Optical electronegativity and refractive index of materials

Transcription

1 May 1998 Ž. Optical Materials Optical electronegativity and refractive index of materials R.R. Reddy, Y. Nazeer Ahammed, K. Rama Gopal, D.V. Raghuram Department of Physics, Sri KrishnadeÕaraya UniÕersity, Anantapur , India Received 7 October 1997; accepted 30 October 1997 Abstract Simple correlations between the energy gap, optical electronegativity and the refractive index are given for various classes of materials such as semiconductors, insulators and oxides. There has been no report in the literature on the direct estimation of optical electronegativity for the wide variety of materials using energy gap values. The present method performance is compared with Moss and Ravindra s relationships. A simple analysis on the average percentage deviation for low and high n value materials is also presented. The average percentage deviation in the present approach reveals that the method proposed proves its identity and soundness compared to that of Moss and Ravindra s relationships. A good agreement is observed between the computed and literature values of refractive indices. q 1998 Elsevier Science B.V. 1. Introduction The refractive index is one of the fundamental properties of a material, because it is closely related to the electronic polarizability of ions and the local field inside the material. The evaluation of refractive indices of semiconductors is of considerable importance for applications in integrated optic devices such as switches, filters and modulators, etc., where the refractive index of a material is the key paramewx 1. The ternary chalcopyrites ter for device design have recently received considerable attention due to their importance for the development and fabrication of various technological devices. These compounds exhibit a high non-linear susceptibility and birefringence which leads to efficient second harmonic generation and phase matching w x. These chalcopyrites have many practical applications in the Corresponding author. field of fiber optics, sensors and communication devices. The most interesting and fundamental properties of materials are the optical energy gap or absorption edge and the refractive index. Therefore many attempts have been made to find more relationships between parameters both from the point of view of fundamental interest and also as a technologw5 1 x. There have been several attempts to ical aid obtain correlation between band gaps, single bond energy, atomic numbers, electronegativities and rew10 13 x. For the first time Moss w6x succeeded in systemising the extensive experimental fractive indices data on energy gap and high frequency refractive index and proposed an empirical relationship bewx 7 has developed a different tween them. Ravindra relationship between the energy gap and refractive index. Finkenrath w1x has mentioned that Ravindra s relationship shows very large deviations for small Ž F 0.3 ev. and large energy gaps Ž G 3.5 ev.. Ravindra s relationship cannot occur if n G.1 and it also predicts unrealistic results for low n values r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. Ž. PII S

2 96 R.R. Reddy et al.roptical Materials Table 1 Material Energy Optical Refractive gap, electro- index, n E Ž ev. negativity, D x g present Duffy s present known Moss Ravindra study values study values ZnO ZnS ZnSe ,6.8 ZnTe CdO CdS CdSe CdTe HgSe CuCl CuBr CuI BN AIN AlP AlAs AlSb GaN GaP GaAs GaSb InP InAs InSb SiC PbSe PbTe CuAlS CuAlSe CuAlTe CuGaS CuGaSe CuGaTe CuInTe AgAlS AgAlSe AgAlTe AgGaS AgGaSe AgGaTe AgInSe AgInTe ZnSiP ZnSiAs ZnGeP ZnGeAs ZnSnP CdSiAs CdSiP CdGeP

3 Ž. Table 1 continued R.R. Reddy et al.roptical Materials Material Energy Optical Refractive gap, electro- index, n E Ž ev. negativity, D x g present Duffy s present known Moss Ravindra study values study values CdSnP CuInSnSe AgInSnSe CuInGeSe CuGaSnSe AgInGeSe AgGaSnSe AgGaGeSe AgAlSnSe CuGaGeSe CuAlSnSe AgAlGeSe CuAlGeSe Pb Sn Te x 1yx Pb0.8Sn 0.Te Pb0.9Sn 0.1Te PbxSn1yxSe PbSe Pb0.9Sn 0.1Se Pb0.88Sn 0.1Se Ga x Al1yx As Ga 0. Al 0.8 As Ga 0.6 Al 0. As GaAs CdGeŽ P As. x 1yx CdGeŽ P As CdGeŽ P As CdSeP GeTe CsI CsBr NA CsCl NA NaCl NA NaBr NA KCl NA KBr NA RbCI NA RbBr NA NiF NA B O NA 3 SiO NA Al O NA MgO NA CaO SrO BaO MnO FeO ZnO GeO

4 98 R.R. Reddy et al.roptical Materials Table 1 Ž continued. Material Energy Optical Refractive gap, electro- index, n E Ž. g ev negativity, D x present Duffy s present known Moss Ravindra study values study values SbCO HgO Bi O PbO SnO Ga O CdO Se O CeO TiO Cr O FeO CoO NiO Cu O MoO Average percentage deviation Moss proposed that the relationship performance was also low in ionic cases Ž mostly alkali halides.. In view of the above shortcomings, the authors have arrived at a simple relationship for the estimation of refractive indices. Its validity is tested in various classes of materials such as semiconductors, insulators and oxides. The results have been compared with Moss and Ravindra s relationships. The estimated refractive indices are in good agreement with the literature values and also better than the results of Moss and Ravindra.. Theory Duffy w9,15x has introduced the concept of optical electronegativity and its uses in estimating many physico-chemical parameters of materials. The correlation between energy gap and optical electronegativw9,15x in venous ity has been enlightened by Duffy binary systems. The Duffy expression is as follows D x s0.688 E g, Ž 1. where D x sx anion yx cation with x anion and x cation being the optical electronegativities of the anion and cation, respectively. Moss w5,6x proposed a general relationship based on the concept that in a dielectric energy, levels are scaled by a factor, ` i.e. n E s Const. Ž 95.. Ž. g Ravindra et al. w7,16x have proposed another linear relationship, namely ns.08y0.6 E g. Ž 3. Recently Reddy and Nazeer w1x have proposed an empirical relationship between refractive index and optical electronegativity and is as follows: nsyln 0.10D x. Ž. For simple systems D x can be easily estimated Ž x yx. anion cation. In the case of ternary and complex systems, the D x estimation is somewhat difficult. In order to overcome the difficulty, the authors have chosen Eq. Ž. 1 for the calculation of the optical electronegativity of complex systems. Once D x values are estimated utilising E values quoted in g

