Drift Velocity, Mobility & Relaxation Time: What Makes Current Flow?

When you connect a battery across any material, you're setting the stage for a dance of electrons. But it’s not as simple as they all running in sync. The reality? Electrons drift — and they take their sweet time.

Let’s explore the most underrated yet crucial concepts in electronics: Drift Velocity, Mobility, Collision Time, and Relaxation Time.

 What Is Drift Velocity?

When both terminals of a material are connected to a battery, an electric field is applied across the material. This field pushes the negatively charged electrons, causing them to move opposite to the electric field.

But electrons don’t rush straight — they bump into atoms, scatter, and zigzag. The result is a slow average movement called Drift Velocity.

Drift Velocity:

It is the average velocity with which free charge carriers (like electrons or holes) drift under the influence of an electric field.

Electrons are constantly colliding with positive and negative ions in the lattice:

• Positive ions attract electrons.

• Negative ions repel them. The stronger the negative charge, the greater the repulsion.

• Holes don’t repel or attract — they’re just places electrons can go.

The net result is a slow and steady flow of electrons — opposite to conventional current direction.

Drift Velocity Is Proportional to the Electric Field 

Drift velocity is directly proportional to the electric field applied:

To convert this into an equation, we add a proportionality constant called mobility (µ):

If you’re calculating for electrons, use µₙ (mobility of electrons).

If you’re calculating for holes, use µₚ (mobility of holes).

What is Mobility?

Mobility tells us how easily a charge carrier (electron or hole) can move through a material when an electric field is applied.

It’s defined as:

In simple terms:

“Mobility is a measure of how quickly an electron or hole can move through a semiconductor under the influence of an electric field.”

Higher mobility means:

• Faster electrons

• Better conductivity

• Lower resistance

Collision Time – What Slows the Electrons?

Electrons don’t flow in a vacuum — they collide with atoms, impurities, and vibrations.

The average time between two collisions is called Collision Time (τ).

During each collision, electrons lose direction and speed, then resume drifting — repeating the process. This is why drift velocity is much slower than random thermal speed.

What Happens When the Electric Field is Switched Off?

Here’s a cool concept to think about:

What happens if we suddenly switch off the electric field in a conductor or semiconductor?

Do electrons stop moving instantly? Nope.

Just like a moving car doesn’t come to a halt the moment you hit the brakes, electrons continue to drift momentarily due to their inertia. This delay before they completely stop is called Relaxation Time.

What is Relaxation Time?

Relaxation Time (τ) is the time taken for the drift current or electron motion to reduce to zero after the external electric field is removed.

It’s a key concept in:

• Designing fast-switching circuits

• High-speed communication

• Understanding transient behavior in electronics

Drift Current Density:

Total Drift Current:

Where:

• J = Drift current density (A/m²)

• I = Drift current (A)

• N = Number of charge carriers per unit volume (m⁻³)

• e = Charge of an electron (1.6 × 10⁻¹⁹ C)

• A = Cross-sectional area of the conductor (m²)

• V_d = Drift velocity (m/s)

Key Insight:

Drift velocity is directly proportional to current.

As current increases, drift velocity also increases — and vice versa.

 Exponential Decay of Current (After Field Removal)

When the electric field is suddenly removed, the current decays exponentially over time. This behavior is modeled by:

Important Note: This curve is similar to what we observe in capacitor discharge or signal fall-off in high-speed systems.

Summary Recap:

• Drift velocity: Slow average motion of electrons under an electric field

• Mobility (µ): Indicates how easily carriers move — higher µ = faster movement

• Collision time: Time between two collisions

• Relaxation time: Time taken to stop after field is turned off

These aren't just theoretical — they govern everything from basic circuits to semiconductor device performance and VLSI speed.

Coming up next in the EDC Series: We explore Conductivity, Resistivity, and how the charge carriers and their motion directly define a material’s ability to conduct electricity.

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