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Phys. Status Solidi B 246, No. 1, 192–199 (2009) / DOI 10.1002/pssb.200844242 p s sbasic solid state physics

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Correlation between ionic charge and the optical properties of zinc blende and complex crystal structured solids

A. S. Verma*

Department of Physics, B.S.A. College, Mathura 281004, India, and Department of Physics, Sanjay Institute of Engineering and Management, Mathura 281406, India

Received 10 June 2008, revised 7 September 2008, accepted 16 September 2008 Published online 24 October 2008

PACS 78.20.Bh, 78.20.Ci * e-mail ajay_phy@rediffmail.com, Phone: +91 565 2423417, Mob.: +91 9412884655

© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction Most of the physical world around us and a large part of modern technology are based on solid materials. The extensive research devoted to the physics and chemistry of solids during the last quarter of a century has led to great advances in understanding of the properties of solids in general. So it is interesting to study the behav-iour and various properties of different solids. One of the properties of semiconductors which are very important for device applications is the band gap. The best values of the band gap are obtained by optical absorption. If the band gap is sufficiently small, thermal excitation can promote an electron from the valence band to the conduction band. If impurities are present in the band gap, thermal excitation can also be used to excite an electron from an impurity level to the conduction band. Thus, the measurements of electrical resistance of the specimen as a function of tem-perature can be used to determine the band gap of the specimen. Recently [1–12]’ frequent attempts have been made to understand the electronic, mechanical, elastic and optical properties of zinc blende (AIIBVI and AIIIBV) and chalcopyrite (AIBIIIC2

VI and AIIBIVC2V) semiconductors. This

is because of their interesting semi-conducting properties

and various practical applications in the field of non-linear optics, electronics, photovoltaic detectors, light emitting diodes and solar cells etc. Structurally chalcopyrite com-pounds are derived from that of the binary sphalerite struc-ture (AIIBVI and AIIIBV) with a slight distortion. Therefore, like binary compounds they have a high non-linear suscep-tibility. However because of the presence of two types of bonds in chalcopyrites they become anisotropic. This ani-sotropy gives rise to high birefringence. High non-linear susceptibility coupled with high birefringence in these compounds makes them very useful for efficient second harmonic generation and phase matching. There is a great deal of interest, both experimental and theoretical in the solid state properties of semiconductors. The refractive index, optical electronegativity and energy gap of semiconductors represent two fundamental physical aspects that characterize their optical and electronic prop-erties. The applications of semiconductors as electronic, optical and optoelectronic devices are very much deter-mined by the nature and magnitude of these elementary material properties. These properties also aid in the per-formance assessment of energy gap engineered structures

An overview of the understanding of correlation betweenionic charge and the optical properties of zinc blende andchalcopyrite crystal structured solids is presented here. Wehave presented three expressions relating the refractive index(n), energy gap (Eg) and optical electronegativity (Δχ) for thetransition metal chalcogenides and pnictides (AIIBVI andAIIIBV) and chalcopyrites (AIBIIIC2

VI and AIIBIVC2

V) with theproduct of ionic charges and nearest neighbor distance d (Å).

The refractive index (n), energy gap (Eg) and optical electro-negativity (Δχ) of these solids exhibit a linear relationshipwhen plotted on a log–log scale against the nearest neighbourdistance d (Å), but fall on different straight lines according tothe ionic charge product of the compounds. We have appliedthe proposed relation on these solids and found a better agree-ment with the experimental data as compared to the valuesevaluated by earlier researchers.

