Analysis of optoelectronic properties of ANB⁸⁻N type binary solids

Analysis of optoelectronic properties of A

B

type binary solids

B P Singh, S Tripti & Vipnesh Singh

Department of Physics, Institute of Basic Sciences, Khandari, Agra 282 002 E-mail: drbps.ibs@gmail.com

Received 16 March 2007; revised 14 March 2008; accepted 28 April 2008

The dependence of refractive index for I-VII, II-VI, III-V semiconductors including alkali halides on the energy band gap and the optical electronegativity difference has been studied. The relationships have been established for estimating the refractive index of materials. In addition, an interrelation between the energy band gap, polarizability and magnetic susceptibility has also been investigated. The computed values of the parameters are then compared with the literature values.

Keywords: Energy gap, Refractive index, Electronic polarizability, Magnetic susceptibility

1 Introduction

In view of much importance of semiconductors and alkali halides, theoretical prediction of their different physical properties has attracted much attention

. The evaluation of refractive indices of semiconductors is of considerable importance for potential applications in integrated optical devices such as switches, filters and modulators, whereas the refractive index of materials is the key parameter for designing various devices

. The refractive index is closely related to the electronic polarizability of ions and the local field inside the materials. Electronic polarizability for different crystals has been calculated by several workers using the dielectric theory of Phillips

. Magnetic susceptibility plays a vital role in understanding the structure and the nature of chemical bonding in semiconductors and ionic crystals

. Moss

has proposed a general relationship based on the concept that, in dielectric theory, energy levels are scaled by a factor ∈

, i.e

E

n

= constant … (1)

Reddy et al.

have proposed another empirical relationship between refractive index and optical electronegativity. Ravindra et al.

proposed a linear relation governing the variation of the optical refractive index n with the energy gap (E

) between bonding and antibonding states

n = 4.08 – 0.62 E

… (2)

Gopal

modified the Penn-model

for the high frequency dielectric constant ∈ of semiconductors to obtain a general formula relating n and E

. This formula is as follows:

2 2

) 1 (

B E n A

g

+ +

= … (3)

where A and B are numerical constants.

In the present study, the dependence of refractive index n and energy gap E

on ∆ X, the electronegativity difference between constituent atoms of the compound semiconductors has been studies. Also the inter-connection between polarizability and magnetic susceptibility has been investigated.

2 Theory

For the present study, the relation considered for refractive index and energy gap E

is as follows:

4 /

)

( X D n F

−

= ∆ … (4)

where F is dependent on the semiconductor group and its value is found to be proportional to the ratio of the valence electron plasmon and the Fermi energies and D is unique numerical constant.

85 .

)

( 45 .

4 X

E

= ∆ … (5)

where ∆ X is the electronegativity .

However, a careful analysis reveals that Eqs (4) and (5) do not satisfy precisely the available data for the energy gap. For example, the values of E

determined from Eq. (5) are compared with the known values reported in the literature (Tables 1-3). On the other hand, it is found that the ratio E

/∆X remains remarkably constant between 3.72-4.19, 3.87-5.15 and 4.22-5.90 for I-VII, II-VI and III-V groups of semiconductor compounds respectively. Thus a linear relationship between E

and ∆ X appears to be more appropriate and simple.

In place of Eq. (4), a simple relationship proposed in this study is as follows:

5 .

)

( X n f

= ∆ … (6)

This relation has been found to hold good with a constant value of f for each group of compound such

as I-VII (f = 2.35), II-VI (f = 2.5), and III-V (f = 2.0) compounds. Values of refractive index obtained from Eq. (6) along with the experimental values are reported in Tables 1-3. The values of refractive index obtained in the present study are found in good agreement with the experimental values. Thus Eq. (6) represents a simple empirical relationship. The constant f in Eq. (6) may be assigned to contain both the valence electron plasma and the Fermi-energies. It can be expressed as

m m

f p

E

f = ( η ω .

) = ( 2 . 5 ) … (7) The value of m is considered to be characteristic of each semiconductor group. This is in accordance with the results of present study. It is found that m = 0.93247, 1.00 and 0.75647 for I-VII, II-VI and III-V groups of semiconductor respectively.

Table 1―Values of energy gap (Eg), refractive index (n), electronic polarizability (α) and magnetic susceptibility(χd) for I-VII binary compounds

Energy gap (Eg) (eV) Refractive index (n) Electronic polarizability (α)

(10^-24 cm³)

Magnetic susceptibility (χd)

(10^-6 cm mol^-1) Solids Electro-

negativity difference

(∆X) Calculated

Eq.(5) Ref.

