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Heats of formation of AIIBIVCV2 crystal semiconductors
Volume 46, number 2
CIKMICAL PHYSICS LETTERS
HEATS OF FORMATION OF AttBt%;
I March 1977
CRYSTAL SEMICONDUCTORS
K.N. SAXENA and R.G. ANIKHINDI * Department of Physrcs, Iiolkar Science College. Indore (M. P.), India Reccivcd 27 September 1976
The effective spin-orbit splitting of the valence band in AIIBIVCY scmxonductors ts first obtatncd by considering two bonds tn these crystals. The resultmg sphttmgs UC used to prcdlct the heats of tormdtion of these crystals. The values obtained are blghly encouraging.
1. introduction
PhIllips and van Vechten [l] have redefined the concept of clcctronegativity and calculated the heats of formation of a number of ANBsWN tetrahedral semicmnducting compounds. Garbato et al. [2] recently introduced the concept of an average nuclear effective charge to describe some important physical properties of AtxlBV and AllBrvCz compounds. It is of interest to mention here that many of these properties may be successfully investigated by using a single atomic parameter, namely the valence band splitting of the bonded atoms [3,4]. The atomic spin-orbit splitting (A,) which character&s the energy of the valence state is a fundamental parameter in the sense that it is an experimentally obscrvablc quantity.
2. Discussion It was recently reported [S] that the heats of formation of AtUBv intermetalhc semlconductors can be evaluated using the relation
- Mf = 37.61 exp(-A!‘-v) where Ail-vis
- 10.13,
(1)
the valence band splitting for the
* Present address: University Tcachmg Department of Physics, Vlgyan Bhawan, Indore-452001 (M.P.), indla.
III-V compounds. The valence band splittmgs for III-V and II-VI compounds can be computed by the procedure suggested by Cardona [6] using the spectroscopic values [7] for the spin-orbit splittings of the bonded atoms. The ternary compounds of general form&x AttB*Cy are analogues of A~IIBV. The atoms in these crystals are also tetrahedrally coordinated_ As the situation practiwlly remams unaltered one should expect relation (I) to give satisfactory results, provided that we know the effective valence band splittings for ArnBtVCz compounds. In order to evaluate the effective band splittings for AI1BwCT crystals, we consider the average contrlbutions to the effective valence band splittings by two kinds of bonds: for example in ZnSrP2 we consider two bonds Zn-P and SI-P. In the case Zn-I?, the Zn atom can contrlbute only two electrons, so the spin-orbit contribution for tha bond may be close to the splittmg in ZnS, similarly in the Si-P bond the splitting contribution may be close to the Al-P splitting value. This approach has some justification as the splittings change gradually along a particular row in the periodic table. So it is not unrealistic to replace the atoms of group VB by the adjacent atoms of group VIB, and the atoms of group IVB by the adjacent atoms of group IIIB respectively so far as the splitting contributions are concerned. In fact what 1s being done is that we move a step forward for the anion in the first bond and retreat by 377
Table I Heats of formation Material
of A”B’vCy
semiconductors
and other relevant data Calculated effective valencebands splittings (eV)
Equivalent bonds
Bonds considered
--
Zn Cd Zn Cd Zn Cd Zn Cd Zn Cd Zn Cd
Si P_i Si Pz Cc P2 Ge P2 Sn P2 Sn Pz Si A% SI A% Cc As2 Ge As2 Sn Aa Sn A%
1 March 1977
CHEMICAL PHYSICS LETTERS
Volume 46, number 2
Zn-P, Si-P Cd-P, Q-P Zn-P. Ge-P Cd-P, Gc-P Zn-P. Sn-P Cd-P, Zn-P Zn-As. Si-Ac Cd-As, Si-As Zn-As. Gc-As Cd-As, Ge-As Zn-As, Zn-As Cd-A<, Sn-Ar
Zn-S, Cd-S, Zn-S, Cd-S, Zn-S, Cd-S, Zn-Se. Cd-SC. Cd-Se, Cd-Se. Zn-Se, Cd-Se.
AI-P AI-P Ga-P Gc-P In-P In-P Al- AF Al-As Ge-As Q-As In-A, In--A5
0.073 0.093 0 098 0.12 0.133 0.150 0.35 0.37 0.38 0.40 0.41 0.43 .-_--.--
Eg(eV) cxpt.a) 2.3 22 1.8 1.7 1.46 1.16 I .64 0.85 0.53 0.65 0.26 ---
Heats of formation,
-OTlt(kcal/eq.
