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Science · Advanced Physics
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(b) Consider the following diagram for the resistivity ρ of a sample as a function of temperature T 100 50 100 200 300 TIK) The resistivity (p) of the sample can be accounted for by considering contri- butions from both the impurities (Pimpurity) and the phonons (Pphonons). The number of electron collisions with phonons is proportional to the number den- sity (ns)of the phonons and is given by: where z 8p/T with Θ the Debye temperature and T the temperature and y= , where wD s the Debye frequency. Is the material a metal or an insulator? Which contribution to the electron scattering dominates at low temperature (very near 0K). Give a reason for your answer. Res istiv heresses 2 2Around 25 K the resistivity is dominated by electrons being scattered by both é impurities and phonons. if) By considering scattering off phonons only, show that: Assume that in the correct limit K where K is a constant and that 9 (iii) Is the material a good conductor, assuming that τ = 3x10-16 s and the electron 3] ev- the electron momenta change, when scattered off a phonon is small. velocity is 1x108 cm s-1 at300 K?
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