Effect of Electric and Magnetic Fields on the SelfConsistent Potential at the Surface of a Degenerate Semiconductor
Abstract
We have performed a selfconsistent calculation of the potential in the accumulation layer at the surface of a degenerate semiconductor and of the boundstate energies which that potential supports in the presence of a perpendicular electric field of appropriate sign and strength. The calculation is carried out in the Hartree approximation appropriate to the small r_{s} values found in moderately doped, narrowbandgap materials, using a parametric scheme which enormously simplifies the calculation. This makes it feasible to study the effect of a quantizing magnetic field on the selfconsistent potential and the boundstate energies. Bound states and mobile states are determined from the same Schrödinger equation. We derive and make extensive use of a onedimensional Friedel sum rule, and show that there is a sudden rearrangement of mobile charge which compensates for what would otherwise be a discontinous charge alteration when the number of bound states changes in response to changes in the external fields. Simple models are presented which reproduce the results of the selfconsistent calculation and which are useful in interpreting the meaning of the detailed numerical results. Magnetooscillations of the potential caused by a perpendicular magnetic field are studied in detail. The observable magnetooscillations in the potential here arise from Landaulevel quantization of the bound states only. We compare the results with earlier calculations in which the mobile states were treated using linearresponse theory and we find that the role played by the Landaulevel quantization of the mobile electron states is, in this nonlinear treatment, quite unimportant, supporting the conclusion which we drew from the linear surfacescreening approximation of our earlier work.
 Publication:

Physical Review B
 Pub Date:
 January 1972
 DOI:
 10.1103/PhysRevB.5.475
 Bibcode:
 1972PhRvB...5..475B