Effective-mass approximation for shallow donors in uniaxial indirect band-gap crystals and application to 4H-SiC

• The effective-mass theory is applied for description of the electronic states of shallow donors in indirect band-gap uniaxial crystals, which have three different components of the electron effective-mass tensor, and two different components of the tensor of the dielectric constant. The Hamiltonian in the resulting Schrödinger equation for the envelope function has D2h symmetry and, after proper parametrization, a nonvariational numerical method is used for its solution. Two particular cases of D∞h symmetry are identified and discussed separately. The comparison between theory and experiment for the 4H polytype of silicon carbide is revised using the least-squares method to determine the binding energies of the ground state of the most shallow nitrogen donor in this material, its valley-orbit split-off counterpart, and the mean value of the dielectric constant, and completed with calculation of the theoretical transition probabilities. In addition, the lowest-lying binding energies of the states, between which optical transitions are allowed, are calculated on a grid of values of the two parameters describing the anisotropy and the tabulated values can be used for interpolation to describe other materials. © 2006 The American Physical Society.

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