Paul P. Rugheimer

Practical design and simulation of silicon-based quantum-dot qubits

Spins based in silicon provide one of the most promising architectures for quantum computing. Quantum dots are an inherently scalable technology. Here, we combine these two concepts into a workable design for a silicon-germanium quantum bit. The novel structure incorporates vertical and lateral tunneling, provides controlled coupling between dots, and enables single electron occupation of each dot. Precise modeling of the design elucidates its potential for scalable quantum computing. For the first time it is possible to translate the requirements of faulttolerant error correction into specific requirements for gate voltage control electronics in quantum dots. We demonstrate that these requirements are met by existing pulse generators in the kHzMHz range, but GHz operation is not yet achievable. Our calculations further pinpoint device features that enhance operation speed and robustness against leakage errors. We find that the component technologies for silicon quantum dot quantum computers are already in hand. Quantum computing offers the prospect of breaking out of the classical von Neumann paradigm that dominates present-day computation. It would enable huge speedups of certain very hard problems, notably factorization. Constructing a quantum computer (QC) presents many challenges, however. Chief among these is scalability: the 10 qubits needed for simple applications far exceed the potential of existing implementations. This requirement points strongly in the direction of Si-based electronics for QC. Silicon devices offer the advantage of long spin coherence times, fast operation, and a proven record of scalable integration. Specific Si-based qubit proposals utilize donor-bound nuclear or electronic spins as qubits. However, quantum dots can also be used to house electron spins, and they have the advantage that the electrostatic gates controlling qubit operations are naturally aligned to each qubit. These proposals describe an intriguing possibility. Our aim here is to describe a new SiGe qubit design, and, just as importantly, to carry out detailed modeling of a specific design for the first time. Modeling provides a proof of principle, pinpoints problem areas, and suggests new directions. The fundamental goal of our design is the ability to reduce the electron occupation of an individual dot precisely to one, as in vertically coupled structures. It may be possible to use the spin of multi-electron quantum dots as qubits, but single occupation is clearly desirable. The spin state “up” = 0 or “down” = 1 , stores the quantum bit of information. At the same time, it is necessary to have tunable coupling between neighboring dots. This is achieved by controlled movement of electrons along the quantum well that contains two dots. The solution is to draw on two distinct quantum dot technologies: lateral and vertical tunneling quantum dots. The design, shown in Fig. 1, incorporates a back-gate that serves as an electron reservoir, a quantum well that confines electrons vertically, and split top gates that provide lateral confinement by electrostatic repulsion. All semiconductor layers are formed of strainrelaxed x xGe Si 1 except the quantum well, which is pure, strained Si. Relaxation is achieved by step-graded compositional growth on a Si wafer. Here, we consider the composition 077 . 0 = x , consistent with a quantum well band offset meV 84 ≅ ∆ c E , with respect to theSpins based in silicon provide one of the most promising architectures for quantum computing. A scalable design for silicon-germanium quantum-dot qubits is presented. The design incorporates vertical and lateral tunneling. Simulations of a four-qubit array suggest that the design will enable single electron occupation of each dot of a many-dot array. Performing two-qubit operations has negligible effect on other qubits in the array. Simulation results are used to translate error correction requirements into specifications for gate-voltage control electronics. This translation is a necessary link between error correction theory and device physics.

Nanomechanics: Response of a strained semiconductor structure

The nanomechanical properties of thin silicon films will become increasingly critical in semiconductor devices, particularly in the context of substrates that consist of a silicon film on an insulating layer (known as silicon-on-insulator, or SOI, substrates). Here we use very small germanium crystals as a new type of nanomechanical stressor to demonstrate a surprising mechanical behaviour of the thin layer of silicon in SOI substrates, and to show that there is a large local reduction in the viscosity of the oxide on which the silicon layer rests. These findings have implications for the use of SOI substrates in nanoelectronic devices.

Quantitative analysis of electric force microscopy: The role of sample geometry

Quantitative electric force microscopy (EFM) is usually restricted to flat samples, because vertical sample topography traditionally makes quantitative interpretation of EFM data difficult. Many important samples, including self-assembled nanostructures, possess interesting nanoscale electrical properties in addition to complex topography. Here we present techniques for analysis of EFM images of such samples, using voltage modulated EFM augmented by three-dimensional simulations. We demonstrate the effectiveness of these techniques in analyzing EFM images of self-assembled SiGe nanostructures on insulator, report measured dielectric properties, and discuss the limitations sample topography places on quantitative measurement.

