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Silicon Quantum Electronics

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Nonlocal coupling of two donorbound electrons
We report the results of an experiment investigating coherence and correlation effects in a system of coupled donors. Two donors are strongly coupled to two leads in a parallel configuration within a nanowire field effect transistor. By applying a magnetic field we observe interference between two donorinduced Kondo channels, which depends on the Aharonov–Bohm phase picked up by electrons traversing the structure. This results in a nonmonotonic conductance as a function of magnetic field and clearly demonstrates that donors can be coupled through a manybody state in a coherent manner. We present a model which shows good qualitative agreement with our data. The presented results add to the general understanding of interference effects in a donorbased correlated system which may allow us to create artificial lattices that exhibit exotic manybody excitations.

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Magnetic flux tuning of FanoKondo interplay in a parallel double quantum dot system
We investigate the FanoKondo interplay in an AharonovBohm ring with an embedded noninteracting quantum dot and a Coulomb interacting quantum dot. Using a slaveboson meanfield approximation we diagonalize the Hamiltonian via scattering matrix theory and derive the conductance in the form of a Fano expression, which depends on the meanfield parameters. We predict that in the Kondo regime the magnetic field leads to a gapped energy level spectrum due to hybridization of the noninteracting QD state and the Kondo state, and can quantummechanically alter the electron's path preference. We demonstrate that an abrupt symmetry change in the Fano resonance, as seen experimentally, could be a consequence of an underlying Kondo channel.

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Balanced ternary addition using a gated silicon nanowire
Ternary logic has the lowest cost of complexity, here, we demonstrate a CMOS hardware implementation of a ternary adder using a silicon metaloninsulator single electron transistor. Gate dependent rectifying behavior of a single electron transistor (SET) results in a robust threevalued output as a function of the potential of the single electron transistor island. Mapping logical, ternary inputs to the three gates controlling the potential of the single electron transistor island allows us to perform complex, inherently ternary operations, on a single transistor.

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Coherent transport through a double donor system in silicon
In this letter, we describe the observation of the interference of conduction paths induced by two donors in a nanoscale silicon transistor, resulting in a Fano resonance. This demonstrates the coherent exchange of electrons between two donors. In addition, the phase difference between the two conduction paths can be tuned by means of a magnetic field, in full analogy to the Aharonov–Bohm effect. One of the crucial ingredients for donor based quantum computation is phase coherent manipulation of electrons. This has not been achieved as yet, and this work presents a stepping stone.

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Heterointerface effects on the charging energy of the shallow D− ground state in silicon: Role of dielectric mismatch
Donor states in Si nanodevices can be strongly modified by nearby insulating barriers and metallic gates. Experimental results indicate a strong reduction in the charging energy of isolated As dopants in Si nonplanar field effect transistors relative to the bulk value. By studying the problem of two electrons bound to a shallow donor within the effective mass approach, we find that the measured reduction in the charging energy (measurements also presented here) may be due to a combined effect of the insulator screening and the proximity of metallic gates.

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Orbital Stark effect and quantum confinement transition of donors in silicon
Adiabatic shuttling of single impurity bound electrons to gateinduced surface states in semiconductors has attracted much attention in recent times, mostly in the context of solidstate quantum computer architecture. A recent transport spectroscopy experiment for the first time was able to probe the Stark shifted spectrum of a single donor in silicon buried close to a gate. Here, we present the full theoretical model involving largescale quantum mechanical simulations that was used to compute the Stark shifted donor states in order to interpret the experimental data. Use of atomistic tightbinding technique on a domain of over a million atoms helped not only to incorporate the full band structure of the host, but also to treat realistic device geometries and donor models, and to use a large enough basis set to capture any number of donor states. The method yields a quantitative description of the symmetry transition that the donor electron undergoes from a threedimensional Coulomb confined state to a twodimensional (2D) surface state as the electric field is ramped up adiabatically.
In the intermediate field regime, the electron resides in a superposition between the atomic donor states and the 2D surface states. In addition to determining the effect of field and donor depth on the electronic structure, the model also provides a basis to distinguish between a phosphorus and an arsenic donor based on their Stark signature. The method also captures valleyorbit splitting in both the donor well and the interface well, a quantity critical to silicon qubits. The work concludes with a detailed analysis of the effects of screening on the donor spectrum.

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Engineered valleyorbit splittings in quantumconfined nanostructures in silicon
An important challenge in silicon quantum electronics in the few electron regime is the potentially small energy gap between the ground and excited orbital states in 3D quantum confined nanostructures due to the multiple valley degeneracies of the conduction band present in silicon. Understanding the “valleyorbit” (VO) gap is essential for silicon qubits, as a large VO gap prevents leakage of the qubit states into a higher dimensional Hilbert space. The VO gap varies considerably depending on quantum confinement, and can be engineered by external electric fields. In this work we investigate VO splitting experimentally and theoretically in a range of confinement regimes. We report measurements of the VO splitting in silicon quantum dot and donor devices through excited state transport spectroscopy. These results are underpinned by largescale atomistic tightbinding calculations involving over 1 million atoms to compute VO splittings as functions of electric fields, donor depths, and surface disorder. The results provide a comprehensive picture of the range of VO splittings that can be achieved through quantum engineering.

