EbersMollmodel

The Ebers–Moll model is a physics-based mathematical description of a bipolar junction transistor (BJT) introduced by John J. Ebers and Samuel Moll in 1954. It expresses the emitter, base, and collector currents as nonlinear functions of the base–emitter and base–collector voltages. The model captures forward-active, reverse-active, and saturation regions by using two controlling diodes and transport factors that describe carrier flow across the transistor.

The core equations relate the terminal currents to the voltages as follows (with V_T = kT/q, the thermal voltage):

I_E = I_Es [exp(V_BE / V_T) − 1] − α_R I_CS [exp(V_BC / V_T) − 1]

I_C = α_F I_Es [exp(V_BE / V_T) − 1] − I_CS [exp(V_BC / V_T) − 1]

I_B = I_E − I_C

Here, I_Es and I_CS are the forward-emitter and reverse-saturation currents, respectively; α_F and α_R are forward and reverse transport factors (related to current gains). These equations describe how carrier injection across the base–emitter and base–collector junctions generates the observed currents, with the base current arising from the difference between emitter and collector currents.

Applications and scope: the Ebers–Moll model provided the foundational understanding of BJT behavior and influenced early transistor analysis and circuit design, as well as compact models used in early circuit simulators. It forms the basis for more advanced analytic models, such as the Gummel–Poon model, and remains a reference for understanding exponential transistor behavior. Limitations include its neglect of high-level injection effects, series resistances, and frequency-dependent phenomena, making it less accurate for modern high-speed or high-current devices without extensions.