Early effect
The Early effect, named after its discoverer James M. Early, is the variation in the effective width of the base in a bipolar junction transistor (BJT) due to a variation in the applied base-to-collector voltage.
A greater reverse bias across the collector–base junction, for example, increases the collector–base depletion width, thereby decreasing the width of the charge carrier portion of the base.
In Figure 1, the neutral (i.e. active) base is green, and the depleted base regions are hashed light green.
The neutral emitter and collector regions are dark blue and the depleted regions hashed light blue.
Under increased collector–base reverse bias, the lower panel of Figure 1 shows a widening of the depletion region in the base and the associated narrowing of the neutral base region.
The collector depletion region also increases under reverse bias, more than does that of the base, because the collector is less heavily doped than the base.
The principle governing these two widths is charge neutrality.
Base-narrowing has two consequences that affect the current: Both these factors increase the collector or "output" current of the transistor with an increase in the collector voltage, but only the second is called Early effect.
In the forward active region the Early effect modifies the collector current (
), as typically described by the following equations:[1][2] where Some models base the collector current correction factor on the collector–base voltage VCB (as described in base-width modulation) instead of the collector–emitter voltage VCE.
[3] Using VCB may be more physically plausible, in agreement with the physical origin of the effect, which is a widening of the collector–base depletion layer that depends on VCB.
Computer models such as those used in SPICE use the collector–base voltage VCB.
[4] The Early effect can be accounted for in small-signal circuit models (such as the hybrid-pi model) as a resistor defined as[5] in parallel with the collector–emitter junction of the transistor.
This resistor can thus account for the finite output resistance of a simple current mirror or an actively loaded common-emitter amplifier.
In keeping with the model used in SPICE and as discussed above using
the resistance becomes: which almost agrees with the textbook result.
varies with DC reverse bias
[citation needed] In the MOSFET the output resistance is given in Shichman–Hodges model[6] (accurate for very old technology) as: where
= channel-length modulation parameter, usually taken as inversely proportional to channel length L. Because of the resemblance to the bipolar result, the terminology "Early effect" often is applied to the MOSFET as well.
The following assumptions are involved when deriving ideal current-voltage characteristics of the BJT[7] It is important to characterize the minority diffusion currents induced by injection of carriers.
With regard to pn-junction diode, a key relation is the diffusion equation.
A solution of this equation is below, and two boundary conditions are used to solve and find
The following equations apply to the emitter and collector region, respectively, and the origins
apply to the base, collector, and emitter.
A boundary condition of the emitter is below: The values of the constants
are zero due to the following conditions of the emitter and collector regions as
There is therefore a linear relationship between excess hole density and
Similarly, an expression of the collector current is derived.
An expression of the base current is found with the previous results.
