Explain Transistor Current Components:

The various transistor current components which flow across the forward-biased emitter junction and reverse biased collector junction are indicated in Fig. 10.11. The current flowing into the emitter is referred to as the emitter current and designated as I_E. The emitter current I_E consists of two constituents (hole current I_hE due to crossing of holes from emitter into the base and electron current I_eE due to crossing of electrons from base into the emitter).

In a commercial transistor the emitter is heavily doped and the base is very lightly doped and, therefore, electron current I_eE is negligibly small in comparison to hole current I_hE. Thus the entire emitter current I_E in a P-N-P transistor is due to flow of holes from emitter to the base. It is to be noted that the indicated direction of I_E external to the transistor is the conventional current direction.

All the holes crossing the emitter junction J_E do not reach the collector junction J_C because some of them combine with the electrons in the N-type base. If I_hC is the hole current at collector junction J_C, there must be a bulk recombination current I_hE less I_hC leaving the base, as shown in Fig. 10.11. In fact electrons enter the base region through the base lead to replenish those electrons which have been lost by recombination with the holes injected into the base across the emitter junction J_E. The holes on reaching the collector junction J_C cross this junction and enter the collector P-region.

If the emitter were open circuited, I_E would have been zero and then I_hC also would have been zero. Under these conditions, the base and collector would act as a reverse-biased diode and the collector current I_C would be equal to that reverse saturation current I_CBO (or simply I_CO).

When the emitter circuit is closed i.e., when I_E ≠ 0, then from Fig. 10.11

For a P-N-P transistor, I_CO consists of holes moving across junction J_C from base region to collector region and electrons crossing junction J_C in the opposite direction.

In the active region operation with emitter junction J_E forward biased, the collector current is given as

where α is the fraction of the total current I_E which constitutes I_hC.

It is to be noted that the indicated direction of emitter current I_E external to the transistor is the conventional current direction. Base current I_B and collector current I_C are also shown external to the transistor conventional current direction. According to the Kirchhoff s first law total current flowing into the transistor must be equal to the total current flowing out of it. So emitter current I_E is equal to the sum of collector and base currents l_C and I_B.

Let us now define different parameters which relate the transistor current components discussed above.

Emitter Efficiency: The emitter or injection efficiency denoted by γ is defined as the ratio of current of injected carriers at J_E to the total emitter current

where I_hE is the injected hole diffusion current at emitter junction and l_eE is the injected electron diffusion current at emitter junction.

Transport Factor: Transport factor, denoted by β, is defined as the ratio of injected carrier current reaching J_C to the injected carrier current at J_E

Large Signal Current Gain α: The term α has already been defined above. However, α can alternatively be defined from Eq. (10.4). From Eq. (10.4) α may be defined as the ratio of collector current increment from cutoff value (I_C = I_CO) to l_C and the emitter current increment from cutoff value (I_E = 0) to I_E. Thus, we may write

Term α is called the large signal current gain of a common base transistor. The parameter α is extremely important in transistor theory. It is to be pointed here that α is not constant, but varies with emitter current I_E, collector voltage V_CB, and the temperature. Typically α lies in the range 0.95 to 0.99.

From Eqs. (10.2) and (10.8) we have

For an efficient transistor we would like β and γ to be very near unity i.e., the emitter current should be due mostly to holes (γ = 1) and most of the injected holes should eventually participate in the collector current (β ≈ 1).

The product βγ is defined as the factor α, called the current gain ratio, which represents the emitter-to-collector current amplification. There is no real amplification between these currents, since α is lesser than unity. On the other hand, the relation between collector current and base current is more promising for amplification.

DC Current Gain: If I_CO is negligibly small in comparison to l_C, α approximately equals I_C/I_E. This is referred to as the dc current gain of the common base (CB) transistor and is denoted by α_dc

Thus

α_dc is always positive and less than unity.

Small Signal Current Gain α_ac: Small signal current gain α_ac is defined as the ratio of change in collector current to change in emitter current

α_ac is always positive but less than unity (very close to unity). It also varies with I_E, V_CB and temperature.

Generalized Expression For Collector Current: We know that a small reverse current flows across a P-N junction diode due to thermally generated minority carriers that are propelled by the barrier potential. When the junction is reverse biased, this reverse current increases slightly. For moderate reverse-bias voltages, the reverse current attains its saturation value, I_S (or I₀). Because the collector-base junction of a transistor is reverse biased, there is likewise a reverse current due to thermally generated carriers. Of course this “reverse” current, in the context of a transistor, is in the same direction as the main (collector) current flowing through the device due to the injection of minority carriers into the base. The total collector current is, therefore, the sum of these two transistor current components: the injected minority carriers and the thermally generated minority carriers

The reverse current I_CBO is given by the volt-ampere relationship of equation I = I₀(e^V/ηVT-1) with I₀ replaced by -I_CO and V by V_C where symbol V_C represents the voltage drop across junction J_C from the P-side to the N-side and the complete expression for collector current l_C may be written as

If V_C is negative and is of large magnitude in comparison with that of V_T, Eq. (10.12) reduces to Eq. (10.4).

The physical interpretation of Eq. (10.12) is that the P-N junction diode current crossing the collector junction J_C is supplemented by a fraction α of the current I_E flowing in the emitter.