Topological Insulators and Superconductors from String Theory

Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and supercondutors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K-theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K-theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the $\theta$-term in various dimensions. This sheds light on topological insulators and superconductors beyond non-interacting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).Comment: 13 pages, 3 figures;references update

Characterization Of Thermal Stresses And Plasticity In Through-Silicon Via Structures For Three-Dimensional Integration

Through-silicon via (TSV) is a critical element connecting stacked dies in three-dimensional (3D) integration. The mismatch of thermal expansion coefficients between the Cu via and Si can generate significant stresses in the TSV structure to cause reliability problems. In this study, the thermal stress in the TSV structure was measured by the wafer curvature method and its unique stress characteristics were compared to that of a Cu thin film structure. The thermo-mechanical characteristics of the Cu TSV structure were correlated to microstructure evolution during thermal cycling and the local plasticity in Cu in a triaxial stress state. These findings were confirmed by microstructure analysis of the Cu vias and finite element analysis (FEA) of the stress characteristics. In addition, the local plasticity and deformation in and around individual TSVs were measured by synchrotron x-ray microdiffraction to supplement the wafer curvature measurements. The importance and implication of the local plasticity and residual stress on TSV reliabilities are discussed for TSV extrusion and device keep-out zone (KOZ).Microelectronics Research Cente

From modes to movement in the behavior of C. elegans

Organisms move through the world by changing their shape, and here we explore the mapping from shape space to movements in the nematode C. elegans as it crawls on a planar agar surface. We characterize the statistics of the trajectories through the correlation functions of the orientation angular velocity, orientation angle and the mean-squared displacement, and we find that the loss of orientational memory has significant contributions from both abrupt, large amplitude turning events and the continuous dynamics between these events. Further, we demonstrate long-time persistence of orientational memory in the intervals between abrupt turns. Building on recent work demonstrating that C. elegans movements are restricted to a low-dimensional shape space, we construct a map from the dynamics in this shape space to the trajectory of the worm along the agar. We use this connection to illustrate that changes in the continuous dynamics reveal subtle differences in movement strategy that occur among mutants defective in two classes of dopamine receptors

Stress-Induced Delamination Of Through Silicon Via Structures

Continuous scaling of on-chip wiring structures has brought significant challenges for materials and processes beyond the 32 nm technology node in microelectronics. Recently three-dimensional (3-D) integration with through-silicon-vias (TSVs) has emerged as an effective solution to meet the future interconnect requirement. Thermo-mechanical reliability is a key concern for the development of TSV structures used in die stacking as 3-D interconnects. This paper examines the effect of thermal stresses on interfacial reliability of TSV structures. First, the three-dimensional distribution of the thermal stress near the TSV and the wafer surface is analyzed. Using a linear superposition method, a semi-analytic solution is developed for a simplified structure consisting of a single TSV embedded in a silicon (Si) wafer. The solution is verified for relatively thick wafers by comparing to numerical results obtained by finite element analysis (FEA). Results from the stress analysis suggest interfacial delamination as a potential failure mechanism for the TSV structure. Analytical solutions for various TSV designs are then obtained for the steady-state energy release rate as an upper bound for the interfacial fracture driving force, while the effect of crack length is evaluated numerically by FEA. Based on these results, the effects of TSV designs and via material properties on the interfacial reliability are elucidated. Finally, potential failure mechanisms for TSV pop-up due to interfacial fracture are discussed.Aerospace Engineerin

Thermomechanical Characterization And Modeling For TSV Structures

Continual scaling of devices and on-chip wiring has brought significant challenges for materials and processes beyond the 32-nm technology node in microelectronics. Recently, three-dimensional (3-D) integration with through-silicon vias (TSVs) has emerged as an effective solution to meet the future technology requirements. Among others, thermo-mechanical reliability is a key concern for the development of TSV structures used in die stacking as 3-D interconnects. This paper presents experimental measurements of the thermal stresses in TSV structures and analyses of interfacial reliability. The micro-Raman measurements were made to characterize the local distribution of the near-surface stresses in Si around TSVs. On the other hand, the precision wafer curvature technique was employed to measure the average stress and deformation in the TSV structures subject to thermal cycling. To understand the elastic and plastic behavior of TSVs, the microstructural evolution of the Cu vias was analyzed using focused ion beam (FIB) and electron backscattering diffraction (EBSD) techniques. Furthermore, the impact of thermal stresses on interfacial reliability of TSV structures was investigated by a shear-lag cohesive zone model that predicts the critical temperatures and critical via diameters.Microelectronics Research Cente

