Mobility in Semiconductor Physics

 

1. Introduction

In semiconductor physics, mobility is one of the most important parameters that determines how well a material conducts electricity. It describes how quickly charge carriers (electrons and holes) can move through a semiconductor when an electric field is applied.

Mobility directly affects the performance of electronic devices such as diodes, transistors, and integrated circuits. Materials with higher mobility allow faster signal transmission and better efficiency.

2. Definition of Mobility

Mobility is defined as:

The drift velocity of charge carriers per unit electric field.

This means it tells us how fast electrons or holes move when an electric field is applied.

3. Mathematical Expression

μ= v_d/E

Where:

μ = mobility (m²/V·s)

 v_d = drift velocity of charge carriers

 E = electric field

4. Drift Velocity and Mobility

When an electric field is applied to a semiconductor

Charge carriers experience a force

 They accelerate but frequently collide with atoms

Due to collisions, they move with an average velocity called drift velocity

Mobility tells how easily carriers achieve this drift velocity.

5. Types of Mobility

1. Electron Mobility (μₑ)

Movement of electrons in the conduction band

 Higher than hole mobility

 Electrons are lighter and move faster

2. Hole Mobility

Movement of holes in the valence band

 Lower than electron mobility

Holes are not real particles but absence of electrons

6. Relation Between Mobility and Conductivity

Mobility is directly related to electrical conductivity.

σ= nq μ

Where:

σ = electrical conductivity

 n  = number of charge carriers

 q  = charge of electron

 μ = mobility

For Semiconductors:

 σ = q (n μ_e + p μ_h)

Where:

 n= electron concentration

 p  = hole concentration

7. Physical Meaning of Mobility

Mobility represents:

Ease of movement of charge carriers

Scattering effects inside the material

 Quality of the crystal structure

 High mobility → carriers move easily → better conductivity

 Low mobility → more collisions → poor conductivity

8. Factors Affecting Mobility

1. Temperature

 As temperature increases:

  Lattice vibrations increase

  Collisions increase

  Mobility decreases

Mobility ∝ 1 / Temperature (approximately)

2. Impurity Concentration

 Doping introduces impurities

 More impurities → more scattering

 Mobility decreases

3. Crystal Structure

Perfect crystal → fewer defects → high mobility

 Defective crystal → low mobility

4. Electric Field Strength

At low fields → mobility is constant

 At very high fields → velocity saturates → mobility reduces

9. Mobility in Different Materials

Material	Electron Mobility (cm²/V·s)	Hole Mobility (cm²/V·s)
Silicon (Si)	~1350	~480
Germanium (Ge)	~3900	~1900
Gallium Arsenide (GaAs)	~8500	~400

 

 Electron mobility is always greater than hole mobility.

10. Mobility and Relaxation Time

Mobility can also be expressed as:

μ = q τ/m*

Where:

 τ = relaxation time (time between collisions)

 m* = effective mass of carrier

Interpretation

Larger relaxation time → fewer collisions → higher mobility

Smaller effective mass → easier movement → higher mobility

11. Importance of Mobility

Mobility plays a crucial role in semiconductor devices:

1. Determines Conductivity

Higher mobility → higher current flow

2. Affects Device Speed

High mobility → faster switching

 Used in high-speed electronics

3. Important in Transistors

 Mobility affects current gain and response time

4. Used in Material Selection

High mobility materials used in advanced devices

12. Applications

Transistors (MOSFETs, BJTs)

Integrated circuits

Solar cells

LEDs

 High-speed communication devices

13. Mobility Vs Drift Velocity

Mobility	Drift Velocity
Property of material	Motion of carriers
Independent of field (low field)	Depends on electric field
Unit: m²/V·s	Unit: m/s

 

14. Mobility in Intrinsic and Extrinsic Semiconductors

Intrinsic Semiconductor

 Equal electrons and holes

Mobility depends only on temperature

Extrinsic Semiconductor

Doped material

Mobility affected by impurity scattering

15. Limitations of Mobility

 Not constant at high electric fields

 Affected by many factors

Different for electrons and holes

Conclusion

Mobility is a key concept in semiconductor physics that describes how easily charge carriers move under an electric field. It is directly related to conductivity and plays a vital role in determining the efficiency and speed of electronic devices.

Understanding mobility helps in designing better semiconductors and improving modern electronic technology. High mobility materials are essential for faster, smaller, and more efficient electronic devices.