Applicability of the High Field Model: A Preliminary Numerical Study

In a companion presentation, we have discussed the theory of a mesoscopic/macroscopic model, which can be viewed as an augmented drift-diffusion model. Here, we describe how that model is used. The device we consider for this presentation is the one dimensional GaAs n+-n-n+ structure of length 0.8μm. First, a full hydrodynamic (HD) model, proven reliable when compared with Monte Carlo simulations, is used to simulate the device via the ENO finite difference method. As applied to the full device, the new model is not necessarily superior to traditional drift-diffusion (DD). Indeed, when we plot the quantity η = μ0E/ √ kT0 m , where μ0 is the mobility constant and E = −φ′ is the electric field, we verify that the high field assumption η > 1, required for the high field model, is satisfied only in an interval given approximately by [0.2, 0.5]. When we run both the DD model and the new high field model in this restricted interval, with boundary conditions of concentration n and potential φ provided by the HD results, we demonstrate that the new model outperforms the DD model. This indicates that the high field and DD models should be used only in parts of the device, connected by a transition kinetic regime. This will be a domain decomposition issue involving interface conditions and adequate numerical methods.