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Far-infrared magnetooptical generalized ellipsometry determination of free-carrier parameters in semiconductor thin film structures

Published online by Cambridge University Press:  11 February 2011

Tino Hofmann ,
Marius Grundmann ,
Craig M. Herzinger ,
Mathias Schubert  and
Wolfgang Grill
Tino Hofmann
Affiliation:
Solid State Physics and Acoustics Group, Faculty of Physics and Geosciences, University of Leipzig, GERMANY
Marius Grundmann
Affiliation:
Solid State Physics and Acoustics Group, Faculty of Physics and Geosciences, University of Leipzig, GERMANY
Craig M. Herzinger
Affiliation:
J.A. Woollam Co., Lincoln, NE, USA
Mathias Schubert
Affiliation:
Solid State Physics and Acoustics Group, Faculty of Physics and Geosciences, University of Leipzig, GERMANY
Wolfgang Grill
Affiliation:
Solid State Physics and Acoustics Group, Faculty of Physics and Geosciences, University of Leipzig, GERMANY
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Abstract

In accord with the Drude model, the free-carrier contribution to the dielectric function at infrared wavelengths is proportional to the ratio of the free-carrier concentration N and the effective mass m*, and the product of the optical mobility μ and m*. Typical infrared optical experiments are therefore sensitive to the free-carrier mass, but determination of m* from the measured dielectric function requires an independent experiment, such as an electrical Hall-effect measurement, which provides either N or μ. Highly-doped zincblende III-V-semiconductors exposed to a strong external magnetic field exhibit non-symmetric magnetooptical birefringence, which is inversely proportional to m*. If the spectral dependence of the magnetooptical dielectric function tensor is known, the parameters N, m* and μ can be determined independently from optical measurements alone. Generalized ellipsometry measures three complex-valued ratios of normalized Jones matrix elements, from which the individual tensor elements of the dielectric function of arbitrarily anisotropic materials in layered samples can be reconstructed. We present the application of generalized ellipsometry to semiconductor layer structures at far-infrared wavelengths, and determine the magnetooptical dielectric function for n-GaAs and n-AlGaInP for wavelengths from 100 μm to 15 μm. We obtain the effective electron mass and mobility results of GaAs in excellent agreement with results obtained from Hall-effect and Shubnikov-de-Haas experiments. The effective electron mass in disordered n-AlGaInP obtained here is in very good agreement with previous k·p calculations. (Far)-infrared magnetooptic generalized ellipsometry may open up new avenues for non-destructive characterization of free-carrier properties in complex semiconductor heterostructures.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 744: Symposium M – Progress in Semiconductors II–Electronic and Optoelectronic Applications , 2002 , M5.32
Copyright
Copyright © Materials Research Society 2003

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References

REFERENCES

1. Schubert, M., Hofmann, T., and Herzinger, C. M., J. Opt. Soc. Am. A 20, 3. Feb. (2003).Google Scholar
2. Drude, P., The theory of optics, translated from German by Mann, C. R. and Millikan, R. A., (Longmans, Green, and Co., 1902).Google Scholar
3. Wolfe, C. M., Holonyak, N. Jr, and Stillmann, G. E., Physical properties of semiconductors, (Prentice-Hall, Englewood Cliffs, NJ, 1989).Google Scholar
4. Pidgeon, C. R., Free carrier optical properties of semiconductors, in Balkanski, M., ed., Handbook of semiconductors, Vol. 2, (North-Holland, Amsterdam, 1980).Google Scholar
5. Zunger, A., MRS Bull. 22, 20 (1997)Google Scholar
6. Kasic, A., Schubert, M., Einfeldt, S., Hommel, D., and Tiwald, T. E., Phys. Rev. B 62, 7365 (2000).Google Scholar
7. Azzam, R. M. A. and Bashara, N. M., Ellipsometry and polarized light, (North-Holland, Amsterdam, 1984).Google Scholar
8. Azzam, R. M. A. and Bashara, N. M., J. Opt. Soc. Am. 62, 1521 (1972).Google Scholar
9. Schubert, M., Rheinländer, B., Johs, B., Herzinger, C. M., Woollam, J. A., J. Opt. Soc. Am. A 13, 875 (1996).Google Scholar
10. Röseler, A., Infrared Spectroscopic Ellipsometry, (Akademie-Verlag, Berlin, 1992).Google Scholar
11. Schubert, M., Infrared Ellipsometry on III-V semiconductor layer structures (Habilitationsschrift, Universität Leipzig, 2002); Full text available at http://www.uni-leipzig.de/~hlp/ellipsometrie.Google Scholar
12. Raymond, A., Robert, J. L., and Bernard, C., J. Phys. C 12, 2289 (1979).Google Scholar
13. Hofmann, T., Leibiger, G., Pietzonka, I., Gottschalch, V., Schubert, M., Phys. Rev. B 64, 155206 (2001).Google Scholar
14. Hofmann, T., Schubert, M., Herzinger, C.M., Pietzonka, I., Appl. Phys. Lett. submittedGoogle Scholar