Silver Gallium Selenide (AgGaSe2) Silver Gallium Sulfide (AgGaS2)

Silver Gallium Selenide (AgGaSe2) Silver Gallium Sulfide (AgGaS2) LUIS ART0S Insfituto Jaime Almera Consejo Superior de Investigaciones Cientificas (C.S,I.C.) Barcelona, SPAIN

AgGaS2 and AgGaSe2 are I-III-VI 2 compounds that belong to the chalcopyrite family. All these compounds have space-group symmetry I42d, and they are considered as derived from II-VI binary zincblende semiconductors. In ideal chalcopyrite crystals, the c parameter of the unit cell should be twice the a parameter, and the anions should be at equal distance from both cations, ocupying positions (88 88 89 and their equivalent positions in the unit cell. However, two important structural anomalies take place in real ternary chalcopyrite compounds. One is the so-called tetrahedral distortion, which takes into account the displacement of the anions toward the smaller cations; it is characterized by the parameter u, defined as U = 1 +

( g A G 2 __

dBcZ)/a,

where d A c and dBc stand for the distances existing between the anions and cations I and III, respectively. The second structural change corresponds to the tetragonal compression that makes the c parameter different from twice the a parameter. This tetragonal compression is measured by the parameter tx = c / 2 a . For AgGaS2 these structural parameters take the values u - 0.304 and / ~ - 0.894, whereas for AgGaSe2 the values are u - 0.276 and ix - 0.896 [1]. In the II-VI zincblende compounds, the fundamental gap corresponds to transitions occurring at the center of the Brillouin zone between the threefolddegenerate F~5 level, which constitutes the top of the valence band, and the nondegenerate f'l level, which constitutes the bottom of the conduction band. In the AgGaS2 and AgGaSe 2 chalcopyrite compounds, because of the existence of the tetragonal crystal field, the threefold degeneracy of the f'15 level is lifted in such a way that a nondegenerate /'4 level lies above a doubly degenerate/-'5 level. If the spin-orbit interaction is taken into account, /-'5 573 HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS III

Copyright 9 1998 by Academic Press. All rights of reproduction in any form reserved ISBN 0-12-544423-0/$25.00.

574

Luis Art0s

splits into F 6 and F 7, whereas/"4 and F1 convert into/'7 and/"6, respectively. So, three structures can be observed in the fundamental-gap region in the optical spectra of the AgGaS2 and AgGaSe2 chalcopyrite compounds. The first one corresponds to transitions that occur at the fundamental gap between F 7 and F6 levels, and it is labeled the A transition. The two other structures are due to transitions ocurring between/'6 and F 6 levels (B transition) and between F 7 and F 6 levels (C transition).

I

OPTICAL PROPERTIES OF AgGaSe2

For AgGaSe2, these three structures A, B, and C have been measured at 5 K by means of reflectivity at near-normal incidence to take place at 1.804, 2.00, and 2.27 eV, respectively [2]. Taking into account the excitonic character of the A transition, the measurement of the fundamental excitonic state, as well as of its first excited state, allowed the determination of the gap value of AgGaSe2 at liquid-helium temperatures to be Eg = 1.824 eV [2]. A similar value of Eg = 1.830 eV has been reported by other authors [3]. The pressure dependence of the band gap was found to be 5.3 meV/kbar with an atmospheric-pressure band-gap value of 1.80 eV at 300 K by means of absorption measurements under hydrostatic pressure [4]. An anomalous dependence of the band gap on temperature was found between 5 and 300 K [5]. So, a positive temperature coefficient + 1.0 • 10 - 4 eV K-1 was found between 5 and 70 K, whereas a negative temperature coefficient of - 1 . 4 • 10 - 4 eV K - ] was found between 110 and 300 K. This anomalous behavior of the band gap with temperature is related to the hybridization between the d orbitals of Ag and the Se p orbitals that takes place in the AgGaSe2 compound. At energies higher than the fundamental band gap, only unpolarized reflectivity measurements performed at room temperature from 1.2 to 25 eV [6] and polarized wavelength-modulated reflectivity performed at room temperature and 10 K up to 5.5 eV [7] have been reported. To estimate the n and k values in this energy region, a Kramers-Kronig analysis from the unpolarized reflectivity data reported up to 25 eV [6] has been carried out. At higher energies, we used the extrapolation suggested by Cardona and Greenaway [8], who consider a minus fourth-power reflectivity dependence of the energy. For the low-energy end, we have fitted an analytical curve to the monotonically decreasing reflectivity data measured below the band gap, which has been extrapolated to zero energy. The values of the refractive indices obtained by using this extrapolation are consistent with the values of the refractive indices obtained experimentally in the transparent region [9]. The values obtained for n and k from the fundamental-band-gap energy up to 25 eV are listed in Table I.

Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2)

575

Optical absorption on thin films of thickness between 250 and 750 nm in the range 3.0-1.5 eV were reported [10], and the corresponding values of the extinction coefficient k in this energy range are listed in Table I. To read the values of the absorption coefficient from the graph displayed by Murthy et al. [10], we have digitized the curve. Hereafter, the same procedure has been carried out to obtain the data from the different reported graphs. Soliman [ 11] measured the transmittance and reflectance of thin films with different thickness in the range 0.5-2.0/xm and, from these experimental data, he calculated n and k by means of Murmann's formulae. The reported data have been listed in Table I. Experimental measurements of n or k have been reported in the transparent region of this compound. Boyd et al. [9] determined accurately the refractive indices by measuring the minimum-deviation angle on a prism of angle close to 20 ~ cut from the crystal boule. They measured no and ne values in the range 0.725-13.5 ~m with four decimal figures as shown in Table I. According to these authors, the presence of imperfections in their samples precludes obtaining reliable absolute values of the absorption-coefficient dispersion, and they could only determine relative variations of the absorption coefficient with wavelength. Consequently, the corresponding k values are not listed in Table I. We have fitted the measured values of Boyd et al. [9] to the modified Sellmeier-type dispersion formula [12] of the form B

rt 2 = A +

DA 2

+ ~ .

