Calculation of GaPxN1-x III-V Ternary Semiconductor Band Energy Gap

Abstract: GaPxN1-x 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 GaP 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 GaPxN1-x 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 GaPxN1-x 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 GaPxN1-x 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 P 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 GaPxN1-x III-V Ternary Semiconductor.

9) The fair agreement between calculated and reported values of Band Energy Gaps of GaP 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 GaPxN1-x III-V Ternary Semiconductor

Objective: The main Objective of this paper is to calculate GaPxN1-x III-V Ternary Semiconductor Band Energy Gap values

Purpose: The purpose of study is GaPxN1-x 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 GaPxN1-x 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 GaPxN1-x XM value 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 XN value 3 2.894883 2.843714 2.79345 2.744074 2.69557 2.647924 2.60112 2.555144 2.50998

XM/XN 0.6 0.621787 0.632975 0.644365 0.655959 0.667762 0.679778 0.692009 0.704461 0.717137

(XM/XN)2 0.36 0.386619 0.400657 0.415206 0.430282 0.445906 0.462098 0.478877 0.496266 0.514286

XM-XN -1.2 -1.09488 -1.04371 -0.99345 -0.94407 -0.89557 -0.84792 -0.80112 -0.75514 -0.70998

(XM-XN)2 1.44 1.198769 1.08934 0.986942 0.891275 0.802046 0.718976 0.641794 0.570242 0.504072

2(XM-XN)2 2.713209 2.295438 2.127766 1.98198 1.854815 1.743572 1.646013 1.560268 1.484773 1.418211

(2(XM-XN)2)1/4 1.283426 1.230882 1.207761 1.186519 1.167011 1.149106 1.132683 1.117635 1.103863 1.091277

28.8/(2(XM-XN)2)1/4 22.43994 23.39786 23.84578 24.27268 24.67842 25.06297 25.42636 25.76871 26.0902 26.39109

ALPHA-M 37.49 41.029 42.7985 44.568 46.3375 48.107 49.8765 51.646 53.4155 55.185 RO-VALUES 6.10 5.903 5.8045 5.706 5.6075 5.509 5.4105 5.312 5.2135 5.115 M-VALUES 83.73 85.427 86.2755 87.124 87.9725 88.821 89.6695 90.518 91.3665 92.215

ALPHA-M*RO/M 2.731267 2.835101 2.879426 2.918886 2.953622 2.98377 3.00946 3.030818 3.047963 3.061013

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 6.89E+24 7.15E+24 7.26E+24 7.36E+24 7.45E+24 7.52E+24 7.59E+24 7.64E+24 7.69E+24 7.72E+24

1-(4PIN/3)*ALPHAM*RO/M 6.89E+24 7.15E+24 7.26E+24 7.36E+24 7.45E+24 7.52E+24 7.59E+24 7.64E+24 7.69E+24 7.72E+24

1+2*(4PIN/3)*ALPHAM*RO/M 1.38E+25 1.43E+25 1.45E+25 1.47E+25 1.49E+25 1.5E+25 1.52E+25 1.53E+25 1.54E+25 1.54E+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 11.69893 11.92289 12.13634 12.33921 12.53148 12.71318 12.88435 13.0451 13.19554

Eg value 2.387795 2.588006 2.699356 2.819158 2.948232 3.087495 3.237974 3.40082 3.577324 3.768945

X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1-x value 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

Compound XM value 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 XN value 2.465615 2.422033 2.379222 2.337168 2.295857 2.255276 2.215412 2.176254 2.137787 2.1

XM/XN 0.730041 0.743177 0.75655 0.770163 0.784021 0.798128 0.81249 0.82711 0.841992 0.857143

(XM/XN)2 0.53296 0.552312 0.572368 0.593151 0.614689 0.637009 0.66014 0.68411 0.708951 0.734694

XM-XN -0.66561 -0.62203 -0.57922 -0.53717 -0.49586 -0.45528 -0.41541 -0.37625 -0.33779 -0.3

(XM-XN)2 0.443043 0.386925 0.335498 0.288549 0.245874 0.207276 0.172567 0.141567 0.1141 0.09 2(XM-XN)2 1.359468 1.307604 1.261813 1.221411 1.185811 1.154506 1.127062 1.103102 1.0823 1.06437

