diode is usually only of tens of volts, so if the circuit application applies a reverse voltage to the IGBT, an additional series diode must be used. The minority carriers injected into the N-drift region take time to enter and exit or recombine at turn-on and turn-off. This results in longer switching times, and hence higher compared to a power MOSFET. The on-state forward voltage drop in IGBTs behaves very differently from power MOSFETS. The MOSFET voltage drop can be modeled as a resistance, with the voltage drop proportional to current. By contrast, the IGBT has a diode-like voltage drop (typically of the order of 2V) increasing only with the log of the current. Additionally, MOSFET resistance is typically lower for smaller blocking voltages, so the choice between IGBTs and power MOSFETS will depend on both the blocking voltage and current involved in a particular application. In general, high voltage, high current and low switching frequencies favor the IGBT while low voltage, medium current and high switching frequencies are the domain of the MOSFET. IGBT models Circuits with IGBTs can be developed and modeled with various circuit simulating computer programs such as SPICE, Saber, and other programs. To simulate an IGBT circuit, the device (and other devices in the circuit) must have a model which predicts or simulates the device's response to various voltages and currents on their electrical terminals. For more precise simulations the effect of temperature on various parts of the IGBT may be included with the simulation. Two common methods of modeling are available: device physics-based model, equivalent circuits or macromodels. SPICE simulates IGBTs using a macromodel that combines an ensemble of components like FETs and BJTs in a Darlington configuration. An alternative physics-based model is the Hefner model, introduced by Allen Hefner of the National Institute of Standards and Technology. Hefner's model is fairly complex that has shown very good results. Hefner's model is described in a 1988 paper and was later extended to a thermo-electrical model which include the IGBT's response to internal heating. This model has been added to a version of the Saber simulation software. IGBT failure mechanisms The failure mechanisms of IGBTs includes overstress (O) and wearout(wo) separately. The wearout failures mainly include bias temperature instability (BTI), hot carrier injection (HCI), time-dependent dielectric breakdown (TDDB), electromigration (ECM), solder fatigue, material reconstruction, corrosion. The overstress failure mainly include electrostatic discharge (ESD), latch-up, avalanche,