Semiconductor Physics – Intrinsic Material In an intrinsic (pure) semiconductor at thermal equilibrium, the number of free electrons in the conduction band is equal to the number of mobile holes in the valence band. Is this statement correct?

Introduction / Context:
Intrinsic semiconductors (such as ultra-pure silicon or germanium) are undoped crystals in which all electrical carriers are generated thermally by breaking covalent bonds. A core conceptual fact is the equality of electron and hole concentrations at equilibrium. This question tests your understanding of carrier generation–recombination balance and charge neutrality in intrinsic materials.

Given Data / Assumptions:

• Material is intrinsic (no intentional donors or acceptors).
• Thermal equilibrium is assumed (no illumination injection, no external bias creating non-equilibrium conditions).
• Standard semiconductor band model with conduction and valence bands.

Concept / Approach:

In an intrinsic semiconductor, every electron promoted to the conduction band leaves behind one vacancy (a hole) in the valence band. Therefore, the electron concentration n and hole concentration p satisfy n = p = ni, where ni is the intrinsic carrier concentration determined by the bandgap and temperature. Charge neutrality and mass-action law reinforce this result: n * p = ni^2 and, for intrinsic material, n = p = ni.

Step-by-Step Solution:

Verification / Alternative check:

Using the mass-action law n * p = ni^2: in intrinsic material, symmetry and neutrality give n = p = ni. Any deviation (n ≠ p) implies unbalanced ionized impurities or non-equilibrium injection, which contradicts the intrinsic, equilibrium premise.

Why Other Options Are Wrong:

• False: contradicts the electron–hole pair generation mechanism.
• True only at very high temperature: equality holds at any temperature in equilibrium, although ni changes strongly with temperature.
• Cannot be determined: it can be determined from the definition of intrinsic semiconductor.

Common Pitfalls:

Confusing intrinsic (n = p) with extrinsic n-type (n ≫ p) or p-type (p ≫ n); overlooking that illumination or bias can create non-equilibrium where n ≠ p even in otherwise pure material.

Final Answer:

True