phys. stat. sol. (b), 243, No. 15, 4025–4034 (2006) / DOI 10.1002/pssb.200642229

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

Electronic and optical properties of zinc blende

and complex crystal structured solids

A. S. Verma* and S. R. Bhardwaj

Department of Physics, B. S. A. College, Mathura 281004, India

Received 30 April 2006, revised 12 July 2006, accepted 19 July 2006

Published online 5 September 2006

PACS 77.22.Ch, 78.20.Ci

The dielectric description of ionicity developed by Phillips and Van Vechten has been successfully em-

ployed in a wide range of semi-conductors and insulators. However, the applicability of this Phillips and

Van Vechten (PV) dielectric analysis has been limited to only the simple ANB8–N compounds, which con-

tain only one type of bond. Levine has extended the theory of PV to multi bond and complex crystals. Le-

vine’s theory of ionicity has been used to calculate the various bond parameters for the chalcopyrites. In

this paper a simple method based on the product of ionic charge and nearest-neighbor distance of solids, is

proposed for the calculation of ionic gap (Ec), average energy gap (Eg), crystal ionicity (fi) and dielectric

constant (ε) of zinc blende (AIIBVI and AIIIBV) and chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors.

We find the ionic gap (Ec) and average energy gap (Eg) are inversely related to product of ionic charge and

nearest-neighbor distance. Our evaluated values are in excellent agreement with the values reported by

different researchers.

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

Recently, frequent attempts [1–12] have been made to understand the electronic, mechanical, elastic and optical properties of zinc blende (AIIBVI and AIIIBV) and chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semicon-

ductors. 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. The concept of crystal ionicity of chemical bonding has been proved to be very useful in the charac-terization of molecular and solid state properties and there exist many ionicity scales proposed to corre-late with a wide range of chemical and physical properties such as elastic constants, cohesive energy, heat of formation, bulk modulus, crystal structure etc [13]. Phillips and Van Vechten [14–16], Levine [13] and several other researchers [17–21] have developed various theories and calculated ionicity for the case of simple compounds. In practice these theories require elaborate computation, and have been developed only for the limited semiconductors. Therefore, we thought it would be of interest to give an alternative explanation for the ionic (Ec), average energy gaps (Eg), crystal ionicity (fi) and dielectric constant (ε) in zinc blende (AIIBVI and AIIIBV) and chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors.

Structurally chalcopyrite compounds are derived from that of the binary sphalerite structure (III–V and II–VI) with a slight distortion. Therefore, like binary compounds they have a high non-linear susceptibil-ity. However because of the presence of two types of bonds in chalcopyrites they become anisotropic. This anisotropy gives rise to high bifringence. High non-linear susceptibility coupled with high bifrin-gence in these compounds makes them very useful for efficient second harmonic generation and phase matching. In this paper we propose a method based on the product of ionic charge theory of solids for the

* Corresponding author: e-mail: ajay_phy@rediffmail.com, Phone: +91 565 2423417

4026 A. S. Verma and S. R. Bhardwaj: Properties of zinc blende and complex crystalline solids

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

calculation of the ionic gaps (Ec), average energy gaps (Eg), crystal ionicity (fi) and dielectric constant (ε) in zinc blende (AIIBVI and AIIIBV) and chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors. The ionic

charge of a metal changes, when it undergoes a chemical combination and forms a compound. 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. We have calculated electronic and optical properties of zinc blende (AIIBVI and AIIIBV) and chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors using this idea. In our proposed rela-

tion only few parameters such as the nearest-neighbor distance and ionic charge on cation and anion are required as input, to evaluated various electronic and optical properties of these compounds and the method turns out to be widely applicable.

2 Theory, results and discussion

The average energy gap can be separated into the homopolar and the heteropolar parts according to the following relations [14–16]:

2

gE = 2

hE + 2

c,E

(1)

if = 2 2

c g/ ,E E (2)

h

E = 39.74 /d 2.48 , (3)

g

E = 14.4 b {(ZA/ro) – (n/m) × (ZB/rο)} s o

e ,K r- (4)

where Eg is the average energy gap of a crystal; fi is the fractional ionicity; d is the nearest-neighbor distance (bond length), Ec the heteropolar part of average energy gap for A

mB

n compounds, b the pre-

screening factor, s o

eK r- the Thomas–Fermi screening factor, and r

ο = d/2. The numerical factors in Eqs.

