Atom-by-Atom Construction of a Quantum Device Jason R. Petta* Department of Physics, Princeton University, Princeton, New Jersey 08544, United States ABSTRACT: Scanning tunneling microscopes (STMs) are conventionally used to probe surfaces with atomic resolution. Recent advances in STM include tunneling from spin-polarized and superconducting tips, time-domain spectroscopy, and the fabrication of atomically precise Si nanoelectronics. In this issue of ACS Nano, Tettamanzi et al. probe a single-atom transistor in silicon, fabricated using the precision of a STM, at microwave frequencies. While previous studies have probed such devices in the MHz regime, Tettamanzi et al. probe a STM-fabricated device at GHz frequencies, which enables excited-state spectroscopy and measurements of the excited-state lifetime. The success of this experiment will enable future work on quantum control, where the wave function must be controlled on a time scale that is much shorter than the decoherence time. We review two major approaches that are being pursued to develop spin-based quantum computers and highlight some recent progress in the atom-by-atom fabrication of donor-based devices in silicon. Recent advances in STM lithography may enable practical bottom-up construction of largescale quantum devices. KEYWORDS: Kane quantum computer, quantum device, spectroscopy, silicon, phosphorus he field of quantum information science aims to harness the coherence of quantum states for applications in quantum computing and quantum sensing. Trapped ions, semiconductor quantum dots, and superconducting devices are among the leading contenders for building a scalable quantum computer.1−3 Approaches based on semiconductors are being intensely pursued, as semiconductor devices can be readily produced using well-established lithography techniques. The preferred quantum degree of freedom in semiconductors is spin, as it is well-isolated from the environment.4 Silicon, in particular, is an excellent host material for spin quantum bits (qubits), as it can be chemically and isotopically purified, leading to seconds-long spin coherence times.5,6 Spin-Based Quantum Computing: Dots and Donors. The Loss−DiVincenzo proposal and Kane quantum computer proposal have resulted in a firestorm of experimental activity aimed at building a spin-based quantum computer.7,8 These proposals are alike in that they both suggest using spins in semiconductors to build qubits. However, at a device level, they differ significantly in terms of the level of control that is needed in the placement of the individual qubits. Loss and DiVincenzo focused on lithographically defined semiconductor quantum dots. They suggested that a spin could be initialized in the ground state at high magnetic fields and low temperatures, controlled using the standard electron spin resonance (ESR) toolbox, and read out using a process called spin-to-charge conversion.7 Electrical control of wave function overlap results in a gate voltage tunable exchange coupling,
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© 2017 American Chemical Society
which, when combined with ESR, can be used to implement a CNOT gate. A CNOT gate is a logical operation that is an essential ingredient in the development of a universal quantum computer. Spin initialization, control with ESR, exchange coupling, and readout were first demonstrated in GaAs quantum dots.9−11 A high-fidelity two-qubit gate was recently demonstrated in a silicon device.12 On the heels of the Loss−DiVincenzo proposal, Bruce Kane suggested building a quantum computer from single 31P donors in Si.8 The 31P donor nucleus serves as a simple I = 1/2 nuclear spin system that can be controlled using nuclear magnetic resonance. Gate control of the electronic wave function is used to mediate nuclear spin interactions. Another donor-based approach is to use the donor electron spin as the qubit and to modulate the electronic exchange coupling using electrostatic gates. Although the quantum control aspects of dots and donors are similar, the characteristic length scales of the two systems are dramatically different. Lithographically defined quantum dots have dimensions in the range of ∼50−100 nm, which is well within the limits of today’s semiconductor processing tools, whereas donor-based qubits require placement with nearly atomic-scale precision. We focus the remainder of this Perspective on advances in donor placement and control. Exchange Coupling Donor Pairs. Ion implantation is conventionally used to implant donors in silicon. Serious efforts have been made to improve the accuracy of ion implantation by Published: March 10, 2017 2382
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Figure 1. (a) Schematic illustrating the general scanning tunneling microscope (STM) lithography process flow. (1) A clean Si surface is passivated with hydrogen. (2) Electrons from a voltage-biased STM tip selectively desorb hydrogen from the silicon surface. (3) The sample is exposed to PH3 molecules that get absorbed by the exposed silicon. Hydrogen serves as a mask and protects the remaining areas of the surface. (4) An annealing step incorporates the P atoms into the uppermost layer of the Si lattice. (5) An epitaxial Si capping layer buries the P-doped layer. (b) Example of a STM-patterned device.
