Schrödinger–Poisson–drift–diffusion modeling of wurtzite materials in cylindrical geometries

Abstract

A Schrödinger–Poisson–drift–diffusion framework is presented for efficient simulation of semiclassical carrier transport near equilibrium. To reduce computational cost, a partitioned scheme is employed in which drift–diffusion equations are solved across the full device, while the Schrödinger equation is applied selectively in regions where quantum confinement is significant. Conduction-band states are computed using a one-band effective mass Hamiltonian. For the valence band, we introduce a novel six-band k⋅p Hamiltonian for wurtzite materials formulated in cylindrical coordinates that leads to a real and symmetric Hamiltonian when discretized using the finite element method. Computed quantum states modify the carrier statistics via an effective potential term that couples into the drift–diffusion model. Assuming a linear dependence of quantum energy levels on the local potential, the proposed drift–diffusion scheme achieves convergence in typically five iterations per voltage step. This approach captures quantum effects in complex geometries while reducing a 3D problem to an equivalent 2D formulation. Efficiency of the method is demonstrated for a nanowire superlattice structure.