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Donors in silicon are now demonstrated as one of the leading candidates forimplementing qubits and quantum information processing. Single qubitoperations, measurements and long coherence times are firmly established, butprogress on controlling two qubit interactions has been slower. One reason forthis is that the inter donor exchange coupling has been predicted to oscillatewith separation, making it hard to estimate in device designs. We present amultivalley effective mass theory of a donor pair in silicon, including both acentral cell potential and the effective mass anisotropy intrinsic in the Siconduction band. We are able to accurately describe the single donor propertiesof valley-orbit coupling and the spatial extent of donor wave functions,highlighting the importance of fitting measured values of hyperfine couplingand the orbital energy of the $1s$ levels. Ours is a simple framework that canbe applied flexibly to a range of experimental scenarios, but it is nonethelessable to provide fast and reliable predictions. We use it to estimate theexchange coupling between two donor electrons and we find a smoothing of itsexpected oscillations, and predict a monotonic dependence on separation if twodonors are spaced precisely along the [100] direction.

Exchange coupling between silicon donors: the crucial role of the central cell and mass anisotropy