Framework for Donor-Qubit Spatial Metrology in Silicon with Depths Approaching the Bulk Limit

Impurities in silicon are fundamental to a variety of modern nanoscale technologies working in both classical and quantum regimes of operation. The aggressive miniaturization of electronic devices has reduced their size to the nanometer scale, where the exact count and positioning of a few impurity atoms dictates their overall operation and performance. In the emerging area of quantum hardware development, single-impurity spins in silicon form excellent qubits and identifying their exact locations is important to engineer two-qubit interactions for high-fidelity quantum operations and the associated quantum control systems. This work reports a theoretical framework for the spatial metrology of single-impurity atoms in silicon with exact atomic precision for impurity depths approaching the bulk limit. The application of a carefully designed electric field pulls the impurity wave functions toward the surface, leading to spatially resolved scanning tunneling microscope images of electronic states exhibiting features that distinctly depend on the exact locations of the impurity atoms beneath the silicon surface. After verification of the developed metrology technique for individual atom positions, we train a machine-learning algorithm that can autonomously perform the metrology with high throughput in the presence of noise commensurate with experimental measurements. A future experimental implementation of the established capability for impurity-atom characterization is anticipated to play an important role in the design of a wide range of electronic and quantum devices.