Computation of charge collection probability for any collecting junction shape

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.