EA 2 - 1

/~2 __ C

The fit has been performed using the 43 reported experimental points. When the wavelengths are expressed in micrometers, the following parameters for the no and ne dispersions in the range 0.725-13.5/.zm are obtained: Ao Bo Co Do Eo

= 1.002933 = 8.596864E03 = -2.523862E03 = 1.399621E01 = 5.725267

Ae Be Ce De Ee

= 1.000687 = 1.308038E04 = -3.035824E03 = 4.860614 = 3.512771

Here, the subindices o or e denote ordinary or extraordinary rays, respectively. The RMS deviation of the measured refractive indices and the values calculated from the preceeding dispersion formula are 0.48% and 0.70% for n o and no, respectively. Catella et al. [13] performed polarized mid-IR transmission in the region below the band gap on several different samples. The values of the extinction coefficient k listed in Table I are obtained from their transmission curves for ordinary and extraordinary rays in the range 0.73-2.6/xm. Reflectivity measurements in the reststrahlen region have been reported

576

Luis Art0s

by several authors [14-16]. Kanellis and Kampas [14] calculated from the polarized reflectivity data, using the classical dispersion theory, the n and k dispersion curves from 400 to 10 cm -1 for both polarizations. The values they obtained are listed in Table I. The data of Table I are plotted in Figs. l a and b for AgGaSe2.

Ii

OPTICAL PROPERTIES OF AgGaS2

The three electronic transitions near the fundamental gap have been found to be at 2.679, 2.91, and 2.94 eV for A, B, and C transitions, respectively, from reflectivity measurements at 5 K [17]. The differences found in the gap values reported for this compound are greater than usual, which can be explained taking into account that AgGaS2 crystals are frequently found to be nonstoichiometric. Some authors [18] have observed variation of the color of the crystals depending on their proximity to the stoichiometric composition. At liquid-helium temperature, excitonic behavior has been found by several authors, who reported values of about 2.72 eV for the fundamental gap [17, 19, 20]. A fundamental-band-gap value of 2.70 eV at room temperature and a pressure dependence of this gap of 2.2 meV/kbar were found by absorption measurements under hydrostatic pressure [4]. As happens for the AgGaSe2 compound, the AgGaS2 crystals also present an anomalous behavior of the fundamental band gap with temperature: The temperature coefficient was positive up to 80 K with a value of 1.0 • 10 - 4 eV K-1, whereas from 110 K to room temperature the coefficient was found to be - 2 . 2 • 10 - 4 eV K - 1 [5]. At energies higher than the fundamental gap, unpolarized reflectivity measurements at room temperature from 1.2 up to 25 eV [6] and to 10 eV [21] have been reported, as well as polarized reflectivity at 80 K up to 7 eV [22]. By applying a Kramers-Kronig analysis to the reflectivity data [6] using the extrapolations discussed earlier, the n and k dispersions from 25 eV to the band-gap energy have been calculated, and their values are listed in Table II. Absorption measurements on polycrystalline AgGaS2 at room temperature have been performed up to about 7 eV [23]. The values of the extinction coefficient k obtained from these measurements are listed in Table II. In the transparent region, the indices no and n e were measured in the range 0.49-13.0/xm by the minimum-deviation-angle method on a prism of angle close to 30 ~ cut from the crystal boule [24]. The values are given in Table II. Absorption-coefficient measurements were also performed up to 12.5 ~m, but according to the authors, the presence of cracks and voids in the crystal made absolute values unreliable, and consequently, only relative variations are meaningful. We have fitted the measured values of Boyd et al. [24] to the modified

Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2)

577

Sellmeier-type dispersion formula mentioned earlier. The fit has been performed using the 50 reported experimental points. The following parameters have been obtained for the no and ne dispersions in the range 0.49-13.0 p~m when the wavelength is in micrometers: Ao Bo Co Do Eo

= 0.966201 = 2.689302E03 = -9.541617E02 = 1.903090E01 = 9.426157

Ae Be Ce De Ee

= 1.000010 = 3.372195E03 = - 1.061937E03 = 1.007695E01 = 7.290825

The RMS deviation between the measured refractive indices and the values calculated from the dispersion formula are 3.7% and 0.97% for no and ne, respectively. The existence of optical activity in a non-enantiomorphous crystal was first demonstrated by Hobden [25] by taking advantage of the unusual property that, for the AgGaS2 crystal, the birefringence changes sign at 4974 A. So, the accidental isotropy of the crystal at this wavelength allowed its optical activity to be seen without the difficulties arising from the presence of birefringence. Measurement of no and ne by the prism method for six different wavelengths in the transparent region up to 0.67 /xm was also reported in this paper, the measured values being close to those obtained by Boyd et al. [24]. Chemla et al. [26] measured the transmission of the crystal in the range 0.5-13.0/xm for ordinary and extraordinary rays. The extinction coefficients k listed in Table II have been obtained from these transmission curves. The temperature dependence of the refractive indices of AgGaS2 crystals was determined by Bhar et al. [27] by means of the classical minimum-deviation technique controlling the prism temperature from room temperature up to 90 ~ C. The nondispersive value of the thermooptic coefficient d n / d T was found to be 15.5 • 10-5/~ in the temperature range studied. In the reststrahlen region, polarized reflectivity measurements were performed from 400 to 40 cm -1 by Holah et al. [28]. By using the classical dispersion theory, they calculated the n and k dispersion curves throughout this range. The corresponding values are listed in Table II. The data in Table II are plotted in Figs. 2a and b for AgGaS2.

