The concentration of donor impurity atoms in silicon is Nd=10^15 cm^-3. Assume an electron mobi

step 1 In this question we have to find the resistivity and the conductivity of the given material. So

The concentration of donor impurity atoms in silicon is...

The concentration of donor impurity atoms in silicon is $N_{d}=10^{15} \mathrm{~cm}^{-3}$. Assume an electron mobility of $\mu_{n}=1300 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$ and a hole mobility of $\mu_{p}=450 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$. (a) Calculate the resistivity of the material. ( $b$ ) What is the conductivity of the material?

The concentration of donor impurity atoms in silicon is $N_{d}=10^{15} \mathrm{~cm}^{-3}$. Assume an electron mobility of $\mu_{n}=1300 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$ and a hole mobility of $\mu_{p}=450 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$.
(a) Calculate the resistivity of the material.
( $b$ ) What is the conductivity of the material?

Key Concepts

Conductivity in Semiconductors

Conductivity is a measure of how easily electric current flows through a material. In semiconductors, it is determined by both the concentration of charge carriers (electrons and holes) and their mobilities. The relationship is typically given by ? = q (n?? + p??), where q is the electron charge, n and p are the electron and hole concentrations, and ?? and ?? are their respective mobilities.

Resistivity

Resistivity is the reciprocal of conductivity and quantifies how strongly a material opposes the flow of electric current. It is defined by the equation ? = 1/?. Calculating the resistivity of a semiconductor involves determining its conductivity from the carrier concentrations and mobilities, then taking the inverse to find how resistant the material is to current flow.

Carrier Mobility

Carrier mobility refers to how quickly charge carriers (electrons or holes) can move through a semiconductor when an electric field is applied. It is a critical factor in determining the conductivity because higher mobility allows for greater current flow for a given carrier concentration. Mobility is affected by various scattering mechanisms within the material.

Semiconductor Doping

Doping involves intentionally introducing impurities into a semiconductor to modify its electrical properties. In the case of donor doping in silicon, pentavalent atoms add extra electrons, increasing the concentration of free electrons and thereby enhancing conductivity. Doping creates an extrinsic semiconductor where the majority carrier concentration is controlled by the dopant atoms.

Extrinsic Semiconductors

Extrinsic semiconductors are materials whose electrical properties are dominated by impurities (dopants) rather than the intrinsic electron-hole pairs generated in pure materials. In an n-type semiconductor, donor impurities provide extra electrons as the majority carriers. This concept is crucial for analyzing and calculating the conductivity and resistivity based on dopant concentrations and carrier mobilities.

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