3D Multi-Subband Ensemble Monte Carlo Simulator of FinFETs and nanowire transistors

In this paper we present the development of a 3D Multi Subband Ensemble Monte Carlo (3DMSB-EMC) tool targeting the simulation of nanoscaled FinFETs and nanowire transistors. In order to deliver computational efficiency, we have developed a self-consistent framework that couples a MSB- EMC transport engine for a 1D electron gas with a 3DPoisson- 2DSchro ̈dinger solver. Here we use a FinFET with a physical channel length of 15nm as an example to demonstrate the appli- cability and highlight the benefits of the simulation framework. A comparison of the 3DMSB-EMC with Non-Equilibrium Green’s Functions (NEGFs) in the ballistic limit is used to verify and validate our approach

Random Discrete Dopant Induced Variability in Negative Capacitance Transistors

In this work we investigate the impact of random discrete dopants (RDD) induced statistical variability in ferroelectric negative capacitance field effect transistors (NCFETs). We couple the 3D `atomistic' statistical device simulator GARAND with the Landau - Khalatnikov equation of the ferroelectric for this study. We found that the negative capacitance effect provided by the ferroelectric layer can lead to suppression of the RDD induced variability in the threshold voltage (Vt), OFF-current (IOFF), and ON-current (ION). This immunity to RDD induced variability increases with increase in the ferroelectric thickness

Partitions of graphs into small and large sets

Let $G$ be a graph on $n$ vertices. We call a subset $A$ of the vertex set $V(G)$ \emph{$k$-small} if, for every vertex $v \in A$, $\deg(v) \le n - |A| + k$. A subset $B \subseteq V(G)$ is called \emph{$k$-large} if, for every vertex $u \in B$, $\deg(u) \ge |B| - k - 1$. Moreover, we denote by $\varphi_k(G)$ the minimum integer $t$ such that there is a partition of $V(G)$ into $t$ $k$-small sets, and by $\Omega_k(G)$ the minimum integer $t$ such that there is a partition of $V(G)$ into $t$ $k$-large sets. In this paper, we will show tight connections between $k$-small sets, respectively $k$-large sets, and the $k$-independence number, the clique number and the chromatic number of a graph. We shall develop greedy algorithms to compute in linear time both $\varphi_k(G)$ and $\Omega_k(G)$ and prove various sharp inequalities concerning these parameters, which we will use to obtain refinements of the Caro-Wei Theorem, the Tur\'an Theorem and the Hansen-Zheng Theorem among other things.Comment: 21 page

Physical Simulation of Si-Based Resistive Random-Access Memory Devices

We present a newly-developed three-dimensional (3D) physical simulator suitable for the study of resistive random-access memory (RRAM) devices. We explore the switching behavior of Si-rich silica (SiOx) RRAM structures, whose operation has been successfully demonstrated experimentally at ambient conditions [1]. The simulator couples self-consistently a simulation of oxygen ion and electron transport to a self-heating model and the `atomistic' simulator GARAND. The electro-thermal simulation model provides many advantages compared to the classical phenomenological models based on the resistor breaker network. The simulator is validated with respect to experimental data and captures successfully the memristive behavior of the simulated SiOx RRAMs, by reconstructing the conductive filament formation and destruction phenomena in the 3D space. The simulation framework is useful for exploring the little-known physics of SiOx RRAMs, and providing efficient designs, in terms of performance, variability and reliability, for both memory devices and circuits

The Graves Theorem Revisited II: Robust Convergence of the Newton Method

AMS subject classification: 65J15, 47H04, 90C30.Based on the original proof of the Graves theorem [9] we study the convergence of the Newton method for the solution of the equation f (x) = y, uniform with respect to the starting point and the parameter y. We show that the surjectivity of the Jacobian implies the Aubin continuity, relative to the supremum norm, of the map taking the starting point and the parameter y to the set of all Newton sequences. These results complement our previous paper [4].This work was supported by The National Science Foundation. The revised version of this paper was prepared during author’s visit at the University of Zürich, Switzerland

Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that the derivative of f is Lipschitz continuous. As an application, we give a characterization of the uniform local Q-quadratic convergence of the sequential quadratic programming method applied to a perturbed nonlinear program

Radical Theatre in Contemporary Nigeria: A Review of the Contributions of Saint Gbilekaa

The practice of radical theatre in the world generally has taken different dimensions in other to achieve different results by different scholars. In Nigeria and most countries of the world, radical theatre is gradually been metamorphosed into community theatre or theatre for development. This paper is a review of the contributions of one of the leading scholars on radical theatre in contemporary Nigeria-Saint Gbilekaa. Fundamentally, the paper reviews Saint Gbilekaa’s book, Radical Theatre in Nigeria where so many issues on theory and criticism in the study of drama and theatre are raised. The paper concludes that, given the nature of our society, if the theatre is to be used as a weapon of collective struggle and human mobilization and liberation, it must encourage the people to protest and resist all oppressive structures in the society. If this is done, our leaders will be on their toes in delivering the desired quality of leadership needed by the people