(3) and (4) and the following ones are given for d expressed in Å and energy in eV. The most generalized form of the above equations has been discussed by Levine [13] in detail. The equations given by Levine reduce to those of PV when only one type of bond is present in the crystal. In order to determine the bond ionicity of chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) crystals which are

tetrahedrally coordinated, the average energy gap Eg, XY of the X–Y bond can be separated into the ionic gap Ec, XY and covalent Eh, XY parts. Presently, V. Kumar [22–24] has shown that the electronic properties for chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) compounds in terms of plasmon energy ħωp can be written as

follows. For the A–C bond in AIIBIV V

2C :

Eh, AC (eV) = 0.05118(ħωp, AC)ν , (5)

Ec, AC (eV) = 5.904bAC(ħωp, AC)µ × exp [–5.971(ħωp, AC)–µ/2] , (6)

for the B–C bond in AIIBIV V

2C :

Eh, BC (eV) = 0.04158(ħωp, BC)ν , (7)

Ec, BC (eV) = 1.81bBC(ħωp, BC)µ × exp [–6.4930(ħωp, BC)–µ/2] , (8)

for the A–C bond in AIBIII VI

2C :

Eh, AC (eV) = 0.0246(ħωp, AC)v , (9)

Ec, AC (eV) = 7.3208b(ħωp, AC)2/3 × exp [–8.026(ħω’p, AC)–1/3 (ħωp, AC)–2/3] , (10)

for the B–C bond in AIBIII VI

2C :

Eh, BC (eV) = 0.0416(ħωp, BC)ν , (11)

phys. stat. sol. (b) 243, No. 15 (2006) 4027

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Original

Paper

Ec, BC (eV) = 5.53b(ħωp, BC)2/3 × exp [–6.5058(ħωp, BC)–2/3] , (12)

for AIIBVI zinc blende crystals:

Eh (eV) = 0.04584(ħωp)ν , (13)

Ec (eV) = 10.722(ħωp)2/3 × exp [–6.2554(ħωp)

–1/3] . (14)

Here Eh and Ec are the homopolar and ionic gaps, respectively. In these equations ħωp is given in eV, ν and µ are constants, and b is prescreening factor. In the above theory the authors have used a number of constants to evaluate the above parameters. The physical meaning of Eq. (4) is that Ec is given by the difference between the screened Coulomb potentials of atoms A and B having core charges ZA and ZB. These potentials are to be evaluated at the covalent radii r

ο. Only a small part of the electrons are in the bond, the rest screen the ion cores, reducing

their charge by the Thomas-Fermi screening factor s o

eK r- , which affects the chemical trend in a com-

pound. This screening factor, as well as the bond length, is related to the effective number of free elec-trons in the valence band. The ionic charge also depends directly on the effective number of free elec-trons in the valence band. Thus, there must be some correlation between the physical process, which involves the ionic contribution Ec to the average energy gap Eg and the product of ionic charge of a com-pounds (Z1Z2). Where Z1 and Z2 are the ionic charges on cation and anion respectively. A detailed study for ionic charges of chalcopyrite has been presented in reference [25]. According to ref. [25], the valency of copper in all chalcopyrite compounds appears to be one and it is well known that gallium, aluminium and indium always have valency three. Thus we can write the valence structures of the compounds as A+B3+ 2

2C

- (A = Cu, Ag; B = Al, Ga, In; C = S, Se, Te) and A2+B4+ 3

2C

- (A = Zn, Cd; B = Si, Ge, Sn; C = P, As). Krishnan–Roy theory [26], Jayaraman et al. [27] and Sirdeshmukh et al. [28] found that substantially reduced ionic charges must be used to get better agreement with experimental values. The crystal ionicity of chalcopyrite compounds exhibits a linear relationship when plotted against nearest-neighbor distance,

0.4900

0.5000

0.8200

0.8100

1.2200 1.2400 1.2600

0.5025

ZnSiP

ZnSnP

ZnSiAs

ZnSnAs

CdSiP

CdSnP

2

2

2

2

2

2

CuAlS

CuAlSe

CuAlTe

2

2

2

d0.24

i

A B C chalcopyrite semiconductorsII IV V2

↑

↓A B C chalcopyrite semiconductorsI III VI

2

For A C bonds⎯

Cry

stal

ioni

city

(f)

Fig. 1 Plot of ionicity and nearest-neighbor dis-

tance for A–C bonds in chalcopyrite (AIIBIV V

2C and

AIBIII VI

2C ) semiconductors. In this figure, the crystal

ionicity (AIIBIV V

2C ) lies on the line nearly parallel to

the line for the AIBIII VI

2C . In this figure all values taken

from V. Kumar relations [22, 23].