[11-13, 24]

Eg/∆X

Calculated Eq.(6) Ref.

[22 - 24] Calculated

Eq.(8) Ref. [25] Calculated Eq.(9) Ref.

[24, 26]

LiF 3.0 11.32 9.49 3.77 1.36 1.39 0.85 0.89 -12.3 -10.1 LiCl 2.0 8.02 7.02 4.01 1.66 1.66 3.00 2.98 -30.5 -24.3 LiBr 1.8 7.33 5.91 4.07 1.75 1.78 4.04 4.12 -39.4 -34.7 LiI 1.5 6.28 4.38 4.19 1.92 1.95 7.14 6.15 -65.8 -50.1 NaF 3.1 11.64 9.99 3.76 1.33 1.34 1.34 1.15 -16.5 -16.4 NaCl 2.1 8.36 8.13 3.98 1.62 1.54 3.75 3.24 -37.0 -30.3 NaBr 1.9 7.68 7.21 4.04 1.70 1.64 4.93 4.38 -47.0 -41.0 NaI 1.6 6.64 6.00 4.15 1.86 1.77 7.26 6.41 -66.8 -57.0 KF 3.2 11.96 9.77 3.74 1.31 1.36 1.80 1.99 -20.4 -23.6 KCl 2.2 8.70 8.59 3.95 1.58 1.49 4.97 4.08 -47.3 -39.0 KBr 2.0 8.02 7.96 4.01 1.66 1.56 6.32 5.22 -58.8 -49.1 KI 1.7 6.99 6.88 4.11 1.80 1.68 8.97 7.25 -81.4 -63.8 RbF 3.2 11.96 9.43 3.74 1.31 1.4 2.26 2.54 -24.3 -31.9 RbCl 2.2 8.70 8.56 3.95 1.58 1.49 5.71 4.63 -53.6 -46.0 RbBr 2.0 8.02 8.02 4.01 1.66 1.55 7.21 5.77 -66.4 -56.4 RbI 1.7 6.99 7.15 4.11 1.80 1.65 10.12 7.80 -91.1 -72.2 CsF 3.3 12.28 8.65 3.72 1.29 1.48 2.67 3.60 -27.8 -44.5 CsCl 2.3 9.03 7.50 3.93 1.55 1.61 5.31 5.69 -50.2 -56.7 CsBr 2.1 8.36 6.95 3.98 1.62 1.67 5.99 6.83 -56.0 -67.2 CsI 1.8 7.33 5.88 4.07 1.75 1.79 9.29 8.86 -84.0 -82.6

CuF 2.1 8.36 - 3.98 1.62 1.58 2.71 - -28.1 -

CuCl 1.1 4.83 - 4.39 2.24 1.93 5.41 - -51.0 - CuBr 0.9 4.07 - 4.52 2.48 2.10 7.18 - -66.1 -

CuI 0.6 2.88 - 4.80 3.03 2.35 9.80 - -88.4 -

AgF 2.0 8.02 - 4.01 1.66 1.70 3.17 - -32.0 -

AgCl 1.0 4.45 - 4.45 2.35 2.00 6.12 - -57.1 - AgBr 0.9 4.07 - 4.52 2.48 2.15 7.24 - -66.6 - AgI 0.6 2.88 - 4.80 3.03 2.22 11.32 - -101.3 -

Table 2—Values of energy gap (E_g), refractive index (n), electronic polarizability (α) and magnetic susceptibility(χ_d) for II-VI binary compounds.

Energy gap (Eg) (eV)

Refractive index (n)

Electronic polarizability (α)

(10^-24 cm³)

Magnetic susceptibility (χd)

(10^-6 cm mol^-1) Solids Electro-

negativity difference

(∆X) Calculated

Eq.(5) Ref.

[11-13, 24]

E_g/∆X

Calculated

Eq.(6) Ref.

[22 - 24] Calculated

Eq.(8) Ref.

[27, 28] Calculated

Eq.(9) Ref.

