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Bond ionicity and susceptibility in aIbIIIc2VI compounds
J. Phys. Chem. Solids Vol. 48, No. 9. pp. 827431, Printed in Great Britain.
1987 0
llo22-3697187 1987 Pergamon
s3.00 + 0.00 Journals Ltd.
BOND IONICITY AND SUSCEPTIBILITY IN A’ B’” CT1 COMPOUNDS v. KUMAR Department of Instrumentation, Central Mining Research Station, Barwa Road, Dhanbad 826001, India (Received
31 December
1986; accepted 6 February
1987)
Abstract--The electronic susceptibilities, energy gaps and the bond ionicities of some A’B”‘Cz’ chalcopyrite compounds have been calculated from their plasmon energy. The effect of delocalization of noble metal d-electrons has been taken into account while calculating these parameters in the case of the At-C”’ bond. A comparison is made between the present results and the results of previous calculations. Keywords: ABC, chalcopyrite compounds, bond ionicity, electronic susceptibility, dielectric properties.
1. INTRODUCTION
2. CALCULATION OF BOND IONIClTY
In recent years increasing attention has been given towards the study of A’B”‘C~’ chalcopyrite compounds. This is because of their potential for various practical applications in nonlinear optics, photovoltaic detectors, light emitting diodes, solar cells, etc. The energy gaps and other dielectric properties, electronic and electrical properties have been studied by several workers [l-13]. There have been many types of theoretical approaches to the calculation of energy gaps and the ionicity (J;) of the chemical bond in this family of compounds. The first approach for simple binary compounds was given by Pauling [111 based on thermochemical effects and electronegativity. Phillips and Van Vechten [7-91 have defined the average energy gap in terms of homopolar (covalent) and heteropolar (ionic) parts using spectroscopic definitions and the one-electron model orig inally suggested by Penn [13]. This theory of Phillips and Van Vechten [7-91 has been extended to multibond and complex crystals by Levine [lo], Neumann [4] and several other workers [6, 14, 151including the effect of d-electrons. Coulson et al. [ 161have used the LCAO-MO approximation to calculate these energy gaps. Recently the author [17] has proposed a simple model based on the plasmon oscillation theory of solids for the calculation of the homopolar (Eh) and heteropolar (C) energy gaps, and the ionicity in the rocksalt, zinc-blende and CsCl crystal structures. In the present paper, the purpose is to extend the analysis of the homopolar and heteropolar energy gaps, and the ionicity reported previously [17] in the case of A’B”‘C~’ semiconductors with A’ = Cu and Ag. The electronic susceptibility and dielectric constant of AI-C” and B1”Cv’ bonds have been calculated. In the calculation of the energy gaps of the A’-CV’ bond the effect of the d-electrons of the noble metal has also been taken into account. The calculated values of these parameters are in fair agreement with the values reported by other workers.
In order to determine the ionicity of A’-(?’ and B”‘-Cv’ bonds in A’B”‘C~’ compounds the effective number of valence electrons, N$, can be written in terms of individual bond properties as
827
N: = (n$/vg)
(1)
where n: = (2:/N:
+ Z$/N:),
(2)
n$’ is the number of valence electrons per bond, Z{ and Zj are the number of valence electrons of the atoms a and j, Ns and N$ are the coordination numbers of the atoms and vi is the bond volume. In the case of A’@‘%? compounds eqn (2) reduces to the simple form n: = (Z:+ Z$)/N:, since N,= Nefl= N,, = 4 for these crystals, which yield for AI-C”’ and B”‘-Cv’ bonds ncAc = (11 f 6)/4 = 17/4 and n,“, = (3 + 6)/4 = 9/4, respectively. The bond volume, vg = 4 d:,J3fi for the chalcopyrite structures, where dGa is the bond length for the A’-CV’ bond, and can be written in terms of the plasmon energy as d&t&)
= 19.67(hwp,Ac)-2’3
(3)
d&A)
= 15.91(ho,,,c)-“‘.
(4)
and
It is also useful to express the average energy gap (E:) in terms of homopolar and heteropolar parts as (E;)2 = W2
+ (C”)2
(5)
and the fractional ionicity as f: = (C~)*/(E;)‘.
