Computation of Conductance and Capacitance for IC Interconnects on a General Lossy Multilayer Substrate

In this paper a simple method for analysis and modelling of transmission interconnect lines on general lossy multilayer substrates at high bit rates is presented. The analysis is based on semi-analytical Green's function approach and recurrence relation between the coefficients of potential in n and n + 1 layers, respectively. The electromagnetic concept of free charge density is applied. It allows us to obtain integral equations between electric scalar potential and charge density distributions. These equations are solved by the Galerkin procedure of the Method of Moments. New approach is especially adequate to model 2-D layered structures with planar boundaries for frequencies up to 20GHz (quasistationary field approach). The transmission line parameters (capacitance and conductance per unit length) for the given interconnect multilayer geometry are computed. A discussion of the calculated line admittance in terms of technological and geometrical parameters of the structure is given. A comparison of the numerical results from the new procedure with the techniques presented in the previous publications are provided, too

Transmission Lines in CMOS: An Explorative Study

On-chip transmission line modelling and design become increasingly important as frequencies are continuously going up. This paper explores possibilities to implement transmission lines on CMOS ICs via coupled coplanar strips. EM-field simulations with SONNET are used to estimate important transmission line properties like characteristic impedance, propagation velocity and loss in a 0.18 micron CMOS Technology. Both metal losses and substrate losses are modeled. Special attention is paid to the effect of the Silicon substrate, in particular to the so called “slow-wave mode” that can occur in the Si-SiO2 system

Modeling and characterization of on-chip interconnects, inductors and transformers

Ph.DNUS-SUPELEC JOINT PH.D. PROGRAMM

3D modeling and integration of current and future interconnect technologies

Title from PDF of title page viewed June 21, 2021Dissertation advisor: Masud H. ChowdhuryVitaIncludes bibliographical references (pages 133-138)Thesis (Ph.D.)--School of Computing and Engineering and Department of Physics and Astronomy. University of Missouri--Kansas City, 2021To ensure maximum circuit reliability it is very important to estimate the circuit performance and signal integrity in the circuit design phase. A full phase simulation for performance estimation of a large-scale circuit not only require a massive computational resource but also need a lot of time to produce acceptable results. The estimation of performance/signal integrity of sub-nanometer circuits mostly depends on the interconnect capacitance. So, an accurate model for interconnect capacitance can be used in the circuit CAD (computer-aided design) tools for circuit performance estimation before circuit fabrication which reduces the computational resource requirement as well as the time constraints. We propose a new capacitance models for interconnect lines in multilevel interconnect structures by geometrically modeling the electrical flux lines of the interconnect lines. Closed-form equations have been derived analytically for ground and coupling capacitance. First, the capacitance model for a single line is developed, and then the new model is used to derive expressions for the capacitance of a line surrounded by neighboring lines in the same and the adjacent layers above and below. These expressions are simple, and the calculated results are within 10% of Ansys Q3D extracted values. Through silicon via (TSV) is one of the key components of the emerging 3D ICs. However, increasing number of TSVs in smaller silicon area leads to some severe negative impacts on the performance of the 3D IC. Growing signal integrity issues in TSVs is one of the major challenges of 3D integration. In this paper, different materials for the cores of the vias and the interposers are investigated to find the best possible combination that can reduce crosstalk and other losses like return loss and insertion loss in the TSVs. We have explored glass and silicon as interposer materials. The simulation results indicate that glass is the best option as interposer material although silicon interposer has some distinct advantages. For via cores three materials - copper (Cu), tungsten (W) and Cu-W bimetal are considered. From the analysis it can concluded that W would be better for high frequency applications due to lower transmission coefficient. Cu offers higher conductivity, but it has larger thermal expansion coefficient mismatch with silicon. The performance of Cu-W bimetal via would be in between Cu and W. However, W has a thermal expansion coefficient close to silicon. Therefore, bimetal Cu-W based TSV with W as the outer layer would be a suitable option for high frequency 3D IC. Here, we performed the analysis in terms of return loss, transmission coefficient and crosstalk in the vias. Signal speed in current digital systems depends mainly on the delay of interconnects. To overcome this delay problem and keep up with Moore’s law, 3D integrated circuit (vertical integration of multiple dies) with through-silicon via (TSV) has been introduced to ensure much smaller interconnect lengths, and lower delay and power consumption compared to conventional 2D IC technology. Like 2D circuit, the estimation of 3D circuit performance depends on different electrical parameters (capacitance, resistance, inductance) of the TSV. So, accurate modeling of the electrical parameters of the TSV is essential for the design and analysis of 3D ICs. We propose a set of new models to estimate the capacitance, resistance, and inductance of a Cu-filled TSV. The proposed analytical models are derived from the physical shape and the size of the TSV. The modeling approach is comprehensive and includes both the cylindrical and tapered TSVs as well as the bumps. On-chip integration of inductors has always been very challenging. However, for sub- 14nm on-chip applications, large area overhead imposed by the on-chip capacitors and inductors has become a more severe concern. To overcome this issue and ensure power integrity, a novel 3D Through-Silicon-Via (TSV) based inductor design is presented. The proposed TSV based inductor has the potential to achieve both high density and high performance. A new design of a Voltage Controlled Oscillator (VCO) utilizing the TSV based inductor is also presented. The implementation of the VCO is intended to study the feasibility, performance, and real-world application of the proposed TSV based inductor.Introduction -- Background of capacitance modeling of on-chip interconnect -- Accurate modeling of interconnect capacitance in multilevel interconnect structures for sub 22nm technology -- Analysis of different materials and structures for through silicon via and through glass via in 3D integrated circuits -- Impacts of different shapes of through-silicon-via core on 3D IC performance -- Accurate electrical modeling of cu-filled through-silicon-via (TSV) -- Design and characterize TSV based inductor for high frequency voltage-controlled oscillator design -- Conclusion and future wor

