Calculation of AlxGa1-xN III-V Ternary Semiconductor Band Energy Gap

Abstract: AlxGa1-xN III-V Ternary semiconductor is very important as an x of a constituent in the semiconductor is going to have significant changes in calculating Physical Property like Band Energy Gap. These Ternary Compounds can be derived from binary compounds AlN and GaN by replacing one half of the atoms in one sub lattice by lower valence atoms, the other half by higher valence atoms and maintaining average number of valence electrons per atom. The subscript X refers to the alloy content or concentration of the material, which describes proportion of the material added and replaced by alloy material. This paper represents the AlxIn1-xSb III-V Ternary Semiconductor Band Energy Gap values

Keywords: Band Energy Gap, Composition, Electro Negativity, Molecular weight, density, optical polarizability.

Introduction: 1) In this opening talk of AlxGa1-xN III-V Ternary Semiconductor Band Energy Gap Electronegativity values of Ternary Semiconductors are denoted by symbols XM and XN and Band Energy Gap is denoted by Eg 2) Linus Pauling first proposed Electro Negativity in 1932 as a development of valence bond theory,[2] it has been shown to correlate with a number of other chemical properties. 3) The continuous variation of physical properties like Electro Negativity of ternary compounds with relative concentration of constituents is of utmost utility in development of solid-state technology. 4) In the present work, the solid solutions belonging to AlxGa1-xN III-V Ternary Semiconductor Band Energy Gap have been investigated. In order to have better understanding of performance of these solid solutions for any particular application, it becomes quite necessary to work on the physical properties like Electro Negativity of these materials. 5) Recently no other class of material of semiconductors has attracted so much scientific and commercial attention like the III-V Ternary compounds. 6) Doping of Al component in a Binary semiconductor like GaN and changing the composition of do pant has actually resulted in lowering of Band Energy Gap. 7) Thus effect of do pant increases the conductivity and decreases the Band Energy Gap and finds extensive applications 8) The present investigation relates Band Energy Gap and Electro Negativity with variation of composition for AlxGa1-xN III-V Ternary Semiconductor. 9) The fair agreement between calculated and reported values of Band Energy Gaps of AlN and GaN Binary semiconductors give further extension of Band Energy Gaps for Ternary semiconductors. 10) The present work opens new line of approach to Band Energy Gap studies in AlxGa1-xN III-V Ternary Semiconductor

Objective: The main Objective of this paper is to calculate AlxGa1-xN III-V Ternary Semiconductor Band Energy Gap values

Purpose: The purpose of study is AlxGa1-xN III-V Ternary Semiconductor Band Energy Gap and effect of concentration in Electro Negativity values of III-V Ternary Semiconductors to represent additivity principle even in very low concentration range. This paper includes Electro Negativity values of III-V ternary semiconductors and Band Energy Gap values in composition range (0 Theoretical Impact: Formula: Eg=[28.8/(2(XM-XN)2)1/4*(1-f12/1+2*f12)]POWER (XM/XN)2 Where:f12=[4pN/3]*[aM12*r12]/M12 Electro Negativity values of Elemental Semiconductors:

Compound Al Ga As In P Sb N E.N value 1.5 1.8 2 1.7 2.1 1.9 3

Electro Negativity values of AlxGa1-xN III-V Ternary Semiconductor

X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1-x value 1 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5

Compound AlxGa1-xN XM value1.8 1.767479 1.75144 1.73555 1.719797 1.70419 1.688726 1.673401 1.658215401 1.643168 XN value 3 3 3 3 3 3 3 3 3 3

(XM/XN)2 0.36 0.347109 0.340838 0.33468 0.3286335 0.322696 0.316866 0.311141 0.305519813 0.3 (XM-XN)21.44 1.519107 1.558902 1.59884 1.6389197 1.679122 1.719441 1.759865 1.800385911 1.840994

2(XM-XN)22.7132087 2.866136 2.946294 3.029 3.1143253 3.202331 3.293087 3.386665 3.483133842 3.582568 (2(XM-XN)2)1/4 1.2834259 1.30114 1.310144 1.31924 1.3284371 1.337724 1.347103 1.356573 1.366131611 1.375779 28.8/(2(XM-XN)2)1/4 22.43994 22.13443 21.98232 21.8307 21.679611 21.5291 21.37921 21.22997 21.08142419 20.9336

ALPHA-M 37.49 36.8 36.4 36.1 35.7 35.3 35 34.6 34.3 33.9 RO-VALUES 6.1 5.82 5.67 5.53 5.39 5.25 5.11 4.96 4.82 4.68 M-VALUES 83.73 79.5 77.3 75.2 73 70.9 68.8 66.6 64.5 62.4 ALPHA-M*RO/M2.7312672 2.694038 2.669961 2.65469 2.6359315 2.613893 2.599564 2.576817 2.563193798 2.5425

