Donor wave functions in Si gauged by STM images

The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wave functions will withstand an experimental test. Such wave functions have recently been probed by scanning tunneling spectroscopy, revealing localized patterns of resonantly enhanced tunneling currents. We show that the shape of the conducting splotches resembles a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the nonmonotonic features of the current profile are consistent with the charge density fluctuations observed between successive ${001}$ atomic planes, including a counterintuitive reduction of the symmetry---a heritage of the lowered point group symmetry at these planes. A model-independent analysis of the diffraction figure constrains the value of the electron wave vector to ${k}₀=(0.82\ifmmode\pm\else\textpm\fi{}0.03)(2\ensuremath{\pi}/{a}_{\mathrm{Si}})$. Unlike prior measurements, averaged over a sizable density of electrons, this estimate is obtained directly from isolated electrons. We further investigate the model-specific anisotropy of the wave function envelope, related to the effective mass anisotropy. This anisotropy appears in the KL variational wave function envelope as the ratio between Bohr radii $b/a$. We demonstrate that the central-cell-corrected estimates for this ratio are encouragingly accurate, leading to the conclusion that the KL theory is a valid model not only for energies but for wave functions as well.