Quantum states of atomic systems can be directly addressed using quantum optical microscopes. However, solid-state microscopy techniques cannot typically achieve both local measurements and control of the state due to their measurement mechanism or the presence of a globally conductive substrate that impedes local gate control. Here we report a solid-state quantum microscope that can control and locally probe the wavefunctions of atomic quantum dots in silicon. Our microscope consists of a scanning tunnelling microscope tip, source and gate electrodes defined on an insulating silicon substrate by subsurface antimony implantation and phosphorus dopants incorporated with atomic precision. In contrast to conventional semiconductor qubit devices, the macroscopic electrodes are fabricated before patterning the nanoscale elements. A light-assisted method is designed to make the substrate conductive to stabilize the microscope tip close to the quantum dots, before reversing to an insulator for local gating and spectroscopy. We show that the microscope can be used to tune and map the charge states of single and double quantum dots, as well as control the relative electrochemical potential between two dots.
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The data that support the findings of this study are available from the corresponding authors upon reasonable request.
Koenraad, P. & Flatté, M. E. Single dopants in semiconductors. Nat. Mater. 10, 91–100 (2011).
Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).
Gross, C. & Bakr, W. S. Quantum gas microscopy for single atom and spin detection. Nat. Phys. 17, 1316–1323 (2021).
He, Y. et al. A two-qubit gate between phosphorus donor electrons in silicon. Nature 571, 371–375 (2019).
Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017).
Kindem, J. M. et al. Control and single-shot readout of an ion embedded in a nanophotonic cavity. Nature 580, 201–204 (2020).
Yin, C. et al. Optical addressing of an individual erbium ion in silicon. Nature 497, 91–94 (2013).
Thiele, S. et al. Electrically driven nuclear spin resonance in single-molecule magnets. Science 344, 1135–1138 (2014).
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).
Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019).
Muhonen, J. et al. Storing quantum information for 30 seconds in a nanoelectronic device. Nat. Nanotechnol. 9, 986–991 (2014).
Hanson, R. et al. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).
Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015).
Koiller, B., Hu, X. & Das Sarma, S. Exchange in silicon-based quantum computer architecture. Phys. Rev. Lett. 88, 027903 (2001).
Vandersypen, L. M. K. et al. Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent. npj Quantum Inf. 3, 34 (2017).
Zimmerman, N. M., Huang, P. & Culcer, D. Valley phase and voltage control of coherent manipulation in Si quantum dots. Nano Lett. 17, 4461–4465 (2017).
Voisin, B. et al. Valley interference and spin exchange at the atomic scale in silicon. Nat. Commun. 11, 6124 (2020).
Mazurenko, A. et al. A cold-atom Fermi-Hubbard antiferromagnet. Nature 545, 462–466 (2017).
Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).
Dehollain, J. P. et al. Nagaoka ferromagnetism observed in a quantum dot plaquette. Nature 579, 528–533 (2020).
Crommie, M. F. et al. Confinement of electrons to quantum corrals on a metal surface. Science 262, 218–220 (1993).
Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014).
Martínez-Blanco, J. et al. Gating a single-molecule transistor with individual atoms. Nat. Phys. 11, 640–644 (2015).
Paul, W. et al. Control of the millisecond spin lifetime of an electrically probed atom. Nat. Phys. 13, 403–407 (2017).
Drost, R. et al. Topological states in engineered atomic lattices. Nat. Phys. 13, 668–671 (2017).
Kempkes, S. N. et al. Robust zero-energy modes in an electronic higher-order topological insulator. Nat. Mater. 18, 1292–1297 (2019).
Topinka, M. A. et al. Imaging coherent electron flow from a quantum point contact. Science 289, 2323–2326 (2000).
Woodside, M. T. & McEuen, P. L. Scanned probe imaging of single-electron charge states in nanotube quantum dots. Science 296, 1098–1101 (2002).
Shapir, I. et al. Imaging the electronic Wigner crystal in one dimension. Science 364, 870–875 (2019).
