Dopant metrology in advanced FinFETs

Ultra-scaled FinFET transistors bear unique fingerprint-like device-to-device differences attributed to random single impurities. This paper describes how, through correlation of experimental data with multimillion atom tight-binding simulations using the NEMO 3-D code, it is possible to identify the impurity's chemical species and determine their concentration, local electric field and depth below the Si/SiO$_{\mathrm{2}}$ interface. The ability to model the excited states rather than just the ground state is the critical component of the analysis and allows the demonstration of a new approach to atomistic impurity metrology.Comment: 6 pages, 3 figure

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.Comment: 4 pages, 4 figure

Magnetic Field Probing of an SU(4) Kondo Resonance in a Single Atom Transistor

Semiconductor nano-devices have been scaled to the level that transport can be dominated by a single dopant atom. In the strong coupling case a Kondo effect is observed when one electron is bound to the atom. Here, we report on the spin as well as orbital Kondo ground state. We experimentally as well than theoretically show how we can tune a symmetry transition from a SU(4) ground state, a many body state that forms a spin as well as orbital singlet by virtual exchange with the leads, to a pure SU(2) orbital ground state, as a function of magnetic field. The small size and the s-like orbital symmetry of the ground state of the dopant, make it a model system in which the magnetic field only couples to the spin degree of freedom and allows for observation of this SU(4) to SU(2) transition.Comment: 12 pages, 10 figures, accepted for publication in Physical Review Letter

Heterointerface effects on the charging energy of shallow D- ground state in silicon: the role of dielectric mismatch

Donor states in Si nanodevices can be strongly modified by nearby insulating barriers and metallic gates. We report here experimental results indicating a strong reduction in the charging energy of isolated As dopants in Si FinFETs 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 small charging energy may be due to a combined effect of the insulator screening and the proximity of metallic gates.Comment: 7 pages, 6 figure

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 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.Comment: 4 pages, 4 figures. (The current version (v3) is the result of splitting up the previous version (v2), and has been completely rewritten

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 3D Coulomb confined state to a 2D surface state as the electric field is ramped up adiabatically. In the intermediate field regime, the electron resides in a superposition between the states of the atomic donor potential and that of the quantum dot like states at the surface. 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.Comment: 10 pages, 10 figures, journa

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 measure- ments. 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 bandstructure of the host, applied fields, and interfaces. An applied field pulls the loosely bound D- electron towards 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 ultra-scaled FinFETs validates the model results and provides physical insights. We also report measured D-data showing for the first time the presence of bound D-excited states under applied fields

A hybrid double-dot in silicon

We report electrical measurements of a single arsenic dopant atom in the tunnel-barrier of a silicon SET. As well as performing electrical characterization of the individual dopant, we study series electrical transport through the dopant and SET. We measure the triple points of this hybrid double dot, using simulations to support our results, and show that we can tune the electrostatic coupling between the two sub-systems.Comment: 11 pages, 6 figure

Stark tuning of the charge states of a two-donor molecule in silicon

Gate control of phosphorus donor based charge qubits in Si is investigated using a tight-binding approach. Excited molecular states of P2+ are found to impose limits on the allowed donor separations and operating gate voltages. The effects of surface (S) and barrier (B) gates are analyzed in various voltage regimes with respect to the quantum confined states of the whole device. Effects such as interface ionization, saturation of the tunnel coupling, sensitivity to donor and gate placement are also studied. It is found that realistic gate control is smooth for any donor separation, although at certain donor orientations the S and B gates may get switched in functionality. This paper outlines and analyzes the various issues that are of importance in practical control of such donor molecular systems.Comment: 8 pages, 9 figure

Level Spectrum of Single Gated As Donors

We study the electrical transport through single As donors incorporated in the channel of a FinFET, i.e. a donor in a three-terminal geometry. By means of spectroscopic measurements in conjuction with a NEMO-3D model, we can identify the excited states and associate them with either the donors Coulomb potential, a triangular well at the interface or a hybridized combination of the two. The correspondence between the transport measurements, the theoretical model and the local environment provides an atomic understanding of actual gated donors in a nanostructure