Question bank — Compound semiconductors (GaN, GaAs, SiC) overview

False. A wider gap makes it harder to thermally free carriers, so wide-gap crystals are more insulating at room temperature — their prize is surviving high fields/heat, not conductivity.

False. High mobility only wins for high-frequency, low-power jobs (RF, optics). GaAs has a small gap and low breakdown field, so it is useless for high-power switching.

False. SiC is indirect-gap: light emission needs a phonon too, so it is a poor emitter. Being a compound doesn't grant efficient light — being direct-gap does.

False. SiC is IV–IV (silicon and carbon are both group IV). The general rule is that valence electrons average to about 4 per atom, and IV+IV already averages exactly 4.

False. Doping shifts carrier concentration (Doping and carrier concentration), not the gap size or gap type. Silicon's gap is 1.12 eV (infrared) and indirect, so it can never efficiently emit visible blue light.

False. At high fields carrier velocity saturates, so mobility's advantage fades; and mobility says nothing about how much voltage the device can block. Speed and power tolerance are separate axes.

False. Sapphire has a lattice mismatch $f\approx 16\%$ with GaN, which spawns many dislocations; native GaN has $f=0$ and far fewer defects. See Epitaxy and crystal growth.

False. "Better" depends on the job. Direct is better for emitting light; but for high-power/high-heat switching the gap width and thermal conductivity matter more than gap type.

The average is $(3+5)/2=4$ per atom, not 8. Each atom still forms the same 4 tetrahedral bonds; averaging to 4 is exactly why the lattice is stable.

It gives $\lambda$ in nanometres when $E_g$ is in eV, because $hc\approx 1240\text{eV⋅nm}$. Units must match the constant used.

Their gaps are almost equal (3.26 vs 3.4 eV). SiC's real power edge is ~3× better heat conduction and a robust native oxide/substrate, not a bigger gap.

Sapphire is an insulator (Al₂O₃), not a semiconductor, and its mismatch is $f\approx 16\%$ — the opposite of matching. Buffer layers are needed precisely because of this.

The dependence is a strong super-linear power law, commonly quoted between $E_{crit}\propto E_g^2$ and $E_g^{2.5}$ (the exact exponent depends on the material and measurement), never linear. So doubling $E_g$ raises the field roughly four- to six-fold, which is why wide-gap materials block far more than their gap ratio suggests.

By energy conservation the photon carries the full gap it fell across, so a 2 eV drop gives a 2 eV photon. See Energy bands and bandgap.

We use it because there is no cheap bulk boule for GaN and (traditionally) SiC, and because two elements have different vapour pressures (As boils off before Ga melts). Epitaxy lays atomic layers on a substrate to sidestep both problems.

Blue light needs a ~2.7 eV photon, so you need a wide gap; and you need a direct gap so recombination emits a photon efficiently. GaN (3.4 eV, direct) has both; Si (1.12 eV, indirect) has neither.

Breakdown is impact ionization: an electron must gain ~$E_g$ of energy from the field before it scatters. A bigger gap demands a bigger field to reach that energy, so $E_{crit}$ rises steeply (super-linearly) with $E_g$.

Because it blocks the same voltage in a much thinner drift region (high $E_{crit}$ = more volts per micron). The thinner, less-doped-thickness layer means less resistance and less heat loss. Relevant to Power electronics & MOSFETs.

Its electron mobility (~8500) is ~6× silicon's, so transistors switch at the tens-of-GHz frequencies 4G/5G need. Its direct gap also lets it emit the 850 nm infrared used in fiber and remotes.

GaN forms a fast two-dimensional electron gas (the thin, low-scattering electron sheet defined above) at a heterojunction, ideal for high-frequency HEMTs. SiC's superior heat conduction and native oxide/substrate suit the very hottest, highest-voltage switches.

Straining atoms to line up stores elastic energy that grows with film thickness; past a critical thickness it becomes cheaper to create a defect than to keep straining, so dislocations nucleate.

The two elements have very different vapour pressures — arsenic evaporates before gallium even melts — so the melt loses stoichiometry. Special sealed or epitaxial methods are needed instead.

An insulator: with no thermal energy, no electrons are lifted across the gap, so the conduction band is empty. Wider gaps only make this more true.

It is satisfied trivially — both Si and C are group IV, so the average is $(4+4)/2=4$ with no imbalance to correct.

Essentially none from mismatch, because $a_{\text{film}}=a_{\text{substrate}}$ so atoms line up 1-to-1 with no strain — this is the ideal (native-substrate) case in Epitaxy and crystal growth.

No. Lasing needs efficient photon emission, which indirect gaps suppress (a phonon must assist). High mobility helps speed, not light output — a wrong-axis fix.

Higher temperature thermally frees more carriers; a narrow gap frees them easily, so leakage current climbs and thermal runaway sets in at a lower temperature. Wide-gap materials tolerate more heat before hitting the same failure boundary.

$\lambda =1240/E_g\to \infty$ — the "photon" becomes infinitely long-wavelength (zero-energy), i.e. a vanishing gap emits essentially nothing usable. This is the limiting behaviour of the $hc/E_g$ relation.