Computation with DNA on surfaces

DNA computation has the potential to tackle computationally difficult problems that have real-world implications. The parallel search capabilities of DNA make it a valuable tool to approach problems that have a large number of possible solutions, for which conventional computers have limited potential. Surface science can play a significant role in harnessing the parallel nature of DNA for computation. This article briefly reviews conventional computing architecture, discusses DNA computation, and describes the role of surface science in DNA computation.

Self-organized quantum dots

We review the concepts and principal experimental results pertaining to the self-assembly and self-ordering of quantum dots in semiconductor systems. We focus on the kinetics and thermodynamics of the formation and evolution of coherently strained 3D islands, and the effects of strain on nucleation, growth, and island shape. We also discuss ongoing research on methods to control the density, size, and size distributions of strained islands, both within a single strained layer and in quantum dot (QD) multilayers.

Strain engineering, self-assembly, and nanoarchitectures in thin SiGe films on Si

We review recent experimental results pertaining to the self-assembly and self-ordering of quantum dots (QDs) in semiconductor systems. In particular, we focus on attempts to control the density, size, and size distributions of strained islands, both within a single strained layer and in quantum dot multilayers. We also discuss the factors affecting vertical ordering in multilayers such as the nature of the strain field produced by buried islands and the thickness of the spacer layer.

Electrically isolated SiGe quantum dots

A variation of electric force microscopy (EFM) is used to measure the electrical isolation of SiGe quantum dots (QDs). The SiGe QDs are grown on mesas of ultrathin silicon on insulator. Near the mesa edges, the thin silicon layer has been incorporated into the QDs, resulting in electrically isolated QDs. Away from the edges, the silicon layer is not incorporated and has a two-dimensional resistivity of less than 800 TΩ per sq, resulting in relatively short RC times for charge flow on the mesa. The EFM technique we use here is a powerful probe of samples and devices with floating-gate geometries.

Polymer light emitting diodes and poly(di-n-octylfluorene) thin films as fabricated with a microfluidics applicator

A microfluidics applicator is used in the fabrication of a polyfluorene based polymer light emitting diode (PLED). This procedure results in a single contiguous polymer trace and, as a consequence of the high deposition speed, shows unusual characteristics in both the film morphology and polymer microstructure. These aspects are studied using fluorescence microscopy, profilometry, and optical absorption and emission spectroscopies. Room temperature analysis of the poly(di-n-octylfluorene) indicates that the combination of high-speed deposition and rapid drying process traps the polymer into a metastable conformational state. Optical spectroscopy at reduced temperature identifies emission from at least two distinct conformational chromophores. At elevated temperature there is an abrupt, irreversible transition to a more conventional structural form. Electroluminesence data from PLED test devices are shown and this demonstrates some of the unique opportunities afforded by this method of polymer film formati...

Microfabricated strained substrates for Ge epitaxial growth

The manipulation of strain in micromachined silicon structures presents an opportunity in the control of surface processes in epitaxial growth. With appropriate fabrication techniques, the magnitude, crystallographic direction, and symmetry of the strain at a Si surface can be precisely controlled with this strategy. Synchrotron x-ray microdiffraction techniques allow simultaneous independent measurements of the strain and bending in these structures and serve to calibrate the fabrication process. Bending is the dominant source of strain in a microfabricated Si bridge loaded at its ends by silicon nitride thin films that we have used as a strained substrate in studies of Ge epitaxial growth. The total strain difference between the top and bottom of the bent bridge exceeds 10−3 in present structures and can potentially be increased in optimized devices. These micromachined substrates complement other methods for producing strained silicon and silicon–germanium structures for improved electrical device perf...

Spontaneous transition from epitaxially constrained to equilibrium Ge nanocrystals on silicon-on-insulator (1 0 0)

Epitaxial constraints define the stress-driven self-assembly of faceted nanocrystals and in particular one of their key characteristics––their shape. Here we identify a technologically relevant system, Ge islands grown on ultrathin siliconon-insulator (SOI) substrate in which nanocrystals, whose shape is initially defined by epitaxial constraints, spontaneously overcome those constraints and transform to their equilibrium shape. Ge nanocrystals on ultrathin SOI form initially as huts and then transform into domes, similar to the sequence of epitaxially constrained shapes they assume on bulk Si(1 0 0). While the sequence on bulk Si ends here, we observe further dramatic morphological changes on ultrathin SOI: a spontaneous transformation to equilibrium-shaped Ge nanocrystals. 2003 Elsevier Science B.V. All rights reserved.