Question bank — Why silicon dominates over germanium

False. Silicon's gap is ~1.12 eV, germanium's ~0.66 eV — silicon's wall is taller by ~0.46 eV, which is exactly why silicon leaks less.

True — and that is the goal. A taller wall means fewer electrons get thermally kicked into the conduction band, so pure silicon is a poorer conductor than pure germanium. We want a clean, low-current OFF state.

True at the material level: Ge electron mobility (~3900) beats Si (~1500 cm²/V·s). But speed is only one axis; leakage, heat and oxide quality decide the mass market (see Carrier mobility and drift velocity).

False. "Faster" loses to "doesn't overheat, doesn't leak, has a buildable oxide, is cheap." Manufacturability and reliability beat raw speed — that's why your CPU is silicon.

False. The 1947 Bell Labs transistor was germanium; silicon displaced it around the late 1950s–60s once the oxide and thermal advantages proved decisive.

False — it rises with temperature. More heat means more electrons have enough energy to jump the gap: $n_i\propto T^{3/2}{e}^{-E_g/2k_{B}T}$, and both factors grow with $T$.

True. The exponential factor gives $n_i(\text{Ge})/n_i(\text{Si})\approx e^{8.9}\approx 7.3\times 10^3$ — consistent with $n_i^{Si}\approx 10^{10}$ vs $n_i^{Ge}\approx 2\times 10^{13}{\text{cm}}^{-3}$.

False. Silicon grows tough, insulating, chemical-resistant SiO₂; germanium's GeO₂ is soft, thermally unstable and water-soluble — it dissolves, so you cannot build a reliable insulating layer on Ge (see SiO2 and the planar process).

False. Silicon is ~28% of the crust (sand, quartz); germanium is a trace element (~1.5 ppm) recovered as a byproduct. Silicon is vastly cheaper.

True. Because $n_i\propto e^{-E_g/2k_{B}T}$, a larger $E_g$ makes $n_i$ climb more slowly, so it only swamps the dopants at a higher temperature — Si works to ~150 °C, Ge fails much earlier.

The error is the missing factor of 2. That $e^{-E_g/k_{B}T}$ describes the pair product $np=n_i^2$; since $n_i=\sqrt{np}$, the exponent halves → $n_i\propto e^{-E_g/2k_{B}T}$.

Atomic mass is not the mechanism. Ge leaks more because its smaller bandgap lets far more electrons be thermally excited across it — leakage is set by $E_g$ relative to $k_{B}T$, not by atomic weight.

A minimized gap gives huge OFF-state leakage and heat. A semiconductor's value is controllability — a clean OFF state (needs a decent gap) plus a controlled ON state, not maximum raw conduction.

SiO₂ does far more: it masks regions during processing, insulates between devices, and underpins the whole planar process by which ICs are mass-produced (see MOSFET operation and the gate oxide). Gate insulation is just one of its jobs.

The failure condition is relative: it fails when intrinsic carriers $n_i$ rise to rival the dopant concentration $N_D$. There's no universal absolute threshold; it depends on how heavily the material was doped (see Doping n-type and p-type).

Because one broken bond makes an electron and a hole — a pair. The pair product $np$ carries the full $e^{-E_g/k_{B}T}$, and $n_i=\sqrt{np}$ takes a square root, halving the exponent.

$k_{B}T$ is the typical thermal energy jostling each particle at temperature $T$ (via Fermi-Dirac distribution and thermal excitation). Comparing $E_g$ to $k_{B}T$ tells you how "easy" the jump is: small $E_g/k_{B}T$ → many hops, large → few.

A switch must have a clean OFF (nearly no current) that you then choose to turn ON. A material that already conducts freely can't give you a quiet OFF state — the bandgap is what supplies it.

Once the SiO₂ native oxide and silicon's superior thermal tolerance were understood, they enabled reliable, mass-produced ICs. Germanium's dissolving oxide and low temperature ceiling could not compete.

Mobility only sets how fast carriers drift under a field. It does nothing about leakage or heat, and in dense chips those — plus oxide/yield — dominate. Fast-but-leaky loses.

$n_i$ eventually rises above the dopant level $N_D$; the material behaves as if intrinsic, doping loses control, and the device fails. The smaller-gap material (Ge) reaches this point at a lower temperature.

Zero. With no thermal energy, no electron can be lifted across the gap: $e^{-E_g/2k_{B}T}\to 0$ as $T\to 0$, so a pure semiconductor is a perfect insulator at absolute zero.

The one with the stable, insulating native oxide — this is the silicon-vs-germanium story with leakage held equal. Oxide quality alone can decide manufacturability.

Yes — infrared detection. A small gap responds to lower-energy (longer-wavelength) photons, so Ge makes good fiber-optic and IR photodetectors, where Si's larger gap is blind.

Yes — wide-bandgap materials tolerate more heat and higher fields precisely because $n_i$ stays negligible longer. Silicon is the sweet spot for general electronics, not the extreme; the same $E_g$-vs-leakage logic keeps scaling.