Polarization-induced electron island in semiconductor grain placed into pyroelectric matrix

We consider the electron distribution in an n-type semiconductor grain inserted into a pyroelectric matrix. We show that for typical values of parameters, the electric field induced in the grain by the pyroelectric spontaneous polarization is very strong and cannot be screened by the electrons in the grain. This field removes the electrons from donors and leads to the formation of a two-dimensional electron island on the surface of the grain with the size much smaller than the grain size. This effect can be used for creation of small two-dimensional quantum dots.