(6)
828
V. KUMAR
The expression energy gaps AZ = (Z, - Zc) the noble metal
for the homopolar and heteropolar for the B”‘-C”’ bond, where = 3 and there is no involvement of d-electrons, can be written as:
E ~.BC= O.O416(hw,,,c)’ eV
(7)
and c,, = 5.53 b(hw,# x exp[- 6.5058(hw,ac)-‘“I
eV,
(8)
where the constant v = 1.6533. Similarly the case of the A’-C”’ bond where AZ = (Z&A, - Zc) = (11 - 6) = 5, can be written as: E ,,.*c = O.O246(hw,,&v eV
configuration of Cu, which is 3 d9 4 s2, is only 1.38 eV above the valence-electron ground state configuration 3 d” 4 s’ [18]. Thus, it has been found by several workers [lo, 191 that it is necessary to include all the d-electrons (Zcu,Ag= 11) when evaluating the effective number of valence electrons, N:, in the calculation of the plasmon energy ho, from the forthcoming equation (13). In the present calculation the average value of the prescreening factor b has been taken as 1.8 [4] while calculating the homopolar and heteropolar energy gaps of the B”‘-C”’ and Cu-C”’ bonds, and 1.99 [lo] in the case of the Ag-C”’ bond. Neumann’s value of bAg_c= 1.8 also gives reasonably good results, but an underestimation of ionicity for the AggC”’ bond, while the value for b,,c of 1.99 gives excellent agreement with previous estimates.
(9) 3. CALCULATION SUSCEPTIBILITY AND
and
The electronic susceptibility for complex crystal structures is given by the relation
C,, = 7.3208 b(h~‘,~c)*‘~ x exp[ - 8.026(hw’,,,)‘~3(h~,_,,,)-2’3]
OF ELECTRONIC DIELECTRIC CONSTANT
eV,
(10) X” = (hQ;)*l(E:)*,
where Z&Ap = Z,[S/b exp(-K,r,)] = Z,a, S is the transition or noble metal core screening factor which includes all the s-, p-, and d-electrons, while b . exp( - KJ,) is the usual Thomas-Fermi factor for the C”’ atoms, which includes only the s- and pelectrons. Taking d-electrons into consideration Z&,, has been calculated for the A’-C”’ bond in A’B’*‘Cy’ semiconductors as equal to 11 [l 11. The effective value of Z = (Z, + Zs) has been taken as 17 and 9 for the A’-C”’ and B”‘-C”’ bonds, respectively while calculating the plasmon energy from eqn (13). The Thomas-Fermi wave number K, for the A’-C”’ bond can be written as:
&AC = [~($~li;;no;,*c)‘~~,
(11)
where (hQ;)2 = (47~e2Nflm)DpAF = (Fw;)~D”A~,
(13)
e and m are the charge and mass of electrons, Dfl and A’ are correction factors of the order of unity accounting for the influence of the d-electrons. A detailed discussion of Dfl and A’ has been given elsewhere [9, 10, 171 and will not be presented here. The constant A” is related to the average energy gap and the Fermi-energy of the valence electrons. The Fermi-energy E_$ can be written as [2&22]: ES = 0.2948(F1w:)~‘~ eV.
where (hw;,c) is the plasmon energy for the A’-C”’ bond, which has been evaluated using n,,,c = 714 [4] considering only the effect of s - and p-electrons. This is because of the effect of delocalization of the noble metal d-electron which is weak, especially for the CuB”‘C~’ compounds, where they are situated around the A’ atom. Therefore, it is assumed that the screening of the C”’ core is mainly due to s- and p-electrons. The effect of delocalization of the noble metal d-electrons is different for the CuB”‘CY’ and AgB”‘C~’ compounds [4], which shows that there should be a different b,, for these compound families. However, the differences in the values of b,, are quite small because Kf ‘Y (N&)li6. In the case of Cu and Ag, the d-electrons are loosely bound, unlike the usual tightly-bound d-core state of Zn and Cd which are the following elements in the periodic table. The lowest excited state
(12)
(14)
