Nonlinear Dependence of Photocarrier Radiometry Signals from p-Si Wafers on Optical Excitation Intensity

Abstract

The dependence of the photocarrier radiometric (PCR) signal on the intensity of exciting superbandgap laser radiation was investigated. It was shown that the amplitude of the PCR signal exhibits a supralinear dependence on laser intensity I0βI0β , with nonlinearity coefficient/exponent β such that 1≤β≤21≤β≤2 . The power dependence of the amplitude is an important indicator of the photoexcited carrier recombination physics in semiconductors ranging between monopolar (β=1)(β=1) and bipolar (β=2)(β=2) limits. The study was made with laser beams of varying wavelength, power, and spotsize and with semiconductor silicon wafers with different transport parameters, especially recombination lifetime. One-dimensional and three-dimensional models of the nonlinear PCR signal dependence on β vs modulation frequency were developed. It was found that the conventional linear approach using β=1β=1 is not always consistent with experimental slopes of amplitude vs power and it may yield erroneous values of the electronic transport properties. Consideration of the fundamental and second harmonic amplitudes and phases of the PCR signal showed that the physical origin of the nonlinear dependence of the PCR amplitude on laser intensity is consistent with high-optical-injection of free-carriers in the semiconductor. The value of β can also be determined by the second harmonic-to-fundamental-amplitude ratio and is controlled by the carrier relaxation time dependence on the optically injected excess diffusive photocarrier density wave.