ISRO EC 2023 Q.46: solution and answer

Official answer: DSource: ISRO's revised and final answer key of 16 February 2024

1. GaAs is a direct-bandgap III-V compound with a small electron effective mass, so its electron mobility is about $8500{\text{cm}}^2/\text{V s}$ against about $1400{\text{cm}}^2/\text{V s}$ for Si. Option (a) is true.

2. Higher mobility means electrons reach high drift velocity at modest fields and cross the channel in a shorter time, so the transit time is shorter. GaAs devices (MESFETs, HEMTs) therefore work at microwave and millimetre-wave frequencies where ordinary Si devices struggle. Option (b) is true.

3. GaAs has a wider bandgap ($\approx 1.42\text{eV}$ against $1.12\text{eV}$ for Si), so the intrinsic carrier concentration $n_i\propto e^{-E_g/2kT}$ is far lower, about $10^6{\text{cm}}^{-3}$ against $10^{10}{\text{cm}}^{-3}$ at room temperature. Junction leakage current depends on $n_i^2$ (diffusion component) or $n_i$ (generation component), so it is much lower, and a semi-insulating GaAs substrate also reduces leakage between devices. Option (c) is true.

4. All three statements are advantages of GaAs over Si, so the answer is (d), all of the above.