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for continuous and optical absorption of broad band spec-tral sources. In addition, devices such as photonic crystals, wave guides, solar cells and detectors require a pre-knowledge of the refractive index, optical electronegativity and band gap. The band gap determines the threshold for absorption of photons in semiconductors. Experimental and also theoretical methods for calculating these material properties have been well understood and established for binary and ternary semiconductors [2–4]. Due to the diffi-culties of the experimental process and its cost as well as difficulties of getting accurate values of refractive index, band gap and optical electronegativity and due to the long process as well as complicated computational methods and a series of approximations, such a method has always been the complicated one, researchers moved to calculate these parameter through theoretical methods. In the past few years, a number of theoretical calculations based on em-pirical relations have become an essential part of material research. Empirical formulas mostly found to be simple, easy to use and it gave a better value for physical param-eters. Advances in high performance computing techniques allow materials scientists to evaluate refractive index, band gap and optical electronegativity based on empirical meth-ods. Empirical relations have become widely recognized as the method of choice for computational solid-state studies. In modern high-speed computer techniques, they allow re-searchers to investigate many structural and physical prop-erties of materials only by computation or simulation instead of by traditional experiments. In many cases em-pirical relations do not give highly accurate results for each specific material, but they still can be very useful. In par-ticular, the simplicity of empirical relations allows a broader class of researchers to calculate useful properties, and often trends become more evident. Empirical concepts such as valence, empirical radii, ionicity and plasmon energy are then useful [10, 13, 14]. These concepts are di-rectly associated with the character of the chemical bond and thus provide means for explaining and classifying many basic properties of molecules and solids. Recently, the author [15–20] have been evaluated the structural, electronic, mechanical and ground state proper-ties of binary and ternary crystals with the help of ionic charge theory of solids. This is due to the fact that the ionic charge depends on the number of valence electrons, which changes when a metal forms a compound. Therefore we thought it would be of interest to give an alternative expla-nation for refractive index, band gap and optical electro-negativity of zinc blende (AIIBVI and AIIIBV) and chalcopy-rite (AIBIIIC2

VI and AIIBIVC2V) semiconductors.

2 Theoretical concepts Optical electronegativity is one of the most important parameter in understanding the nature of chemical bonding, and several important physical parameters can be predicted by using it. Some empirical models were established that can predict optical electro-negativity of binary and complex structured solids from se-lected atomic properties of their constituent elements. The

correlation between band gap (Eg) and optical electronega-tivity has been enlightened by Duffy [21, 22] in verious bi-nary systems. Duffy [21, 22] has made an attempt to de-scribe the metallic character of chemical bonding for com-pounds that are inadequately described in a solely “ionic/covalent” framework from the point of view of band gap electronegativity. Optical absorptions for a semicon-ductor or insulator arise through electron transfers from the valence band to the conduction band. The transfer of elec-trons from an anion to a cation and the associated optical ab-sorption is known as “electron transfer” or “charge transfer absorption”. Duffy [21, 22] has well established the above concept and introduced it in terms of the “optical electro-negativity”. According to him the optical electronegetivity (Δχ*) may be determine by the following relation:

Δχ* = 0.2688 Eg , (1)

where Δχ* = χ*anion–χ*cation with χ*anion and χ*cation being the optical electronegativities of the anion and cation resepec-tively. Recently, Reddy et al. [23], have proposed an em-pirical relationship between refrative index (n) and optical electronegetivity (Δχ*) of solids and is as follows:

Δχ* = 25.54/n4 . (2)

First, Moss [24, 25], proposed a general relationship based on the concept that in a dielectric energy, levels are scaled by a factor ε∞

2 (where ε∞ = n2 is the optical dielectric con-stant), i.e.

Eg = (95/n4) eV . (3)

Ravindra et al. [26, 27], have proposed another linear rela-tionship,

n = 4.084–0.62Eg . (4)

Based on the oscillatory theory, Herve and Vandamme [29], have proposed the following for the refractive index:

21 ( / ) ,g

n A E B= + + (5)

where

A = 13.6 and B = 3.4 eV .

Recently, Anani et al. [35], have proposed an empirical re-lationship between referative index (n) and band gap (Eg) of solids and is as follows:

Eg = (17–5n) eV . (6)

The energy gap (Eg) of semiconducting or insulating com-pounds, involves transference of an electron from the valence band to the conduction band. Since, usually, the valence band involves primarily orbitals of the anion, while the conduction band involves primarily orbitals of cation, it seems reasonable to expect some numerical pa-rameter, e.g. ionisation energy, electronegativity, etc., of cation and anion to be correlatable with Eg. The problem has been discussed in detail [24–28], but correlations