[24, 26]

MgO 1.93 7.78 7.20 4.03 1.80 1.63 -6.1

MgS 1.27 5.45 3.90 4.29 2.22 2.26 4.44 4.53 -41.7 MgSe 1.20 5.20 2.98 4.33 2.28 2.43 5.66 6.00 -51.4 MgTe 0.79 3.64 2.60 4.61 2.81 2.65 9.22 8.82 -79.9 CaO 2.50 9.70 6.15 3.88 1.58 1.82 2.22 2.90 -23.9 -27.88 CaS 1.50 6.28 5.40 4.19 2.04 2.12 5.85 6.13 -52.9 -45.46 CaSe 1.40 5.92 5.00 4.23 2.11 2.26 7.06 7.62 -62.6 -61.15 SrO 2.50 9.70 5.80 3.88 1.58 1.80 2.90 3.72 -29.3 -35.04 SrS 1.50 6.28 4.80 4.19 2.04 2.10 6.56 6.80 -58.6 -57.99 SrSe 1.40 5.92 4.60 4.23 2.11 2.21 8.05 8.47 -70.5 -75.50 SrTe 1.10 4.83 4.00 4.39 2.38 2.41 10.73 10.84 -91.9 -92.96 BaO 2.55 9.86 5.20 3.87 1.57 1.98 3.45 5.22 -33.7 -55.07 BaS 1.60 6.64 4.00 4.15 1.98 2.15 7.75 8.61 -68.1 -75.77 BaSe 1.50 6.28 3.35 4.19 2.04 2.27 8.74 9.88 -76.0 ZnO 1.90 7.68 3.20 4.04 1.81 2.00 2.48 2.86 -26.0 -32.60 ZnS 0.90 4.07 3.70 4.52 2.64 2.39 6.43 5.91 -57.5 -49.18 ZnSe 0.80 3.68 2.58 4.60 2.80 2.43 7.30 6.53 -64.5 -63.62 ZnTe 0.50 2.47 2.10 4.94 3.54 2.70 9.54 8.14 -82.4 -67.00 CdO 0.67 3.17 2.60 4.73 3.05 2.68 -6.1 -45.95 CdS 0.90 4.07 2.40 4.52 2.64 2.38 7.87 7.20 -69.1 -63.30 CdSe 0.86 3.91 1.70 4.55 2.70 2.44 9.28 8.10 -80.3 -82.00 CdTe 0.38 1.96 1.44 5.15 4.06 3.23 -6.1

Table 3—Values of energy gap (Eg), refractive index (n), electronic polarizability (α) and magnetic susceptibility (χd) for III-V binary compounds.

Energy gap

(Eg) (eV) Refractive

index (n) Electronic polarizability (α)

(10^-24 cm³)

Magnetic susceptibility (χ_d)

(10^-6 cm mol^-1) Solids Electro-

negativity difference

(∆X) Calculated Eq.(5)

Ref.

[11-13, 24]

Eg/∆X

Calculated Eq.(6)

Ref.

[22 - 24]

Calculated Eq.(8)

Ref.

[27, 28]

Calculated Eq.(9)

Ref.

[24, 26]

AlN 1.43 6.03 3.80 4.22 1.67 2.2 1.86 2.79 -4.1 AlP 0.60 2.88 3.00 4.80 2.58 2.75 5.25 5.51 -21.4 AlAs 0.50 2.47 3.40 4.94 2.83 2.92 7.40 7.55 -32.4 AlSb 0.40 2.04 1.50 5.11 3.16 3.19 10.44 10.49 -48.0 GaN 1.40 5.92 3.40 4.23 1.69 2.24 2.07 3.10 -5.2 GaP 0.50 2.47 2.24 4.94 2.83 2.9 6.74 6.85 -29.1 -30.00 GaAs 0.37 1.91 1.40 5.17 3.29 3.3 8.22 8.24 -36.6 -33.30 GaSb 0.24 1.32 0.81 5.51 4.08 3.75 11.29 10.94 -52.4 -38.40 InN 1.26 5.42 2.40 4.30 1.78 2.35 3.11 4.45 -10.5 InP 0.41 2.09 1.25 5.09 3.12 3.1 8.95 8.92 -40.4 -45.60 InAs 0.30 1.60 0.36 5.33 3.65 3.51 10.65 10.47 -49.1 -55.30 InSb 0.23 1.28 0.18 5.55 4.17 3.96 13.67 13.42 -64.5 -65.90

According to the classical theory of dielectric constant, electronic polarizability for a material can be calculated with the help of the Lorentz-Lorenz relation

cm 10 3.95 2 .

1

2

2

⎟⎟ ⎠ × ×

⎞

⎜⎜ ⎝

⎛ +

= −

d M n

α n … (8)

where M and d are molecular weight and density of the compounds respectively.

It is interesting to investigate the relationship between polarizability (α) and diamagnetic susceptibility . For this purpose plots of versus α for different compounds are shown in Fig. 1.