dimers along a dimer row for a P to bond to the Si substrate.17 An annealing step incorporates the P into the upper layer of Si. Lastly, the P atoms are buried by a Si capping layer that is grown at low temperature. The process yields n-doped nanostructures that are atomically abrupt in three dimensions, with active doping far above both the solid solubility limit and the metal-to-insulator transition. Devices formed in this way are conductive at T ∼ 100 mK, making them useful for quantum computing applications. Scanning tunneling microscope lithography has greatly evolved since the 1994 demonstration of controlled hydrogen desorption.15 The tunneling mode enables slow high-resolution patterning, with the precision of a sniper rifle. As an alternative, the STM can be operated in high-voltage field emission (HVFE) mode, with a tip bias of ∼10 V and tip−sample distance exceeding a few nanometers. The relatively high voltage and tip−sample distance enlarge the desorption spot size and increase the patterning rate by nearly a factor of 100.18 Thus, HVFE STM is analogous to an electron blunderbuss, where the lack of precision is offset by the speed gained from having a large electron spread, which enables patterns to be written quickly. Scanning tunneling microscope lithography approaches to building quantum devices are being pursued at a number of institutions, including Sandia National Laboratories in Albuquerque, NM, and IBM in Zurich, Switzerland; elements of a quantum computer based on STM lithography have been demonstrated at the University of New South Wales in Australia. Scanning Tunneling Microscopy Fabrication of a Single-Atom Transistor. In 2012, Fuechsle et al. demonstrated the fabrication of a single atom transistor in Si.17 They used STM lithography to incorporate a single P atom in the surface layer of Si. Source and drain electrodes and a pair of gate electrodes enabled the donor to be electrically probed. A STM image of the device is shown in Figure 2a. By measuring the conductance through the donor as a function of gate voltage, the authors were able to extract a charging energy of 47 meV, which is in excellent agreement with other measurements in bulk Si. Critically, and unlike implanted samples, the STM lithography approach enables the sample to be imaged, and the donor position localized, before overgrowth with the Si capping layer. The agreement between the charging energy of the single donor device and measurements on bulk Si, as well as predictions from theory, give added confidence that Fueschsle
using resists to mask the implantation to specific regions of the substrate and detectors to sense when a single ion enters the substrate.13 Unfortunately, the ions are implanted at high energy and ricochet around the crystal lattice, leading to “straggle” or placement inaccuracies that can be as large as 10 nm, which is on the order of critical feature sizes for quantum devices. Just how important is ion placement in a donor-based quantum computer architecture? In 2002, Koiller, Hu, and Das Sarma calculated the donor electron exchange energy in Si.14 Silicon has six equivalent conduction band minima, termed “valleys”, that are located about 85% of the way between the center of the Brillouin zone and the zone edge. Koiller et al. showed that interference between these valleys causes the exchange energy to oscillate rapidly with donor separation. Donor placement with accuracy on a 0.235 Å length scale may be needed for fine control of the exchange coupling. The extremely small length scale highlights the need for atomicscale placement, which cannot presently be achieved through ion implantation or other conventional lithographic approaches.14 Scanning Tunneling Microscope Lithography. Fortunately, a process exists that allows P donors to be precisely positioned in the Si lattice. In 1994, Lyding et al. demonstrated that electrons from a biased scanning tunneling microscope (STM) tip can be used to desorb hydrogen selectively from a Si surface, thereby enabling atomically precise chemical functionalization of a surface.15 Since then, the Simmons group in Sydney has adapted this concept to demonstrate a complete fabrication process for placing P atoms in a silicon device with nano- to atomic-scale precision.16 The STM lithography process is outlined in Figure 1a. First, a bare piece of Si wafer is flash cleaned at high temperature in ultrahigh vacuum. The clean Si surface is then passivated with hydrogen. Nanoscale patterning is achieved using a STM tip. The most common patterning mode is called “tunneling mode”, where the tip is biased at a few volts with respect to the sample, and the tip hovers 1−2 nm above the sample surface. Electrons from the tip hit the sample, causing hydrogen to desorb from the surface. Phosphine (PH3) gas is then added to the ultrahigh vacuum chamber, where it incorporates with the exposed Si atoms. In the unexposed areas, the H passivation serves as a mask that prevents PH3 incorporation. Previous research has shown that there must be at least three sequential depassivated 2383
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overlap and can be large, with exchange gate operations as short as 200 ps demonstrated in GaAs double quantum dots.11 Single spin control with ESR also requires transmission of highbandwidth signals to the active region of the device.10 It is therefore important to demonstrate that a new device platform is capable of responding to high-frequency electrical excitation. Tettamanzi et al. demonstrate that their STM-fabricated single-atom transistor is up to the task. They measure the current through the single-atom transistor as a function of gate voltage and focus on the single-electron charging transition associated with the neutral D0 state and the ionized D+ state of the P atom.20 The Coulomb charging energy can be overcome by bringing the energy of the D+ and D0 states into resonance with the leads by adjusting the gate voltage. When these states are in resonance, a Coulomb blockade peak in the current is observed. Since this resonance condition is dependent on the gate voltages, it can be used as a diagnostic for the coupling of high-frequency excitations into the device. Specifically, the application of an oscillating gate voltage will cause the energy of the donor states to oscillate. In direct current (dc) transport measurements of the charge current, this excitation will result in doubling of the Coulomb blockade peak. Tettamanzi et al. observe a doubling up to frequencies approaching 13 GHz. They also show that high-frequency signals can be applied to two separate gates and synchronized with high precision. These results are significant, as they demonstrate that STM-fabricated gate electrodes with charge densities in the range of 2 × 1014 cm−2 are capable of transmitting the high-speed signals that are needed for quantum control. In comparison, quantum dot devices fabricated with high-resistance polysilicon gates can have bandwidth limitations above 1 GHz.
