Theoretical study on influence of photon reabsorption on photocarrier radiometric characteristics of silicon wafers

Abstract

In microelectronic and photovoltaic industry, semiconductors are the base materials in which impurities or defects have a serious influence on the properties of semiconductor-based devices. The determination of the electronic transport properties, i.e., the carrier bulk lifetime (<inline-formula><tex-math id="M41">\begin{document}$\tau $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181889_M41.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181889_M41.png"/></alternatives></inline-formula>), diffusion coefficient (<i>D</i>) and front surface recombination velocity (<i>S</i>₁), is important in the evaluation of semiconductor materials. In this paper, the influence of reabsorption of spontaneously emitted photons within silicon wafers on conventional frequency domain photocarrier radiometric (PCR) is theoretically analyzed. The model with photon reabsorption, proposed by our previous paper, in which both band-to-band absorption and free carrier absorption are taken into account, is used. It is shown that the influence strongly depends on not only the doping level, but also the excess carrier density and its distribution, which are sensitive to the electronic transport properties. The influences of photon reabsorption on PCR amplitude and phase increase with doping level and carrier lifetime increasing. While, as the diffusion coefficient and the front surface recombination velocity increase, the influence of photon reabsorption on PCR amplitude decreases but on PCR phase increases. If photon reabsorption is ignored in the determination of the electronic transport parameters for high-doping silicon wafers via multi-parameter fitting, there are large errors for the fitted results. For a sample with <inline-formula><tex-math id="M42">\begin{document}$\tau $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181889_M42.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181889_M42.png"/></alternatives></inline-formula> = 50 μs, <i>D</i> = 20 cm²/s, and <i>S</i>₁ = 10 m/s, if the effect of photon reabsorption is ignored, the fitting results with conventional PCR model are 55.66 μs, 19.98 cm²/s, and 11.94 m/s, and the corresponding deviations from the true value are 11.33%, 0.10%, and 19.40%, respectively. In addition, simulation results show the effect of photon reabsorption can be greatly reduced with a suitable filter in front of the detector, while still enabling the majority of the emitted signal to be captured. For example, with a 1100 nm long-pass filter, the fitted results for the same sample above are 51.43 μs, 20.19 cm²/s, and 9.88 m/s with the relative errors of 2.86%, 0.95%, and 1.23%, respectively. It should be pointed out that an infinitely steep cut-on edge of the long-pass filter is assumed in our simulations, while in fact the influences of the filter on PCR signal and the fitted results should be further considered.