A method for determining a two-dimensional spectrum of a specified carrier having a specified mobility and density in a material of an electronic device, the method including performing a magnetic field-dependent Hall measurement on the material of the electronic device; determining, using the magnetic field-dependent Hall measurement, a probability density function of a conductance of the material of the electronic device, wherein the probability density function describes a spectrum of a plurality of m-carriers, wherein the plurality of m-carriers includes the specified carrier having the specified mobility and density; and determining an electrical transport of a plurality of electrons and holes inside the material of the electronic device by observing a variation of the probability density function with any of the specified mobility and density of the specified carrier.