Large-signal device simulation in time- and frequency-domain: a comparison

The aim of this paper is to compare the most common time- and frequency-domain numerical techniques for the determination of the steady-state solution in the physics-based simulation of a semiconductor device driven by a time-periodic generator. The shooting and harmonic balance (HB) techniques are applied to the solution of the discretized drift-diffusion device model coupled to the external circuit embedding the semiconductor device, thus providing a fully nonlinear mixed mode simulation. The comparison highlights the strong and weak points of the two approaches, basically showing that the time-domain solution is more robust with respect to the initial condition, while the HB solution provides a more rapid convergence once the initial datum is close enough to the solution itsel

Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques

Process variations are a major concern in today's chip design since they can significantly degrade chip performance. To predict such degradation, existing circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically too slow. Therefore, novel fast stochastic simulators are highly desired. This paper first reviews our recently developed stochastic testing simulator that can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we develop a fast hierarchical stochastic spectral simulator to simulate a complex circuit or system consisting of several blocks. We further present a fast simulation approach based on anchored ANOVA (analysis of variance) for some design problems with many process variations. This approach can reduce the simulation cost and can identify which variation sources have strong impacts on the circuit's performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulatorComment: Accepted to IEEE Custom Integrated Circuits Conference in June 2014. arXiv admin note: text overlap with arXiv:1407.302

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Analog quantum simulation of the Rabi model in the ultra-strong coupling regime

The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation (RWA). The RWA breaks down in the ultra-strong coupling (USC) regime, where the effective coupling strength $g$ is comparable to the energy $\omega$ of the bosonic mode, and remarkable features in the system dynamics are revealed. We demonstrate an analog quantum simulation of an effective quantum Rabi model in the USC regime, achieving a relative coupling ratio of $g/\omega \sim 0.6$. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.Comment: 20 pages, 13 figure

Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic balance approach

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS: PART

Numerical Simulation of Electronic Systems Based on Circuit- Block Partitioning Strategies

Numerical simulation of complex and heterogeneous electronic systems can be a very challenging issue. Circuits composed of a combination of analog, mixed-signal and digital blocks or even radio frequency (RF) blocks, integrated in the same substrate, are very difficult to simulate as a whole at the circuit level. The main reason is because they contain a lot of state variables presenting very distinct properties and evolving in very widely separated time scales. Examples of practical interest are systems-on-a-chip (SoCs), very common in mobile electronics applications, as well as in many other embedded electronic systems. This chapter is intended to briefly review some advanced circuit-level numerical simulation techniques based on circuit-block partitioning schemes, which were especially designed to address the simulation challenges brought by this kind of circuits into the computer-aided-design (CAD) field

Assessment of thermal instabilities and oscillations in multifinger heterojunction bipolar transistors through a harmonic-balance-based CAD-oriented dynamic stability analysis technique

We present a novel analysis of thermal instabilities and oscillations in multifinger heterojunction bipolar transistors (HBTs), based on a harmonic-balance computer-aided-design (CAD)-oriented approach to the dynamic stability assessment. The stability analysis is carried out in time-periodic dynamic conditions by calculating the Floquet multipliers of the limit cycle representing the HBT working point. Such a computation is performed directly in the frequency domain, on the basis of the Jacobian of the harmonic-balance problem yielding the limit cycle. The corresponding stability assessment is rigorous, and the efficient calculation method makes it readily implementable in CAD tools, thus allowing for circuit and device optimization. Results on three- and four-finger layouts are presented, including closed-form oscillation criteria for two-finger device