Semiconductors : Drift Velocity vs Electric field

Drift Velocity vs Electric Field : Understanding Saturation and Behavior Across Ranges

In semiconductor physics, the relationship between drift velocity and electric field is not always linear. This blog explores how electrons behave under increasing electric field strengths and explains why drift velocity saturates at high fields. We also touch upon the roles of internal and external electric fields in influencing carrier motion.

What is Drift Velocity?


Drift velocity refers to the average velocity attained by electrons or holes when an electric field is applied across a semiconductor.

  • It’s the net motion superimposed on random thermal motion.

  • Responsible for current flow in devices like diodes and transistors.

Internal vs. External Electric Fields

Before diving into the graph, it's essential to understand the difference between two types of electric fields:

  • Internal Electric Field:

    • Arises from charges inside the material (due to doping, lattice alignment, etc.).

    • In many cases, internal fields cancel each other, producing no net motion.

  • External Electric Field:

    • Applied from outside the material.

    • Responsible for creating a net force on electrons, leading to drift velocity.

 Only the external electric field causes measurable drift in a semiconductor.

Drift Velocity vs. Electric Field: Three Key Regions

The behavior of drift velocity with increasing electric field can be understood in three distinct regions.

1. Linear Region (0< E < 10³ V/cm )

  • Drift velocity increases linearly with electric field.

  • Behavior: Like a ramp — more electric field → more kinetic energy → more drift.

  • This region follows Ohm’s law:


    where  is drift velocity,  is mobility, and E is electric field.

  • Ideal region for basic circuit operation.

2. Non-linear/Sub-linear Region (10³ V/cm < E < 10⁴ V/cm)

  • Drift velocity increases slowly, deviating from the linear trend.

  • Why? Carriers begin to collide more with the lattice (phonon scattering).

  • Result: Energy gained from the field is lost due to frequent collisions.

  • Increasing electric field has diminishing effect on drift velocity.

3. Saturation Region (E > 10⁴ V/cm)

  • Drift velocity reaches a maximum — known as saturation velocity.

  • No matter how much the electric field increases, drift velocity remains constant.

  • Reason:

    • All electrons are already energized.

    • The semiconductor’s band structure limits how fast carriers can move.

    • No additional free carriers can be excited into conduction.

    • Further increasing the field does not increase current — this is crucial in high-speed transistors like MOSFETs.

Velocity Saturation: Why It Matters

  • Limits maximum current in short-channel devices.

  • Affects switching speed and power dissipation.

  • Designers must account for saturation velocity when modeling device behavior.

Real-World Relevance: Importance of Drift Velocity Behavior

  • CMOS Transistors

    • Limits on current drive and delay times.

  • Power Electronics

    • Impacts high-voltage device performance.
  • RF & Microwave Circuits

    • Affects signal speed and integrity.

  • VLSI Design

    • Determines speed vs. power trade-off.

Summary:

  • Linear Region (0 – 10³ V/cm)
    • Drift velocity increases linearly.
    • Dominated by carrier mobility.

  • Non-linear Region (10³ – 10⁴ V/cm)
    •  Drift velocity increases more slowly.
    •  Due to increased lattice collisions.
  • Saturation Region (> 10⁴ V/cm)

    • Drift velocity becomes constant.
    • Limited by velocity saturation – further increase in electric field has no effect.
To understand the effect of temperature on mobility of semiconductors - Click here

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