• PoissonParameters
    constant relative_dielectric_permitivity Show Notations
    LanguagesArgumentsRendering
    0ε_r
    constant dielectric_permitivity Show Notations
    LanguagesArgumentsRendering
    0ε_s
    multiplicationε_rε_0http://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?multiplicationhttp://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivityhttp://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity
  • Charge
    includes DeviceGeometry
    includes DopingProfile
    includes PoissonParameters
    includes DensityElectrons
    includes FermiPotentialElectrons
    includes ElectrostaticPotential
    includes DensityHoles
    includes FermiPotentialHoles
    constant total_charge Show Notations
    LanguagesArgumentsRendering
    0Q
    [x:Ω](multiplication(uminusq)(bin_minus(addition(Cx)(p(ψx)(φ_px)))(n(ψx)(φ_nx))))http://cds.omdoc.org/urtheories?LambdaPi?lambdaxhttp://mathhub.info/MitM/Models/device?DeviceGeometry?domainhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?multiplicationhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?uminushttp://mathhub.info/MitM/Models?PhysicalConstants?elementary_chargehttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?bin_minushttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?additionhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models/device?DopingProfile?doping_profilexhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models/densities?DensityHoles?density_holeshttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potentialxhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potentialxhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models/densities?DensityElectrons?density_electronshttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potentialxhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potentialx
  • Displacement
    includes ElectrostaticPotential
    includes PoissonParameters
    constant electric_displacement Show Notations
    LanguagesArgumentsRendering
    0D
    [x:Ω](multiplication(uminusε_s)((der([z:ℝ](domain_propz))ψ)x))http://cds.omdoc.org/urtheories?LambdaPi?lambdaxhttp://mathhub.info/MitM/Models/device?DeviceGeometry?domainhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?multiplicationhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?uminushttp://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivityhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models?Base?derhttp://cds.omdoc.org/urtheories?LambdaPi?lambdazhttp://mathhub.info/MitM/numberfields?realnumbers?Realnumbershttp://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/Models/device?DeviceGeometry?domain_propzhttp://mathhub.info/MitM/Models/densities?ElectrostaticPotential?electrostatic_potentialx
  • PoissonEquation
    includes Charge
    includes Displacement
    constant poisson_equation
  • ThermodynamicEquilibrium
    includes Charge
    constant equilibrium_potential_top Show Notations
    LanguagesArgumentsRendering
    0ψ_0_2
    constant equilibrium_potential_bottom Show Notations
    LanguagesArgumentsRendering
    0ψ_0_1
  • PoissonBoundaryConditions
    includes ThermodynamicEquilibrium
    constant potential_top Show Notations
    LanguagesArgumentsRendering
    0ψ_1
    additionψ_0_1U_1http://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?additionhttp://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_bottomhttp://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom
    constant potential_bottom Show Notations
    LanguagesArgumentsRendering
    0ψ_2
    additionψ_0_2U_2http://cds.omdoc.org/urtheories?LambdaPi?applyhttp://mathhub.info/MitM/numberfields?realarith?additionhttp://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium?equilibrium_potential_tophttp://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top