Further, the tetrahedrally coordinated A’B”‘C~’ crystals are composed of equal numbers of A’-C”’ and B”‘-C”’ bonds. The electronic dielectric constant is given by the relation: c’= 1 + I/2(&c + XBc),
(15)
where xACand xBc are the susceptibilities of A’-C”’ and B”‘C” bonds in A’B*“C~’ chalcopyrite compounds, and can be calculated by substituting the respective parameters for these bonds on the righthand side of eqn (12). 4. CONCLUSION
In the present paper we have taken special care of the plasmon energy of A’<“’ bond
n, in calculating
CUAIS, CuAlse, CuAlTe, CuGaS, CuGaSe, CuGaTe, CuInS, CuInSe, CuInTe, AgAlS, A&Se, AtiTer AgGaSa AgGaSe, AgGaTe, AgInS, AgInSe, AaInTe,
Compounds
W)
%%A,
25.110 23.23 1 20.859 1.0850 l.OoOO 23.626 22.176 1.0575 1.0850 20.703 22.231 1.0000 23.061 1.0575 1.0850 20.167 21.536 1.0575 20.090 1.1292 1.1674 18.681 1*OS75 21.201 20.110 1.1292 1.1674 18.905 21.979 1.0575 1.1292 20.513 18.751 1.1674
I .0575
1.0000
D
21.676 19.541 16.927 19.985 18.367 16.758 18.427 19.350 16.182 17.663 16.100 14.612 17.298 16.121 14.846 18.149 16.554 14.685
@V)
E FAC 16.113 14.907 13.385 15.160 14.230 13.284 14.907 14.798 12.941 13.819 12.891 1I .987 13.605 12.904 12.131 14.103 13.163 12.032
5.073 4.461 3.733 4.587 4.047 3.687 4.148 4.407 3.531 3.936 3.508 3.111 3.835 3.514 3.173 4.071 3.631 3.130
W
-%,A, 10.575 9.435 8.035 9.673 8.807 7.945 8.523 9.333 6.635 9.320 8.393 7.510 9.103 8.405 7.649 9.608 8.662 1.554 11.728 10.436 8.859 10.705 9.692 8.758 9.478 10.321 7.516 10.117 9.096 8.128 9.877 9.110 8.281 10.434 9.392 8.176
(W
E&AC 0.813 0.817 0.822 0.816 0.825 0.823 0.808 0.817 0.779 0.848 0.851 0.853 0.849 0.851 0.853 0.847 0.850 0.853
0.78 0.79 0.75 0.77 0.76 0.81 0.77 0.77 0.76 0.85 0.86 0.84 0.86 0.85 0.86 0.85 0.85 0.84
This Neumann work [41 0.65 0.63 0.56 0.66 0.63 0.57 0.68 0.65 0.59 0.70 0.67 0.62 0.70 0.68 0.62 0.72 0.70 0.64
Fl
Bernard
Table 1. Properties of the A’C”’ bond in AiB”‘CY’ compounds
0.846
0.867 0.852
0.785
0.825 0,784
Levine [lOI 4.584 5.240 5.262 4.248 4.838 5.305 4.824 4.607 6.939 4.138 4.767 5.349 4.209 4.762 5.275 4.048 4.658 5.325
4.78 5.42 7.73 4.83 6.00 5.65 5.22 6.38 7.45 4.02 4.65 6.02 3.83 4.78 5.07 4.02 4.64 6.02
This Neumann work [41
4.53
3.68 4.28
5.53
4.43 5.76
Levine 1101
CuAlTe, CuGaS, CuGaSe, CuGaTe, CuInS, CtlInSe, CuInTe, AgAIS, AgA1% AgA1Ter AgGaS, AgGa% AgGaTe, AgInS, AgInSe, AgInTe,
c==%
CUAlS,
1.000 1.0975 1.1650 1.0975 1.2093 1.2876 1.1650 1.2876 1.3739 1.0000 1.0975 1.1650 1.0975 1.2093 1.2876 1.1650 1.2876 1.3739
D
18.295 17.041 15.518 18.163 16.906 15.195 16.453 15.489 14.332 18.708 17.510 15.408 18.598 17.193 15.149 16.313 15.291 13.860
W
%ec 14.211 12.927 11.410 14.079 12.791 11.095 12.336 11.382 10.262 14.640 13.404 11.302 14.526 13.081 11.050 12.196 11.188 9.814
W)
E F,BC 7.671 6.863 5.902 7.584 6.777 5.725 6.494 5.902 5.215 7.943 7.162 5.853 7.869 6.959 5.698 6.408 5.783 4.944
WV
5.083 4.519 3.844 5.022 4.460 3.739 4.265 3.859 3.394 5.274 4.727 3.826 5.222 4.586 3.720 4.205 3.778 3.212
E&BC
WI 0.561 0.566 0.576 0.561 0.567 0.573 0.569 0.572 0.576 0.559 0.564 0.573 0.559 0.566 0.573 0.569 0.573 0.578
This work 0.62 0.65 0.56 0.55 0.55 0.51 0.60 0.60 0.57 0.61 0.63 0.57 0.54 0.54 0.51 0.61 0.60 0.58
Neumann 141 0.54 0.50 0.38 0.54 0.49 0.39 0.61 0.57 0.48 0.56 0.51 0.41 0.54 0.51 0.40 0.64 0.60 0.50
Bernard [61
0.604
0.570 0.561
0.636
0.565 0.563
1101
Levine
compounds
f;.BC
of the B’nC~’ bond in A’B”‘C~’
E h,BC 5.746 5.165 4.479 5.684 5.103 4.336 4.898 4.466 3.960 5.939 5.381 4.430 5.887 5.235 4.316 4.835 4.378 3.758
Table 2. Properties
4.955 5.908 7.102 5.485 6.573 7.951 6.537 7.867 9.114 4.829 5.461 7.073 5.338 6.443 7.978 6.601 7.888 9.494
