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

Direct observation of hole carrier density profiles and their light induced manipulation at the surface of Ge