
35.09
35.71
36.36
37.04
38.46
40.00
41.67
43.48
45.45
47.62
50.00
52.63
55.56
58.82
62.50
66.67
71.43
75.47
76.92
80.00
83.33
85.11
90.91
95.24
97.56
100.0
105.3
111.1
114.3
125.0
137.9
153.8
173.9
200.0
235.3
285.7
363.6
500.0
n
k
k
2.82
3.00
3.18
2.83
2.74
2.7
2.75
3.05
3.98925
3.98272
4.0060 [12]
4.0060
1.02 [12]
1.14
4.0060
1.27
4.0060
4.0063
1.62
2.10
4.0064
2.41
4.0067
2.01
4.0068
4.0067
4.0067
4.0065
4.0061
4.0059
4.0056
4.0052
4.0047
4.0043
1.73
1.59
1.43
1.34
1.10
1.11
1.50
2.04
2.89
4.77 x 10- 3
3.45
3.55
3.3
2.75
1.55
0.85
0.7
0.65
0.85
1.25
1.5
1.53
1.55
1.6
1.6
1.5
1.5
1.55
1.7
2.4
2.8
3.0
2.5
2.1 x 10- 3