Theory of electronic bound states associated with n-type inversion layers on silicon

Abstract

The localized states of an electron bound to a charged impurity at the interface between silicon and silicon dioxide have been investigated [1] using the variational method. The interface was taken to be parallel to a (001) plane of the silicon, and a static electric field perpendicular to the interface was assumed. In a subsequent publication [2] an adiabatic form for the electron wave function was used consisting of the product of two functions, χ( x, y) and ƒ( z), where x and y are Cartesian coordinates parallel to the interface and z is perpendicular to the interface. Both of the functions χ( x, y) and ƒ( z) were determined by the variational procedure. Further calculations were carried out using the adiabatic form of the wave function for the case where the impurity is situated in the silicon dioxide at a distance z 0 from the interface. The binding energies of the ground state and a pair of degenerate excited states were calculated as functions of electric field and distance of the impurity from the interface. They are found to increase with increasing electric field and decrease with increasing distance of the impurity from the interface. The intensity of electric dipole transitions between the ground and excited states was calculated as a function of electric field when the impurity is located at the interface. The effect of screening of the impurity charge by the inversion layer electrons has also been investigated [1]. A comparison of the theoretical results with available experimental data [3] is made.