Transport through a single donor in p-type silicon

Miwa, Jill A.; Mol, Jan A.; Salfi, Joe; Rogge, Sven; Simmons, M. Y.

doi:10.1063/1.4816439

Cited by 20 publications

(14 citation statements)

References 38 publications

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“…Samples with P donors were fabricated by submonolayer PH 3 dosing and well-defined encapsulation by epitaxial silicon, using a procedure similar to the one in Ref. [10], but with an n-type substrate to promote elastic resonant transport [4,11]. Experiments on the donors were carried out with atomic resolution in real space, in the single-electron transport regime with both the tip and a heavily-doped region of the sample, at liquid Helium temperatures, acting as transport reservoirs [12].…”

Section: Real Space Resultsmentioning

confidence: 99%

Donor wave functions in Si gauged by STM images

et al. 2016

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The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wavefunctions will withstand an experimental test. Such wavefunctions have recently been probed by scanning tunneling spectroscopy, revealing localized patterns of resonantly enhanced tunneling currents. We show that the shape of the conducting splotches resemble a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the non-monotonic features of the current profile are consistent with the charge density fluctuations observed between successive {001} atomic planes, including a counterintuitive reduction of the symmetry -a heritage of the lowered point group symmetry at these planes. A model-independent analysis of the diffraction figure constrains the value of the electron wavevector to k0 = (0.82 ± 0.03)(2π/aSi). Unlike prior measurements, averaged over a sizeable density of electrons, this estimate is obtained directly from isolated electrons. We further investigate the model-specific anisotropy of the wave function envelope, related to the effective mass anisotropy. This anisotropy appears in the KL variational wave function envelope as the ratio between Bohr radii b/a. We demonstrate that the central cell corrected estimates for this ratio are encouragingly accurate, leading to the conclusion that the KL theory is a valid model not only for energies but for wavefunctions as well.

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Section: Real Space Resultsmentioning

confidence: 99%

Donor wave functions in Si gauged by STM images

et al. 2016

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“…The P dopants were incorporated in Si by PH 3 dosing. A low P density was overgrown with 2.5 nm of Si by in-situ epitaxy 17 (i.e. a target depth of 4.75a 0 , where a 0 = 0.5431 nm is the Si lattice constant).…”

Section: Stm Measurement Of Dopant Statementioning

confidence: 99%

“…12 Consequently, As dopants measured in these samples were found at random depths in a ∼10 nm thin thermally depleted Si layer below the surface. Samples with P dopants were prepared by incorporating P in Si by a sub-monolayer phosphine (PH 3 ) dosing of the previously flash annealed Si substrate 17 . A sheet density of 5 × 10 11 cm −2 P donors is overgrown epitaxially by ∼2.5 nm (4.75a 0 , where a 0 is Si lattice constant) of Si.…”

Section: S1 Experimental Proceduresmentioning

confidence: 99%

Spatial metrology of dopants in silicon with exact lattice site precision

Usman¹,

Bocquel²,

Salfi³

et al. 2016

Nature Nanotech

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The aggressive scaling of silicon-based nanoelectronics has reached the regime where device function is affected not only by the presence of individual dopants, but more critically their position in the structure. The quantitative determination of the positions of subsurface dopant atoms is an important issue in a range of applications from channel doping in ultra-scaled transistors to quantum information processing, and hence poses a significant challenge. Here, we establish a metrology combining low-temperature scanning tunnelling microscopy (STM) imaging and a comprehensive quantum treatment of the dopant-STM system to pin-point the exact lattice-site location of sub-surface dopants in silicon. The technique is underpinned by the observation that STM images of sub-surface dopants typically contain many atomic-sized features in ordered patterns, which are highly sensitive to the details of the STM tip orbital and the absolute lattice-site position of the dopant atom itself. We demonstrate the technique on two types of dopant samples in silicon -the first where phosphorus dopants are placed with high precision, and a second containing randomly placed arsenic dopants. Based on the quantitative agreement between STM measurements and multi-million-atom calculations, the precise lattice site of these dopants is determined, demonstrating that the metrology works to depths of about 36 lattice planes. The ability to uniquely determine the exact positions of subsurface dopants down to depths of 5 nm will provide critical knowledge in the design and optimisation of nanoscale devices for both classical and quantum computing applications.As we approach the ultimate regime of Feynman's vision 1 of nanotechnology based on atom-by-atom fabrication 2-5 , there is a critical need to match advances in miniaturisation with atomically precise metrology. In conventional CMOS 6 and tunnelling field effect 7,8 transistors the key relationship between doping profile and performance is now dominated by the positions of just a few dopant atoms, and currently cannot be quantitatively determined. Beyond conventional nanoelectronic devices, in quantum processors based on phosphorus dopants in silicon 9 the precise locations of the individual dopants is critical to the design and operation of spin-based quantum logic gates. Previous studies on locating subsurface dopant positions in semiconductors either provide donor depths based on statistical evidence 10 , or only qualitatively locate dopants within a few nanometers region (of the order of 2.5 nm or more)11 . The key metrological challenge in all of the ultra-scaled applications is the ability to determine the position of dopant atoms in the silicon crystal substrate with lattice-site precision, which will drastically transform our understanding at the most fundamental scale leading to devices with optimised functionalities.In this work, we present an atomically precise metrology and demonstrate the pinpointing of the position of subsurface phosphorous (P) and arsenic (As) dopants in si...

