Intrinsic (pure) silicon – relation between electrons and holes For a pure (intrinsic) sample of silicon at thermal equilibrium, what is the relationship between the concentration of free electrons and holes?

Introduction:
Carrier concentrations in semiconductors determine conductivity and device behavior. In intrinsic silicon, electrons and holes are thermally generated in pairs. Understanding their equality at equilibrium underpins key results such as the mass action law and sets a baseline for interpreting doped (extrinsic) semiconductors.

Given Data / Assumptions:

• Intrinsic (undoped) silicon in thermal equilibrium.
• Uniform temperature throughout the sample.
• No external carrier injection or illumination.

Concept / Approach:

In intrinsic material, generation of an electron in the conduction band leaves behind a hole in the valence band. Therefore, electron concentration n equals hole concentration p at all equilibrium temperatures, i.e., n = p = ni (the intrinsic carrier concentration), though ni itself depends exponentially on temperature and bandgap. This equality holds regardless of the absolute value of ni as long as the sample remains intrinsic and at equilibrium.

Step-by-Step Solution:

Verification / Alternative check:

Mass action law states n * p = ni^2; with no doping, charge neutrality and symmetry yield n = p = ni, confirming the result.

Why Other Options Are Wrong:

Options B and D describe doped (n- or p-type) behavior; Option C limits equality to low temperature, which is incorrect; Option E confuses intrinsic temperature concepts with dominance of one carrier type.

Common Pitfalls:

Assuming unequal carriers in intrinsic material; ignoring that illumination or bias can create non-equilibrium conditions (which is outside this question).

Final Answer:

the number of holes and free electrons is always equal