The transistor
Perhaps the most important application of semiconductors is in the transistor. The transistor consists of two semiconductor junctions very close together. Its operation is based in part on the same principles that we just described for the semiconductor diode—the rectifying junction. Suppose we make a little bar of germanium with three distinct regions, a $p$-type region, an $n$-type region, and another $p$-type region, as shown in Fig. 14–11(a). This combination is called a $p$-$n$-$p$ transistor. Each of the two junctions in the transistor will behave much in the way we have described in the last section. In particular, there will be a potential gradient at each junction having a certain potential drop from the $n$-type region to each $p$-type region. If the two $p$-type regions have the same internal properties, the variation in potential as we go across the crystal will be as shown in the graph of Fig. 14–11(b). Now let’s imagine that we connect each of the three regions to external voltage sources as shown in part (a) of Fig. 14–12. We will refer all voltages to the terminal connected to the left-hand $p$-region so it will be, by definition, at zero potential. We will call this terminal the emitter. The $n$-type region is called the base and it is connected to a slightly negative potential. The right-hand $p$-type region is called the collector, and is connected to a somewhat larger negative potential. Under these circumstances the variation of potential across the crystal will be as shown in the graph of Fig. 14–12(b). Let’s first see what happens to the positive carriers, since it is primarily their behavior which controls the operation of the $p$-$n$-$p$ transistor. Since the emitter is at a relatively more positive potential than the base, a current of positive carriers will flow from the emitter region into the base region. A relatively large current flows, since we have a junction operating with a “forward voltage”—corresponding to the right-hand half of the graph in Fig. 14–10. With these conditions, positive carriers or holes are being “emitted” from the $p$-type region into the $n$-type region. You might think that this current would flow out of the $n$-type region through the base terminal $b$. Now, however, comes the secret of the transistor. The $n$-type region is made very thin—typically $10^{-3}$ cm or less, much narrower than its transverse dimensions. This means that as the holes enter the $n$-type region they have a very good chance of diffusing across to the other junction before they are annihilated by the electrons in the $n$-type region. When they get to the right-hand boundary of the $n$-type region they find a steep downward potential hill and immediately fall into the right-hand $p$-type region. This side of the crystal is called the collector because it “collects” the holes after they have diffused across the $n$-type region. In a typical transistor, all but a fraction of a percent of the hole current which leaves the emitter and enters the base is collected in the collector region, and only the small remainder contributes to the net base current. The sum of the base and collector currents is, of course, equal to the emitter current. Now imagine what happens if we vary slightly the potential $V_b$ on the base terminal. Since we are on a relatively steep part of the curve of Fig. 14–10, a small variation of the potential $V_b$ will cause a rather large change in the emitter current $I_e$. Since the collector voltage $V_c$ is much more negative than the base voltage, these slight variations in potential will not affect appreciably the steep potential hill between the base and the collector. Most of the positive carriers emitted into the $n$-region will still be caught by the collector. Thus as we vary the potential of the base electrode, there will be a corresponding variation in the collector current $I_c$. The essential point, however, is that the base current $I_b$ always remains a small fraction of the collector current. The transistor is an amplifier; a small current $I_b$ introduced into the base electrode gives a large current—$100$ or so times higher—at the collector electrode. What about the electrons—the negative carriers that we have been neglecting so far? First, note that we do not expect any significant electron current to flow between the base and the collector. With a large negative voltage on the collector, the electrons in the base would have to climb a very high potential energy hill and the probability of doing that is very small. There is a very small current of electrons to the collector. On the other hand, the electrons in the base can go into the emitter region. In fact, you might expect the electron current in this direction to be comparable to the hole current from the emitter into the base. Such an electron current isn’t useful, and, on the contrary, is bad because it increases the total base current required for a given current of holes to the collector. The transistor is, therefore, designed to minimize the electron current to the emitter. The electron current is proportional to $N_n(\text{base})$, the density of negative carriers in the base material while the hole current from the emitter depends on $N_p(\text{emitter})$, the density of positive carriers in the emitter region. By using relatively little doping in the $n$-type material $N_n(\text{base})$ can be made much smaller than $N_p(\text{emitter})$. (The very thin base region also helps a great deal because the sweeping out of the holes in this region by the collector increases significantly the average hole current from the emitter into the base, while leaving the electron current unchanged.) The net result is that the electron current across the emitter-base junction can be made much less than the hole current, so that the electrons do not play any significant role in operation of the $p$-$n$-$p$ transistor. The currents are dominated by motion of the holes, and the transistor performs as an amplifier as we have described above. It is also possible to make a transistor by interchanging the $p$-type and $n$-type materials in Fig. 14–11. Then we have what is called an $n$-$p$-$n$ transistor. In the $n$-$p$-$n$ transistor the main currents are carried by the electrons which flow from the emitter into the base and from there to the collector. Obviously, all the arguments we have made for the $p$-$n$-$p$ transistor also apply to the $n$-$p$-$n$ transistor if the potentials of the electrodes are chosen with the opposite signs.