Theory of drift diffusion modelling

1. Introduction

OghmaNano’s electrical model is a flexible drift–diffusion framework that can be run in 1D, 2D, or full 3D, depending on the options selected. This makes it applicable across a wide range of devices: 1D for standard solar cells, 2D for planar devices such as OFETs, and 3D for more complex architectures such as bulk heterojunctions. What makes OghmaNano’s implementation distinctive is its detailed treatment of trap states. Users can define their own trap state distributions in energy space, allowing a physically realistic description of disordered materials. Trap-assisted recombination is treated explicitly through the full Shockley–Read–Hall formalism as a function of both energy and position. This approach is crucial for accurately modeling disordered semiconductors, where trap distributions strongly affect carrier mobility, recombination rates, and transient responses. (See Disordered Materials for further discussion.) By avoiding the assumption that all trap states are always in equilibrium, OghmaNano enables the correct simulation of transients such as time-of-flight (ToF) and CELIV measurements, alongside steady-state operation. Ordered materials can also be modeled by simply switching off traps.

The solver architecture is designed for flexibility and performance. At its core, OghmaNano can either solve the entire set of coupled drift–diffusion and Poisson equations within a single 1D/2D/3D Jacobian system, or use Alternating Direction Implicit (ADI) methods, solving in successive slices along different spatial directions. For even greater control, the solvers for Poisson’s equation, the electron continuity equation, and the hole continuity equation can be run independently and then coupled iteratively. In addition, the full solver core is scriptable via LuaScript, making it possible to set up custom workflows, parameter scans, or hybrid simulation strategies. This gives researchers both the robustness of a ready-to-use multiphysics solver and the flexibility to extend or tailor simulations to their own needs. The remainder of this section introduces the underlying physics of the drift–diffusion model: the description of carrier transport via drift and diffusion, the solution of Poisson’s equation for the electrostatic potential, and the use of Fermi–Dirac statistics to describe carrier populations.