Direct Observation of Hole Carrier-Density Profiles and Their Light-Induced Manipulation at the Surface of Ge

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.