ShaneLogic/deep-level-center-modeling

Deep Level Center Modeling

When to Use

Apply this skill when:

• Defect has a strong core potential and short-range potential
• Wavefunction of ground state remains localized close to defect core
• Defect connects to BOTH conduction and valence bands (extending through entire Brillouin zone)
• Defect does not follow one specific band under perturbation (alloying/pressure)
• Hydrogenic effective mass approximation fails to describe the defect

Core Workflow

1. Identify Deep Center Characteristics

Confirm the defect exhibits these fundamental properties:

• Ground state wavefunction is highly localized near the defect core
• Energy levels are connected to both conduction and valence bands
• Behavior is not tied to a single band under alloying or pressure perturbations
• Defect is best described by a short-range potential model

2. Apply Square Well Potential Model

Use a 1D rectangular well model with parameters:

• V0: Depth of the potential well (in energy units)
• a: Half-width of the potential well (in length units)
• nq: Quantum number

Key relationships:

• Eigenstate energies increase quadratically with nq: E ~ nq²
• This contrasts with hydrogen-like defects where eigenstates decrease as 1/nq²
• Use electron rest mass (electron is close to center)

3. Evaluate Coulomb Tail Effects

For charged deep centers:

• The long-range Coulomb potential tail dominates higher excited states
• Higher excited states become hydrogen-like (shallow-like)
• Ground state shows deep level behavior when short-range potential is large (>10 eV)
• Expected spectrum: One or several deep levels, followed by hydrogen-like shallow levels near bands

4. Assess Core Potential Depth

Use atomic electronegativity as an indicator for:

• The depth of the square well
• The strength of the core potential

Key Variables

| Variable | Type | Description | |----------|------|-------------| | V0 | Energy | Depth of the potential well | | a | Length | Half-width of the potential well | | nq | Integer | Quantum number |

Output Interpretation

The skill produces:

• Eigenstate energy values calculated from the square well model
• Classification of defect as deep vs shallow based on localization and potential characteristics
• Energy level spectrum structure (deep levels followed by shallow hydrogen-like levels for charged centers)