poisson.omdoc
This is a theory containing the static dielectric permitivity constant
of the semiconductor.
PoissonParameters
The relative dielelectric permitivity constant denoted by ε_r.
constant relative_dielectric_permitivity
type
parsing-notationε_r (precedence 0)
The static dielelectric permitivity constant denoted by ε_s.
constant dielectric_permitivity
type
definitionε_rε_0
parsing-notationε_s (precedence 0)
This is a theory containing the total charge entering
the right side of Poisson's equation.
Charge
structure DeviceGeometry
domain?DeviceGeometry
structure DopingProfile
domain?DopingProfile
structure PoissonParameters
domain?PoissonParameters
structure DensityElectrons
domain?DensityElectrons
structure FermiPotentialElectrons
domain?FermiPotentialElectrons
structure ElectrostaticPotential
domain?ElectrostaticPotential
structure DensityHoles
domain?DensityHoles
structure FermiPotentialHoles
domain?FermiPotentialHoles
The total charge denoted by Q composed of doping profile C and
electron and hole densities n and p, defined by
Q = q(C+p - n).
constant total_charge
typeΩ
definition[x:Ω]((-q)(((Cx)+(p(ψx)(φ_px)))-(n(ψx)(φ_nx))))
parsing-notationQ (precedence 0)
This is a theory containing the electric displacement.
Displacement
structure ElectrostaticPotential
domain?ElectrostaticPotential
structure PoissonParameters
domain?PoissonParameters
Expression for electric displacement denoted by D = -ε_s d/dx ψ
constant electric_displacement
typeΩ
definition[x:Ω]((-ε_s)((ψ'([z:](domain_propz)))x))
parsing-notationD (precedence 0)
This is a theory containing Poissons equation.
PoissonEquation
structure Charge
domain?Charge
structure Displacement
domain?Displacement
Defintion of the Poisson equation with total charge
as right hand side.
constant poisson_equation
type((D'([z:](domain_propz)))((pred([z:](domain_propz))))Q)
This is a theory containing build-in potential in
thermodynamic equilibrium.
ThermodynamicEquilibrium
structure Charge
domain?Charge
Value of build-in potential ψ_0 at top contact guranteeing
local charge neutrality.
constant equilibrium_potential_top
type
parsing-notationψ_0_2 (precedence 0)
Value of build-in potential ψ_0 at bottom contact guranteeing
local charge neutrality.
N.B. the build-in potential is given as U_b = ψ_0_2-ψ_0_1 (Check!)
constant equilibrium_potential_bottom
type
parsing-notationψ_0_1 (precedence 0)
This is a theory containing the boundary values for the Poisson eqauation.
PoissonBoundaryConditions
structure ThermodynamicEquilibrium
domain?ThermodynamicEquilibrium
Boundary value for electrostatic potential at top contact
for an applied voltage U_1.
constant potential_top
type
definitionψ_0_1+U_1
parsing-notationψ_1 (precedence 0)
Boundary value for electrostatic potential at bottom contact
for an applied voltage U_2.
N.B.: the applied bias voltage is U_bias = U_2-U_1
constant potential_bottom
type
definitionψ_0_2+U_2
parsing-notationψ_2 (precedence 0)