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MagneticField Probing of an SU(4) Kondo Resonance in a SingleAtom Transistor
Semiconductor devices have been scaled to the point that transport can be dominated by only a single dopant atom. As a result, in a Si fintype field effect transistor Kondo physics can govern transport when one electron is bound to the single dopant. Orbital (valley) degrees of freedom, apart from the standard spin, strongly modify the Kondo effect in such systems. Owing to the small size and the slike orbital symmetry of the ground state of the dopant, these orbital degrees of freedom do not couple to external magnetic fields which allows us to tune the symmetry of the Kondo effect. Here we study this tunable Kondo effect and demonstrate experimentally a symmetry crossover from an SU(4) ground state to a pure orbital SU(2) ground state as a function of magnetic field. Our claim is supported by theoretical calculations that unambiguously show that the SU(2) symmetric case corresponds to a pure valley Kondo effect of fully polarized electrons.

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Ternary logic implemented on a single dopant atom field effect silicon transistor
We provide an experimental proof of principle for a ternary multiplier realized in terms of the charge state of a single dopant atom embedded in a fin field effect transistor (FinFET). Robust reading of the logic output is made possible by using two channels to measure the current flowing through the device and the transconductance. A read out procedure that allows for voltage gain is proposed. Long numbers can be multiplied by addressing a sequence of FinFET transistors in a row.

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Electric field reduced charging energies and twoelectron bound excited states of single donors in silicon
Article/Letter to the Editor 
Applied Sciences
20110919

Author: 
Rahman, R.
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Lansbergen, G.P.
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Verduijn, J.
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Tettamanzi, G.C.
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Park, S.H.
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Collaert, N.
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Biesemans, S.
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Klimeck, G.
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Hollenberg, L.C.L.
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Rogge, S.

We present atomistic simulations of the D0 to D− charging energies of a gated donor in silicon as a function of applied fields and donor depths and find good agreement with experimental measurements. A selfconsistent field largescale tightbinding method is used to compute the D− binding energies with a domain of over 1.4 million atoms, taking into account the full band structure of the host, applied fields, and interfaces. An applied field pulls the loosely bound D− electron toward the interface and reduces the charging energy significantly below the bulk values. This enables formation of bound excited D− states in these gated donors, in contrast to bulk donors. A detailed quantitative comparison of the charging energies with transport spectroscopy measurements with multiple samples of arsenic donors in ultrascaled metaloxidesemiconductor transistors validates the model results and provides physical insights. We also report measured D− data showing the presence of bound D− excited states under applied fields.

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LifetimeEnhanced Transport in Silicon due to Spin and Valley Blockade
We report the observation of lifetimeenhanced transport (LET) based on perpendicular valleys in silicon by transport spectroscopy measurements of a twoelectron system in a silicon transistor. The LET is manifested as a peculiar current step in the stability diagram due to a forbidden transition between an excited state and any of the lower energy states due to perpendicular valley (and spin) configurations, offering an additional current path. By employing a detailed temperature dependence study in combination with a rate equation model, we estimate the lifetime of this particular state to exceed 48 ns. The twoelectron spinvalley configurations of all relevant confined quantum states in our device were obtained by a largescale atomistic tightbinding simulation. The LET acts as a signature of the complicated valley physics in silicon: a feature that becomes increasingly important in silicon quantum devices.

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Drain current modulation in a nanoscale fieldeffecttransistor channel by single dopant implantation
Article/Letter to the Editor 
Applied Sciences
20100630

Author: 
Johnson, B.C.
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Tettamanzi, G.C.
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Alves, A.D.C.
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Thompson, S.
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Yang, C.
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Verduijn, J.
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Mol, J.A.
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Wacquez, R.
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Vinet, M.
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Sanquer, M.
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Rogge, S.
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Jamieson, D.N.

Keywords: 
elemental semiconductors · ion beam effects · MOSFET · silicon

We demonstrate single dopant implantation into the channel of a silicon nanoscale metaloxidesemiconductor fieldeffecttransistor. This is achieved by monitoring the drain current modulation during ion irradiation. Deterministic doping is crucial for overcoming dopant number variability in present nanoscale devices and for exploiting single atom degrees of freedom. The two main ion stopping processes that induce drain current modulation are examined. We employ 500 keV He ions, in which electronic stopping is dominant, leading to discrete increases in drain current and 14 keV P dopants for which nuclear stopping is dominant leading to discrete decreases in drain current.

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Single Ion Implantation into SiBased Devices
Article/Letter to the Editor 
Applied Sciences
20101231

Author: 
Johnson, B.C.
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Tettamanzi, G.C.
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Yang, C.
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Alves, A.D.C.
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Van Donkelaar, J.
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Thompson, S.
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Verduijn, J.
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Mol, J.A.
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Wacquez, R.
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Vinet, M.
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Dzurak, A.S.
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Sanquer, M.
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Rogge, S.
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Jamieson, D.N.

Deterministic doping is crucial for overcoming dopant number variability in present nanoscale devices and for exploiting single atom degrees of freedom. The development of determinisitic doping schemes is required. Here, two approaches to the detection of single ion impact events in Sibased devices are reviewed. The first is via specialized PiN structures where ions are directed onto a target area around which a field effect transistor can be formed. The second approach involves monitoring the drain current modulation during ion irradiation. We investigate the detection of both high energy He+ and 14 keV P+ dopants. The stopping of these ions is dominated by ionization and nuclear collisions, respectively. The optimization of the implant energy for a particular device and postimplantation processing are also briefly considered.

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