Screening length in presence of attractive traps

The electrostatic screening length due to non-equilibrium electrons in the presence of shallow attractive traps, at low lattice temperatures, has been calculated here for a wide range of electric field. The range covers from a field corresponding to a weakly heated ensemble up to a value for the onset of impurity breakdown. Compared to the results obtained under the condition of thermodynamic equilibrium, the screening length due to non-equilibrium carriers becomes field dependent and moreover, its dependence upon the lattice temperature is now quite complicated. The numerical results for high purity Ge and Si show that the screening length assumes a maximum value at some electric field. The strength of this field again changes with the change of the lattice temperature.