Carrier Diffusivity Measurement in Silicon Wafers Using Free Carrier Absorption

In this article, it has been shown that the modulated free carrier absorption method (MFCA) can be used to determine unambiguously and without contact the carrier diffusivity of semiconductor wafers. The linear dependence of the phase on the distance of pump and probe beams are investigated with computer simulation, and then it has been found that at high frequency the slope of the MFCA phase versus distance depends solely on the carrier diffusivity. Hence, the carrier diffusivity can be extracted from the slope of the phase versus distance. Experiments were carried out on an n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-type Si wafer with 7 Ω·\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega \, \cdot $$\end{document} cm to 10 Ω·\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega \, \cdot $$\end{document} cm resistivity and (525 ±\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm $$\end{document} 20) μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}m thickness. Comparing the experimental fitted results to those by fitting the MFCA amplitude and phase on the pump-probe-beam separation measured at several modulation frequencies to the rigorous three-dimensional carrier diffusion model, the fitted results by both methods agreed well. This shows that the simplified model can be used to determine the carrier diffusivity with high precision.