ShaneLogic/acoustic-phonon-scattering-mobility
.claude/skills/acoustic-phonon-scattering-mobility/SKILL.md
Calculate electron mobility limited by acoustic phonon scattering in direct bandgap semiconductors and determine directional elastic constants. Use when analyzing temperature-dependent mobility, phonon scattering effects, or elastic properties in specific crystallographic directions.
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SKILL.md
- name:
- acoustic-phonon-scattering-mobility
- description:
- Calculate electron mobility limited by acoustic phonon scattering in direct bandgap semiconductors and determine directional elastic constants. Use when analyzing temperature-dependent mobility, phonon scattering effects, or elastic properties in specific crystallographic directions.
Acoustic Phonon Scattering Mobility
When to Use
- Calculating temperature-dependent electron mobility in direct bandgap semiconductors
- Analyzing mobility when acoustic phonon scattering is the dominant mechanism
- Determining longitudinal elastic constants for specific crystal directions
- Characterizing semiconductor transport at temperatures above phonon freeze-out
Prerequisites
- Semiconductor must have a direct bandgap (T^(-3/2) dependence NOT observed for indirect bandgap)
- Temperature high enough for acoustic phonon scattering to be predominant
- Deformation potential (Ξ) must be known
- Elastic tensor components (c_ik) known for directional calculations
Calculate Electron Mobility from Acoustic Phonon Scattering
Use when acoustic phonon scattering dominates and semiconductor has direct bandgap.
Formula (Eq. 17.14)
μ_n,ac = √(38π) × m_n^(5/2) / (e × k × h × T^(4/3) × c_l^(3/2) × Ξ²)
Key Temperature Dependence
- μ ∝ T^(-3/2) at higher temperatures
- This dependence is characteristic of direct bandgap semiconductors
- For indirect bandgap: intervalley scattering dominates, T^(-3/2) NOT observed
Important Considerations
- Deformation potential Ξ: Used here has only slowly varying components in space
- Effective mass: Requires proper mix of density-of-state and mobility effective masses (Eq. 17.15)
- Indirect bandgap limitation: Intervalley scattering has significant influence
Calculate Directional Elastic Constants
Use when calculating elastic response for longitudinal acoustic phonons in specific crystallographic directions.
Longitudinal Elastic Constant (c_l) by Direction
For (100) direction:
c_l = c_11
For (110) direction:
c_l = 1/3(c_11 + c_12 + c_44)
For (111) direction:
c_l = 1/3(c_11 + 2c_12 + c_44)
Where
- c_ik = components of the elastic tensor
- Formulas represent weighted averages based on geometric projection along crystallographic directions
- Directional dependencies arise from anisotropic nature of crystal lattices
Key Variables
| Variable | Description | |----------|-------------| | μ_n,ac | Electron mobility due to acoustic phonon scattering (cm²/V·s) | | m_n | Electron effective mass | | T | Temperature (K) | | c_l | Longitudinal elastic constant | | Ξ | Deformation potential (eV) | | c_11, c_12, c_44 | Components of the elastic tensor |
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