Bernard Kapidani

Tunnel FETs for Ultralow Voltage Digital VLSI Circuits: Part I—Device–Circuit Interaction and Evaluation at Device Level

This paper and the companion work present the results of a comparative study between the tunnel-FETs (TFETs) and conventional MOSFETs for ultralow power digital circuits targeting a VDD below 500 mV. For this purpose, we employed numerical TCAD simulations, as well as mixed device-circuit and lookup-table simulations using either the SENTAURUS or the Verilog-A environment. In particular, in this paper, we explore the device-circuit interaction in n- and p-type TFETs, and propose a design leading to a good tradeoff between the current leakage and transistor imbalance at ultralow VDD, as required in ultralow voltage systems. Then, we systematically compare the IOFF, ION, effective capacitance, OFF-state and ON-state stacking factors for TFETs, SOI, and bulk MOSFETs in a wide range of VDD. These results allow us to infer preliminary indications about the amenability for an aggressive voltage scaling of TFETs compared with MOSFETs, which will be further developed in the companion paper. We also report simulation results for the sensitivity of the transistors to the variation of some key device parameters. Even these process variation results set the stage for a more thorough investigation addressed in the companion paper about the limits imposed by process variability to voltage scaling for either TFETs or MOSFETs circuits.

An Arbitrary-Order Discontinuous Skeletal Method for Solving Electrostatics on General Polyhedral Meshes

This paper presents a numerical method to obtain high order of convergence for electrostatic problems solved on general polyhedral meshes. The method is based on high-order local reconstructions of differential operators from face and cell degrees of freedom.

Computation of Relative 1-Cohomology Generators From a 1-Homology Basis for Eddy Currents Boundary Integral Formulations

Efficient boundary integral formulations based on stream functions for solving eddy current problems in thin conductors, which are modeled by the orientable combinatorial two-manifold with boundary, need generators of the first relative cohomology group to make the problem well defined. The state-of-the-art technique is to compute directly the relative cohomology generators with a combinatorial algorithm having linear worst-case complexity. In this paper, we propose to compute the relative cohomology generators from the homology generators, introducing a novel and general algorithm whose running time is again linear in the worst case. The advantage is that one may use an off-the-shelf software to compute the homology generators and implement only a simple and cheap procedure to obtain the required relative cohomology generators. Although the presented applications relate to ac power systems, the proposed technique is of general interest, and may be used for other applications in computational science and engineering.

Fast Computation of Cuts With Reduced Support by Solving Maximum Circulation Problems

We present a technique to efficiently compute optimal cuts required to solve 3-D eddy current problems by magnetic scalar potential formulations. By optimal cuts, we mean the representatives of (co)homology generators with minimum support among the ones with a prescribed boundary. In this paper, we obtain them by starting from the minimal (co)homology generators of the combinatorial two-manifold representing the interface between conducting and insulating regions. Optimal generators are useful because they reduce the fill-in of the sparse matrix and ease human-guided basis selection. In addition, provided that the mesh is refined enough to allow it, they are not self-intersecting. The proposed technique is based on a novel graph-theoretic algorithm to solve a maximum circulation network flow problem in unweighted graphs that typically runs in linear time.

- Formulation with Higher-Order Hierarchical Basis Functions for Nonsimply Connected Conductors

This paper presents in detail the extension of the - formulation for eddy currents based on higher-order hierarchical basis functions so that it can automatically deal with conductors of arbitrary topology. To this aim, we supplement the classical hierarchical basis functions with nonlocal basis functions spanning the first de Rham cohomology group of the insulating region. Such nonlocal basis functions may be efficiently and automatically found in negligible time with the recently introduced Dlotko–Specogna (DS) algorithm. The approach presented in this paper merges techniques together which to some extent already existed in literature but they were never grouped together and tested as a single unit.

Topoprocessor: An Efficient Computational Topology Toolbox for h -Oriented Eddy Current Formulations

When solving eddy-current problems containing topologically non-trivial conductors with formulations using the magnetic scalar potential in the insulators, cohomology generators are necessary to obtain a well-defined problem. The Dłotko–Specogna (DS) algorithm is a simple and efficient tool to compute the lazy generators of the first cohomology group of the insulator that can be used in such potential design. This paper introduces an upgrade in the DS algorithm that speeds up the execution for very complicated geometries. Moreover, this paper provides, for the first time, a detailed comparison of computational resources needed for the topological pre-processing by our toolbox and by the tool to compute a standard cohomology basis available in the mesh generator GMSH. In addition, we make our implementation of DS algorithm available for download on request for non-profit use as a Topoprocessor package.

Topoprocessor: An efficient computational topology toolbox for h-oriented eddy current formulations

When solving eddy-current problems containing topologically non-trivial conductors with formulations using the magnetic scalar potential in the insulators, cohomology is recognized to be the only safe tool to obtain a well posed problem. This paper presents an efficient implementation of the recently introduced DS algorithm to compute the first lazy cohomology group generators of a tetrahedral mesh. The code will be available for download on request for non-profit use. Secondly, for the first time, the computational time required by the proposed toolbox for the topological pre-processing is compared with another freely available alternative on the same input mesh.

An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes

We present a numerical method named mixed high order (MHO) to obtain high order of convergence for electrostatic problems solved on general polyhedral meshes. The method, based on high-order local reconstructions of differential operators from face and cell degrees of freedom, exhibits a moderate computational cost thanks to hybridization and static condensation that eliminate cell unknowns. After surveying the method, we assess its effectiveness for 3-D problems by comparing, for the first time in literature, its performances with classical conforming finite elements. Moreover, we emphasize the algebraic equivalence of MHO in the lowest order with the analog formulation obtained with the discrete geometric approach or the finite-integration technique.

A comparative performance analysis of time-domain formulations for wave propagation problems

This paper presents an analysis of the performances of competing approaches in the numerical solution of wave propagation problems in the time domain, with focus on the advantages of an approach based on a FD-TD scheme on two interlocked grids over known FIT and FEM approaches.

T-Ω formulation with higher order hierarchical basis functions for non simply connected conductors

This paper extends the T-Ω formulation for eddy currents based on higher order hierarchical basis functions so that it can deal with conductors of arbitrary topology. To this aim we supplement the classical hierarchical basis functions with non-local basis functions spanning the first de Rham cohomology group of the insulating region. Such non-local basis functions may be efficiently found in negligible time with the recently introduced DS algorithm.