TOTAL 4*PI*N 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 4*PI*N/3 VALUES 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 (4PIN/3)*ALPHAM*RO/M 6.887E+24 6.79E+24 6.73E+24 6.7E+24 6.647E+24 6.59E+24 6.56E+24 6.5E+24 6.46343E+24 6.41E+24

1-(4PIN/3)*ALPHAM*RO/M 6.887E+24 6.79E+24 6.73E+24 6.7E+24 6.647E+24 6.59E+24 6.56E+24 6.5E+24 6.46343E+24 6.41E+24 1+2*(4PIN/3)*ALPHAM*RO/M 1.377E+25 1.36E+25 1.35E+25 1.3E+25 1.329E+25 1.32E+25 1.31E+25 1.3E+25 1.29269E+25 1.28E+25

1-phi12/1+phi12 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 28.8/(2(XM-XN)2)1/4*(1-phi12/1+2*phi12) 11.21997 11.06721 10.99116 10.9153 10.839806 10.76455 10.68961 10.61499 10.5407121 10.4668

Eg value2.3877948 2.303538 2.263744 2.22541 2.188481 2.152886 2.118571 2.085479 2.053558296 2.022759

X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1-x value0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

XM value1.628256 1.613481 1.598839 1.58433 1.569953 1.555706 1.541588 1.527599 1.513737 1.5 XN value 3 3 3 3 3 3 3 3 3 3

(XM/XN)2 0.29458 0.289258 0.284032 0.2789 0.273861 0.268913 0.264055 0.259284 0.2546 0.25 (XM-XN)21.88168 1.922436 1.963253 2.004122 2.045035 2.085985 2.126964 2.167965 2.208979 2.25 (2(XM-XN)2)1/4 1.385513 1.395333 1.405237 1.415224 1.425293 1.435443 1.445673 1.455981 1.466365 1.476826 28.8/(2(XM-XN)2)1/4 20.78653 20.64024 20.49477 20.35014 20.20637 20.06349 19.92152 19.78048 19.6404 19.50128

ALPHA-M 33.5 33.2 32.8 32.5 32.1 31.7 31.4 31 30.7 30.3 RO-VALUES 4.54 4.4 4.25 4.11 3.97 3.83 3.69 3.54 3.4 3.26 M-VALUES 60.2 58.1 55.9 53.8 51.7 49.5 47.4 45.3 43.1 40.99 ALPHA-M*RO/M2.526412 2.514286 2.493739 2.482807 2.464932 2.452747 2.44443 2.422517 2.42181 2.409807

TOTAL 4*PI*N 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 7.56E+24 4*PI*N/3 VALUES 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 2.52E+24 (4PIN/3)*ALPHAM*RO/M 6.37E+24 6.34E+24 6.29E+24 6.26E+24 6.22E+24 6.18E+24 6.16E+24 6.11E+24 6.11E+24 6.08E+24

1-(4PIN/3)*ALPHAM*RO/M 6.37E+24 6.34E+24 6.29E+24 6.26E+24 6.22E+24 6.18E+24 6.16E+24 6.11E+24 6.11E+24 6.08E+24 1+2*(4PIN/3)*ALPHAM*RO/M 1.27E+25 1.27E+25 1.26E+25 1.25E+25 1.24E+25 1.24E+25 1.23E+25 1.22E+25 1.22E+25 1.22E+25

1-phi12/1+phi12 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 28.8/(2(XM-XN)2)1/4*(1-phi12/1+2*phi12) 10.39326 10.32012 10.24738 10.17507 10.10318 10.03174 9.96076 9.890242 9.820199 9.75064

Eg value1.993034 1.964338 1.936628 1.909863 1.884006 1.859018 1.834865 1.811513 1.788931 1.767088

Doping of Al component in a Binary semiconductor like GaN and changing the composition of do pant has actually resulted in lowering of Band Energy Gap.

Future Plans: 1) Current data set of Electro Negativity values of AlxGa1-xN III-V Ternary Semiconductors and Band Energy Gap values include the most recently developed methods and basis sets are continuing. The data is also being mined to reveal problems with existing theories and used to indicate where additional research needs to be done in future. 2) The technological importance of the ternary semiconductor alloy systems investigated makes an understanding of the phenomena of alloy broadening necessary, as it may be important in affecting semiconductor device performance.

Conclusion: 1) This paper needs to be addressed theoretically so that a fundamental understanding of the physics involved in such phenomenon can be obtained in spite of the importance of ternary alloys for device applications. 2) Limited theoretical work on Electro Negativity values and Band Energy Gap of AlxGa1-xN III-V Ternary Semiconductors with in the Composition range of (0 Results and Discussion: Electro Negativity values of Ternary Semiconductors are used in calculation of Band Energy Gaps and Refractive indices of Ternary Semiconductors and Band Energy Gap is used for Electrical conduction of semiconductors. This phenomenon is used in Band Gap Engineering.

Acknowledgments. – This review has benefited from V.R Murthy, K.C Sathyalatha contribution who carried out the calculation of physical properties for several ternary compounds with additivity principle. It is a pleasure to acknowledge several fruitful discussions with V.R Murthy.

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