Substrate Skin Effect Research Articles

A Wideband Scalable and SPICE-Compatible Model for On-Chip Interconnects Up to 110 GHz

A fully scalable and SPICE compatible wideband model of on-chip interconnects valid up to 110 GHz is presented in this paper. The series branches of the proposed multisegment model consist of an RL ladder network to capture the skin and proximity effects, as well as the substrate skin effect. Their values are obtained from a technique based on a modified effective loop inductance approach and complex image method. A CG network is used in the shunt branches of the model, which accounts for capacitive coupling through the oxide and substrate loss due to the electrical field, as well as the impact of dummy metal fills. The values of these elements are determined by analytical and semiempirical formulas. The model is validated by a full-wave electromagnetic field solver, as well as measurements. The simulated S-parameters of the model agree well with the measured S-parameters of on-chip interconnects with different widths and lengths over a wide frequency range from dc up to 110 GHz.

High frequency modelling approach of on‐chip interconnects considering conductor and substrate skin effects

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.

Characterization and analysis of the effects of silicon‐substrate thickness on inductor performance

AbstractIn this paper, the effects of the thickness of silicon substrate with backside metalization on inductor performance are investigated, and the experimental results show that thinner substrate with backside metalization results in smaller inductance, lower quality factor, and slightly higher resonant frequency. For a circular spiral inductor with substrate thickness of 50 μm, the inductance L of the 8‐turn inductor would be degraded by about 22%, compared to that with substrate thickness of 150 μm; correspondingly, the quality factor Q decreases by about 16%. The measured results also show that the inductor performance with substrate thickness of 150 μm and above does not depend upon the substrate thickness. The optimization of inductor performance involves a trade‐off between the “substrate skin effect (SSE)” and thermal conductivity. It is believed that the demonstrated results will be useful for the design and packaging of RF integrated circuits (RFICs). © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 41: 70–73, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20050

Highly Accurate Quasi-Static Modeling of Coupled Interconnects in CMOS Technology

A new analytic model is presented (the model is based on the induced current density distribution inside silicon substrate) to calculate frequency dependent mutual inductance and resistance per unit length of coupled on-chip interconnects in CMOS technology. The validity of the proposed model has been checked by a comparison with a quasi-TEM spectral domain numerical simulation and equivalent-circuit modeling procedure. It is found that the silicon semiconducting substrate skin effect must be considered for the accurate prediction of the high-frequency characteristics of VLSI interconnects.

Highly accurate closed form approximation for frequency-dependent line impedance of a lossy silicon substrate IC interconnect

A new analytic model is presented to calculate the frequency-dependent distributed self and mutual inductance and the associated distributed series resistance of silicon semiconducting IC interconnects. The method is based on the induced current density distribution inside silicon substrate. The validity of the proposed model has been checked by a comparison with a quasi-TEM spectral domain approach and equivalent-circuit modeling procedure. It is found that the silicon semiconducting substrate skin effect must be considered for the accurate prediction of the high-frequency characteristics of IC interconnects.

Simple and accurate expressions for distributed mutual inductance and resistance of semiconducting interconnects

An analytic model is presented (based on the induced current density distribution inside a silicon substrate) to calculate the frequency-dependent distributed mutual inductance and the associated distributed series mutual resistance of silicon semiconducting integrated circuit (IC) interconnects. The validity of the proposed model was checked by a comparison with a quasi-static transmission electron microscopy spectral domain approach and an equivalent-circuit modeling procedure. It is found that the silicon semiconducting substrate skin effect must be considered for accurate prediction of the high-frequency characteristics of IC interconnects.

Distributed inductance and resistance per‐unit‐length formulas for VLSI interconnects on silicon substrate

AbstractA new analytic model is presented (the model is based on the induced current density distribution inside silicon substrate) to calculate the frequency‐dependent distributed inductance and the associated distributed series resistance of silicon semiconducting VLSI interconnects. The validity of the proposed model has been checked by a comparison with CAD‐oriented modeling methodology in conjunction with a quasi‐TEM spectral‐domain approach. It is found that the silicon semiconducting substrate skin effect must be considered for the accurate prediction of the high‐frequency characteristics of VLSI interconnects. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 302–304, 2001.

Characterization and modeling of multiple coupled on-chip interconnects on silicon substrate

A quasi-magnetostatic integral formulation approach is applied to compute the frequency-dependent series resistance and inductance parameters for coupled microstrip on-chip interconnects on silicon. The method is based on the simultaneous discretization of interconnect conductors and silicon substrate, and takes into account the substrate skin effect (eddy currents), as well as the conductor skin and proximity effects. An efficient equivalent-circuit model based on "effective substrate current loops" is extracted from the frequency-dependent R and L parameters for a class of coupled microstrip-type on-chip interconnects. The frequency response of the proposed model consisting of only passive R, L elements agrees well with the broad-band characteristics of the distributed resistance and inductance parameters of the interconnect obtained by electromagnetic simulation. Model extraction results are presented for asymmetric coupled interconnects to demonstrate the proposed method.