Self-consistent procedure including envelope function normalization for full-zone Schr?dinger-Poisson problems with transmitting boundary conditions

摘要： In the quantum mechanical simulation of exploratory semiconductor devices, continuum methods based on a k·p/envelope function model have the potential to significantly reduce the computational burden compared to prevalent atomistic methods. However, full-zone k·p/envelope function simulation approaches are scarce and existing implementations are not self-consistent with the calculation of the electrostatic potential due to the lack of a stable procedure and a proper normalization of the multi-band envelope functions. Here, we therefore present a self-consistent procedure based on a full-zone spectral k·p/envelope function band structure model. First, we develop a proper normalization for the multi-band envelope functions in the presence of transmitting boundary conditions. This enables the calculation of the free carrier densities. Next, we construct a procedure to obtain self-consistency of the carrier densities with the electrostatic potential. This procedure is stabilized with an adaptive scheme that relies on the solution of Poisson’s equation in the Gummel form, combined with successive underrelaxation. Finally, we apply our procedure to homostructure In0.53Ga0.47As tunnel field-effect transistors (TFETs) and staggered heterostructure GaAs0.5Sb0.5/In0.53Ga0.47As TFETs and show the importance of self-consistency on the device predictions for scaled dimensions.