Question: How does the energy gap of an intrinsic semiconductor effectively change when doped with a (a) trivalent impurity, and (b) pentavalent impurity? Justify your answer in each case.

Step 1 (Governing Principle): [0.5 Mark]

Doping an intrinsic semiconductor introduces discrete energy levels within the forbidden energy gap ($E_g$). These levels are located very close to the valence band or the conduction band, effectively reducing the energy required for charge carriers to participate in conduction, although the actual band gap of the host material remains physically unchanged.

Step 2 (Step-by-Step Analysis): [1.0 Mark]

• (a) Trivalent Impurity (p-type doping): The trivalent impurity (e.g., Boron, Indium) creates an acceptor energy level ($E_a$) just above the valence band ($E_v$). The energy gap between the acceptor level and the valence band is very small ($\approx 0.01 \text{ eV}$ to $0.05 \text{ eV}$). This allows electrons from the valence band to easily jump into the acceptor level, creating holes in the valence band.
• (b) Pentavalent Impurity (n-type doping): The pentavalent impurity (e.g., Phosphorus, Arsenic) creates a donor energy level ($E_d$) just below the conduction band ($E_c$). The energy gap between the donor level and the conduction band is also very small ($\approx 0.01 \text{ eV}$ to $0.05 \text{ eV}$). This allows donor electrons to be easily excited into the conduction band.

Step 3 (Final Concluded Answer): [0.5 Mark]

The effective energy gap decreases because the impurity atoms introduce intermediate energy states. $$E_{\text{effective}} \approx E_g - \Delta E$$ Where $\Delta E$ represents the small energy difference between the impurity level and the respective band edge. Consequently, the energy required for conduction is significantly lowered compared to the intrinsic semiconductor.

💡 EL10 Concept Insight: Think of the energy gap like a high wall that electrons need to jump over to conduct electricity. Doping is like placing a small "stepping stone" (the impurity level) very close to the top or bottom of the wall, making it much easier for the electrons to reach the other side!