Constant-dipole-matrix-element model for Faraday rotation in amorphous semiconductors

Abstract

A model is presented which describes the interband Faraday rotation in amorphous semiconductors by means of a constant dipole matrix element. The model is applied to a-Se, a-AszSe3, and a-As2S3. The parameters which fit the Faraday rotation data and those which describe the corresponding behavior of optical absorption at higher photon energies are more consistent than was the case with earlier descriptions in the constant-momentum-matrix-element model. The energy parameters which are obtained are discussed in terms of the corresponding mobility and crystalline band gaps.Faraday rotation (FR) is the rotation of the plane of polarization of a polarized electromagnetic wave in a material under the influence of a longitudinal magnetic field. Interband FR in amorphous semiconductors has been discussed in the literature for a number of materials. ' Unlike crystalline semiconductors where the effect can be attributed primarily to direct transitions between extended states in valence and conduction bands, it is not clear which process determines the effect in amorphous materials. In a recent paper the problem was analyzed and it was shown that the FR formula for direct transitions in crystals may also be applied to glasses if a correlation between states in valence and conduction bands is assumed.The energy gap Eg", which can be determined from FR measurements as a function of frequency, is the lowest energy of the contributing transitions. As only transitions between extended states are involved, it is reasonable to compare Eg" with the mobility gap Eg which can be defined as the distance between the edges E, and E, of extended states in conduction and valence bands.Until now all formulas describing FR as a function of the frequency co, for the crystalline as well as for the amorphous state, have been derived under the assumption that the momentum matrix element is constant, independent of the transition energy. We will call this the constant-momentum-matrix (CMM) model in what follows. In this paper we present a constant-dipole-matrix (CDM) model and we show that the energy gap Ez" which is then obtained is in better agreement with the energy gaps associated with the optical absorption at the corresponding energies.Faraday rotation at photon energies below the energy gap is directly related to other optical effects such as dispersion of the refractive index and absorption at higher energies. The absorption may be described by Ez, the imaginary part of the complex dielectric function c. =c. &+i c2. Kramers-Kronig transformations allow cl to be calculated from c2. From c&, in turn, the refractive index n may be determined and thus the FR angle 0 through the Becquerel relation O~codn/des for diamagnetic materials. The result for co &cog may be written as follows: 0D to e i ( co )d co n0(co) =(const)co f (co'co ) with %cog:Eg 6) is the measurement frequency. From FR. the fact that FR in amorphous materials can be described by a dispersion equation for direct transitions in crystals, it then follows in the CMM model that fo...

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