4028 A. S. Verma and S. R. Bhardwaj: Properties of zinc blende and complex crystalline solids

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

A B C chalcopyrite semiconductorsII IV V

2

↑

↓A B C chalcopyrite semiconductorsI III VI

2

0.2100

0.2200

0.5800

0.5700

1.2200 1.2400 1.2600

0.5575

ZnSnP

ZnSiAs

ZnSnAsCdSnAs

2

2

22

2

CuAlS

CuAlSe

CuAlTe

2

2

2

d0.24

i

0.5600

AgAlSe

2

CdSnP

For B C bonds⎯

Cry

stal

ioni

city

(f)

but fall on two nearly parallel straight lines according to the ionic charge product of the compounds, which are presented in the following Fig. 1 and 2. Using this idea for getting better agreement with theo-retical data for ionic gap (Ec), average energy gap (Eg), crystal ionicity ( fi) and dielectric constant (ε) of AIIBVI, AIIIBV, AIBIIIC2

VI and AIIBIV V

2C semiconductors may be written in terms of product of ionic

charges as follows. For zinc blende and the A–C bond in AIIBIV V

2C and AIBIII VI

2C chalcopyrites:

Ec, AC (eV) = 90/(Z1Z2)0.7 d 2 , (15)

Eg, AC (eV) = 96/(Z1Z2)0.5 d 2.12 , (16)

for the B–C bond in AIIBIV V

2C and AIBIII VI

2C chalcopyrites:

Ec, BC (eV) = 275/(Z1Z2)1.25 d 2 , (17)

Eg, BC (eV) = 106/(Z1Z2)0.5 d 2.12 . (18)

Here Z1 and Z2 are the ionic charges and d is the nearest-neighbor distance in Å. After solving Eqs. (2) and (15)–(18), crystal ionicity ( fi) may be written as follows. For zinc blende and the A–C bond in AIIBIV V

2C and AIBIII VI

2C chalcopyrites:

fi = 0.87891 × d 0.24/(Z1Z2)0.4 , (19)

for the B–C bond in AIIBIV V

2C and AIBIII VI

2C chalcopyrites:

fi = 6.731 × d 0.24/(Z1Z2)1.5 . (20)

Fig. 2 Plot of ionicity and nearest-neighbor distance

for B–C bonds chalcopyrite (AIIBIV V

2C and AIBIII VI

2C )

semiconductors. In this figure the crystal ionicity

(AIIBIV V

2C ) lies on the line nearly parallel to the line for

the AIBIII VI

2C . In this figure all values taken from V.

Kumar relations [22, 23].

phys. stat. sol. (b) 243, No. 15 (2006) 4029

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Original

Paper

The dielectric constant εXY of the X–Y bond is given by the well-known relation [13, 17]

εXY = 1 + (ħωp, XY)2/(Eg, XY)2 , (21)

electronic susceptibility (χXY) = εXY – 1 . (22)

A detailed discussion of electronic properties for chalcopyrites has been given elsewhere [10, 13, 23, 24] and will not be presented here. Using Eqs. (15)–(22), the ionic gaps (Ec), average energy gaps (Eg), crystal ionicity (fi), dielectric constant (ε) and electronic susceptibility (χ) for zinc blende (AIIBVI and AIIIBV) and A–C and B–C bonds in chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors has been calculated. The results are pre-

sented in Tables 1–7. The calculated values are in fair agreement with the values reported by Levine [13] and V. Kumar [22–24]. In the present model the ionic gaps (Ec,XY), average energy gaps (Eg, XY), crystal ionicity (fi,XY) and electronic susceptibility (χXY) can be calculated without having any knowledge of the experimental value of the dielectric constant while the earlier models require this value in their calculation.