5 the literature w6,7,17 19 x, the refractive indices can then easily be estimated by Eq. Ž.. The estimated D x values are in good agreement with the Duffy s w9,15x optical electronegativity difference for binary Ž systems D x sx yx. anion cation. This enables us to evaluate D x values for ternary and other systems. There has been no theoretical model so far which predicts refractive indices for semiconductors, insulators and oxides with the optical electronegativity concept. Eq. Ž. is tested in more than 100 variety of compounds. R.R. Reddy et al.roptical Materials Results and discussion The estimated values of refractive index on the basis of Eqs. Ž.Ž. 1 for semiconductors, insulators and oxides are presented in Table 1. The necessary Table Percentage deviation for low and high n value materials Material % deviation present Moss Ravindra method relationship relationship Low n Ž 1to. ZnO CsI CsBr NA CeCl NA NaCl NA NaBr NA KCl NA KBr NA RbCl NA RbBr NA NiF NA B O NA 3 SiO NA Al O NA MgO NA CaO SrO BaO GeO Ga O SeO High n Ž to6. GeTe ZnGeAs PbSe Ž. Fig. 1. B indicates Eq., indicates the Moss relationship and e indicates the Ravindra relationship. data have been taken from the literature w6,7,17 19 x. The values of n in the present study are in good agreement with the available experimental data w6,7,10,15,17 x. There has been no report in the literature on the direct estimations of optical electronegativity for the wide variety of materials using E g values. The average percentage deviation is estimated and presented in Table 1. The minimum percentage deviation in the present approach indicates the improvement of the empirical relationships prow5,6x and Ravindra w7,16 x. The pre- posed by Moss sent method performance is comparatively better than the Moss relationship. Careful observation of the average percentage deviation presented in Table, reveals that the estimated refractive index for the materials who s refractive index lies between 1 and, and and 6 has an applicability superior to that of Moss and Ravindra. Fig. 1 shows the graphical representation of the present approach, the Moss relationship and Ravindra s relationship. For clarity purposes Fig. is exclusively drawn for the materials whose refractive index lies between 1.5 and.5 and also indicates specific deviation in comparison with the experimental values. A significant deviation has been observed in the case of lead salts and InSb,

6 100 R.R. Reddy et al.roptical Materials study it is possible to correlate refractive index and the nature of bonding of the material. Acknowledgements The authors are thankful to Professor T.S. Moss for his kind encouragement and also to Professor J.V. Narlikar, Director, IUCAA, Pune, for the financial support. Ž. Fig.. B indicates Eq., indicates the Moss relationship and e indicates the Ravindra relationship. etc. Moss has pointed out that Ravindra s relationship cannot occur if ng.5 and its applicability is poor for low n. In the case of GeTe, CsI, CaO, SrO, BaO, GeO, Ga O3 and SeO 3, the Ravindra relationship predicts unrealistic results and the average percentage deviation is more than 30. Finkenrath w1x has widely discussed the shortcomings of the Ravindra relationship at low and high values of n. The inclusion of optical electronegativity has direct bearing on the concept of chemical bonding. The magnitude of D x indicates the nature of the bonding in the materials. If D x is high, the material is considered ionic in nature and if its magnitude is less the materials are consider to be covalent in nature. It is also noticed that for the molecules whose D x value is less, its refractive index is high. From this References wx 1 D.K. Ghosh, L.K. Samanta, Infrared Phys. 6 Ž wx D.S. Chemla, P.J. Kupecek, D.S. Robertson, R.C. Smith, Opt. Commun. 3 Ž wx 3 D.S. Chemla, Phys. Rev. Lett. 6 Ž wx N.A. Goryunova, L.B. Zlatkin, E.K. Ivonov, J. Phys. Chem. Solids 31 Ž wx 5 T.S. Moss, Proc. Phys. Soc. B 63 Ž wx 6 T.S. Moss, Phys. Status Solidi Ž. b 131 Ž wx 7 N.M. Ravindra, S. Anuch, V.K. Srinvastava, Phys. Status Solidi Ž. b 93 Ž k115. wx 8 G. Dionne, J.C. Woolley, Phys. Rev. B. 6 Ž wx 9 J.A. Duffy, Bonding, Energy Level and Bonds in Inorganic Solids, Longman, England, w10x R.R. Reddy, S. Anjaneyulu, Phys. Status Solidi Ž. b 17 Ž 199. k91. w11x R.R. Reddy, Y. Nazeer Ahammed, Infrared Phys. 36 Ž w1x R.R. Reddy, Y. Nazeer Ahammed, Cryst. Res. Technol. 30 Ž w13x R.R. Reddy, M. Ravi Kumar, T.V.R. Rao, Infrared Phys. 3 Ž w1x H. Finkenrath, Infrared Phys. 8 Ž w15x J.A. Duffy, Phys. C 13 Ž w16x V.P. Gupla, N.M. Ravindra, Phys. Status Solidi Ž. b 100 Ž w17x A. Kumar, N.M. Ravindra, R. Rath, J. Phys. Chem. Solids 0 Ž w18x N.V. Joshi, Photoconductivity, Marcel Dekker, New York, w19x D.R. Lide Ž Ed.., CRC Handbook of Chemistry and Physics, 7th ed., CRC Press, Tokyo,