Search

Strain is extensively used to controllably tailor the electronic properties of materials. In the context of indirect band-gap semiconductors such as silicon, strain lifts the valley degeneracy of the six conduction band minima, and by extension the valley states of electrons bound to phosphorus donors. Here, single phosphorus atoms are embedded in an engineered thin layer of silicon strained to 0.8% and their wave function imaged using spatially resolved spectroscopy. A prevalence of the out-of-plane valleys is confirmed from the real-space images, and a combination of theoretical modelling tools is used to assess how this valley repopulation effect can yield isotropic exchange and tunnel interactions in the xy-plane relevant for atomically precise donor qubit devices. Finally, the residual presence of in-plane valleys is evidenced by a Fourier analysis of both experimental and theoretical images, and atomistic calculations highlight the importance of higher orbital excited states to obtain a precise relationship between valley population and strain. Controlling the valley degree of freedom in engineered strained epilayers provides a new competitive asset for the development of donor-based quantum technologies in silicon.

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

Determination of qubit initialisation and measurement fidelity is important for the overall performance of a quantum computer. However, the method by which it is calculated in semiconductor qubits varies between experiments. In this paper we present a full theoretical analysis of electronic single-shot readout and describe critical parameters to achieve high fidelity readout. In particular, we derive a model for energy selective state readout based on a charge detector response and examine how to optimise the fidelity by choosing correct experimental parameters. Although we focus on single electron spin readout, the theory presented can be applied to other electronic readout techniques in semiconductors that use a reservoir.

The realization of the surface code for topological error correction is an essential step towards a universal quantum computer1–3. For single-atom qubits in silicon4–7, the need to control and read out qubits synchronously and in parallel requires the formation of a two-dimensional array of qubits with control electrodes patterned above and below this qubit layer. This vertical three-dimensional device architecture8 requires the ability to pattern dopants in multiple, vertically separated planes of the silicon crystal with nanometre precision interlayer alignment. Additionally, the dopants must not diffuse or segregate during the silicon encapsulation. Critical components of this architecture—such as nanowires9, single-atom transistors4 and single-electron transistors10–have been realized on one atomic plane by patterning phosphorus dopants in silicon using scanning tunnelling microscope hydrogen resist lithography11,12. Here, we extend this to three dimensions and demonstrate single-shot spin read-out with 97.9% measurement fidelity of a phosphorus dopant qubit within a vertically gated single-electron transistor with <5 nm interlayer alignment accuracy. Our strategy ensures the formation of a fully crystalline transistor using just two atomic species: phosphorus and silicon.

Electron spin qubits formed by atoms in silicon have large (tens of millielectronvolts) orbital energies and weak spin–orbit coupling, giving rise to isolated electron spin ground states with coherence times of seconds1,2. High-fidelity (more than 99.9 per cent) coherent control of such qubits has been demonstrated3, promising an attractive platform for quantum computing. However, inter-qubit coupling—which is essential for realizing large-scale circuits in atom-based qubits—has not yet been achieved. Exchange interactions between electron spins4,5 promise fast (gigahertz) gate operations with two-qubit gates, as recently demonstrated in gate-defined silicon quantum dots6–10. However, creating a tunable exchange interaction between two electrons bound to phosphorus atom qubits has not been possible until now. This is because it is difficult to determine the atomic distance required to turn the exchange interaction on and off while aligning the atomic circuitry for high-fidelity, independent spin readout. Here we report a fast (about 800 picoseconds) SWAP two-qubit exchange gate between phosphorus donor electron spin qubits in silicon using independent single-shot spin readout with a readout fidelity of about 94 per cent on a complete set of basis states. By engineering qubit placement on the atomic scale, we provide a route to the realization and efficient characterization of multi-qubit quantum circuits based on donor qubits in silicon.

Fault-tolerant quantum computation requires qubit measurements to be both high fidelity and fast to ensure that idling qubits do not generate more errors during the measurement of ancilla qubits than can be corrected. Towards this goal, we demonstrate single-shot readout of semiconductor spin qubits with 97% fidelity in 1.5 μs. In particular, we show that we can engineer donor-based single-electron transistors (SETs) in silicon with atomic precision to measure single spins much faster than the spin decoherence times in isotopically purified silicon (270 μs). By designing the SET to have a large capacitive coupling between the SET and target charge, we can optimally operate in the "strong-response" regime to ensure maximal signal contrast. We demonstrate single-charge detection with a signal-to-noise ratio (SNR) of 12.7 at 10 MHz bandwidth, corresponding to a SET charge sensitivity (integration time for SNR=2) of 2.5 ns. We present a theory of the shot-noise sensitivity limit for the strong-response regime which predicts that the present sensitivity is about one order of magnitude above the shot-noise limit. By reducing cold amplification noise to reach the shot-noise limit, it should be theoretically possible to achieve high-fidelity, single-shot readout of an electron spin in silicon with a total readout time of approximately 36 ns.

