Quantization effects in ZnO accumulation layers in contact with an electrolyte

Accumulation layers with excess surface-electron concentration $\Delta N$ of ${10}^{14}$ ${\mathrm{cm}}^{-2\mathrm{}}$ were produced on ZnO surfaces in contact with an electrolyte. Measurements of $\Delta N$ as a function of the surface potential barrier are presented, as well as detailed results of self-consistent quantum calculations. The self-consistent calculations were carried out on the basis of the effective-mass approximation. They take into account the exchange interaction and the penetration of the surface-electron wave functions into the electrolyte. The agreement between theory and experiment is reasonably good.