DesignCon On-Chip Power Supply Noise and Reliability Analysis for Multi-Gigabit I/O Interfaces

Transcription

1 DesignCon 2010 On-Chip Power Supply Noise and Reliability Analysis for Multi-Gigabit I/O Interfaces Ralf Schmitt, Rambus Inc. [ Hai Lan, Rambus Inc. Ling Yang, Rambus Inc.

2 Abstract Verifying the power supply quality of the interface PHY is crucial to achieve multi- Gigabit data rates. The nature of high-speed interfaces, which are large mixed-signal fullcustom designs, are challenging for commercial EDA tools. We are presenting an on-chip supply analysis flow that allows us to analyze supply noise analysis even for large interface designs with high accuracy. This analysis flow provides information for static IR drop and transient AC noise waveforms and accurate predicts supply noise for every device location. The results are further used to predict the impact of supply noise on the system margin of the interface. Authors Biography Ralf Schmitt is Senior Engineering Manager at Rambus Inc. He received his Ph.D. in Electrical Engineering from the Technical University of Berlin, Germany. Since 2002, he is with Rambus Inc, Los Altos, California, where he is a senior engineering manager responsible for signal and power integrity on chip, package, and system level. His professional interests include signal and power integrity, timing analysis, clock distribution, and high-speed interface design. Hai Lan is a Senior Member of Technical Staff at Rambus Inc., where he has been working on on-chip power integrity and jitter analysis for multi-gigabit interfaces. He received his Ph.D. in Electrical Engineering from Stanford University, M.S. in Electrical and Computer Engineering from Oregon State University, and B.S. in Electronic Engineering from Tsinghua University in 2006, 2001, and 1999, respectively. His professional interests include design, modeling, and simulation for mixed-signal integrated circuits, substrate noise coupling, power and signal integrity, and high-speed interconnects. Ling Yang is Senior Staff Engineer at Rambus Inc. She received her MSEE from the University of Illinois Urbana-Champaign. Since 2000, she is with Rambus Inc, Los Altos, California, where she is responsible for power integrity for on chip, system measurements, and signal integrity at package and system level. Her professional interests include on-chip signal integrity, power integrity, clock distribution, board and package level signal integrity and high-speed system measurements.

3 I. Introduction Power integrity is a critical design parameter for modern high-speed I/O interface systems. Operating at data rates in the Gigabit range requires high-quality supply voltages, achieved by careful optimization of the power supply system on silicon, package, and PCB. In the on-chip power delivery network, supply noise is primarily generated through two effects: The first contribution of on-chip supply noise is caused the resistance of the on-chip power supply grid, which is in general much higher than the supply resistance in the package or the PCB. Drawing circuit currents through the resistive power grid causes IR drops, reduce the voltage available at the circuit. The second contribution of on-chip supply noise is due to the is the non-zero Power Supply Impedance Z PDN (f), dominated by the interaction between inductance package inductance and on-chip decoupling capacitors, which generates supply fluctuations as a response to current changes in the system. Both supply noise contributions have to be analyzed to assure that the system meets the Power Integrity requirements necessary to achieve the target performance. On-chip power integrity is a challenge for all silicon designs, not only for high-speed I/O interfaces. As a result, the EDA industry has developed tools to support the analysis of on-chip supply noise. The primary target of these tools is usually large SoC (System on Chip) designs that are dominated by digital circuit blocks. High-speed I/O Interface systems, however, have characteristics that are quite different from usual SoC designs and which make the on-chip power supply analysis more challenging. High-speed interface systems are mixed-signal by nature, containing many analog circuit blocks generated in a full-custom design methodology. Estimating the device currents in such a design requires analog or mixed-signal simulations, quite different from the cell current estimation of digital gates used in most EDA tools. Additionally, I/O interface systems are often very large, covering a substantial portion of the total chip area, making a simulation of the circuits, using analog or mixed-signal simulators, even more challenging. Finally, the accuracy requirement for the supply noise analysis are very high, usually much higher than for digital circuits, due to the high sensitivity of highspeed I/Os to supply noise. We are presenting a Power Integrity analysis strategy that allows us to analyze supply quality for large mixed-signal interface systems with an accuracy required for high-speed I/O data rates. In this analysis flow, we are combining the current results from external simulations, used for the verification of individual circuit blocks, with the power grid analysis capability of a commercial EDA tool. Special attention is paid to the current distribution inside individual circuit blocks. We will show how a strategy that uses a gradual improvement of current assignment resolution is used to provide supply noise results of increasing accuracy during the maturity of the design. We will also show how the current assignment refinement process can be used to resolve false violations of IR drop hot spots and electro-migration violations. Using the presented current assignment strategy we can achieve supply noise prediction, both for IR drop as well as for AC noise, with a resolution down to every

