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In this paper a method for analysis and modelling of transmission interconnect lines with zero or nonzero thickness on Si–SiO₂ substrate is presented. The analysis is based on semi‐analytical expressions for the frequency‐dependent transmission line admittances. 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. This new model represents narrow and thick line interconnect behaviour over a wide range of frequencies up to 20 GHz. The accuracy of the developed method in this work is validated by comparing with the rigorous simulation data obtained by full‐wave electromagnetic solver and CAD‐oriented equivalent‐circuit modelling approach. The response of the proposed model is shown to be in good agreement with the frequency‐dependent capacitance and conductance characteristics of general coupled multiconductor on‐chip interconnects.

Simple and accurate high frequency modelling approach of on‐chip interconnects on a lossy silicon substrate, that considers conductor and substrate skin effects, is presented. The closed‐form formulas for the frequency‐dependent series impedance parameters are obtained using a closed‐form integration method and the vector magnetic potential equation. The proposed frequency‐dependent inductance L(f) and resistance R(f) per unit length formulas are shown to be in good agreement with the electromagnetic solutions.

New analytical approximation for the frequency‐dependent impedance matrix components of symmetric VLSI interconnect on lossy silicon substrate are derived. The results have been obtained by using an approximate quasi‐magnetostatic analysis of symmetric coupled microstrip on‐chip interconnects on silicon. We assume that the magnetostatic field meets the boundary conditions of a single isolated infinite line; therefore, the boundary conditions for the conductors in the structure are approximately satisfied. The derivation is based on the approximate solution of quasi‐magnetostatic equations in the structure (dielectric and silicon semi‐space), and takes into account the substrate skin‐effect. Comparisons with published data from circuit modeling or full‐wave numerical analyses are presented to validate the inductance and resistance expressions derived for symmetric coupled VLSI interconnects. The analytical characterization presented in this paper is well situated for inclusion into CAD codes in the design of RF and mixed‐signal integrated circuits on silicon.

This paper highlights the electrical behaviour of the interconnects on a 120‐pin Ball Grid Array (BGA) package from 500 MHz upto 8 GHz. The measurements are made using IMEC's MCM‐D thin film technology as the substrate and with a test set‐up called MoPoM (MCM‐on‐Package‐on‐MCM). The interconnects are classified based on length and measured with adjacent interconnects grounded as well as floating. Circuit models are extracted from the measurement and the simulation respectively for an RF interconnect including the wirebond. Comparison of the circuit models with each other and with the measurement show agreement atleast upto 6 GHz. One of the interconnects is also measured before and after globtopping and a considerable change in the impedance match is observed. The effect of package loading is found to be negligible.

High Q on‐chip inductors and low loss on‐chip interconnects and transmission lines are an important roadblock for the further development of Si‐based technologies at RF and microwave frequencies. In this paper, inductors are realized on standard Si wafers (20 Ω.cm) using MCM‐D processing. This consists of realizing two low K dielectric layers (BCB) and a thick Cu interconnect layer. Inductors with 5 μm lines and spaces are demonstrated for a 5 μm thick Cu layer, hereby leading to a very compact and high performance inductors: Q‐factors in the range of 25 to 30 have been obtained for inductances in the range of 1 to 5 nH. It is also shown how the Q‐factor and resonance frequency vary as a function of the inductor layout parameters and the thickness of the BCB and Cu layers. The realized 50 Ω CPW lines (lateral dimension of 40 μm) have a measured loss of only 0.2 dB/mm at 25 GHz.

This study aims to design and validate a theoretical model for capacitive imaging (CI) sensors that incorporates the interelectrode shielding and surrounding shielding electrodes. Through experimental verification, the effectiveness of the theoretical model in evaluating CI sensors equipped with shielding electrodes has been demonstrated.

The study begins by incorporating the interelectrode shielding and surrounding shielding electrodes of CI sensors into the theoretical model. A method for deriving the semianalytical model is proposed, using the renormalization group method and physical model. Based on random geometric parameters of CI sensors, capacitance values are calculated using both simulation models and theoretical models. Three different types of CI sensors with varying geometric parameters are designed and manufactured for experimental testing.

