Each device is defined by one property, and that property names its application: a-i, b-iii, c-iv, d-ii — option 1.

b — why negative resistance makes an oscillator. Both sides of a tunnel diode's junction are doped degenerately, so the depletion layer is only about 10 nm across and carriers tunnel straight through at small forward bias. As the bias rises further the occupied states on one side stop lining up with empty states on the other, the tunnelling window closes, and current falls while voltage rises:

\(\dfrac{dI}{dV}\lt0\ \text{between}\ V_{P}\ \text{and}\ V_{V}\)

Placed across a tuned circuit, that negative resistance cancels the circuit's positive loss resistance, so an oscillation once started neither decays nor needs any feedback path. Because tunnelling has essentially no transit delay, it works into the tens of gigahertz.

c — why the zener regulates. In breakdown its characteristic is almost vertical: a large change of current produces a very small change of voltage, so the dynamic resistance

\(r_{z}=\dfrac{\Delta V}{\Delta I}\)

is only a few ohms. Fed through a series resistor, it absorbs whatever current the load does not take and holds the voltage across itself constant.

d — why the PIN switches. Its thick intrinsic layer stores charge for hundreds of nanoseconds, so above about 1 MHz that charge cannot follow the RF cycle. The diode stops rectifying and becomes a linear resistor whose value is set by the DC bias — a fraction of an ohm forward, kilohms reverse. Being linear, it introduces no distortion, which is precisely what a microwave switch or attenuator requires.

Note how b and d are complementary : the tunnel diode is prized for a strong non-linearity, the PIN diode for the absence of one, and each application follows from that single fact.

Hence, the correct code is a-i, b-iii, c-iv, d-ii.