The electronic structure of the three-particle donor bound exciton (D$^0$X) in silicon is computed using a large-scale atomic orbital tight-binding method within the Hartree approximation. The calculations yield a transition energy close to the experimentally measured value of 1150 meV in bulk, and show how the transition energy and transition probability can change with applied fields and proximity to surfaces, mimicking the conditions of realistic devices. The spin-resolved transition energy from a neutral donor state (D$^0$) to D$^0$X depends on the three-particle Coulomb energy, and the interface and electric field induced hyperfine splitting and heavy-hole-light-hole splitting. Although the Coulomb energy decreases as a result of Stark shift, the spatial separation of the electron and hole wavefunctions by the field also reduces the transition dipole. A bulk-like D$^0$X dissociates abruptly at a modest electric field, while a D$^0$X at a donor close to an interface undergoes a gradual ionization process. Our calculations take into account the full bandstructure of silicon and the full energy spectrum of the donor including spin directly in the atomic orbital basis and treat the three-particle Coulomb interaction self-consistently to provide quantitative guidance to experiments aiming to realize hybrid opto-electric techniques for addressing donor qubits.
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