Figure 2. (a) Scanning tunneling microscope image of a singleatom transistor. Adapted with permission from ref 17. Copyright 2012 Macmillan Publishers Limited. A single P atom is coupled by tunneling to source (S) and drain (D) electrodes, enabling measurements of the electrical conductance. (b) Energy level diagram at small (left) and large (right) source−drain bias VSD. At large source−drain bias, transport can proceed through both the ground and excited states. (c) Excited-state relaxation rate ΓES can be extracted using a pulsed-gate measurement approach.
et al. are indeed measuring the electrical current through a single donor atom. Time Domain SpectroscopyToward Quantum Control of a STM-Fabricated Single-Atom Transistor. In the same way that optical absorption and transmission measurements can be used to determine the electronic structure of gases, electrical conductance measurements can provide a precise determination of the energy level structure of nanofabricated quantum devices. Although the fabrication of quantum devices and the probing of their electronic energy level structure are important first steps, achieving time-domain control of a single quantum state is one of the ultimate goals in quantum information science. In P-doped Si, impressive quantum control has been demonstrated in devices with randomly implanted P ions.19 Although low-frequency conductance measurements have been performed on STMfabricated single-atom transistors, a demonstration of highfrequency control of such a device has been lacking. In particular, it is not clear if the STM-fabricated gates are capable of coupling high-frequency signals to the single-atom transistor. High-resistance gates will lead to long pulse rise times (due to RC time constants) that are problematic for accurate quantum control. It is also important to gauge the stability of STMfabricated devices under high-frequency excitation.
In this issue of ACS Nano, Tettamanzi et al. take an important first step toward quantum control of donors in STMfabricated devices. Conventional dc transport measurements enable the excitedstate spectrum of an artificial atom to be probed. With highspeed electrical control of the donor within reach, it becomes feasible to measure excited-state relaxation times. For example, pump−probe methods were first implemented in quantum dots in the late 1990s to measure orbital and singlet−triplet relaxation rates.21 Today, pump−probe methods are routinely used in semiconductor quantum dots to measure single spin relaxation rates and to read out the state of a qubit after quantum manipulations.9,19 Electrical conductance measurements can yield insight into the excited-state level spectrum. A small source−drain bias VSD is applied across the donor. If the source−drain bias is less than the energy difference between the ground state and excited state, electronic transport can only proceed through the ground-state level, leading to a measurable current (see the left panel of Figure 2b). Once the bias voltage exceeds the excited-state energy, electron transport can proceed through both the excited state and the ground state (see the right panel of Figure 2b). Since there are more pathways for electron transport, there will generally be an increase in current or a peak in conductance when the excited state becomes accessible. Such spectroscopy data are shown in Figure 5c of Tettamanzi et al.20
Although the fabrication of quantum devices and the probing of their electronic energy level structure are important first steps, achieving timedomain control of a single quantum state is one of the ultimate goals in quantum information science. In this issue of ACS Nano, Tettamanzi et al. take an important first step toward quantum control of donors in STMfabricated devices.20 Their measurements are performed on a STM-fabricated single-atom transistor, similar to the one shown in Figure 2a. In a realistic spin-based quantum computing device architecture, a gate voltage will be used to tune the exchange energy. Exchange coupling is set by wave function 2384
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REFERENCES
Time-domain measurements can probe the loading and unloading of these levels, as well as relaxation between the ground state and the excited state. In these measurements, the electrochemical potential of the donor is modulated with a high-frequency square pulse waveform. The voltage pulse repeatedly raises and lowers the donor energy levels with respect to the chemical potential of the source and drain electrodes. In a simple model, there are three characteristic electronic transition rates, which are illustrated in Figure 2c: (1) the rate at which electrons tunnel from the source to the donor ΓS, (2) the rate at which electrons tunnel from the donor to the drain ΓD, and (3) the relaxation rate from the excited state to the ground state ΓES. By controlling the rise time of the pulse, Tettamanzi et al. can vary the rate of tunneling through the excited state relative to the ground state. For example, if the rise time is long compared to 1/ΓS and 1/ΓES, the electrons will not have a significant probability of occupying the excited state (either the ground state will first fill with an electron or the electron will relax from the excited state to the ground state before it can tunnel to the drain). As a result, the authors observe an excited-state feature that is sensitive to the pulse rise time. These data enable the authors to place a lower bound on the excited-state relaxation rate ΓES > 2.5 GHz.
