Quantum Size Effect And Electric-Field Effect In Thin Bi Films

Calculations are presented for the occurrence of quantum size effects in the electric field effect in thin films of bismuth. The penetration of the applied field is treated in a self-consistent Thomas-Fermi type of approximation. The local value of the conductivity depends on the applied electrostatic potential and is calculated in the relaxation time approximation. The state dependence of the relaxation time is taken to vary inversely as the density of states, similar to earlier calculations for bismuth films. The film conductance shows abrupt changes with applied field for thicknesses which have the Fermi level close to a step in the electronic density of states. The temperature dependence of this quantum size effect is also considered.