Calculating Resistivity and Conductivity in Doped Semiconductors: a Practical Guide

Understanding how to calculate resistivity and conductivity in doped semiconductors is essential for designing electronic devices. This guide provides practical steps to perform these calculations based on doping levels and material properties.

Basics of Resistivity and Conductivity

Resistivity is a measure of how strongly a material opposes the flow of electric current. Conductivity is the inverse of resistivity and indicates how easily current can pass through a material. Both properties depend on the material’s composition and doping level.

Calculating Resistivity

The resistivity ((rho)) of a doped semiconductor can be calculated using the formula:

(rho = frac{1}{q times mu times N})

Where:

• q = elementary charge (~1.6 × 10^-19 C)
• μ = mobility of charge carriers (cm²/V·s)
• N = doping concentration (cm^-3)

By substituting known values, you can determine the resistivity of the doped semiconductor.

Calculating Conductivity

Conductivity ((sigma)) is calculated as the reciprocal of resistivity:

(sigma = q times mu times N)

This formula shows that increasing doping concentration or carrier mobility enhances conductivity.

Practical Example

Suppose a silicon semiconductor is doped with a concentration of 1 × 10¹⁷ cm^-3. If the mobility of electrons is 1350 cm²/V·s, then:

Resistivity:

(rho = frac{1}{(1.6 times 10^{-19}) times 1350 times 1 times 10^{17}})

Conductivity:

(sigma = (1.6 times 10^{-19}) times 1350 times 1 times 10^{17})