Boundary Condition for the Modeling of Open‐circuitedDevices in Non‐equilibrium

Abstract

A boundary condition specifically designed to model open-circuited devices in a macroscopic device simulator is introduced. Other simulation techniques have relied on an external circuit model to regulate the current flow out of a contact thus allowing the potential to remain the controlled variable at the boundary. The limitations of these methods become apparent when modeling open-circuited devices with an exceptionally small or zero output current. In this case, using a standard ohmic-type Dirichlet boundary condition would not yield satisfactory results and attaching the device to an arbitrarily large load resistance is physically and numerically unacceptable. This proposed condition is a true current controlled boundary where the external current is the specified parameter rather than the potential. Using this model, the external current is disseminated into electron and hole components relative to their respective concentration densities at the contact. This model also allows for the inclusion of trapped interface charge and a finite surface recombination velocity at the contact. An example of the use of this boundary condition is performed by modeling a silicon avalanche photodiode operating in the flux integrating mode for use in an imaging system. In this example, the device is biased in steady-state to just below the breakdown voltage and then open-circuited. The recovery of the isolated photodiode back to its equilibrium condition is then determined by the generation lifetime of the material, the quantity of signal and background radiation incident upon the device, and the impact ionization rates.