A variety of effects occur in bipolar transistors, which are not included in the ideal transistor model. These include the base-width modulation effects and the current due to recombination in the depletion layers. High injection effects, base spreading resistance and emitter current crowding are described next. We conclude this section with the temperature dependence and breakdown mechanisms in BJTs.

5.4.1. Base-width modulation

As the voltages applied to the base-emitter and base-collector junctions are changed, the depletion layer widths and the quasi-neutral regions vary as well. This causes the collector current to vary with the collector-emitter voltage as illustrated in Figure 5.4.1.

A variation of the base-collector voltage results in a variation of the quasi-neutral width in the base. The gradient of the minority-carrier density in the base therefore changes, yielding an increased collector current as the collector-base current is increased. This effect is referred to as the Early effect. The Early effect is observed as an increase in the collector current with increasing collector-emitter voltage as illustrated with Figure 5.4.2. The Early voltage, V_A, is obtained by drawing a line tangential to the transistor I-V characteristic at the point of interest. The Early voltage equals the horizontal distance between the point chosen on the I-V characteristics and the intersection between the tangential line and the horizontal axis. It is indicated on the figure by the horizontal arrow.

The change of the collector current when changing the collector-emitter voltage is primarily due to the variation of the base-collector voltage, since the base-emitter junction is forward biased and a constant base current is applied. The collector current depends on the base-collector voltage since the base-collector depletion layer width varies, which also causes the quasi-neutral width, w_B^', in the base to vary. This variation can be calculated for a piece-wise uniformly-doped transistor using the ideal transistor mode as described by equations (5.2.10) and (5.3.1):

This variation can be expressed by the Early voltage, V_A, which quantifies what voltage variation would result in zero collector current.

It can be shown that the Early voltage also equals the majority carrier charge in the base, Q_B, divided by the base-collector junction capacitance, C_j,BC = _s/(x_p,BC + x_n,BC), where x_p,BC and x_n,BC are given by (5.2.6) and (5.2.7):

The Early voltage can also be linked to the output conductance, r₀, which equals:

In addition to the Early effect, there is a less pronounced effect due to the variation of the base-emitter voltage, which changes the ideality factor of the collector current. However, the effect at the base-emitter junction is much smaller since the base-emitter junction capacitance is larger and the base-emitter voltage variation is very limited since the junction is forward biased. This effect does lead to a variation of the ideality factor, n, given by:

The collector current is therefore of the following form:

Where the I_C,s is the collector saturation current.

The Early voltage equals:

The saturation voltage equals:

An extreme case of base-width modulation is punchthrough. As the collector-emitter voltage is increased, the quasi-neutral width of the base decreases, so that it eventually becomes zero. The collector current becomes very large and no longer depends on the voltage applied to the base. This mode of operation is undesirable since most performance characteristics degrade as one approaches punchthrough. The rapid increase of the collector current at the punchthrough voltage can cause the destruction of the transistor due to excessive power dissipation. Punchthrough is therefore one of the possible breakdown modes of a bipolar transistor described in section 5.4.6.

5.4.2. Recombination in the depletion region

So far, we have ignored the recombination in the depletion region. As in a p-n diode, the recombination in the depletion region causes an additional diode current. We can identify this contribution to the current because of the different voltage dependence as described in section 4.4.4. An example is provided with Figure 5.4.3. Shown are the collector and base current of a silicon bipolar transistor, biased in the forward active mode of operation with V_BC = -12 V, as a function of the base-emitter voltage. This type of plot is also called a Gummel plot.

The current due to recombination in the depletion region can be observed as an additional base current between V_BE = 0.2 and 0.4 V. The collector current does not include this additional current, since recombination in the depletion region does not affect the flow of electrons through the base.

5.4.3. High injection effects

High injection effects occur in a bipolar junction transistor, just like in a p-n diode. Since under forward active bias only the base-emitter diode is forward biased, one only has to explore the high-injection effects of the base-emitter diode. Again is it the lower doped side of the p-n diode where high injection will occur first so that we examine the high-injection condition in the base region. The onset of high injection is therefore expected if the collector current is equal or larger than:

or for:

As for a p-n diode, high injection modifies the ideality factor of the collector current, making it approximately equal to 2. The ideality factor of the base current however remains unchanged since the minority carrier density in the emitter does not exceed the majority carrier density in the emitter until:

The net effect is that the current gain decreases with increasing bias, or:

This current gain reduction is by itself already a good reason to not bias a bipolar junction transistor into high-injection. High-injection also reduces the transit time through the base, as discussed in section 5.5.3, which further reduces its usefulness. In most practical cases and especially when the base is thin and highly doped, high injection will not even be observed in a bipolar transistor, as the effect of series resistances will be dominant instead. Heterojunction bipolar transistors have a much higher base doping so that high-injection does not occur in such devices.

