Barrier height fluctuations in very small devices due to the discreteness of the dopants

摘要

The spatial fluctuation in barrier heights of a planarhyphen;doped barrier due to the discreteness of the acceptors and their statistical distribution has been calculated by solving Poissonrsquo;s equation in three dimensions. Our model assumes a random distribution of spherical acceptor charges. Nonlinear Thomasndash;Fermi screening has been used to include the effect of free carriers and to determine their positionhyphen;dependent concentration. At 4.2 K we find a range in barrier heights of 30 meV for a barrier with an average value of 0.206 eV. The method by which potential fluctuations broaden the energy distribution of ballistic electrons is illustrated by an example.