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“…These studies have revealed the influence of the semiconductor/vacuum interface on the ionization energy of sub-surface dopants [9,13], the spatially resolved structure of the dopant wavefunction [10][11][12] and the mechanisms for charge-transport through these dopants [9,11,14]. Here, we use STS to measure the energy difference between the heavy-hole and light-hole states of individual B acceptors less than 2 nm away from the surface.…”

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Interface-induced heavy-hole/light-hole splitting of acceptors in silicon

Mol

Salfi

Rahman

et al. 2015

Applied Physics Letters

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The energy spectrum of spin-orbit coupled states of individual sub-surface boron acceptor dopants in silicon have been investigated using scanning tunneling spectroscopy (STS) at cryogenic temperatures. The spatially resolved tunnel spectra show two resonances which we ascribe to the heavyand light-hole Kramers doublets. This type of broken degeneracy has recently been argued to be advantageous for the lifetime of acceptor-based qubits [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 1 meV for all acceptors within the experimentally accessible depth range (< 2 nm 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. Meanwhile, rapid progress in scanning tunnelling microscopy (STM) based lithography has paved the way towards atomically precise placement of dopant atoms [3]. While phosphorous donors in silicon remains among the most compelling candidates for dopant-based quantum computing to date, other impurity systems have recently drawn considerable attention. In particular, boron acceptors could provide a pathway towards electrically addressable spin-qubits via spin-orbit coupling [4] analogues to electrically driven spin manipulation in gate defined electron [5,6] and hole [7] quantum dots in III-V materials. Compared with other spin-orbit qubits, acceptors in silicon have several advantages: gates are not required for hole confinement and each qubit experiences the same confinement potential; furthermore the holespin decoherence, due to the nuclear spin bath, can be effectively eliminated by isotope purification of the silicon host.Unlike the ground state of donor-bound electrons in silicon, the acceptor-bound hole ground state is four-fold degenerate, reflecting the heavy-hole/light-hole degeneracy of the silicon valence band. Recent theoretical work has suggested the regime of long lifetimes for acceptors with a four-fold degenerate ground state is only accessible for small magnetic fields [4]. Interestingly, this work also suggests that symmetry breaking due to strain or electric fields could yield longer-lived qubits based on acceptor-bound holes at higher magnetic fields. The symmetry breaking perturbation of biaxial strain [4] renders the lowest two (qubit) levels within a Kramers degenerate pair, such that they do not directly couple to electric fields. Quantum confinement could provide a similar form of protection. In this Letter we demonstrate that the symmetry-reduction of a potential boundary renders the lowest two levels Kramers degenerate and heavy-hole like. Recent transport spectroscopy studies of an individual acceptor embedded in nano-scale transistors have shown that for acceptors ∼10 nm away from an interface the bulk-like four-fold degeneracy is maintained [8]. Here we demonstrate that the presence of a nearby interface (<2 nm) lift...

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Transport through a single donor in p-type silicon

Cited by 20 publications

References 38 publications

Donor wave functions in Si gauged by STM images

Donor wave functions in Si gauged by STM images

Spatial metrology of dopants in silicon with exact lattice site precision

Interface-induced heavy-hole/light-hole splitting of acceptors in silicon

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