Energy and concentration nonequilibrium and nonlinear charge transport phenomena in semiconductors in a magnetic field in hot electrons approximation

When external electric (E-x) and magnetic (H-y) fields are applied to a semiconductor nonequilibrium charge carriers appear that are redistributed perpendicularly to the fields. We show that under weak recombination the nonequilibrium electron together with the hole concentration and nonequilibrium electron temperature are related by a linear function of the coordinate z. The nonequilibrium electron temperature and electron and the hole concentration have a term proportional to HyEx and another term proportional to E-x(2). The nonequilibrium temperature shows a dependence of the z-coordinate and includes the effects of the electron-phonon interaction as well as the absorption of heat over the surfaces of the sample. Additionally, the nonequilibrium temperature and charge carriers modified the density of current from the Ohm law. The redistribution of charge carriers originate two new contributions to the magnetoresistance, one of the contributions is linked to the diffusion of charge carriers along the z-axis, the other one is related to the thickness 2b of the sample and the heat absorption over the surfaces. Another effect that modified the density of current is associated with the absorption of heat over the surfaces of the sample, this contribution is proportional to HyEx and can change sign if the electric or magnetic field is inverted. In the case of a null magnetic field, the nonlinear temperature and electron (and hole) concentration are originated by the external electric field and the relaxation mechanism over the surfaces of the sample. The current-voltage characteristic deviates from the linear response due to the nonequilibrium charge carriers.