Investigation of Lattice Energy in III-V Ternary Semiconductors

Abstract: III-V Ternary Semi conductors have relation between refractive index, Composition and Lattice Energy. This is the first attempt to correlate refractive index and Composition with Lattice Energy. The theoretical results in Lattice Energy of III-V Ternary Semiconductors agree fairly well with experimental data. Refractive index data of semi conductors is the only one parameter required to estimate all the above parameters

Keywords: Refractive index, Composition, force constants, and lattice energy.

Introduction: 1)III-V Ternary Semi conductors were investigated through Hall effect and photoluminescence measurements. 2)These Materials determine carrier concentration, mobility, and sheet resistivity and luminescence measurements. 3)High quality Ternary Compounds is used in many next generation optoelectronic devices. 4)The structural and optical properties of Ternary Semi conductor nano structures are self-formed in inverted tetrahedral pyramids. 5)Photoluminescence and Cathode-luminescence Spectroscopy are used to study band gap structure. 6)Doping of solute composition in III-V Ternary Semi conductors yields transparent conductive coatings. 7)Lattice Energy is related to Structural property of Physical properties in III-v Ternary Semi conductors. 8)In this paper, a number of equations have been proposed to estimate Lattice Energy for III-V Ternary semiconductors. 9)An analysis of Lattice Energy was applied to 24 different III-V ternary alloy semiconductors. 10)In this paper, a number of equations have been proposed to estimate Lattice Energy for III-V Ternary semiconductors.

Objective: The main objective of this paper is to show variation of Lattice Energy (U12) with composition (x) in 24 III-V Ternary Semi conducting Compounds.

Purpose: The purpose of study is effect of composition in Lattice Energy (U12) of 24 III-V Ternary Semi conducting Compounds to represent additivity principle even in very low composition range

Theoretical Impact: 1)III-V Ternary Semi conducting compounds represents substitution pseudo binary alloys. There have been numerous experimental studies of the Structural properties of III-V Ternary Semi conducting compounds. These experimental Studies have mostly been limited to the reflectance or absorption spectroscopy in the narrow spectral range. 2)An excellent agreement with the experimental data is obtained for the entire investigated spectral region and for all compositions 3)The properties of III-V Ternary Semi conducting compounds is in additive nature if solute composition is less than solvent composition. 4)The main aim of modeling the Structural properties of a ternary alloy is to make the calculation of the physical constants for compositions with no available experimental data possible. 5)In this paper we present a method that can accurately and reliably determine the Lattice Energy as a function of composition (x). 6)If the dependence of the physical constants on the alloy composition is known, spectroscopic ellipsometry can be used to monitor the alloy composition. 7)The first approach of this paper is to determine the physical parameters for particular compositions and then to find the physical function describing the dependence of the physical parameters on the alloy Composition (x). 8)The second approach of this paper is to simultaneously fit in the data sets for all available compositions in order to minimize the discrepancies between the calculated and the experimental Data over the entire energy and composition range.

Lattice Energy of Binary Compounds:

Compound AlN AlP AlAs AlSb GaN GaP GaAs GaSb InN InP InAs InSb n value 2.2 2.8 2.92 3.19 2.24 2.9 3.3 3.8 2.35 3.1 3.51 3.96 k3n -0.4 -0.5 -0.5 -0.6 -0.4 -0.5 -0.6 -0.7 -0.4 -0.6 -0.62 -0.7 k2*k3n -241 -302 -320 -350 -246 -318 -362 -412 -258 -340 -385 -435 k5n -0.8 -1 -1 -1.1 -0.8 -1 -1.2 -1.3 -0.8 -1.1 -1.25 -1.41 k4*k5n -68 -85 -90 -98 -69 -90 -102 -116 -73 -96 -108 -122 U value 248 204 191 170 245 193 161 125 236 177 144.4 108.9

Lattice Energy of Ternary Compounds: X=Composition Formula: (U12)= U1 (x) + U2 (1-X) U1= Lattice Energy of first Binary Compound U2= Lattice Energy of second Binary Compound

1) AlxGa1-xAs Compound AlxGa1-xAs=AlAs+GaAs x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 161 164 166 167 169 170 172 173 175 176 Compound AlxGa1-xAs x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 177.5 179 181 182 184 185 187 188 190 191

2) InxGa1-xAs Compound InxGa1-xAs = InAs + GaAs x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 161 159 159 158 157 156 155 154 154 153 Compound InxGa1-xAs x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 151.9 151 150 149 149 148 147 146 145 144 3) InxGa1-xP Compound InxGa1-xP = InP + GaP x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 193 191 191 190 189 188 187 187 186 185

Compound InxGa1-xP x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 184.2 183 183 182 181 180 179 179 178 177 4) AlxIn1-xAs Compound AlxIn1-xAs = AlAs + InAs x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 144 149 151 154 156 158 161 163 165 168

compound AlxIn1-xAs x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 170 172 175 177 179 182 184 186 189 191

5) AlxIn1-x Sb Compound AlxIn1-x Sb = AlSb + InSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 245 237 232 228 224 220 216 211 207 203

Compound AlxIn1-x Sb x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 198.8 195 190 186 182 178 174 169 165 161

6) GaAsxN1-x Compound GaAsxN1-x= GaAs + GaN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 193 190 188 187 185 183 182 180 179 177

Compound GaAsxN1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 175.4 174 172 171 169 167 166 164 163 161

7) GaAsxP1-x Compound GaAsxP1-x=GaAs+GaP x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 245 245 245 246 246 246 246 246 246 247