REFERENCES

1. H. W. Spiess, V. Haeberln, G. Brandt, A. Rauber, and J. Schneider, Phys. Status Solidi B 62, 183 (1974). 2. L. Artds, Y. Bertrand, and C. Ance, J. Phys. C: Solid State Phys. 19, 5937 (1986). 3. B. Tell and H. M. Kasper, Phys. Rev. B 4, 4455 (1971). 4. A. Jayaraman, V. Narayanamurti, H. M. Kasper, M. A. Chin, and R. G. Maines, Phys. Rev. B 14, 3516 (1976). 5. L. Artds and Y. Bertrand, Solid State Commun. 61, 733 (1987).

578 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

Luis Art0s

L. Artds, Y. Bertrand, and A. L6pez-Soler, J. Phys. C: Solid State Phys. 20, 111 (1987). B. Sermage and G. Fishman, Inst. Phys. Confer Ser. 35, 139 (1977). M. Cardona and D. L. Greenaway, Phys. Rev. 133, 1685 (1964). G. D. Boyd, H. M. Kasper, J. H. McFee, and F. G. Storz, IEEE J. Quantum Electron. 8, 900 (1972). Y. S. Murthy, B. S. Naidu, and P. J. Reddy, Vacuum 41, 1448 (1990). H. S. Soliman, J. Phys. D: Appl. Phys. 28, 764 (1995). E Zernike, J. Opt. Soc. Am. 54, 1215 (1964). G. C. Catella, L. R. Shiozawa, J. R. Hietanen, R. C. Eckardt, R. K. Route, R. S. Feigelson, D. G. Cooper, and C. L. Marquardt, Appl. Opt. 32, 3948 (1993). G. Kanellis and K. Kampas, J. Phys.(Paris) 38, 833 (1977). A. Miller, G. D. Holah, W. D. Dunnett, and G. Iseler, Phys. Status Solidi B 78, 569 (1976). J. Camassel, L. Artds and J. Pascual, Phys. Rev. B 41, 5717 (1990). L. Arttis and Y. Bertrand, J. Phys. C: Solid State Phys. 20, 1365 (1987). P. Korczak and C. Staff, J. Cryst. Growth 41, 146 (1974). B. Tell and H. M. Kasper, Phys. Rev. B 6, 3008 (1972). P. Yu, W. J. Anderson, and Y. S. Park, Solid State Commun. 13, 1883 (1973). R. L. Hengehold and F. L. Pedrotti, J. Appl. Phys. 46, 5202 (1975). J. Austinat, H. Nelkowski, and W. Scrittenlacher, Solid State Commun. 37, 285 (1981). H. V. Campe, J. Phys. Chem. Solids 44, 1019 (1983). G. D. Boyd, H. Kasper, and J. H. McFee, IEEE J. Quantum Electron 7, 563 (1971). M. V. Hobden, Nature (London) 216,678 (1967); M. V. Hobden, Acta Crystallogr. A 24, 676 (1968). D. S. Chemla, P. J. Kupecek, D. S. Robertson, and R. C. Smith, Opt. Commun. 3, 29 (1971). G. C. Bhar, D. K. Ghosh, P. S. Ghosh, and D. Schmitt, Appl. Opt. 22, 2492 (1983). G. D. Holah, J. S. Webb, and H. Montgomery, J. Phys. C: Solid State Phys. 7, 3875 (1974).

Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2)

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Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2)

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Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2)

583

TABLE I Values of n and k for AgGaSez Obtained from Various References a

eV 25.0 24.0 23.0 22.0 21.0 20.5 19.0 18.0 17.5 17.0 16.0 15.5 15.0 14.5 14.0 13.5 13.0 12.5 12.0 11.5 11.0 10.5 10.0 9.50 9.00 8.50 8.00 7.50 7.00 6.50 6.00 5.50 5.00 4.50 4.00 3.90 3.80 3.70 3.60 3.50 3.40 3.30 3.20 3.10 3.00 2.90

cm- 1 2.016E5 1.936E5 1.855E5 1.774E5 1.694E5 1.653E5 1.532E5 1.452E5 1.411E5 1.371E5 1.290E5 1.250E5 1.210E5 1.169E5 1.129E5 1.089E5 1.049E5 1.008E5 9.679E4 9.275E4 8.872E4 8.469E4 8.066E4 7.662E4 7.259E4 6.856E4 6.452E4 6.049E4 5.646E4 5.243E4 4.839E4 4.436E4 4.032E4 3.630E4 3.226E4 3.146E4 3.065E4 2.984E4 2.904E4 2.823E4 2.742E4 2.662E4 2.581E4 2.500E4 2.420E4 2.339E4