Modelling of interconnects in 3DIC based on layered green functions

As traditional CMOS scaling pace gradually slows down, three-dimensional (3D) integration offers another dimension of in the ”More-than-Moore” era. In this dissertation, a number of investigations were conducted to better model interconnects in 3D integrated circuit (IC), to evaluate electrical behavior including delay, power consumption, signal integrity (SI), and power integrity (PI) for 3D ICs. Partial Element Equivalent Circuit (PEEC) method with layered Green’s function is studied here, since it consumes less computational resources and provides better physical insight to model the interconnects in 3DIC for high-speed digital circuits. The work is organized as a series of papers. The first paper reviewed the fundamental methods to derive layered Green’s function in spectral domain using discrete complex image method (DCIM) and analyzed the effects of each Green function terms to model silicon interconnects. The second paper proposed a unique method to extract poles near branch cut in complex kp plane, to accurately extract surface wave effects. The last paper proposed a new equivalent circuit model for coplanar waveguide (CPW) structure on 3DIC. The silicon effects on series inductance were also studied by employing the modified Green functions with semiconductor images at a complex distance from spectral-domain analysis. --Abstract, page iii

Copper / low-k technological platform for the fabrication of high quality factor above-IC passive devices

Modern communication devices demand challenging specifications in terms of miniaturization, performance, power consumption and cost. Every new generation of radio frequency integrated circuits (RF-ICs) offer better functionality at reduced size, power consumption and cost per device and per integrated function. Passive devices (resistors, inductors, capacitors, antennas and transmission lines) represent an important part of the cost and size of RF circuits. These components have not evolved at the same level of the transistor devices, especially because their performance is strongly degenerated when they scale down in size. The low resistivity silicon used to build the transistors also imposes prohibitive levels of RF losses to these passive devices. Radio frequency microelectromechanical systems (RF MEMS) are enabling technologies capable to bring significant improvement in the electrical performances and expressive size and cost reduction of these functions, with unparallel introduction of new functionalities, unimaginable to attain when using bulky, externally connected discrete components. High quality factor (Q) inductors are amongst ones of the most needed components in RF circuits and at the same time ones that are most affected by thin metallization and substrate related losses, demanding considerable research effort. This thesis presents a contribution toward the development of thick metal fabrication technologies, covering also the design, modeling and characterization of high quality factor and high self-resonant frequency (SRF) RF MEMS passive devices, with a special emphasis on spiral inductors. A new approach using damascene-like interconnect fabrication steps associated to low κ dielectrics (polyimide), highly-conductive thick copper electroplating, chemical mechanical polishing (CMP) and tailored substrate properties delivered quality factors in excess of 40 and self resonant frequencies in excess of 10 GHz, performances in the current state-of-the-art for integrated spiral inductors built on top of silicon wafers. Furthermore, the developed process steps are compatible with back-end processing used to fabricate modern IC interconnects and have a low thermal budget (< 250 °C), what makes it a good choice to build above-IC passives without degenerating the performance of passivated RF-CMOS circuits. Deep reactive ion etching (DRIE) of quartz substrates was also studied for the fabrication of spiral inductors, offering excellent RF performances (Q exceeding 40 and SRF exceeding 7 GHz). A new doubly-functional quartz packaging concept for RF MEMS devices was developed. This technique process both sides of the packaging wafer: the top is used to embed high quality factor copper inductors while the bottom is thermo-mechanically bonded to another RF MEMS wafer, offering a semi-hermetic SU-8 epoxy-based seal. The bonding process was optimized for high yield, to be compatible with SF6-plasma-released MEMS and to present low level of RF losses. Band pass filters for the GSM (1.8 GHz) and WLAN (5.2 GHz) standards were fabricated and characterized by RF measurements and full wave electromagnetic simulations. Although further development is need in order to predict the frequency response accurately, insertion losses as low as 1.2 dB were demonstrated, levels that cannot be usually attained using on-chip passives. Systematic analysis, RF measurements, electromagnetic simulations and equivalent circuit extraction were used to model the behavior of the fabricated devices and establish a methodology to deliver optimum performances for a given technological profile and specified performance targets (quality factor, inductance and frequency bandwidth). A simple yet accurate physics-based analytical model for spiral inductors was developed and proved to be accurate in terms of loss estimation for thick metal layers. This model is capable to accurately describe the frequency-dependent behavior of the device below its first resonant frequency over a large device design space. The model was validated by both measurements and full wave electromagnetic simulations and is well suited to perform numeric optimization of designs. The proposed models were also systematized in a Matlab® toolbox

