ShaneLogic/asymptotic-model-simplification

Asymptotic Model Simplification

When to Use This Skill

Use this skill when you need to:

• Compare numerical simulation results to asymptotic analytic solutions
• Validate numerical models against analytic expressions
• Analyze carrier transport in materials with hole-dominated recombination
• Obtain separate analytic expressions for charge carrier concentrations

Prerequisites

Before applying this skill, ensure you have:

• Realistic parameter estimates from Eq. (18)
• A numerical model with SRH (Shockley-Read-Hall) recombination physics
• Understanding of the physical limits where electron density is not extremely small

Procedure

Step 1: Apply Realistic Parameters

Use the realistic parameter estimates provided in Eq. (18) for your model configuration.

Step 2: Simplify Bulk Recombination

Modify the bulk recombination rate R(n, p) to be linear and monomolecular:

R(n, p) = gamma * p

where:

• gamma = 2.4 (recombination coefficient)
• p = local hole concentration

Step 3: Eliminate Surface Recombination

Set both surface recombination rates to zero:

• R_l(p) = 0 (left surface)
• R_r(n) = 0 (right surface)

Step 4: Verify the Approximation

Confirm that:

• Electron pseudo-lifetime is much less than hole pseudo-lifetime
• Material properties match monomolecular hole-dominated recombination behavior
• Electron density is not vanishingly small in the regions of interest

Step 5: Compare Results

Run your simplified model and compare directly to the asymptotic analytic solutions.

Key Variables

| Variable | Type | Description | |----------|------|-------------| | R(n, p) | Expression | Bulk recombination rate (simplified) | | gamma | Float | Recombination coefficient (typically 2.4) | | p | Variable | Local hole concentration | | R_l(p) | Expression | Left surface recombination rate | | R_r(n) | Expression | Right surface recombination rate |

Limitations

This simplification breaks down where:

• Electron density is very small
• The monomolecular limit of the SRH law does not apply
• Material behavior deviates from hole-dominated recombination