Ballistic hot-electron transport in nanoscale semiconductor heterostructures: Exact self-energy of a three-dimensional periodic tight-binding Hamiltonian

As the length scale for semiconductor heterostructures approaches the regime of the lattice constant, our current theory for calculating ballistic hot-electron transport becomes inapplicable. In this case, a method such as the Green’s function formalism should be used to calculate ballistic electron transmission functions from the exact, periodic lattice potential. We present a method for directly calculating the exact surface Green’s function for three-dimensional periodic leads which is necessary for such a scheme. Except in cases of high crystal symmetry, the method is limited by the difficulty to solve a nonsymmetric matrix Riccati equation.