SINGLY-IONIZED-IMPURITY SCATTERING IN DEGENERATE MATERIAL

The work of Blatt has been extended to include ionized-impurity scattering in degenerate n-type material having a single-valley conduction band and a spherical effective mass. The transport cross section Q has been calculated for a potential of the Thomas-Fermi type where the inverse screening length is fixed by the Friedel sum rule. By writing the Schrödinger equation in terms of dimensionless variables, we have found that, as a consequence of the sum rule, Qk2 is a universal function of a0k, where a0 is the first Bohr radius in the material and k is the Fermi wave number. A comparison of the computed Qk2 with QBk2 (the Born-approximation result for Thomas-Fermi screening, which is also a universal function of a0k) shows that for a0k<0.3. the Born approximation overestimates the resistivity, a result which is typical for metals. However, for larger a0k, which corresponds to many degenerately doped semiconductors, the Born approximation understimates the resistivity, the discrepancy being as much as 51% at a0k=0.8. For a0k>10, the Born approximation is in error by no more than 3%. © 1968 The American Physical Society.