Efficacy of the Method of Four Coefficients to Determine Charge-Carrier Scattering

The investigation of the electronic properties of semiconductors from transport measurements (i.e., resistivity, Hall, and Seebeck coefficient measurements) is challenging due to the averaging of charge-carrier dynamics inherent in such measurements. Here, we investigate the incorporation of a fourth measurement of electronic transport, the Nernst coefficient, into the analysis, termed the method of four coefficients. This approach yields the Fermi level, effective mass, scattering exponent, and relaxation time prefactor. We begin with a review of the underlying mathematics and investigate the mapping between the four-dimensional material property and transport coefficient spaces. We then investigate how the traditional single-parabolic band method yields a single, potentially incorrect point on the solution subspace. This uncertainty can be resolved through Nernst coefficient measurements and we map the span of the ensuing subspace. We conclude with an investigation of how sensitive the analysis of transport coefficients is to experimental error for different sample types.