This work 4.26 4.76 7.19 5.59 6.80 9.17 6.02 7.30 9.35 4.26 4.76 7.19 5.59 6.80 9.17 6.02 7.30 9.35
Neumann [41
x
7.41
5.84 7.04
5.99
6.07 7.04
DOI
Levine GalC 5.769 6.574 7.182 5.866 6.705 7.628 6.680 7.237 9.026 5.483 6.114 7.211 5.773 6.602 7.626 6.324 7.273 8.494
A*B”‘Cp compounds
(noble metal compounds) while earlier workers [7-lo] have neglected this in their calculations. Further, earlier models require the experimental values of the optical dielectric constant for the calculation of Eht C and f; but in the current model one can predict the order of these parameters without having any knowledge of the experimental value of &. The values of the homopolar (E,,) and heteropolar (C) energy gaps and the ionicity (f;) of the A’-C”’ and B”‘Xv’ bond in A’B”‘C~’ semiconductors have been calculated from eqns (6HlO). Using these values of E,, and C the average energy gap (ES), eiectronic susceptibility (2) and dielectric constant (6) have been calculated and presented in Tables 1 and 2. Our calculated values are in fair agreement with the values reported by various workers. Thus, it is possible to predict the order of E,,, C, A, x and 6 in A*B”‘Cy’ compounds from their plasmon loss values without having any knowledge of the experimental value of the dielectric constant. Ac~o~ledg~en~-The author is grateful to Dr. B. Singh, Director, Central Mining Besearcfi Station, Dhanbad, for his continuing inspiration and for giving permission to publish this paper. The author is also grateful ta Dr. S. C. Srivastava for his valuable advice and cooperation. REFERENCES 1. 2. 3. 4.
Chelikowsky J. R., Phys. Rev. Lett. Sa, 961 (1986). Enders P., Phys. Status S&di b 131, 489 (1985). Cohen M. L., Phys. Rep. Ilg, 293 (1984). Neumann H., Cry& Res. Tech. 18, 1299, 1391,665,981 (1983).
831
5. Catlow C. R. A. and Stoneham A. M., J. Phys. C (Solid
Sr.) 16, 4321 (1983). 6. Bernard M. J., Physique LSz&.I 36, C3 (1975). 7. Phillips J. C., Hi&&hts bf -~o&%msed-Matter Theory LXXXIX Corso Sot. Italiana di Fisica. Bologna. Italv. p* $77 (i985); Rev. AL&d. Phys. 4% 3i7 (19%);~ Ph&: Rev. B 29, 5583 (f984). 8. Phillips 1. C. and Van Vechten J, A., Whys. Ren IrU, 709 (1969); Phys. ffev. 32, 2147 (1970). 9. Van Vechten J. A., Phys. Rev, B1, 3351 (1970); Phys. Rev. 182, 891 (1969); Phys. Rev. X87, 1007 (1969). 10. Levine B. F., Phys. Rev. B7,2591,2600 (1973); J. them. Phys. 59, 1463 (1973); Phys. Rev. Lert. 25, 44 (1970). 11. Paulin I,., Phys. Rev. Lett. 23,480 (1969); Phys. Today, p. 9, Feb. (1971); The Nature qf the Chemicat Bond, Cornell Universitv Press. Ithaca. New York (1960). 12, Srinivasan G., P&s. R&. 178, i244 (1969). . I 13. Penn D. R., Phys. Ben. 128, 2893 (1962). 14. Chemla D. S., Phys. Rev. Lett. 26, 1441 (1971). 15. Fischer J. E., Glickman M. and Van Vechten J. A., Proc. Int. Conf. Phys. Semicond., Roma, Italy, p. 541 (1976). 16. Coulson C. A., Redei L. B. and Stocker D., Proc. R. Sot. (Land.) 370, 257 (1962). 17. Srivastava V. &mar, Phys. Rev. I329, 6993 (1984); Phys. Lett. A IO2, 127 (1984); J. Phys. C (Solid ft.) 19, 5689 (1986). 18. Backer R. B. and Goudsmith S,, A&&c Energy Sfates, McGraw-Hill, New York (1932). 19 Wample S. H. and Dome&a M. D., Jr., Phys. Rev. 33, 1338 (1971). 20. Pines D., Elementary Excitation in Solids, pp. 58 and 92. W. A. Benjamin, New York (1964). 21. Martan L., Leder L. B. and Mendlawitz H., Advances in Electronics and Electron Physics (Edited by L. Martom), Vol. 7, p. 225. Academic Press, New York (1955). 22. Rooke 6. A., srtft X-ray Band Spectra rutd the Eketronic Structure OXMet& and Mzteriak @!&ted by D. J, Fabian}, p. 6. Academic Press, New York (1968).
