ShaneLogic/chalcogen-impurities-silicon

Chalcogen Impurities in Silicon

When to Use

• Calculating energy levels for chalcogen (O, S, Se, Te) impurities in silicon
• Analyzing ground state splitting (A1, E, T2) of deep donors
• Investigating chalcogen pair formation and symmetry properties
• Studying pressure coefficients of deep donor states

Analyze Single Chalcogen Donors

1. Identify Donor Type

   • Chalcogens (O, S, Se, Te) act as deep donors
   • Often form associates (especially Oxygen) or act as double donors

2. Analyze Ground States (Deep)

   • The 1s ground state splits due to crystal field into three components:
     • A1: Non-degenerate (Deepest)
     • E: Doubly degenerate
     • T2: Threefold degenerate
   • Use binding energies from reference data (Table 10.1)

3. Analyze Excited States (Shallow)

   • p-states are shallow and follow effective mass (hydrogen-like) approximation
   • Example: 2p0 ~11.5 meV (close to E_Hydrogen ~11.75 meV)

4. Pressure Coefficient Analysis

   • Compare hydrostatic pressure coefficient of ground state (1s) to hydrogen-like centers
   • Larger coefficient (~ -1.7 to -1.8 x 10^-8 eV/Pa for S/Se) indicates connection to conduction bands (X-valley)

Analyze Chalcogen Pairs

1. Determine Center Nature

   • Molecular pairs of S, Se, or Te act as single, deep centers
   • Depth: Slightly lower than single chalcogen substitutionals
   • Excited states: Very close to corresponding hydrogen-like states

2. Identify Structure and Symmetry

   • Incorporation: (111) axial symmetry
   • Ground states: Four distinct 1s ground states (A1g, Eg, Eu, A1u)

3. Assess Anisotropy

   • Any pair is anisotropic, even in isotropic crystal
   • Orientation examples: [100], [010], or [001] for nearest-neighbor pairs
   • Optical excitation is polarization-dependent

4. Consider Mixed Pairs

   • Mixed pairs are observed (e.g., Si:S;Se or Si:Se;Te)

Output

• Specific binding energies for A1, E, T2 states
• Characterization of deep center state and symmetry
• Identification of shallow vs deep characteristics