194 A. S. Verma: Correlation between ionic charge and the optical properties of zinc blende

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which have been made are restricted to small groups of compounds and no overall correlation has yet been found to operate for ternary compounds generally. Any change in the crystallographic environment of an atom is related to core electrons via the valence electrons. The change in wavefunction that occurs for the outer electrons usually means a displacement of electric charge in the valence shell so that the interaction between valence, shell and core electrons is changed. This leads to a change in binding en-ergy of the inner electron and to a shift in the position of the absorption edge. The ionic charge of any compound depends on the valence electrons, and changes when a metal forms a compound. In the previous work, [15–20], we proposed simple expressions for the electronic, optical and mechanical properties such as heteropolar energy gaps (Ec), average energy gaps (Eg), crystal ionicity (fi), dielec-tric constant (ε∞), electronic susceptibility (χ), cohesive energy (Ecoh), bulk modulus (B) and microhardness (H) of rocksalt, zinc blende and chalcopyrite structured solids in terms of the product of ionic charges of cation and anion by the following relations:

Lattice energy (U in kcal/mol) = C(Z1Z2)D/ ,d

(7)

Dielectric constant (ε∞) = C(Z1Z2)Dd 2 , (8)

where C and D are constants, which depend upon crystal structures and d is the nearest-neighbour distance in Å. Z1 and Z2 are the ionic charges on the cation and anion, re-spectively. Using this idea to get better agreement with ex-perimental and theoretical data, for the refractive index (n), optical electronegativity (Δχ*) and band gap (Eg) of zinc blende and chalcopyrite crystals may be written in terms of product of ionic charges: For zinc blende crystals (AIIBVI and AIIIBV)

Refractive index (n) = 0.29 (Z1Z2)0.25d 2 , (9a)

Optical electronegativity (Δχ*) = 105/(Z1Z2)0.33d 5 ; (9b)

For chalcopyrite crystals (AIBIIIC2VI and AIIBIVC2

V)

Refractive index (n) = 0.31 (Z1Z2Z3)0.15d 2 , (10a)

Optical electronegativity (Δχ*) = 133/(Z1Z2Z3)0.33d 5 ,

(10b)

Band gap (Eg) = 500/(Z1Z2Z3)0.33d 5 eV , (11)

where d is the nearest-neighbour distance in Å and Z1, Z2 and Z3 are the ionic charges on the A, B and C2, respec-tively. A detailed study for ionic charges of chalcopyrite has been presented in previous works [16, 18]. It is obvi-ous that the valence structures of the compounds can be written as A+B3+C2

2– (A = Cu, Ag; B = Al, Ga, In; C = S, Se, Te) and A2+B4+C2

3– (A = Zn, Cd; B = Si, Ge, Sn; C = P, As). Therefore the product of ionic charge is 12 for AIBIIIC2

VI and 48 for AIIBIVC2V. It is well known that in chal-

copyrites each cation has four equal anion bonds but each anion has four (two + two) different cation bonds, this fact

gives anion–cation distances dAC and dBC. In this relation d is average nearest neighbour distance and for AIBIIIC2

VI and AIIBIVC2V chalcopyrites can be calculated by

(d AC + d BC)/2. 3 Results and discussion The refractive index, opti-cal electronegativity and band gap are important optical and electronic properties of a material. The band gap de-termines the threshold for absorption of photons in semi-conductors. The refractive index in the semiconductor is a measure of its transparency to incident spectral radiation. Moss [24, 25], propose a basic relationship between these two properties using the general theory of photoconductiv-ity which was based on the photo effect studies of Mott and Gurney [30], Smekal [31], Zwicky [32], Gudden and Pohl [33] and Pearson and Bardeen [34]. Pauling [13], was the first to establish the nature of chemical bonding using the electronegativity concept. It may be observed from the tables that as the (Δχ*) values for the group of semicon-ductors with the common cation decreases, their refractive index increases. The trend is quite reverse in the case of ionic molecules. Most of the chalcopyrites energy gap (Eg) and optical electronegativity (Δχ*) values lie between 0.95 eV, 3.00 eV, 0.2 eV and 0.9eV respectively. Accord-ing to Pauling [13], the nature of crystal structure can also be understood with the help of the ionicity. Electronegativ-ity difference of the compound elements will give an idea of degree of ionicity. The magnitude of optical electro-negativity indicates the nature of the bonding in the mate-rials. If Δχ* is high, the material is considered as ionic in nature and if its magnitude is less, the materials are said to be covalent in nature. Further relations were developed as a modification or addition to the Moss and Ravindra rela-tions. While the Moss formula is limited by the structure of the material, the Ravindra relation is restricted by the re-fractive index. From the Ravindra relation, the refractive index cannot be greater than a value of 4.1, which corre-sponds to an energy gap of 6.587 eV. In an effort to broaden the application of these two concepts, several authors [2, 3, 23], have presented variations of the Moss and Ravindra relations. Although the properties of the AIBIIIC2

