Delay Extraction Based Equivalent Elmore Model For RLC On-Chip Interconnects

As feature sizes for VLSI technology is shrinking, associated with higher operating frequency, signal integrity analysis of on-chip interconnects has become a real challenge for circuit designers. For this purpose, computer-aided-design (CAD) tools are necessary to simulate signal propagation of on-chip interconnects which has been an active area for research. Although SPICE models exist which can accurately predict signal degradation of interconnects, they are computationally expensive. As a result, more effective and analytic models for interconnects are required to capture the response at the output of high speed VLSI circuits. This thesis contributes to the development of efficient and closed form solution models for signal integrity analysis of on-chip interconnects. The proposed model uses a delay extraction algorithm to improve the accuracy of two-pole Elmore based models used in the analysis of on-chip distributed RLC interconnects. In the proposed scheme, the time of fight signal delay is extracted without increasing the number of poles or affecting the stability of the transfer function. This algorithm is used for both unit step and ramp inputs. From the delay rational approximation of the transfer function, analytic fitted expressions are obtained for the 50% delay and rise time for unit step input. The proposed algorithm is tested on point to point interconnections and tree structure networks. Numerical examples illustrate improved 50% delay and rise time estimates when compared to traditional Elmore based two-pole models

Analysis of crosstalk and field coupling to lossy MTL's in a SPICE environment

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficienc

Compact Parameterized Black-Box Modeling via Fourier-Rational Approximations

We present a novel black-box modeling approach for frequency responses that depend on additional parameters with periodic behavior. The methodology is appropriate for representing with compact low-order equivalent models the behavior of electromagnetic systems observed at well-defined ports and/or locations, including dependence on geometrical parameters with rotational symmetry. Examples can be polarization or incidence angles of a plane wave, or stirrer rotation in reverberation chambers. The proposed approach is based on fitting a Fourier-rational model to sampled frequency responses, where frequency dependence is represented through rational functions and parameter dependence through a Fourier series. Several examples from different applications are used to validate and demonstrate the approach

Analytic Delay Model of RLC Interconnects using Numerical Inversion of the Laplace Transform

Signal integrity analysis for on-chip interconnect becomes increasingly important in high-speed designs. SPICE, a conventional circuit simulator, can provide accurate prediction for interconnects, however, using SPICE is extremely computationally expensive. On the other hand, explicit moment matching technique can produce unstable poles for highly accurate approximations and implicit moment matching technique can obtain more accurate approximations at the expense of computational complexity. This thesis presents an analytic model to efficiently estimate the signal delays of RLC on-chip interconnects. It uses the numerical inversion of Laplace transform (NILT) to obtain time function, suitable for transient analysis. Since the integration formula of the NILT is numerically stable for higher order approximations, the developed algorithm provides a mechanism to increase the accuracy for delay estimation. Numerical examples are implemented and compared with HSPICE, two-pole model and Passive Reduced-Order Interconnect Macromodeling Algorithm (PRIMA) to illustrate the efficiency and validity of the proposed work

Investigation of Interconnect and Device Designs for Emerging Post-MOSFET and Beyond Silicon Technologies

Title from PDF of title page viewed May 31, 2017Dissertation advisor: Masud H. ChowdhuryVitaIncludes bibliographical references (pages 94-108)Thesis (Ph.D.)--School of Computing and Engineering and Department of Physics and Astronomy. University of Missouri--Kansas City, 2016The integrated circuit industry has been pursuing Moore’s curve down to deep nanoscale dimensions that would lead to the anticipated delivery of 100 billion transistors on a 300 mm² die operating below 1V supply in the next 5-10 years. However, the grand challenge is to reliably and efficiently take the full advantage of the unprecedented computing power offered by the billions of nanoscale transistors on a single chip. To mitigate this challenge, the limitations of both the interconnecting wires and semiconductor devices in integrated circuits have to be addressed. At the interconnect level, the major challenge in current high density integrated circuit is the electromagnetic and electrostatic impacts in the signal carrying lines. Addressing these problems require better analysis of interconnect resistance, inductance, and capacitance. Therefore, this dissertation has proposed a new delay model and analyzed the time-domain output response of complex poles, real poles, and double poles for resistance-inductance capacitance interconnect network based on a second order approximate transfer function. Both analytical models and simulation results show that the real poles model is much faster than the complex poles model, and achieves significantly higher accuracy in order to characterize the overshoot and undershoot of the output responses. On the other hand, the semiconductor industry is anticipating that within a decade silicon devices will be unable to meet the demands at nanoscale due to dimension and material scaling. Recently, molybdenum disulfide (MoS₂) has emerged as a new super material to replace silicon in future semiconductor devices. Besides, conventional field effect transistor technology is also reaching its thermodynamic limit. Breaking this thermal and physical limit requires adoption of new devices based on tunneling mechanism. Keeping the above mentioned trends, this dissertation also proposed a multilayer MoS₂ channel-based tunneling transistor and identifies the fundamental parameters and design specifications that need to be optimized in order to achieve higher ON-currents. A simple analytical model of the proposed device is derived by solving the time-independent Schrodinger equation. It is analytically proven that the proposed device can offer an ON-current of 80 A/m, a subthreshold swing (S) of 9.12 mV/decade, and a / ratio of 10¹².Introduction -- Previous models on interconnect designs -- Proposed delay model for interconnect design -- Investigation of tunneling for field effect transistor -- Study of molybdenum disulfide for FET applications -- Proposed molybdenum disulfide based tunnel transistor -- Conclusion -- Appendix A. Derivation of time delay model -- Appendix B. Derivation of tunneling current model Appendix C. Derivation of subthreshold swing mode

Modelling and analysis of crosstalk in scaled CMOS interconnects

The development of a general coupled RLC interconnect model for simulating scaled bus structures m VLSI is presented. Several different methods for extracting submicron resistance, inductance and capacitance parameters are documented. Realistic scaling dimensions for deep submicron design rules are derived and used within the model. Deep submicron HSPICE device models are derived through the use of constant-voltage scaling theory on existing 0.75µm and 1.0µm models to create accurate interconnect bus drivers. This complete model is then used to analyse crosstalk noise and delay effects on multiple scaling levels to determine the dependence of crosstalk on scaling level. Using this data, layout techniques and processing methods are suggested to reduce crosstalk in system

Modeling for the Computer-Aided Design of Long Interconnects

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