(a) Energy-Band Diagrams and Electron-Hole Pair Formation

Step 1 (Diagrammatic Representation): [1 Mark]

• Conductors: The conduction band and valence band overlap, or the forbidden energy gap is zero.
• Semiconductors: The forbidden energy gap ($E_g$) is small (approx. $1\text{ eV}$ for Silicon).
• Insulators: The forbidden energy gap ($E_g$) is very large (typically $> 3\text{ eV}$).

[Note: Students must draw three separate diagrams showing the Conduction Band (CB) and Valence Band (VB) with the respective gaps.]

Step 2 (Mechanism of Electron-Hole Pair Formation): [0.5 Mark]

At room temperature, thermal energy ($k_BT$) is supplied to the semiconductor. When this thermal energy is greater than or equal to the forbidden energy gap ($E_g$), electrons in the valence band gain enough energy to break their covalent bonds and jump into the conduction band.

The vacancy left behind in the valence band is called a hole. Thus, an electron-hole pair is generated.

(b) Comparison of Carbon and Silicon

Step 3 (Scientific Reasoning): [1.5 Marks]

Although Carbon and Silicon belong to the same group and have the same lattice structure, their electrical properties differ due to the magnitude of their energy band gaps:

• In Carbon (Diamond), the forbidden energy gap is very large, approximately $E_g \approx 5.4\text{ eV}$. At room temperature, thermal energy is insufficient to excite electrons from the valence band to the conduction band, making it an insulator.
• In Silicon, the forbidden energy gap is relatively small, approximately $E_g \approx 1.1\text{ eV}$. At room temperature, sufficient thermal energy is available to excite a significant number of electrons to the conduction band, making it a semiconductor.

💡 EL10 Concept Insight: Think of the energy gap like a wall; in Silicon, the wall is low enough that electrons can "hop" over it using room-temperature heat, but in Carbon, the wall is so high that the electrons are stuck in place, unable to move and conduct electricity.