Dusan Petranovic

On accurate full-chip extraction and optimization of TSV-to-TSV coupling elements in 3D ICs

In this paper, we present a multiple-TSV based TSV-to-TSV coupling model and extraction methods that consider the impact of depletion region, the silicon substrate effect, and the electrical field distribution around TSVs. Our studies show that these factors have a significant impact on the individual and full-chip scale TSV-to-TSV coupling. Our effort leads to a simplified coupling model that is accurate and efficient on timing, power, and signal integrity in full-chip scale. In order to alleviate the coupling noise in full-chip level 3DIC, we propose grounded guard rings that are more effective than grounded TSV insertion. Results show that our approach reduces coupling noise on TSV nets up to 27.3% with only 7.65% area overhead.

Silicon Effect-Aware Full-Chip Extraction and Mitigation of TSV-to-TSV Coupling

This paper presents a silicon effect-aware multiTSV model. Through-silicon-via (TSV) depletion region, silicon substrate discharging path and electrical field distribution around TSV neighbor are modeled and studied in full-chip design. Verification with field solver and full-chip TSV-to-TSV coupling analysis in both the worst case and the average case show this model is accurate and efficient. It is found that 3-D nets receive more noise than their 2-D counterparts due to TSV-to-TSV coupling. To alleviate this coupling noise on TSV nets, two new optimization methods are investigated. One way is to utilize guard rings around the victim TSV so as to form a stronger discharging path, an alternative approach is to adopt differential signal transmission to improve noise immunity. These techniques have been implemented on 3-D IC designs with TSVs placed regularly or irregularly. Full-chip analysis results show that our approaches are effective in noise reduction with small area overhead.

Robust verification of 3D-ICs: Pros, cons and recommendations

A robust verification methodology for 3D-IC design is presented. This approach addresses the challenge of delivering a familiar verification solution with minimal disruption to existing design and verification flows. The proposed method provides a generic framework that allows users to specify their own 3D-IC design stacks for verification with TSVs, flip-chips or wire-bonded dies.

Simple and Accurate Models for Capacitance Considering Floating Metal Fill Insertion

In this paper, we analyze and model the impact of floating dummy fill on the signal capacitance considering various parameters including signal dimensions, dummy shape and dimensions. Intra-layer dummy has its greatest impact on coupling capacitance while inter-layer dummy has larger impact on the ground capacitance component. Based on this analysis, we propose simple capacitance models (Cc for intra-layer dummy and Cg for inter-layer dummy). To consider realistic cases with both signals and metal fill in adjacent layers, we apply a weighting function approach to the Cg model. We verify this model using benchmark circuits and find that total net capacitance with floating fill can be extracted within ~1% of field solver results on average with total extraction runtime reductions of up to 40%. When evaluating the incremental capacitance due to fill alone, average error of the models range from 2%-15% across benchmarks and fill-related runtime overhead is reduced by 60%-88%.

Fast and Accurate Full-chip Extraction and Optimization of TSV-to-Wire Coupling

In this paper, for the first time, we model and extract the parasitic capacitance between TSVs and their surrounding wires in 3D IC. For a fast and accurate full-chip extraction, we propose a pattern-matching-based algorithm that considers the physical dimensions of TSVs and neighboring wires and captures their field interactions. Our extraction method is accurate within 1.9% average error for a full-chip-level design while requiring negligible runtime and memory compared with a field solver. We also observe that TSV-to-wire capacitance has a significant impact on the noise of TSV-based connections and the longest path delay. To reduce TSV-to-wire coupling, we present two full-chip optimization methods, i.e., increasing KOZ and guard ring protection that are shown to be highly effective in noise reduction with minimal overhead.

An effective loop inductance model for general non-orthogonal interconnect with random capacitive coupling

We propose a first-ever analytic inductance model for practical on-chip interconnects with random signal lines. Validity of the effective loop inductance approach and determination of return paths through random capacitive coupling are investigated using a full-wave solver, leading to a frequency-dependent RLC model. Non-orthogonal interconnects are also investigated and included in our model.

