Spatial metrology of dopants in silicon with exact lattice site precision

Journal name:
Nature Nanotechnology
Volume:
11,
Pages:
763–768
Year published:
DOI:
doi:10.1038/nnano.2016.83
Received
Accepted
Published online

Abstract

Scaling of Si-based nanoelectronics has reached the regime where device function is affected not only by the presence of individual dopants, but also by their positions in the crystal. Determination of the precise dopant location is an unsolved problem in applications from channel doping in ultrascaled transistors to quantum information processing. Here, we establish a metrology combining low-temperature scanning tunnelling microscopy (STM) imaging and a comprehensive quantum treatment of the dopant–STM system to pinpoint the exact coordinates of the dopant in the Si crystal. The technique is underpinned by the observation that STM images contain atomic-sized features in ordered patterns that are highly sensitive to the STM tip orbital and the absolute dopant lattice site. The demonstrated ability to determine the locations of P and As dopants to 5 nm depths will provide critical information for the design and optimization of nanoscale devices for classical and quantum computing applications.

At a glance

Figures

  1. STM-based metrology for the exact position of subsurface dopants in silicon.
    Figure 1: STM-based metrology for the exact position of subsurface dopants in silicon.

    a, Illustration of the STM set-up used to measure atomically resolved subsurface dopant images. The dopant charge density distribution (|ΨD|2) calculated from a tight-binding simulation over a large volume of the Si lattice is shown, colour-coded to highlight its variation as a function of distance from the dopant atom. A P dopant is positioned a few nanometres below the surface (z = 0) and is highlighted in red. The 2 × 1 reconstruction results in the formation of dimer rows at the z = 0 surface. The vertical shaded area in the vacuum region (between the sample and the STM tip) illustrates tunnelling of a single electron from the P dopant state in Si through the vacuum region to a single W atom at the STM tip apex. The measured atomically resolved image of the normalized tunnelling current is shown (P-1-Exp). The x and y axes represent [100] and [010] crystallographic directions, respectively. b, The theoretical framework involves the quantum mechanical treatment of the four linked components of the STM set-up, as follows: (1) multi-million atom calculation of the dopant ground-state wavefunction with 2 × 1 surface reconstruction (ΨD(r)); (2) calculation of wavefunction decay in the vacuum region ( 2ΨD/T − κ2ΨD/T; ref. 26); (3) determining the Bardeen tunnelling current34, which is proportional to the tunnelling matrix element evaluated as a surface integral on the separation surface χ between the STM tip and the sample26; and (4) establishing the STM tip state (ΨT(r)) from the derivative rule26. The final calculated image of the normalized tunnelling current (P-1-Th) is shown. c, Direct quantitative comparison of the STM image and the images computed over a number of atomic positions leads to a unique identification of the subsurface dopant location in the Si lattice.

  2. STM tip orbital dependence.
    Figure 2: STM tip orbital dependence.

    Theoretically computed images for the P-1 dopant as a function of the individual orbitals in the STM tip state (ΨT). Each image is labelled by the corresponding tip orbital (top left of each image), the corresponding orbital symmetry in the xy plane (top right of each image) and the differential operator based on Chen's derivative rule26 applied to the sample wavefunction (bottom right of each image). Note that an s tip orbital will give an image directly proportional to the modulus squared of the wavefunction, without any derivative. The tip height is taken to be 2.5 Å and the dopant depth is 4.75a0. Each tip orbital produces a very different image of the dopant wavefunction, and only the dz2−(1/3)r2 orbital image (highlighted by the red border) captures the symmetry of the atomic features present in the measured data P-1-Exp shown in Fig. 1b.

  3. Unique lattice site assignment for the P-1 dopant by depth analysis.
    Figure 3: Unique lattice site assignment for the P-1 dopant by depth analysis.

    a, To identify the exact location of the measured P-1-Exp image, theoretically computed images are shown as a function of plane depth n once the location group has been identified from the image symmetry (for details see Supplementary Fig. 4). The computed image at a depth of 4.75a0 (highlighted by the red border), corresponding to n = 4, exhibits the best quantitative agreement with the measured P-1-Exp image, as is evident from the comparator peaks. b, Plot of pixel-by-pixel CP and feature-by-feature CF comparators between the P-1-Exp image and the theoretical images in a. The best agreement with the P-1-Exp image is uniquely identified at a dopant depth of 4.75a0 (m = 3/4, n = 4, i = 7) by the joint peaks of both comparator parameters. The corresponding depth plane analyses for the other dopants in the set (P-2-Exp, As-1-Exp and As-2-Exp) are shown in Supplementary Fig. 9.

  4. Pinpointing dopant location with single-lattice-site precision.
    Figure 4: Pinpointing dopant location with single-lattice-site precision.

    a,b, Theoretically computed and experimentally measured images (normalized equivalently) for dopants P-1 (a) and P-2 (b) at final determined lattice site positions and (depth = 4.75a0), respectively. Despite being at the same depth from the z = 0 surface, the symmetries of the P-1 and P-2 images reflect the different positions relative to the surface dimer rows (directly underneath the dimer and between the two dimer rows, respectively). The location of the dopants is therefore uniquely determined in terms of depth and with respect to the surface dimer positions. c, Illustration of the relevant Si lattice sites in the Si crystal structure. The topmost surface of the Si is hydrogen passivated (H atoms are shown in purple). At the z = 0 surface, dimer rows are shown along the direction perpendicular to the page (indicated by the atoms in grey). The three categories of lattice positions are shown as blue, green and red atoms with respect to the dimer rows: green = positions directly below the dimer rows, red = positions between two dimer rows, and blue = positions at the edges of a dimer row. Due to symmetry properties, green and red positions would correspond to unique patterns of features in the images, whereas blue positions simply lead to 180° rotation of the image features. d,e, Theoretically computed and experimentally measured images (normalized equivalently) are shown for dopants As-1 (d) and As-2 (e) at final determined lattice site positions (depth = 3.5a0) and (depth = 9a0), respectively.

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Author information

Affiliations

  1. Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Parkville, 3010 Victoria, Australia

    • M. Usman &
    • L. C. L. Hollenberg
  2. Centre for Quantum Computation and Communication Technology, School of Physics, The University of New South Wales, Sydney, 2052 New South Wales, Australia

    • J. Bocquel,
    • J. Salfi,
    • B. Voisin,
    • M. Y. Simmons &
    • S. Rogge
  3. Electrical and Computer Engineering Department, Purdue University, West Lafayette, Indiana 47907, USA

    • A. Tankasala &
    • R. Rahman

Contributions

L.C.L.H. and M.U. formulated the theoretical framework for the metrology scheme, including tight-binding calculations of the STM images with generic tip orbitals with input from J.S. M.U. performed the theoretical calculations. J.B., J.S., B.V., M.Y.S. and S.R. designed and conducted the STM measurements. L.C.L.H. and M.U. wrote the manuscript with input from all authors.

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The authors declare no competing financial interests.

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