| name | advanced-transport-modeling |
| description | Configure and apply advanced transport model features including quasi-Fermi level input handling and steric effects in ion transport. Use when modeling high ion vacancy densities, enabling non-Boltzmann statistics, or setting flexible doping parameters for transport layers. |
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:
- Direct carrier density (doping_density)
- Quasi-Fermi Level (QFL)
Configuration Procedure
-
Set Parameters Independently for Each Layer:
- ETL may use doping density input
- HTL may use QFL input simultaneously
- Each layer treated independently
-
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
-
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
