Prediction of Potential Barrier at Crystallite Boundaries in Poly- and Nanocrystalline Semiconductors

Abstract

The distribution of the potential and the parameters of the potential barrier for electrons in semiconductor crystallite is numerically calculated. The calculations are made in a spherical crystallite with uniformly distributed surface states and uniformly distributed donors. It is considered in the calculations that the surface charge is screened both by the ionized donors and on free electrons; the contibution of free electrons should not be neglected in semiconductors with a high concentration of free electrons. It is demonstrated that the height of the potential barrier depends non-monotonically on the concentration of the donors in the crystallite. Moreover, in the curve of the height of the potential barrier as a function of the concentration of the donors, it is possible to highlight two segments corresponding to the cases of the complete and partial depletion of the crystallite. The height of the potential barrier increases with the concentration of the donors in the first segment and decreases in the second segment. It is established that the height of the potential barrier increases with the increase in the concentration of the surface states. The possibility of the existence of surface potential barriers in nano- and polycrystalline metal-oxide semiconductors, which are applied as a sensitive layer of gas sensors, is estimated. It is concluded that if the crystallite radius in metal-oxide semiconductors does not exceed 10 nm the sensor’s sensitivity to gas could hardly be attributed to the usual barrier model. It is demonstrated that shape of crystallite and the contribution of free electrons to screening of surface charge have to be taken into account to calculation of width of potential barrier.