(1) Monroe, C.; Kim, J. Scaling the Ion Trap Quantum Processor. Science 2013, 339, 1164−1169. (2) Devoret, M. H.; Schoelkopf, R. J. Superconducting Circuits for Quantum Information: An Outlook. Science 2013, 339, 1169−1174. (3) Awschalom, D. D.; Bassett, L. C.; Dzurak, A. S.; Hu, E. L.; Petta, J. R. Quantum Spintronics: Engineering and Manipulating Atom-Like Spins in Semiconductors. Science 2013, 339, 1174−1179. (4) Hanson, R.; Kouwenhoven, L. P.; Petta, J. R.; Tarucha, S.; Vandersypen, L. M. K. Spins in Few-Electron Quantum Dots. Rev. Mod. Phys. 2007, 79, 1217−1265. (5) Zwanenburg, F. A.; Dzurak, A. S.; Morello, A.; Simmons, M. Y.; Hollenberg, L. C. L.; Klimeck, G.; Rogge, S.; Coppersmith, S. N.; Eriksson, M. A. Silicon Quantum Electronics. Rev. Mod. Phys. 2013, 85, 961−1019. (6) Tyryshkin, A. M.; Tojo, S.; Morton, J. J. L.; Riemann, H.; Abrosimov, N. V.; Becker, P.; Pohl, H. J.; Schenkel, T.; Thewalt, M. L. W.; Itoh, K. M.; Lyon, S. A. Electron Spin Coherence Exceeding Seconds in High-Purity Silicon. Nat. Mater. 2012, 11, 143−147. (7) Loss, D.; DiVincenzo, D. P. Quantum Computation with Quantum Dots. Phys. Rev. A: At., Mol., Opt. Phys. 1998, 57, 120−126. (8) Kane, B. E. A Silicon-Based Nuclear Spin Quantum Computer. Nature 1998, 393, 133−137. (9) Elzerman, J. M.; Hanson, R.; van Beveren, L. H. W.; Witkamp, B.; Vandersypen, L. M. K.; Kouwenhoven, L. P. Single-Shot Read-Out of an Individual Electron Spin in a Quantum Dot. Nature 2004, 430, 431−435. (10) Koppens, F. H. L.; Buizert, C.; Tielrooij, K. J.; Vink, I. T.; Nowack, K. C.; Meunier, T.; Kouwenhoven, L. P.; Vandersypen, L. M. K. Driven Coherent Oscillations of a Single Electron Spin in a Quantum Dot. Nature 2006, 442, 766−771. (11) Petta, J. R.; Johnson, A. C.; Taylor, J. M.; Laird, E. A.; Yacoby, A.; Lukin, M. D.; Marcus, C. M.; Hanson, M. P.; Gossard, A. C. Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots. Science 2005, 309, 2180−2184. (12) Veldhorst, M.; Yang, C. H.; Hwang, J. C. C.; Huang, W.; Dehollain, J. P.; Muhonen, J. T.; Simmons, S.; Laucht, A.; Hudson, F. E.; Itoh, K. M.; Morello, A.; Dzurak, A. S. A Two-Qubit Logic Gate in Silicon. Nature 2015, 526, 410−414. (13) Jamieson, D. N.; Yang, C.; Hopf, T.; Hearne, S. M.; Pakes, C. I.; Prawer, S.; Mitic, M.; Gauja, E.; Andresen, S. E.; Hudson, F. E.; Dzurak, A. S.; Clark, R. G. Controlled Shallow Single-Ion Implantation in Silicon Using an Active Substrate for Sub-20-keV Ions. Appl. Phys. Lett. 2005, 86, 202101. (14) Koiller, B.; Hu, X.; Das Sarma, S. Exchange in Silicon-Based Quantum Computer Architecture. Phys. Rev. Lett. 2002, 88, 027903. (15) Lyding, J. W.; Shen, T. C.; Hubacek, J. S.; Tucker, J. R.; Abeln, G. C. Nanoscale Patterning and Oxidation of H-Passivated Si(100)-2 × 1 Surfaces with an Ultrahigh-Vacuum Scanning Tunneling Microscope. Appl. Phys. Lett. 1994, 64, 2010−2012. (16) Ruess, F. J.; Oberbeck, L.; Simmons, M. Y.; Goh, K. E. J.; Hamilton, A. R.; Hallam, T.; Schofield, S. R.; Curson, N. J.; Clark, R. G. Toward Atomic-Scale Device Fabrication in Silicon using Scanning Probe Microscopy. Nano Lett. 2004, 4, 1969−1973. (17) Fuechsle, M.; Miwa, J. A.; Mahapatra, S.; Ryu, H.; Lee, S.; Warschkow, O.; Hollenberg, L. C. L.; Klimeck, G.; Simmons, M. Y. A Single-Atom Transistor. Nat. Nanotechnol. 