Computation of charge collection probability for any collecting junction shape.

Abstract

Electron-beam-induced current (EBIC) of the

scanning electron microscope (SEM) has been widely used for

semiconductor devices and materials characterizations. The

charge collection probability within a collecting junction plays an

important role in determining the EBIC current. The

conventional approach starts by solving the continuity equation

to obtain the charge carrier density and then the analytical

expression for the charge collection probability. Knowing the

analytical expression of the charge collection probability

enhances the study and development of the measurement

technique. However, the conventional method usually requires

lot of mathematical effort and the derived analytical expression is

valid only for one particular junction shape. This paper presents

a simple and straight forward computational method for the

charge collection probability distribution within the charge

collecting junction well by utilizing the reciprocity theorem and

finite difference method with the junction shape serves as the

boundary conditions. It not only simplifies the computation but

also applicable to any junction shape as long as the drift-diffusion

model remains valid. This method was verified using a U-shaped

junction well.