List the band gaps at room temperature.

Sort ascending.

\(0.67 \lt 3.2 \lt 5.47 \lt 6.2\)

which is Germanium, Silicon carbide, Diamond, Aluminium nitride — that is (a), (c), (b), (d), option 1.

How to get this right without memorising four numbers. Band gap tracks bond strength, and bond strength tracks the atomic spacing and the ionicity of the bond.

Start at the bottom. Germanium is unmistakably the smallest — it is a classical semiconductor with a gap below that of silicon (1.12 eV), which is why germanium diodes turn on at 0.3 V rather than 0.7 V and why they leak badly above about 75 °C. Every option except 4 puts it first or last; only options 1 and 2 put it first, so this single fact halves the field.

Now settle the top. Diamond and aluminium nitride are both insulators by any practical measure. Between them, AlN has the larger gap because its bond is partly ionic — the electronegativity difference between aluminium and nitrogen adds to the covalent binding — whereas diamond's bond is purely covalent. That places AlN last and eliminates option 2.

Silicon carbide sits in between at about 3 eV: shorter, stronger bonds than in silicon because carbon is a small atom, but not as extreme as pure diamond.

Why the wide-gap materials matter. Intrinsic carrier concentration falls exponentially with the gap,

\(n_i \propto e^{-E_g/2kT}\)

so a wide-gap device leaks far less and can run far hotter — SiC power devices operate above 200 °C where silicon fails. The breakdown field also rises with E_g, which is why SiC and GaN dominate modern high-voltage power electronics, and why AlN and diamond are pursued for ultraviolet emitters and extreme-environment electronics.

Hence, the ascending order is Germanium, Silicon carbide, Diamond, Aluminium nitride.