Sensitivity analysis of laterally resolved free carrier absorption determination of electronic transport properties of silicon wafers

Abstract

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.

Measurement accuracy analysis of the free carrier absorption determination of the electronic transport properties of silicon wafers

“…The excess carrier absorption in the probe beam (freecarrier absorption) induces the fractional modulation of the probe beam intensity, which is proportional to the number of free carriers that the probe beam encounters along its path within the sample. Then the MFCA signal can be expressed as follows: [18] ∆I(ω; r)…”

“…( 1) that the entire MFCA data contain information of the transport properties of the specimen, the size of both the pump and the probe beams and their separation, as well as the modulation frequency of the pump beam. Therefore, the three transport parameters, τ , D, and s 1 , of the semiconductor wafer can be extracted by measuring the dependence of the MFCA signal on the modulation frequency (FS-MFCA) [2] or on the pump-probe-beam separation (LR-MFCA) [17,18] via multi-parameter fitting.…”

“…Here, the mean square variance for LR-MFCA is defined in Ref. [18] and that for FS-MFCA defined in Ref. [19].…”

“…The experimental parameters and their respective errors are set according to the experimental details. [17,18] In our simulations, RSRV is fixed to 10 4 cm/s, since RSRV has little effect on the MFCA signal and is an insignificant transport parameter of silicon wafers used in micro-electronic devices. [8] In the MFCA experiment, the amplitude and phase measurement errors depend on the time constant of the lock-in amplifier.…”

“…Until recently, a laterally resolved MFCA technique (LR-MFCA) was proposed by Zhang et al, [17] which has a number of potential advantages over conventional MFCA and other existing methods, and it has been employed to characterize the electronic transport properties of semiconductors. It was justified in a previous paper [18,19] that unlike the dependences of conventional frequency-scan MFCA (FS-MFCA) and PCR signals on the modulation frequency, the LR-MFCA signals are dependent on the pump-probebeam separation and highly sensitive to the lifetime and FSRV, especially to the diffusivity and thus D, τ and s 1 can be simultaneously obtained with high precision. However, until now, no quantitative analysis has yet been done regarding the relative determination accuracies of the transport properties by the FSand LR-MFCAs.…”