  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 GaAs thin films over a wide range of
carrier densities ($2\times 10^{17}$ to $1\times 10^{19}$ cm$^{-3}$). The
spectral shift and broadening of CL spectra induced by shallow dopant states
and band filling are the signature doping. We fit the whole spectral lineshapes
with the generalized Planck's law and refined absorption models to extract the
bandgap narrowing (BGN) 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 density using CL. Taking
advantage of the high spatial resolution of CL, it can be used to map the
doping in GaAs nanostructures, and it could be extended to other semiconductor
materials.
