ShaneLogic/drift-diffusion-transport-physics
.claude/skills/drift-diffusion-transport-physics/SKILL.md
Model charge transport in perovskite solar cells using drift-diffusion equations. Apply conservation equations, flux equations, and Poisson's equation for perovskite, ETL, and HTL regions. Use when setting up the core physics model for PSC simulations.
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SKILL.md
- name:
- drift-diffusion-transport-physics
- description:
- Model charge transport in perovskite solar cells using drift-diffusion equations. Apply conservation equations, flux equations, and Poisson's equation for perovskite, ETL, and HTL regions. Use when setting up the core physics model for PSC simulations.
Drift-Diffusion Transport Physics
When to Use
- Setting up the core physics model for PSC drift-diffusion simulations
- Defining transport equations for perovskite absorber layer (0 < x < b)
- Modeling electron and hole transport layers (ETL and HTL)
- Establishing boundary conditions at metal contacts and interfaces
Perovskite Layer (0 < x < b)
Conservation Equations
Apply continuity equations balancing generation, recombination, and flux divergence:
- Conduction Electrons: Continuity equation
- Valence Holes: Continuity equation
- Halide Ion Vacancies: Continuity equation
Flux Equations (Drift-Diffusion)
For each carrier type, flux includes:
- Drift term (electric field dependence)
- Diffusion term (concentration gradient)
- Thermodiffusion term (temperature gradient)
Current densities: J_n (electrons), J_p (holes), J_P (vacancies)
Poisson's Equation
Couple electric potential (φ) to charge densities:
∇²φ = -(q/ε)(n - p + P - N̂_0)
where N̂_0 is constant, uniform background density of immobile cation vacancies.
Source Terms
- Photo-generation: G(x, t)
- Recombination: R(n, p)
Transport Layers
Electron Transport Layer (ETL): -bE < x < 0
- Model: Majority carriers (free electrons) only
- Equations: Conservation + Flux + Poisson's
- Statistics: Uses ETL-specific statistical integral S_E
Hole Transport Layer (HTL): b < x < b+bH
- Model: Majority carriers (holes) only
- Equations: Conservation + Flux + Poisson's
- Statistics: Uses HTL-specific statistical integral S_H
Boundary Conditions
ETL/Metal Contact (x = -bE)
Ohmic condition:
n = g_E * S_E^-1(E_ct - V(t) + T_E)
where E_ct is cathode workfunction and V(t) is applied voltage.
HTL/Metal Contact (x = b+bH)
Ohmic condition with parasitic resistance:
p = g_H * S_H^-1(E_an - V(t) + T_H)
where E_an is anode workfunction.
Built-in Voltage: V_bi = E_ct - E_an
Interface Continuity (x=0, x=b)
Flux Continuity
J_n(0-) = J_n(0+) - R̂_l
where R̂_l represents interface recombination.
Potential Continuity
φ(0-) = φ(0+)
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