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.
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, IC, in response to an applied base current, IB:
Where the term (M - 1) IC 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 one finds that the common emitter breakdown voltage equals:
The common emitter breakdown voltage as characterized by the open base breakdown voltage, VBCEO, is therefore significantly less than the open emitter breakdown voltage, VBCBO.
Comparison of BJT breakdown in common emitter mode (left curve) versus breakdown in common base mode (right curve) for a BJT with VBCBO = 1000V and b = 100