This document discusses key concepts in conducting and superconducting materials including relaxation time, collision time, Fermi energy, and mean free path. It defines relaxation time as the average time between collisions of an electron with the lattice. Mean free path is defined as the average distance traveled by an electron between collisions. The document derives an equation showing the mean free path is proportional to the Fermi velocity divided by the probability of collision per unit time. It also relates relaxation time and collision time, stating they are equal for isotropic materials.

1. ELECTRICAL ENGINEERING
MATERIALS: CONDUCTING &
SUPERCONDUCTING MATERIALS
MR. ASIF L. JAMADAR

2. RELAXATION TIME, COLLISION TIME, FERMI ENERGY & MEAN
FREE PATH
 Relaxation Time
 Mean Free Path
 Collision are caused by thermal or
structure imperfection in lattice
Vx is not equal to zero
 At any instant the velocity is given by,
2

3.  The rate of change of velocity due to collision becomes
 The fractional force due to collision may be expressed as,
 The modified equation of electrons become
 In the absence of the external forces (-eE), the free motion satisfies,
 If is the initial drift velocity in non-equilibrium distribution then the
approach to equilibrium can be described by the solution of above equation,

4.  Consider relation of collision time of an electron with its probability of collision.
 Let dt/τc be the probability of an electron collide with lattice during short time dt
 We can write,
 From probability theory,
 In terms of dt/τc we have,
 From above equations,
 By comparing first & last equation,

5.  By integrating the above eaquation for R(t)=1 at t=0 then,
 The probability that collision occurs before time (t + dt)
 The probability that collision occurs before time t
 Therefore the probability that collision occurs during time dt, between time t &
(t + dt) is,
 Keeping the above equation in view, the average time that elapses between
collision may be written as

6.  We know,
 By substituting the above equation and solving the integral, we get,
 For isotropy material, the mean time of collision is same as the relaxation time
that is,
τc = τr
 The mean path of an electron ( λ ) is defined as
 WF is the Fermi level of electrons (Fermi Energy)

7.  At any temperature T, the probability of a state corresponding to an energy W
being occupied by an electron is given by
 The velocity of an electron with Fermi energy ( VF) is given by,
 So Mean Free Path is
 The magnitude of WF is of the order of several electron volts.

8. THANK
YOU
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