advanced-transport-modeling

# Advanced Transport Modeling ## When to Use - Setting transport layer doping parameters with quasi-Fermi level specifications - Modeling high ion vacancy densities approaching saturation - Enabling steric hindrance effects in ion transport - Configuring non-Boltzmann statistics in transport layers - Bypassing manual Boltzmann distribution conversions ## Quasi-Fermi Level Input Handling ### Flexible Input Options Transport layer parameters can be set using EITHER: 1. Direct carrier density (doping_density) 2. Quasi-Fermi Level (QFL) ### Configuration Procedure 1. **Set Parameters Independently for Each Layer:** - ETL may use doping density input - HTL may use QFL input simultaneously - Each layer treated independently 2. **When User Sets QFL:** a. System calculates relevant doping density automatically b. Uses the specific statistical model assigned to that layer c. Applies inverse statistical integral S^-1 3. **When User Sets Doping Density:** a. Direct specification without conversion b. Compatible with standard workflows **Advantage:** Bypasses manual conversion required by Boltzmann distributions. ## Steric Effects - Modified Drift Model ### When to Enable - Ion vacancy density P approaches P_lim (site density) - High ion concentrations cause lattice site blocking - Standard Poisson-Nernst-Planck (PNP) assumes P << P_lim (invalid at high densities) ### Activation Condition `IF (Steric effects enabled AND NonlinearFP = 'Drift') THEN apply modified drift flux` ### Modified Ion Flux Equation **Electrochemical Potential:** ``` μ = k_B T ln(γ P / P_lim) + φ ``` **Activity Coefficient (Lattice Diffusion):** ``` γ = (1 - P / P_lim)^-1 ``` **Mobility with Steric Effects:** ``` M = γ D_I / (k_B T) ``` **Modified Ion Flux F_P:** ``` F_P = -D_I (∂P/∂x) + (qP / k_B T)(∂φ/∂x) [1 / (1 - P/P_lim)] ``` ### Physical Justification - Based on hopping model where adjacent sites may be occupied - Enforces maximum of one ion per lattice site - Prevents unphysical ion concentrations exceeding site availability - Divisor [1/(1-P/P_lim)] increases drift term as density approaches limit ## Key Parameters ### Steric Effects - P: Ion vacancy density - P_lim: Density of anion sites (max vacancy density) - D_I: Constant diffusion coefficient - φ: Electric potential - q: Elementary charge - k_B: Boltzmann constant - T: Temperature ### QFL Input - QFL: Quasi-Fermi level input by user - doping_density: Calculated or input carrier density