Abstract
Accurate and numerically efficient models for the complex dielectric function vs wavelength and material characteristics are essential for the use of nondestructive optical techniques such as spectroscopic ellipsometry or reflectometry. These optical techniques are commonly used for real-time and run-to-run monitoring and control of growth and etch processes to determine a material's composition and thickness. In this work, we discuss an improved composition-dependent model for the complex dielectric function for lattice-matched In1-xGaxAsyP1-y/InP systems valid over the entire composition range 0 ≤ y ≤ 1. We describe our model, which is an extension of the critical point parabolic band method and is based on the model proposed by Charles Kim et al. for the AxGa1-x/GaAs system. We demonstrate the quality of the model in fitting optical data for individual compositions and compare our results to other established models including the harmonic oscillator approximation and the model of Adachi. Using results obtained from the individual fits, we generate a composition-dependent model that is valid for the entire range of lattice-matched compositions. Also, we show how this model can be used to accurately determine the composition (±0.01) of an unknown material whose dielectric response has been obtained using spectroscopic ellipsometry or a similar technique.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R.M.A. Azzam and N. M. Bashara,Ellipsometry and Polarized Light (Elsevier Publications, 1977).
David E. Aspnes,Handbook of Optical Solids, ed. E. Palik, (Academic Press, 1985), p. 89.
David E. Aspnes,Characterization of Semiconductors and Semiconductor Structures by Photometric and Ellipsometric Techniques (SPIE, 1987).
O.S. Heavens,Optical Properties of Thin Solid Films (Dover, 1955).
F. Bassani and G. Pastori Parravicini,Electronic States and Optical Transitions in Solids (Pergamon Press, 1975).
J.A. van Vechten,Phys. Rev. 182 (3), 891 (1969).
Jasprit Singh,Physics of Semiconductors and Their Heterostructures (McGraw-Hill, 1993).
Sadao Adachi,Physical Properties of III-V Semiconductor Compounds: InP, InAs, GaAs, GaP, InGaAs, and InGaAsP (John Wiley and Sons, 1992).
S.M. Kelso, D.E. Aspnes, M.A. Pollack and R.E. Nahory,Phys. Rev. B 26 (12), 6669 (1982).
Charles C. Kim, Ph.D. thesis, University of Illinois at Chicago, 1991.
Charles C. Kim, James W. Garland, H. Abad and Paul M. Raccah,Phys. Rev. B 45 (20), 11749 (1992).
C.C. Kim, J.W. Garland and P.M. Raccah,Phys. Rev. B 47 (14), 1876(1993).
D.E. Aspnes and H.J. Stocker,J. Vac. Sci. Technol. 21 (2), 413 (1982).
H. Ehrenreich and M.L. Cohen,Phys. Rev. 115 (4), 786 (1959).
M. Erman, J.B. Theeten, N. Vodjdani and Y. Demay,J. Vac. Sci. Technol. B 1 (2), 328 (1983).
Donald W. Marquardt,J. Soc. Indust. Appl. Math. 11 (2), 431 (1963).
W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling,Numerical Recipes in C (Cambridge University Press, 1988).
Ernesto H. Perea, Emilio E. Mendez and Clifton G. Fonstad,Appl. Phys. Lett. 36 (12), 978 (1980).
Sadao Adachi,Phys. Rev. B 39 (17), 12612 (1989).
David E. Aspnes, private communication.
Sadao Adachi,Phys. Rev. B 35 (14), 7454 (1987).
Fred L. Terry, Jr,J. Appl. Phys. 70 (1), 409 (1991).
Sadao Adachi, private communication.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kamlet, L.I., Terry, F.L. A composition-dependent model for the complex dielectric function of In1 xGaxAsyP1− y lattice-matched to InP. J. Electron. Mater. 24, 2005–2013 (1995). https://doi.org/10.1007/BF02653024
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02653024