1987 0
llo22-3697187 1987 Pergamon
s3.00 + 0.00 Journals Ltd.
BOND IONICITY AND SUSCEPTIBILITY IN A’ B’” CT1 COMPOUNDS v. KUMAR Department of Instrumentation, Central Mining Research Station, Barwa Road, Dhanbad 826001, India (Received
31 December
1986; accepted 6 February
1987)
Abstract--The electronic susceptibilities, energy gaps and the bond ionicities of some A’B”‘Cz’ chalcopyrite compounds have been calculated from their plasmon energy. The effect of delocalization of noble metal d-electrons has been taken into account while calculating these parameters in the case of the At-C”’ bond. A comparison is made between the present results and the results of previous calculations. Keywords: ABC, chalcopyrite compounds, bond ionicity, electronic susceptibility, dielectric properties.
1. INTRODUCTION
2. CALCULATION OF BOND IONIClTY
In recent years increasing attention has been given towards the study of A’B”‘C~’ chalcopyrite compounds. This is because of their potential for various practical applications in nonlinear optics, photovoltaic detectors, light emitting diodes, solar cells, etc. The energy gaps and other dielectric properties, electronic and electrical properties have been studied by several workers [l-13]. There have been many types of theoretical approaches to the calculation of energy gaps and the ionicity (J;) of the chemical bond in this family of compounds. The first approach for simple binary compounds was given by Pauling [111 based on thermochemical effects and electronegativity. Phillips and Van Vechten [7-91 have defined the average energy gap in terms of homopolar (covalent) and heteropolar (ionic) parts using spectroscopic definitions and the one-electron model orig inally suggested by Penn [13]. This theory of Phillips and Van Vechten [7-91 has been extended to multibond and complex crystals by Levine [lo], Neumann [4] and several other workers [6, 14, 151including the effect of d-electrons. Coulson et al. [ 161have used the LCAO-MO approximation to calculate these energy gaps. Recently the author [17] has proposed a simple model based on the plasmon oscillation theory of solids for the calculation of the homopolar (Eh) and heteropolar (C) energy gaps, and the ionicity in the rocksalt, zinc-blende and CsCl crystal structures. In the present paper, the purpose is to extend the analysis of the homopolar and heteropolar energy gaps, and the ionicity reported previously [17] in the case of A’B”‘C~’ semiconductors with A’ = Cu and Ag. The electronic susceptibility and dielectric constant of AI-C” and B1”Cv’ bonds have been calculated. In the calculation of the energy gaps of the A’-CV’ bond the effect of the d-electrons of the noble metal has also been taken into account. The calculated values of these parameters are in fair agreement with the values reported by other workers.
In order to determine the ionicity of A’-(?’ and B”‘-Cv’ bonds in A’B”‘C~’ compounds the effective number of valence electrons, N$, can be written in terms of individual bond properties as
827
N: = (n$/vg)
(1)
where n: = (2:/N:
+ Z$/N:),
(2)
n$’ is the number of valence electrons per bond, Z{ and Zj are the number of valence electrons of the atoms a and j, Ns and N$ are the coordination numbers of the atoms and vi is the bond volume. In the case of A’@‘%? compounds eqn (2) reduces to the simple form n: = (Z:+ Z$)/N:, since N,= Nefl= N,, = 4 for these crystals, which yield for AI-C”’ and B”‘-Cv’ bonds ncAc = (11 f 6)/4 = 17/4 and n,“, = (3 + 6)/4 = 9/4, respectively. The bond volume, vg = 4 d:,J3fi for the chalcopyrite structures, where dGa is the bond length for the A’-CV’ bond, and can be written in terms of the plasmon energy as d&t&)
= 19.67(hwp,Ac)-2’3
(3)
d&A)
= 15.91(ho,,,c)-“‘.
(4)
and
It is also useful to express the average energy gap (E:) in terms of homopolar and heteropolar parts as (E;)2 = W2
+ (C”)2
(5)
and the fractional ionicity as f: = (C~)*/(E;)‘.
