Dependence of Bond length of III-V Ternary Semiconductors On Refractive Indices and Composition

Abstract: Ternary semiconductors have important relationships between refractive index, Plasmon energy, electronic polarizability, bond length, micro hardness, bulk modulus, force constants and lattice energy. An attempt has been made for the first time to correlate only one physical parameter with others. The calculated values are in good agreement with the experimental values as well as with the values reported in the literature. Refractive index data is the only one parameter required to estimate all the above parameters.

Keywords: Refractive index, electronic polarizability, bond length, Micro hardness, bulk modulus, force constants, and lattice energy.

Introduction: 1) III-V Ternary Semiconductors provide the material basis for a number of well-established commercial technologies, new cutting-edge classes of electronic and Opto-electronic devices. 2)The operating characteristics of the devices depend on the Physical properties of constituent Materials. 3) Successfully developed several empirical relationships between plasmon energy (nwp12), micro hardness (H12), and bulk modulus (B12), refractive index (n12), Bond length (d12), Electronic Polarizabilities (ae12), Lattice Energy (U12). 4) Most of the correlations discussed above are directly linked with Bond length (d12). Bond length (d12) and refractive index (n12) are well related with each other. 5)The evaluation of refractive indices of an III-V Ternary semiconductor is of considerable importance for different applications, where the refractive index of the material is the Key parameter for the device design. 6)The calculated values of these parameters are in good agreement with the values reported by different investigators, as well as with experimental values. 7)In this paper, a number of equations have been proposed to estimate bond length (d12) for III-V Ternary semiconductors.

Objective: The main objective of this paper is to show variation of Bond length (d12) With composition (x) in III-V Ternary Semi conducting Compound.

Purpose: The purpose of study is effect of composition in Bond length (d12) of III-V Ternary Semi conducting Compound 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 Physical 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 physical 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 physical parameters 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. Bond length of Binary compounds:

Compound AlN AlP AlAs AlSb GaN GaP GaAs GaSb InN InP InAs InSb n value 2.2 2.75 2.92 3.19 2.24 2.9 3.3 3.75 2.35 3.1 3.51 3.96 K2n 0.52008 0.6501 0.690288 0.754116 0.529536 0.68556 0.78012 0.8865 0.55554 0.73284 0.829764 0.936144 Bond length 1.949626 2.220334 2.311382 2.463723 1.968149 2.300479 2.52863 2.812454 2.02 2.411858 2.657329 2.9556

Bond length of Ternary compounds: Formula: d12= d1 (x)+d2 (1-x) Where 1) d1=Bond length of first binary compound 2) d2=Bond length of second binary compound

1) 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 (d12) 2.52863 2.506905 2.496043 2.48518 2.474318 2.463456 2.452593 2.441731 2.430868 2.420006 X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.409144 2.398281 2.387419 2.376556 2.365694 2.354832 2.343969 2.333107 2.322244 2.311382

2) InxGa1-xAs

X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.53 2.543 2.5495 2.556 2.5625 2.569 2.5755 2.582 2.5885 2.595 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.6015 2.608 2.6145 2.621 2.6275 2.634 2.6405 2.647 2.6535 2.66

3) Compound InGaP X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.3 2.311 2.3165 2.322 2.3275 2.333 2.3385 2.344 2.3495 2.355 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.3605 2.366 2.3715 2.377 2.3825 2.388 2.3935 2.399 2.4045 2.41 4) Compound AlInAs X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.66 2.625 2.6075 2.59 2.5725 2.555 2.5375 2.52 2.5025 2.485 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.4675 2.45 2.4325 2.415 2.3975 2.38 2.3625 2.345 2.3275 2.31

5) Compound AlInSb X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.95 2.901 2.8765 2.852 2.8275 2.803 2.7785 2.754 2.7295 2.705 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.6805 2.656 2.6315 2.607 2.5825 2.558 2.5335 2.509 2.4845 2.46

6) Compound GaAsN X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 1.97 2.026 2.054 2.082 2.11 2.138 2.166 2.194 2.222 2.25 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.278 2.306 2.334 2.362 2.39 2.418 2.446 2.474 2.502 2.53

7) Compound GaAsP X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.3 2.323 2.3345 2.346 2.3575 2.369 2.3805 2.392 2.4035 2.415 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.4265 2.438 2.4495 2.461 2.4725 2.484 2.4955 2.507 2.5185 2.53

