Perovskite mobile ion solver
Hybrid perovskites are well known for exhibiting significant ionic motion under applied bias or illumination. This slow redistribution of mobile ions (such as iodide, bromide, or vacancies) leads to current–voltage hysteresis, bias-dependent degradation, and transient phenomena that cannot be captured by purely electronic drift–diffusion models. To account for this behaviour, OghmaNano includes a dedicated mobile ion solver, implemented following the approach introduced by Calado et al..
The governing equation for the ionic flux is given by a drift–diffusion form:
\[ \boldsymbol{J_a} = q \mu_a a_{f} \nabla E_{v} \;-\; q D_a \nabla a_{f}, \label{eq:pdrive} \]
where:
- \(q\) is the elementary charge,
- \(\mu_a\) is the mobility of the mobile ionic species,
- \(a_f\) is the free ion density,
- \(E_v\) is the electrostatic potential, and
- \(D_a\) is the diffusion coefficient of the ions, related to \(\mu_a\) by the Nernst–Einstein relation.
The time evolution of the ionic density is then obtained from the continuity equation:
\[ \nabla \cdot \boldsymbol{J_a} = - q \frac{\partial a}{\partial t}, \label{eq:contp} \]
This pair of equations describes how ions drift in response to local electric fields and diffuse down concentration gradients, while also ensuring particle conservation. Boundary conditions are used to represent blocking or injecting contacts, depending on the physical scenario under investigation.
In practice, solving these equations alongside the electronic drift–diffusion equations allows OghmaNano to reproduce key experimental features of perovskite devices, including hysteresis in JV curves, slow transient currents, and the redistribution of the internal electric field under bias stress. This makes the ion solver an essential tool for interpreting perovskite device behaviour beyond the steady-state electronic picture.