ShaneLogic/depletion-width-collection-model

Voltage-Dependent Depletion Width Collection Model

When to Use

Apply this skill when:

• Modeling pn-homojunction solar cells with voltage-dependent depletion width
• Analyzing CdTe-based solar cells with known material parameters
• Calculating collection efficiency that varies with applied voltage
• Need to relate I-V characteristics to carrier collection physics

Prerequisites

Ensure the following parameters are available:

• NA: Acceptor density (cm⁻³)
• VB: Built-in potential (V)
• VD: Diffusion voltage (V)
• α: Effective optical absorption constant (cm⁻¹)
• L: Diffusion length (cm)

Execution Steps

1. Calculate Voltage-Dependent Depletion Width

Compute the depletion width as a function of applied voltage:

W(V) = [2εε₀(VD - V)/eNA]^(1/2)

Where:

• ε = relative permittivity of the material
• ε₀ = vacuum permittivity
• e = elementary charge

2. Calculate Field Distribution

Model the electric field in the depletion region:

F(x) = (2eNA/εε₀)^(1/2) × (VB - V)^(1/2) × [1 - (2x/W)]

3. Calculate Basic Collection Efficiency

Compute the collection efficiency accounting for absorption:

ηc(V) = 1 - exp(-αW(V)/(1 + αL))

4. Calculate Photo-Electric Collection Efficiency

For complete collection efficiency including field-dependent effects:

ηc(V) = (1 - exp(-αW(V)/(1 + αL))) × (μF₀(V)/(S + μF₀(V)))

Where:

• μ = carrier mobility
• F₀(V) = field at the junction interface
• S = surface recombination velocity

5. Parameter Extraction for CdTe Cells

When working with CdTe solar cells:

• Use weighted CdTe absorption coefficient for α approximation
• Extract parameters from measured I-V characteristics under sunlight
• Four fitting parameters remain: α, NA, L, VD

Output

Returns collection efficiency values that account for:

• Optical absorption in the depletion region
• Carrier diffusion from quasi-neutral regions
• Voltage-dependent depletion width modulation
• Field-dependent carrier collection at interfaces