Dependence of Plasmon energy of III-V Ternary Semiconductors On Refractive Indices and Composition

Abstract: Interesting relationships have been found between refractive index, Plasmon energy, electronic polarizability, bond length, micro hardness, bulk modulus, force constants and lattice energy on Ternary semiconductors. 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, plasmon energy, electronic polarizability, bond length, Micro hardness, bulk modulus, force constants, and lattice energy.

INTRODUCTION 1) Recently, much attention has been given to the study of III-V Ternary tetrahedral semiconductors because of their potential applications in linear and nonlinear optics, solar cells, light emitting diodes, laser diodes, and integrated optical devices, such as switches, modulators, filters, etc. 2) The evaluation of refractive indices of a semiconductor is of considerable importance for different applications, where the refractive index of the material is the Key parameter for the device design. 3) On the basis of Phillips and Van Vechten's' quantum dielectric theory, the refractive index, plasmon energy, and energy gap are interrelated. 4) 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). 5) Most ofthe correlations discussed above are directly linked with plasmon energy (nwp). Plasmon energy (nwp) and refractive index (n12) are well related with each other. 6) Sincere efforts have been made for correlating the above parameters, but still many uncertainties exist, on how different physical parameters affect the structural, elastic and solid state properties of Ternary semiconductor materials. 7) In this paper, a number of equations have been proposed to estimate plasmon energy , (nwp12), electronic polarisability (ae12), bond length (d12),force constants (a,b), microhardness(H12), bulk modulus (B12) and lattice energy (U12) for III-V Ternary semiconductors. 8)The calculated values of these parameters are in good agreement with the values reported by different investigators, as well as with experimental values. 9)Some compounds of this III-V Ternary semiconductors family are potential candidates for infrared detectors used in military applications because the Physical Properties of III-V Ternary semiconducting compounds play an important role in device development and fabrication, it is worthwhile to discuss the Physical properties in terms of structure, stability, bonding.

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

Purpose: The purpose of study is effect of composition in plasmon energy of III-V Ternary Semi conducting Compound to represent additivity principle even in very low composition range.

Theoretical impact: 1) III-V Ternary Semiconducting compounds represents a substitution pseudo binary alloys. There have been numerous experimental studies of the Physical properties of III-V Ternary Semiconducting 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 Semiconducting 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.

lasmon energy of Binary Compounds:

compond 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 bn value -0.78012 -0.97515 -1.03543 -1.13117 -0.7943 -1.02834 -1.17018 -1.32975 -0.83331 -1.09926 -1.24465 -1.40422 (nwp) 21.96601 18.07386 17.01652 15.46288 21.65665 17.13763 14.87135 12.67798 20.82817 15.96432 13.80417 11.76819

1) plasmon energy of Ternary Compounds: FORMULA: (nwp12)= nwp1(X)+ nwp2(1-X)

1) AlxGa1-xAs=AlAs+GaAs nwp1=17.01652 nwp2=14.87135 Compound AlGaAs x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 14.87135 15.08587 15.19313 15.30038 15.40764 15.5149 15.62216 15.72942 15.83668 15.94394

Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 16.05119 16.15845 16.26571 16.37297 16.48023 16.58749 16.69474 16.802 16.90926 17.01652 Similarly: 2) InGaAs Compound InGaAs x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 14.87135 14.76463 14.71127 14.65791 14.60456 14.5512 14.49784 14.44448 14.39112 14.33776

Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 14.2844 14.23104 14.17768 14.12432 14.07097 14.01761 13.96425 13.91089 13.85753 13.80417

3) InGaP Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 17.13763 17.0203 16.96163 16.90297 16.8443 16.78564 16.72697 16.66831 16.60964 16.55098

x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 16.49231 16.43364 16.37498 16.31631 16.25765 16.19898 16.14032 16.08165 16.02299 15.96432

4) AlInAs Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 13.80417 14.12541 14.28602 14.44664 14.60726 14.76788 14.92849 15.08911 15.24973 15.41035 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 15.57096 15.73158 15.8922 16.05282 16.21343 16.37405 16.53467 16.69529 16.8559 17.01652

5) AlInSb Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 11.76819 12.13766 12.32239 12.50713 12.69186 12.8766 13.06133 13.24607 13.4308 13.61554 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 13.80027 13.985 14.16974 14.35447 14.53921 14.72394 14.90868 15.09341 15.27815 15.46288

6) GaAsN Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 17.13763 16.911 16.79769 16.68437 16.57106 16.45775 16.34443 16.23112 16.1178 16.00449 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 15.89118 15.77786 15.66455 15.55123 15.43792 15.32461 15.21129 15.09798 14.98466 14.87135

7) GaAsP Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 21.65665 20.97812 20.63886 20.29959 19.96033 19.62106 19.2818 18.94253 18.60327 18.264 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 17.92474 17.58547 17.24621 16.90694 16.56768 16.22841 15.88915 15.54988 15.21062 14.87135

