driftdiffusion

Drift-diffusion, or the drift-diffusion model, is a semiclassical approach to describing charge transport in semiconductor devices. It describes how charge carriers move under the influence of electric fields (drift) and concentration gradients (diffusion). The fundamental variables are electron density n, hole density p, and the electrostatic potential φ. The electron and hole current densities are J_n = q μ_n n E + q D_n ∇n and J_p = q μ_p p E - q D_p ∇p, where E is the electric field given by E = -∇φ, μ is the carrier mobility, and D is the diffusion coefficient. The diffusion and mobility are related by the Einstein relation D = μ k_B T/q. The carrier continuity equations couple transport to generation and recombination: ∂n/∂t = (1/q) ∇·J_n + G - R and ∂p/∂t = -(1/q) ∇·J_p + G - R. Poisson’s equation, ∇·(ε ∇φ) = q(p - n + N_D^+ - N_A^-), determines the electrostatic potential from charge distribution. Boundary conditions specify carrier densities or fluxes and the contact potential.

The drift-diffusion model is widely used in device simulation (TCAD) for diodes, transistors, solar cells, and light-emitting devices. It is typically solved self-consistently with models for recombination-generation, mobility, and sometimes quantum or degeneracy corrections in doped or nanoscale regions. Limitations include neglect of ballistic transport, quantum confinement, and nonlocal effects in very small or high-field structures, where more advanced approaches such as hydrodynamic models or quantum transport methods may be more appropriate.