Mobility of Electrons

Mobility of electrons is an important concept in Current Electricity because it connects the electric field, drift velocity, and microscopic current flow in conductors and semiconductors. The source material defines mobility, derives its formula, relates it to current density, and notes its temperature dependence and use in semiconductor physics.

Mobility is the magnitude of drift velocity per unit electric field.

μ = \[\frac {∣v_d​∣}{E}\]​

where:

Step 1: Force on an electron

When an electric field E is applied, an electron experiences a force:

This force produces acceleration of the electron. 

Step 2: Acceleration of the electron

Using Newton’s second law,

where m is the mass of the electron. 

Step 3: Drift velocity

If τ is the average time between two successive collisions, then

So,

This is the expression for drift velocity. 

Step 4: Mobility formula

Mobility is the drift velocity per unit electric field. Therefore,

Substituting the expression for v_d,

Hence, mobility depends on charge, relaxation time, and mass of the charge carrier. 

• Mobility measures how quickly charge carriers respond to an applied electric field. 
• If mobility is high, carriers move more easily, and drift velocity is larger for the same electric field. 
• If mobility is low, the motion of carriers is more strongly hindered by collisions. 

Easy analogy

• Imagine students walking through a corridor.
• If the corridor is clear, they move easily; this is like high mobility.
• If the corridor is crowded, motion is obstructed; this is like low mobility.

From the microscopic current relation,

Using

we get

This relation connects mobility with current density in a conductor. 

Important point

• If the electric field E = 1 V m⁻¹, then the numerical value of mobility equals the drift velocity.

In semiconductors, current may be carried by both electrons and holes. The source material notes that hole mobility is smaller than electron mobility. 

Important concept

• Mobility decreases with increase in temperature. 
• At higher temperatures, collisions become more frequent. 
• Therefore, relaxation time τ decreases, and mobility also decreases because μ = eτ/m.

Quick chain

Temperature increases → collisions increase → relaxation time decreases → mobility decreases