(6)
828
V. KUMAR
The expression energy gaps AZ = (Z, - Zc) the noble metal
for the homopolar and heteropolar for the B”‘-C”’ bond, where = 3 and there is no involvement of d-electrons, can be written as:
E ~.BC= O.O416(hw,,,c)’ eV
(7)
and c,, = 5.53 b(hw,# x exp[- 6.5058(hw,ac)-‘“I
eV,
(8)
where the constant v = 1.6533. Similarly the case of the A’-C”’ bond where AZ = (Z&A, - Zc) = (11 - 6) = 5, can be written as: E ,,.*c = O.O246(hw,,&v eV
configuration of Cu, which is 3 d9 4 s2, is only 1.38 eV above the valence-electron ground state configuration 3 d” 4 s’ [18]. Thus, it has been found by several workers [lo, 191 that it is necessary to include all the d-electrons (Zcu,Ag= 11) when evaluating the effective number of valence electrons, N:, in the calculation of the plasmon energy ho, from the forthcoming equation (13). In the present calculation the average value of the prescreening factor b has been taken as 1.8 [4] while calculating the homopolar and heteropolar energy gaps of the B”‘-C”’ and Cu-C”’ bonds, and 1.99 [lo] in the case of the Ag-C”’ bond. Neumann’s value of bAg_c= 1.8 also gives reasonably good results, but an underestimation of ionicity for the AggC”’ bond, while the value for b,,c of 1.99 gives excellent agreement with previous estimates.
(9) 3. CALCULATION SUSCEPTIBILITY AND
and
The electronic susceptibility for complex crystal structures is given by the relation
C,, = 7.3208 b(h~‘,~c)*‘~ x exp[ - 8.026(hw’,,,)‘~3(h~,_,,,)-2’3]
OF ELECTRONIC DIELECTRIC CONSTANT
eV,
(10) X” = (hQ;)*l(E:)*,
where Z&Ap = Z,[S/b exp(-K,r,)] = Z,a, S is the transition or noble metal core screening factor which includes all the s-, p-, and d-electrons, while b . exp( - KJ,) is the usual Thomas-Fermi factor for the C”’ atoms, which includes only the s- and pelectrons. Taking d-electrons into consideration Z&,, has been calculated for the A’-C”’ bond in A’B’*‘Cy’ semiconductors as equal to 11 [l 11. The effective value of Z = (Z, + Zs) has been taken as 17 and 9 for the A’-C”’ and B”‘-C”’ bonds, respectively while calculating the plasmon energy from eqn (13). The Thomas-Fermi wave number K, for the A’-C”’ bond can be written as:
&AC = [~($~li;;no;,*c)‘~~,
(11)
where (hQ;)2 = (47~e2Nflm)DpAF = (Fw;)~D”A~,
(13)
e and m are the charge and mass of electrons, Dfl and A’ are correction factors of the order of unity accounting for the influence of the d-electrons. A detailed discussion of Dfl and A’ has been given elsewhere [9, 10, 171 and will not be presented here. The constant A” is related to the average energy gap and the Fermi-energy of the valence electrons. The Fermi-energy E_$ can be written as [2&22]: ES = 0.2948(F1w:)~‘~ eV.
where (hw;,c) is the plasmon energy for the A’-C”’ bond, which has been evaluated using n,,,c = 714 [4] considering only the effect of s - and p-electrons. This is because of the effect of delocalization of the noble metal d-electron which is weak, especially for the CuB”‘C~’ compounds, where they are situated around the A’ atom. Therefore, it is assumed that the screening of the C”’ core is mainly due to s- and p-electrons. The effect of delocalization of the noble metal d-electrons is different for the CuB”‘CY’ and AgB”‘C~’ compounds [4], which shows that there should be a different b,, for these compound families. However, the differences in the values of b,, are quite small because Kf ‘Y (N&)li6. In the case of Cu and Ag, the d-electrons are loosely bound, unlike the usual tightly-bound d-core state of Zn and Cd which are the following elements in the periodic table. The lowest excited state
(12)
(14)