/xm 0.04959 0.05166 0.05390 0.05636 0.05904 0.06048 0.06358 0.06889 0.07085 0.07293 0.07749 0.07997 0.08266 0.08555 0.08856 0.09184 0.09537 0.09919 0.1033 0.1078 0.1127 0.1181 0.1240 0.1305 0.1378 0.1459 0.1550 0.1653 0.1771 0.1907 0.2066 0.2254 0.2478 0.2755 0.3100 0.3179 0.3263 0.3351 0.3444 0.3542 0.3647 0.3757 0.3874 0.3999 0.4133 0.4275

n 0.845 [6] 0.835 0.824 0.812 0.799 0.791 0.768 0.748 0.739 0.732 0.721 0.721 0.716 0.715 0.719 0.725 0.730 0.731 0.734 0.739 0.743 0.738 0.731 0.738 0.784 0.825 0.864 0.965 1.146 1.247 1.341 1.493 1.683 1.911 2.175 2.211 2.253 2.298 2.372 2.438 2.602 2.712 2.804 2.868 2.905 2.925

k 0.095 [6] 0.106 0.119 0.133 0.151 0.160 0.195 0.227 0.248 0.270 0.321 0.345 0.372 0.405 0.437 0.467 0.495 0.527 0.564 0.605 0.643 0.681 0.749 0.852 0.933 1.010 1.097 1.252 1.324 1.311 1.378 1.470 1.553 1.552 1.512 1.501 1.502 1.514 1.543 1.546 1.508 1.442 1.353 1.243 1.141 1.047

(continued) "References shown in brackets.

584

Luis Art0s TABLE I

(Continued)

AgGaSe2 --1

/.~m

2.80 2.70 2.60 2.50 2.40 2.30 2.20 2.10 2.00 1.90 1.80

2.258E4 2.178E4 2.097E4 2.016E4 1.936E4 1.855E4 1.774E4 1.694E4 1.613E4 1.532E4 1.452E4

0.4428 0.4592 0.4769 0.4960 0.5166 0.5391 0.5636 0.5904 0.6199 0.6526 0.6888

3.02 2.93 2.84 2.75 2.65 2.55 2.48 2.40 2.33 2.26 2.19 2.14 2.09 2.04 2.00 1.95 1.90 1.85 1.80 1.79 1.78 1.76 1.75 1.74 1.73

2.436E4 2.363E4 2.291E4 2.218E4 2.137E4 2.057E4 2.000E4 1.936E4 1.879E4 1.823E4 1.766E4 1.726E4 1.686E4 1.645E4 1.613E4 1.573E4 1.532E4 1.492E4 1.452E4 1.444E4 1.436E4 1.420E4 1.412E4 1.403E4 1.395E4

0.4105 0.4232 0.4366 0.4509 0.4679 0.4862 0.4999 0.5166 0.5321 0.5486 0.5661 0.5794 0.5932 0.6078 0.6199 0.6358 0.6526 0.6702 0.6888 0.6927 0.6965 0.7045 0.7085 0.7126 0.7167

2.398 2.300 2.218 2.138 2.070 2.009 1.937 1.884 1.829 1.771

1.934E4 1.855E4 1.789E4 1.724E4 1.669E4 1.621E4 1.563E4 1.520E4 1.475E4 1.429E4

0.517 0.539 0.559 0.580 0.599 0.617 0.640 0.658 0.678 0.70O

eV

cm

2.938 2.951 2.952 2.943 2.933 2.927 2.918 2.917 2.905 2.889 2.894

0.964 0.885 0.804 0.732 0.672 0.616 0.563 0.507 0.451 0.400 0.345 0.247 [10] 0.252 0.257 0.259 0.262 0.259 0.257 0.254 0.245 0.226 0.196 0.186 0.179 0.167 0.142 0.119 0.103 0.088 0.066 0.056 0.041 0.028 0.016 0.011 0.008

3.1241111 3.089 3.058 3.028 2.999 2.974 2.943 2.922 2.898 2.872

0.276 [11] 0.255 0.219 0.204 0.190 0.168 0.133 0.108 0.084 0.040

Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2) TABLE I

585

(Continued)

AgGaSez

eV 1.720 1.676 1.636 1.554 1.481 1.382 1.309 1.216 1.128 1.033 0.9530 0.8856 0.8260 0.7739 0.7280 0.6872 0.6512 0.6199 eV 1.710 1.653 1.550 1.459 1.378 1.306 1.240 1.127 1.033 0.9537 0.8856 0.7749 0.6889 0.6119 0.5635 0.5166 0.4768 0.4428 0.4132 0.3875 0.3646 0.3444 0.3263 0.3100 0.2755 0.2480

cm- ~ 1.387E4 1.351E4 1.319E4 1.253E4 1.195E4 1.115E4 1.056E4 9.804E3 9.099E3 8.333E3 7.686E3 7.143E3 6.662E3 6.242E3 5.872E3 5.543E3 5.252E3 5.000E3 cm-~ 1.379E4 1.333E4 1.250E4 1.177E4 1.111E4 1.053E4 1.000E4 9.091E3 8.333E3 7.692E3 7.143E3 6.250E3 5.556E3 5.000E3 4.545E3 4.167E3 3.846E3 3.571E3 3.333E3 3.125E3 2.941E3 2.778E3 2.632E3 2.500E3 2.222E3 2.000E3

/xm 0.721 0.740 0.758 0.798 0.837 0.897 0.947 1.020 1.099 1.200 1.301 1.400 1.501 1.602 1.703 1.804 1.904 2.000

n 2.850 2.831 2.812 2.781 2.754 2.727 2.710 2.690 2.674 2.661 2.651 2.644 2.639 2.634 2.631 2.629 2.625 2.624

/xm

no

0.725 0.750 0.800 0.850 0.900 0.950 1.00 1.10 1.20 1.30 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 4.50 5.00