4 single device in the design. Using these local supply noise waveforms, we are able to predict the Power Supply Induced Jitter in the I/O interface. II. On-chip PI Analysis Challenges II.1. PI Analysis Requirements Power supply noise has significant impact on the performance of electronic systems in general and of interface systems in particular. Supply noise generates timing variations inside the interface link that cause jitter and reduce the timing margin of the interface system. If supply noise gets larger, it can also generate signal distortions, reducing the voltage margin of the interface system, and eventually cause functional failures in the system. The Power Distribution Network (PDN) has to provide power supplies of sufficient quality to meet the functionality and performance targets of the electronic system [1], [2]. Figure 1 shows the range of possible supply voltages at a system component and an example waveform. The supply voltage varies over time around an average voltage which can be different from the nominal supply voltage, e.g. due to component tolerances in the Voltage Regulator Module or voltage drops due to resistance in the supply path. Figure 1: Supply Voltage over Time at Silicon Device (Example) Silicon devices are designed to operate over a range of parameter variations for Process, Supply Voltage, and Temperature (PVT variations). Extensive simulations are used to verify that the device will function for any combination of PVT parameters the device might encounter during operation. The voltage range for these simulations covers the entire range of possible supply voltage values at the device generated by DC offset as well as AC noise. Power Integrity analysis has to verify that the supply voltage stays in this pre-defined supply voltage range for all operating conditions to assure the functionality of the system over the PVT variation range.

5 Meeting the voltage range requirement, however, does not necessarily guarantee system performance, especially not for high-speed I/O systems. Simulations over the PVT variation range verify that the circuit will function correctly for any voltage in the specified range, but these simulations assume a constant supply voltage over time. Changes of the supply voltage over time, shown as AC supply noise in Figure 1, can cause delay variations in circuit components and signal waveform distortions that are not covered by PVT corner simulations. For example, Power Supply Induced Jitter (PSIJ) caused by AC supply noise is a major source of jitter in electronic systems and can limit the achievable clock frequency of devices as well as the data rate of I/O interface systems. The sensitivity of system performance to AC supply noise is often a strong function of the noise frequency itself. Supply noise of equal amplitude can have very different impact on the system performance, depending on the frequency of the noise. Power Integrity analysis, therefore, also has to analyze the spectrum of supply noise, to verify that the noise impact on system margin is well inside the pre-defined budget for this component in this system. II.2. On-Chip Power Supply Noise Contributions The on-chip power distribution contributes to supply noise primarily in two separate frequency ranges: at DC and at medium to high frequencies (>100 MHz) [2]. On-chip wires are highly resistive, due to the very thin on-chip metal layers, causing resistive voltage loss (IR drop) on the on-chip power grid. In contrast to IR drop in PCB and package, on-chip IR drop is location dependent, i.e. some circuits, close to supply pads, might see no IR drop at all while other circuits, far away from supply pads, experience the maximum possible IR drop. It is therefore not possible to compensate onchip IR drop by raising the nominal voltage. Additionally, switching activity of on-chip circuits generates high-frequency supply noise, which is controlled using on-chip capacitors. The capacitance of the on-chip supply system also affects supply noise during package/chip resonance at medium frequencies. During package/chip resonance, the inductance of the package supply, together with inductance contributions from the PCB environment, creates an LC resonance with the capacitance of the on-chip power distribution system. This resonance can generate excessive supply nose when excited by the system. The frequency and amplitude of noise during package/chip resonance is dependent on the supply design at the PCB, the package, and the on-chip supply network as well as the circuit activity exciting this resonance in the system. II.3. On-Chip PI Analysis Steps The following PI analysis steps are required to analyze the on-chip supply system for high-speed I/O interfaces: Static IR drop analysis: In this analysis, the power supply network is extracted as a resistive network. Ideal voltage sources are attached to the supply pads, and static (average) currents are assigned to all circuits. The resulting map of IR drops in the on-chip power supply

