Electrical Mobility Calculator
Calculate electrical mobility and diffusion using Einstein-Smoluchowski relation
Einstein-Smoluchowski Relation
Electrical Mobility (μ)
Temperature (T)
Charge (q)
Results
Material Examples
Copper (electrons)
Silicon (electrons)
Na⁺ in water
Key Concepts
Electrical Mobility
Velocity per unit electric field
Diffusion Constant
Rate of spreading in thermal motion
Drift Velocity
Average velocity in electric field
Charge Carriers
Electrons, holes, or ions
Physical Constants
Boltzmann Constant
kB = 1.381 × 10⁻²³ J/K
Elementary Charge
e = 1.602 × 10⁻¹⁹ C
Room Temperature
T = 293.15 K (20°C)
Understanding Electrical Mobility
What is Electrical Mobility?
Electrical mobility (μ) is a fundamental property that describes how quickly charge carriers (electrons, holes, or ions) move through a material when subjected to an electric field. It's defined as the drift velocity per unit electric field strength.
Einstein-Smoluchowski Relation
This fundamental relation connects the random thermal motion of particles (characterized by the diffusion constant D) to their response to external electric fields (characterized by electrical mobility μ).
Physical Interpretation
Diffusion Constant (D):
Measures how fast particles spread due to thermal motion
Mobility (μ):
Measures how fast particles move in an electric field
Temperature (T):
Higher temperature increases both diffusion and thermal energy
Applications and Examples
Semiconductors
- • Silicon: electron mobility ≈ 1350 mm²/(V⋅s)
- • Germanium: electron mobility ≈ 3900 mm²/(V⋅s)
- • GaAs: electron mobility ≈ 8500 mm²/(V⋅s)
- • Temperature dependence: μ ∝ T⁻³/²
Electrolytes
- • Na⁺ in water: ≈ 0.052 mm²/(V⋅s)
- • Cl⁻ in water: ≈ 0.079 mm²/(V⋅s)
- • H⁺ in water: ≈ 0.363 mm²/(V⋅s)
- • Depends on ion size and hydration
Mathematical Relationships
Einstein Relation
D = μ kB T / |q|
Drift Velocity
vd = μ E
Conductivity
σ = n q μ