Where is the Fermi level in a degenerate semiconductor?

Inside the conduction band (n+) or valence band (p+)

A few kT inside the gap from a band edge

Always above the conduction band in p-type

Which statement is true for a non-degenerate semiconductor?

Boltzmann statistics apply and np = ni^2 holds

Fermi-Dirac statistics are needed and np = ni^2 fails

np = ni^2 holds only for degenerate doping

Why is light emission poor in an indirect gap semiconductor like Si?

A transition needs a phonon as well as a photon because CB min and VB max are at different k

The CB minimum and VB maximum are at the same k

It has no electrons in the conduction band

2081 Bhadra · 2+2 marks

Degenerate semiconductors; direct vs indirect bandgap

Short answer

Non-degenerate: moderate doping, Fermi level in gap, Boltzmann statistics, np=ni². Degenerate: heavy doping, Fermi level inside band, Fermi-Dirac statistics. Direct bandgap (GaAs): CB min and VB max at same k, efficient photon emission. Indirect (Si): different k, requires phonon, poor light emission.

Differentiate between degenerate and non-degenerate semiconductors. Also write the difference between direct and indirect bandgap semiconductor with examples.

Degenerate vs non-degenerate

Point	Non-degenerate	Degenerate
Doping	Light/moderate ( $\ll N_c$ )	Very heavy ( $\gtrsim 10^{19}$ cm $^{-3}$ in Si)
Fermi level	In the gap, a few $kT$ from band edges	Inside CB (n $^+$ ) or VB (p $^+$ )
Statistics	Boltzmann; $np = n_i^2$ holds	Fermi-Dirac; $np = n_i^2$ fails
Behaviour	Semiconductor-like	Metal-like

Direct vs indirect band gap

Point	Direct	Indirect
Band edges in E-k	CB min and VB max at same $k$	At different $k$
Transition	Photon only	Needs photon plus phonon
Light emission	Efficient	Very poor
Examples	GaAs, InP, GaN	Si, Ge, GaP
Use	LEDs, lasers	ICs, transistors, solar cells

✓ Answer checked by Claude Opus 5.5 (high effort)

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