6 networks reveals weaknesses in the design of the power supply grid. It is usually the first test of the on-chip power supply design. Dynamic IR drop analysis In the dynamic analysis, the on-chip power supply network is extracted together with decoupling capacitances in the power grid itself as well as in the circuits attached to the grid. The supply pads are connected to an ideal voltage source through an equivalent model of the package and PCB decoupling network, and transient currents are assigned to the circuits on the chip. The results of this analysis are transient supply noise waveforms for the circuit activity used in this analysis. Dynamic IR drop analysis provided feedback about the amount and correct placement of on-chip decoupling capacitors that cannot be obtained by the static IR drop analysis. It also provides insight into the noise spectrum, which is an important input for the estimation of PSIJ discussed later. It requires, however, significantly more analysis time as a static IR drop run and more design insight to provide the required dynamic current waveforms for all circuits. For the design of high-speed I/O interfaces, however, the results of this analysis are essential for the optimization of the supply system. Electromigration analysis in the supply grid (PowerEM) Additional to static and dynamic IR drop analysis, designs usually require an analysis of electromigration risk in the design. Electromigration describes the effect of electrons colliding with particles in the conducting metal structure, moving some of these particles along the direction of current flow. Over time, this material transport can cause gaps in the on-chip wires and vias, interrupting the connection and causing a permanent failure on this chip. For a given temperature the rate of material transport is dependent on the current density. Therefore limits are defined to the current density in every metal and via segment of the power supply grid to ensure that the chip will be functional for a pre-defined operation time at worst-case temperature. Since IR drop analysis provides the amount of current in every segment of the supply grid, PowerEM analysis can be implemented as a post-processing step of the IR drop analysis, dividing the current in every segment by the segment width to calculate the current density and comparing this density with the PowerEM limit. II.4. On-Chip PI Simulation Strategy Simulating a large circuit in its power supply environment is in most cases prohibitively expensive and only feasible for small circuit designs. A better concept, adopted by virtually all available EDA tools for PI analysis, is separating the circuit simulations necessary for current extractions from the analysis of the power supply grid. Figure 2 shows the principle simulation concept for a static IR drop analysis. In a first step, all device or cell currents are analyzed using non-linear circuit simulations or heuristic methods. In the case of static IR drop analysis only the average current has to be estimated. Since the average current of a cell or device is dependent on the actual supply voltage seen by this cell/device, the cell/device currents are estimated as a function of supply voltage.

7 Figure 2: Typical Static IR Drop Analysis Strategy In the next step, the resistance network of the power supply grid is extracted. The cells/devices are replaced by current sources, reflecting the cell/device currents previously extracted for the local voltage in the power grid at the cell/device position. Ideal voltage sources are connected at the positions of supply pads. The resulting netlist can be solved, calculating the voltage at every power grid node, using a fast and computational efficient linear solver. Figure 3 shows the principle simulation concept for dynamic IR drop analysis. Figure 3: Typical Dynamic IR Drop Analysis Strategy In contrast to static IR drop, which only requires average currents for each cell/device at a given voltage, dynamic IR drop analysis requires current waveforms over a switching or timing cycle. It also requires a more complicated power grid model, including capacitances and (optional) inductances, and it requires an equivalent model of the

