Simulating fermions coupled to spin degrees of freedom, relevant for a range of quantum field theories, represents a promising application for quantum simulators. Mapping fermions to qubits is challenging in 2+1 and higher spacetime dimensions, and mapping bosons demands substantial quantum-computational overhead. These features complicate the realization of mixed fermion-boson quantum systems in digital quantum computers. We propose a native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays in silicon. Specifically, we show how to use a dynamical lattice of coupled nuclear spins and conduction-band electrons to realize a quantum field theory: an extended Jackiw-Rebbi model involving coupled fermions and quantum rotors. We demonstrate the feasibility of observing dynamical mass generation and a confinement-deconfinement quantum phase transition in 1+1 dimensions on this platform, even in the presence of strong long-range Coulomb interactions. Furthermore, we employ finite-temperature Hartree-Fock-Bogoliubov simulations to investigate the dynamics of mass generation in two-dimensional square and honeycomb arrays, showing that this phenomenon can be simulated with realistic experimental parameters. Our findings reveal two distinct phases, and demonstrate robustness against the addition of Coulomb interactions. Finally, we discuss experimental signatures of the phases through transport and local charge sensing in dopant arrays. This study lays the foundation for quantum simulations of quantum field theories exhibiting fermions coupled to spin degrees of freedom using donors in silicon.

Spin states in semiconductors provide exceptionally stable and noise-resistant environments for qubits, positioning them as optimal candidates for reliable quantum computing technologies. The proposal to use nuclear and electronic spins of donor atoms in silicon, introduced by Kane in 1998, sparked a new research field focused on the precise positioning of individual impurity atoms for quantum devices, utilising scanning tunnelling microscopy and ion implantation. This roadmap article reviews the advancements in the 25 years since Kane’s proposal, the current challenges, and the future directions in atomic-scale semiconductor device fabrication and measurement. It covers the quest to create a silicon-based quantum computer and expands to include diverse material systems and fabrication techniques, highlighting the potential for a broad range of semiconductor quantum technological applications. Key developments include phosphorus in silicon devices such as single-atom transistors, arrayed few-donor devices, one- and two-qubit gates, three-dimensional architectures, and the development of a toolbox for future quantum integrated circuits. The roadmap also explores new impurity species like arsenic and antimony for enhanced scalability and higher-dimensional spin systems, new chemistry for dopant precursors and lithographic resists, and the potential for germanium-based devices. Emerging methods, such as photon-based lithography and electron beam manipulation, are discussed for their disruptive potential. This roadmap charts the path toward scalable quantum computing and advanced semiconductor quantum technologies, emphasising the critical intersections of experiment, technological development, and theory.

Fabrication of quantum devices by atomic-scale patterning with scanning tunneling microscopy (STM) has led to the development of single/few atom transistors, few-donor/quantum dot devices for spin manipulation, and arrayed few-donor devices for analog quantum simulation. We have developed atomic precision lithography, dopant incorporation, device encapsulation, ex situ device re-location, and contact processes to enable high-yield device fabrication. In this work, we describe a multiscale alignment strategy using Kelvin probe force microscopy to enable the alignment of buried device components to electronic support structures such as source/drain leads, in-plane and top gates, and waveguides while preserving flexibility in the placement of fabricated STM patterns. The required spatial accuracy to bridge the sub-micrometer scale central region of the device to millimeter scale large wire-bond pads is achieved through a multi-step alignment process at various stages of fabrication, including atom-scale device fabrication using STM, re-location and registration, and electron beam lithography for contact leads and pads. This alignment strategy allows imaging small device regions as well as large-scale fiducial marks, thereby bridging the gap from nanometer STM patterns to the millimeter-scale electrical contact fabrication with a 95% yield on more than 150 devices fabricated to date.

Coherent manipulation of electron spins is one of the central challenges of silicon-based quantum computing efforts. Electron spin resonance (ESR) lines, or Oersted lines, allow 10-60 GHz radio frequency (RF) pulses to induce an electromagnetic field that drives Rabi oscillations in a quantum dot interface. The frequency of these Rabi oscillations is directly proportional to the strength of the induced electromagnetic field. We outline a methodology for the design of a printed circuit board and an ESR line that is able to transmit an RF pulse in the 40 GHz regime and induce an oscillating magnetic field onto a qubit device. We propose and implement a novel design by coupling a second symmetrical Oersted line in the opposing direction of the first to act as an antenna for the purpose of monitoring power and magnetic field strength at the embedded device interface.

