Mathematical Models for Nano Science - Politecnico di Milano

Model equations - 1
• Excited state
equation
{ ∂X
∂t = G − k recX − k diss X + γnp in Ω
X (x, 0) = X 0 (x) in Ω.
• No diffusion → ODE → no need for boundary conditions
• Generation term G(x, t): constant, Beer-Lambert
• Dissociation rate constant k diss (E) according to Onsager theory
• Langevin bimolecular recombination γnp
• Electron
equation
⎧
∂n
∂t − 1 q div J n = k diss X − γnp in Ω
⎪⎨
J n = qD n ∇n − qµ n n∇ϕ in Ω
1
γ n
q J n · ν = β n − α n n on Γ A ∪ Γ C
⎪⎩
n(x, 0) = n 0 (x) in Ω.
• Drift-Diffusion model • Scott-Malliaras boundary conditions
• Simplified Poole-Frenkel model for mobility µ(E)