Donor wave functions 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 k0 = (0.82 ± 0.03)(2π/aSi). 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.

Exact location of dopants below the Si(001):H surface from scanning tunneling microscopy and density functional theory

“…We observe highly anisotropic features superimposed on the surface atomic lattice that we have interpreted as arising from the ground state wave function of neutral donors in analogy with previous reports of dopant wave function mapping in GaAs [22,23]. For donor depths beyond 12 layers we find even more diffuse surface features in agreement with a recent report where such features were assigned to As donors approximately 20 atomic layers beneath the surface based on bulk k · p and tight-binding calculations [24,25]; more recent reports [26,27] show that both these approaches give excellent agreement with experiment. This type of semiempirical approach allows for large-scale calculations and will correctly capture the long-range behavior of the dopant wave function, which is particularly important for dopants far from the surface.…”

Electronic states and valley-orbit coupling in linear and planar molecules formed by coupled P donors in silicon

“…The polarization of Z-valley is even larger in P 6 The symmetry of six phosphorus donors arranged in a hexagonal structure have richer valley interference patterns than in the triatomic structures discussed above. This is due to a complex superposition of the six phase factors in Eq.…”

“…Each one of the thousand energy spectra is plotted in Fig. 7 as a red thin line for P 6 13 {100} and a blue thin line for P 6 The electron densities for other energy states of the hexagonal structures P 6 17 {110} and P 6 13 {100} are reported in Supplementary Information. …”

Disordered Si:P nanostructures as switches and wires for nanodevices

“…Comparisons with experiments show that this multivalley central cell corrected dopant approximation gives an accurate description of the single impurity spectrum [26] and the corresponding wave functions [28], as well as the two impurities spectra in ionized [29] and neutral excited states [30]. The computationally advan- tage is clear: By incorporating the Si matrix explicitly in the orbitals, this approach allows the investigation of shallow donor systems of mesoscopic dimensions, a prohibitive task for a full atomistic approach.…”