8 package and system level supply network. But although dynamic IR analysis uses a much more complicated simulation model than static IR drop analysis, it still follows the same basic strategy of separating cell/device current extraction and power grid simulation. II.5. PI Analysis Challenges of High-Speed I/O Interfaces There are commercial design tools available from several EDA companies that address the Power Integrity analysis steeps described above. Virtually all of these tools, in particular all tools that are targeting large designs, are using the analysis strategy described in Figure 2 and 3, separating the cell/device current extraction from the power grid simulation. Many of these tools are primarily targeting digital SoC designs. The current waveforms of individual digital gates can be easily characterized for different switching conditions, and different algorithms and heuristics are available to estimate the switching distribution even in large designs. High-speed I/O interfaces are quite different from digital SoC designs. Figure 4 shows the design hierarchy of a typical high-speed parallel interface design. High-speed I/O interfaces, especially wide parallel interfaces, are large mixed-signal designs, following a hierarchical full-custom design style. It consists of a mix of digital, analog, and mixedsignal circuit blocks with many hierarchy levels. The size of these interface designs can be substantial, exceeding more than 10% of the entire chip area, and make it prohibitive to simulate the entire interface with a general-purpose simulation tool like Spice. Figure 4: Design Hierarchy of High-Speed I/O Interface Design The design style of these interface systems pose new challenges to some of the model extraction steps of the PI analysis: Supply Grid Extraction: There are only minor differences in this step between SoC designs and high-speed I/Os. SoC designs often extract the power grid only down to the power pins of (digital) cells, while in high-speed I/O designs the power grid has to be extracted down to the individual contacts of devices. Both extraction requirements are usually supported by commercial PI tools.

9 Device Capacitance Extraction: Extracting intentional decoupling cells is the same for SoC and for I/O designs. The extraction of intrinsic capacitance, however, is very different for digital and analog circuits. Intrinsic capacitance is the capacitance of circuits that are currently not active. The extraction algorithm in PI tools is usually targeting digital gate designs and is not easily applicable for mixed-signal designs of I/O systems. Cell/Device Current Extraction: Extracting cell/device currents is the largest challenge for on-chip PI analysis of I/O designs. The currents of digital gates, which are used in SoC designs, are easy to extract gate by gate using a simple circuit simulation or an easy heuristic estimation. For mixed-signal circuits, however, an analog simulation of an entire circuit block is necessary to extract device currents. This requires an understanding of the design that is not available for an automated tool. Extracting accurate device currents and importing these currents into the PI analysis is the biggest challenge for the PI analysis of I/O designs. In the next section we will discuss in detail how this problem can be addressed to achieve hogh-quality analysis results in a high-speed I/O design. III. Power Integrity Analysis Flow for I/O Design As discusses earlier, the on-chip Power Integrity analysis of high-speed I/O designs has to meet the following requirements: Verify that the design meets the Power Supply Budget For on-chip PI analysis this means verifying that static IR drop and on-chip AC noise are meeting the budget allocated for these components. Meet the reliability target of the chip design In order to meet the target reliability over the projected lifetime of the system, all metal connection in the chip design have to meet the EM limits for this lifetime target ( Power On Hours, POH). The analysis of EM risks in supply lines, PowerEM analysis, is a post-processing step of the (static and dynamic) IR drop analysis. However, as will be discussed later in this section, it requires a very accurate current assignment in the design to avoid false violations, and therefore has an impact on the current assignment strategy for high-speed I/O designs. Meet the link jitter requirements of the interface design One important source of link jitter is supply noise, causing Power Supply Induced Jitter (PSIJ). Since PSIJ is a strong function of the noise spectrum, on-chip PI analysis of high-speed I/O designs has to estimate not only the AC noise amplitude, but also the spectrum of this noise. Commercial on-chip PI tools provide functionality for each of these requirements. However, the Pi analysis of high-speed I/O design requires from these tools a combination of large capacity and high accuracy that is difficult to match for the hierarchical full-custom designs style of high-speed I/O interfaces. Tools that separate the