2.8452 [9] 2.8191 2.7849 2.7598 2.7406 2.7552 2.7132 2.6942 2.6806 2.6705 2.6624 2.6516 2.6432 2.6376 2.6336 2.6304 2.6286 2.6261 2.6245 2.6231 2.6221 2.6213 2.6200 2.6189 2.6166 2.6144

k 0.019 0.001

ko

ne

ke

2.8932 [9] 2.8415 2.7866 2.7522 2.7275 2.7085 2.6934 2.6712 2.6554 2.6438 2.6347 2.6224 2.6131 2.6071 2.6027 2.5992 2.5968 2.5943 2.5925 2.5912 2.5899 2.5889 2.5876 2.5863 2.5840 2.5819

(continued)

586

Luis Art0s TABLE I

(Continued)

AgGaSe 2 eV

cm

--1

0.2254 0.2067 0.1907 0.1772 0.1653 0.1550 0.1458 0.1377 0.1306 0.1240 0.1181 0.1127 0.1078 0.1033 0.09919 0.09537 0.09184

1.818E3 1.667E3 1.538E3 1.429E3 1.333E3 1.250E3 1.176E3 1.111E3 1.053E3 1.000E3 9.524E2 9.091E2 8.696E2 8.333E2 8.000E2 7.692E2 7.407E2

1.692 1.680 1.666 1.655 1.644 1.631 1.606 1.581 1.560 1.538 1.518 1.496 1.474 1.325 1.204 1.159 1.097 1.060 1.016 0.9763 0.9465 0.9117 0.8793 0.8551 0.8266 0.7749 0.7336 0.6966 0.6595

1.364E4 1.355E4 1.344E4 1.335E4 1.326E4 1.316E4 1.295E4 1.276E4 1.258E4 1.241E4 1.224E4 1.206E4 1.189E4 1.068E4 9.709E3 9.346E3 8.850E3 8.547E3 8.197E3 7.874E3 7.634E3 7.353E3 7.092E3 6.897E3 6.667E3 6.250E3 5.917E3 5.618E3 5.319E3

/~m

no

5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5

2.6128 2.6113 2.6094 2.6070 2.6049 2.6032 2.6009 2.5988 2.5964 2.5939 2.5917 2.5890 2.5868 2.5837 2.5805 2.5771 2.5731

0.733 0.738 0.744 0.749 0.754 0.760 0.772 0.784 0.795 0.806 0.817 0.829 0.841 0.936 1.03 1.07 1.13 1.17 1.22 1.27 1.31 1.36 1.41 1.45 1.50 1.60 1.69 1.78 1.88

ko

ne

ke

2.5800 2.5784 2.5765 2.5743 2.5723 2.5704 2.5681 2.5659 2.5635 2.5608 2.5585 2.5555 2.5536 2.5505 2.5473 2.5439 2.5404 6.5E-06 [13] 4.0E-06 2.9E-06 2.5E-06 2.3E-06 2.2E-06 2.1E-06 2.1E-06 2.0E-06 2.0E-06 2.0E-06 2.0E-06 2.0E-06 1.8E-06 1.8E-06 1.8E-06 1.8E-06 1.9E-06 1.9E-06 2.0E-06 2.0E-06 2.0E-06 2.1E-06 2.2E-06 2.2E-06 2.3E-06 2.4E-06 2.5E-06 2.6E-06

1.4E-05 [13] 1.0E-05 5.5E-06 3.7E-06 2.9E-06 2.5E-06 2.2E-06 2.0E-06 2.0E-06 1.9E-06 1.9E-06 1.8E-06 1.8E-06 1.7E-06 1.7E-06 1.8E-06 1.9E-06 2.3E-06 2.7E-06 3.0E-06 3.1E-06 3.0E-06 2.7E-06 2.5E-06 2.4E-06 2.4E-06 2.4E-06 2.6E-06 2.8E-06

Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2) TABLE I

587

(Continued)

AgGaSez eV 0.6274 0.5990 0.5713 0.5367 0.5166 0.4959 0.4787 46.00E-3 44.76E-3 43.52E-3 42.28E-3 41.04E-3 39.80E-3 38.56E-3 37.32E-3 36.08E-3 34.72E-3 33.48E-3 32.36E-3 31.12E-3 30.87E-3 30.50E-3 30.00E-3 29.88E-3 28.64E-3 27.40E-3 26.04E-3 24.80E-3 23.56E-3 22.19E-3 21.08E-3 20.33E-3 19.84E-3 19.09E-3 18.47E-3 17.73E-3 17.36E-3 16.61E-3 16.12E-3 14.88E-3 13.64E-3 12.40E-3 11.16E-3 9.919E-3 8.679E-3 7.439E-3

cm- ~ 5.076E3 4.831E3 4.608E3 4.329E3 4.167E3 4.000E3 3.861E3 371 361 351 341 331 321 311 301 291 280 270 261 251 249 246 242 241 231 221 210 200 190 179 170 164 160 154 149 143 140 134 130 120 110 100 90.0 80.0 70.0 60.0

/xm

no

1.97 2.07 2.17 2.31 2.40 2.50 2.59 26.95 27.70 28.49 29.33 30.21 31.15 32.15 33.22 34.36 35.71 37.04 38.31 39.84 40.16 40.65 41.32 41.49 43.29 45.25 47.62 50.00 52.63 55.87 58.82 60.98 62.50 64.94 67.11 69.93 71.43 74.63 76.92 83.33 90.91 100.0 111.1 125.0 142.9 166.7

ko

ne

2.8E-06 2.9E-06 3.1E-06 3.4E-06 3.5E-06 3.7E-06 3.8E-06 2.348 [14] 2.317 2.280 2.247 2.191 2.114 2.024 1.870 1.697 1.351 0.544 0.528 1.826 3.655 6.862 6.850 6.124 4.226 3.690 3.361 3.169 3.054 2.935 2.748 2.642 2.747 3.225 3.133 2.872 2.744 2.799 3.541 3.304 3.135 3.053 2.969 3.095 3.119 3.051

