Au-SN Flip-Chip Solder Bump for Microelectronic and Optoelectronic Applications

As an alternative to the time-consuming solder pre-forms and pastes currently used, a co-electroplating method of eutectic Au-Sn alloy was used in this study. Using a co-electroplating process, it was possible to plate the Au-Sn solder directly onto a wafer at or near the eutectic composition from a single solution. Two distinct phases, Au5Sn and AuSn, were deposited at a composition of 30at.%Sn. The Au-Sn flip-chip joints were formed at 300 and 400 degrees without using any flux. In the case where the samples were reflowed at 300 degrees, only an (Au,Ni)3Sn2 IMC layer formed at the interface between the Au-Sn solder and Ni UBM. On the other hand, two IMC layers, (Au,Ni)3Sn2 and (Au,Ni)3Sn, were found at the interfaces of the samples reflowed at 400 degrees. As the reflow time increased, the thickness of the (Au,Ni)3Sn2 and (Au,Ni)3Sn IMC layers formed at the interface increased and the eutectic lamellae in the bulk solder coarsened.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

One parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps

In the recent paper [Chru\'{s}ci\'{n}ski and Wudarski, arXiv:1105.4821], it was conjectured that the entanglement witnesses arising from some generalized Choi maps are optimal. We show that this conjecture is true. Furthermore, we show that they provide a one parameter family of indecomposable optimal entanglement witnesses.Comment: 3 page

ESL Based Cylindrical Shell Elements with Hierarchical Shape Functions for Laminated Composite Shells

We introduce higher-order cylindrical shell element based on ESL (equivalent single-layer) theory for the analysis of laminated composite shells. The proposed elements are formulated by the dimensional reduction technique from three-dimensional solid to two-dimensional cylindrical surface with plane stress assumption. It allows the first-order shear deformation and considers anisotropic materials due to fiber orientation. The element displacement approximation is established by the integrals of Legendre polynomials with hierarchical concept to ensure the C0-continuity at the interface between adjacent elements as well as C1-continuity at the interface between adjacent layers. For geometry mapping, cylindrical coordinate is adopted to implement the exact mapping of curved shell configuration with a constant curvature with respect to any direction in the plane. The verification and characteristics of the proposed element are investigated through the analyses of three cylindrical shell problems with different shapes, loadings, and boundary conditions

On the conditions for the existence of Perfect Learning and power law in learning from stochastic examples by Ising perceptrons

In a previous letter, we studied learning from stochastic examples by perceptrons with Ising weights in the framework of statistical mechanics. Under the one-step replica symmetry breaking ansatz, the behaviours of learning curves were classified according to some local property of the rules by which examples were drawn. Further, the conditions for the existence of the Perfect Learning together with other behaviors of the learning curves were given. In this paper, we give the detailed derivation about these results and further argument about the Perfect Learning together with extensive numerical calculations.Comment: 28 pages, 43 figures. Submitted to J. Phys.

Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement

We develop a numerical approach for quantifying entanglement in mixed quantum states by convex-roof entanglement measures, based on the optimal entanglement witness operator and the minimax optimization method. Our approach is applicable to general entanglement measures and states and is an efficient alternative to the conventional approach based on the optimal pure-state decomposition. Compared with the conventional one, it has two important merits: (i) that the global optimality of the solution is quantitatively verifiable, and (ii) that the optimization is considerably simplified by exploiting the common symmetry of the target state and measure. To demonstrate the merits, we quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of three-qubit full-rank mixed states composed of the GHZ state, the W state, and the white noise, the simplest mixtures of states with different genuine multipartite entanglement, which have not been quantified before this work. We discuss some general properties of the form of the optimal witness operator and of the convex structure of mixed states, which are related to the symmetry and the rank of states

Learning from Minimum Entropy Queries in a Large Committee Machine

In supervised learning, the redundancy contained in random examples can be avoided by learning from queries. Using statistical mechanics, we study learning from minimum entropy queries in a large tree-committee machine. The generalization error decreases exponentially with the number of training examples, providing a significant improvement over the algebraic decay for random examples. The connection between entropy and generalization error in multi-layer networks is discussed, and a computationally cheap algorithm for constructing queries is suggested and analysed.Comment: 4 pages, REVTeX, multicol, epsf, two postscript figures. To appear in Physical Review E (Rapid Communications

A 12b 50MS/s 2.1mW SAR ADC with redundancy and digital background calibration

A 12-bit 50MS/s SAR ADC implemented in 65nm CMOS technology is presented. The design employs redundancy to relax the DAC settling requirement and to provide sufficient room for errors such that the static nonlinearity caused by capacitor mismatches can be digitally removed. The redundancy is incorporated into the design using a tri-level switching scheme and our modified split-capacitor array to achieve the highest switching efficiency while still preserving the symmetry in error tolerance. A new code-density based digital background calibration algorithm that requires no special calibration signals or additional analog hardware is also developed. The calibration is performed by using the input signal as stimulus and the effectiveness is verified both in simulation and through measured data. The prototype achieves a 67.4dB SNDR at 50MS/s, while dissipating 2.1mW from a 1.2V supply, leading to FoM of 21.9fJ/conv.-step at Nyquist frequency.MIT Masdar Progra

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

Mutual Information of Population Codes and Distance Measures in Probability Space

We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system size. A theory of the rate of saturation of the MI is developed. We show that this rate is controlled by a distance function between the response probabilities induced by different stimuli. This function, which we term the {\it Confusion Distance} between two probabilities, is related to the Renyi $\alpha$-Information.Comment: 11 pages, 3 figures, accepted to PR