THE USE OF THE FINITE DIFFERENCE METHOD FOR CALCULATION OF ELECTRONIC STATES IN MIS-STRUCTURE WITH SINGLE DONOR 1

Abstract

Numerical modeling of electronic state evolution due to non-uniform external electric field in the structure metal-insulator-semiconductor with solitary donor center is carried out. Considering a nanometer disc-shaped gate as a source of the electric field, the problem for the Laplace equation in multilayered medium is solved numerically to determine the distribution of the gate potential. The energy spectrum of a bound electron is calculated from the problem for the stationary Schrödinger equation. Finite difference schemes are constructed to solve both the problems. Difference scheme for the Schrödinger equation takes into account cusp condition for the wave function at the donor location. To solve the problem for the Laplace equation, asymptotic boundary conditions for approximating the external field potential at large distances from the gate in different layers are suggested. These conditions allow to reduce the calculation domain for the electrostatic problem essentially. The effect of the boundary conditions on the accuracy of calculating the potential and energies is investigated. Using the developed difference schemes, the dependences of the energy spectrum of the bound electron on the gate potential are calculated, and the values of critical potential at which the wave function of the electron is relocated are determined. It has been found on the basis of calculation results, that governing parameter for the description of electronic behavior is the potential difference between the donor and semiconductor surface. It has been shown that critical potential difference does not depend on dielectric thickness and permittivity.