Further, the tetrahedrally coordinated A’B”‘C~’ crystals are composed of equal numbers of A’-C”’ and B”‘-C”’ bonds. The electronic dielectric constant is given by the relation: c’= 1 + I/2(&c + XBc),
(15)
where xACand xBc are the susceptibilities of A’-C”’ and B”‘C” bonds in A’B*“C~’ chalcopyrite compounds, and can be calculated by substituting the respective parameters for these bonds on the righthand side of eqn (12). 4. CONCLUSION
In the present paper we have taken special care of the plasmon energy of A’<“’ bond
n, in calculating
CUAIS, CuAlse, CuAlTe, CuGaS, CuGaSe, CuGaTe, CuInS, CuInSe, CuInTe, AgAlS, A&Se, AtiTer AgGaSa AgGaSe, AgGaTe, AgInS, AgInSe, AaInTe,
Compounds
W)
%%A,
25.110 23.23 1 20.859 1.0850 l.OoOO 23.626 22.176 1.0575 1.0850 20.703 22.231 1.0000 23.061 1.0575 1.0850 20.167 21.536 1.0575 20.090 1.1292 1.1674 18.681 1*OS75 21.201 20.110 1.1292 1.1674 18.905 21.979 1.0575 1.1292 20.513 18.751 1.1674
I .0575
1.0000
D
21.676 19.541 16.927 19.985 18.367 16.758 18.427 19.350 16.182 17.663 16.100 14.612 17.298 16.121 14.846 18.149 16.554 14.685
@V)
E FAC 16.113 14.907 13.385 15.160 14.230 13.284 14.907 14.798 12.941 13.819 12.891 1I .987 13.605 12.904 12.131 14.103 13.163 12.032
5.073 4.461 3.733 4.587 4.047 3.687 4.148 4.407 3.531 3.936 3.508 3.111 3.835 3.514 3.173 4.071 3.631 3.130
W
-%,A, 10.575 9.435 8.035 9.673 8.807 7.945 8.523 9.333 6.635 9.320 8.393 7.510 9.103 8.405 7.649 9.608 8.662 1.554 11.728 10.436 8.859 10.705 9.692 8.758 9.478 10.321 7.516 10.117 9.096 8.128 9.877 9.110 8.281 10.434 9.392 8.176
(W
E&AC 0.813 0.817 0.822 0.816 0.825 0.823 0.808 0.817 0.779 0.848 0.851 0.853 0.849 0.851 0.853 0.847 0.850 0.853
0.78 0.79 0.75 0.77 0.76 0.81 0.77 0.77 0.76 0.85 0.86 0.84 0.86 0.85 0.86 0.85 0.85 0.84
This Neumann work [41 0.65 0.63 0.56 0.66 0.63 0.57 0.68 0.65 0.59 0.70 0.67 0.62 0.70 0.68 0.62 0.72 0.70 0.64
Fl
Bernard
Table 1. Properties of the A’C”’ bond in AiB”‘CY’ compounds
0.846
0.867 0.852
0.785
0.825 0,784
Levine [lOI 4.584 5.240 5.262 4.248 4.838 5.305 4.824 4.607 6.939 4.138 4.767 5.349 4.209 4.762 5.275 4.048 4.658 5.325
4.78 5.42 7.73 4.83 6.00 5.65 5.22 6.38 7.45 4.02 4.65 6.02 3.83 4.78 5.07 4.02 4.64 6.02
This Neumann work [41
4.53
3.68 4.28
5.53
4.43 5.76
Levine 1101
CuAlTe, CuGaS, CuGaSe, CuGaTe, CuInS, CtlInSe, CuInTe, AgAIS, AgA1% AgA1Ter AgGaS, AgGa% AgGaTe, AgInS, AgInSe, AgInTe,
c==%
CUAlS,
1.000 1.0975 1.1650 1.0975 1.2093 1.2876 1.1650 1.2876 1.3739 1.0000 1.0975 1.1650 1.0975 1.2093 1.2876 1.1650 1.2876 1.3739
D
18.295 17.041 15.518 18.163 16.906 15.195 16.453 15.489 14.332 18.708 17.510 15.408 18.598 17.193 15.149 16.313 15.291 13.860
W
%ec 14.211 12.927 11.410 14.079 12.791 11.095 12.336 11.382 10.262 14.640 13.404 11.302 14.526 13.081 11.050 12.196 11.188 9.814
W)
E F,BC 7.671 6.863 5.902 7.584 6.777 5.725 6.494 5.902 5.215 7.943 7.162 5.853 7.869 6.959 5.698 6.408 5.783 4.944
WV
5.083 4.519 3.844 5.022 4.460 3.739 4.265 3.859 3.394 5.274 4.727 3.826 5.222 4.586 3.720 4.205 3.778 3.212
E&BC
WI 0.561 0.566 0.576 0.561 0.567 0.573 0.569 0.572 0.576 0.559 0.564 0.573 0.559 0.566 0.573 0.569 0.573 0.578
This work 0.62 0.65 0.56 0.55 0.55 0.51 0.60 0.60 0.57 0.61 0.63 0.57 0.54 0.54 0.51 0.61 0.60 0.58
Neumann 141 0.54 0.50 0.38 0.54 0.49 0.39 0.61 0.57 0.48 0.56 0.51 0.41 0.54 0.51 0.40 0.64 0.60 0.50
Bernard [61
0.604
0.570 0.561
0.636
0.565 0.563
1101
Levine
compounds
f;.BC
of the B’nC~’ bond in A’B”‘C~’
E h,BC 5.746 5.165 4.479 5.684 5.103 4.336 4.898 4.466 3.960 5.939 5.381 4.430 5.887 5.235 4.316 4.835 4.378 3.758
Table 2. Properties
4.955 5.908 7.102 5.485 6.573 7.951 6.537 7.867 9.114 4.829 5.461 7.073 5.338 6.443 7.978 6.601 7.888 9.494