2012, 7, 242−246. (18) Rudolph, M.; Carr, S. M.; Subramania, G.; Ten Eyck, G.; Dominguez, J.; Pluym, T.; Lilly, M. P.; Carroll, M. S.; Bussmann, E. Probing the Limits of Si:P Delta-Doped Devices Patterned by a Scanning Tunneling Microscope in a Field-Emission Mode. Appl. Phys. Lett. 2014, 105, 163110. (19) Morello, A.; Pla, J. J.; Zwanenburg, F. A.; Chan, K. W.; Tan, K. Y.; Huebl, H.; Mottonen, M.; Nugroho, C. D.; Yang, C. Y.; van Donkelaar, J. A.; Alves, A. D. C.; Jamieson, D. N.; Escott, C. C.; Hollenberg, L. C. L.; Clark, R. G.; Dzurak, A. S. Single-Shot Readout of an Electron Spin in Silicon. Nature 2010, 467, 687−691. (20) Tettamanzi, G. C.; Hile, M. G.; House, M. G.; Fuechsle, M.; Rogge, S.; Simmons, M. Y. Probing the Quantum States of a Single
OUTLOOK The fast electrical control of the charge states demonstrated by Tettamanzi et al. opens the door for future quantum control experiments in STM-patterned donor-based devices.20 Electrical control of the donor energy levels can be adapted for experiments involving spin. At high magnetic fields, the Zeeman splitting of the donor electronic state can exceed the thermal energy. In this configuration, the donor potential could be tuned carefully with respect to the chemical potential of the source and drain electrodes, such that only a spin-up electron can tunnel off of the donor. Spin-selective tunneling forms the basis of many qubit readout approaches.9,11,19,22 Looking beyond spin-dependent tunneling, fast gate voltage control of the exchange energy between two STM-fabricated donors is an incredibly important milestone. When combined with ESR, exchange gates can be used to implement a CNOT gate.7 Lastly, although tunneling-based lithography provides high precision, it is slow. Therefore, the incorporation of radio frequency STM techniques with HVFE patterning could greatly accelerate progress in the field of atom-by-atom constructed quantum devices.18,23 AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Notes
The author declares no competing financial interest.
ACKNOWLEDGMENTS This work is supported by the Army Research Office (W911NF-15-1-0149), the U.S. National Science Foundation (DMR-1409556), and the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4535. Figure 1b is courtesy of S. Misra and E. Bussmann, Sandia National Laboratories Center for Integrated Nanotechnologies, a U.S. DOE BES user facility. 2385
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Atom Transistor at Microwave Frequencies. ACS Nano 2017, DOI: 10.1021/acsnano.6b06362. (21) Fujisawa, T.; Austing, D. G.; Tokura, Y.; Hirayama, Y.; Tarucha, S. Allowed and Forbidden Transitions in Artificial Hydrogen and Helium Atoms. Nature 2002, 419, 278−281. (22) Petersson, K. D.; McFaul, L. W.; Schroer, M. D.; Jung, M.; Taylor, J. M.; Houck, A. A.; Petta, J. R. Circuit Quantum Electrodynamics with a Spin Qubit. Nature 2012, 490, 380−383. (23) Kemiktarak, U.; Ndukum, T.; Schwab, K. C.; Ekinci, K. L. Radio-Frequency Scanning Tunnelling Microscopy. Nature 2007, 450, 85−88.
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