We present a donor-based quadruple-quantum-dot device, designed to host two singlet-triplet qubits fabricated by scanning tunnelling microscope lithography, with just two leads per qubit. The design is geometrically compact, with each pair of dots independently controlled via one gate and one reservoir. The reservoirs both supply electrons for the dots and measure the singlet-triplet state of each qubit via dispersive sensing. We verify the locations of the four phosphorus donor dots via an electrostatic model of the device. We study one of the observed singlet-triplet states with a tunnel coupling of 39 GHz and a S0-to-T- decay of 2 ms at zero detuning. We measure a 5 GHz electrostatic interaction between two pairs of dots separated by 65 nm. The results outline a low-gate-density pathway to a scalable 1D building block of atomic-precision singlet-triplet qubits using donors with dispersive readout.

We measure singlet-triplet mixing in a precision fabricated double donor dot comprising 2 and 1 phosphorus atoms separated by 16 ± 1 nm. We identify singlet and triplet-minus states by performing a sequential independent spin readout of the two electron system and probe its dependence on magnetic field strength. The relaxation of singlet and triplet states is measured to be 12.4 ± 1.0 s and 22.1 ± 1.0 s, respectively, at Bz = 2.5 T.

© 2018 The Author(s). Substitutional donor atoms in silicon are promising qubits for quantum computation with extremely long relaxation and dephasing times demonstrated. One of the critical challenges of scaling these systems is determining inter-donor distances to achieve controllable wavefunction overlap while at the same time performing high fidelity spin readout on each qubit. Here we achieve such a device by means of scanning tunnelling microscopy lithography. We measure anti-correlated spin states between two donor-based spin qubits in silicon separated by 16 ± 1 nm. By utilising an asymmetric system with two phosphorus donors at one qubit site and one on the other (2P-1P), we demonstrate that the exchange interaction can be turned on and off via electrical control of two in-plane phosphorus doped detuning gates. We determine the tunnel coupling between the 2P-1P system to be 200 MHz and provide a roadmap for the observation of two-electron coherent exchange oscillations.

Two-electron states bound to donors in silicon are important for both two-qubit gates and spin readout. We present a full configuration interaction technique in the atomistic tight-binding basis to capture multielectron exchange and correlation effects taking into account the full band structure of silicon and the atomic-scale granularity of a nanoscale device. Excited s-like states of A1 symmetry are found to strongly influence the charging energy of a negative donor center. We apply the technique on subsurface dopants subjected to gate electric fields and show that bound triplet states appear in the spectrum as a result of decreased charging energy. The exchange energy, obtained for the two-electron states in various confinement regimes, may enable engineering electrical control of spins in donor-dot hybrid qubits.

Phosphorus donor impurities in silicon are a promising candidate for solid-state quantum computing due to their exceptionally long coherence times and high fidelities. However, individual addressability of exchange coupled donors with separations ~15 nm is challenging. We show that by using atomic precision lithography, we can place a single P donor next to a 2P molecule 16 ± 1 nm apart and use their distinctive hyperfine coupling strengths to address qubits at vastly different resonance frequencies. In particular, the single donor yields two hyperfine peaks separated by 97 ± 2.5 MHz, in contrast to the donor molecule that exhibits three peaks separated by 262 ± 10 MHz. Atomistic tight-binding simulations confirm the large hyperfine interaction strength in the 2P molecule with an interdonor separation of ~0.7 nm, consistent with lithographic scanning tunneling microscopy images of the 2P site during device fabrication. We discuss the viability of using donor molecules for built-in addressability of electron spin qubits in silicon.

© 2017 The Author(s). We report quantum transport measurements on two dimensional (2D) Si:P and Ge:P ω-layers and compare the inelastic scattering rates relevant for weak localization (WL) and universal conductance fluctuations (UCF) for devices of various doping densities (0.3-2.5 × 1018m-2) at low temperatures (0.3-4.2 K). The phase breaking rate extracted experimentally from measurements of WL correction to conductivity and UCF agree well with each other within the entire temperature range. This establishes that WL and UCF, being the outcome of quantum interference phenomena, are governed by the same dephasing rate.