Table 1 In this table we have presented the values of ionic gaps (Ec) and average energy gaps (Eg) of

A–C bond in chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors.

solids dAC Ec [13] Ec [22, 23] Ec [this work] Eg [13] Eg [22, 23] Eg [this work]

CuAlS2 2.29 10.575 10.565 11.728 11.719 CuAlSe2 2.42 9.435 9.460 10.436 10.425 CuAlTe2 2.60 8.035 8.196 8.859 8.954 CuGaS2 2.39 9.95 9.673 9.699 10.964 10.705 10.704 CuGaSe2 2.49 7.87 8.807 8.936 8.888 9.692 9.813 CuGaTe2 2.61 7.945 8.133 8.758 8.881 CuInS2 2.49 8.52 8.523 8.936 9.617 9.478 9.813 CuInSe2 2.43 9.333 9.382 10.321 10.334 CuInTe2 2.66 6.635 7.830 7.516 8.531 AgAlS2 2.54 9.320 8.587 10.117 9.408 AgAlSe2 2.66 8.393 7.830 9.096 8.531 AgAlTe2 2.79 7.510 7.117 8.128 7.710 AgGaS2 2.57 9.87 9.103 8.388 10.60 9.877 9.177 AgGaSe2 2.66 8.56 8.405 7.830 9.275 9.110 8.531 AgGaTe2 2.77 7.649 7.220 8.281 7.829 AgInS2 2.51 9.608 8.794 10.434 9.648 AgInSe2 2.63 8.15 8.662 8.010 8.862 9.392 8.739 AgInTe2 2.79 7.554 7.117 8.176 7.710 ZnSiP2 2.375 4.10 4.584 4.552 6.119 6.530 6.263 ZnGeP2 2.389 4.08 4.541 4.499 6.134 6.465 6.186 ZnSnP2 2.416 4.07 4.414 4.399 6.038 6.273 6.040 ZnSiAs2 2.464 3.73 4.225 4.229 5.655 5.989 5.793 ZnGeAs2 2.482 3.71 4.157 4.168 5.582 5.887 5.705 ZnSnAs2 2.508 3.68 4.061 4.082 5.480 5.744 5.580 CdSiP2 2.561 4.17 3.875 3.915 5.682 5.647 5.338 CdGeP2 2.559 4.12 3.882 3.921 5.652 5.478 5.347 CdSnP2 2.588 4.04 3.785 3.834 5.519 5.334 5.221 CdSiAs2 2.640 3.98 3.618 3.684 5.354 5.088 5.005 CdGeAs2 2.642 3.94 3.612 3.679 5.317 5.080 4.997 CdSnAs2 2.670 3.87 3.527 3.602 5.205 4.983 4.887

4030 A. S. Verma and S. R. Bhardwaj: Properties of zinc blende and complex crystalline solids

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

Table 2 In this table we have presented the values of ionic gaps (Ec) and average energy gaps (Eg) of

and B–C bond in chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors.

solids dBC Ec [13] Ec [22, 23] Ec [this work] Eg [13] Eg [22, 23] Eg [this work]

CuAlS2 2.29 5.746 5.584 7.671 7.471 CuAlSe2 2.40 5.165 5.084 6.863 6.764 CuAlTe2 2.56 4.479 4.469 5.902 5.899 CuGaS2 2.30 5.60 5.684 5.536 7.45 7.584 7.402 CuGaSe2 2.42 5.10 5.103 5.001 6.80 6.777 6.646 CuGaTe2 2.59 4.336 4.366 5.725 5.755 CuInS2 2.46 5.49 4.898 4.839 6.39 6.494 6.419 CuInSe2 2.56 4.466 4.469 5.902 5.899 CuInTe2 2.70 3.960 4.017 5.215 5.269 AgAlS2 2.26 5.939 5.734 7.943 7.683 AgAlSe2 2.36 5.381 5.258 7.162 7.009 AgAlTe2 2.57 4.430 4.434 5.853 5.850 AgGaS2 2.27 5.64 5.887 5.683 7.47 7.869 7.611 AgGaSe2 2.39 5.02 5.235 5.127 6.70 6.959 6.824 AgGaTe2 2.60 4.316 4.332 5.698 5.708 AgInS2 2.47 4.835 4.800 6.408 6.364 AgInSe2 2.58 4.71 4.378 4.400 6.70 5.783 5.802 AgInTe2 2.76 3.758 3.844 4.944 5.029 ZnSiP2 2.254 2.45 2.720 2.424 5.84 5.95 5.463 ZnGeP2 2.324 2.60 2.546 2.280 5.56 5.54 5.120 ZnSnP2 2.485 2.71 2.183 1.994 4.97 4.70 4.443 ZnSiAs2 2.350 2.54 2.478 2.230 5.41 5.38 5.001 ZnGeAs2 2.407 2.12 2.347 2.125 4.97 5.07 4.753 ZnSnAs2 2.557 1.53 2.045 1.883 4.16 4.38 4.182 CdSiP2 2.247 2.59 2.739 2.439 5.94 6.00 5.500 CdGeP2 2.325 2.68 2.538 2.278 5.59 5.52 5.116 CdSnP2 2.486 2.71 2.181 1.992 4.96 4.69 4.439 CdSiAs2 2.348 2.64 2.543 2.233 5.46 5.42 5.010 CdGeAs2 2.421 2.21 2.317 2.101 4.95 5.00 4.695 CdSnAs2 2.572 1.59 2.017 1.861 4.14 4.32 4.130

