Question

For an intrinsic semiconductor at temperature $T=0K$, which of the following statement is true?

• A. All energy states in the valence band are filled with electrons and all energy states in the conduction band are empty of electrons.
• B. All energy states in the valence band are empty of electrons and all energy states in the conduction band are filled with electrons.
• C. All energy states in the valence and conduction band are filled with holes.
• D. All energy states in the valence and conduction band are filled with electrons.

Hint:

At $T=0K$, intrinsic semiconductors behave like perfect insulators since there are no free carriers (conduction band empty). Conductivity begins only at $T>0K$.

Answer 1

The Correct Option is A

Step 1: Understanding the physical situation at T = 0K
At absolute zero, all electrons occupy the lowest available energy states. Since there is no thermal energy, no electron can be excited across the forbidden energy gap. Thus, in an intrinsic semiconductor, the energy distribution is "frozen" in the lowest possible configuration.

Step 2: Condition of the valence band
The valence band, which contains the highest energy states that are normally filled in the ground state, will be completely filled with electrons. This is because every available electron occupies the lowest possible energy states up to the top of the valence band. No vacancies (holes) exist in the valence band at this temperature.

Step 3: Condition of the conduction band
The conduction band, which lies above the forbidden gap, requires energy input for electrons to move into it. At T = 0K, such excitations are impossible, hence the conduction band is completely empty. This directly distinguishes the intrinsic semiconductor at 0K from a conductor (where some states in the conduction band are filled).

Step 4: Eliminate wrong options
- (A) Valence full, conduction empty → Correct, matches exactly the semiconductor at 0K.
- (B) Conduction full, valence empty → Incorrect, this would describe a very different system, not an intrinsic semiconductor.
- (C) Presence of holes at 0K → Incorrect, since a filled valence band has no holes by definition.
- (D) Both bands filled with electrons → Incorrect, that would imply metallic behavior, which contradicts the semiconductor model.

Final Answer:
\[ \boxed{\text{At T = 0K, valence band full, conduction band empty. Correct option = (A).}} \]