From these plots the linear relationship found is as follows:

) χ

(

χ

B

d

= A +

− χ . α … (9)

where A and B are determined from the plots. The values of A and B for I-VII and II-VI compounds are

8.13 and 6.16, and for III-V compounds are 5.12 and 5.46 (Fig. 1). Such a linear relationship has also been supported by earlier workers. The values of electronic polarizability (α) and magnetic susceptibility determined in I-VII, II-VI and III- V group of semiconductor compounds respectively are given in Tables 1-3 along with the known values reported in the literature.

) χ (

3 Results and Discussion

A simple relationship for studying the refractive index, energy gap, electronegativity difference, polarizability and magnetic susceptibility for I-VII, II- VI and III-V compounds has been presented. It is found that the behaviour of different materials within a group of compounds is almost similar but significantly different from the compounds of other groups. Even in I-VII compounds, the behaviour of Cu halides and Ag halides is different from that for alkali halides. Similarly in II-VI group of compounds the behaviour of Zn chalcogenides and Cd chalcogenides is also different than that for alkaline earth chalcogenides. This is mainly because of different nature of the chemical bond of these compounds as found by Phillips and Van Vechten

. It is also observed from the tables that, the energy gap values and magnetic susceptibility for the group of semiconductors with common cation decrease, while the refractive index and electronic polarizability increase. The good agreement between calculated and experimental electronic polarizabilities indicates the correctness of the estimated refractive indices in the present work. It is interesting to note that all the groups of compounds studied exhibit a linear variation in the value of magnetic susceptibility with electronic polarizability.

Acknowledgement

Authors are thankful to Prof Jai Shanker for valuable discussions. They are also thankful to Mrs Sudha Singh for her help in the computational work.

Fig. 1—Plots of magnetic susceptibility (χd) versus electronic polarizability (α) for binary compounds.

References

1 Sirdeshmukh D B & Srinivas K, J Mater Sci, 21 (1986) 4117.

2 Ghosh D K & Samanta P J, Infrared Phys, 26 (1986) 335.

3 Phillips J C, Phys Rev Lett, 19 (1967) 415.

4 Phillips J C, Phys Rev, 166 (1968) 832.

5 Phillips J C, Rev Mod Phys, 42 (1970) 3117.

6 Phillips J C, Bonds and Bands in semiconductors (Academic Press, New York), (1973) 46.

7 Phillips J C, Phys Rev, 168 (1968) 905.

8 Reddy R R, Nazeer ahammed Y, Rama Gopal K, et al., Indian J Pure & Appl Phys, 40 (2002) 471.

9 Reddy R R, Nazeer ahammed Y, Rama Gopal K, et al., J Magn Magnetic Matter, 192 (1999) 516.

10 Kuchek P W, Chapman B E, Bubb W A, et al., Conc Magn Reson, A18 (2003) 56.

11 Moss T S, Proc Phys Soc, B 63 (1950) 167.

12 Moss T S, Phys Status Solidi (b), 131 (1985) 415.

13 Reddy R R, Nazeer ahammed Y, Rama Gopal K &

Raghuram D V, Opt Mater, 10 (1998) 95.

14 Ravindra N M , Auluck S & Srivastava V K, Phys Stat Solidi (b), 93 (1979) 155.

15 Gopal V, Infrared Phys, 22 (1982) 255.

16 Penn D R, Phys Rev, 128 (1962) 2093.

17 Salem M A, Chinese J Phys, 41(3) (2003) 288.

18 Salem M A, Turk J Phys, 27 (2003) 569.

19 Ravindra N M, Bhardwaj R P, Kumar K S & Srivastava V K, Infrared Phys, 21 (1981) 369.

20 Van Vechten J A, Phys Rev, 182 (1969) 891.

21 Van Vechten J A, Phys Rev, 187 (1969) 1007.

22 Ravindra N M, Auluck S & Srivastava V K, Phys Status Solidi (b) 93 (1979) K115.

23 Kumar A, Ravindra N M & Rath R, J Phys Chem Solids, 40 (1979) 1141.

24 David R Lide (ed.), CRC Handbook of Chemistry and Physics, 74^th Edn., (CRC Press, Tokyo), 1993-94.

25 Kittel C, Introduction to Solid State Physics, (John Wiley, New York), (1967).

26 Landolt-Bornstein in Eigenschaften der Materie in Inneren Aggregatzustanden, Part 10 (Ed.) K.H. Helwege, A M Helwege (springer, Berlin), (1967).

27 Reddy R R, Kumar M R & Rao T V R, Infrared Phys, 34 (1993) 103.

28 Moss T S, Burrel G J & Ellis B, Semiconductor Opto- Electronics (Butterworths, London) (1973).