isolated Si atoms

Si crystal

Ĥ=E Density Functional Theory (DFT) Replaces the exact multi-electron Schrȍdinger equation with an approximate single-electron Schrȍdinger equation. Electron moves in a periodic potential determined by the background electron density and the symmetry of the crystal lattice. Numerically optimizes energy of single electron crystal orbitals. DFT is applicable to systems with a relatively large number of electrons. (Not practical using conventional Hartree-Fock methods.) Ĥ=E

Real-space calculation of electronic structure 27 unit cells (3x3x3) 276 Si atoms Passivated [100]-oriented crystallite with 240 surface H atoms 4104 electrons 4404 electronic states including core, surface, and band states Geometry of pure Si crystallite was optimized using a gradient corrected potential with the “HCTH” exchange functional.

pure silicon energy quantum number

pure silicon conduction “band” energy quantum number

pure silicon conduction “band” energy valence “band” quantum number

pure silicon conduction “band” energy “band” gap valence “band” quantum number

pure silicon conduction “band” energy “band” gap valence “band” quantum number

pure silicon conduction “band” energy “band” gap valence “band” quantum number

pure silicon conduction “band” energy “band” gap valence “band” quantum number

P-doped silicon

P-doped silicon conduction “band” “band” gap energy valence “band” donor state “band” gap valence “band” quantum number

P-doped silicon conduction “band” “band” gap energy valence “band” donor state “band” gap valence “band” quantum number

B-doped silicon

B-doped silicon conduction “band” energy valence “band” quantum number acceptor state valence “band” quantum number

B-doped silicon conduction “band” energy valence “band” quantum number acceptor state valence “band” quantum number

Density Functional Theory (DFT) Confirms that valence and conduction band orbitals are de-localized (in agreement with classical electron gas in a periodic background potential). Confirms that doping introduces donor and acceptor orbitals at the band edges. Confirms that donor and acceptor orbitals are localized with dopant atoms and in addition exhibit the tetrhedral symmetry charcteristic of the crystal lattice