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Analysis and synthesis of onchip spiral inductors
 IEEE Trans. Electron Devices
, 2005
"... Abstract—This paper presents a physically based compact model for estimating highfrequency performance of spiral inductors. The model accurately accounts for skin and proximity effects in the metal conductors as well as eddy current losses in the substrate. The model shows excellent agreement with ..."
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Abstract—This paper presents a physically based compact model for estimating highfrequency performance of spiral inductors. The model accurately accounts for skin and proximity effects in the metal conductors as well as eddy current losses in the substrate. The model shows excellent agreement with measured data mostly within 10 % across a variety of inductor geometries and substrate dopings up to 20 GHz. A webbased spiral inductor synthesis and analysis tool COILS, which makes use of the compact models, is presented. An optimization algorithm using binary searches speeds up the synthesis of inductor designs. Index Terms—Eddy current, ground shield, inductor, patterned ground shield, proximity effect, Qfactor, radiofrequency (RF) integrated circuit, skin effect, spiral inductor. I.
Analytical Expressions for HighFrequency VLSI Interconnect Impedance Extraction in the Presence of a Multilayer Conductive Substrate
"... Abstract—We propose an efficient method to accurately compute the frequencydependent impedance of VLSI interconnects in the presence of multilayer conductive substrates. The resulting accuracy (errors less than 3%) and CPU time reduction (more than an order of magnitude) emerge from three differen ..."
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Abstract—We propose an efficient method to accurately compute the frequencydependent impedance of VLSI interconnects in the presence of multilayer conductive substrates. The resulting accuracy (errors less than 3%) and CPU time reduction (more than an order of magnitude) emerge from three different ingredients: a 2D Green’s function approach with the correct quasistatic limit, a modified discrete complex images approximation to the Green’s function, and a continuous dipole expansion to evaluate the magnetic vector potential at the short distances that are relevant to VLSI interconnects. This approach permits the evaluation of the selfimpedance and mutualimpedance of multiconductor current loops, including substrate effects, in terms of easily computable analytical expressions that involve their relative separations and the electromagnetic parameters of the multilayer substrate. Index Terms—Green’s function, high frequency, impedance, magnetic dipole, parasitic extraction, substrate, VLSI interconnect. I.
EPEEC: Comprehensive SPICECompatible Reluctance Extraction for HighSpeed Interconnects above Lossy Multilayer Substrate
"... Abstract — With continuous advances in radio frequency (RF) mixedsignal very large scale integration (VLSI) technology, the creation of eddy currents in lossy multilayer substrates has made the already complicated interconnect analysis and modeling issue more challenging. To account for substrate l ..."
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Abstract — With continuous advances in radio frequency (RF) mixedsignal very large scale integration (VLSI) technology, the creation of eddy currents in lossy multilayer substrates has made the already complicated interconnect analysis and modeling issue more challenging. To account for substrate losses, traditional electromagnetic methods are often computationally prohibitive for today’s VLSI geometries. In this paper, an accurate and efficient interconnect modeling approach – EPEEC (Eddycurrentaware Partial Equivalent Element Circuit) – is proposed. Based on complex image theory, it extends the traditional partial equivalent element circuit (PEEC) model to simultaneously take multilayer substrate eddy current losses and frequency dependent effects into consideration. To accommodate even larger scale onchip interconnect networks, EPEEC develops a new SPICEcompatible reluctance extraction algorithm by applying sparsification in the inverse inductance domain with an extended window algorithm. Comparing with several industry standard inductance and fullwave solvers, such as FastHenry and Sonnet R ○ , EPEEC demonstrates within 1.5 % accuracy while providing over 100X speedup. Index Terms — Interconnect, substrate, eddy current, interconnect modeling, inductance extraction, parasitic extraction, reluctance, complex image theory. I.
Wong “Compact Modeling of High Frequency Phenomena for OnChip Spiral Inductors
 In IEEE Journal of SolidState Circuits
, 1998
"... This paper presents a physicsbased compact model for predicting high frequency performance of spiral inductors. The model accurately accounts for skin effect and proximity effect in the metal conductors as well as eddy current loss in the silicon substrate at high frequencies. Skin effect is modele ..."
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This paper presents a physicsbased compact model for predicting high frequency performance of spiral inductors. The model accurately accounts for skin effect and proximity effect in the metal conductors as well as eddy current loss in the silicon substrate at high frequencies. Skin effect is modeled accurately up to 20 GHz using a reduced partial element equivalent circuit formulation (PEEC). Proximity effect in multiturn inductors is modeled using an “effective width ” approach. Substrate eddy current is modeled with an effective substrate image current profile, which accounts for dependence on substrate resistivity, oxide thickness, and inductor trace width. The model shows excellent agreements with measured data across a variety of inductor geometries and substrate resistivities up to 20 GHz. This model can be applied to modeling onchip coplanar lines at high frequencies. Keywords: Onchip inductors, coplanar lines, pskin effect, proximity effect, substrate eddy current loss.
EFFICIENT IMPEDANCE COMPUTATION FOR MULTI CONDUCTOR TRANSMISSION LINES OF RECTANGU
"... Abstract—An efficient numerical solution is presented for computing perunitlength impedance of metallic rectangular transmission lines backed by semiinfinite lossy substrate. We formulate the problem into the set of integral equations, the kernel of which is analytically expressed in terms of spe ..."
