Spectroscopy of few-electron single-crystal silicon quantum dots

Journal name:
Nature Nanotechnology
Volume:
5,
Pages:
502–505
Year published:
DOI:
doi:10.1038/nnano.2010.95
Received
Accepted
Published online

Abstract

A defining feature of modern CMOS devices1 and almost all quantum semiconductor devices2, 3, 4, 5, 6, 7, 8, 9 is the use of many different materials. For example, although electrical conduction often occurs in single-crystal semiconductors, gates are frequently made of metals and dielectrics are commonly amorphous. Such devices have demonstrated remarkable improvements in performance over recent decades, but the heterogeneous nature of these devices can lead to defects at the interfaces between the different materials, which is a disadvantage for applications in spintronics10, 11 and quantum information processing12, 13, 14, 15, 16. Here we report the fabrication of a few-electron quantum dot in single-crystal silicon that does not contain any heterogeneous interfaces. The quantum dot is defined by atomically abrupt changes in the density of phosphorus dopant atoms, and the resulting confinement produces novel effects associated with energy splitting between the conduction band valleys. These single-crystal devices offer the opportunity to study how very sharp, atomic-scale confinement—which will become increasingly important for both classical and quantum devices—influences the operation and performance of devices.

At a glance

Figures

  1. Few-electron single-crystal silicon quantum dot device.
    Figure 1: Few-electron single-crystal silicon quantum dot device.

    a, STM image of the central device region acquired during hydrogen lithography, showing a four-terminal dot device with source (S) and drain (D) leads and two in-plane gates (G1, G2). The bright patches, which have been outlined for clarity, indicate hydrogen-desorbed regions where phosphorus donors will eventually be incorporated from the gaseous precursor molecule phosphine (PH3). b, Close-up image with dimer-row resolution showing the desorbed patch that will become the quantum dot. The dot is coupled to co-planar source and drain leads via tunnel gaps. All distances in a,b are in nanometres. c, By overlaying a grid with dimer-row spacing, we can count the number of desorbed silicon dangling bonds in the dot area. d, Potential phosphorus incorporation sites are highlighted in green, with stray dangling bonds (DB) and single bare silicon dimers indicated in red.

  2. Stability diagram of the few-electron single-crystal silicon quantum dot.
    Figure 2: Stability diagram of the few-electron single-crystal silicon quantum dot.

    a, False-colour plot of the conductance dI/dVSD as a function of the voltage at gate G1, VG1, and bias voltage VSD. To limit the maximum current through the device, the bias voltage window was decreased as VG1 was made more positive, resulting in a trapezoidal plot. Conductance resonances are visible as bright lines of increased conductance running parallel to the edges of the Coulomb diamonds. b, Gate G1 is slightly closer to the D lead than the S lead, so making VG1 more negative will decrease the asymmetry of the tunnel coupling between the dot and the leads.

  3. Excited-state spectrum of a few-electron single-crystal silicon quantum dot.
    Figure 3: Excited-state spectrum of a few-electron single-crystal silicon quantum dot.

    a, Close-up view of one of the Coulomb blockade transitions (white square in Fig. 2a) reveals a high density of conduction resonances with an average energy spacing of ~100 µeV. b, Top: Two-dimensional projection of the Brillouin zone corresponding to a phosphorus sheet of density 0.125 ML (see Methods). Bottom: Corresponding band structure along one axis in k-space. Individual bands are indicated by the following colour code: Γ1 (blue), Γ2 (green) and Δ (pink). Note that distinct Δx- and Δy-bands are shown in the top of the panel. c, Density of states for a 0.125-ML-doped two-dimensional sheet in the effective mass approximation. The corresponding single-electron energy levels are shown for a seven-donor, seven-electron quantum dot. Inset shows the valley splitting of the four Δ-levels near the Fermi energy (EF = 0). d, Combinatorial procedure for computing multi-electron energy levels, using the single-electron energies shown in c. e, Theoretical result for the quantum dot excitation spectrum corresponding to a. Positive energies (VSD > 0) correspond to a seven-donor, seven-electron dot, and negative energies (VSD < 0) correspond to an eight-electron dot. Bolder lines indicate the presence of two levels that are nearly degenerate.

  4. Contribution of the tunnelling density of states from the irregularly shaped leads.
    Figure 4: Contribution of the tunnelling density of states from the irregularly shaped leads.

    a, Left: Single-electron density of states for a long rectangular lead of width 5.3 nm, oriented at 42.5° relative to the ( 00) direction. Results are shown for the Γ1-band (blue), Γ2-band (green), Δx-band (pink) and Δy-band (purple). Right: Single-electron density of states for the realistic lead shape visible in Fig. 1a. b, Typical Δx-eigenstates for the two lead geometries studied in a. For example, the lowest state in the right-hand column does not contribute significantly to the density of states, because this wavefunction has almost no weight in the narrow portion of the lead. The colour scale displays wavefunction amplitudes. For visual clarity, all the amplitudes were linearly rescaled to have the same minimum and maximum values.

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Author information

Affiliations

  1. Centre for Quantum Computer Technology, University of New South Wales, Sydney NSW 2052, Australia

    • Martin Fuechsle,
    • S. Mahapatra,
    • F. A. Zwanenburg &
    • Michelle Y. Simmons
  2. University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

    • Mark Friesen &
    • M. A. Eriksson

Contributions

M.Fu. carried out the fabrication and measurements. M.Fr. conducted the theoretical work. M.Fu., S.M., F.Z., M.S. and M.E. analysed the data. M.S. planned the project. M.Fu., M.S., M.Fr. and M.E. prepared the manuscript.

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The authors declare no competing financial interests.

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