Yidnekachew S. Mekonnen

Embedded Multi-die Interconnect Bridge (EMIB) -- A High Density, High Bandwidth Packaging Interconnect

The EMIB dense MCP technology is a new packaging paradigm that provides localized high density interconnects between two or more die on an organic package substrate, opening up new opportunities for heterogeneous on-package integration. This paper provides an overview of EMIB architecture and package capabilities. First, EMIB is compared with other approaches for high density interconnects. Some of the inherent advantages of the technology, such as the ability to cost effectively implement high density interconnects without requiring TSVs, and the ability to support the integration of many large die in an area much greater than the typical reticle size limit are highlighted. Next, the overall EMIB architecture envelope is discussed along with its constituent building blocks, the package construction with the embedded bridge, die to package interconnect features. Next, the EMIB assembly process is described at a high level. Finally, high bandwidth signaling between the die is discussed and the link bandwidth envelope is quantified.

Comparative Study of Convolution and Order Reduction Techniques for Blackbox Macromodeling Using Scattering Parameters

In this paper, a fast convolution method using scattering parameters is presented for the macromodeling of blackbox multiport networks. The method is compared to model-order reduction passive macromodeling techniques in terms of robustness and computational efficiency. When scattering parameters are used as the transfer functions, convolution calculations can be accelerated to achieve superior performance and the resulting procedure leads to a robust, accurate, and efficient macromodel generation scheme. This paper examines the formulation of the convolution method. Model-order reduction techniques are reviewed and benchmark comparisons are performed.

Acceleration of Spectral Domain Approach for Generalized Multilayered Shielded Microstrip Interconnects Using Two Fast Convergent Series

A simple and versatile approach for the acceleration of the spectral domain approach for generalized shielded microstrip interconnects is presented. This approach uses asymptotic expansion for the Bessels function and the Greens function followed by an approximation of infinite summation using two fast convergent sine cosine series. The asymptotic expansion coefficients of the Greens functions are found by a combination of analytical and numerical approaches. The infinite summation involved in the computation of the elements of the Galerkin matrix is accelerated using two fast convergent sine cosine series. The use of a few entire-domain basis functions gives very accurate results for the propagation constants for any mode in the general case of a multilayered shielded microstrip line. In addition to this, closed-form expressions are developed to choose the number of terms and some parameters to adaptively accelerate the convergence of the second type of fast convergent series for a given accuracy. This approach can be extended to handle multiple interconnects in the same layer and in different layers and also to include the effect of finite thickness and conductivity.

Efficient and accurate modeling of effective medium for interconnects in lossy shielded layered medium using fast convergent series

An approach for fast and accurate modeling of multiple interconnects in lossy shielded multilayered medium using the spectral domain approach has been presented. The acceleration in the evaluation of the elements of the MoM matrix has been achieved using asymptotic approximation of the Greens function and the basis function followed by a quick approximation of the infinite series summation using a combination of two different types of fast convergent series (FCS). This approach is very versatile and can also be used to accelerate the spectral domain approach after inclusion of finite thickness and conductivity approximations. Also, it can be used to accelerate the spectral domain approach for multiple interconnects in different layers.

A novel approach to accelerate spectral domain approach for shielded microstrip lines using the Levin transformations and summation-by-parts

A novel approach, which uses the Levin transformations or the hybrid of the Levin transformations and summation-by-parts, is presented for the acceleration of the slowly convergent series that asymptotically behave as 1/nk and sinusoidal functions divided by nk. This approach does not need the asymptotic expansion for the Greens functions and the Bessel functions, which saves the work for finding the asymptotic expansion coefficients. This approach has been applied to the acceleration of the infinite series summation in the shielded microstrip problem solved by the spectral domain approach (SDA) for obtaining accurate solutions of the propagation constant. Effective criteria of calculating the number of terms used in direct summation before applying the Levin transformations have been developed in this application. This approach can be easily extended to handle the multilayered shielded microstrip structure.

Homogenization of Periodic Objects Embedded in Layered Media

An effective medium modeling technique is proposed to homogenize the periodic objects embedded in layered media. The homogenization is based on the same scattering coefficients. An integral equation based approach is adopted to solve the scattering problem of original structures. Our modeling results are compared with Maxwell-Garnett mixing formula and published results. Good agreements have been observed. Periodic metal patches embedding in layered dielectric structure is fabricated and measured to validate the modeling technique. The difference between experiment results and proposed modeling results is less than 3%.

Acceleration of Spectral Domain Immitance Approach for Generalized Multilayered Shielded Microstrips Using the Levin’s Transformation

This letter reports on the acceleration of the infinite series summation in the multilayered shielded microstrip with multiple strips by using the spectral domain immitance approach (SDIA) and the Levins transformation. This technique does not need the asymptotic expansion for the Greens functions and the basis functions by recasting the matrix elements into the form that is evaluated by the Levins transformation. It greatly saves the work for finding the asymptotic expansion coefficients. Using only the first leading term extraction, the overall acceleration performance is further improved. Convergence properties of SDIA by using this method match with or are even better than other acceleration techniques with high order leading term extraction.

The extrapolation methods in acceleration of SDA for shielded microstrip lines

Two popular extrapolation methods, Shanks and Levins transformations, are compared to calculate slowly convergent series. The Levin v transform works well for both alternating and monotonic series. Numerical results indicate that the v transform converges similarly to super convergent series (SCS) method in spectral domain approach (SDA) for shielded microstrip lines. But the new approach does not involve the leading term extraction.

Equivalent model for shielded microstrip transmission lines over lossy layered substrates

An equivalent model for a lossy shielded microstrip line on layered media is constructed by replacing the layered media with a single effective medium and a detailed analysis of its validity at different frequencies and different range of dimensions has been presented for application to on chip interconnects. The relative permittivity for a single layer microstrip which results in the same propagation constant for the dominant mode as the layered one at a given frequency is considered to be the equivalent. The results show that this model is frequency independent for layered structures when the given frequency and frequency of operation are less than the transition frequency (i.e. the frequency at which there is a significant change in the equivalent dielectric constant (∊req)). For frequencies higher than the transition frequency the equivalent model is not frequency independent but it gives good results for the higher order mode although it is derived using the dominant mode. Also it is seen that at low frequency ∊req depends on the layers near to the signal metal but at higher frequencies it depends on the layer with the highest value of ∊r irrespective of its location w.r.t to the metal strip.

Efficient spectral domain analysis of multilayered shielded microstrip using two super convergent series

An efficient approach to speed up the spectral domain analysis for the general case of shielded microstrip has been presented. It uses asymptotic expansion for the Bessels function and the Greens function which are involved in the computation of the elements of the Galerkin matrix. The coefficients in the asymptotic expansion of the Greens functions are obtained by a combination of analytical and numerical approaches. Efficient computation of the infinite summation obtained after leading term extraction is done using two different super convergent sine cosine series. Very accurate results for the propagation constants in the general case of a multilayered shielded microstrip line can be obtained using a few basis functions.