Thermomechanical Reliability Challenges For 3D Interconnects With Through-Silicon Vias

Continual scaling of on-chip wiring structures has brought significant challenges for materials and processes beyond the 32 nm technology node in microelectronics. Recently threedimensional (3-D) integration with through-silicon-vias (TSVs) has emerged as an effective solution to meet the future interconnect requirement. Among others, thermo-mechanical reliability is a key concern for the development of TSV structures used in die stacking as 3-D interconnects. This paper examines the effects of thermally induced stresses on interfacial reliability of TSV structures. First, three-dimensional distribution of the thermal stress near the TSV and the wafer surface is analyzed. Using a linear superposition method, a semi-analytic solution is developed for a simplified structure consisting of a single TSV embedded in a silicon (Si) wafer. The solution is verified for relatively thick wafers by comparing to numerical results From finite element analysis (FEA). The stress analysis suggests interfacial delamination as a potential failure mechanism for the TSV structure. An analytical solution is then obtained for the steady-state energy release rate as the upper bound for the interfacial fracture driving force, while the effect of crack length is evaluated numerically by FEA. With these results, the effects of the TSV dimensions (e.g., via diameter and wafer thickness) on the interfacial reliability are elucidated. Furthermore, the effects of via material properties are discussed.Aerospace Engineerin

Field-driven topological glass transition in a model flux line lattice

We show that the flux line lattice in a model layered HTSC becomes unstable above a critical magnetic field with respect to a plastic deformation via penetration of pairs of point-like disclination defects. The instability is characterized by the competition between the elastic and the pinning energies and is essentially assisted by softening of the lattice induced by a dimensional crossover of the fluctuations as field increases. We confirm through a computer simulation that this indeed may lead to a phase transition from crystalline order at low fields to a topologically disordered phase at higher fields. We propose that this mechanism provides a model of the low temperature field--driven disordering transition observed in neutron diffraction experiments on ${\rm Bi_2Sr_2CaCu_2O_8\, }$ single crystals.Comment: 11 pages, 4 figures available upon request via snail mail from [email protected]

Linking horizontal and vertical transports of biomass fire emissions to the Tropical Atlantic Ozone Paradox during the Northern Hemisphere winter season: climatology

International audienceDuring the Northern hemisphere winter season, biomass burning is widespread in West Africa, yet the total tropospheric column ozone values (<30 DU) over much of the Tropical Atlantic Ocean (15° N?5° S) are relatively low. At the same time, the tropospheric column ozone values in the Southern Tropical Atlantic are higher than those in the Northern Hemisphere (ozone paradox). We examine the causes for low tropospheric column ozone values by considering the horizontal and vertical transport of biomass fire emissions in West Africa during November through March, using observed data which characterizes fires, aerosols, horizontal winds, precipitation, lightning and outgoing longwave radiation. We have found that easterly winds prevail in the lower troposphere but transition to westerly winds at pressure levels lower than 500 hPa. A persistent anticyclone over West Africa at 700 hPa is responsible for strong easterly winds, which causes a net outflow of ozone/ozone precursors from biomass burning in West Africa across the Atlantic Ocean towards South America. The lowest outgoing longwave radiation (OLR) and highest precipitation rates are generally found over the central Atlantic, some distance downstream of fires in West Africa making the vertical transport of ozone and ozone precursors less likely and ozone destruction more likely. However, lightning over land areas in Central Africa and South America can lead to enhanced ozone levels in the upper troposphere especially over the Southern tropical Atlantic during the Northern Hemisphere winter season