Magnetic Freeze-Out of Electrons in Extrinsic Semiconductors

The density of states was derived and the statistics of conduction electrons were studied for the case of a strongly doped compensated semiconductor in an external magnetic field. The tail of the density of states and the spread in the energy distribution of impurity levels were investigated, and the temperature and magnetic field dependences of the concentration of electrons not localized in impurities were calculated. It is shown that, because of the tail of the density of states, this concentration approaches a finite limit when $T\to 0$. The freeze-out of carriers begins when the magnetic field attains such a value that the binding energy becomes larger than the rms potential energy of an electron in the field of the impurities. For sufficiently large magnetic fields, the Fermi level will drop into the tail, although the electrons may remain degenerate. This last conclusion will also be true for uncompensated semiconductors.