Mathematical Models for Nano Science - Politecnico di Milano

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