# Microscopic properties of electrical resistance

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1. Apr 26, 2014

### Jimmy87

I have recently been learning about the microscope properties which dictates electrical resistance. The main equation (resistivity) in my textbook is:

$\rho$ = 2m/qN$\tau$ where $\tau$ is the time between collisions of electrons with the atoms, q is the charge of the electron, N is the number of free electrons and m is the mass of the electron.

These properties are fixed for a given material. I am quite comfortable with why certain materials have more free electrons than others. But I was wondering if anyone knows what determines the time between collisions for a resistor ($\tau$). Say if a certain material has less time between collisions then what is it about the material that determines this? Is it to do with the density of the material, so a more dense material has more atoms per unit volume so there would be less time between collisions?

Thanks for any help

2. Apr 27, 2014

### DrDu

The theory is much more involved because due to the quantum mechanical behaviour, scattering in an ideal lattice does not lead to resistivity. It is mostly scattering from impurities and defects, and, in very pure samples, also from phonons, i.e. fluctuations from the ideal positions of the ions. So the scattering time depends on concentration of impurities and on temperature.

3. Apr 27, 2014

### ZapperZ

Staff Emeritus
I recommend you read this paper by Valla et al.

http://arxiv.org/abs/cond-mat/9904449

On the top of page 2, they wrote down all the factors that influences the scattering rate, which is the inverse of the collision time. You will see the type of scattering in a typical fermi liquid metal that can influence charge transport.

Zz.

Last edited: Apr 27, 2014