8) AlGaN Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 21.65665 21.68759 21.70305 21.71852 21.73399 21.74946 21.76493 21.78039 21.79586 21.81133 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 21.8268 21.84227 21.85773 21.8732 21.88867 21.90414 21.91961 21.93507 21.95054 21.96601

9) AlGaP Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 17.13763 17.23125 17.27806 17.32488 17.37169 17.4185 17.46531 17.51212 17.55893 17.60575 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 17.65256 17.69937 17.74618 17.79299 17.8398 17.88661 17.93343 17.98024 18.02705 18.07386

10) InGaN Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 21.65665 21.5738 21.53238 21.49095 21.44953 21.40811 21.36668 21.32526 21.28383 21.24241 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 21.20099 21.15956 21.11814 21.07671 21.03529 20.99387 20.95244 20.91102 20.86959 20.82817

11) InAsSb Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 11.76819 11.97179 12.07359 12.17539 12.27719 12.37898 12.48078 12.58258 12.68438 12.78618 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 12.88798 12.98978 13.09158 13.19338 13.29518 13.39697 13.49877 13.60057 13.70237 13.80417

12) InGaSb Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 12.67798 12.587 12.54151 12.49602 12.45053 12.40504 12.35955 12.31406 12.26857 12.22309 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 nwp12) 12.1776 12.13211 12.08662 12.04113 11.99564 11.95015 11.90466 11.85917 11.81368 11.76819

13) AlInP Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 15.96432 16.17527 16.28075 16.38623 16.49171 16.59718 16.70266 16.80814 16.91361 17.01909 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 17.12457 17.23004 17.33552 17.441 17.54648 17.65195 17.75743 17.86291 17.96838 18.07386

14) AlGaSb Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 12.67798 12.95644 13.09567 13.2349 13.37413 13.51336 13.65259 13.79182 13.93105 14.07028 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 14.20951 14.34874 14.48797 14.6272 14.76643 14.90566 15.04489 15.18412 15.32335 15.46258

15) GaAsSb

x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 12.68 12.899 13.0085 13.118 13.2275 13.337 13.4465 13.556 13.6655 13.775 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 13.8845 13.994 14.1035 14.213 14.3225 14.432 14.5415 14.651 14.7605 14.87

16) InAsN Compound x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 20.82817 20.12577 19.77457 19.42337 19.07217 18.72097 18.36977 18.01857 17.66737 17.31617 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 16.96497 16.61377 16.26257 15.91137 15.56017 15.20897 14.85777 14.50657 14.15537 13.80417

17) InPAs Compound x value 0.0 0.1 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 13.80417 14.02019 14.12819 14.2362 14.34421 14.45222 14.56022 14.66823 14.77624 14.88425 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 14.99225 15.10026 15.20827 15.31628 15.42428 15.53229 15.6403 15.74831 15.85631 15.96432

18) AlAsSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 nwp12 15.46288 15.61824 15.69593 15.77361 15.85129 15.92897 16.00665 16.08434 16.16202 16.2397 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 16.31738 16.39506 16.47275 16.55043 16.62811 16.70579 16.78347 16.86116 16.93884 17.01652

19) AlAsP x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 18.07386 17.96813 17.91526 17.86239 17.80953 17.75666 17.70379 17.65092 17.59806 17.54519 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 17.49232 17.43946 17.38659 17.33372 17.28086 17.22799 17.17512 17.12225 17.06939 17.01652

20) GaPSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 12.67798 13.12395 13.34693 13.56991 13.79289 14.01588 14.23886 14.46184 14.68482 14.90781 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 15.13079 15.35377 15.57675 15.79974 16.02272 16.2457 16.46868 16.69167 16.91465 17.13763

21) InPSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 11.76819 12.1878 12.39761 12.60742 12.81722 13.02703 13.23684 13.44664 13.65645 13.86626 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 14.07606 14.28587 14.49567 14.70548 14.91529 15.12509 15.3349 15.54471 15.75451 15.96432

22) AlPSb x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 15.46288 15.72398 15.85453 15.98508 16.11563 16.24617 16.37672 16.50727 16.63782 16.76837 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 16.89892 17.02947 17.16002 17.29057 17.42112 17.55166 17.68221 17.81276 17.94331 18.07386

23) AlInN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 20.82817 20.94195 20.99885 21.05574 21.11263 21.16952 21.22641 21.28331 21.3402 21.39709 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 21.45398 21.51087 21.56777 21.62466 21.68155 21.73844 21.79533 21.85223 21.90912 21.96601

24) GaPN x value 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (nwp12) 21.65665 21.20475 20.9788 20.75285 20.5269 20.30094 20.07499 19.84904 19.62309 19.39714 Compound x value 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (nwp12) 19.17119 18.94524 18.71929 18.49334 18.26739 18.04143 17.81548 17.58953 17.36358 17.13763

Variation of plasmon energy with composition (x) is given. It has been observed from figure that Hole Mobility decreases and increase continuously (x=0.0-1.0) with the increase of Mercury (Hg) 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 Bond length of III-V Ternary Semiconductors On Refractive Indices and Composition. 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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