Table 3 In this table we have presented the values of crystal ionicity ( fi) of A–C and B–C bonds in

chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors.

solids fi [13], A–C

fi [22, 23], A–C

fi [29], A–C

fi [30], A–C

fi [our], A–C

fi [13], B–C

fi [22, 23], B–C

fi [29], B–C

fi [30], B–C

fi [our], B–C

CuAlS2 0.813 0.78 0.65 0.813 0.561 0.62 0.54 0.559 CuAlSe2 0.817 0.79 0.63 0.824 0.566 0.65 0.50 0.565 CuAlTe2 0.822 0.75 0.56 0.838 0.576 0.56 0.38 0.574 CuGaS2 0.825 0.816 0.77 0.66 0.821 0.565 0.561 0.55 0.54 0.559 CuGaSe2 0.784 0.825 0.76 0.63 0.829 0.563 0.567 0.55 0.49 0.566 CuGaTe2 0.823 0.81 0.57 0.839 0.573 0.51 0.39 0.576 CuInS2 0.785 0.808 0.77 0.68 0.829 0.636 0.569 0.60 0.61 0.569 CuInSe2 0.817 0.77 0.65 0.824 0.572 0.60 0.57 0.574 CuInTe2 0.779 0.76 0.59 0.842 0.576 0.57 0.48 0.581

phys. stat. sol. (b) 243, No. 15 (2006) 4031

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Original

Paper

Table 3 continued

solids fi [13], A–C

fi [22, 23], A–C

fi [29], A–C

fi [30], A–C

fi [our], A–C

fi [13], B–C

fi [22, 23], B–C

fi [29], B–C

fi [30], B–C

fi [our], B–C

AgAlS2 0.848 0.85 0.70 0.833 0.559 0.61 0.56 0.557 AgAlSe2 0.851 0.86 0.67 0.842 0.564 0.63 0.51 0.563 AgAlTe2 0.853 0.84 0.62 0.852 0.573 0.57 0.41 0.575 AgGaS2 0.867 0.849 0.86 0.70 0.835 0.570 0.559 0.54 0.54 0.558 AgGaSe2 0.852 0.851 0.85 0.68 0.842 0.561 0.566 0.54 0.51 0.565 AgGaTe2 0.853 0.86 0.62 0.851 0.573 0.51 0.40 0.576 AgInS2 0.847 0.85 0.72 0.831 0.569 0.61 0.64 0.569 AgInSe2 0.846 0.850 0.85 0.70 0.840 0.604 0.573 0.60 0.60 0.575 AgInTe2 0.853 0.84 0.64 0.852 0.578 0.58 0.50 0.584 ZnSiP2 0.438 0.493 0.528 0.117 0.2088 0.197 ZnGeP2 0.442 0.493 0.529 0.219 0.2112 0.198 ZnSnP2 0.455 0.495 0.530 0.298 0.2162 0.202 ZnSiAs2 0.436 0.498 0.533 0.220 0.2122 0.199 ZnGeAs2 0.446 0.499 0.534 0.182 0.2140 0.200 ZnSnAs2 0.450 0.500 0.535 0.135 0.2180 0.203 CdSiP2 0.539 0.502 0.538 0.191 0.2085 0.197 CdGeP2 0.532 0.502 0.538 0.231 0.2113 0.198 CdSnP2 0.536 0.504 0.539 0.298 0.2163 0.202 CdSiAs2 0.553 0.506 0.542 0.234 0.2202 0.199 CdGeAs2 0.549 0.506 0.542 0.199 0.2144 0.200 CdSnAs2 0.553 0.501 0.543 0.148 0.2184 0.203

