Physical Processes in a Transistor

We will see how, say, an n-p-n transistor operates with its load disconnected (static operation or operation at no-load), when only sources of direct supply voltages, U_BE and U_CE, are connected into the circuit. The emitter junction is forward-biased, and the collector junction is reverse-biased. Therefore, the resistance of the emitter junction is low, and for a normal current to flow across this junction it will suffice to apply a voltage, U_BE, of a few tenths of a volt. The resistance of the collector junction is high, and U_CE is usually from several volts to tens of volts.

Fig. 4.2. Motion of electrons and holes in an n-p-n and a p-n-p transistor

An increase in the forward input voltage U_BE brings about a fall in the height of the potential barrier at the emitter junction and a proportionate increase in the emitter current I_E flowing across that junction. The electrons are injected from the emitter into the base and also diffuse through the base into the collector region, thereby boosting the collector current (Fig. 4.2).

If the base is narrow enough and its hole concentration is low, most of the electrons swept across the base will not have time to recombine with holes in the base, but will reach the collector junction. Very few of the electrons recombine with holes in the base. Recombina­tion gives rise to the base current that flows in the base lead:

I_E = I_C + I_B . (4.1)

The emitter current is controlled by the voltage existing across the emitter junction, but the current reaching the collector is somewhat smaller in value-it may be called the controlled collector current, I_Cc. This happens because some of the carriers injected from the emitter into the base recombine. Therefore,

I_Cc = α I_E , (4.2)

where α is the emitter-to-collector current gain of a transistor connected in a common-base circuit (also called the alpha current factor). It may range in value from 0.97 to 0.998.

There is one more, very small current (not over a few microamperes) always flowing across the collector junction, symbolized as I_C0 (Fig. 4.3). It is called the reverse collector leakage current. Thus the total collector current is:

I_C = αI_E + I_C0 . (4.3)

Fig. 4.3. Currents in a transistor

Let us re-write Eq. (4.3) so that I_C is a function of I _B. On replacing I_E with the sum I_C + I_B, we get:

I_C = α(I_C + I_B)+ I_C0 .

On solving the above equation for I_C , we obtain:

On denoting:

and (4.4) and (4.5)

we may finally write:

I_C =βI_B + I_CE0 , (4.6)

where β is the beta current gain factor of a transistor connected in a common-emitter circuit. It is always greater than unity and practical values up to 500 are often used.

If α = 0.99, then:

.

Even minor changes in α lead to great changes in β. Similarly to α, β is a very important parameter of transistors. If we know β, we can always find α by the equation:

. (4.7)

The current I_CE0 is the reverse emitter current when the base is open, that is, when I_B = 0.

I_CE0 = (β+1) I_C0. (4.8)

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