March CRF: an Efficient Test for Complex Read Faults in SRAM Memories

In this paper we study Complex Read Faults in SRAMs, a combination of various malfunctions that affect the read operation in nanoscale memories. All the memory elements involved in the read operation are studied, underlining the causes of the realistic faults concerning this operation. The requirements to cover these fault models are given. We show that the different causes of read failure are independent and may coexist in nanoscale SRAMs, summing their effects and provoking Complex Read Faults, CRFs. We show that the test methodology to cover this new read faults consists in test patterns that match the requirements to cover all the different simple read fault models. We propose a low complexity (?2N) test, March CRF, that covers effectively all the realistic Complex Read Fault

The Solution of the Relativistic Schrodinger Equation for the δ′\delta'-Function Potential in 1-dimension Using Cutoff Regularization

We study the relativistic version of Schr\"odinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultra-violet divergent, and the resultant expression cannot be renormalized in the usual sense. Therefore a general procedure has been developed to derive different physical properties of the system. The procedure is used first on the non-relativistic case for the purpose of clarification and comparisons. The results from the relativistic case show that this system behaves exactly like the delta function potential, which means it also shares the same features with quantum field theories, like being asymptotically free, and in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point.Comment: 32 pages, 5 figure

Self-adjoint Extensions for Confined Electrons:from a Particle in a Spherical Cavity to the Hydrogen Atom in a Sphere and on a Cone

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states lo calized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge-Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r potential.Comment: 22 pages, 9 Figure

Variation aware analysis of bridging fault testing

This paper investigates the impact of process variation on test quality with regard to resistive bridging faults. The input logic threshold voltage and gate drive strength parameters are analyzed regarding their process variation induced influence on test quality. The impact of process variation on test quality is studied in terms of test escapes and measured by a robustness metric. It is shown that some bridges are sensitive to process variation in terms of logic behavior, but such variation does not necessarily compromise test quality if the test has high robustness. Experimental results of Monte-Carlo simulation based on recent process variation statistics are presented for ISCAS85 and -89 benchmark circuits, using a 45nm gate library and realistic bridges. The results show that tests generated without consideration of process variation are inadequate in terms of test quality, particularly for small test sets. On the other hand, larger test sets detect more of the logic faults introduced by process variation and have higher test quality

Dynamic and Leakage Power-Composition Profile Driven Co-Synthesis for Energy and Cost Reduction

Recent research has shown that combining dynamic voltage scaling (DVS) and adaptive body bias (ABB) techniques achieve the highest reduction in embedded systems energy dissipation [1]. In this paper we show that it is possible to produce comparable energy saving to that obtained using combined DVS and ABB techniques but with reduced hardware cost achieved by employing processing elements (PEs) with separate DVS or ABB capability. A co-synthesis methodology which is aware of tasks’ power-composition profile (the ratio of the dynamic power to the leakage power) is presented. The methodology selects voltage scaling capabilities (DVS, ABB, or combined DVS and ABB) for the PEs, maps, schedules, and voltage scales applications given as task graphs with timing constraints, aiming to dynamic and leakage energy reduction at low hardware cost. We conduct detailed experiments, including a real-life example, to demonstrate the effectiveness of our methodology. We demonstrate that it is possible to produce designs that contain PEs with only DVS or ABB technique but have energy dissipation that are only 4.4% higher when compared with the same designs that employ PEs with combined DVS and ABB capabilities

Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls

We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.Comment: 23 pages 18 figure

Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the δ\delta-Function Potential in 1-dimensional Relativistic Quantum Mechanics

We consider the Schr\"odinger equation for a relativistic point particle in an external 1-dimensional $\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudo-differential operator $H = \sqrt{p^2 + m^2}$. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics

Majorana Fermions in a Box

Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical lattice as quantum simulators. This motivates the theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in $(1+1)$-d are characterized by a 1-parameter family, $\lambda = - \lambda^*$, of self-adjoint extensions, for Majorana fermions $\lambda$ is restricted to $\pm i$. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schr\"odinger equation that does not suffer from these problems.Comment: 23 pages, 2 figure