# 5.2 The Bipolar Transistor - Principle of operation

A bipolar junction transistor consists of two back-to-back p-n junctions, which share a thin common region with width, wB. Contacts are made to all three regions, the two outer regions called the emitter and collector and the middle region called the base. The structure of an NPN bipolar transistor is shown in Figure 5.1 (a). The device is called "bipolar" since its operation involves both types of mobile carriers, electrons and holes.

(a)

(b)

Figure 5.1 (a) Structure and sign convention of a NPN bipolar junction transistor. (b) Electron and hole flow under forward active bias, VBE > 0 and VBC = 0.

Since the device consists of two back-to-back diodes, there are depletion regions between the quasi-neutral regions. The width of the quasi neutral regions in the emitter, base and collector are indicated with the symbols wE', wB' and wC' and are calculated from

 (5.1)

 (5.2) (5.3)

where the depletion region widths are given by:

 (5.4) (5.5) (5.6) (5.7)

The sign convention of the currents and voltage is indicated on Figure 5.1 (a). The base and collector current are positive if a positive current goes into the base or collector contact. The emitter current is positive for a current coming out of the emitter contact. This also implies that:

 (5.8)

The base-emitter voltage and the base-collector voltage are positive if a more positive voltage is applied to the base contact.

The operation of the device is illustrated with Figure 5.1 (b). We consider the forward active bias mode of operation, obtained by forward biasing the base-emitter junction and reverse biasing the base-collector junction. To simply the discussion further, we also set VCE = 0. Electrons diffuse from the emitter into the base and holes diffuse from the base into the emitter. This carrier diffusion is identical to that in a p-n junction. However, what is different is that the electrons can diffuse as minority carriers through the quasi-neutral region in the base. Once the electrons arrive at the base-collector depletion region, they are swept through the depletion layer due to the electric field. These electrons contribute to the collector current. In addition, there are two more currents, the base recombination current and the depletion layer recombination.

The total emitter current is therefore the sum of the electron diffusion current, IE,n, the hole diffusion current, IE,p and the depletion layer recombination current, Ir,d.

 (5.9)

The total collector current is the electron diffusion current, IE,n, minus the base recombination current, Ir,B.

The base current is the sum of the hole diffusion current, IE,p, the base recombination current, Ir,B and the depletion layer recombination current, Ir,d.

 (5.11)

The transport factor is defined as the ratio of the collector and emitter current:

Using Kirchoff's current law and the sign convention shown in Figure 5.1 (a), we find that the base current equals the difference between the emitter and collector current. The current gain is defined as the ratio of the collector and base current and equals:

 (5.13)

This explains how a bipolar junction transistor can provide current amplification. If the collector current is almost equal to the emitter current, the transport factor, a, approaches one. The current gain, b, can therefore become much larger than one.

To facilitate further analysis, we now rewrite the transport factor, a, as the product of the emitter efficiency, gE, the base transport factor, aT, and the depletion layer recombination factor, dr.

 (5.14)

The emitter efficiency, gE, is defined as the ratio of the electron current in the emitter, IE,n, to the sum of the electron and hole current diffusing across the base-emitter junction, IE,n + IE,p.

The base transport factor, aT, equals the ratio of the current due to electrons injected in the collector, to the current due to electrons injected in the base.

Recombination in the depletion-region of the base-emitter junction further reduces the current gain, as it increases the emitter current without increasing the collector current. The depletion layer recombination factor, dr, equals the ratio of the current due to electron and hole diffusion across the base-emitter junction to the total emitter current:

 (5.17)

5.1 ¬ ­ ® 5.

© Bart J. Van Zeghbroeck, 1996, 1997, 1998
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