ShaneLogic/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