ShaneLogic/constant-energy-surfaces-brillouin-zone
.claude/skills/constant-energy-surfaces-brillouin-zone/SKILL.md
Construct and interpret constant energy surfaces within Brillouin zones to analyze semiconductor band structure, visualize electron behavior near band edges, and determine effective mass. Use when analyzing E(k) dispersion relations, determining effective mass tensors, or visualizing how lattice potential influences electron states.
$ install --global
skillsauthnpx skillsauth add ShaneLogic/SolarLab constant-energy-surfaces-brillouin-zoneInstall this skill globally with one command. Works with Claude Code, Cursor, and Windsurf.
Security Scan Results
3 of 9 scanners reported clean
Some scanners were skipped, did not run, or reported a non-clean status. Review each row below.
3
Scanners Passed
9
Scanners in report
Clean
TrivyContainer and dependency vulnerability scanner
95%
Clean
SemgrepStatic code analysis for vulnerabilities
95%
Clean
mcp-scan (Snyk)Model Context Protocol security validation
95%
Skipped
Snyk (dep)Open source security scanning
50%
Skipped
Socket.devSupply chain security analysis
50%
Skipped
VirusTotalMulti-engine malware detection
50%
Skipped
CrowdStrikeAdvanced threat intelligence
50%
Skipped
OSV-ScannerOpen Source Vulnerability database check
50%
Skipped
OWASP Dep-Check
50%
Last scanned: Apr 16, 2026, 11:27 AM6.4s3 files scanned
SKILL.md
- name:
- constant-energy-surfaces-brillouin-zone
- description:
- Construct and interpret constant energy surfaces within Brillouin zones to analyze semiconductor band structure, visualize electron behavior near band edges, and determine effective mass. Use when analyzing E(k) dispersion relations, determining effective mass tensors, or visualizing how lattice potential influences electron states.
Constant Energy Surfaces in Brillouin Zone
When to Use
Use this skill when:
- Visualizing band shape near conduction band minimum (Ec) or valence band maximum (Ev)
- Analyzing E(k) dispersion relations in three dimensions
- Determining effective mass from band curvature
- Evaluating degree of lattice influence on electron behavior
- Assessing isotropic vs anisotropic electron transport properties
Prerequisites
- Understanding of E(k) dispersion relation
- Knowledge of Brillouin zone geometry
- Familiarity with semiconductor band edges (Ec and Ev)
Constraints
- Applies near band edges (Ec and Ev)
- k(E) is single-valued within each band
- k(E) is monotonic within each band
Procedure
1. Identify Analysis Region
Select the appropriate band edge:
- Bottom of conduction band (near Ec), OR
- Top of valence band(s) (near Ev)
2. Construct Constant Energy Surface
Sequentially fill the band with electrons:
- Electrons populate states within E(k) up to energy E₁
- Determine corresponding wavevector k₁(E₁)
- Map the surface in k-space at this energy level
3. Visualize Surface Evolution
For primitive cubic lattice:
- Electrons initially contained in small sphere at zone center
- Sphere grows parabolically in radius with increasing electron filling
- Radius increases with increasing value of k
Interpretation
Surface Shape Indicators
| Surface Shape | Physical Meaning | |--------------|------------------| | Spherical | Quasi-free electron behavior, minimal lattice influence | | Non-spherical / Distorted | Substantial lattice influence, electron-lattice interaction |
Effective Mass Determination
- Spherical surfaces → scalar effective mass (isotropic)
- Non-spherical surfaces → tensor effective mass (anisotropic)
- Surface curvature relates to effective mass: m* ∝ [∂²E/∂k²]⁻¹
Analysis of Surface Evolution
- Examine family of equi-energy surfaces through Brillouin zone
- Increasing binding potential shows evolution from spherical to distorted shapes
- Shading indicates degree of electron filling
- Track how surface deformation changes with energy
Related Skills
ShaneLogic/driftfusion-licensing-guidelines
development
VerifiedTrustedCommunity
Understand and comply with Driftfusion software licensing terms, including the open-source AGPL v3.0 frontend and proprietary MATLAB pdepe solver backend. Use when using, modifying, or distributing Driftfusion code.
1SKILL.mdUpdated Apr 16, 2026
ShaneLogic/driftfusion-initialization
development
VerifiedTrustedCommunity
Initialize the Driftfusion simulation environment and create parameter objects. Use this skill when starting a new MATLAB session or setting up device properties for simulation.
1SKILL.mdUpdated Apr 16, 2026
ShaneLogic/driftfusion-device-structure
development
VerifiedTrustedCommunity
Define device layer structure, configure spatial and time meshes, and build device structures with interface grading. Use this skill when setting up the physical geometry and discretization of a simulation device.
1SKILL.mdUpdated Apr 16, 2026
ShaneLogic/driftfusion-analysis-plotting
research
VerifiedTrustedCommunity
Analyze simulation solutions, calculate physical quantities, and generate plots. Use this skill when processing completed simulations, extracting currents/densities, or visualizing results.
1SKILL.mdUpdated Apr 16, 2026