Effect of magnetic field on the screening due to hot electrons in the presence of shallow attractive traps

The electrostatic screening of the perturbation potential due to lattice imperfections has been investigated here in the presence of crossed electric and non-quantizing magnetic fields, under conditions where the lifetime of the carriers of the non-equilibrium ensemble in a semiconductor is controlled by shallow attractive traps. The screening characteristics are obtained in the general case of any mechanism of energy and momentum scattering of the hot carriers in the strong and weak magnetic field limits. For some definite scattering mechanisms, however, the characteristics are calculated in the presence of any finite value of the magnetic field. The results show interesting characteristic features that are quite different from what one can obtain for an ensemble of carriers that is in thermodynamic equilibrium with the lattice atoms. It has been observed that, depending upon the prevalent conditions with respect to the dominant momentum and energy relaxation processes and the strength of the applied electric field, the presence of the magnetic field sometimes brings in significant changes in both the qualitative and the quantitative aspects of the field dependence of the screening length. Apart from that, the screening length now shows a rather complex and altogether different dependence upon the lattice temperature. The numerical results featuring the interesting characteristics under different prevalent conditions are presented for Ge. It has been explained in what novel way the present problem describes the dependence of the screening length due to an ensemble of hot electrons on the external electric and magnetic fields. The limitations of the present theory, as well as its possible applicability for the characterization of semiconductors under high field conditions at low lattice temperatures, are discussed.