8) Compound AlGaN X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 1.97 1.968 1.967 1.966 1.965 1.964 1.963 1.962 1.961 1.96 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 1.959 1.958 1.957 1.956 1.955 1.954 1.953 1.952 1.951 1.95

9) Compound AlGaP X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.3 2.292 2.288 2.284 2.28 2.276 2.272 2.268 2.264 2.26 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.256 2.252 2.248 2.244 2.24 2.236 2.232 2.228 2.224 2.22

10) Compound InGaN X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 1.97 1.975 1.9775 1.98 1.9825 1.985 1.9875 1.99 1.9925 1.995 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 1.9975 2 2.0025 2.005 2.0075 2.01 2.0125 2.015 2.0175 2.02

11) Compound InAsSb X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.95 2.921 2.9065 2.892 2.8775 2.863 2.8485 2.834 2.8195 2.805 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.7905 2.776 2.7615 2.747 2.7325 2.718 2.7035 2.689 2.6745 2.66

12) Compound InGaSb X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.81 2.824 2.831 2.838 2.845 2.852 2.859 2.866 2.873 2.88 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.887 2.894 2.901 2.908 2.915 2.922 2.929 2.936 2.943 2.95

13) Compound AlInP X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.41 2.391 2.3815 2.372 2.3625 2.353 2.3435 2.334 2.3245 2.315 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.3055 2.296 2.2865 2.277 2.2675 2.258 2.2485 2.239 2.2295 2.22

14) Compound AlGaSb X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.81 2.775 2.7575 2.74 2.7225 2.705 2.6875 2.67 2.6525 2.635 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.6175 2.6 2.5825 2.565 2.5475 2.53 2.5125 2.495 2.4775 2.46

15) Compound GaAsSb X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.81 2.782 2.768 2.754 2.74 2.726 2.712 2.698 2.684 2.67 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.656 2.642 2.628 2.614 2.6 2.586 2.572 2.558 2.544 2.53

16) Compound InAsN X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.02 2.084 2.116 2.148 2.18 2.212 2.244 2.276 2.308 2.34 Compound X value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.372 2.404 2.436 2.468 2.5 2.532 2.564 2.596 2.628 2.66

17) Compound InPAs X value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.66 2.635 2.6225 2.61 2.5975 2.585 2.5725 2.56 2.5475 2.535 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.5225 2.51 2.4975 2.485 2.4725 2.46 2.4475 2.435 2.4225 2.41 18) Compound AlAsSb x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.66 2.635 2.6225 2.61 2.5975 2.585 2.5725 2.56 2.5475 2.535 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.3775 2.37 2.3625 2.355 2.3475 2.34 2.3325 2.325 2.3175 2.31

19) Compound AlAsP x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.2695 2.274 2.2785 2.283 2.2875 2.292 2.2965 2.301 2.3055 2.31 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.2695 2.274 2.2785 2.283 2.2875 2.292 2.2965 2.301 2.3055 2.31

20) Compound GaPSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.81 2.759 2.7335 2.708 2.6825 2.657 2.6315 2.606 2.5805 2.555 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.5295 2.504 2.4785 2.453 2.4275 2.402 2.3765 2.351 2.3255 2.3

21) Compound InPSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.95 2.896 2.869 2.842 2.815 2.788 2.761 2.734 2.707 2.68 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.653 2.626 2.599 2.572 2.545 2.518 2.491 2.464 2.437 2.41 22) Compound AlPSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.46 2.436 2.424 2.412 2.4 2.388 2.376 2.364 2.352 2.34 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.328 2.316 2.304 2.292 2.28 2.268 2.256 2.244 2.232 2.22

23) Compound AlInN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 2.02 2.013 2.0095 2.006 2.0025 1.999 1.9955 1.992 1.9885 1.985 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 1.9815 1.978 1.9745 1.971 1.9675 1.964 1.9605 1.957 1.9535 1.95 24) Compound GaPN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (d12) 1.97 2.003 2.0195 2.036 2.0525 2.069 2.0855 2.102 2.1185 2.135 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (d12) 2.1515 2.168 2.1845 2.201 2.2175 2.234 2.2505 2.267 2.2835 2.3

Variation of Bond length with composition (x) is given. It has been observed that Bond length increase continuously (x=0.0-1.0) with the increase of composition so it exhibit linearity nature and can extend to other regions also.

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 Bond length of 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 Physical 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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