Scott List

Experimental validation of crosstalk simulations for on-chip interconnects using S-parameters

Since the design of advanced microprocessors is based on simulation tools, accurate assessments of the amount of crosstalk noise are of paramount importance to avoid logic failures and less-than-optimal designs. With increasing clock frequencies, inductive effects become more important, and the validity of assumptions commonly used in simulation tools and approaches is unclear. We compared accurate experimental S-parameters with results derived from both magneto-quasi-static and full-wave simulation tools for simple crosstalk structures with various capacitive and inductive couplings, in the presence of parallel and orthogonal conductors. Our validation approach made possible the identification of the strengths and weaknesses of both tools as a function of frequency, which provides useful guidance to designers who have to balance the tradeoffs between accuracy and computation expenses for a large variety of cases

A novel technique for full-wave modeling of large-scale three-dimensional high-speed on/off-chip interconnect structures

This paper presents a novel, rigorous, and fast method for full-wave modeling of high-speed interconnect structures. In this method, the original wave propagation problem is represented into a generalized eigenvalue problem. The resulting eigenvalue representation can comprehend conductor and dielectric losses, arbitrary dielectric and conductor configurations, and arbitrary materials such as dispersive, and anisotropic media. The edge basis function is employed to accurately represent the unknown field, and the triangular element is adopted to flexibly model arbitrary geometry. A mode-matching technique applicable to lossy system is developed to solve large-scale 3D problems by using 2D-like CPU time and memory. A circuit-based extraction technique is developed to obtain S-parameters from the unknown fields. The proposed technique can generate S-parameters, full-wave RLGC, propagation constants, characteristic impedances, voltage, current, and field distributions, and hence yield a comprehensive representation of interconnect structures. Experimental and numerical results demonstrate its accuracy and efficiency.

Experimental validation of crosstalk simulations for on-chip interconnects at high frequencies using S-parameters

Since advanced microprocessors are designed based on simulation tools, accurate assessments of the amount of crosstalk noise are of paramount importance to avoid logic failures and less-than-optimal designs. With increasing clock frequencies, inductive effects become more important, and the validity of assumptions commonly used in simulation tools and approaches is unclear. We compared accurate experimental S-parameters with results derived from both magneto-quasi-static and fullwave simulation tools, for simple crosstalk structures with various capacitive and inductive couplings, in the presence of parallel and orthogonal conductors. Our validation approach made possible the identification of the strengths and weaknesses of both tools as a function of frequency, which provides useful guidance to designers who have to balance the trade-offs between accuracy and computation expenses for a large variety of cases.

Determining the shape and periodicity of nanostructures using small‐angle X‐ray scattering

The semiconductor industry is exploring new metrology techniques capable of meeting the future requirement to characterize three-dimensional structure where the critical dimensions are less than 10 nm. X-ray scattering techniques are one candidate owing to the sub-A wavelengths which are sensitive to internal changes in electron density. Critical-dimension small-angle X-ray scattering (CDSAXS) has been shown to be capable of determining the average shape of a line grating. Here it is used to study a set of line gratings patterned via a self-aligned multiple patterning process, which resulted in a set of mirrored lines, where the individual line shapes were asymmetric. The spacing between lines was systematically varied by sub-nm shifts. The model used to simulate the scattering was developed in stages of increasing complexity in order to justify the large number of parameters included. Comparisons between the models at different stages of development demonstrate that the measurement can determine differences in line shapes within the superlattice. The shape and spacing between lines within a given set were determined to sub-nm accuracy. This demonstrates the potential for CDSAXS as a high-resolution nanostructure metrology tool.

10nm three-dimensional CD-SEM metrology

The shape and dimensions of a challenging pattern have been measured using a model-based library scanning electron microscope (MBL SEM) technique. The sample consisted of a 4-line repeating pattern. Lines were narrow (10 nm), asymmetric (different edge angles and significant rounding on one corner but not the other), and situated in a complex neighborhood, with neighboring lines as little as 10 nm or as much as 28 nm distant. The shape cross-section determined by this method was compared to transmission electron microscopy (TEM) and critical dimension small angle x-ray scattering (CD-SAXS) measurements of the same sample with good agreement. A recently-developed image composition method was used to obtain sharp SEM images, in which blur from vibration and drift were minimized. A Monte Carlo SEM simulator (JMONSEL) produced a model-based library that was interpolated to produce the best match to measured SEM images. Three geometrical and instrument parameterizations were tried. The first was a trapezoidal geometry. In the second one corner was significantly rounded. In the last, the electron beam was permitted to arrive with stray tilt. At each stage, the fit to the data improved by a statistically significant amount, demonstrating that the measurement remained sensitive to the new parameter. Because the measured values represent the average unit cell, the associated repeatabilities are at the tenths of a nanometer level, similar to scatterometry and other area-averaging techniques, but the SEM’s native high spatial resolution also permitted observation of defects and other local departures from the average.

Evaluation of the effect of data quality on the profile uncertainty of critical dimension small angle x-ray scattering

Abstract. A line grating prepared via a self-aligned quadruple patterning method was measured using critical dimension small angle x-ray scattering. A Monte Carlo Markov chain algorithm was used to analyze the uncertainty of the model fit over subsets of the full angular range and for a time series with decreasing signal-to-noise in order to determine the effect of the data quality on the final profile shape uncertainty. These results show how the total measurement time can be reduced while maintaining satisfactory profile shape uncertainty. We found that the typical measurement conditions are highly oversampled and can be reduced considerably with only marginal effect on the shape uncertainty. A comparison is made between the synchrotron measurements and a laboratory system, demonstrating that both measurements result in similar structures.