ShaneLogic/auger-recombination-modeling

Auger Recombination Modeling

Use this skill when:

• Simulating perovskite solar cells under high illumination intensity
• Modeling high carrier density conditions where three-particle processes matter
• Fitting experimental J-V curves that show Auger-dominated losses
• Comparing different recombination mechanisms (SRH, radiative, Auger)
• Investigating non-ideal device behavior at high voltages

Auger Recombination Fundamentals

Auger recombination is a three-particle process where:

• An electron and hole recombine
• The excess energy is transferred to a third carrier (electron or hole)
• Rate scales with the cube of carrier density

Prerequisites:

• Carrier densities n and p
• Auger coefficients A_n (electron-dominated) and A_p (hole-dominated)
• Intrinsic carrier density n_i

Calculate Auger Recombination Rate

Use the Auger recombination formula:

R_Auger = (A_n * n + A_p * p) * (n * p - n_i²)

Where:

• R_Auger: Auger recombination rate [m⁻³ s⁻¹]
• A_n: Electron Auger coefficient [m⁶ s⁻¹]
• A_p: Hole Auger coefficient [m⁻¹ s⁻¹]
• n: Electron density [m⁻³]
• p: Hole density [m⁻³]
• n_i: Intrinsic carrier density [m⁻³]

Critical constraint: This formulation ensures R_Auger = 0 when n * p = n_i² (thermal equilibrium)

Total Bulk Recombination Rate

Combine all recombination mechanisms:

R(n,p) = R_SRH + R_rad + R_Auger

Where:

• R_SRH: Shockley-Read-Hall (trap-assisted) recombination
• R_rad: Radiative/bimolecular recombination
• R_Auger: Auger recombination

Configure Auger Parameters

Enable Auger recombination in simulation parameters:

% Auger coefficients
Augn = 1e-42;  % Electron-dominated Auger rate [m^6 s^-1]
Augp = 1e-42;  % Hole-dominated Auger rate [m^6 s^-1]

% Default values (if not specified)
% Augn = 0     % Auger disabled
% Augp = 0

Advanced Generation Modeling

When enabling Auger recombination, also consider spectral generation:

% Generation rate G(x,t) - supports spectrum
% Default: Eq. (31) - single wavelength
% Specify custom G for realistic solar spectra
G = @(x,t) custom_generation_profile(x,t);

Optional parameters for advanced modeling:

• Immobile ion distributions: DI = 0 (default) or specify ion diffusion coefficient
• Wavelength-dependent absorption profiles
• Time-varying illumination conditions

When Auger Matters

Auger recombination becomes significant when:

High carrier densities:

• Strong illumination (full sun or concentrated)
• High injection conditions
• n * p ≫ n_i²

Material properties:

• High Auger coefficients (material-dependent)
• Small bandgap materials
• Certain perovskite compositions

Device operation:

• Near open-circuit voltage
• Under high forward bias
• In high-efficiency devices where other losses minimized

Implementation Notes

• Auger rate is added to continuity equations for electrons and holes
• In IonMonger, modify parameters file with Augn and Augp
• Default model assumes simple generation and no Auger if parameters omitted
• Auger coefficients typically in range 10⁻⁴¹ to 10⁻⁴⁴ m⁶ s⁻¹ for perovskites

Verification

Always verify:

1. R_Auger = 0 at thermal equilibrium (n*p = n_i²)
2. Positive recombination rate under non-equilibrium
3. Reasonable magnitude compared to other recombination mechanisms
4. Units consistency (m⁻³ s⁻¹ for all R terms)