Table 4 In this table we have presented the values of dielectric constant of A–C and B–C bonds in

chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors and plasmon energies taken from Refs. [22, 23].

solids ħωp, (A–C)

ħωp, (B–C)

ε(A–C), [22, 23]

ε(A–C), [13]

ε(A–C), [our]

ε(B–C), [22, 23]

ε(B–C), [13]

ε(B–C), [our]

CuAlS2 25.110 18.295 5.591 6.997 CuAlSe2 23.231 17.041 5.966 7.347 CuAlTe2 20.859 15.518 6.427 7.920 CuGaS2 23.626 18.163 5.43 5.872 7.07 7.021 CuGaSe2 22.176 16.906 6.76 6.107 8.04 7.471 CuGaTe2 20.703 15.195 6.434 7.971 CuInS2 22.231 16.453 6.53 6.132 6.99 7.570 CuInSe2 23.061 15.489 5.980 7.894 CuInTe2 20.167 14.332 6.588 8.399 AgAlS2 21.536 18.708 6.240 6.929 AgAlSe2 20.090 17.510 6.546 7.241 AgAlTe2 18.681 15.408 6.871 7.937 AgGaS2 21.201 18.598 4.68 6.337 6.84 6.971 AgGaSe2 20.110 17.193 5.28 6.557 8.04 7.348 AgGaTe2 18.905 15.149 6.831 8.044 AgInS2 21.979 16.313 6.190 7.571 AgInSe2 20.513 15.291 5.53 6.510 8.41 7.946 AgInTe2 18.751 13.860 6.915 8.596 ZnSiP2 15.294 18.757 6.486 6.84 6.963 10.931 10.41 12.789

4032 A. S. Verma and S. R. Bhardwaj: Properties of zinc blende and complex crystalline solids

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

Table 4 continued

solids ħωp, (A–C)

ħωp, (B–C)

ε(A–C), [22, 23]

ε(A–C), [13]

ε(A–C), [our]

ε(B–C), [22, 23]

ε(B–C), [13]

ε(B–C), [our]

ZnGeP2 15.198 17.944 6.526 6.84 7.036 11.494 11.55 13.283 ZnSnP2 14.907 16.203 6.648 6.84 7.091 12.93 12.65 14.300 ZnSiAs2 14.473 17.620 6.839 7.95 7.242 11.731 11.80 13.414 ZnGeAs2 14.316 16.997 6.913 7.95 7.300 12.223 14.29 13.788 ZnSnAs2 14.094 15.524 7.021 7.95 7.380 13.568 18.08 14.780 CdSiP2 13.659 18.845 7.239 6.99 7.550 10.874 10.41 12.740 CdGeP2 13.675 17.905 7.232 6.99 7.540 11.521 11.55 13.249 CdSnP2 13.446 16.194 7.355 6.99 7.633 12.922 12.65 14.309 CdSiAs2 13.050 17.642 7.579 8.22 7.799 11.603 11.80 13.400 CdGeAs2 13.035 16.850 7.588 8.22 7.805 12.343 14.29 13.880 CdSnAs2 12.831 15.388 7.730 8.22 7.894 13.710 18.08 14.882

Table 5 In this table we have presented the values of electronic susceptibility of A–C and B–C bonds

in chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors.