VI and AIIBIVC2V chalcopyrite semiconductors have

been extensively investigated and some of these com-pounds have attracted attention for practical applications [28], the knowledge of their electronic and optical proper-ties such as band gap (Eg), refractive index (n) and optical electronegativity (Δχ*) are rather incomplete. Experimen-tal data are available for few compounds for chalcopyrite series AIBIIIC2

VI and AIIBIVC2V

, so there are many properties of the solid solution, which have not been investigated. Because, ionic charges of compound depends on the va-lence electrons, which changes when a metal forms a com-pound. Therefore we thought it would be of interest to give an alternative explanation for refractive index, band gap and optical electronegativity of zinc blende (AIIBVI and AIIIBV) and chalcopyrite (AIBIIIC2

VI and AIIBIVC2V) semicon-

ductors.

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2.00 2.25 2.501.75

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CdSiAs2

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A B C SemiconductorsII IV V2

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Ø

AgA lSe2

CuAlS2

AgA lTe2

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ZnSiAs2

ZnGeP2

ZnSnP2

A B C SemiconductorsI III VI2

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Ø

0.25

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0.40

0.00

AgG aS2

AgA lS 2

ZnSiP2

Ø0.35

0.30CdGeP2

Figure 1 Plot of log Δχ* (optical electronegativity) against log d 5 (d = nearest neighbour distance) for AIBIIIC2

VI and AIIBIVC2

V chalcopyrite semiconductors. In the plots of log Δχ* vs. log d 5, AIBIIIC2

VI chalcopyrites lie on line nearly parallel to the line for AIIBIVC2

V chalcopyrites. In this plot all data are taken from Ref. [2]. We have plotted log Δχ* vs. log d 5 and log Eg vs. log d 5 curves for AIBIIIC2

VI and AIIBIVC2V chalcopyrites,

which are presented in the following Figs. 1 and 2. For

2.00 2.25 2.501.75

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CdGeP2

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Ø

AgAlS e2

CuAlS2

CuAlTe2

0.25ZnSiAs2

ZnGeP2

ZnSnP2

AB C SemiconductorsI III VI2

Z Z Z = 121 2 3

Ø

0.45

0.40

0.50

0.20

AgG aS 2

AgAlS2

ZnSiP2

Ø

Figure 2 Plot of log Eg (band gap) against log d 5 (d = nearest neighbour distance) for AIBIIIC2

VI and AIIBIVC2V chalcopyrite

semiconductors. In the plots of log Eg vs. log d 5, AIBIIIC2VI chal-

copyrites lie on line nearly parallel to the line for AIIBIVC2V chal-

copyrites. In this plot all data are taken from Ref. [2].

2.00 2.25 2.501.75

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CdS

ZnTe

AlAs

ZnSe

ZnS

GaP

AlP

InP

log

Dc

log d

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Ø

5

Z Z = 91 2

0.5

0.3

Z Z = 41 2

A B SemiconductorsII V I

ØØ

Ø

Figure 3 Plot of log Δχ* (optical electronegativity) against log d 5 (d = nearest neighbour distance) for AIIIBV and AIIBVI semiconductors. In the plots of log Δχ* vs. log d 5, AIIIBV semi-conductors lie on line nearly parallel to the line for AIIBVI semi-conductors. In this plot all data are taken from Ref. [2]. zinc blende crystal structures, we have plotted log Δχ* vs. log d 5 curve for AIIIBV and AIIBVI semiconductors, which is presented in the following Fig. 3 and have plotted log n vs. log d 2 curve for AIIIBV, AIIBVI, AIBIIIC2

