Analysis of modulated free-carrier absorption measurement of electronic transport properties of silicon wafers

Based on a three-dimensional modulated free carrier absorption (MFCA) model, theoretical analysis is performed to investigate the dependences of MFCA amplitude and phase on the electronic transport properties (the carrier lifetime, the carrier diffusivity, and the front surface recombination velocity) at different pump-to-probe separations and different modulation frequencies. The sensitivity of the multi-parameter estimate employing the dependences of the MFCA amplitude and phase on the modulation frequency at several pump-to-probe separations is theoretically compared with that employing the dependences on the pump-to-probe separation measured at several modulation frequencies. Simulation results show that the two approaches have comparable sensitivities to the electronic transport properties of silicon wafers. As for the MFCA experiments, the frequency scan data measured at different pump-to-probe separations have higher signal-to-noise ratios and therefore should be preferable to the simultaneous determination of the multiple transport properties.