Spin Contamination

  The ground state of the silicon atoms in the bulk solid is a closed shell configuration. If a single up- or down-spin electron is excited from the valence band to the conduction band, the wave function then has a spin contamination, i.e. it is no longer an eigenstate of the operator. It is possible to avoid this contamination either by exciting simultaneously the electron with opposite spin, to create a biexciton, or to use a superposition of determinantal products to obtain a spin singlet state. This superposed trial wavefunction is a generalisation of the trial wavefunction introduced in chapter ,

 

A spin-singlet wavefunction for diamond-structure silicon can be obtained from Eq.(), by the superposition of two determinantal products,

 

where indicates a Slater determinant in which one of the ground state orbitals has been replaced by an excited state orbital. In the first product, the down-spin determinant contains the ground state orbitals and the up-spin determinant has one of the ground state orbitals replaced by an excited state orbital. In the second product the up-spin determinant contains the ground state orbitals and the down-spin determinant has one of the ground state orbitals replaced with an excited state orbital.