Valley Splitting

Objective:

• Explain experimentally observed suppression in valley-splitting in miscut (100) Si QWs
• Study effect of alloy disorder and step roughness at Si/SiGe interface on the electronic structure

Approach:

• Model miscut Si QWs along with SiGe buffers to include strain and atomistic alloy disorder in SiGe buffer
• Strain relaxation: VFF-Keating
• Magnetic field: Peierl's substitution
• Step roughness: replicate experimentally observed surface morphology on the atomistic grid

Impact

• Alloy disorder in SiGe and step roughness at Si/SiGe interface is crucial to accurately model valley-splitting
• Model predicts experimentally observed valley-splitting without any ad-hoc fitting parameters

Objective:

• Resolve discrepancies in experimentally observed and theoretically predicted valley degeneracies
• Study effect of surface morphology on the electronic structure

Approach:

• Supercell tight-binding calculations to model surface miscuts
• Effective mass based valley-projection model to determine the directions of valley-minima of large supercells

Impact:

• Atomistic basis representation is essential to capture the effect of mono-atomic steps on the electronic structure
• Surface miscut of (111) Si is found to be the origin of breaking of 6 fold valley degeneracy into lower 2 fold and higher 4 fold valley degeneracies

Results

• Flat (111) Si QW shows 6 fold valley degeneracy
• Miscut causes 2-4 splitting due to different effective masses in confinement direction

Objective:

• Resolve discrepancies in experimentally observed and theoretically predicted valley degeneracies
• Study effect of surface morphology on the electronic structure
• Research on modulation of valley splitting by strain and electric field

Approach:

• Bandstructure: Nearest neighbor sp3d5s* tight - binding model
• Strain: VFF keating
• Surface miscut: extended supercell method (automatically included during geometry construction )

Results

• Two degeneracy lifting mechanisms are identified in flat QW.
• Strain and electric field enhance both types of valley splitting.
• Wafer miscuts give rise to 4 fold degeneracy and resolve experiment inconsistency.