Siming Pan

Modeling and Application of Multi-Port TSV Networks in 3-D IC

Through-silicon-via (TSV) enables vertical connectivity between stacked chips or interposer and is a key technology for 3-D integrated circuits (ICs). While arrays of TSVs are needed in 3-D IC, there only exists a frequency-dependent resistance, inductance, conductance and capacitance circuit model for a pair of TSVs with coupling between them. In this paper, we develop a simple yet accurate circuit model for a multiport TSV network (e.g., coupled TSV array) by decomposing the network into a number of TSV pairs and then applying circuit models for each of them. We call the new model a pair-based model for the multiport TSV network. It is first verified against a commercial electromagnetic solver for up to 20 GHz and subsequently employed for a variety of examples for signal and power integrity analysis.

An equivalent three-dipole model for IC radiated emissions based on TEM cell measurements

An equivalent dipole model is proposed in this paper to represent the source of radiated electromagnetic emissions from an integrated circuit (IC). The height of an IC is usually much smaller than its length and width, so only three dipole moments are sufficient to characterize an IC in terms of its electromagnetic emissions. The dipole moments can be extracted from three TEM cell measurements. The radiated fields from the IC can then be calculated based on the extracted dipole sources. This IC emission model with three dipole moments is validated using the far-field measurements in a semi anechoic chamber for a test IC. For complex structures, it is desirable that the extracted dipole moments can be incorporated into a commercial full-wave tool as equivalent sources to simulate the radiations from an IC. This is demonstrated using an approach developed in this paper.

Analytical expressions for transfer function of supply voltage fluctuation to jitter at a single-ended buffer

In this paper, the transfer function of a supply voltage fluctuation to jitter is analytically solved for a single ended buffer in closed-form expressions. The expressions for the jitter transfer function is validated by comparison with HSPICE simulation, and applied to an example for statistical jitter estimation.

Equivalent mixed-mode characteristic impedances for differential signal vias

Differential signal via structures in multi-layer printed circuit boards (PCBs) and packages are studied using an equivalent coupled multi-conductor transmission-line model. Thus, easy-to-understand transmission-line concepts, such as mixed-mode characteristic impedances and propagation constants, can be used to characterize the performance of differential signal via structures in a signal path. The closed-form expressions of per-unit-length parameters in the equivalent coupled multi-conductor transmission-line model are derived based on a physics-based via circuit model with parallel-plane impedances and via-plate capacitances. Mode conversions are discussed for different via structures. Effects of geometrical parameters on equivalent differential via impedances are studied in the paper as well. The proposed method provides a straightforward approach to design differential via structures for better signal integrity.

Equivalent transmission-line model for vias connected to striplines in multilayer print circuit boards

Vias are typical discontinuities for high-speed signal transmission in printed circuit boards. Previous work has studied the through-hole via connections from the top layer to the bottom between microstrip traces and proposed an equivalent transmission-line model for impedance matching between traces and vias. In this paper, the equivalent transmission-line model is extended for the via structures connected to striplines based on modal decomposition. Both single-ended and differential cases are discussed, and the effects of the model parameters on the performance of signal transition are also investigated. The extended equivalent transmission-line model is accurate and fast to be embedded in circuit simulators for via and link-path analysis. Further, it could provide straightforward criteria to design and optimize via structures for better signal integrity.

Optimization of power delivery network design for multiple supply voltages

Great power demands and low-power techniques have increased the requirements on the power delivery network, especially with multiple supply voltages. In this paper, methods for optimizing decoupling capacitor allocation and placement for multiple power nets are presented. Based on a physics-based circuit model extraction for the PCB-PDN structures, a two-level optimization procedure is proposed. First, stackup and potential locations and patterns for power and ground vias are optimized based on design guidelines. In the second step, distribution and allocation of decoupling capacitors are optimized targeting for the system-level PDN performance among multiple supply voltages by an integer linear programming (ILP) algorithm. The physical properties of the decoupling capacitors are described as circuit elements in the equivalent circuit model. Thus, instead of full-wave analysis, only efficient circuit simulations are needed in the optimization process. The proposed optimization methods are applied in a complex system including integrated circuit with multiple supply voltages. Compared to the original unoptimized design, the optimized PDN impedance for the worst designed power nets improved 400% with the same cost of decoupling.

Fast admittance computation for TSV arrays

A fast method to calculate the admittance matrix of Through Silicon Vias (TSVs) is proposed in this paper. The silicon dioxide layers are equivalently modelled using the bound charge on the conductor surfaces as well as on the dielectric interface between the silicon dioxide and the silicon regions. Unknown surface densities of both the free and bound charge are expanded using the axial harmonics. Galerkins method is then applied to obtain the capacitance and conductance matrices. The proposed method is validated with a full-wave 2D cross-sectional analysis tool for a typical TSV pair structure. Comparisons with popular closed-form expressions are also discussed.

Capacitance Calculation for Via Structures Using an Integral Equation Method Based on Partial Capacitance

In this paper, a new integral equation formulation for via structures is developed for the capacitance extraction between vias and planes. The formulation is initially developed for axially symmetric geometries and then extended to axially asymmetric geometries by changing the circular ring cells to arc cells. The extended method can be used to calculate the shared-antipad via structure, which is widely used in high-speed differential signal interconnects. In addition, the image theory is used to handle inhomogeneous media, and a new technique is given to reduce computational costs for via-to-plane structures based on properties of the capacitance-matrix elements. The proposed method is validated with a commercial finite element method-based tool for several practical via structures. The extracted capacitance is also incorporated into the physics-based via model and validated with full-wave simulations.

Applying feature selective validation (FSV) as an objective function for data optimization

Feature Select Validation (FSV) is a widely used validation method for data comparison. FSV provides a quantitative standard to describe the similarity between two sets of data. In this paper, the application of the FSV technique is extended to data optimization. The raw data obtained from simulations or measurements are often non-ideal for further processing. Several techniques, such as data perturbation, can be used to improve the data quality in certain aspects. However, after modifications the new data could be very different to the original one. Using FSV as an objective function for the optimization process is discussed in this paper, in an example of causality enforcement, to ensure the enforced casual data has the minimum deviations from the original data. The results demonstrate that the proposed approach in this paper is effective for data modification and optimization.

Comparison among different via models based on Feature Selective Validation technique

A new approach is proposed in this paper to validate different uncertain approaches without knowing a standard reference by applying the Feature Selective Validation (FSV) technique. New reference is established by the weighted average of the various approaches. Four via modeling methods including physics-based circuit model, equivalent transmission line model, multiple scattering model, and full wave model are compared and validated by the approach proposed in this paper to illustrate the effectiveness of different via modeling techniques.