  Precise control of doping in single nanowires (NWs) is essential for the
development of NW-based devices. Here, we investigate a series of MBE-grown
GaAs NWs with Be (p-type) and Si (n-type) doping using high-resolution
cathodoluminescence (CL) mapping at low- and room-temperature. CL spectra are
analyzed selectively in different regions of the NWs. Room-temperature
luminescence is fitted with the generalized Planck law and an absorption model,
and the bandgap and band tail width are extracted. For Be-doped GaAs NWs, the
bandgap narrowing provides a quantitative determination of the hole
concentration ranging from about $1\times 10^{18}$ to $2\times
10^{19}$~cm$^{-3}$, in good agreement with the targeted doping levels.
High-resolution maps of the hole concentration demonstrate the homogeneous
doping in the pure zinc-blende segment. For Si-doped GaAs NWs, the electron
Fermi level and the full-width at half maximum of low-temperature CL spectra
are used to assess the electron concentration to approximately $3\times
10^{17}$ to $6\times 10^{17}$~cm$^{-3}$. These findings confirm the difficulty
to obtain highly-doped n-type GaAs NWs, maybe due to doping compensation.
Notably, signatures of high concentration (5--9$\times 10^{18}$~cm$^{-3}$) at
the very top of NWs are unveiled.
