Imaging Dopant-Based Quantum Devices in Si

Atom-based devices can be fabricated in Si using scanned-probe lithography to place P dopants with near atomic precision. Such devices have received tremendous attention as potential atomic-scale solid-state qubits. Theoretical procedures and rules have been developed to use scanning tunneling microscopy (STM) to image and locate individual dopants with atomic precision a few nanometers from a Si surface. Real devices will have qubits formed from multiple, nearby dopants and atomic-scale wires made from high densities of dopants. Determining the geometry of such multiple-dopant qubits and assessing the quality of atomic-scale wires will be an essential step in device fabrication.
We extend the theory needed to use STM to image and define the geometry of multi dopant regions. The starting point is a tight-binding description of dopants in Si, including surface passivation, reconstruction and image charge effects. We consider the imaging of two-dopant geometries and then extend the investigations to consider multiple dopants. We propose rules for imaging two dopants and explore possible generalizations for more complicated structures for determining relative dopant positions.