G. P. Lansbergen

Transport Spectroscopy of a Single Dopant in a Gated Silicon Nanowire

We report on spectroscopy of a single dopant atom in silicon by resonant tunneling between source and drain of a gated nanowire etched from silicon on insulator. The electronic states of this dopant isolated in the channel appear as resonances in the low temperature conductance at energies below the conduction band edge. We observe the two possible charge states successively occupied by spin-up and spin-down electrons under magnetic field. The first resonance is consistent with the binding energy of the neutral D0 state of an arsenic donor. The second resonance shows a reduced charging energy due to the electrostatic coupling of the charged D- state with electrodes. Excited states and Zeeman splitting under magnetic field present large energies potentially useful to build atomic scale devices.

Orbital Stark effect and quantum confinement transition of donors in silicon

Adiabatic shuttling of single impurity bound electrons to gate-induced surface states in semiconductors has attracted much attention in recent times, mostly in the context of solid-state 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 large-scale quantum mechanical simulations that was used to compute the Stark shifted donor states in order to interpret the experimental data. Use of atomistic tight-binding 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 three-dimensional Coulomb confined state to a two-dimensional (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 valley-orbit 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.

Subthreshold channels at the edges of nanoscale triple-gate silicon transistors

The authors investigate the subthreshold behavior of triple-gate silicon field-effect transistors by low-temperature transport experiments. These three-dimensional nanoscale devices consist of a lithographically defined silicon nanowire surrounded by a gate with an active region as small as a few tens of nanometers down to 50×60×35?nm3. Conductance versus gate voltage shows Coulomb blockade oscillations with a large charging energy due to the formation of a small potential well below the gate. According to dependencies on device geometry and thermionic current analyses, the authors conclude that subthreshold channels, a few nanometers wide, appear at the nanowire edges, hence providing an experimental evidence for the corner effect.

Lifetime-Enhanced Transport in Silicon due to Spin and Valley Blockade

We report the observation of lifetime-enhanced transport (LET) based on perpendicular valleys in silicon by transport spectroscopy measurements of a two-electron 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 two-electron spin-valley configurations of all relevant confined quantum states in our device were obtained by a large-scale atomistic tight-binding simulation. The LET acts as a signature of the complicated valley physics in silicon: a feature that becomes increasingly important in silicon quantum devices.

Magnetic-Field Probing of an SU(4) Kondo Resonance in a Single-Atom 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 fin-type 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 s-like 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.

Electric Field Reduced Charging Energies and Two-Electron Bound Excited States of Single Donors in Silicon

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 self-consistent field large-scale tight-binding 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 metal-oxide-semiconductor 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.

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 (Fin-FET). 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 Fin-FET transistors in a row.

Engineered valley-orbit splittings in quantum-confined 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 “valley-orbit” (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 large-scale atomistic tight-binding 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.

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.

Reconfigurable Logic Devices on a Single Dopant Atom—Operation up to a Full Adder by Using Electrical Spectroscopy

A silicon field-effect transistor is operated as a logic circuit by electrically addressing the ground and excited electronic states of an embedded single dopant atom. Experimental results-complemented by analytical and computational calculations-are presented. First, we show how a complete set of binary logic gates can be realized on the same hardware. Then, we show that these gates can be operated in parallel on the very same dopant up to the logic level of a full adder. To use the device not as a switch but as a full logic circuit, we make essential use of the excited electronic states of the dopant and of the ability to shift their energy by gating. The experimental ability to use two channels to measure the current flowing through the device and the conductance (dI/dV) allows for a robust reading of the output of the logic operations.