Help with electrical resistivity equation

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SUMMARY

The discussion centers on the electrical resistivity equation, specifically the formula ρ = (m/ne²)(1/τ). Key variables include m, the effective mass of charge carriers; n, the number density of free charge carriers; e, the elementary charge; and τ, the relaxation time. The effective mass for free electrons in silicon is approximately 0.35 times the electron mass. Understanding these variables is crucial for analyzing electrical resistivity in materials.

PREREQUISITES
  • Understanding of electrical resistivity concepts
  • Familiarity with semiconductor physics
  • Knowledge of charge carriers in solids
  • Basic grasp of band theory in materials science
NEXT STEPS
  • Research the effective mass of charge carriers in different materials
  • Study the role of relaxation time (τ) in electrical conductivity
  • Explore the relationship between band structure and electrical properties
  • Learn about the calculation of number density (n) in semiconductors
USEFUL FOR

This discussion is beneficial for physics students, materials scientists, and electrical engineers seeking to deepen their understanding of electrical resistivity and its underlying principles.

niqolas619
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Homework Statement



I'm just trying to understand what the variables in this equation represent. This is part of a study of electrical resistivity lab that I am doing. I don't have my Kittel book with me, and the lab manual for some reason doesn't define these variables.

Homework Equations



[tex]\rho = \frac{m}{ne^2} \frac{1}{\tau}[/tex]

The Attempt at a Solution



I could kind of guess at some of them - m = atomic mass, e = elementary charge, [tex]\tau[/tex] = relaxation time...but what about n? And I'm not sure about m, either.
Thanks.
 
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n is the number density of the free charge carriers, electrons in the conduction band or holes in the valence band, and m is their effective mass, which is not the same as the electron mass, as it is connected to the band structure. For free electrons in silicon, the effective mass is about 0.35 times the electron mass.

ehild
 

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