Mathematical Models for Nano Science - Politecnico di Milano

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Model equations - 3 • Poisson equation ⎧ ( ) −div ε∇ϕ = −qn in Ω n ( ) −div ε∇ϕ = +q ( p − n ) in Ω ⎪⎨ H ( ) −div ε∇ϕ = +qp in Ω p ϕ = V appl − V bi ⎪⎩ ϕ = 0 on Γ A on Γ C • Applied and bias potential → Dirichlet boundary conditions • The dielectric constant ε may vary in the materials • The electric potential ϕ and the normal component of the electric displacement field −ε∇ϕ · ν are continuous
Interface lumping - 1 • Device thickness ≫ active layer thickness (∼ 10 2 /∼ 10 0 nm) • Still a certain number of nodes in Ω H is needed Idea • Neglect the thickness of the active layer • Assume the phenomena to occur just on the mathematical interface Γ • Many nodes Γ C Γ N Ω n Γ hν Ω p Γ N New computational domain • Less nodes • Same definition Γ A
Page 1 and 2: Mathematical Models for Nano Scienc
Page 3 and 4: Math Research Group Prof. Riccardo
Page 5 and 6: Bulk Heterojunction solar cells lig
Page 7 and 8: • Hole equation Model equations -
Page 9 and 10: Spatial discretization Triangulatio
Page 11 and 12: Numerical results - 1 • Ideal BHJ
Page 13 and 14: Bilayer solar cells light current a
Page 15: Model equations - 2 • Geminate pa
Page 19 and 20: Numerical results - 1 Ω p Γ Γ C
Page 21 and 22: Numerical results - 3 • Very comp
Page 23 and 24: Activity at CNST - SuperC • Photo

Mathematical Models for Nano Science - Politecnico di Milano

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