In an intrinsic semiconductor at room temperature, the number of free electrons is:

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The correct answer is Option C: Equal to the number of holes. In an intrinsic semiconductor, charge carriers are generated solely due to thermal agitation. Since each broken covalent bond produces one free electron and one hole simultaneously, the concentration of electrons is exactly equal to the concentration of holes.

Step-by-Step Solution & Concepts:
In an intrinsic semiconductor, charge carriers are generated solely due to thermal agitation. Since each broken covalent bond produces one free electron and one hole simultaneously, the concentration of electrons is exactly equal to the concentration of holes.

Working Principle: Thermal energy at room temperature provides sufficient energy to break covalent bonds in the crystal lattice. This process creates an electron-hole pair. Because no doping agents (impurities) are present, the rate of electron generation must equal the rate of hole generation, maintaining electrical neutrality.

Key Formulas: $n = p = n_{i}$ — intrinsic carrier concentration equilibrium where $n$ is electron density, $p$ is hole density, and $n_{i}$ is intrinsic carrier density; $n \cdot p = n_{i}^{2}$ — the law of mass action

Key Points: Intrinsic semiconductors are pure semiconductors without doping.; Charge neutrality is maintained globally in an intrinsic crystal.; The Fermi level for an intrinsic semiconductor lies almost exactly at the middle of the energy band gap.

Advantages: Provides a baseline for understanding extrinsic (doped) semiconductors.; High purity levels allow for predictable modeling in device physics.

Disadvantages: Low conductivity at room temperature compared to extrinsic semiconductors.; Highly sensitive to temperature fluctuations.

Applications: Used as a substrate material in microchip manufacturing.; Fundamental to the study of p-n junction diodes and transistors.

Additional Info: The intrinsic carrier concentration $n_{i}$ is temperature-dependent and is given by $n_{i} = A T^{3/2} \exp\left(-\frac{E_{g}}{2kT}ight)$.. Option A is incorrect as it describes n-type semiconductor characteristics.. Option B is incorrect as it describes p-type semiconductor characteristics.

Answer: C is correct — In an intrinsic semiconductor, the thermal generation of charge carriers results in an equal number of free electrons and holes.

Exam Tip: Always remember that while $n = p$ in intrinsic materials, the product $n 	imes p$ remains constant at a fixed temperature even when dopants are added (Mass Action Law).

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Option A: Greater than the number of holes

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Option B: Less than the number of holes

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Option D: Zero

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