solids χ [29], A–C

χ [22], A–C

χ [13], A–C

χ [this work], A–C

χ [29], B–C

χ [22], B–C

χ [13], B–C

χ [this work], B–C

CuAlS2 4.78 4.584 4.591 4.26 4.955 5.997 CuAlSe2 5.42 5.240 4.966 4.76 5.908 6.347 CuAlTe2 5.262 5.427 7.19 7.102 6.920 CuGaS2 4.83 4.248 4.43 4.872 5.59 5.485 6.07 6.021 CuGaSe2 6.00 4.838 5.76 5.107 6.80 6.573 7.04 6.471 CuGaTe2 5.65 5.305 5.434 9.17 7.951 6.971 CuInS2 5.22 4.824 5.53 5.132 6.02 6.537 5.99 6.570 CuInSe2 6.38 4.607 4.980 7.30 7.867 6.984 CuInTe2 7.45 6.939 5.588 9.35 9.114 7.399 AgAlS2 4.02 4.138 5.240 4.26 4.829 5.929 AgAlSe2 4.65 4.767 5.546 4.76 5.461 6.241 AgAlTe2 6.02 5.349 5.871 7.19 7.073 6.937 AgGaS2 3.83 4.209 3.68 5.337 5.59 5.338 5.84 5.971 AgGaSe2 4.78 4.762 4.28 5.557 6.80 6.443 7.04 6.348 AgGaTe2 5.07 5.275 5.831 9.17 7.978 7.044 AgInS2 4.02 4.048 5.190 6.02 6.601 6.571 AgInSe2 4.64 4.658 4.53 5.510 7.30 7.888 7.41 6.946 AgInTe2 6.02 5.325 5.915 9.35 9.494 7.596 ZnSiP2 5.963 11.789 ZnGeP2 6.036 12.283 ZnSnP2 6.091 13.300 ZnSiAs2 6.242 12.414 ZnGeAs2 6.300 12.788 ZnSnAs2 6.380 13.780 CdSiP2 6.550 11.740 CdGeP2 6.540 12.249 CdSnP2 6.633 13.309 CdSiAs2 6.799 12.400 CdGeAs2 6.805 12.880 CdSnAs2 6.894 13.882

phys. stat. sol. (b) 243, No. 15 (2006) 4033

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Original

Paper

Table 6 In this table we have presented the values of ionic gaps (Ec) and average energy gaps (Eg) of

zinc blende semiconductors.

solids d Ec [13] Ec [24, 34] Ec [this work] Eg [13] Eg [22, 23] Eg [this work]

AlP 2.36 3.76 3.31 3.47 6.04 5.18 AlAs 2.43 3.82 3.36 3.27 5.81 4.87 AlSb 2.66 3.08 2.71 2.73 4.68 4.02 GaP 2.36 3.30 2.90 3.47 5.76 5.18 GaAs 2.45 2.92 2.51 3.22 5.21 4.79 GaSb 2.65 2.13 1.87 2.75 4.14 4.05 InP 2.54 3.35 2.95 3.00 5.16 4.44 InAs 2.61 2.74 2.41 2.84 4.58 4.19 InSb 2.81 2.15 1.89 2.45 3.76 3.58 ZnS 2.34 6.16 6.05 6.23 7.82 7.73 7.92 ZnSe 2.46 5.51 5.57 5.64 6.98 7.09 7.12 ZnTe 2.64 4.38 4.54 4.89 5.66 5.75 6.13 CdS 2.54 5.78 5.10 5.29 7.01 6.47 6.65 CdSe 2.62 5.31 4.97 6.42 6.23 CdTe 2.81 4.43 4.19 4.32 5.40 5.29 5.37 HgS 2.53 5.08 5.33 6.45 6.71 HgSe 2.63 4.14 4.93 5.22 6.18 HgTe 2.93 3.97 4.92

Table 7 In this table we have presented the values of dielectric constant (ε ) and crystal ionicity ( fi) of

zinc blende semiconductors.

solids ħωp [32] ε [5] ε [31] ε [this work] fi [13] fi [24] fi [this work]

AlP 8.323 7.54 0.388 0.386d 0.449 AlAs 9.404 8.51 0.432 0.430d 0.452 AlSb 10.24 0.433 0.431d 0.462 GaP 16.8 9.495 9.11 11.52 0.328 0.325d 0.449 GaAs 16.0 12.302 10.88 12.16 0.315 0.303d 0.453 GaSb 14.9 14.44 14.53 0.265 0.264d 0.461 InP 13.9 9.706 9.61 10.80 0.421 0.419d 0.457 InAs 13.7 13.559 12.03 11.69 0.359 0.357d 0.460 InSb 13.2 15.68 14.60 0.329 0.327d 0.468 ZnS 16.68b 5.70c 5.20a 5.44 0.621 0.613 0.619 ZnSe 15.78b 5.90c 6.00a 5.91 0.623 0.617 0.627 ZnTe 13.80b 6.70c 7.28 6.07 0.599 0.626 0.637 CdS 14.87b 5.30a 6.00 0.679 0.621 0.631 CdSe 6.00a 0.684 0.636 CdTe 13.09b 7.21 6.94 0.675 0.629 0.647 HgS 14.85b 5.90 0.622 0.631 HgSe 12.98b 5.41 0.629 0.637 HgTe 0.653 aRef. [13], bRef. [24], cRef. [33], dRef. [34]