0.118 [14] 0.102 0.100 0.122 0.137 0.141 0.159 0.188 0.269 0.913 2.410 4.744 5.637 5.770 2.657 1.403 0.282 0.132 0.110 0.112 0.120 0.126 0.229 0.456 0.752 0.613 0.381 0.317 0.408 0.959 0.550 0.152 0.127 0.123 0.113 0.335 0.088 0.064

ke 3.2E-06 3.6E-06 3.9E-06 4.0E-06 3.9E-06 3.8E-06 3.8E-06

2.420 [14] 2.389 2.354 2.307 2.277 2.201 2.107 1.961 1.784 1.389 0.488 0.422 1.519 4.264 7.291 5.912 5.324 3.960 3.425 3.135 2.879 2.639 2.376 1.911 1.854 1.928 2.644 3.341 4.493 4.523 4.348 4.192 3.926 3.730 3.581 3.497 3.444 3.387 3.349

0.073 [ 141 0.145 0.658 2.150 5.197 6.776 4.945 1.982 0.572 0.171 0.093 0.109 0.138 0.205 0.342 0.741 1.115 1.746 2.591 2.621 1.784 1.160 0.723 0.501 0.280 0.158 0.095

(continued)

588

Luis Art0s TABLE I

(Continued)

AgGaSez

eV 6.199E-3 4.959E-3 3.720E-3 2.480E-3

cm- 1 50.0 40.0 30.0 20.0

/xm 200.0 250.0 333.3 500.0

no 3.028 3.005 2.988 2.971

ko 0.047

ne 3.317 3.298 3.285 3.260

TABLE II Values of n and k for AgGaSz Obtained from Various References a

eV 25.0 24.0 23.0 22.0 21.0 20.0 19.5 19.0 18.5 18.0 17.5 17.0 16.5 16.0 15.5 15.0 14.5 14.0 13.5 13.0 12.5 12.0 11.6 11.0 10.5 10.0 9.50 9.00 8.50 8.00 7.50 7.00 6.50 6.00

cm- ~ 2.016E5 1.936E5 1.855E5 1.774E5 1.694E5 1.613E5 1.573E5 1.532E5 1.492E5 1.452E5 1.411E5 1.371E5 1.331E5 1.290E5 1.250E5 1.210E5 1.169E5 1.129E5 1.089E5 1.049E5 1.009E5 9.679E4 9.356E4 8.872E4 8.469E4 8.066E4 7.662E4 7.259E4 6.856E4 6.452E4 6.049E4 5.646E4 5.243E4 4.839E4

/zm 0.04959 0.05166 0.05390 0.05636 0.05904 0.06199 0.06358 0.06226 0.06702 0.06889 0.07085 0.07293 0.07514 0.07749 0.08000 0.08266 0.08555 0.08856 0.09184 0.09537 0.09919 0.1033 0.1069 0.1127 0.1181 0.1240 0.1305 0.1378 0.1459 0.1550 0.1653 0.1771 0.1907 0.2066

"References given in brackets.

n 0.827 [6] 0.822 0.822 0.816 0.815 0.810 0.807 0.805 0.803 0.805 0.807 0.805 0.808 0.810 0.813 0.819 0.826 0.832 0.842 0.858 0.874 0.886 0.900 0.917 0.934 0.958 1.008 1.083 1.126 1.213 1.292 1.317 1.415 1.564

k 0.185 [6] 0.206 0.222 0.245 0.264 0.291 0.306 0.321 0.341 0.360 0.374 0.396 0.416 0.439 0.464 0.491 0.515 0.545 0.577 0.610 0.637 0.669 0.698 0.742 0.790 0.846 0.925 0.955 1.007 1.063 1.058 1.110 1.240 1.266

ke

Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2) TABLE II

589

(Continued)

AgGaSz eV

cm- 1

~m

5.50 5.00 4.50 4.00 3.90 3.80 3.70 3.60 3.50 3.40 3.30 3.20 3.10 3.00 2.90 2.80 2.75 2.70

4.436E4 4.033E4 3.630E4 3.226E4 3.146E4 3.065E4 2.984E4 2.904E4 2.823E4 2.742E4 2.662E4 2.581E4 2.500E4 2.420E4 2.339E4 2.258E4 2.218E4 2.178E4

0.2254 0.2478 0.2755 0.3100 0.3179 0.3263 0.3351 0.3444 0.3542 0.3647 0.3757 0.3874 0.3999 0.4133 0.4275 0.4428 0.4509 0.4592

6.54 6.29 6.06 5.80 5.55 5.31 5.05 4.80 4.56 4.32 4.06 3.91 3.71 3.51 3.41 3.32 3.20 3.11 2.90 2.70 2.50

5.275E4 5.073E4 4.888E4 4.678E4 4.476E4 4.283E4 4.073E4 3.871E4 3.678E4 3.484E4 3.275E4 3.154E4 2.992E4 2.831E4 2.750E4 2.678E4 2.581E4 2.508E4 2.339E4 2.178E4 2.016E4