(2(XM-XN)2)1/4 1.079797 1.069348 1.059861 1.051273 1.043527 1.036571 1.030355 1.024835 1.019969 1.015718

28.8/(2(XM-XN)2)1/4 26.67167 26.9323 27.17338 27.39536 27.5987 27.78391 27.95152 28.10208 28.23616 28.35432

ALPHA-M 56.9545 58.724 60.4935 62.263 64.0325 65.802 65.575 69.341 71.1105 72.88 RO-VALUES 5.0165 4.918 4.8195 4.721 4.6225 4.524 4.4255 4.327 4.2285 4.13 M-VALUES 93.0635 93.912 94.7605 95.609 96.4575 97.306 98.1545 99.003 99.851 100.7

ALPHA-M*RO/M 3.070078 3.075269 3.076687 3.074435 3.068608 3.0593 2.956585 3.0306 3.011394 2.989021

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 7.74E+24 7.75E+24 7.76E+24 7.75E+24 7.74E+24 7.71E+24 7.46E+24 7.64E+24 7.59E+24 7.54E+24 #VALUE! 7.74E+24 7.75E+24 7.76E+24 7.75E+24 7.74E+24 7.71E+24 7.46E+24 7.64E+24 7.59E+24 7.54E+24

1+2*(4PIN/3)*ALPHAM*RO/M 1.55E+25 1.55E+25 1.55E+25 1.55E+25 1.55E+25 1.54E+25 1.49E+25 1.53E+25 1.52E+25 1.51E+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) 13.33583 13.46615 13.58669 13.69768 13.79935 13.89196 13.97576 14.05104 14.11808 14.17716

Eg value 3.977323 4.204315 4.452025 4.72284 5.019478 5.345037 5.703058 6.097602 6.53333 7.015613

Doping of P 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 GaPxN1-x 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 GaPxN1-x III-V Ternary Semiconductors with in the Composition range of (0 3) Our results regarding the Electro Negativity values and Band Energy Gap of III-V Ternary Semiconductors are found to be in reasonable agreement with the experimental data

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.

References: 1) IUPAC Gold Book internet edition: "Electronegativity".

2) Pauling, L. (1932). "The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the Relative Electronegativity of Atoms". Journal of the American Chemical Society 54 (9): 3570–3582..

3) Pauling, Linus (1960). Nature of the Chemical Bond. Cornell University Press. pp. 88–107. ISBN 0801403332

. 4) Greenwood, N. N.; Earnshaw, A. (1984). Chemistry of the Elements. Pergamon. p. 30. ISBN 0-08-022057-6.

5) Allred, A. L. (1961). "Electronegativity values from thermochemical data". Journal of Inorganic and Nuclear Chemistry 17 (3–4): 215–221..

6) Mulliken, R. S. (1934). "A New Electroaffinity Scale; Together with Data on Valence States and on Valence Ionization Potentials and Electron Affinities". Journal of Chemical Physics 2: 782–793..

7) Mulliken, R. S. (1935). "Electronic Structures of Molecules XI. Electroaffinity, Molecular Orbitals and Dipole Moments". J. Chem. Phys. 3: 573–585..

8) Pearson, R. G. (1985). "Absolute electronegativity and absolute hardness of Lewis acids and bases". J. Am. Chem. Soc. 107: 6801..

9) Huheey, J. E. (1978). Inorganic Chemistry (2nd Edn.). New York: Harper & Row. p. 167.

10) Allred, A. L.; Rochow, E. G. (1958). "A scale of electronegativity based on electrostatic force". Journal of Inorganic and Nuclear Chemistry 5: 264..

11) Prasada rao., K., Hussain, O.Md., Reddy, K.T.R., Reddy, P.S., Uthana, S., Naidu, B.S. and Reddy, P.J., Optical Materials, 5, 63-68 (1996).

12) Ghosh, D.K., Samantha, L.K. and Bhar, G.C., Pramana, 23(4), 485 (1984).

13) CRC Handbook of Physics and Chemistry, 76th edition.

14) Sanderson, R. T. (1983). "Electronegativity and bond energy". Journal of the American Chemical Society 105: 2259

15) Murthy, Y.S., Naidu, B.S. and Reddy, P.J., “Material Science &Engineering,”B38, 175 (1991)

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