3 Conclusion

The proposed empirical relations have been applied to evaluate ionic gap (Ec), average energy gap (Eg), crystal ionicity ( fi), dielectric constants (ε) and electronic susceptibility of zinc blende (AIIBVI and AIIIBV)

4034 A. S. Verma and S. R. Bhardwaj: Properties of zinc blende and complex crystalline solids

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

and chalcopyrite (AIBIII VI

2C and AIIBIV V

2C ) semiconductors. We come to the conclusion that product of

ionic charges of any compound is very important parameter for calculating electronic and optical proper-ties. What is remarkable in Figs. 1 and 2 is that the data points for the chalcopyrite (AIBIII VI

2C and

AIIBIV V

2C ) semiconductors fall on two nearly parallel straight lines, which depends on the product

of ionic charge. The ionic gap (Ec) and average energy gap (Eg) of these materials is inversely related to inter atomic distance and the product of ionic charges and dielectric constants (ε) and electronic susceptibility (χ) of these materials is directly related to inter atomic distance and the product of ionic charges. It is also to be note worthy that the proposed relations are simpler widely applicable and values are in better agreement with reported data as compared to empirical relation proposed by previous researchers. The method presented in this work will be helpful to the material scientists for finding new materials with desired ionic gap (Ec), average energy gap (Eg), crystal ionicity (fi), dielectric constants (ε) and electronic susceptibility (χ) among the series of structurally similar mate-rials.

References

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

[2] S. Q. Wang and H. Q. Ye, J. Phys.: Condens. Matter 14, 9579 (2002).

[3] S. Q. Wang and H. Q. Ye, J. Phys.: Condens. Matter 15, 5307 (2003).

[4] S. Q. Wang and H. Q. Ye, J. Phys.: Condens. Matter 15, L197 (2003).

[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] S. Q. Wang and H. Q. Ye, phys. stat. sol. (b) 240, 45 (2003).

[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(1), 99–102 (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).

[13] B. F. Levine, Phys. Rev. B 7, 2591 (1973); Phys. Rev. B 7, 2600 (1973); J. Chem. Phys. 59, 1463 (1973); Phys.

Rev. Lett. 25, 44 (1970).

[14] J. C. Phillips, Bonds and Bands in Semiconductors (Academic Press, New York, 1973).

[15] J. C. Phillips and Van Vechten, Phys. Rev. B 2, 2147 (1970); Phys. Rev. 183, 709 (1969).

[16] J. A. Van Vechten, Phys. Rev. B 1, 3351 (1970); Phys. Rev. 182, 891 (1969); Phys. Rev. 187, 1007 (1969).

[17] D. R. Penn, Phys. Rev. 128, 2093 (1962).

[18] P. R. Sarode, phys. stat. sol. (b) 88, K35 (1978).

[19] A. Garcia and M. L. Cohen, Phys. Rev. B 47, 4215 (1993).

[20] M. Ferhat, A. Zaoui, M. Certier, and B. Khelifa, phys. stat. sol. (b) 195, 415 (1996).

[21] A. C. Sharma and S. Auluck, Phys. Rev. B 28, 965 (1983).

[22] V. Kumar, J. Phys. Chem. Solids 48, 827 (1987).

[23] V. Kumar, Phys. Rev. B 36, 5044 (1987).

[24] V. Kumar Srivastava, J. Phys. C, Solid State Phys. 19, 5689 (1986).

[25] M. M. Ballal and C. Mande, J. Phys. C, Solid State Phys. 11, 837 (1978).

[26] K. S. Krishnan and S. K. Roy, Proc. R. Soc. London 210, 481 (1952).

[27] A. Jayaraman, B. Batlogg, R. G. Maines, and H. Bach, Phys. Rev. B 26, 3347 (1982).

[28] D. B. Sirdeshmukh and K. G. Subhadra, J. Appl. Phys. 59, 276 (1986).

[29] H. Neumann, Cryst. Res. Technol. 18, 1299, 1391, 665, 901 (1983).

[30] M. J. Bernard, Physique [Suppl.] 36, C3 (1975).

[31] B. R. Nag, Appl. Phys. Lett. 65, 1938 (1994).

[32] S. Sen, D. N. Bose, and M. S. Hegde, phys. stat. sol. (b) 129, K65 (1985).

[33] S. V. Adhyapak, S. M. Kanetkar, and A. S. Nigavekar, Nuovo Cimento 35, B179 (1976).

[34] W. Kucharczyk, phys. stat. sol. (b) 180, K27 (1993).