VI and AIIBIVC2V semi-

conductors, which are presented in the following Figs. 4 and 5. In Figs. 1, 2 and 5, we observe that in the plot of op-tical electronegativity and nearest neighbour distance, band

0.25

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0.55

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0.65

0.7 0.75 0.8 0.85 0.9 0.95

log d2

logn

II-VI Semiconductors

III-V Semiconductors

Figure 4 (online colour at: www.pss-b.com) Plot of log n (re-fractive index) against log d 2 (d = nearest neighbour distance) for AIIIBV and AIIBVI semiconductors. In the plots of log n vs. log d 2, AIIIBV semiconductors lie on line nearly parallel to the line for AIIBVI semiconductors. In this plot all experimental data are taken from Ref. [23].

196 A. S. Verma: Correlation between ionic charge and the optical properties of zinc blende

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0.45

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0.7 0.75 0.8 0.85 0.9

log d2

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II-IV-V2

Figure 5 Plot of log n (refractive index) against log d 2 (d = nearest neighbour distance) for AIBIIIC2

VI and AIIBIVC2V chalcopy-

rite semiconductors. In the plots of log n vs. log d 2, AIBIIIC2VI

chalcopyrites lie on line nearly parallel to the line for AIIBIVC2V

chalcopyrites. In this plot all experimental data are taken from Ref. [23].

gap and nearest neighbour distance and refractive index and nearest neighbour distance, the AIBIIIC2

VI chalcopyrites lie on line nearly parallel to the line for the AIIBIVC2

V chalcopyrites. In Figs. 3 and 4, we observe that in the plot of optical elec-tronegativity and nearest neighbour distance and refractive index and nearest neighbour distance, the group AIIIBV semi-conductors lie on line nearly parallel to the group AIIBVI semiconductors. From these figures it is quite obvious that the refractive index, optical electronegativity and band gap trends in these compounds decreases with increases nearest neighbour distance and fall on different straight lines accord-ing to the ionic charge product of the compounds. The physical concept behind the Eq. (9) is that the refractive in-dex is related to the high frequency dielectric constant of the crystals [24, 25]. The dielectric constant also depends on the product of ionic charges [18]. Thus, there must be a correla-tion between refractive index and product of ionic charges. According to Moss [24, 25] and Reddy et al. [23] relations band gap and optical electronegativity depends on the re-fractive index. So according to above description there must be a correlation between product of ionic charges and band gap and optical electronegativity. The proposed empirical relations (9)–(11) have been applied to evaluate refractive index, optical electronegativity values for AIIIBV, AIIBVI, AIBIIIC2

VI and AIIBIVC2V semiconductors and band gap for

AIBIIIC2VI and AIIBIVC2

V semiconductors. The values so ob-tained are presented in the following Tables 1 and 3 com-pared with the experimental and theoretical data reported so far. We note that he evaluated values of refractive index, op-tical electronegativity and band gap by the our proposed re-lations are in close agreement with the experimental data as compared to the values reported by previous researchers so far. Using the present model, we can calculate these material properties of other new compounds without the knowledge of the experimental data except the nearest neighbour dis-tance very easily.

Table 1 In this table we have presented the values of optical electronegativity (Δχ*) for zinc blende (AIIIBV and AIIBVI) semi-conductors. The value of product of ionic charge (Z1Z2) = 4 for AIIBVI and (Z1Z2) = 9 for AIIIBV semiconductors.

solids d [15] Δχ* [2] Δχ* Duffy’s [2, 21, 22]

Δχ* [this work]

ZnS 2.34 0.948 1.05 0.947 ZnSe 2.46 0.691 0.80 0.738 ZnTe 2.64 0.605 0.70 0.518 CdS 2.52 0.643 0.70 0.654 CdSe 2.62 0.455 0.45 0.538 CdTe 2.81 0.385 0.35 0.379 HgS 2.53 0.641 HgSe 2.63 0.568 0.528 HgTe 2.80 0.386 AlP 2.36 0.804 0.80 0.695 AlAs 2.43 0.578 0.60 0.600 AlSb 2.66 0.428 0.40 0.382 GaP 2.36 0.600 0.60 0.695 GaAs 2.45 0.361 0.40 0.576 GaSb 2.65 0.217 0.20 0.389 InP 2.54 0.340 0.30 0.481 InSb 2.81 0.048 0.10 0.290 BSb 2.24 0.902 TiP 2.49 0.531 TiAs 2.58 0.445 TiSb 2.75 0.323

