Concept:The extra valence electron of a donor atom is loosely bound and requires only a small ionization energy to be excited into the conduction band.
Formula:$$\Delta E_d = E_c - E_d \approx 0.045\text{ eV} \quad (\text{for Phosphorus in Silicon})$$
Solution:- The donor electron orbits the positively charged donor core in a hydrogen-like state with a small binding energy.
- In the band diagram, this donor energy level (\( E_d \)) is located inside the forbidden gap, approximately \( 0.045\text{ eV} \text{ to } 0.05\text{ eV} \) below the conduction band edge \( E_c \).
- Thermal energy at room temperature (\( k_B T \approx 0.026\text{ eV} \)) is sufficient to ionize these levels into the conduction band.
Why other options are incorrect:- Option A: The donor level lies near the conduction band, far from the valence band.
- Option B: Deep-level impurities sit near the center of the bandgap, whereas standard shallow dopants sit close to the band edges.
- Option D: Donor states lie within the bandgap below \( E_c \).
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