We investigate spin and charge dynamics of a quantum dot of phosphorus atoms coupled to a radio-frequency single-electron transistor (SET) using full counting statistics. We show how the magnetic field plays a role in determining the bunching or antibunching tunneling statistics of the donor dot and SET system. Using the counting statistics, we show how to determine the lowest magnetic field where spin readout is possible. We then show how such a measurement can be used to investigate and optimize single-electron spin-readout fidelity.

The ability to apply gigahertz frequencies to control the quantum state of a single P atom is an essential requirement for the fast gate pulsing needed for qubit control in donor-based silicon quantum computation. Here, we demonstrate this with nanosecond accuracy in an all epitaxial single atom transistor by applying excitation signals at frequencies up to ≈13 GHz to heavily phosphorus-doped silicon leads. These measurements allow the differentiation between the excited states of the single atom and the density of states in the one-dimensional leads. Our pulse spectroscopy experiments confirm the presence of an excited state at an energy ≈9 meV, consistent with the first excited state of a single P donor in silicon. The relaxation rate of this first excited state to the ground state is estimated to be larger than 2.5 GHz, consistent with theoretical predictions. These results represent a systematic investigation of how an atomically precise single atom transistor device behaves under radio frequency excitations.

We develop a method for patterning a buried two-dimensional electron gas (2DEG) in silicon using low kinetic energy electron stimulated desorption (LEESD) of a monohydride resist mask. A buried 2DEG forms as a result of placing a dense and narrow profile of phosphorus dopants beneath the silicon surface; a so-called δ -layer. Such 2D dopant profiles have previously been studied theoretically, and by angle-resolved photoemission spectroscopy, and have been shown to host a 2DEG with properties desirable for atomic-scale devices and quantum computation applications. Here we outline a patterning method based on low kinetic energy electron beam lithography, combined with in situ characterization, and demonstrate the formation of patterned features with dopant concentrations sufficient to create localized 2DEG states.

Scaling up to large arrays of donor-based spin qubits for quantum computation will require the ability to perform high-fidelity readout of multiple individual spin qubits. Recent experiments have shown that the limiting factor for high-fidelity readout of many qubits is the lifetime of the electron spin. We demonstrate the longest reported lifetimes (up to 30 s) of any electron spin qubit in a nanoelectronic device. By atomic-level engineering of the electron wave function within phosphorus atom quantum dots, we can minimize spin relaxation in agreement with recent theoretical predictions. These lifetimes allow us to demonstrate the sequential readout of two electron spin qubits with fidelities as high as 99.8%, which is above the surface code fault-tolerant threshold. This work paves the way for future experiments on multiqubit systems using donors in silicon.

We report the development of a high-sensitivity semiconductor charge sensor based on a quantum dot coupled to a single lead designed to minimize the geometric requirements of a charge sensor for scalable quantum-computing architectures. The quantum dot is fabricated in Si:P using atomic precision lithography, and its charge transitions are measured with rf reflectometry. A second quantum dot with two leads placed 42 nm away serves as both a charge for the sensor to measure and as a conventional rf single-electron transistor (rf SET) with which to make a comparison of the charge-detection sensitivity. We demonstrate sensitivity equivalent to an integration time of 550 ns to detect a single charge with a signal-to-noise ratio of 1 compared with an integration time of 55 ns for the rf SET. This level of sensitivity is suitable for fast (<15 μs) single-spin readout in quantum-information applications, with a significantly reduced geometric footprint compared to the rf SET.

Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological insulators, ultracold atoms, and many others. However, the non-Abelian gauge field, while playing the most fundamental role in particle physics, up to now has remained a purely theoretical construction in many-body physics. In this paper, we report an observation of a non-Abelian gauge field in a spin-orbit coupled quantum system. The gauge field manifests itself in quantum magnetic oscillations of a hole doped two-dimensional (2D) GaAs heterostructure. Transport measurements were performed in tilted magnetic fields, where the effect of the emergent non-Abelian gauge field was controlled by the components of the magnetic field in the 2D plane.