10 cell/device current extraction from the simulation step, described in Figures 2 and 3, have enough capacity to analyze large I/O designs, but current extraction is a severe challenge. In contrast, tools derived from fast circuit simulators that simulate the entire design in its supply environment can predict accurate currents even in full-custom mixed-signal designs, but they are limited to designs much smaller than many I/O interfaces. For the accurate analysis of high-speed I/O interfaces we need a combination of both concepts that combines the current estimation of circuit-level simulations with the capacity of a fast power grid analysis with pre-defined current profiles. In the following sections we will present PI analysis flows addressing these challenges. III.1. Static PI Analysis III.1.1. General Overview of Analysis Methodology In the static PI analysis, consisting of static IR drop analysis and average current PowerEM analysis, the on-chip power grid is analyzed using average currents for all circuits in the design. The analysis provides a map of IR drop over the entire power supply routing, revealing weaknesses in the design of the power supply grid. It also points out metal segments violating the current density limits for average currents in the design. Static IR drop analysis is the most important verification of the on-chip power supply implementation and a mandatory sign-off analysis for any chip design. Figure 5 shows the principle schematic of a static power grid analysis. Figure 5: Schematic of Static Power Grid Analysis The on-chip power supply network is extracted as a resistance-only network. Since only static currents are used in this analysis, there is no need to extract capacitances of either the supply routing itself or the circuits connected to the supply network. Ideal voltage sources are connected to the power grids at the positions of supply pads. Voltage sources are representing the cell/device currents and are connected to the power grid at the location of the cells/devices, e.g. at the contacts to individual devices.

11 III.1.2. Current Assignment Strategy The cell/device currents are time-average currents for the worst-case activity in the design. Our concept is to use the best-available current information for each block in the design, to achieve the best-possible accuracy in current assignment. For digital Place & Route (P&R) blocks, commercial PI tools provide several algorithms to estimate the average current for each cell instance, based on block layout, switching probability, and library information obtained by cell characterization simulations. Figure 6 shows the flow diagram of such a current estimation. The results are current information for every cell instance inside the P&R block. Figure 6: (Average) Cell Current Estimation in P&R Block In mixed-signal circuit blocks, much less information is available for the PI tool about the circuits inside the circuit block. The concept of switching probability is usually not applicable to mixed-signal circuits, and often these blocks are designed in a full-custom approach without standardized cell libraries. In general, the PI tool does not have enough information to estimate the total current of the block in a simple and determined way as for digital P&R blocks. Estimating the current requires an understanding of the setup and input sequences of input signals that only the designer himself will have. Therefore, it is best to provide the block current from external simulations, based on mixed-signal simulations done for circuit verification by the circuit designer himself. Figure 7 shows the resulting current assignment flow. Figure 7: (Average) Device Current Estimation in Mixed-Signal / Full-Custom Blocks

12 The PI tool is used to distribute the total block current to the devices inside the circuit block. This allows a device-level current assignment, necessary for a complete IR drop and PowerEM analysis of the entire supply network, based on block-level current assignments. Depending on the used PI tool different strategies are available for this current distribution. All of these strategies are using the device sizes in the design to identify how the total current will likely distribute between different devices. They do not distinguish between different circuit topologies like digital gates and analog circuits, although in reality the current for a given device size can be vary substantially dependent on the circuit this device is used in. In order to analyze the accuracy of current assignment inside a large circuit block using a PI tool algorithm, we assigned current to the toplevel block of a large design and used the PI tool to distribute the current inside the entire design. We then compared the currents assigned to sub-blocks with circuit simulations results that were used predict the total toplevel block current. Figure 8 shows the result of this comparison. Figure 8: Comparison of sub-block currents using PI tool vs. circuit simulations Figure 8 shows that there are large differences between the sub-block currents distributed by the PI tool and simulated using circuit simulations. A detailed analysis showed that most of these differences were caused by two issues: Large devices (e.g. power clamps) with little current during normal operation Too much current assigned to digital circuits, too little current assigned to analog circuits, in mixed-signal blocks. This experiment shows that a block-level current assignment as used in our flow needs a way to refine the distributions of currents to sub-blocks. In particular, it is necessary to assign small currents to sub-blocks or devices with known little current dissipation, and it