0.1896 0.1971 0.2046 0.2138 0.2234 0.2335 0.2455 0.2583 0.2719 0.2870 0.3054 0.3171 0.3342 0.3532 0.3636 0.3735 0.3875 0.3987 0.4275 0.4592 0.4959

eV 2.531 2.480 2.362 2.254 2.156

cm-~ 2.041E4 2.000E4 1.905E4 1.818E4 1.739E4

n 1.784 1.939 2.173 2.515 2.542 2.569 2.578 2.590 2.589 2.590 2.587 2.586 2.586 2.597 2.609 2.601 2.601 2.606

k 1.314 1.305 1.283 1.080 1.006 0.944 0.875 0.820 0.766 0.717 0.672 0.634 0.600 0.566 0.518 0.468 0.450 0.429 0.479 [23] 0.496 0.510 0.539 0.559 0.569 0.590 0.620 0.643 0.693 0.687 0.350 0.329 0.320 0.320 0.291 0.258 0.235 0.208 0.158 0.141

/zm

no

0.490 0.500 0.525 0.550 0.575

2.7148 [24] 2.6916 2.6503 2.6190 2.5944

ko

ne

ke

2.7287 [24] 2.6867 2.6239 2.5834 2.5537

(continued)

590

Luis Artes TABLE II

(Continued)

AgGaS2 eV 2.067 1.984 1.908 1.837 1.772 1.653 1.550 1.459 1.377 1.306 1.240 1.127 1.033 0.9537 0.8856 0.8266 0.7749 0.6889 0.6199 0.5635 0.5166 0.4768 0.4428 0.4132 0.3875 0.3646 0.3444 0.3263 0.3100 0.2755 0.2480 0.2254 0.2067 0.1907 0.1772 0.1653 0.1550 0.1458 0.1377 0.1306 0.1240 0.1181 0.1127 0.1078 0.1033 0.09919 0.09537

-1

/xm

1.667E4 1.600E4 1.539E4 1.482E4 1.429E4 1.333E4 1.250E4 1.177E4 1.111E4 1.053E4 1.000E4 9.091E3 8.333E3 7.692E3 7.143E3 6.667E3 6.250E3 5.556E3 5.000E3 4.545E3 4.167E3 3.846E3 3.571E3 3.333E3 3.125E3 2.941E3 2.778E3 2.632E3 2.500E3 2.222E3 2.000E3 1.818E3 1.667E3 1.538E3 1.429E3 1.333E3 1.250E3 1.176E3 1.111E3 1.053E3 1.000E3 9.524E2 9.091 E2 8.696E2 8.333E2 8.000E2 7.692E2

0.600 0.625 0.650 0.675 0.700 0.750 0.800 0.850 0.900 0.950 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 4.50 5.00 5.50 6.O0 6.5O 7.00 7.50 8.00 8.50 9.00 9.50 10.0 10.5 11.0 11.5 12.0 12.5 13.0

cm

no

2.5748 2.5577 2.5437 2.5310 2.5205 2.5049 2.4909 2.4802 2.4716 2.4644 2.4582 2.4486 2.4414 2.4359 2.4315 2.4280 2.4252 2.4206 2.4164 2.4161 2.4119 2.4102 2.4094 2.4080 2.4068 2.4062 2.4046 2.4024 2.4024 2.4003 2.3955 2.3938 2.3908 2.3874 2.3827 2.3787 2.3757 2.3699 2.3663 2.3606 2.3548 2.3486 2.3417 2.3329 2.3266 2.3177 2.3076

ko

ne

2.5303 2.5116 2.4961 2.4824 2.5706 2.4540 2.4395 2.4279 2.4192 2.4118 2.4053 2.3954 2.3881 2.3819 2.3781 2.3745 2.3716 2.3670 2.3637 2.3684 2.3583 2.3567 2.3559 2.3545 2.3534 2.3522 2.3511 2.3491 2.3488 2.3461 2.3419 2.3401 2.3369 2.3334 2.3291 2.3252 2.3219 2.3163 2.3121 2.3064 2.3012 2.2948 2.2880 2.2789 2.2716

ke

Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2) TABLE II

591

(Continued)

AgGaS2 eV

cm- 1

2.522 2.472 2.270 2.145 2.110 1.857

2.034E4 1.994E4 1.831E4 1.730E4 1.702E4 1.498E4

2.234 2.175 2.112 2.070 1.990 1.887 1.705 1.556 1.425 1.328 1.241 1.042 0.8920 0.7897 0.7045 0.6424 0.5904 0.5414 0.5020 0.4643 0.4382 0.4119 0.4092 0.3397 0.2931 0.2545 0.2266 0.2030 0.1851 0.1694 0.1566 0.1461 0.1364 0.1292 0.1252 0.1042 0.09184 0.08670

1.802E4 1.754E4 1.704E4 1.669E4 1.605E4 1.522E4 1.376E4 1.255E4 1.149E4 1.071E4 1.001E4 8.403E3 7.194E3 6.369E3 5.682E3 5.181E3 4.762E3 4.367E3 4.049E3 3.745E3 3.534E3 3.322E3 3.300E3 2.740E3 2.364E3 2.053E3 1.828E3 1.637E3 1.493E3 1.366E3 1.263E3 1.178E3 1.100E3 1.042E3 1.010E3 8.403E2 7.407E2 6.993E2

/a,m 0.4916 0.5016 0.5461 0.5780 0.5876 0.6678 0.555 0.570 0.587 0.599 0.623 0.657 0.727 0.797 0.870 0.934 0.999 1.19 1.39 1.57 1.76 1.93 2.10 2.29 2.47 2.67 2.83 3.01 3.03 3.65 4.23 4.87 5.47 6.11 6.70 7.32 7.92 8.49 9.09 9.60 9.90 11.9 13.5 14.3

no

ko

2.700 [25] 2.683 2.619 2.587 2.579 2.529

ne

ke

2.710 [25] 2.676 2.585 2.546 2.537 2.481 8.6E-05 [26] 3.3E-05 3.1E-05 3.1E-05 3.0E-05 3.0E-05 3.0E-05 3.0E-05 3.3E-05 3.7E-05 4.1E-05 5.1E-05 6.2E-05 7.2E-05 8.5E-05 9.6E-05 1.1E-04 1.2E-04 1.4E-04 1.5E-04 1.7E-04 1.8E-04 1.8E-04 2.3E-04 2.7E-04 3.2E-04 3.6E-04 4.1E-04 4.6E-04 5.0E-04 5.5E-04 6.0E-04 6.5E-04 7.0E-04 7.4E-04 9.6E-04 1.3E-03 1.8E-03

