EMPIRICAL RELATION FOR ELECTRONIC AND OPTICAL PROPERTIES OF BINARY TETRAHEDRAL SEMICONDUCTORS

The concept of ionicity developed by Phillips and Van Vechten originated from the dielectric analysis of the semiconductors and insulators have been used to evaluate various bond parameters of binary tetrahedral (AIIBVI and AIIIBV) semiconductors. An overview of the understanding of correlation between atomic number and the opto-electronic properties of zinc blende crystal structured solids is presented here. In this paper, an advance hypothesis of average atomic number of the elements in a compound has been used to evaluate intrinsic electronic and optical parameters such as ionic gap (Ec), average energy gap (Eg), crystal ionicity (fi) and dielectric constant () of binary tetrahedral semiconductors.

The largest part of modern technology on the earth is based on solid state materials. Ample research dedicated to the physics and chemistry of solids during the past four decades has produced sizeable breakthroughs in comprehending the properties of solids as a whole. So, it is captivating to go through the behaviour and various properties of other solids. The modern microelectronic industry uses the semiconductors of particular omnitriangulated nature in zinc blende crystallographic structure. This nature gives rise to unique physical properties in materials. A great amount of theoretical and experimental work has been completed in recent past on mechanical, structural and optical properties of zinc blende (A III B V and A II B VI ) semiconductors [1][2][3][4][5][6][7]. It is due to their exciting semiconducting properties and various practical applications in the area of non-linear optical laser devices, photovoltaic detectors, light emitting diodes, solar cells, and integrated optical devices such as switches, filters and modulators. The hypothesis of crystal ionicity of chemical bonding has been demonstrated its potential in the characterization of molecular and solid state properties. This proposed various ionicity scales to associate with a broad spectrum of physical and chemical properties such as cohesive energy, elastic constants, heat of formation, crystal structure, bulk modulus etc [8]. Levine [8], Phillips and Van Vechten [9][10][11], and many more researchers [12][13][14][15][16] have evolved several theories and evaluated ionicity in the case of basic compounds.
Because of the trouble related to the experimental procedure and its price, also complicacies in getting correct values of physical properties, researchers moved to evaluating the physical properties of solids by means of theoretical methods. But owning to the elaborated process, as well difficult computational methods require a sequence of approximation; these methods have always been complex and developed for only limited semiconductors [17]. Consequently, we realized it would be of immense interest to present an another possible interpretation of the ionic gap (Ec), average energy gap (E g ), crystal ionicity (f i ) and dielectric constant (ϵ) in binary tetrahedral (A II B VI and A III B V ) semiconductors.
Numerous researchers have attempted to evaluate electronic and optical parameters of binary tetrahedral semiconductors with the help of ionic charge and valance electrons. But considering the different screening factors present in compound crystallography, we have used a new concept of average atomic number of interacting elements in a compound and found excellent results comparable to previous workers for the ionic gap (E c ), average energy gap (E g ), crystal ionicity (f i ) and dielectric constant (ϵ) in binary tetrahedral (A II B VI and A III B V ) semiconductors. In our suggested relations only few variables such as atomic number and ionic charge on cation and anion are needed as input data, to calculate many electronic and optical properties of these compounds and the method emerge relevant to other materials, too.

THEORY, RESULTS AND DISCUSSION
As stated in modified theory of dielectric of solids [9][10][11][18][19][20] for tetrahedral coordinated compounds, average energy gap (Eg), connected bonding and anti binding (sp 3 ) hybridized orbital can be separated into two shares due to symmetric and anti symmetric portions of the potential inside a unit cell. These shares are ionic or heteropolar (E c ) and covalent or homopolar (E h ), which can be expressed in the following relation: The ionic or heteroploar share E c is inversely related to the bond length d as: where K 1 is an arbitrary constant and depends on the difference between valence states of an atom and is given by where A and K 2 are constants, which remain unaffected in different crystal structures with values A = 40.468 eV/Å . and K 1 = 2.5. These values are A= 39.74 and K 1 = 2.48 as reported by PVV [10]. Therefore, the values of E c and E h depend on number of bonds emerge from cations and bond length.
The crystal ionicity f i of the chemical bond is expressed as the fraction of ionic character as follows.
V. Kumar [22][23][24] has expressed those electronic properties of zinc blende (A II B VI and A III B V ) crystals in terms of Plasmon energy ħω p as follows: Here ħω p is in eV, ν is a constant. E c and E h are the ionic and homopolar gaps, respectively. Jayaraman et al. [25], Srideshmukh et al. [26], and Krishnan et al. [27] established that significantly reduced ionic charges must be used to obtain better agreement with experimental values of these parameters. Verma et al. [28] have been applied this concept for obtaining better agreement with theoretical data for ionic gap (E c ), average energy gap (E g ), crystal ionicity (f i ) and dielectric constant (ϵ) of binary tetrahedral (A II B VI and A III B V ) semiconductor, which can be expressed in terms of product of ionic charges as follows: For binary tetrahedral (zinc blende) semiconductors: E g = 90 .
. ⁄ Here, Z 1 and Z 2 are the ionic charges and d is the bond length in Å. On solving equations (2) and (7,8), crystal ionicity f i can be expressed as follows: Levine and Penn [8,29] have given the relation for dielectric constant ϵ as follows: Considering the above empirical relations and using the concept of product of ionic charges given by Verma at el. [28] and our hypothesis of average atomic number of elements in the binary tetrahedral semiconductor, we have proposed following empirical relations for electronic and optical parameters such as ionic gap (E c ), average energy gap (E g ), crystal ionicity (f i ) and dielectric constant (ϵ) and further evaluated their values. The evaluated values are in excellent agreement with the values reported by Levine [8], V. Kumar [22][23][24]. Our endeavour of determining ionic gap E c , average energy gap E g , crystal ionicity f i , and dielectric constant ϵ has not been required experimental values of the dielectric constant although the previous models needed this value in their computations except Verma et al. [28]. These values are presented in the table 1 and 2.
We have found dielectric constant (ϵ) same as given in relation (10). Here, Z 1 , Z 2 are ionic charges and , are atomic numbers of the elements in the compound. SUMMARY AND CONCLUSIONS The suggested empirical relations have been applied to calculate ionic gap E c , average energy gap E g , crystal ionicity f i , and dielectric constant ϵ of binary tetrahedral (A II B VI and A III B V ) semiconductors. This shows average atomic number of the elements in the compounds is a crucial parameter for evaluating electronic and optical properties. The ionic gap (E c ) and average energy gap (E g ) of these compounds have been found inversely proportional to the average atomic number and product of ionic charges of the compounds. The crystal ionicity (f i ) is directly related to average atomic number and inversely to product of ionic charges, while dielectric constant (ϵ) is directly related to both the parameters. This is interesting to note that the suggested relations are straightforward, extensively relevant and values obtained are in good agreement with published values as compared to earlier workers. The hypothesis proposed herein will be supportive to the researchers for exploring new analogous materials with aimed ionic gap (E c ), average energy gap (E g ), crystal ionicity (f i ) and dielectric constant (ϵ). Arguably this hypothesis may easily be broadened to ternary tetrahedral semiconductors, for which work is in progression out comes will be revealed in expected paper.