1. Discuss the limiting form of the current-voltage characteristic of an ideal p-n junction rectifier, such as that discussed in Section 13.1, as the temperature approaches zero. What determines the maximum temperature of practical operation for the device?
2. Show that the application of the exact boundary conditions (12.3-1) and (12.3-2) to the solutions (13.1-14) and (13.1-15) for the p-n junction rectifier of Section 13.1, wherein the variation of majority carrier concentration due to the presence of the excess minority carrier distribution is not neglected, leads to a current-voltage characteristic of the form
You may assume that the mobility ratio b is sufficiently close to unity that the concentration profiles (13.1-14) and (13.1-15) are not seriously affected by ambipolar transport phenomena. Note that this equation predicts that which means, in effect, that the internal junction potential barrier is never completely “flattened out” even for extremely large currents. The expression clearly reduces to the previous result for reverse voltages and forward voltages which are small compared with ϕ0.
Experimentally, under high current conditions, rather than behaving as predicted above, the deviation of the current-voltage curve from the ideal form as given by (13.1-23) is found to be in just the opposite direction, as shown in the accompanying diagram. The reason for this lies not so much in the fact that the above expression does not correctly represent the relation between the junction voltage drop and the current, but rather in the fact that (a) at high currents, large additional ohmic voltage drops occur in the bulk regions on either side of the junction, and (b) under high current conditions an alloyed rectifier structure of finite size may act as a three-region p-(intrinsic)-n structure, where all the carriers injected into the moderately doped n-region are constrained to remain there until they recombine. This region then becomes flooded with electron-hole pairs, the concentration of these pairs rising to a value much in excess of the normal equilibrium majority carrier concentration, whereupon the region behaves very much like an intrinsic semiconductor layer. The metallic contact on the opposite side of this layer, usually made with a solder containing a fairly large concentration of donor impurities, forms a thin, heavily doped, recrystallized n-type layer which terminates the other side of the device. An investigation of the characteristics of a device of this type (such as that set forth in the next chapter) results in a current-voltage relation which is in quite good agreement with those observed in actual rectifiers of this type under such conditions.