13 is also necessary to assign currents explicitly to separate analog or digital sub-blocks inside a larger mixed-signal block. III.1.3. Sub-Block Current Assignment In order to improve the current assignment inside larger blocks, we are using a hierarchical current assignment strategy that allows block current assignments on any design hierarchy level. The current distribution procedure then makes sure that all currents are distributed between different sub-blocks in best-fit way. Figure 9 shows a flow diagram of this current distribution procedure. Figure 9: Hierarchical Current Distribution Procedure (Example) In this example, a block named top contan some circuits and two sub-blocks, each of them containing sub-blocks themselves. There are currents known for the block top itself (I top ) as well as for the sub-blocks s sub2 and sub12 (I sub2 and I sub12 ). In step 1, the current I top is assigned to the block top. In step 2, currents are assigned to the two sub-blocks sub2 and sub12 with known currents I sub2 and I sub12. In step 3, all circuits inside top, but not covered by the sub-blocks sub2 and sub12 are collected ( Rest ). The remaining current of I top not accounted for by I sub2 and I sub12 is distributed among the Rest circuits. The resulting sub-block current assignment assigns the correct know currents to all blocks with known currents ( top, sub2, and sub12 ) and distributes the remaining currents as good as possible among the remaining circuits. This current distribution procedure allows a continuous refinement of the current distribution in the design. Consider the case where sub12 is a cell with large transistor (e.g. a power clamp) but negligible current dissipation in normal operation. If only the

14 block current I top is known, a large amount of I top would be assigned to sub12 by the PI tool due to the large transistor inside sub12, leaving little current for the remaining circuits inside top. Assigning the correct small current I sub12 to the block sub12 corrects this issue. Now almost the entire current I top is available for the remaining circuits outside sub12. To illustrate the improvement using the hierarchical current assignment procedure we simulated the IR drop on a smaller design assigning only currents to the toplevel design and leaving the current distribution to the PI tool. We then compared these results with an analysis that uses a hierarchical current assignment as described above. Figure 10 shows the results of this comparison. Figure 10: IR Drop Results for Toplevel and for Hierarchical Current Assignment The comparison shows that although the same amount is assigned in both designs, the IR drop for the toplevel current assignment is almost 3 times higher than for the more accurate hierarchical current assignment. III.1.4. Current Distribution Refinement in PowerEM Analysis Figure 10 has shown that a more accurate current assignment can have a significant impact on the accuracy of the IR drop map. It has even bigger impact on PowerEM results, since PowerEM violations are dependent on local current densities. An excessive sub-block current will likely cause large PowerEM violations in the power lines at this sub-block, but will also hide violations at other sub-blocks, since the excessive current of the first sub-block reduced the current assignment to all other sub-blocks. A continuous refinement of the current distribution inside the design using hierarchical current assignments can be used to remove false violations from the PowerEM analysis and correct the current distribution in the design to reveal real violations instead. Figure 11 shows the current refinement flow used in PowerEM analysis to remove false violations and refine the accuracy of the current distribution.

15 Figure 11: Current Refinement Flow for PowerEM Analysis Improvement When a violation is reported in the PowerEM analysis, the cell that causes this violation is identified in the layout of the design. If this cell is among the blocks with explicit current assignment, then the cell current is correct (by construction) and the violation has to be fixed. If, however, the cell is not among the blocks with explicit current assignment, the expected cell current is verified using circuit simulation results. If the assigned current was correct, the violation is real and has to be fixed. If the current assigned to the cell was incorrect, an explicit current will be assigned to this cell in the next analysis iteration. If the explicit current assignment does not fix this violation, it will be re-visited after the next analysis iteration. Using this refinement methodology, the accuracy of the analysis continually improves, leading to more accurate IR drop and PowerEM results. This procedure is far superior to a simple waiver process where false violations are simply ignored. In a waiver process, the same false violations are reported again in every analysis iteration, and the inaccurate current distribution that lead to the false violations in the first place is never corrected, leaving other real violations undetected. III.2. Dynamic IR Drop Analysis III.2.1. Motivation Dynamic IR drop analysis is necessary for high-speed I/O interfaces to verify that the design meets the AC supply noise budget. It verifies that a sufficient amount of on-chip capacitors are available in the design to stabilize the voltage during switching activities, and also that these capacitors are placed at the correct locations where they can effectively suppress supply noise.

