Abstract:
A new quantum model of electron accumulation at positively charged boundaries of semiconductor films has been developed. It is based on the well-known concepts of quantum confinement of transverse electron motion in a uniform electric field, the role of which is played by the effective field of attraction to positive surface donor centers. Electrons with a surface density equal to the donor concentration occupy the corresponding quasi-discrete states according to the Fermi statistics. At reasonable concentrations all the electrons of the accumulation layer are mainly concentrated at the first quantum-confinement level. Ultra-high built-in fields on the order of the atomic level (10$^8$ V/cm) correspond to the onset of filling the third level. The potential profile, which describes the interaction of the accumulation-layer electrons with other charged particles (including holes) is calculated by double integration of the Poisson equation with the electron density in the form of squares of the corresponding segments of the Airy function. Its boundary value–the surface potential–describes the effect of the electron-accumulation layer on the external electric circuit. The obtained dependence of the surface potential on the resulting boundary electric field (including that induced by the built-in charge) is easily transformed into the corresponding capacitance-voltage characteristics.
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