1.8E-04 [26] 3.9E-05 3.2E-05 3.1E-05 3.0E-05 3.0E-05 3.3E-05 3.7E-05 4.1E-05 5.1E-05 6.2E-05 7.2E-05 8.5E-05 9.6E-05 1.1E-04 1.2E-04 1.4E-04 1.5E-04 1.7E-04 1.8E-04 1.8E-04 2.3E-04 2.7E-04 3.2E-04 3.6E-04 4.1E-04 4.6E-04 5.1E-04 5.7E-04 6.3E-04 7.0E-04 7.7E-04 8.3E-04 1.0E-03 1.3E-03 1.8E-03

(continued)

592

Luis Art0s TABLE I I

(Continued)

AgGaS2 eV 0.08266 0.07005 0.06927 0.06739 0.06595 0.06457 0.06293 0.06168 0.05990 0.05932 57.41E-3 56.28E-3 55.05E-3 53.81E-3 52.45E-3 51.21E-3 49.84E-3 48.73E-3 47.36E-3 46.12E-3 45.75E-3 45.13E-3 45.01E-3 43.77E-3 42.40E-3 41.16E-3 40.17E-3 39.92E-3 39.30E-3 38.81E-3 37.69E-3 36.33E-3 34.96E-3 33.72E-3 32.48E-3 31.24E-3 29.88E-3 28.76E-3 27.77E-3 27.52E-3 26.53E-3 26.16E-3 24.92E-3 23.56E-3 22.32E-3 21.08E-3

cm

--1

6.667E2 5.650E2 5.587E2 5.435E2 5.319E2 5.208E2 5.076E2 4.975E2 4.831E2 4.785E2 463 454 444 434 423 413 402 393 382 372 369 364 363 353 342 332 324 322 317 313 304 293 282 272 262 252 241 232 224 222 214 211 201 190 180 170

/xm

no

15.0 17.7 17.9 18.4 18.8 19.2 19.7 20.1 20.7 20.9 21.60 22.03 22.52 23.04 23.64 24.21 24.88 25.45 26.18 26.88 27.10 27.47 27.55 28.33 29.24 30.12 30.86 31.06 31.55 31.95 32.89 34.13 35.46 36.76 38.17 39.68 41.49 43.10 44.64 45.O5 46.73 47.39 49.75 52.63 55.56 58.82

ko

ne

3.0E-03 4.7E-03 3.3E-03 3.4E-03 3.5E-03 3.8E-03 3.9E-03 3.9E-03 4.9E-03 8.7E-03 1.875 [28] 1.826 1.759 1.665 1.522 1.319 1.010 0.471 0.237 1.721 3.029 3.810 3.674 0.988 0.605 1.398 3.580 5.690 6.652 5.846 4.408 3.721 3.362 3.059 2.842 2.617 2.345 2.060 2.550 3.195 3.897 3.801 3.502 3.091 2.938 2.915

0.152 [28] 0.475 1.507 3.329 4.177 1.513 0.546 1.082 2.250 4.421 6.061 5.554 2.394 0.866 0.246 0.139 0.134 0.125 0.126 0.172 0.374 1.O90 1.947 1.850 1.020 0.637 0.364 0.358 0.437 0.619

ke

3.0E-03

5.1E-03 4.3E-03 4.6E-03 4.8E-03 6.2E-03

1.931 [28] 1.870 1.792 1.721 1.591 1.439 1.112 0.568 0.340 1.819 2.063 5.526 5.185 3.868 3.200 2.856 2.696 2.625 2.550 2.498 2.377 2.268 2.100 1.969 1.694 1.305 0.855 0.964 1.416 2.013 3.419 5.216 4.695 4.110 3.679 3.458

0.131 [281 0.554 1.838 4.605 4.645 3.417 0.870 0.257 0.079 0.023 0.021 0.026 0.020 0.021 0.026 0.038 0.058 0.083 0.198 0.504 1.227 2.216 3.374 3.831 4.050 2.657 0.912 0.435 0.187 0.111

Silver Gallium Selenide (AgGaSe2), Silver Gallium Sulfide (AgGaS2)

593

T A B L E II (Continued)

AgGaSz eV 19.84E-3 18.60E-3 17.48E- 3 16.12E-3 14.88E-3 13.64E-3 12.40E-3 11.16E-3 9.919E-3 8.679E-3 7.439E-3 6.323E-3

cm- ~ 160 150 141 130 120 110 100 90 80 70 60 51

~m 62.50 66.67 70.92 76.92 83.33 90.91 100.0 111.1 125.0 142.9 166.7 196.1

no 3.048 3.332 3.473 3.482 3.454 3.420 3.373 3.333 3.300 3.276 3.248 3.230

ko 0.754 0.723 0.546 0.345 0.203 0.135 0.136

ne 3.353 3.292 3.241 3.193 3.153 3.129 3.104 3.069 3.051 3.048 3.031 3.017

ke 0.077

0.065 0.056 0.038