Scattering in quantum simulations of silicon nanowire transistors

One of the most interesting devices under exploration now is the nanowire transistor. Because of the size of these devices, there have been many approaches to implement full quantum mechanical simulations. To date, most of these approaches have considered only ballistic transport or impurity scattering through the self-consistent potential. However, in order to understand the operation of any type of semiconductor device, one must consider the effects of scattering. For many years, Monte Carlo has been the workhorse that has yielded great insight into the operation of a wide variety of semiconductor devices because of the ease in treating various scattering effects, and these approaches have been modified for simple quantum effects. But in these very small devices, a more exact treatment of the quantum effects is required. To address this problem, we have developed a proper real-space self-energy which can be included within the Hamiltonian formalism for either the recursive scattering matrix approach or the non-equilibrium Green's function approach. More importantly, this treatment with the proper self-energy is norm-conserving but converts the Hamiltonian to a non-Hermitian form, as expected. When the model is applied to a gated quantum wire transistor structure under bias, we find that the scattering due to phonons causes the electrons to scatter to higher subbands than previously available during simple ballistic transport, with the result that the ballistic-to-diffusive transition in Si devices occurs for gate lengths of the order of 1 nm.