Laterally resolved modulated free-carrier absorption (MFCA) is applied to the simultaneous determination of the electronic transport properties of semiconductor wafers. A rigorous three-dimensional carrier diffusion model is used to fit the observed dependences of the MFCA signal amplitude and phase on the separation between the pump and probe laser spots, measured at several modulation frequencies covering an appropriate range. This leads to a simultaneous and unambiguous determination of the values of three transport parameters, namely, the minority-carrier lifetime τ, the carrier diffusivity D, and the front surface recombination velocity s1. The extracted values for a n-type Si wafer with a resistivity of 7–10Ωcm are 53μs (τ), 16.6cm2∕s (D), and <200cm∕s (s1), respectively.
Simulations are performed to investigate the uniqueness of simultaneous determination of electronic transport properties (the carrier lifetime, the carrier diffusivity, and the front surface recombination velocity) of silicon wafers by laterally resolved modulated free carrier absorption (MFCA) and multiparameter fitting. The dependences of MFCA amplitude and phase on these transport properties at different pump-probe-beam separations and modulation frequencies are analyzed. The uncertainties of the fitted parameter values are analyzed by investigating the dependences of a mean square variance including both the amplitude error and phase error on corresponding electronic transport parameters. Simulation results show that the electronic transport parameters can be determined accurately through fitting experimental MFCA data carrying both frequency- and space-domain information of carrier diffusion to a rigorous MFCA model. Among the three transport parameters, the carrier diffusivity can be determined most precisely, with an uncertainty of less than ±5%, due to the highest sensitivity of the laterally resolved MFCA signal to the diffusivity. The highly accurate determination of the diffusivity further improves the precision of the carrier lifetime and the front surface recombination velocity values simultaneously determined via multiparameter fitting. Experiments were performed with a silicon wafer and the results were in good agreement with the theoretical simulations.
Computer simulations are carried out to investigate the sensitivity of simultaneous determination of three electronic transport properties (carrier lifetime, carrier diffusivity, and front surface recombination velocity) of silicon wafers by modulated free carrier absorption (MFCA) via a multiparameter fitting procedure. The relative accuracy of the transport parameter determination by laterally resolved MFCA (LR-MFCA), in which the amplitude and phase are measured as functions of the pump-probe-beam separation at several modulation frequencies covering an appropriate range, and by conventional frequency-scan MFCA (FS-MFCA), in which only the modulation frequency dependences of the amplitude and phase are recorded, is theoretically analyzed and experimentally estimated by calculating the dependence of the mean square variance on individual transport parameter via a multiparameter estimation process. Simulated and experimental results show that the determination of the transport properties of silicon wafers by LR-MFCA are more accurate, compared with that by FS-MFCA. Comparative experiments are performed with a silicon wafer and the estimated uncertainties of the carrier diffusivity; lifetime and front surface recombination velocity are approximately ±3.7%, ±25%, and ±35% for LR-MFCA and ±7.5%, ±31%, and ±24% for FS-MFCA, respectively.
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