4 Conclusion There are several methods in determin-ing optical properties in semiconductors, but due to the small changes of the unit cell dimensions, the accuracy of determining these parameters always have been unpredict-able. Furthermore, we found that in the compounds inves-tigated here, the refractive index, optical electronegativity and band gap exhibit a linear relationship when plotted on a log–log scale against the nearest neighbour distance (Å), but fall on different straight lines according to the ionic charge product of the compounds, which are presented in Figs. 1–5. From the results and discussion obtained by us-ing the proposed empirical relation, it is quite obvious that the refractive index, optical electronegativity and band gap reflecting the optical and electronic properties can be ex-pressed in terms of product of ionic charges and nearest neighbour distance of these materials. The calculated val-ues are presented in Tables 1–3. According to this idea we may evaluate all-important properties of binary and ternary solids using their ionic charge and nearest neighbour dis-tance, which are basic parameters. An excellent agreement between the author’s calculated values of these material properties and the values reported by different researchers has been found. It is also to be note worthy that proposed empirical relation is simpler, widely applicable and values obtained are in better agreement with experiment data as compared to the empirical relations proposed by previous researchers. The method presented in this work will be helpful to material scientists for finding new materials

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Table 2 In this table we have presented the values of band gap (Eg in eV) and optical electronegativity (Δχ*) for AIBIIIC2VI and

AIIBIVC2V semiconductors.

solids d (Å) [16] Eg (eV) [2, 23] Δχ* [2, 23] Eg (eV) [this work] Δχ* [this work]

CuAlS2 2.29 3.50 0.938 3.50 0.930 CuAlSe2 2.40 2.70 0.723 2.77 0.736 CuAlTe2 2.58 2.06 0.552 1.93 0.512 CuGaS2 2.30 2.40 0.643 3.42 0.910 CuGaSe2 2.42 1.70 0.455 2.65 0.706 CuGaTe2 2.60 1.00 0.268 1.85 0.493 CuInS2 2.40 2.77 0.736 CuInSe2 2.51 2.21 0.588 CuInTe2 2.68 0.95 0.254 1.59 0.424 AgAlS2 2.40 3.13 0.838 2.77 0.736 AgAlSe2 2.51 2.55 0.683 2.21 0.588 AgAlTe2 2.68 2.27 0.608 1.59 0.424 AgGaS2 2.42 2.70 0.723 2.65 0.706 AgGaSe2 2.53 1.80 0.482 2.12 0.565 AgGaTe2 2.69 1.10 0.294 1.56 0.416 AgInS2 2.49 2.30 0.612 AgInSe2 2.61 1.24 0.332 1.82 0.484 AgInTe2 2.78 1.00 0.268 1.33 0.353 CuFeS2 2.30 3.42 0.910 ZnSiP2 2.31 2.10 0.562 2.12 0.564 ZnGeP2 2.35 1.98 0.533 1.95 0.517 ZnSnP2 2.45 1.66 0.444 1.58 0.420 ZnSiAs2 2.41 1.70 0.456 1.71 0.456 ZnGeAs2 2.44 1.15 0.308 1.61 0.429 ZnSnAs2 2.53 1.35 0.358 CdSiP2 2.40 2.45 0.656 1.75 0.466 CdGeP2 2.44 1.72 0.461 1.61 0.429 CdSnP2 2.54 1.17 0.313 1.32 0.351 CdSiAs2 2.49 1.55 0.415 1.46 0.387 CdGeAs2 2.53 1.35 0.358 CdSnAs2 2.62 1.13 0.300

Table 3 In this table we have presented the values of refractive index (n) for zinc blende (AIIIBV and AIIBVI), AIBIIIC2VI and AIIBIVC2