Compound GaAsxP1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 246.7 247 247 247 247 247 248 248 248 248

8) AlxGa1-x N Compound AlxGa1-x N = AlN + GaN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 193 194 195 195 196 196 197 197 198 199

Compound AlxGa1-x N x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 199.1 200 200 201 201 202 202 203 203 204

9) AlxGa1-x P Compound AlxGa1-x P = AlP + GaP x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 193 194 195 195 196 196 197 197 198 199

Compound AlxGa1-x P x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 199.1 200 200 201 201 202 202 203 203 204

10) InxGa1-x N Compound InxGa1-x N = InN + GaN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 245 244 244 243 243 242 242 241 241 241

Compound InxGa1-x N x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 240.1 240 239 239 238 238 237 237 236 236

11) InAsxSb1-x Compound InAsxSb1-x = InAs + InSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 109 112 114 116 118 120 121 123 125 127

Compound InAsxSb1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 128.4 130 132 134 136 137 139 141 143 144

12) InxGa1-x Sb Compound InxGa1-x Sb = InSb + GaSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 125 123 123 122 121 120 119 119 118 117

Compound InxGa1-x Sb x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 116.1 115 115 114 113 112 111 111 110 109

13) AlxIn1-x P Compound AlxIn1-x P = AlP + InP x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 177 180 181 182 184 185 186 188 189 191

Compound AlxIn1-x P x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 191.9 193 195 196 197 199 200 201 203 204

14) AlxGa1-x Sb Compound AlxGa1-x Sb = AlSb + GaSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 125 130 132 134 136 139 141 143 145 148

Compound AlxGa1-x Sb x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 149.8 152 154 157 159 161 163 166 168 170

15) GaAsxSb1-x Compound GaAsxSb1-x = GaAs + GaSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 125 129 130 132 134 136 138 139 141 143

Compound GaAsxSb1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 144.8 147 148 150 152 154 156 157 159 161

16) InAsxN1-x Compound InAsxN1-x = InAs + InN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 236 227 222 218 213 209 204 199 195 190

Compound InAsxN1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 185.6 181 176 172 167 163 158 154 149 144

17) InPxAs1-x Compound InPxAs1-x = InP + InAs x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 144 148 149 151 153 154 156 157 159 161

Compound InPxAs1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 162.3 164 166 167 169 170 172 174 175 177

18) AlAsxSb1-x Compound AlAsxSb1-x = AlAs + AlSb x value 0.6 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 170 172 173 174 175 176 177 178 179 181

Compound AlAsxSb1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 181.6 183 184 185 186 187 188 189 190 191

19) AlAsxP1-x Compound AlAsxP1-x = AlAs + AlP x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 204 203 202 201 201 200 199 199 198 198

Compound AlAsxP1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 196.9 196 196 195 194 194 193 192 192 191

20) GaPxSb1-x Compound GaPxSb1-x = GaP + GaSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 125 132 135 139 142 145 149 152 156 159

Compound GaPxSb1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 162.4 166 169 173 176 179 183 186 190 193

21) InPxSb1-x Compound InPxSb1-x = InP + InSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 109 116 119 123 126 129 133 136 140 143

Compound InPxSb1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 146.4 150 153 157 160 163 167 170 174 177 22) AlPxSb1-x Compound AlPxSb1-x = AlP + AlSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 170 173 175 177 179 180 182 184 185 187

Compound AlPxSb1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 188.7 190 192 194 196 197 199 201 202 204

23) AlxIn1-x N Compound AlxIn1-x N = AlN + InN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 236 237 238 238 239 240 240 241 241 242

Compound AlxIn1-x N x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 242.6 243 244 244 245 246 246 247 247 248

24) GaPxN1-x Compound GaPxN1-x = GaP + GaN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (U12) 245 240 237 235 232 229 227 224 222 219

Compound GaPxN1-x x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (U12) 216.4 214 211 209 206 203 201 198 196 193

Variation of Lattice Energy (U12) with composition (x) is given. It has been observed that Lattice Energy (U12) increase for some compounds and decreases for some compounds (x=0.0-1.0) with the increase of composition.

Future Plans: 1) Current data set to 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:

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 Dependence of Lattice Energy (U12) in III-V Ternary Semiconductors On Refractive Indices and Composition. The semiconductors have been carried out because of computational complexities and difficulties associate with disorder in the alloys. Polycrystalline ternary composition materials find application in tunable detectors and in other optoelectronic devices. Our results regarding the Structural properties of the ternary alloys are found to be in reasonable agreement with the experimental data.

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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Contributors: 1) Dr R R Reddy obtained his PhD (Physics) from the S.V. University, Tirupati, in 1981. He joined Sri Krishnadevaraya University, Anantapur, in 1985 and is presently working as Associate Professor. He worked as CSIR postdoctoral fellow and CSIR pool Scientist and also guided Phil and PhD research scholars in the field of spectroscopy, solid state physics, chemical physics, polymer physics, optoelectronics and glasses. He Has published 130 research papers in national international journals and also presented 36 research papers in the conferences. He has undertaken nine research projects of ISRO and UGC. He is a member of the Lydian Science Congress Association, Laser Society of India, and a life member of ISTE, New Delhi.

2) Dr K Rnma Gopal obtained his PhD (Physics) from the Sri Krishnadevaraya University, Anantapur, in 2001. Presently, he is working as Research Associate in the lndian Space Research Organization (ISRO) for the past one-and-a-half years. He has published29 research papers in the leading journals of India. He is a life member of Acoustic Society of India, Asian Journal of Physics and IASTA, Mumbai.

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