Bleszynski-Jayich, A. C. et al. Imaging a one-electron InAs quantum dot in an InAs/InP nanowire. Phys. Rev. B 77, 245327 (2008).
Tachizaki, T., Hayashi, K., Kanemitsu, Y. & Hirori, H. On the progress of ultrafast time-resolved THz scanning tunneling microscopy. APL Mater. 9, 060903 (2021).
Yang, K. et al. Coherent spin manipulation of individual atoms on a surface. Science 366, 509–512 (2019).
LeRoy, B. J. et al. Three-terminal scanning tunneling spectroscopy of suspended carbon nanotubes. Phys. Rev. B 72, 075413 (2005).
Tsai, H. Z. et al. A molecular shift register made using tunable charge patterns in one-dimensional molecular arrays on graphene. Nat. Electron. 3, 598–603 (2020).
Fuechsle, M. et al. A single-atom transistor. Nat. Nanotechnol. 7, 242–246 (2012).
Ng, K. S. H. et al. Scanned single-electron probe inside a silicon electronic device. ACS Nano 14, 9449–9455 (2020).
Kim, J. C., Kline, J. S. & Tucker, J. R. Fabrication of contact electrodes in Si for nanoelectronic devices using ion implantation. Appl. Surf. Sci. 239, 335–341 (2005).
Ward, D. R. et al. All-optical lithography process for contacting nanometer precision donor devices. Appl. Phys. Lett. 111, 193101 (2017).
Ramanayaka, A. N. et al. STM patterned nanowire measurements using photolithographically defined implants in Si(100). Sci. Rep. 8, 1790 (2018).
Nylandsted Larsen, A. et al. The nature of electrically inactive antimony in silicon. J. Appl. Phys. 59, 1908–1917 (1986).
Wang, Y. et al. Highly tunable exchange in donor qubits in silicon. npj Quantum Inf. 2, 16008 (2016).
Hile, S. J. et al. Addressable electron spin resonance using donors and donor molecules in silicon. Sci. Adv. 4, eaaq1459 (2018).
Mądzik, M. T. et al. Precision tomography of a three-qubit donor quantum processor in silicon. Nature 601, 348–353 (2022).
Wyrick, J. et al. Atom-by-atom fabrication of single and few dopant quantum devices. Adv. Funct. Mater. 29, 1903475 (2019).
Roche, B. et al. A tunable, dual mode field-effect or single electron transistor. Appl. Phys. Lett. 100, 032107 (2012).
Weber, B. et al. Spin blockade and exchange in Coulomb-confined silicon double quantum dots. Nat. Nanotechnol. 9, 430–435 (2014).
Weber, B. et al. Engineering independent electrostatic control of atomic-scale (~4 nm) silicon double quantum dots. Nano Lett. 12, 4001–4006 (2012).
Wijnheijmer, A. P. et al. Single Si dopants in GaAs studied by scanning tunneling microscopy and spectroscopy. Phys. Rev. B 84, 125310 (2011).
Rontani, M. & Molinari, E. Imaging quasiparticle wave functions in quantum dots via tunneling spectroscopy. Phys. Rev. B 71, 233106 (2005).
Salfi, J. et al. Quantum simulation of the Hubbard model with dopant atoms in silicon. Nat. Commun. 7, 11342 (2016).
Usman, M. et al. Spatial metrology of dopants in silicon with exact lattice site precision. Nat. Nanotechnol. 11, 763–768 (2016).
Salfi, J. et al. Spatially resolving valley quantum interference of a donor in silicon. Nat. Mater. 13, 605–610 (2014).
Keith, D. et al. Benchmarking high fidelity single-shot readout of semiconductor qubits. New J. Phys. 21, 063011 (2019).
Bonet, E., Deshmukh, M. M. & Ralph, D. C. Solving rate equations for electron tunneling via discrete quantum states. Phys. Rev. B 65, 045317 (2002).
Broome, M. A. et al. Two-electron spin correlations in precision placed donors in silicon. Nat. Commun. 9, 980 (2018).
Hallam, T. et al. Effective removal of hydrogen resists used to pattern devices in silicon using scanning tunneling microscopy. Appl. Phys. Lett. 86, 143116 (2005).
