Microscopic properties of electrical resistance

  1. Jimmy87

    Jimmy87 248
    Gold Member

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

    [itex]\rho[/itex] = 2m/qN[itex]\tau[/itex] where [itex]\tau[/itex] 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 ([itex]\tau[/itex]). 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. jcsd
  3. DrDu

    DrDu 4,112
    Science Advisor

    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.
    1 person likes this.
  4. ZapperZ

    ZapperZ 29,763
    Staff Emeritus
    Science Advisor
    Gold Member

    I recommend you read this paper by Valla et al.


    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.

    Last edited: Apr 27, 2014
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