Drift occurs when electric field is applied to a semiconductor and free electrons move or drift towards the positive terminal of the voltage source.
We know from equation
$$Drift Velocity=Mobility*Electric Field$$
that with increase in electric field the drift velocity increases.But why?With increase in electric field only the number of electrons from the negative terminal of the voltage source increases.Why does drift velocity increases with increase in number of electrons from the negative terminal?
Thanks for your time.
[Physics] Why drift velocity increases with increase in applied electric field
electric-fieldselectronssemiconductor-physicssolid-state-physics
Related Solutions
The way mobility depends on average scattering time of the carriers is given here:
A simple model gives the approximate relation between scattering time (average time between scattering events) and mobility. It is assumed that after each scattering event, the carrier's motion is randomized, so it has zero average velocity. After that, it accelerates uniformly in the electric field, until it scatters again. The resulting average drift mobility
where q is the elementary charge, m* is the carrier effective mass, and τ is the average scattering time.
If the effective mass is anisotropic (direction-dependent), m* is the effective mass in the direction of the electric field.
The higher the temperature , i.e. the more kinetic energy the carriers have, the faster they will meet a scattering center. So in a simple model the higher the temperature the smaller the mobility.
With increasing temperature, phonon concentration increases and causes increased scattering. Thus lattice scattering lowers the carrier mobility more and more at higher temperature. Theoretical calculations reveal that the mobility in non-polar semiconductors, such as silicon and germanium, is dominated by acoustic phonon interaction.
A rough human size analogy for slow motion (long scattering time, low temperature) versus fast: A crowd in a square listening to a speaker. They are still except for random mobility of changing places for friends or access to seats.... There will be no problem with mobility, i.e a person can go through the crowd easily. If an explosion is heard , everybody will start running and hitting each other (high temperature low mobility) . People die trampled in panic situations.
It is a thermal effect, the corresponding "force" is a so called stochastic force and not a fundamental force, but rather an effective description of entropic effects. Having a temperature causes the charge carriers to move about randomly, and therefore they tend to move from regions with high concentration to regions with low concentrations.
At first it is just like dissolving sugar in water: Near the surface of the sugar there is a high sugar concentration, so the random thermal motion of the sugar molecules tends to transport the sugar away from the source (as less sugar flows back from the region with lower concentration, than flows to the region with lower concentration). But now something happens that has no analogue in the comparison with sugar: Because the diffusing objects are charge carriers, an electric field forms, which counteracts the motion of the particles, so a steady state is reached.
The equations for the steady state of this process are described at the Wikipedia page on the p-n junction.
Best Answer
Statistically, electrons undergo random collisions with the crystal lattice of the conductor. This makes their velocity vectors just after one of these collisions purely random($v_i$). Now suppose we apply an electric field $\vec E$ across the conductor. Think of this field as an agent who introduces slight order in this chaos of randomly moving electrons. Due to this order, electrons have a tendency to move in a particular direction. Assume the mass of electron to be $m$ and charge to be $e$. Then the velocity $V_i$ of the ith electron between 2 consecutive collisions is given by :
$\vec V_i = \vec v_i + \frac{e.\vec E.t}{m}$ where t is the time elapsed after the first collision.
Averaging both sides over the average time beetween 2 successive collisions (relaxation time $\tau$)
$\lt \vec V_i \gt = \lt \vec v_i \gt + \frac{e\tau.\vec E}{m}$
The lhs is the drift velocity and the 2nd term is zero because just after collision, the direction of motion is random. Thus,
$\vec v_d = \frac{e.\vec E. \tau}{m}$
As the electric field increases, more order is introduced in the system and hence the drift velocity increases. The mathematical variation is given by the last eqn above.