A New Technique for Including Overshoot Phenomena in Conventional Drift-Diffusion Simulators

Multilevel solution of augmented drift‐diffusion equations

“…These oscillations eventually pollute the solution enough to cause divergence of the Gummel iterations. The augmented results with γ = 1.5 × 10 ‐11 cm 2 /V compare favourably with those in [8] and are qualitively similar to those in [6]. Figure 2 shows results from [22] for the same device and bias using a Monte Carlo model and two hydrodynamic models.…”

“…The model problem used for valuation and numerical tests is an n ‐ i ‐ n diode with n + = 5 × 10 17 cm ‐2 and i = 2 × 10 15 cm ‐2 and abrupt junctions. The problem was chosen for comparison to existing results for augmented drift‐diffusion, hydrodynamic and Monte Carlo simulations[6, 8, 22]. Although the problem is 1D, a 2D solver is used with zero flux Neumann conditions as natural boundary conditions on the boundaries parallel to the x ‐axis.…”

“…The drift‐diffusion equations can be augmented to accommodate hot carrier effects by adding a velocity term to the electron current density expression. This added term is proportional to the total rate of change of the electric field E [6, 7] or to the spatial rate of change of E [8, 9]. In one dimension we get…”

“…Hence, only the mobility coefficient changes, while the structure of the equations is unchanged and existing methods and software can be applied to obtain information on hot carrier effects. The factor γ is determined either experimentally or numerically using Monte Carlo tests and is a function of E and dE / dt , with the dependence shown in[6, 7]. For the purposes of this research, it was assumed to be constant for E > 0 or E < 0, and an odd function of E .…”

“…The drift‐diffusion equations of semiconductor device theory have proven to be robust and efficient for modelling a practical range of semiconductor problems[1, 2, 3, 4]. The validity of the drift‐diffusion approximation breaks down, however, at small device lengths due to the fact that it does not model non‐local electric field effects, including velocity overshoot, which are important in regions where the electric field is changing rapidly[5, 6, 7, 8, 9, 10, 11]. The discretized hydrodynamic equations, which do model non‐local effects, are much more expensive to solve at present.…”