The primary purpose of this program was to develop atomically precise fabrication techniques for semiconductor systems that places dopant atoms in a single buried (100) atomic plane in silicon with near atomic precision to create unprecedented structures that can be used for a wide variety of quantum experiments, devices, and potentially designer quantum materials. The potential impacts on reducing industrial energy use are many: 1) optimized and more energy efficient industrial processes via more efficient computational approaches, 2) dramatically improved materials for industrial use including higher critical-temperature superconductors eliminating losses in electrical transmission, 3) the better understanding of quantum chemistry via Analog Quantum Simulation(AQS) in the near term and universal quantum computing in the longer term that will lead to new industrial processes with smaller or zero production of greenhouse gases.

The doping of Si using the scanning probe hydrogen depassivation lithography technique has been shown to enable placing and positioning small numbers of P atoms with nanometer accuracy. Several groups have now used this capability to build devices that exhibit desired quantum behavior determined by their atomistic details. What remains elusive, however, is the ability to control the precise number of atoms placed at a chosen site with 100% yield, thereby limiting the complexity and degree of perfection achievable. As an important step toward precise control of dopant number, we explore the adsorption of the P precursor molecule, phosphine, into atomically perfect dangling bond patches of intentionally varied size consisting of three adjacent Si dimers along a dimer row, two adjacent dimers, and one single dimer. Using low temperature scanning tunneling microscopy, we identify the adsorption products by generating and comparing to a catalog of simulated images, explore atomic manipulation after adsorption in select cases, and follow up with incorporation of P into the substrate. For one-dimer patches, we demonstrate that manipulation of the adsorbed species leads to single P incorporation in 12 out of 12 attempts. Based on the observations made in this study, we propose this one-dimer patch method as a robust approach that can be used to fabricate devices where it is ensured that each site of interest has exactly one P atom.

The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved. Here, we fabricate 3 × 3 arrays of single/few-dopant quantum dots with finite disorder and demonstrate tuning of the electron ensemble using gates and probe the many-body states using quantum transport measurements. By controlling the lattice constants, we tune the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from metallic to Mott insulating behavior. We simulate thermally activated hopping and Hubbard band formation using increased temperatures. As atomically precise fabrication continues to improve, these results enable a new class of engineered artificial lattices to simulate interactive fermionic models.

Scientists have long studied the physics of highly disordered conducting systems, seeking to understand the multitude of quantum phenomena that govern how electrons move through material systems. Recently, research into silicon-based quantum computing has made disordered conducting systems, such as Si:P monolayers embedded in isotopically pure Si, technically relevant. Consequently, applying and advancing the theoretical frameworks developed to describe electron behavior in disordered systems is a necessary objective in this field of research. This study investigates key components of dopant-based Si quantum computing devices: embedded regions of highly doped delta layers (delta layers). We examine the transport behavior and the electron-electron interaction (EEI) physics in embedded Si:P delta layers by means of self-consistent magnetotransport measurements. Parameters associated with the electronic transport offer a meaningful quantitative characterization of delta-layer quality and dopant diffusion. In addition, by examining EEI behaviors in a set of samples with embedded Si:P delta layers produced with different PH3 exposure procedures prior to Si encapsulation, we show how details of material synthesis affect the dimensionality of charge carrier interactions in embedded Si:P delta layers. The relationship between delta-layer confinement and EEI screening lengths is established here. This understanding will help validate important models used for device simulation and design and lead to improvements in the control of electrostatic gating of and tunneling transport through Si:P single atom transistors.

Atomically precise donor-based quantum devices are a promising candidate for solid-state quantum computing and analog quantum simulations. However, critical challenges in atomically precise fabrication have meant systematic, atomic scale control of the tunneling rates and tunnel coupling has not been demonstrated. Here using a room temperature grown locking layer and precise control over the entire fabrication process, we reduce unintentional dopant movement while achieving high quality epitaxy in scanning tunnelling microscope (STM)-patterned devices. Using the Si(100)2 × 1 surface reconstruction as an atomically-precise ruler to characterize the tunnel gap in precision-patterned single electron transistors, we demonstrate the exponential scaling of the tunneling resistance on the tunnel gap as it is varied from 7 dimer rows to 16 dimer rows. We demonstrate the capability to reproducibly pattern devices with atomic precision and a donor-based fabrication process where atomic scale changes in the patterned tunnel gap result in the expected changes in the tunneling rates.