Inductors in high-performance silicon radio frequency integrated circuits : analysis, modeling, and design considerations

Spiral inductors are a key component of mixed-signal and analog integrated circuits (IC's). Such circuits are often fabricated using silicon-based technology, owing to the inherent low-cost and high volume production aspects. However, semiconducting substrate materials such as silicon can have adverse effects on spiral inductor performance due to the lossy nature of the material. Since the operating requirements of many high performance IC's demand reactive components that have high Quality Factor's (Q's), and are thus low loss devices, the need for accurate modeling of such structures over lossy substrate media is key to successful circuit design. The Q's of commonly available off-chip inductors are in the range of 50- 100 for frequencies ranging up to a few gigahertz. Since off-chip inductors must be connected through package pins, solder bumps, etc., which all contribute additional loss and thus lower the apparent Q of an external device, the typical on-chip Q requirement for a given RFIC design is generally lower than that for an off-chip spiral solution. However, a spiral inductor that was designed and fabricated originally in a low loss technology such as thin-film alumina may have substantially worse performance in regard to Q if it is used in a silicon-based technology, owing to the conductive substrate. For this reason, it is imperative that semiconducting substrate effects be accurately accounted for by any modeling effort for monolithic spirals in RFICs. This thesis presents a complete modeling solution for both single and multi-level spiral inductors over lossy silicon substrates, along with design considerations and methods for mitigation of the undesirable performance effects of semiconducting substrates. The modeling solution is based on Spectral Domain Approach (SDA) solutions for frequency dependent complex capacitive (i.e. both capacitance and conductance) parasitic elements combined with a quasi-magnetostatic field solution for calculation of the frequency dependent complex inductive (i.e. both inductance and resistance) terms. The effects of geometry and process variations are considered as well as the incorporation of Patterned Ground Shields (PGS) for the purpose of Q enhancement. Proposals for future extensions of this work are discussed in the concluding chapter

On-chip Spiral Inductor/transformer Design And Modeling For Rf Applications

Passive components are indispensable in the design and development of microchips for high-frequency applications. Inductors in particular are used frequently in radio frequency (RF) IC\u27s such as low-noise amplifiers and oscillators. High performance inductor has become one of the critical components for voltage controlled oscillator (VCO) design, for its quality factor (Q) value directly affects the VCO phase noise. The optimization of inductor layout can improve its performance, but the improvement is limited by selected technology. Inductor performance is bounded by the thin routing metal and small distance from lossy substrate. On the other hand, the in-accurate inductor modeling further limits the optimization process. The on-chip inductor has been an important research topic since it was first proposed in early 1990\u27s. Significant amount of study has been accomplished and reported in literature; whereas some methods have been used in industry, but not released to public. It is of no doubt that a comprehensive solution is not exist yet. A comprehensive study of previous will be first address. Later author will point out the in-adequacy of skin effect and proximity effect as cause of current crowding in the inductor metal. A model method embedded with new explanation of current crowding is proposed and its applicability in differential inductor and balun is validated. This study leads to a robust optimization routine to improve inductor performance without any addition technology cost and development