What Is the Semiconductor Carrier Drift-Diffusion & Einstein Relation Calculator?
The drift-diffusion equation is the foundational model of electrical charge transport in semiconductor devices.
How Does the Semiconductor Carrier Drift-Diffusion & Einstein Relation Calculator Work?
Drift currents arise from electrostatic forces while diffusion currents arise from thermal Brownian motion down density gradients.
Semiconductor Carrier Drift-Diffusion & Einstein Relation Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
J = q n mu E + q D rac{dn}{dx}, quad D = mu rac{k_B T}{q}
Total carrier transport current density and Einstein relation for diffusivity.
How to Use the Semiconductor Carrier Drift-Diffusion & Einstein Relation Calculator
- Enter carrier density, mobility, electric field, concentration gradient, and temperature.
Step-by-Step Example Calculation
Silicon N-Type Conduction Channel
Input Values:
carrierConcentrationCm3:10000000000000000
carrierMobilityCm2Vs:1200
electricFieldVPerCm:250
concentrationGradientCm4:10000000000000000000
temperatureKelvin:300
Worked Steps: Drift current = 480.6 A/cm², diffusion current = 49.6 A/cm², total current = 530.2 A/cm².
Understanding Your Result
Displays individual drift and diffusion current densities and the Einstein thermal diffusion coefficient.
Factors That Affect the Result
- High electric fields cause velocity saturation; high doping causes impurity scattering that reduces mobility.
When Should You Use This Calculator?
- Diode forward current modeling, bipolar transistor base transport, and solar cell minority carrier collection.
Assumptions & Limitations
- Assumes low-field linear drift without velocity saturation or hot-carrier effects.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard drift-diffusion transport model.