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.