Accuracy analysis for the determination of electronic transport properties of Si wafers using modulated free carrier absorption

Abstract

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.

Three-dimensional transient model for time-domain free-carrier absorption measurement of excess carriers in silicon wafers

“…The modulation frequency 10 kHz was chosen according to the lifetime values of the samples used in the experiments, that is, to have ffiffiffiffiffiffiffiffiffiffi ffi 2pf c s p % 1. 6,22 In this case the temporal profiles of the MFCA signals were approximately most sensitive to the transport parameters, especially the carrier lifetime. The transport behavior of the carriers was monitored by a continuous-wave probe laser beam (1570 nm) with photon energy below the band gap.…”

“…6,21 Briefly, a super-band-gap pump laser beam (660 nm) was square-wave modulated by a function generator and focused onto the sample surface, and excess carriers were generated in the wafer. The modulation frequency 10 kHz was chosen according to the lifetime values of the samples used in the experiments, that is, to have ffiffiffiffiffiffiffiffiffiffi ffi 2pf c s p % 1.…”

“…Modulated free carrier absorption (MFCA) technique has been widely used for semiconductor characterization to determine the electronic transport properties, [1][2][3][4][5][6][7][8] namely, the carrier recombination lifetime, the carrier diffusion coefficient, and the surface recombination velocities. In MFCA, a modulated super-band-gap laser beam (the pump beam) is used to generate free carriers in semiconductor wafers, and the density of the photo-generated free carriers is monitored by a sub-bandgap laser beam (the probe beam) due to the absorption of the probe beam intensity by the photo-generated free carriers.…”

Influence of probe beam size on signal analysis of modulated free carrier absorption technique

“…Due to the absorption of the excess free carriers to the probe beam, the intensity of the transmitted probe beam is modulated, resulting in the MFCA signal. The MFCA signal is the ratio of the modulated ( I) and unmodulated (I) portions of the intensity of the transmitted probe beam [5], which can be expressed as follows: (6) Here r d and I 0 are radius and centre intensity of the probe beam, and d is the separation between the pump and probe beams. I is proportional to the number of excess free carriers in the volume where the probe beam covers.…”

Monitoring of amorfization of the oxygen implanted layers in silicon wafers using photothermal radiometry and modulated free carrier absorption methods

“…Plasma waves can be detected by the measurement of the periodical component of the intensity of the IR radiation of the samples, in a PTR method, or by the measurement of the intensity of the periodical component of the transmitted probing IR beam of light in a MFCA method, or by the periodical photoluminescence in a photocarrier radiometry (PCR) method [1][2][3]. Analysis of the frequency characteristics enables determination of the recombination parameters of semiconductors with the PTR method [4,5] and the MFCA method [6][7][8][9][10][11][12]. For one layer samples, it is possible to determine the lifetime of carriers and the velocity of the surface recombination from the frequency amplitude and phase PTR or MFCA characteristics.…”