Two features identify every optoelectronic device drawn here: which way the light travels (in or out) and how the device is biased.

b → iv. Light emitting diode. The only structure with the light arrow pointing outward and with a forward bias applied. Forward bias injects carriers that recombine radiatively, emitting photons of energy \(h\nu\approx E_g\). Every other device in the list absorbs light; this one generates it.

c → i. Solar cell. Large area, anti-reflection coating, and crucially no external supply — just two terminals delivering power to the outside. That is photovoltaic operation: the light-generated carriers themselves develop the open-circuit voltage. The big area and AR coating are there to collect as much sunlight as possible, which is what distinguishes a solar cell from a photodiode.

a → iii. Pin photodiode. The layer stack is explicitly p–i–n, with the lightly doped intrinsic layer between the two doped regions, and it is reverse biased across a load resistor. The wide intrinsic region gives a thick depletion layer, so more photons are absorbed where the field can sweep the carriers out — high quantum efficiency and fast response.

d → ii. Pn-photodiode. A simple p⁺n junction, again reverse biased, with the depletion width W marked. There is no intrinsic layer, so W is fixed by the doping and the applied bias and cannot be tailored independently — the limitation that the p-i-n structure was invented to remove.

How to work through it quickly. Find the emitter first (light out, forward bias) → LED. Then find the one with no battery → solar cell. The two remaining reverse-biased detectors are separated by whether an intrinsic layer is drawn: with i-layer → p-i-n, without → p-n.

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