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 Schrodinger equation for the envelope function has D-2h symmetry and, after proper parametrization, a nonvariational numerical method is used for its solution. Two particular cases of D-infinity 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.