Schofield, S. et al. Quantum engineering at the silicon surface using dangling bonds. Nat. Commun. 4, 1649 (2013).
Van der Wiel, W. G. et al. Electron transport through double quantum dots. Rev. Mod. Phys. 75, 1–22 (2002).
Kiczynski, M. et al. Engineering topological states in atom-based semiconductor quantum dots. Nature 606, 694–699 (2022).
Le, N. H. et al. Topological phases of a dimerized Fermi-Hubbard model for semiconductor nano-lattices. npj Quantum Inf. 6, 24 (2020).
Škereň, T. et al. Bipolar device fabrication using a scanning tunnelling microscope. Nat. Electron. 3, 524–530 (2020).
Mannini, M. et al. Magnetic behaviour of TbPc2 single-molecule magnets chemically grafted on silicon surface. Nat. Commun. 5, 4582 (2014).
Nickel, A. et al. Electronically driven single-molecule switch on silicon dangling bonds. J. Phys. Chem. C 120, 27027–27032 (2016).
Huff, T. et al. Binary atomic silicon logic. Nat. Electron. 1, 636–643 (2018).
We acknowledge support from the ARC Centre of Excellence for Quantum Computation and Communication Technology (CE170100012), an ARC Discovery Project (DP180102620), Silicon Quantum Computing Pty Ltd, the US Army Research Office (W911NF-17-1-0202) and from the NSW and ACT Nodes of the Australian National Fabrication Facility. J.S. acknowledges support from an ARC DECRA fellowship (DE160101490). B.C.J. and J.C.M. acknowledge the AFAiiR node of the NCRIS Heavy Ion Capability for access to the ion implantation facilities.
M.Y.S. is a director of the company Silicon Quantum Computing Pty Ltd.
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a, Implantation process. The implantation energy is chosen to overcome a 22.5 nm sacrificial oxide barrier. The sample presented here was implanted with a double dose of 60 keV and 100 keV with respective doses of 4 × 1014 and 1 × 1015 cm2. These energies are less than that of the sample presented in the manuscript (70 and 110 keV) to compensate for a thinner oxide (22.5 vs 27 nm). b, Stopping and Range of ions in matter (SRIM) simulations of the implantation profile, for 60 keV (black), 100 keV (red) and total (blue). The concentration peaks around 40 nm in the silicon substrate, and is largely above the metal/insulator transition at the SiO2/Si interface. The lateral range of these implants is less than 20 nm while the diffusion upon flash annealing is less than 25 nm. This is sufficient to ensure Sb is confined to the electrodes and does not diffuse into the regions where the STM is performed.
a, Comparison of the SRIM simulation and (black) and of Rutherford back-scattering (RBS) measurements of a sample annealed at 660∘C for 15h. The depth of the SRIM data was offset to match the onset of the RBS signal, as the sacrificial oxide was etched for the RBS samples. The random data (red) correspond to the total amount of Sb, the channeled data (blue) correspond to interstitial and unactivated Sb atoms. b, Random RBS data for different flash anneal conditions: 660∘C for 15h (red), followed by a 1100∘C/20 s (dark red) or a 1200∘C/20 s flash (brown). The 1100∘C used for the device leaves a high concentration of antimony atoms in the top few nanometers of the silicon substrate. c, Sb sheet density, determined as the area of the random RBS signal, as a function of the flash anneal conditions. The density remains above the metal-insulator transition despite a reduction due to deep diffusion in the substrate. d, Sb activated fraction, determined as 1 − Ac/Ar where Ar and Ac are the area under the random and channeled RBS signals, respectively. The first point (no annealing) is close to zero as annealing is necessary to activate the Sb atoms, it is slightly negative due to a statistical difference between the random and channeled measurements. The activated fraction is above 80% once the sample is annealed, the error bars increase with annealing temperature due to lower Sb counts in the channeled data. The mean values and error bars shown for the sheet density and activated fraction are obtained from least-square Gaussian fits to the RBS measurements, with details given in Supplementary Information Section 1.
