A model for the turn-on characteristics of separate-absorber-multiplier InP-based Geiger-mode Avalanche Photodiodes (APDs) has been developed. Verilog-A was used to implement the model in a manner that can be incorporated into circuit simulations. Rather than using SPICE elements to mimic the voltage and current characteristics of the APD, Verilog-A can represent the first order nonlinear differential equations that govern the avalanche current of the APD. This continuous time representation is fundamentally different than the piecewise linear characteristics of other models. The model is based on a driving term for the differential current, which is given by the voltage overbias minus the voltage drop across the device?s space-charge resistance RSC. This drop is primarily due to electrons transiting the separate absorber. RSC starts off high and decreases with time as the initial breakdown filament spreads laterally to fill the APD. With constant bias voltage, the initial current grows exponentially until space charge effects reduce the driving function. With increasing current the driving term eventually goes to zero and the APD current saturates. On the other hand, if the APD is biased with a capacitor, the driving term becomes negative as the capacitor discharges, reducing the current and driving the voltage below breakdown. The model parameters depend on device design and are obtained from fitting the model to Monte-Carlo turn-on simulations that include lateral spreading of the carriers of the relevant structure. The Monte-Carlo simulations also provide information on the probability of avalanche, and jitter due to where the photon is absorbed in the APD.