Effects of density of doping level on the electrical properties of the near-surface region of p-type Gallium Antimonide (GaSb)

Abstract

In this study, the variation of thermal equilibrium charge carrier densities and the net ionization density in the near-surface depletion with energy bending is described for p-type GaSb. The result indicates band bending increases with doping level. Applying gauss’s law to both the surface and the near-surface region, the net electric field is not linearly varying with position, rather it is a deviated line. Using the relation between the one-dimensional potential gradient and the electric field, The electric field in the near-surface, the transition layer and near the quasi-neutral region are linearly varying with position. Using the fact that the electric field and the energy are zero at the boundary between the depletion layer and the quasi-neutral region, since the surface and volume charge density balance each other the values of the electric field, the energy, and the charge density at the surface are described in terms of the net ionization density inside the entire depletion layer. The value of the energy at the surface can be obtained as a function of doping level using the well-known relation between the bulk and the surface Fermi-level positions. Description of energy at the surface enables us to determine the values the net ionization densities near the surface, at the border between the highly depleted layer and the transition layer; and inside the entire depletion layer and the width of the depletion layer as function of doping density. Upon describing the energy as a function of position in the entire depletion layer, one can describe position dependences of the net ionization density, the carrier densities, the electric field strength and the excess carrier lifetimes in the entire depletion layer. The obtained result revealed that, the energy is bending down quadratically with position from the quasi-neutral region to the surface, the majority carrier density decreases exponentially with position from the quasi-neutral region to the surface, the electric field strength decreases non-linearly with position from the surface to the quasi-neutral region and the excess carrier lifetime decreases exponentially from the surface to the quasi-neutral region. The doping level affects the magnitudes of the surface charge density, the energy and the electric field in the entire depletion layer and the magnitudes of the carrier densities and the excess carrier lifetimes under the surface are found to be unaffected by the doping level of the material since the surface fermi pinning energy is taken a constant value.