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

  • Tino Hofmann (a1), Marius Grundmann (a1), Craig M. Herzinger (a2), Mathias Schubert (a1) and Wolfgang Grill (a1)...
Abstract
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.

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