  We demonstrate that, by using low-energy positive muon ($\mu^+$) spin
spectroscopy as a local probe technique, the profiles of free charge carriers
can be directly determined in the accumulation/depletion surface regions of p-
or n-type Ge wafers. The detection of free holes is accomplished by measuring
the effect of the interaction of the free carriers with the $\mu^+$ probe spin
on the observable muon spin polarization. By tuning the energy of the
low-energy $\mu^+$ between 1 keV and 20 keV the near-surface region between 10
nm and 160 nm is probed. We find hole carrier depletion and electron
accumulation in all samples with doping concentrations up to the $10^{17}$
cm$^{-3}$ range, which is opposite to the properties of cleaved Ge surfaces. By
illumination with light the hole carrier density in the depletion zone can be
manipulated in a controlled way. Depending on the used light wavelength
$\lambda$ this change can be persistent ($\lambda = 405, 457$ nm) or
non-persistent ($\lambda = 635$ nm) at temperatures $< 270$ K. This difference
is attributed to the different kinetic energies of the photo-electrons.
Photo-electrons generated by red light do not have sufficient energy to
overcome a potential barrier at the surface to be trapped in empty surface
acceptor states. Compared to standard macroscopic transport measurements our
contact-less local probe technique offers the possibility of measuring carrier
depth profiles and manipulation directly. Our approach may provide important
microscopic information on a nanometer scale in semiconductor device studies.