2D Quantum Metamaterials, pp. 82-90 (2019) No Access7: Atomically precisely doped semiconductorsJonathan Wyrick and Shashank MisraJonathan WyrickNational Institute of Standards and Technology, USA and Shashank MisraSandia National Laboratories, USAhttps://doi.org/10.1142/9789811206061_0007Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The discovery of scanned probe microscopy thirty-five years ago opened the door to real-space imaging of atoms for the first time. After early successes in fabricating company logos with atomic precision, only recently have workflows produced useful electrical devices, using scanned probe fabrication methods. In particular, the use of hydrogen lithography to create donor-based devices in silicon has seen a surge in activity related to demonstrating the limits of scaling circuit elements to the physical limit of atoms themselves, and for demonstrating control over the charge and spin degrees of freedom of islands containing a small number of donors. This workshop explored the possibility that these dopant islands can serve as a kind of artificial atom, and thus finite-size arrays should exhibit Bloch bands emerging inside the bandgap of silicon from the overlap of shallow dopant levels; and, in certain limits, strong electronic correlations… FiguresReferencesRelatedDetails 2D Quantum MetamaterialsMetrics History PDF download

Atomically precise fabrication has an important role to play in developing atom‐based electronic devices for use in quantum information processing, quantum materials research, and quantum sensing. Atom‐by‐atom fabrication has the potential to enable precise control over tunnel coupling, exchange coupling, on‐site charging energies, and other key properties of basic devices needed for solid‐state quantum computing and analog quantum simulation. Using hydrogen‐based scanning probe lithography, individual dopant atoms are deterministically placed relative to atomically aligned contacts and gates to build single electron transistors, single atom transistors, and gate‐controlled quantum sensing devices. The key steps required to fabricate and demonstrate the essential building blocks needed for spin selective initialization/readout and coherent quantum manipulation are described.

Scanning tunneling microscopy (STM) enables the fabrication of two-dimensional δ-doped structures in Si with atomistic precision, with applications from tunnel field-effect transistors to qubits. The combination of a very small contact area and the restrictive thermal budget necessary to maintain the integrity of the δ layer make developing a robust electrical contact method a significant challenge to realizing the potential of atomically precise devices. We demonstrate a method for electrical contact using Pd2Si formed at the temperature of silicon overgrowth (250 °C), minimizing the diffusive impact on the δ layer. We use the transfer length method to show our Pd2Si contacts have very high yield (99.7% +0.2% -1.5%) and low resistivity (272±41Ωμm) in contacting mesa-etched Si:P δ layers. We also present three terminal measurements of low contact resistance (<1 kΩ) to devices written by STM hydrogen depassivation lithography with similarly high yield (100% +0% -3.2%).

Atomically precise donor-based quantum devices are a promising candidate for scalable solid-state quantum computing. Atomically precise design and implementation of the tunnel coupling in these devices is essential to realize gate-tunable exchange coupling, and electron spin initialization and readout. Current efforts in atomically precise lithography have enabled deterministic placement of single dopant atoms into the Si lattice with sub-nm precision. However, critical challenges in atomically precise fabrication have meant systematic, atomic-scale control of the tunneling coupling has not been demonstrated. Here using a room-temperature grown locking layer and precise control over the entire atomic-scale fabrication process, we demonstrate atomic-scale control of the tunnel coupling in atomically precise single-electron transistors (SETs). Using the naturally occurring Si (100) 2x1 surface reconstruction lattice as an atomically-precise ruler, we systematically vary the number of lattice counts within the tunnel junction gaps and demonstrate exponential scaling of the tunneling resistance at the atomic limit. Using low-temperature transport measurements, we characterize the tunnel coupling asymmetry in a pair of nominally identical tunnel gaps that results from atomic-scale variation in the tunnel junction and show a resistance difference of four that corresponds to half a dimer row pitch difference in the effective tunnel gap distances - the intrinsic limit of hydrogen lithography precision on Si (100) 2x1 surfaces. Our results demonstrate the key capability to do atom-scale design and engineering of the tunnel coupling necessary for solid-state quantum computing and analog quantum simulation.