V semiconductors. The value of product of ionic charge (Z1Z2) = 4 for AIIBVI, (Z1Z2) = 9 for AIIIBV, (Z1Z2Z3) = 12 for AIBIIIC2

VI and (Z1Z2Z3) = 48 for AIIBIVC2

V semiconductors.

solids d (Å) [15, 16] exp. [23] Moss [23] Ravindra [23] [this work]

ZnS 2.34 2.27 2.28 1.89 2.246 ZnSe 2.46 2.43 2.47 2.49 2.482 ZnTe 2.64 2.70 2.55 2.68 2.858 CdS 2.52 2.38 2.51 2.60 2.604 CdSe 2.62 2.49 2.74 3.03 2.815 CdTe 2.81 2.70 2.85 3.19 3.238 HgS 2.53 2.625 HgSe 2.63 2.72 2.59 2.77 2.836 HgTe 2.80 3.215 AlN 1.87 2.16 2.24 1.73 1.756 AlP 2.36 2.75 2.37 2.23 2.798 AlAs 2.43 3.00 2.58 2.75 2.966 AlSb 2.66 3.19 2.78 3.09 3.554 GaP 2.36 2.90 2.55 2.70 2.798 GaAs 2.45 3.30 2.90 3.25 3.015 GaSb 2.65 3.79 3.29 3.58 3.527 InN 2.08 2.173 InP 2.54 3.10 2.94 3.30 3.241

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Table 3 (Continued).

solids d (Å) [15, 16] exp. [23] Moss [23] Ravindra [23] [this work]

InAs 2.61 3.50 4.04 3.86 3.422 InSb 2.81 3.95 4.80 3.97 3.966 BP 1.94 1.890 BAs 2.04 2.090 BSb 2.24 2.520 TiN 2.11 2.236 TiP 2.49 3.114 TiAs 2.58 3.344 TiSb 2.75 3.799 CuAlS2 2.29 2.360 CuAlSe2 2.40 2.60 2.44 2.41 2.592 CuAlTe2 2.58 3.30 2.61 2.81 2.996 CuGaS2 2.30 2.67 2.51 2.60 2.381 CuGaSe2 2.42 2.80 2.74 3.03 2.636 CuGaTe2 2.60 3.30 3.12 3.46 3.042 CuInS2 2.40 2.592 CuInSe2 2.51 2.835 CuInTe2 2.68 3.40 3.17 3.49 3.232 AgAlS2 2.40 2.35 2.15 2.592 AgAlSe2 2.51 2.47 2.50 2.835 AgAlTe2 2.68 2.55 2.68 3.232 AgGaS2 2.42 2.40 2.44 2.41 2.636 AgGaSe2 2.53 2.80 2.70 2.97 2.881 AgGaTe2 2.69 3.30 3.05 3.40 3.256 AgInS2 2.49 2.790 AgInSe2 2.61 2.96 3.31 3.066 AgInTe2 2.78 3.40 3.12 3.46 3.478 CuFeS2 2.30 2.381 ZnSiP2 2.31 3.10 2.60 2.78 2.957 ZnGeP2 2.35 3.10 2.63 2.85 3.060 ZnSnP2 2.45 2.90 2.75 3.06 3.326 ZnSiAs2 2.41 3.10 2.74 3.03 3.218 ZnGeAs2 2.44 3.50 3.02 3.37 3.299 ZnSnAs2 2.53 3.546 CdSiP2 2.40 3.10 2.50 2.56 3.191 CdGeP2 2.44 3.30 2.73 3.02 3.299 CdSnP2 2.54 3.10 3.01 3.36 3.575 CdSiAs2 2.49 3.50 2.80 3.12 3.435 CdGeAs2 2.53 3.547 CdSnAs2 2.62 3.803

with desired refractive index, optical electronegativity and band gap among a series of structurally similar materials.

References

[1] A. E. Merad, M. B. Kanoun, G. Merad, J. Cibert, and H. Aourag, Mater. Chem. Phys. 92, 333 (2005).

[2] R. R. Reddy, Y. N. Ahammed, K. R. Gopal, and D. V. Raghuram, Opt. Mater. 10, 95 (1998).