5.4.4. Base spreading resistance and emitter current crowding

Large area bipolar transistors can have a very non-uniform current distribution due to the resistance of the base layer. Since the base current is applied through the thin base layer, there can be a significant series resistance in large devices. This resistance causes a voltage variation across the base region. This voltage variation then causes a variation of the emitter current density, especially since the emitter current density depends exponentially on the local base-emitter voltage. This effect is minimal in the center of the emitter-base diode and strongly increases toward the edges. In extreme cases, this effect causes the emitter current to occur only at the very edges of the emitter-base diode. The parameters involved include the sheet resistance of the base layer, the emitter current density and the current gain in the device. The characteristic length, l_spreading, can be obtained from a distributed model similar to that of a metal contact to a thin semiconductor layer as described in Section 3.5.4.

Where r_p is the small signal base resistance, R_s,B is the sheet resistance of the base and J_E is the emitter current density. This analysis is only valid if the emitter current density is close to uniform. The emitter current density in a BJT can only be consider close to uniform if the emitter stripe width is less that the characteristic length for a BJT with a one-sided base contact or less that twice the characteristics length for a BJT with a double sided base contact or:

The corresponding value of the base resistance for a uniform emitter current distribution equals:

for a one-sided base contact and

for a double-sided base contact, which effectively has the resistance of two sections with half the emitter stripe width connected in parallel. A series of narrow emitter fingers with alternating base contacts is therefore typically used in large area power devices, resulting in the characteristic interdigitated structure.

5.4.5. Temperature dependent effects in bipolar transistors

The temperature dependence of bipolar transistors depends on a multitude of parameters affecting the bipolar transistor characteristics in different ways.

First we will discuss the temperature dependence of the current gain. Since the current gain depends on both the emitter efficiency and base transport factor, we will discuss these separately.

The emitter efficiency depends on the ratio of the carrier density, diffusion constant and width of the emitter and base. As a result, it is not expected to be very temperature dependent. The carrier densities are linked to the doping densities. Barring incomplete ionization, which can be very temperature dependent, the carrier densities are independent of temperature as long as the intrinsic carrier density does not exceed the doping density in either region. The width is very unlikely to be temperature dependent and therefore also the ratio of the emitter and base width. The ratio of the mobility is expected to be somewhat temperature dependent due to the different temperature dependence of the mobility in n-type and p-type material.

The base transport is more likely to be temperature dependent since it depends on the product of the diffusion constant and carrier lifetime. The diffusion constant in turn equals the product of the thermal voltage and the minority carrier mobility in the base. The recombination lifetime depends on the thermal velocity. The result is therefore moderately dependent on temperature. Typically the base transport reduces with temperature, primarily because the mobility and recombination lifetime are reduced with increasing temperature. Occasionally the transport factor initially increases with temperature, but then reduces again.

5.4.6. Breakdown mechanisms in BJTs

The breakdown mechanisms of BJTs are similar to that of p-n junctions. Since the base-collector junction is reversed biased, it is this junction where breakdown typically occurs. Just like for a p-n junction the breakdown mechanism can be due to either avalanche multiplication as well as tunneling. However, the collector doping in power devices tends to be low-doped either to ensure a large enough breakdown voltage – also called blocking voltage – or to provide a high Early voltage. The collector doping in microwave BJTs is typically higher than that of power devices, yet based on the trade-off between having a short transit time through the base-collector depletion region and having a low base-collector capacitance. As a result, one finds that the collector doping density rarely exceeds 10¹⁸ cm^-3 and tunneling does not occur.

Instead, breakdown is dominated by avalanche multiplication. The large electric field in the base-collector depletion region causes carrier multiplication due to impact ionization. Just like in a p-n diode, this breakdown is not destructive. However, the high voltage and rapidly increasing current does cause large heat dissipation in the device, which can cause permanent damage to the semiconductor or the contacts.

The breakdown voltage of a BJT also depends on the chosen circuit configuration: In a common base mode (i.e. operation where the base is grounded and forms the common electrode between the emitter-base input and collector-base output of the device) the breakdown resembles that of a p-n diode. In a common emitter mode (i.e. operation where the emitter is grounded and forms the common electrode between the base-emitter input and the collector-emitter output of the device) the transistor action further influences the I-V characteristics and breakdown voltage. Base width modulation was described in section 5.4.1 to result in an increase in the collector current with increased collector-emitter voltage. In the extreme case of punchthrough where the base is completely depleted, an even larger increase is observed be it nowhere as abrupt as in the case of avalanche breakdown. Avalanche breakdown of the base-collector junction is further influenced by transistor action in common-emitter mode of operation, since the holes generated by impact ionization are pulled back into the base region which results in an additional base current. This additional base current causes an even larger additional flow of electrons through the base and into the collector due to the current gain of the BJT. This larger flow of electrons in the base-collector junction causes an even larger generation of electron-hole pairs.

To further analyze this effect quantitatively we first write the total collector current, I_C, in response to an applied base current, I_B:

Where the term (M - 1) I_C was added to the base current to include the holes generated due to impact ionization. This equation can be rearranged to yield:

The collector current will therefore approach infinity as the denominator approaches zero. From this equation and combining with equation 4.5.6 one finds that the common emitter breakdown voltage equals:

The common emitter breakdown voltage as characterized by the open base breakdown voltage, VB_CEO, is therefore significantly less than the open emitter breakdown voltage, VB_CBO.