GhlMb)
expt.
this work
24.2 15.R 22.8 14.3 22.9 14.4 13.3 5.2 12.0 3.6 12.4 3.6
19c) 19c)
mol)
24.8 24.2 23.9 23.2 22.8 22.2 16.3 15.8 15.5 15.0 14.9dI 14.8 14.3 -- .-_-
a) Accordmg to Borshchcvski et al. [9].
b) Values predicted by Ghihl [ 21. c) Reported by PW [ I]. d) Reported by Gutbier [lo].
one step for the cation in the second bond. Thus we have two equivalent bonds m which we have again eight valence electrons per atom pair. This scheme is illustrated in table 1. The effective valence band sphttings in these crystals may now be given by an average as AuA(II)B(IV)C2(V) =; [At-”
+ Ar-V]
(2) Relation (1) with the same numerical constants may now bc given as-Mf = 37.61
exp[-AOA(II)B(lV)C2(V)]
-
10.13.
in predicting heats of formatron in cases where the number of valence electrons per atom pair is eight only on the average. The important feature of our results IS that the predicted values are comparable with the available experimental data and are consistent with the results of Ruppel et al. [8] who had found that log Eg was nearly a linear function of the heat of formation for about thirty five elemental or compound scmrconductors. The experimental data for the energy gaps is also given in table 1 for inspection. It is remarkable that useful estimates have been made of an important property not yet measured for many of these caysta1s.
(3)
The values calculated from relaiion (3) are presented in table 1. For comparison the experimental values and those predicted by Garbats et al. (CMM) are also given.
Acknowledgement Thanks are due to Dr. D.S. Joshi, Holkar Science College, Indore and Professor B.K. Nilosay for taking an interest in thus work.
3. Conclusion
References Although we arc unable to rigorously justify our scheme on theoretical
grounds,
at the same time, we
believe it to be of interest as it has proved to be useful 378
[l] J.C. Philhps and J.A. VW Vechten, Phys. Rev. B2 (1970) 2147.
Volume 46, number 2
CHEMICAL PHYSICS LETTERS
[2] L. Garbato, P. Manta and G. Mula, J. Phy\. C6 (1973) 2988. [ 31 K.N. Saxena, N.N. Saxena and R.G. Amkhind, Chem. Phys. Letters 31 (1975) 563. [S] K.N. Saxena. Chcm. Phys. Letters 34 (1975) 440. [S] K.N. Saxena, Chem. Phys. Letters 37 (1976) 140. [6] M. Cardona, In- Semiconductors and semimetals, Vol. 3, cds. R.K. Wdiiardson and A.C. Bear (Academic Press, New York, 1967).
1 March 1377
(7) C.E. Moore. Atomic Energy Levels, N.B.S. CircuIar No. 467 41949). 181 W. Rupell, A. Rose and H.J. Gerritscn. Helv. Phys. Act& 30 (1957) 238. [9] A.S. Borshchevskie, N.A. Goriurura. F.P. KewnanIy and D-N. Nasledov, Phys. Stat. Sol. 21 (1967) 9. [ 101 H. Gutbier, 2. Naturforsch. 16a (1969) 268.
379
CIKMICAL PHYSICS LETTERS
HEATS OF FORMATION OF AttBt%;
I March 1977
CRYSTAL SEMICONDUCTORS
K.N. SAXENA and R.G. ANIKHINDI * Department of Physrcs, Iiolkar Science College. Indore (M. P.), India Reccivcd 27 September 1976
The effective spin-orbit splitting of the valence band in AIIBIVCY scmxonductors ts first obtatncd by considering two bonds tn these crystals. The resultmg sphttmgs UC used to prcdlct the heats of tormdtion of these crystals. The values obtained are blghly encouraging.
1. introduction
PhIllips and van Vechten [l] have redefined the concept of clcctronegativity and calculated the heats of formation of a number of ANBsWN tetrahedral semicmnducting compounds. Garbato et al. [2] recently introduced the concept of an average nuclear effective charge to describe some important physical properties of AtxlBV and AllBrvCz compounds. It is of interest to mention here that many of these properties may be successfully investigated by using a single atomic parameter, namely the valence band splitting of the bonded atoms [3,4]. The atomic spin-orbit splitting (A,) which character&s the energy of the valence state is a fundamental parameter in the sense that it is an experimentally obscrvablc quantity.
2. Discussion It was recently reported [S] that the heats of formation of AtUBv intermetalhc semlconductors can be evaluated using the relation
- Mf = 37.61 exp(-A!‘-v) where Ail-vis
- 10.13,
(1)
the valence band splitting for the
* Present address: University Tcachmg Department of Physics, Vlgyan Bhawan, Indore-452001 (M.P.), indla.