a, Measurement protocol. The transition between the topography mode (feedback loop and light on, Vb = Vg = − 1.6 V) and the spectroscopy mode is defined as follows. The light and feedback loop are first turned off, and then the bias and gate voltages are swept to the initial values of the spectrum to be acquired, which are closer to zero with respect to topography settings. The tip is then brought closer to the sample. This order, gate and bias voltages first before tip height offset, ensures for the tunnel current not to exceed 1 nA, which could create spurious hydrogen desorption at the surface. The spectroscopy diagram shown here is designed to record the tunnel current as a function of the bias voltage, for a fixed gate voltage and tip position. Once the spectroscopy is completed, a transition is implemented to revert back to topography settings. A similar protocol is implemented for spatially resolved spectroscopy. b, Current Isg between the source and the gate when the light is off. In this configuration, the transimpedance amplifier is connected to the gate electrode and the tip was left floating. Minimal leakage current is observed for a large bias range Vb − Vg from -1.5 to +1.5 V, with a linear fit of the region around Vb − Vg = 0 V (black dotted line) yielding Rsg = 9.45 GΩ, similar to other dopant-based devices.
a-c STM images of first three charge transitions for QD#1, same as main text. d Average line cut of the normalised STM images, taken along the horizontal grey section #1 shown in a. The third transition shows more charge distribution in the bottom left corner of the QD designed area. e Average line cut taken along the horizontal grey section #2 shown in a. The third transition shows more charge distribution around the top right section of thew QD designed area.
a, Stability diagram Isd vs Vb, Vg. This QD shows more resonances than QD#1 indicating that more donors have been incorporated. b, Wavefunction image taken at Vg = − 0.35 V and Vb = − 0.23 V. The dashed rectangle highlights the size of the lithography area. Beside drift correction, an additional Fourier filtering was performed for this image as the tunnel current was close to the noise background. c, Wavefunction image taken at Vg = 0 V and Vb = − 0.8 V. At such large occupation number and large source-drain bias, the wavefunction extends outside the lithography area. d, Spectroscopy line Isd vs Vb and x taken across the reservoir and the QD at Vg = 0 V. e, Same as b taken at Vg = -1 V. centred on the QD. The plateaux in tunnel current vs Vb indicate the addition of electrons on the QD. f Spectroscopy line cuts extracted from b and c, see arrows for colour code. There is no tunnel current within the silicon gap away from the QD and the reservoir. The Coulomb plateaux are visible when the tip is located over the QD. The silicon gap completely closes when the tip is above the source reservoir (black line), which evidences the continuity in the metallic contact between the antimony implanted electrode and its atomic-scale phosphorus extension.
a, Topography image of the double dot device lithography, same as main text. b, Quantum state image taken at Vb = Vg = − 0.8 V, same scale as the lithography image. As in the main text, we take as reference to align the furthest dot from the source (called LD). The two dots are barely visible at this lower gate and bias voltages, but direct tunnel current over the reservoir can be evidenced. A diffusion of the source lead Δdlead = 2.0 nm towards the quantum dots can be detected in this image, attributed to the high concentration of dopants in this element. c Large scale topography image (Vb = Vg = − 2.1 V) around the DQD (associated topography image to the quantum state image shown in b), where the dangling bonds can be evidenced as bright features. d Small scale topography image (Vb = Vg = − 2.1 V) around the DQD, corresponding to the dashed square in b and c. A difference in the dangling bond brightness can be observed between the topography and the quantum state images. The silicon substrate is illuminated and conductive in topography mode, resulting in all dangling bonds having a similar brightness. On the contrary, only the dangling bonds close to incorporated dopants (DQD or source) are bright in the quantum state image, as the sample is insulating in this mode and transport must occur through conductive elements.
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Voisin, B., Salfi, J., St Médar, D.D. et al. A solid-state quantum microscope for wavefunction control of an atom-based quantum dot device in silicon. Nat Electron 6, 409–416 (2023). https://doi.org/10.1038/s41928-023-00979-z
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