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Question

Following are semiconductor materials arrange them in ascending order of their band gaps :

(a) Si

(b) Ge

(c) Ga N

(d) Ga As

The correct sequence in ascending order is given by

This question was previously asked in
UGC NET 2016 Paper 1 Question Paper (10-Jul-2016)
The correct answer is

(b), (a), (d), (c)

The four values at 300 K — worth committing to memory:

MaterialEg (eV)TypeTypical use
Ge (b)0.67indirectearly transistors, IR detectors
Si (a)1.12indirectalmost all ICs
GaAs (d)1.42directmicrowave devices, IR LEDs, lasers
GaN (c)3.4directblue/UV LEDs, power devices

Ascending order:

\(Ge \lt Si \lt GaAs \lt GaN \Rightarrow (b),\,(a),\,(d),\,(c)\)

The physical trend behind the numbers. Band gap reflects bond strength. Going down a group the atoms grow larger, the bonds weaken and Eg falls — hence germanium below silicon. Compounds of group III with group V have a partly ionic bond, which is stronger than a purely covalent one, so they sit higher; and within them the gap widens as the atoms get smaller and more electronegative, which is why the nitride GaN towers over the arsenide GaAs.

What each value buys.

A small gap means many thermally generated carriers, since \(n_i\propto e^{-E_g/2kT}\) — so germanium leaks badly and is limited to about 70 °C, while silicon works to 150 °C and GaN devices operate far hotter still.

The gap also fixes the emitted wavelength through \(\lambda(\mu m)=1.24/E_g(eV)\): GaAs at 1.42 eV emits at 870 nm in the infrared, whereas GaN at 3.4 eV reaches 365 nm in the ultraviolet — which is exactly why blue and white LEDs had to wait for gallium nitride.

Hence, the ascending order of band gaps is (b), (a), (d), (c).

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