Ebers-Moll Model of Transistors

Ebers–Moll transistor model, also known as the coupled diode model, was developed by Ebers and Moll in the year 1954. It is an ideal model for a bipolar transistor and is applicable for all four regions of transistor operation. The model involves two ideal diodes and two ideal current sources. Figure below shows the Ebers–Moll model for an NPN transistor.

Ebers–Moll model for an NPN transistor

Figure below shows the Ebers–Moll model for a PNP transistor.

Ebers–Moll model for a PNP transistor

The two diodes represent the base–emitter and the base–collector diodes and are connected back-to-back. The reverse saturation currents through the base–emitter and the base–collector diodes are I_ES and I_CS, respectively. Two current sources are in shunt with the diodes and their values depend upon the current flowing through the diodes. They quantify the transport of minority carriers through the base region, that is, they account for the minority-carrier transport across the base.
The equations for the collector, emitter and base currents in the Ebers–Moll model are given by

The Ebers–Moll parameters are related by the expression

It is impossible to construct a transistor by simply connecting two diodes back-to-back in a series. A cascade arrangement of two diodes exhibits transistor properties only if the carriers injected by one junction diffuse into the second junction.