ShaneLogic/carrier-transport-scattering-analysis
.claude/skills/carrier-transport-scattering-analysis/SKILL.md
Analyze carrier transport behavior in semiconductors including gas-kinetic scattering models, momentum relaxation, and energy relaxation. Use when calculating mobility, mean free path, scattering times, or understanding how carriers lose momentum and energy to the lattice.
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SKILL.md
- name:
- carrier-transport-scattering-analysis
- description:
- Analyze carrier transport behavior in semiconductors including gas-kinetic scattering models, momentum relaxation, and energy relaxation. Use when calculating mobility, mean free path, scattering times, or understanding how carriers lose momentum and energy to the lattice.
Carrier Transport and Scattering Analysis
When to Use
- Calculating carrier mobility, mean free path, or scattering times
- Analyzing how carriers scatter and lose directional momentum
- Understanding energy exchange between carriers and lattice (Joule heating)
- Estimating transport properties from scattering cross-sections
Core Workflow
Step 1: Gas-Kinetic Scattering Model
Calculate basic scattering statistics when analyzing carrier transport.
Calculate Mean Free Path (λ):
λ = 1 / (Nsc × Sn)
Nsc: density of scattering centers (cm⁻³)Sn: scattering cross-section
Calculate Scattering Time (τsc):
τsc = λ / vrms
vrms: root mean square velocity
Estimate Carrier Mobility (Drude):
μ = e × τsc / m
e: elementary chargem: effective mass
Note: This model tends to overestimate tolerable defect densities due to simplified assumptions.
Step 2: Momentum Relaxation Time
Determine how quickly carriers lose directional memory (randomization of path).
Calculate from Scattering Angle:
τm = τsc / (1 - <cosΘ>)
Θ: scattering angle<cosΘ>: average cosine of scattering angle
Scattering Types:
- Isotropic scattering:
<cosΘ>= 0 → τm = τsc - Large angle scattering (Θ > 90°): Memory-erasing events
- Small angle scattering: Multiple events needed → τm > τsc
Alternative from Mobility:
μ = e × τm / m
Step 3: Energy Relaxation Time
Determine how quickly carriers reach thermal equilibrium with the lattice.
Calculate:
τE = ΔE / (dE/dt)
ΔE: average surplus energydE/dt: rate of energy loss
Analyze by Phonon Type:
- Acoustic phonons: Energy loss ~0.1% per event (negligible)
- Equivalent phonon mass:
M* = 2 × k × T_lattice / vs²
- Equivalent phonon mass:
- Optical phonons:
τE / τsc ≈ 1at room temperature - Defect scattering: Energy loss negligible when M >> m
Key Insight:
Momentum relaxes after one or few collisions, but energy takes many more events to dissipate.
Output
- Mean free path (λ) in cm
- Scattering time (τsc) and momentum relaxation time (τm) in seconds
- Energy relaxation time (τE) in seconds
- Carrier mobility (μ) in cm²/V·s
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