Mathematical Models for Nano Science - Politecnico di Milano

Model equations - 1
• Exciton
equation
⎧
∂X
∂t + div J X = G − X τ X
⎪⎨
∂X
∂t + div J X = G − X −
X + ηk rec P
τ X τ diss
J X = −D X ∇X
in Ω n ∪ Ω p
in Ω H
in Ω
X = 0
on Γ C ∪ Γ A
⎪⎩
X (x, 0) = X 0 (x) in Ω.
• Excitons have null net charge → Only diffusion (Fick law)
• Generation term G(x, t): constant, Beer-Lambert
• Exciton lifetime τ X , geminate pair formation time τ diss
• Geminate pair recombination rate constant k rec and triplet
exciton fraction η
• X and J X are continuous in Ω