Abstract
The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modeling of electronic devices on the nanoscale. In this paper we calculate these energy levels from first principles using density functional theory. The wavefunction of the donor electron’s ground state is found to have a form that is similar to an atomic s orbital, with an effective Bohr radius of 1.8 nm. The corresponding binding energy of this state is found to be 41 meV, which is in good agreement with the currently accepted value of 45.59 meV. We also calculate the energies of the excited 1s(T2) and 1s(E) states, finding them to be 32 and 31 meV respectively.
Highlights
Phosphorus donors in silicon have long been important for electronic devices but are seen as central to the development of silicon based quantum information processing[1,2,3,4,5]
Theoretical methods for describing point defects in semiconductors were separable into two categories: “methods for deep defects and methods for shallow defects: the former defect class is treated by ab initio methods, ... while for the latter class approximate one-electron theories ... are used”[16]
It has been shown that shallow defects are within the reach of ab initio methods such as density functional theory (DFT)[17]
Summary
In 1969, Faulkner used effective mass theory (EMT) to calculate the energy levels of the ground and excited states of a donor electron for Group V donor atoms in silicon[20]. These energies are plotted relative to the conduction band minimum of bulk silicon, calculated using a supercell of 10,648 atoms, which is set to energy zero in the figure. The energies of the excited1s(T2) and1s(E) states are found to be in excellent agreement with the accepted values These results constitute the first ab initio calculation of the s manifold energy levels for a single phosphorus donor in silicon. In the future this atomistic model could be expanded beyond the bulk case, to investigate the effect of a nearby surface on the electronic and structural properties of the phosphorus donor. In addition our ab initio model could be extended to investigate many donor systems, which are of current interest[42]
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