Calculation of the grain potential barrier in the poly− and nanocrystalline semiconductors

The distribution of potential and parameters of potential barrier in semiconductor crystallite was calculated numerically. The calculation was carried out in spherical crystallite with evenly distributed donors and surface states. The calculation assumed that the surface charge is screened by both ionized donors and free electrons, the contribution of which cannot be neglected in semiconductors with high concentration of free electrons. The height of potential barrier is shown to nonmonotonically depend on the concentration of donors. The dependence of height of potential barrier on the concentration of donors may be divided into two part. One part of dependence describes the fully depleted crystallite and the second part describes the party depleted crystallite. On the first part the height of potential barrier increases with the donor concentration but on the second part the height of potential barrier decreases. The height of the potential barrier increases with increasing of concentration of surface states. The possibility of existing of potential barriers is estimated in nano− and polycrystalline metal oxide semiconductors used as sensitive layers of gas sensors. It is concluded that if the radius of crystal grains in metal oxide semiconductors does not exceed 10 nm, the explanation of the sensitivity of the sensor to gas by using a commonly barrier model seems unlikely. 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.

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