Max G. Lagally

Synthesis, assembly and applications of semiconductor nanomembranes.

Research in electronic nanomaterials, historically dominated by studies of nanocrystals/fullerenes and nanowires/nanotubes, now incorporates a growing focus on sheets with nanoscale thicknesses, referred to as nanomembranes. Such materials have practical appeal because their two-dimensional geometries facilitate integration into devices, with realistic pathways to manufacturing. Recent advances in synthesis provide access to nanomembranes with extraordinary properties in a variety of configurations, some of which exploit quantum and other size-dependent effects. This progress, together with emerging methods for deterministic assembly, leads to compelling opportunities for research, from basic studies of two-dimensional physics to the development of applications of heterogeneous electronics.

Scanning tunneling microscopy studies of structural disorder and steps on Si surfaces

Scanning tunneling microscopy observations of several forms of disorder on Si surfaces are presented. These include dimer vacancies on Si(001), step bunches associated with a morphological phase transition on vicinal Si(111), and step structure on vicinal Si(001). A recipe for cleaning of Si surfaces to produce a minimum amount of disorder is presented.

Elastically relaxed free-standing strained-silicon nanomembranes

Strain plays a critical role in the properties of materials. In silicon and silicon–germanium, strain provides a mechanism for control of both carrier mobility and band offsets. In materials integration, strain is typically tuned through the use of dislocations and elemental composition. We demonstrate a versatile method to control strain by fabricating membranes in which the final strain state is controlled by elastic strain sharing, that is, without the formation of defects. We grow Si/SiGe layers on a substrate from which they can be released, forming nanomembranes. X-ray-diffraction measurements confirm a final strain predicted by elasticity theory. The effectiveness of elastic strain to alter electronic properties is demonstrated by low-temperature longitudinal Hall-effect measurements on a strained-silicon quantum well before and after release. Elastic strain sharing and film transfer offer an intriguing path towards complex, multiple-layer structures in which each layer’s properties are controlled elastically, without the introduction of undesirable defects.

Determination of roughness correlations in multilayer films for x-ray mirrors

Interfacial roughness in multilayer films may be random or correlated, i.e., replicated from layer to layer. It is shown that these can be separated and quantified using x‐ray diffraction rocking curves and a straightforward analysis. The lateral correlation length along the interfaces can additionally be determined. A quantitative evaluation for W/C multilayers shows that correlated roughness contributes significantly to the total roughness, even at length scales that are surprisingly short, of the order 2–6 nm.

Anisotropy in surface migration of Si and Ge on Si(001)

Abstract The anisotropy in surface migration of Si ad Ge atoms on Si(001) has been investigated by STM analysis of the width of denuded ones at substrate steps that are formed in the spatial distributions of 2D islands after molecular-beam deposition. In both cases, surface migration is at least 1000 times faster along the substrate dimer rows than perpendicular to them.

Atom Motion on Surfaces

Atoms wandering on surfaces lead complex lives. For example, they face many restrictions on their freedom to move. High walls sometimes leave only one road open, and that road may have checkpoints. Such walls and checkpoints are a consequence of the crystal structure of the surface and the interaction between the surface atoms and the wandering atom. The crystal structure in turn is controlled by the nature of the bonding—metallic, covalent, ionic—between atoms in the crystal.

Electronic transport in nanometre-scale silicon-on-insulator membranes

The widely used ‘silicon-on-insulator’ (SOI) system consists of a layer of single-crystalline silicon supported on a silicon dioxide substrate. When this silicon layer (the template layer) is very thin, the assumption that an effectively infinite number of atoms contributes to its physical properties no longer applies, and new electronic, mechanical and thermodynamic phenomena arise, distinct from those of bulk silicon. The development of unusual electronic properties with decreasing layer thickness is particularly important for silicon microelectronic devices, in which (001)-oriented SOI is often used. Here we show—using scanning tunnelling microscopy, electronic transport measurements, and theory—that electronic conduction in thin SOI(001) is determined not by bulk dopants but by the interaction of surface or interface electronic energy levels with the ‘bulk’ band structure of the thin silicon template layer. This interaction enables high-mobility carrier conduction in nanometre-scale SOI; conduction in even the thinnest membranes or layers of Si(001) is therefore possible, independent of any considerations of bulk doping, provided that the proper surface or interface states are available to enable the thermal excitation of ‘bulk’ carriers in the silicon layer.

Direct-bandgap light-emitting germanium in tensilely strained nanomembranes

Silicon, germanium, and related alloys, which provide the leading materials platform of electronics, are extremely inefficient light emitters because of the indirect nature of their fundamental energy bandgap. This basic materials property has so far hindered the development of group-IV photonic active devices, including diode lasers, thereby significantly limiting our ability to integrate electronic and photonic functionalities at the chip level. Here we show that Ge nanomembranes (i.e., single-crystal sheets no more than a few tens of nanometers thick) can be used to overcome this materials limitation. Theoretical studies have predicted that tensile strain in Ge lowers the direct energy bandgap relative to the indirect one. We demonstrate that mechanically stressed nanomembranes allow for the introduction of sufficient biaxial tensile strain to transform Ge into a direct-bandgap material with strongly enhanced light-emission efficiency, capable of supporting population inversion as required for providing optical gain.

Surface self-diffusion of Si on Si(001)

The surface diffusion coefficient of Si atoms on a Si(001) surface is quantitatively determined using scanning tunneling microscopy. The method rests on counting the number of islands that form at various substrate temperatures for a given deposited dose at a given deposition rate. In the simplest situation, the diffusion coefficient is related to the island density by N α D−13 and to the width of denuded zones at steps by WDZαD16. The activation energy for diffusion is Ea = 0.67±0.08 eV an D0≅10−3±1 cm2. The diffusion is highly anisotropic, with the fast direction along the dimer rows.

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.