Influence of Semiconductor Dielectric Function Spatial Dispersion on Charge Electrostatic Energy near the Semiconductor/Vacuum Interface and Field Emission Current

The electrostatic charge energy W near the semiconductor/vacuum interface is calculated for a variety of models describing the semiconductor static dielectric function ε( k ) dependent on a momentum transferred k . It is shown that the correct account of this dependence leads to the finiteness of the energy W and the image force electrostatic field – σW/σz , when z → O, where z is the distance from the interface. The potential barrier shape for the field emission from semiconductors is found and the dependences of the tunnel current density j on the applied field F , the temperature T and the doping impurity concentration n 0 are calculated. It is shown that the spatial dispersion effects of ε( k ) essentially affect the magnitude of j , but do not change the dependence j ( F ) which follows from the Fowler‐Nordheim classical formula.