This work 4.26 4.76 7.19 5.59 6.80 9.17 6.02 7.30 9.35 4.26 4.76 7.19 5.59 6.80 9.17 6.02 7.30 9.35
Neumann [41
x
7.41
5.84 7.04
5.99
6.07 7.04
DOI
Levine GalC 5.769 6.574 7.182 5.866 6.705 7.628 6.680 7.237 9.026 5.483 6.114 7.211 5.773 6.602 7.626 6.324 7.273 8.494
A*B”‘Cp compounds
(noble metal compounds) while earlier workers [7-lo] have neglected this in their calculations. Further, earlier models require the experimental values of the optical dielectric constant for the calculation of Eht C and f; but in the current model one can predict the order of these parameters without having any knowledge of the experimental value of &. The values of the homopolar (E,,) and heteropolar (C) energy gaps and the ionicity (f;) of the A’-C”’ and B”‘Xv’ bond in A’B”‘C~’ semiconductors have been calculated from eqns (6HlO). Using these values of E,, and C the average energy gap (ES), eiectronic susceptibility (2) and dielectric constant (6) have been calculated and presented in Tables 1 and 2. Our calculated values are in fair agreement with the values reported by various workers. Thus, it is possible to predict the order of E,,, C, A, x and 6 in A*B”‘Cy’ compounds from their plasmon loss values without having any knowledge of the experimental value of the dielectric constant. Ac~o~ledg~en~-The author is grateful to Dr. B. Singh, Director, Central Mining Besearcfi Station, Dhanbad, for his continuing inspiration and for giving permission to publish this paper. The author is also grateful ta Dr. S. C. Srivastava for his valuable advice and cooperation. REFERENCES 1. 2. 3. 4.
Chelikowsky J. R., Phys. Rev. Lett. Sa, 961 (1986). Enders P., Phys. Status S&di b 131, 489 (1985). Cohen M. L., Phys. Rep. Ilg, 293 (1984). Neumann H., Cry& Res. Tech. 18, 1299, 1391,665,981 (1983).
831
5. Catlow C. R. A. and Stoneham A. M., J. Phys. C (Solid
Sr.) 16, 4321 (1983). 6. Bernard M. J., Physique LSz&.I 36, C3 (1975). 7. Phillips J. C., Hi&&hts bf -~o&%msed-Matter Theory LXXXIX Corso Sot. Italiana di Fisica. Bologna. Italv. p* $77 (i985); Rev. AL&d. Phys. 4% 3i7 (19%);~ Ph&: Rev. B 29, 5583 (f984). 8. Phillips 1. C. and Van Vechten J, A., Whys. Ren IrU, 709 (1969); Phys. ffev. 32, 2147 (1970). 9. Van Vechten J. A., Phys. Rev, B1, 3351 (1970); Phys. Rev. 182, 891 (1969); Phys. Rev. X87, 1007 (1969). 10. Levine B. F., Phys. Rev. B7,2591,2600 (1973); J. them. Phys. 59, 1463 (1973); Phys. Rev. Lert. 25, 44 (1970). 11. Paulin I,., Phys. Rev. Lett. 23,480 (1969); Phys. Today, p. 9, Feb. (1971); The Nature qf the Chemicat Bond, Cornell Universitv Press. Ithaca. New York (1960). 12, Srinivasan G., P&s. R&. 178, i244 (1969). . I 13. Penn D. R., Phys. Ben. 128, 2893 (1962). 14. Chemla D. S., Phys. Rev. Lett. 26, 1441 (1971). 15. Fischer J. E., Glickman M. and Van Vechten J. A., Proc. Int. Conf. Phys. Semicond., Roma, Italy, p. 541 (1976). 16. Coulson C. A., Redei L. B. and Stocker D., Proc. R. Sot. (Land.) 370, 257 (1962). 17. Srivastava V. &mar, Phys. Rev. I329, 6993 (1984); Phys. Lett. A IO2, 127 (1984); J. Phys. C (Solid ft.) 19, 5689 (1986). 18. Backer R. B. and Goudsmith S,, A&&c Energy Sfates, McGraw-Hill, New York (1932). 19 Wample S. H. and Dome&a M. D., Jr., Phys. Rev. 33, 1338 (1971). 20. Pines D., Elementary Excitation in Solids, pp. 58 and 92. W. A. Benjamin, New York (1964). 21. Martan L., Leder L. B. and Mendlawitz H., Advances in Electronics and Electron Physics (Edited by L. Martom), Vol. 7, p. 225. Academic Press, New York (1955). 22. Rooke 6. A., srtft X-ray Band Spectra rutd the Eketronic Structure OXMet& and Mzteriak @!&ted by D. J, Fabian}, p. 6. Academic Press, New York (1968).