Including inductance in static timing analysis

In this paper analytical expressions are derived for effective load capacitances of RLC interconnects to accurately estimate both the propagation delay and transition time at the output of a CMOS gate. The new effective capacitance calculation technique poses no extra complexity as compared to the RC based approaches but can accommodate inductance. These new expressions are derived based on a generalized driving point admittance. The generalized driving point admittance takes inductance into consideration and hence accounts for the inductive shielding that in some cases can even exceed the resistive shielding in current technologies. Another improvement in the new effective capacitance calculation method is the utilization of a more general waveform shape that accounts for the non-monotonic behavior due to inductance effects. It is shown throughout the paper that two effective capacitances are required for accurate estimation of the propagation delay and rise time with an RLC interconnect load. Simulation results show that the error in propagation delays and rise times when neglecting inductance can be over 60% as compared to an RLC model in realistic interconnects. On the other hand, simulations show that the propagation delay and rise time maximum errors associated with the proposed approach are less than 10% as compared to SPICE.

Multi-TSV and E-Field Sharing Aware Full-chip Extraction and Mitigation of TSV-to-Wire Coupling

The through-silicon-via (TSV) introduces new parasitic components into 3-D ICs. This paper presents a novel method of extracting the parasitic capacitance between TSVs and their surrounding wires. For the first time, we examine electrical field (E-field) sharing effects from multiple TSVs and neighboring wires and their impact on timing, power, and noise with full-chip sign-off analyses. For fast and accurate full-chip extraction, we propose a pattern-matching algorithm that accounts for the physical dimensions of multiple TSVs and neighboring wires and captures all E-field interactions. Compared with the average error of a field solver, that of our extraction method, which requires only 2.4 s runtime and negligible memory for a full-chip 64-point fast Fourier transform (FFT64) design with 330 TSVs, is 0.063fF. Upon extraction of TSV-related parasitics, we observe that TSV-to-wire capacitance significantly increase average TSV net noise and the longest path delay. To reduce TSV-to-wire coupling, we implement two full-chip optimization methods and show that increasing the minimum distance between TSVs and neighboring wires reduces both coupling noise and the aggressor count. Thanks to E-field sharing from grounded wire guard rings, victim TSVs are more effectively shielded from aggressor noise. A full-chip analysis shows that these methods are highly effective in reducing noise with only slight impact on timing and area.

A Novel Moment Based Framework for Accurate and Efficient Static Timing Analysis

A novel methodology for accurate and efficient static timing analysis is presented in this paper. Our methodology uses the traditional cell library table structure with one modification. The cell library tables are filled with the gate output signal moments instead of the gate output 50% delay and output slew. Using only few moments gives much better accuracy and visibility for the gate output waveform than using the time domain information. Simple convolution of the gate output moments with the interconnect moments yields the signal moments at the stage output. The parameters of the gate input signal, which are used for the table access of the successive stage, are directly computed from the predecessor stage output moments using the closed form expressions without having to explicitly transform the frequency domain moments to time domain. Thus, the interconnects and the gates are treated in a unified moment-based homogeneous framework. The proposed approach inherits the classical cell library tables approach efficiency with even reduced computation complexities. As compared to the classical cell library table approach, the proposed approach accounts for the increasingly nonlinear and non-monotonic waveform shapes which are prohibitively difficult to represent in the classical approaches. In contrary to the classical approaches, increasing the accuracy in the novel approach is made flexible and can be achieved by simply using more moments. To illustrate the concept and prove its merits, multiple examples are presented with 2-3 moments which maintain accuracy within 1%-3% as compared to SPICE.

Resistance matrix in crosstalk modeling for multiconductor systems

A complete modal analysis is introduced to derive the crosstalk voltage waveform in multiconductor coupled systems. In addition to the capacitance and inductance matrices, it also includes a resistance matrix. The off diagonal terms of the resistance matrix are related to the return path, which is important for accurate noise modeling at high frequency. It is shown that the error in crosstalk peak noise can be as high as 30% if the return path resistance is ignored. This work completes a previous modal analysis of a multiconductor system and significantly improves accuracy of crosstalk noise estimation, which is becoming increasingly important in design of deep-submicron integrated circuits.