Spin structure of impurity band in semiconductors in two- and three-dimensional cases

The exchange interaction between electrons located at different randomly di stributed impurities is studied for small density of impurities. The single t-triplet splitting 2J(R) is calculated for two Coulomb centers at a distan ce R, interpolated formulas are found which work for all distances R from z ero to infinity. The data from atomic physics are used for the interpolatio n in the three-dimensional case. For the two-dimensional case the original calculations are performed to find asymptotic behavior of the splitting at large R, the splitting for the "two-dimensional helium atom" (R=0), and the splitting at R=a(B), where a(B) is the effective Bohr radius. The spin str ucture of the impurity band is described by the Heisenberg Hamiltonian. The ground state of a system consists of localized singlets. The new results a re obtained for the distribution of the singlet pairs in the ground state,T hese results are exact at low density. The problem is reduced to a nontrivi al geometric problem, which is solved in the mean-field approximation and b y computer modeling. The density of free electrons is found as a function o f temperature and the distribution function of the singlet-triplet transiti ons energies is calculated. Both functions are given in an analytical form. [S0163-1829(99)13631-2].