Surface States - Tamm States

Tamm States

Surface states that are calculated in the framework of a tight-binding model are often called Tamm states. In the tight binding approach, the electronic wave functions are usually expressed as a linear combinations of atomic orbitals (LCAO), see figure 5. In this picture, it is easy to comprehend that the existence of a surface will give rise to surface states with energies different from the energies of the bulk states: Since the atoms residing in the topmost surface layer are missing their bonding partners on one side their orbitals have less overlap with the orbitals of neighboring atoms. The splitting and shifting of energy levels of the atoms forming the crystal is therefore smaller at the surface than in the bulk.

If a particular orbital is responsible for the chemical bonding, e.g. the sp3 hybrid in Si or Ge, it is strongly affected by the presence of the surface, bonds are broken, and the remaining lobes of the orbital stick out from the surface. They are called dangling bonds. The energy levels of such states are expected to significantly shift from the bulk values.

In contrast to the nearly free electron model used to describe the Shockley states, the Tamm states are suitable to describe also transition metals and wide bandgap semiconductors.