diffusionstransport

Diffusionstransport, in short diffusion-transport, is a modeling framework used to describe the motion of particles or carriers when both diffusion due to concentration gradients and directed motion (drift) caused by forces such as electric fields are important. It treats transport as an interplay between random scattering processes that tend to smooth out inhomogeneities and systematic forces that push particles along preferred directions. The diffusion-transport description often arises as an intermediate or practical approximation to more fundamental transport equations, such as the Boltzmann transport equation.

In semiconductor physics, diffusion-transport is most commonly implemented as the drift-diffusion model. For electrons and holes, the current densities combine drift and diffusion terms: J_n = q μ_n n E + q D_n ∇n for electrons and J_p = q μ_p p E − q D_p ∇p for holes, where μ is mobility, D is the diffusion coefficient, E is the electric field, and q is the elementary charge. The carrier densities n and p evolve according to continuity equations, coupled to Poisson’s equation for the electrostatic potential. The Einstein relation D = (k_B T / q) μ ties diffusion to mobility. This framework is widely used for designing and analyzing semiconductor devices and solar cells.

In neutron, photon, or particle transport, a diffusion-transport equation can approximate the full Boltzmann transport equation, improving on pure diffusion theory by incorporating some angular transport effects. It is used in nuclear reactor analysis and radiation shielding, often with transport corrections or higher-order closures.

Limitations include breakdown in the ballistic or strongly nonlocal regime, nanoscale devices, or highly nonuniform fields, where more exact transport descriptions are required.