Element-specific, non-destructive profiling of two-dimensional dopant layers in silicon

Starting points for silicon-based quantum devices can be δ -layers of dopants from group V in the periodic table. Deterministic doping leading to few-atom devices requires these layers to be ultrathin. A recent breakthrough has been to use arsenic rather than phosphorous as dopant, which together with optimized heat treatments has yielded δ -layers acting as quantum wells with widths down to 0.5 nm inferred from magneto-transport and angle-resolved photoemission, techniques sensitive to the conduction electrons only. These widths are considerably smaller than the resolution-limited chemical thickness of 2 nm from the standard measurement technique, namely secondary-ion mass spectroscopy, and so leaves open the question of whether the dopant layers are indeed as thin as the extent of the conduction electron wavefunctions perpendicular to the layers. Here, we present resonant-contrast X-ray reflectometry experiments and analysis—including both full modeling and a simple perturbation approach—to demonstrate that the sub-nm electronic thickness of the δ -layers corresponds to sub-nm chemical thickness. We take advantage of the change in the scattering factor of atoms as their core level resonances are scanned by varying the X-ray energy. In combination with X-ray fluorescence imaging, this enables non-destructive three-dimensional elemental characterization of nano-structured quantum devices.