Donor Wavefunctions in Si Gauged by STM Images

Abstract

The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wavefunctions will withstand an experimental test. Such wavefunctions 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 resemble a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the non-monotonic 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 wavevector to $k_0=(0.82\pm 0.03)(2\pi /a_{Si})$. Unlike prior measurements, averaged over a sizeable 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 wavefunctions as well.

12 pages, 8 figures

References in corpus (3)

• Spatial structure of an individual Mn acceptor in GaAs
• Interface-induced heavy-hole/light-hole splitting of acceptors in silicon
• Spatially resolved resonant tunneling on single atoms in silicon

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• Linear and planar molecules formed by coupled P donors in silicon
• Novel characterisation of dopant-based qubits
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• Anderson Localization of Electrons in Silicon Donor Chains
• Influence of sample momentum space features on scanning tunnelling microscope measurements
• Donors in Ge as Qubits: Establishing Physical Attributes
• Disordered Si:P nanostructures as switches and wires for nanodevices