The atomically precise doping of silicon with phosphorus (Si:P) using scanning tunneling microscopy (STM) promises ultimate miniaturization of field effect transistors. The one-dimensional (1D) Si:P nanowires are of particular interest, retaining exceptional conductivity down to the atomic scale, and are predicted as interconnects for a scalable silicon-based quantum computer. Here, we show that ultrathin Si:P nanowires form one of the most-stable electrical conductors, with the phenomenological Hooge parameter of low-frequency noise being as low as ≈10-8 at 4.2 K, nearly 3 orders of magnitude lower than even carbon-nanotube-based 1D conductors. A in-built isolation from the surface charge fluctuations due to encapsulation of the wires within the epitaxial Si matrix is the dominant cause for the observed suppression of noise. Apart from quantum information technology, our results confirm the promising prospects for precision-doped Si:P structures in atomic-scale circuitry for the 11 nm technology node and beyond.

Using density functional theory and guided by extensive scanning tunneling microscopy (STM) image data, we formulate a detailed mechanism for the dissociation of phosphine (PH3) molecules on the Si(001) surface at room temperature. We distinguish between a main sequence of dissociation that involves PH2+H, PH+2H, and P+3H as observable intermediates, and a secondary sequence that gives rise to PH+H, P+2H, and isolated phosphorus adatoms. The latter sequence arises because PH2 fragments are surprisingly mobile on Si(001) and can diffuse away from the third hydrogen atom that makes up the PH3 stoichiometry. Our calculated activation energies describe the competition between diffusion and dissociation pathways and hence provide a comprehensive model for the numerous adsorbate species observed in STM experiments.

Atomic-scale silicon wires, patterned by scanning tunneling microscopy (STM) and degenerately doped with phosphorus (P), have attracted significant interest owing to their exceptionally low resistivity and semiclassical Ohmic conduction at temperatures as low as T=4.2K. Here, we investigate the transition from semiclassical diffusive to quantum-coherent conduction in a 4.6 nm wide wire as we decrease the measurement temperature. By analyzing the temperature dependence of universal conductance fluctuations (UCFs) and one-dimensional (1D) weak localization (WL) - fundamental manifestations of quantum-coherent transport in quasi-1D metals - we show that transport evolves from quantum coherent to semiclassical at T∼4K. Remarkably, our study confirms that universal concepts of mesoscopic physics such as UCF and 1D WL retain their validity in quasi-1D metallic conductors down to the atomic scale.

We investigate the nonequilibrium charge dynamics of a triple quantum dot and demonstrate how electron transport through these systems can give rise to nontrivial tunneling paths. Using a real-time charge sensing method, we establish tunneling pathways taken by particular electrons under well-defined electrostatic configurations. We show how these measurements map to the chemical potentials for different charge states across the system. We use a modified Hubbard Hamiltonian to describes the system dynamics and show is reproduces all experimental observations.

The long term scaling prospects for solid-state quantum computing architectures relies heavily on the ability to simply and reliably measure and control the coherent electron interaction strength, known as the tunnel coupling, tc. Here, we describe a method to extract the tc between two quantum dots (QDs) utilising their different tunnel rates to a reservoir. We demonstrate the technique on a few donor triple QD tunnel coupled to a nearby single-electron transistor (SET) in silicon. The device was patterned using scanning tunneling microscopy-hydrogen lithography allowing for a direct measurement of the tunnel coupling for a given inter-dot distance. We extract tc = 5.5 ± 1.8 GHz and tc = 2.2 ± 1.3 GHz between each of the nearest-neighbour QDs which are separated by 14.5 nm and 14.0 nm, respectively. The technique allows for an accurate measurement of tc for nanoscale devices even when it is smaller than the electron temperature and is an ideal characterisation tool for multi-dot systems with a charge sensor.

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.

In quantum simulation, many-body phenomena are probed in controllable quantum systems. Recently, simulation of Bose-Hubbard Hamiltonians using cold atoms revealed previously hidden local correlations. However, fermionic many-body Hubbard phenomena such as unconventional superconductivity and spin liquids are more difficult to simulate using cold atoms. To date the required single-site measurements and cooling remain problematic, while only ensemble measurements have been achieved. Here we simulate a two-site Hubbard Hamiltonian at low effective temperatures with single-site resolution using subsurface dopants in silicon. We measure quasi-particle tunnelling maps of spin-resolved states with atomic resolution, finding interference processes from which the entanglement entropy and Hubbard interactions are quantified. Entanglement, determined by spin and orbital degrees of freedom, increases with increasing valence bond length. We find separation-tunable Hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants, establishing dopants as a platform for quantum simulation of the Hubbard model.

