Schrodinger-Poisson self-consistency

Abstract

Abstract In Group IV bulk semiconductors such as Si, it is possible to replace some of the atoms in the lattice by impurity atoms belonging to group V of the periodic table, such as P. The group V impurity atom has an additional electron which is not used in the covalent bonding in the crystal. Due to the effective dielectric constant of the host and its reduced effective mass the electron is weakly bound to the impurity atom forming a hydrogenic structure. In III---V compound semiconductors such as GaAs an analogous impurity doping can be accomplished by using Si which replaces a Ga atom in the GaAs lattice. These impurity atoms, called donors, ionize easily, giving off the bound electron to enable electrical conduction; the binding energy of an Si donor in GaAs is about 5 meV. The conduction is limited by scattering from the ionized impurity atoms, besides other scattering mechanisms. With the advent of molecular beam epitaxy (MBE) it was recognized that the conduction channel and the location of impurity doping can be separated to improve the mobility of carriers. With the remarkable control over the composition and almost atomic perfection in the heterostructure crystals grown by MBE, a quantum well structure can be grown with selective doping only in specified sections of the barrier regions. If the barrier regions alone are doped with impurity atoms, the electrons initially bound to the impurity atoms seek lower energy states and fall into the quantum well. This reduces their probability of being in the barrier region with the ionized impurities, resulting in a reduction in ionized impurity scattering in transport in the in-plane direction. This selective doping of the barrier, or any particular layer for that matter, is called modulation doping.