New techniques for mobility spectrum analysis

Abstract

Mobility spectrum analysis (MSA) is a process of recovering the spectrum of carrier mobilities in an electronic material from a magnetic-field-dependent Hall measurement. This paper first presents a set of useful general properties of MSA that are true for all MSA methods. One such property is that Hall data can be classified as either “physical,” with at least one spectrum of carrier mobilities that exactly fits the data, or “unphysical,” where no mobility spectra exactly fit the data and the analysis must find approximate solutions. Almost all experimental Hall data collected at seven or more magnetic fields are slightly unphysical. The closest approximate solution for such unphysical data is always a set of discrete-carrier mobilities. A new method for multicarrier MSA is presented to display the likely properties of the discrete carriers as two-dimensional spectra vs both mobility and carrier density instead of one-dimensional spectra vs only mobility, as in previous methods. Measurement uncertainties are included as a fundamental part of the analysis so that the user can easily view the resultant uncertainty in the derived carrier properties. A separate method is also presented for reliably determining a smooth, high-entropy spectrum of carrier mobilities, which is constructed as the maximum-entropy linear combination of discrete-carrier solutions to the Hall data. An example using calculated Hall data corresponding to acoustic phonon scattering shows that the technique could potentially be used to measure the continuous mobility distributions that result from different scattering mechanisms.