Spin states of the electrons and nuclei of phosphorus donors in silicon are strong candidates for quantum information processing applications given their excellent coherence times. Designing a scalable donor-based quantum computer will require both knowledge of the relationship between device geometry and electron tunnel couplings, and a spin readout strategy that uses minimal physical space in the device. Here we use radio frequency reflectometry to measure singlet-triplet states of a few-donor Si:P double quantum dot and demonstrate that the exchange energy can be tuned by at least two orders of magnitude, from 20 μV to 8 meV. We measure dot-lead tunnel rates by analysis of the reflected signal and show that they change from 100 MHz to 22 GHz as the number of electrons on a quantum dot is increased from 1 to 4. These techniques present an approach for characterizing, operating and engineering scalable qubit devices based on donors in silicon.

Control of hyperfine interactions is a fundamental requirement for quantum computing architecture schemes based on shallow donors in silicon. However, at present, there is lacking an atomistic approach including critical effects of central-cell corrections and nonstatic screening of the donor potential capable of describing the hyperfine interaction in the presence of both strain and electric fields in realistically sized devices. We establish and apply a theoretical framework, based on atomistic tight-binding theory, to quantitatively determine the strain and electric-field-dependent hyperfine couplings of donors. Our method is scalable to millions of atoms, and yet captures the strain effects with an accuracy level of DFT method. Excellent agreement with the available experimental data sets allow reliable investigation of the design space of multiqubit architectures, based on both strain only as well as hybrid (strain + field) control of qubits. The benefits of strain are uncovered by demonstrating that a hybrid control of qubits based on (001) compressive strain and in-plane (100 or 010) fields results in higher gate fidelities and or faster gate operations, for all of the four donor species considered (P, As, Sb, and Bi). The comparison between different donor species in strained environments further highlights the trends of hyperfine shifts, providing predictions where no experimental data exists. While faster gate operations are realizable with in-plane fields for P, As, and Sb donors, only for the Bi donor, our calculations predict faster gate response in the presence of both in-plane and out-of-plane fields, truly benefiting from the proposed planar field control mechanism of the hyperfine interactions.

We demonstrate the charge sensing of a few-donor double quantum dot precision placed with atomic resolution scanning tunnelling microscope lithography. We show that a tunnel-coupled single electron transistor (SET) can be used to detect electron transitions on both dots as well as inter-dot transitions. We demonstrate that we can control the tunnel times of the second dot to the SET island by ∼4 orders of magnitude by detuning its energy with respect to the first dot.

Sharply defined dopant profiles and low resistivity are highly desired qualities in the microelectronic industry, and more recently, in the development of an all epitaxial Si:P based quantum computer. In this work, we use thin (monolayers thick) room temperature grown silicon layers, so-called locking layers, to limit dopant segregation in highly phosphorus doped silicon monolayers. We present secondary ion mass spectroscopy and atom probe tomography measurements that demonstrate the effectiveness of locking layers in suppressing P segregation. Scanning tunneling micrographs of the surface of the locking layer show that the growth is epitaxial, despite the low growth temperature, while magnetotransport measurements reveal a 50% decrease in the active carrier density. We show that applying a finely tuned rapid thermal anneal can restore the active carrier density to 3.4 × 1014 cm-2 while maintaining ultra sharp dopant profiles. In particular, 75% of the initial deposited P is confined in a layer with a full width at half-maximum thickness of 1.0 nm and a peak P concentration of 1.2 × 1021 cm-3 (2.5 atom %).

A detailed theoretical study of the electronic and transport properties of a single atom transistor, where a single phosphorus atom is embedded within a single crystal transistor architecture, is presented. Using a recently reported deterministic single-atom transistor as a reference, the electronic structure of the device is represented atomistically with a tight-binding model, and the channel modulation is simulated self-consistently with a Thomas-Fermi method. The multi-scale modeling approach used allows confirmation of the charging energy of the one-electron donor charge state and explains how the electrostatic environments of the device electrodes affects the donor confinement potential and hence extent in gate voltage of the two-electron charge state. Importantly, whilst devices are relatively insensitive to dopant ordering in the highly doped leads, a ∼1% variation of the charging energy is observed when a dopant is moved just one lattice spacing within the device. The multi-scale modeling method presented here lays a strong foundation for the understanding of single-atom device structures: essential for both classical and quantum information processing.