III-V compounds. The valence band splittmgs for III-V and II-VI compounds can be computed by the procedure suggested by Cardona [6] using the spectroscopic values [7] for the spin-orbit splittings of the bonded atoms. The ternary compounds of general form&x AttB*Cy are analogues of A~IIBV. The atoms in these crystals are also tetrahedrally coordinated_ As the situation practiwlly remams unaltered one should expect relation (I) to give satisfactory results, provided that we know the effective valence band splittings for ArnBtVCz compounds. In order to evaluate the effective band splittings for AI1BwCT crystals, we consider the average contrlbutions to the effective valence band splittings by two kinds of bonds: for example in ZnSrP2 we consider two bonds Zn-P and SI-P. In the case Zn-I?, the Zn atom can contrlbute only two electrons, so the spin-orbit contribution for tha bond may be close to the splittmg in ZnS, similarly in the Si-P bond the splitting contribution may be close to the Al-P splitting value. This approach has some justification as the splittings change gradually along a particular row in the periodic table. So it is not unrealistic to replace the atoms of group VB by the adjacent atoms of group VIB, and the atoms of group IVB by the adjacent atoms of group IIIB respectively so far as the splitting contributions are concerned. In fact what 1s being done is that we move a step forward for the anion in the first bond and retreat by 377
Table I Heats of formation Material
of A”B’vCy
semiconductors
and other relevant data Calculated effective valencebands splittings (eV)
Equivalent bonds
Bonds considered
--
Zn Cd Zn Cd Zn Cd Zn Cd Zn Cd Zn Cd
Si P_i Si Pz Cc P2 Ge P2 Sn P2 Sn Pz Si A% SI A% Cc As2 Ge As2 Sn Aa Sn A%
1 March 1977
CHEMICAL PHYSICS LETTERS
Volume 46, number 2
Zn-P, Si-P Cd-P, Q-P Zn-P. Ge-P Cd-P, Gc-P Zn-P. Sn-P Cd-P, Zn-P Zn-As. Si-Ac Cd-As, Si-As Zn-As. Gc-As Cd-As, Ge-As Zn-As, Zn-As Cd-A<, Sn-Ar
Zn-S, Cd-S, Zn-S, Cd-S, Zn-S, Cd-S, Zn-Se. Cd-SC. Cd-Se, Cd-Se. Zn-Se, Cd-Se.
AI-P AI-P Ga-P Gc-P In-P In-P Al- AF Al-As Ge-As Q-As In-A, In--A5
0.073 0.093 0 098 0.12 0.133 0.150 0.35 0.37 0.38 0.40 0.41 0.43 .-_--.--
Eg(eV) cxpt.a) 2.3 22 1.8 1.7 1.46 1.16 I .64 0.85 0.53 0.65 0.26 ---
Heats of formation,
-OTlt(kcal/eq.
GhlMb)
expt.
this work
24.2 15.R 22.8 14.3 22.9 14.4 13.3 5.2 12.0 3.6 12.4 3.6
19c) 19c)
mol)
24.8 24.2 23.9 23.2 22.8 22.2 16.3 15.8 15.5 15.0 14.9dI 14.8 14.3 -- .-_-
a) Accordmg to Borshchcvski et al. [9].
b) Values predicted by Ghihl [ 21. c) Reported by PW [ I]. d) Reported by Gutbier [lo].
one step for the cation in the second bond. Thus we have two equivalent bonds m which we have again eight valence electrons per atom pair. This scheme is illustrated in table 1. The effective valence band sphttings in these crystals may now be given by an average as AuA(II)B(IV)C2(V) =; [At-”
+ Ar-V]
(2) Relation (1) with the same numerical constants may now bc given as-Mf = 37.61
exp[-AOA(II)B(lV)C2(V)]
-
10.13.
in predicting heats of formatron in cases where the number of valence electrons per atom pair is eight only on the average. The important feature of our results IS that the predicted values are comparable with the available experimental data and are consistent with the results of Ruppel et al. [8] who had found that log Eg was nearly a linear function of the heat of formation for about thirty five elemental or compound scmrconductors. The experimental data for the energy gaps is also given in table 1 for inspection. It is remarkable that useful estimates have been made of an important property not yet measured for many of these caysta1s.
(3)
The values calculated from relaiion (3) are presented in table 1. For comparison the experimental values and those predicted by Garbats et al. (CMM) are also given.
Acknowledgement Thanks are due to Dr. D.S. Joshi, Holkar Science College, Indore and Professor B.K. Nilosay for taking an interest in thus work.
3. Conclusion
References Although we arc unable to rigorously justify our scheme on theoretical
grounds,
at the same time, we
believe it to be of interest as it has proved to be useful 378
[l] J.C. Philhps and J.A. VW Vechten, Phys. Rev. B2 (1970) 2147.
Volume 46, number 2
CHEMICAL PHYSICS LETTERS
[2] L. Garbato, P. Manta and G. Mula, J. Phy\. C6 (1973) 2988. [ 31 K.N. Saxena, N.N. Saxena and R.G. Amkhind, Chem. Phys. Letters 31 (1975) 563. [S] K.N. Saxena. Chcm. Phys. Letters 34 (1975) 440. [S] K.N. Saxena, Chem. Phys. Letters 37 (1976) 140. [6] M. Cardona, In- Semiconductors and semimetals, Vol. 3, cds. R.K. Wdiiardson and A.C. Bear (Academic Press, New York, 1967).
1 March 1377
(7) C.E. Moore. Atomic Energy Levels, N.B.S. CircuIar No. 467 41949). 181 W. Rupell, A. Rose and H.J. Gerritscn. Helv. Phys. Act& 30 (1957) 238. [9] A.S. Borshchevskie, N.A. Goriurura. F.P. KewnanIy and D-N. Nasledov, Phys. Stat. Sol. 21 (1967) 9. [ 101 H. Gutbier, 2. Naturforsch. 16a (1969) 268.
379