  The characteristics of shallow hydrogen-like muonium (Mu) states in nominally undoped ZnO and CdS (0001) crystals have been studied close to the surface at depths in the range of 10 nm - 180 nm by using low-energy muons, and in the bulk using conventional muSR. The muon implantation depths are adjusted by tuning the energy of the low-energy muons between 2.5 keV and 30 keV. We find that the bulk ionization energy of the shallow donor-like Mu state is lowered by about 10 meV at a depth of 100 nm, and continuously decreasing on approaching the surface. At a depth of about 10 nm the ionization energy is further reduced by 25-30 meV compared to its bulk value. We attribute this change to the presence of electric fields due to band bending close to the surface, and we determine the depth profile of the electric field within a simple one-dimensional model. 
Depth dependence of the ionization energy of shallow hydrogen states in   ZnO and CdS