The energy spectrum of spin-orbit coupled states of individual sub-surface boron acceptor dopants in silicon have been investigated using scanning tunneling spectroscopy at cryogenic temperatures. The spatially resolved tunnel spectra show two resonances, which we ascribe to the heavy- and light-hole Kramers doublets. This type of broken degeneracy has recently been argued to be advantageous for the lifetime of acceptor-based qubits [R. Ruskov and C. Tahan, Phys. Rev. B 88, 064308 (2013)]. The depth dependent energy splitting between the heavy- and light-hole Kramers doublets is consistent with tight binding calculations, and is in excess of 1meV for all acceptors within the experimentally accessible depth range (<2nm from the surface). These results will aid the development of tunable acceptor-based qubits in silicon with long coherence times and the possibility for electrical manipulation.

Using a deterministic single P donor placed with atomic precision accuracy next to a nanoscale silicon quantum dot, we present a way to analyze the energy spectrum of small quantum dots in silicon by tunnel-coupled transport measurements. The energy-level structure of the quantum dot is observed as resonance features within the transport bias triangles when the donor chemical potential is aligned with states within the quantum dot as confirmed by a numeric rate equation solver SIMON. This technique allows us to independently extract the quantum dot level structure irrespective of the density of states in the leads. Such a method is useful for the investigation of silicon quantum dots in the few-electron regime where the level structure is governed by an intricate interplay between the spin- and the valley-orbit degrees of freedom.

We demonstrate high-fidelity electron spin read-out of a precision placed single donor in silicon via spin selective tunneling to either the D+ or D- charge state of the donor. By performing read-out at the stable two electron D0虠D- charge transition we can increase the tunnel rates to a nearby single electron transistor charge sensor by nearly 2 orders of magnitude, allowing faster qubit read-out (1 ms) with minimum loss in read-out fidelity (98.4%) compared to read-out at the D+虠D0 transition (99.6%). Furthermore, we show that read-out via the D- charge state can be used to rapidly initialize the electron spin qubit in its ground state with a fidelity of FI=99.8%.

Abrupt dopant profiles and low resistivity are highly sought after qualities in the silicon microelectronics industry and, more recently, in the development of an all epitaxial Si:P based quantum computer. If we increase the active carrier density in silicon to the point where the material becomes superconducting, while maintaining a low thermal budget, it will be possible to fabricate nanoscale superconducting devices using the highly successful technique of depassivation lithography. In this work, we investigate the dopant profile and activation in multiple high density Si:P Δlayers fabricated by stacking individual layers with intervening silicon growth. We determine that dopant activation is ultimately limited by the formation of P-P dimers due to the segregation of dopants between multilayers. By increasing the encapsulation thickness between subsequent layers, thereby minimizing the formation of these deactivating defects, we are able to achieve an active carrier density of ns = 4.5 ×1014 cm-2 for a triple layer. The results of electrical characterization are combined with those of secondary ion mass spectroscopy to construct a model that accurately describes the impact of P segregation on the final active carrier density in Si:P multilayers. Our model predicts that a 3D active carrier density of 8.5 × 1020 cm-3 (1.7 atom %) can be achieved.

We present an analysis of electron transport through two weakly coupled precision-placed phosphorus donors in silicon. In particular, we examine the (1,1)虠(0,2) charge transition where we predict a type of current blockade driven entirely by the nuclear spin dynamics. Using this nuclear spin blockade mechanism, we devise a protocol to read out the state of single nuclear spins using electron-transport measurements only. We extend our model to include realistic effects such as Stark shifted hyperfine interactions and multidonor clusters. In the case of multidonor clusters we show how nuclear spin blockade can be alleviated, allowing for low magnetic field electron-spin measurements.

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.

We present a study of the phonon and impurity interactions in a shallow two dimensional electron gas formed in Si(001). A highly conductive ultra-narrow n-type dopant δ-layer, which serves as a platform for quantum computation architecture, is formed and studied by angle resolved photoemission spectroscopy (ARPES) and temperature dependent nanoscale 4-point probe (4PP). The bandstructure of the δ-layer state is both measured and simulated. At 100K, good agreement is only achieved by including interactions; electron-impurity scattering (W0=56 to 61meV); and electron-phonon coupling (λ=0.14±0.04). These results are shown to be consistent with temperature dependent 4PP resistance measurements which indicate that at 100K, 8 of the measured resistance is due to impurity scattering with the remaining 1/8 coming from phonon interactions. In both resistance and bandstructure measurements, the impurity contribution exhibits a variability of for nominally identical samples. The combination of ARPES and 4PP affords a thorough insight into the relevant contributions to electrical resistance in reduced dimensionality electronic platforms. © 2014 AIP Publishing LLC.

