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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 methodwithin the Hartree approximation. The calculations yield a transition energyclose to the experimentally measured value of 1150 meV in bulk, and show howthe transition energy and transition probability can change with applied fieldsand proximity to surfaces, mimicking the conditions of realistic devices. Thespin-resolved transition energy from a neutral donor state (D$^0$) to D$^0$Xdepends on the three-particle Coulomb energy, and the interface and electricfield induced hyperfine splitting and heavy-hole-light-hole splitting. Althoughthe Coulomb energy decreases as a result of Stark shift, the spatial separationof the electron and hole wavefunctions by the field also reduces the transitiondipole. 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 ionizationprocess. Our calculations take into account the full bandstructure of siliconand the full energy spectrum of the donor including spin directly in the atomicorbital basis and treat the three-particle Coulomb interactionself-consistently to provide quantitative guidance to experiments aiming torealize hybrid opto-electric techniques for addressing donor qubits.

Bulk and sub-surface donor bound excitons in silicon under electric fields