  The aggressive scaling of silicon-based nanoelectronics has reached the
regime where device function is affected not only by the presence of individual
dopants, but more critically their position in the structure. The quantitative
determination of the positions of subsurface dopant atoms is an important issue
in a range of applications from channel doping in ultra-scaled transistors to
quantum information processing, and hence poses a significant challenge. Here,
we establish a metrology combining low-temperature scanning tunnelling
microscopy (STM) imaging and a comprehensive quantum treatment of the
dopant-STM system to pin-point the exact lattice-site location of sub-surface
dopants in silicon. The technique is underpinned by the observation that STM
images of sub surface dopants typically contain many atomic-sized features in
ordered patterns, which are highly sensitive to the details of the STM tip
orbital and the absolute lattice-site position of the dopant atom itself. We
demonstrate the technique on two types of dopant samples in silicon -- the
first where phosphorus dopants are placed with high precision, and a second
containing randomly placed arsenic dopants. Based on the quantitative agreement
between STM measurements and multi-million-atom calculations, the precise
lattice site of these dopants is determined, demonstrating that the metrology
works to depths of about 36 lattice planes. The ability to uniquely determine
the exact positions of sub-surface dopants down to depths of 5 nm will provide
critical knowledge in the design and optimisation of nanoscale devices for both
classical and quantum computing applications.
