Nonlinear two-layer model for photocarrier radiometry of ion-implanted silicon wafers

A nonlinear two-layer model was developed to describe and analyze Photocarrier Radiometric (PCR) signals of ion-implanted Si wafers which are intrinsically nonlinear with excitation laser power. The thickness of the implantation layer and the optical/electronic damage threshold for different implantation doses were estimated using the Monte Carlo method and the effective medium approximation theory, respectively, which can provide key parameter values for the model to calculate the nonlinearity coefficient, defined as the slope of PCR amplitude versus excitation power in log-log scale. Experimentally, the nonlinearity coefficients of seven c-Si wafers with implantation doses from 1011 to 1016 cm-2 were measured at two different excitation wavelengths (830 and 405 nm), and good agreement between theory and experiment was found. Results show that the nonlinearity coefficient has a negative correlation with the implantation dose, and the coefficient measured at 405 nm is consistently smaller than that measured at 830 nm for each sample. Compared with the conventional PCR models, the nonlinear two-layer model proposed here is more coincident with experimental facts, thus enabling PCR to provide more accurate quantitative characterization of the carrier recombination and transport properties of ion-implanted semiconductor wafers.