The study’s results indicate that the errors of the semianalytical model for the CI sensor are predominantly below 5%, with all errors falling below 10%. This suggests that the semianalytical model, derived using the renormalization group method, effectively evaluates CI sensors equipped with shielding electrodes. The experimental results demonstrate the efficacy of the theoretical model in accurately predicting the capacitance values of the CI sensors.

The theoretical model of CI sensors is described by incorporating the interelectrode shielding and surrounding shielding electrodes into the model. This comprehensive approach allows for a more accurate evaluation of the detecting capability of CI sensors, as well as optimization of their performance.

This paper presents a novel mesoscale RF (mRF) relay that integrates advanced high resolution stereolithography (SL) and micro wire electro discharge machining (μEDM) technologies. Methods and infrastructure for reliable batch assembly of electromechanical actuators and structural parts less than 5 mm³ in volume are described. Switches made using these techniques are expected to have greater power handling capability relative to current micro RF relay products.

The conjecture is that the integration of SL and similar rapid additive manufacturing with other mesofabrication technologies can yield innovative miniature products with novel capabilities. A series of mRF prototypes consisting of a contact mechanism and actuator with return spring were fabricated assembled, inspected, and characterized for electromechanical performance. Characterization results led to specific conclusions regarding capabilities of the mRF product, and the integrated manufacturing technique.

The microassembly apparatus and epoxy‐based fastening system led to durable prototypes within 4 h (excluding a 16‐24 h cure cycle). Relay stroke ranged from 560 to 1,650 μm indicating a relative assembly accuracy of 90 percent. Prototypes demonstrated insertion loss of 1.3 dB at 100 MHz and isolation of better than 30 dB through 300 MHz.

Results indicated that fully functional and robust mesoscale relays are possible using integrated manufacturing with SL. However, prototypes exhibited high contact resistance and lacked assembly precision in the context of contact mechanism stroke. Opportunities exist to reduce contact resistance and switching time.

The research provides a practical new product application for integrated mesoscale rapid manufacturing.

This work represents one of the first examples of a mesoscale relay rapidly manufactured with a combination of μEDM and SL components.

Present 3D electromagnetic simulators have high accuracy but they are time and memory expensive. Owing to a fast and simple expression for inductance is also necessary for initial inductor design. In this paper, new efficient methods for total inductance calculation of meander inductor, are given. By using an algorithm, it is possible to predict correctly all inductance variations introduced by varying geometry parameters such as number of turns, width of conductor or spacing between conductors.

The starting point for the derivation of the recurrent formula is Greenhouse theory. Greenhouse decomposed inductor into its constituent segments. Meander inductor is divided into straight conductive segments. Then the total inductance of the meander inductor is a sum of self‐inductances of all segments and the negative and positive mutual inductances between all combinations of straight segments. The monomial equation for the total inductance of meander inductor has been obtained by fitting procedure. The fitting technique, using the method of least squares, finds the parameters of the monomial equation that minimize the sum of squares of the error between the accurate data and fitted equation. The paper presents new expression for inductance of meander inductor, in the monomial form, which is suitable for optimization via geometric programming. The computed inductances are compared with measured data from the literature.

The first, recurrent, expression has the advantage that it indicates to the designer how the relative contributions of self, positive, and negative mutual inductance are related to the geometrical parameters. The second expression presents the inductance of the meander inductor in the monomial form, so that the optimization of the inductor can be done by procedure of the geometric programming. Simplicity and relatively good accuracy are the advantages of this expression, but on the other hand the physical sense of the expression is being lost. Thus, the effects of various geometry parameters on inductance are analyzed using two expressions and the software tool INDCAL.

Applied flexible efficient methods for inductance calculation of meander inductor are able to significantly increase the speed of RF and sensor integrated circuit design.

For the first time a simple expression for fast inductance calculation for meander inductor in monomial form is presented. It is explained how such an expression is generated, which can be directly implemented in circuit simulators.