[3] R. R. Reddy, Y. N. Ahammed, K. R. Gopal, P. A. Azeem, T. V. R. Rao, and P. M. Reddy, Opt. Mater. 14, 355 (2000).

[4] L. K. Samanta and S. Chatterjee, Infrared Phys. Technol. 46, 370 (2005).

[5] S. Q. Wang and H. Q. Ye, J. Phys.: Condens. Matter 17, 4475 (2005).

[6] N. Guezmir, J. Ouerfelli, and S. Belgacem, Mater. Chem. Phys. 96, 116 (2006).

[7] V. Jayalakshmi, S. Davapriya, R. Murugan, and B. Pala-nivel, J. Phys. Chem. Solids 67, 669 (2006).

[8] M. I. Alonso, K. Wakita, J. Pascual, and N. Yamamoto, Phys. Rev. B 63, 75203 (2001).

[9] Xiaoshu Jiang and W. R. L. Lambrecht, Phys. Rev. B 69, 035201 (2004).

[10] V. Kumar and B. S. R. Sastry, J. Phys. Chem. Solids 66, 99 (2005).

[11] M. B. Kanoun, S. Goumri-Said, A. E. Merad, G. Merad, J. Cibert, and H. Aourag, Semicond. Sci. Technol. 19, 1220 (2004).

[12] H. M. Tutuncu, S. Bagci, G. P. Srivastava, A. T. Albudak, and G. Ugur, Phys. Rev. B 71, 195309 (2005).

Phys. Status Solidi B 246, No. 1 (2009) 199

www.pss-b.com © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

[13] L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cor-nell University Press, Ithaca, 1960).

[14] M. S. Omar, Mater. Res. Bull. 42, 961 (2007). [15] A. S. Verma and S. R. Bhardwaj, J. Phys: Condens. Matter

18, 8603 (2006). [16] A. S. Verma and S. R. Bhardwaj, J. Phys: Condens. Matter

19, 026213 (2007). [17] A. S. Verma and S. R. Bhardwaj, phys. stat. sol. (b) 243,

4025 (2006). [18] A. S. Verma and D. Sharma, Phys. Scr. 76, 22 (2007). [19] A. S. Verma and D. Sharma, phys. stat. sol. (b) 245, 678

(2008). [20] A. S. Verma, A. Kumar, and S. R. Bhardwaj, phys. stat. sol.

(b) 245, 1520 (2008). [21] J. A. Duffy, Bonding, Energy Level and Bonds in Inorganic

Solids (Longman, England, 1990). [22] J. A. Duffy, Phys. Chem. Glasses 42, 151 (2001). [23] R. R. Reddy, K. R. Gopal, K. Narasimhulu, L. S. S. Reddy,

K. R. Kumar, C. V. K. Reddy, and S. N. Ahmed, Opt. Mater. in press (2008).

[24] T. S. Moss, phys. stat. sol. (b) 131, 415 (1985). [25] T. S. Moss, Proc. Phys. Soc. B 63, 167 (1950). [26] N. M. Ravindra and V. K. Srivastava, Infrared Phys. 19, 603

(1979). [27] V. P. Gupta and N. M. Ravindra, phys. stat. sol. (b) 100,

715 (1980). [28] J. L. Shay and J. H. Wernick, Ternary Chalcopyrite Semi-

conductors: Growth, Electronic Properties and Applications (Pergamon Press, Oxford, 1974).

[29] P. J. L. Herve and L. K. J. Vandamme, Infrared Phys. 35, 609 (1994).

[30] N. F. Mott and R. W. Gurney, Electronic Processes and Ionic Crystals (Oxford University, Press, London, 1940).

[31] A. Smekel, Z. Phys. 55, 350 (1929). [32] F. Zwicky, Proc. Natl. Acad. Sci. (USA) 15, 816 (1929). [33] B. Gudden and R. W. Pohl, Z. Phys. 37, 881 (1926). [34] G. L. Pearson and J. Bardeen, Phys. Rev. 75, 865 (1949). [35] M. Anani, C. Mathieu, S. Lebid, Y. Amar, Z. Chama, and

H. Abid, Comput. Mater. Sci. 41, 570 (2008).