The resistivity of pure silicon is about _______.

Question

Examoogle · Accepted Answer

Option B: $6000	ext{ }\Omega	ext{ cm}$

Explanation & Concepts:
Pure (intrinsic) silicon at room temperature ($300	ext{ K}$) has a high electrical resistivity due to a low concentration of charge carriers. The standard value for intrinsic silicon resistivity is approximately $6000	ext{ }\Omega	ext{ cm}$.

Working Principle: In an intrinsic semiconductor, the number of free electrons ($n$) equals the number of holes ($p$), denoted as $n_i$. Resistivity ($ho$) is the inverse of conductivity ($\sigma$), defined by $ho = \frac{1}{q(n_i\mu_n + p_i\mu_p)}$, where $\mu_n$ and $\mu_p$ are mobilities. Because $n_i$ is very small in pure silicon, the denominator is low, resulting in a relatively high resistivity compared to metals.

Key Formulas: $ho = \frac{1}{\sigma}$ — Resistivity is the reciprocal of conductivity; $\sigma = q(n\mu_n + p\mu_p)$ — Conductivity depends on charge carrier concentration and mobility

Key Points: Intrinsic silicon resistivity is temperature-dependent.; Increasing temperature creates more electron-hole pairs, significantly decreasing resistivity.; Doping the silicon with impurities drastically lowers the resistivity.

Advantages: Ideal for creating controllable PN junctions; High sensitivity to temperature (used in thermistors)

Disadvantages: High resistivity makes it unsuitable for low-loss power transmission; Performance is highly sensitive to thermal fluctuations

Applications: Fabrication of transistors and diodes; Semiconductor substrate for Integrated Circuits

Additional Info: Germanium has a much lower intrinsic resistivity of approximately $45	ext{ }\Omega	ext{ cm}$ compared to silicon.. Option D represents the resistivity of a good conductor like copper ($1.68 	imes 10^{-8}	ext{ }\Omega	ext{ m}$).

Answer: B is correct — Pure silicon acts as an intrinsic semiconductor with a resistivity of approximately $6000	ext{ }\Omega	ext{ cm}$ at room temperature.

Exam Tip: Remember that resistivity of semiconductors decreases exponentially with temperature, while for metals, it increases linearly.

Examoogle · Answer

Option A: $100	ext{ }\Omega	ext{ cm}$

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Option C: $3 	imes 10^5	ext{ }\Omega	ext{ cm}$

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Option D: $1.6 	imes 10^{-8}	ext{ }\Omega	ext{ cm}$

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