In this paper we review the state of the art of high n-type doping techniques in germanium alternative to ion implantation. We discuss a novel technique for achieving ultra-high doping based on adsorption and thermal incorporation of P atoms from PH3 or P2 molecules into a Ge surface and subsequent encapsulation by Ge homoepitaxial growth. This process results in the formation of spatially-confined P δ-layers with planar electrically active densities as high as 1×1014 cm-2. Owing to the high morphological quality of the crystal matrix, it is possible to stack an arbitrary number of d-layers and tailor the thickness of spacer layers in between to build an electrically active donor density in excess of 1020 cm-3 in a bottom-up process.

We develop a super-saturation technique to extend the previously established doping density limit for ultra-high vacuum monolayer doping of silicon with phosphorus. Through an optimized sequence of PH3 dosing and annealing of the silicon surface, we demonstrate a 2D free carrier density of ns = (3.6 ± 0.1) × 1014 cm-2, ∼50% higher than previously reported values. We perform extensive characterization of the dopant layer resistivity, including room temperature depth-dependent in situ four point probe measurements. The dopant layers remain conductive at less than 1 nm from the sample surface and importantly, surpass the semiconductor industry target for ultra-shallow junction scaling of <900 Ω-1 at a depth of 7 nm. © 2014 AIP Publishing LLC.

We demonstrate serial electron transport through a donor-based triple quantum dot in silicon fabricated with nanoscale precision by scanning tunnelling microscopy lithography. From an equivalent circuit model, we calculate the electrochemical potentials of the dots allowing us to identify ground and excited states in finite bias transport. Significantly, we show that using a scanning tunnelling microscope, we can directly demonstrate that a ∼1 nm difference in interdot distance dramatically affects transport pathways between the three dots. © 2014 American Chemical Society.

Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements have only probed wavefunctions indirectly, preventing direct experimental access to valley population, donor position and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunnelling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley-perturbation-induced enhancement of spin relaxation will be negligible for depths greater than 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest for emerging schemes proposing to encode information directly in valley polarization. © 2014 Macmillan Publishers Limited.

We have performed transport measurements in tilted magnetic fields in a two-dimensional hole system grown on the surface of a (311)A GaAs crystal. A striking asymmetry of Shubnikov-de Haas oscillations occurs upon reversing the in-plane component of the magnetic field along the low-symmetry [2¯33] axis. As usual, the magnetoconductance oscillations are symmetric with respect to reversal of the in-plane field component aligned with the high-symmetry [011¯] axis. Our observations demonstrate that an in-plane magnetic field can generate an out-of-plane component of magnetization in a low-symmetry hole system, creating new possibilities for spin manipulation.

We demonstrate the locating and imaging of single phosphorus atoms and phosphorus dopant nanostructures, buried beneath the Si(001) surface using scanning lunneling microscopy. The buried dopant nanostructures have been fabricated in a bottom-up approach using scanning tunneling microscope lithography on Si(OOl). We find that current imaging tunneling spectroscopy is suited to locate and image buried nanostructures al room temperature and with residual surface roughness present. From these studies, we can place an upper limit on the lateral diffusion during encapsulation with low- Temperature Si molecular beam epitaxy.

By suppressing an undesirable surface Umklapp process, it is possible to resolve the two most occupied states (1Γ and 2Γ) in a buried two-dimensional electron gas (2DEG) in silicon. The 2DEG exists because of an atomically sharp profile of phosphorus dopants which have been formed beneath the Si(001) surface (a δ-layer). The energy separation, or valley splitting, of the two most occupied bands has critical implications for the properties of δ-layer derived devices, yet until now, has not been directly measurable. Density functional theory (DFT) allows the 2DEG band structure to be calculated, but without experimental verification the size of the valley splitting has been unclear. Using a combination of direct spectroscopic measurements and DFT we show that the measured band structure is in good qualitative agreement with calculations and reveal a valley splitting of 132 ± 5 meV. We also report the effective mass and occupation of the 2DEG states and compare the dispersions and Fermi surface with DFT. © 2014 American Chemical Society.