Quantitative Assessment of Carrier Density by Cathodoluminescence. I. Ga As Thin Films and Modeling

Doping is a fundamental property of semiconductors and constitutes the basis of modern microelectronic and optoelectronic devices. Their miniaturization requires contactless characterization of doping with nanometer-scale resolution. Here, we use low- and room-temperature cathodoluminescence (CL) measurements to analyze $p$-type and $n$-type $\mathrm{Ga}\mathrm{As}$ thin films over a wide range of carrier densities ($2\ifmmode\times\else\texttimes\fi{}{10}^{17}$ to $1\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$). The spectral shift and broadening of CL spectra induced by shallow dopant states and band filling are the signature of doping. We fit the whole spectral lineshapes with the generalized Planck law and refined absorption models to extract the bandgap narrowing and the band tail for both doping types, and the electron Fermi level for $n$ doping. This work provides a rigorous method for the quantitative assessment of $p$-type and $n$-type carrier densities using CL. Taking advantage of the high spatial resolution of CL, it can be used to map the doping in $\mathrm{Ga}\mathrm{As}$ nanostructures, and it could be extended to other semiconductor materials.