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Abstract—An efficient numerical solution is presented for computing perunitlength impedance of metallic rectangular transmission lines backed by semiinfinite lossy substrate. We formulate the problem into the set of integral equations, the kernel of which is analytically expressed in terms of special functions in the quasistatic regime. The method of moments is applied to find the current density distributions in the metal regions, where the discretization of cross sections is performed by using nonuniform grid arranged according to the skin effect. The practical numerical computations concern the influence of the substrate loss on the perunitlength impedance for some types of parallel lines. We thereby show that the substrate loss cannot be neglected at high frequencies. The effectiveness of the proposed method is confirmed by showing that the computed values of resistance satisfy the law of energy conservation with acceptable accuracy. 1.
DESIGN OF SPIRAL INDUCTORS USING EVOLUTIONARY OPTIMISATION
"... ABSTRACT: Simplex and evolutionary optimisation methods are used to determine the optimum topology and geometric parameters of inductors, in order to satisfy electrical design requirements (quality factor, resonance frequency and inductance). The technique simplifies considerably the design of integ ..."
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ABSTRACT: Simplex and evolutionary optimisation methods are used to determine the optimum topology and geometric parameters of inductors, in order to satisfy electrical design requirements (quality factor, resonance frequency and inductance). The technique simplifies considerably the design of integrated spiral inductors on silicon. Various topologies are considered using an accurate, lumpedelement equivalent model, which is sufficiently simple to allow simulations of several hundred iterations to be performed rapidly. The algorithm is highly successful in determining the optimal design parameters, by avoiding convergence to local minima and without requiring good initial estimates. The accuracy of the method is validated both against measured data and results from electromagnetic simulations.
ThreeDimensional Interconnect Modeling for NanoScale VLSI Technologies
, 2006
"... Designing high performance very large scale integration (VLSI) circuits has become more challenging than ever due to deep submicron effects and accelerating timetomarket cycles. With the increasing interconnect delay dominance and strong coupling effects, a small change in the design can cause n ..."
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Designing high performance very large scale integration (VLSI) circuits has become more challenging than ever due to deep submicron effects and accelerating timetomarket cycles. With the increasing interconnect delay dominance and strong coupling effects, a small change in the design can cause new timing violations and result in design iterations. At the same time, the industry trend of integrating higher levels of circuit functionality on one chip and the widespread growth of wireless communication have triggered the proliferation of mixed analogdigital systems. The digital and the analog components share a common lossy substrate, which provides an alternative path for the current to reach difference devices and leads to more significant electromagnetic couplings. Furthermore, the everincreasing complexity of VLSI designs and integration circuit (IC) process technologies increases the mismatch between a circuit fabricated on the wafer and the one designed in the layout tool. Process induced variations can make the circuit performance deviate from the design specification and timingconvergence is getting harder and harder to achieve. Therefore, to perform fast circuit analysis and optimization, efficient extraction of compact
TABLE OF CONTENTS
"... Deliverable: D1.2a Title: D1.2a Report on compact electromagnetic modelling of RF integrated structures ..."
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Deliverable: D1.2a Title: D1.2a Report on compact electromagnetic modelling of RF integrated structures
ACKNOWLEDGEMENTS
, 2005
"... I would like to express my gratitude to all those who gave me the opportunity to complete this thesis. Special thanks are due to my advisor, Dr. Phillip Allen, for his expert guidance, stimulating suggestions, constant encouragement, and neverending supports. I would like to thank my reading commit ..."
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I would like to express my gratitude to all those who gave me the opportunity to complete this thesis. Special thanks are due to my advisor, Dr. Phillip Allen, for his expert guidance, stimulating suggestions, constant encouragement, and neverending supports. I would like to thank my reading committee members, Dr. J. Stevenson Kenney and Dr. Robert K. Feeney, and other committee members, Dr. Waymond R. Scott and Dr. Thomas Morley for their insightful comments and valuable suggestions. I would also like to thank National Semiconductor Corp. for generously providing the fabrication of my test circuits. I would like to give special thanks to my parents for their love, constant encouragement, and moral as well as financial support. Lastly, I would like to thank my three nieces Amanda, Cassie, and Michelle for giving me so much joy during my holiday and semesterbreak visits. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS...............................................................................................iii
Analysis of Frequency and TemperatureDependent Substrate Eddy Currents in OnChip Spiral Inductors Using the Complex Image Method
"... Using the complex image method (CIM), we have analyzed the frequency and temperature dependencies of substrate eddy currents for singleended and differential spiral inductors on a lossy silicon substrate. From our analysis, we have derived a set of accurate closedform expressions for calculating i ..."
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Using the complex image method (CIM), we have analyzed the frequency and temperature dependencies of substrate eddy currents for singleended and differential spiral inductors on a lossy silicon substrate. From our analysis, we have derived a set of accurate closedform expressions for calculating inductances and substrate losses due to substrate eddy currents. Here, we propose a frequencydependent elevenelement equivalent circuit model based on these formulas. We established the validity of the model by comparing the simulated and measured results, which are in good agreement. Index Terms—Complex image method (CIM), differential inductor, eddy currents, greenhouse algorithm, inductor model. I.