ShaneLogic/demarcation-line-trap-classification

Demarcation Line Trap Classification

Classify band gap centers as electron traps, hole traps, or recombination centers using the demarcation line method.

When to Use

Use this skill when:

• Analyzing localized states in semiconductor band gaps
• Determining whether a defect acts primarily as a trap or recombination center
• Studying recombination mechanisms in steady-state conditions
• Characterizing defect behavior in n-type or p-type materials

Prerequisites

Before calculating demarcation lines, ensure you have:

• Electron quasi-Fermi level (EFn) and hole quasi-Fermi level (EFp)
• Electron capture cross-section (sn) and hole capture cross-section (sp)
• Temperature (T)
• Effective density of states (Nc for conduction band, Nv for valence band)
• Band gap energy (Ec - Ev)

Core Procedure

Step 1: Calculate Correction Terms

Calculate the correction terms δi and δj based on capture cross-section ratios:

δi = kT × ln[(sn/sp) × (Nc/Nv) × exp(-(Ec - Ev)/2kT)]
δj = kT × ln[(sp/sn) × (Nv/Nc) × exp(-(Ec - Ev)/2kT)]

Where:

• k = Boltzmann constant (8.617 × 10⁻⁵ eV/K)
• T = Temperature in Kelvin
• sn = Electron capture cross-section (cm²)
• sp = Hole capture cross-section (cm²)
• Nc = Effective density of states in conduction band
• Nv = Effective density of states in valence band
• Ec - Ev = Band gap energy

Step 2: Calculate Demarcation Lines

Compute the electron and hole demarcation lines:

EDn = EFn - δi
EDp = EFp + δj

Where:

• EDn = Electron demarcation line energy
• EDp = Hole demarcation line energy
• EFn = Electron quasi-Fermi level
• EFp = Hole quasi-Fermi level

Step 3: Classify the Center

Apply classification rules based on the center's energy position:

| Center Position | Classification | |----------------|----------------| | Above EDn (closer to conduction band) | Electron trap | | Below EDp (closer to valence band) | Hole trap | | Between EDn and EDp (middle of band gap) | Recombination center |

Key Considerations

• Steady-state assumption: This method applies under steady-state conditions
• Capture cross-section dependence: The sn/sp ratio can change with center occupancy
• Material type: n-type materials typically show a wider range of electron traps, while p-type materials show more hole traps
• Temperature sensitivity: δ values vary with temperature, affecting demarcation line positions

Common Values

• Capture cross-sections typically range from 10⁻¹² to 10⁻²² cm²
• At room temperature, δ values can vary by up to 0.6 eV
• Neutral centers often have sn ~ 10⁻¹⁶ cm², becoming negatively charged after electron capture (sp ~ 10⁻¹⁴ cm²)

Output

The skill provides:

• Electron demarcation line energy (EDn)
• Hole demarcation line energy (EDp)
• Classification of the center (electron trap, hole trap, or recombination center)

For detailed examples, derivation, and edge cases, see references/demarcation-line-details.md.