16 Additionally to this obvious verification purpose, which applies to any design, dynamic IR drop analysis is especially important for high-speed I/O systems since it allows a prediction of Power Supply Induced Jitter (PSIJ) [3]. Supply noise is an important source of link jitter in high-speed interfaces. The magnitude and spectrum of this jitter has an impact on decisions regarding clocking architecture and timing circuit design. A major goal of the power supply design in these interfaces is not to minimize supply noise itself, but to minimize the impact of supply noise on the interface performance. Understanding the AC supply noise generated in the design and its distribution over the circuit area is an important step towards this goal. PSIJ is largely controlled by two parameters: the power supply spectrum and the sensitivity of the interface circuits to noise at different frequencies. Characterizing these two parameters allows the prediction of PSIJ spectrum and total supply induced jitter in the interface. Figure 12 shows a schematic of the prediction flow we are using for PSIJ prediction. Details to this methodology can be found in [4]. Figure 12: PSIJ Prediction Flow Dynamic IR drop analysis allows the prediction of the power supply spectrum seen by the circuits that are sensitive to supply noise. It is therefore an important step in the PSIJ prediction. III.2.2. Flow Setup Compared to static IR drop, there are three major differences in the analysis flow for dynamic analysis: The device currents are transient waveforms over time The extraction of the on-chip power supply system has to cover R as well as C A system-level PDN model is necessary to account for package and system inductance in the supply path Figure 13 shows the schematic of the dynamic IR drop analysis.

17 Figure 13: Schematic of Dynamic IR Drop Analysis Flow The extraction of on-chip capacitances covers both intentional decoupling cells, capacitor cells explicitly placed into the design, as well as intrinsic capacitance, parasitic capacitance provided by the power routing and circuits. Intrinsic capacitance is usually dominated by the capacitance of circuit blocks that are not active at a given time. For digital gates, commercial tools provide algorithms to extract the average capacitance in a larger circuit block based on the switching probability in the block. For analog and mixed-signal circuits the intrinsic capacitance due to inactive circuits is much smaller and much more difficult to estimate. Therefore, intrinsic capacitance is ignored in our flow for analog and mixed-signal blocks, and the power supply design relies on explicit decoupling capacitors for these blocks instead. This makes the analysis slightly pessimistic, but good correlation with noise measurement results confirms that this error is usually very small. For dynamic IR drop analysis it is essential to include a model of the system-level PDN system, in particular a model of the inductance introduced in the supply path by the package inductance and the inductance of PCB capacitors close to the package. Without this supply model, ideal voltage sources would be connected to all on-chip supply pads, which would dramatically under-predict AC supply noise in the chip especially at high frequencies. Using ideal voltage sources at the supply pads, unlimited current can be provided by these sources with infinite edge rate, quickly reacting to any current spike in the design. In reality, however, the inductance of the package and PCB supply system limits the change of the current supply through the package. Especial for high-frequency current changes like switching spikes the necessary charge initially has to be provided largely by the on-chip decoupling capacitors, and the package current will only react to current changes in the lower MHz range and below. III.2.3. Current Extraction and Assignment Strategy Extracting transient current waveform necessary for dynamic IR drop analysis has the same challenges as the extraction of average currents used in static IR drop analysis. For digital gate circuits, commercial PI tools provide different algorithms to estimate transient current waveforms for every instance of the design. For analog or mixed-signal

18 circuit blocks, however, transient current waveforms have to be extracted using external simulations to achieve a reasonable accuracy of the dynamic IR drop analysis. Figure 14 shows the flow diagram of this procedure. Figure 14: Current Assignment Strategy for Mixed-Signal Blocks In this current assignment strategy the PI tool is still used to distribute the transient current waveform to the different devices inside the design. As previously discussed, this distribution of block currents to individual devices can be very inaccurate, especially in mixed-signal circuit blocks. The distribution of currents using the PI tool can be avoided if transient current waveforms are provided for each device from external simulations. This strategy is implemented at the final sign-off stage of our dynamic IR drop flow. In this stage, a complete transistor-level model of the I/O interface is generated to extract all device currents. If the design is too large, prohibiting a simulation of the complete design, the simulation complexity is reduced using a co-simulation approach. For this co-simulation approach we make use of the fact that many blocks inside a large I/O interface are duplicated many times, as seen in Figure 4. A typical example is the bit slice cell that are placed for every bit in the design. Starting from the complete transistor-level circuit description of the interface, duplicate cells are replaced with behavioral models of the cell, leaving only one instance of each circuit block as full-transistor model in the simulation model. The resulting co-simulation model has much smaller complexity than the original full-transistor model and can be simulated using an analog simulator even for large interface designs. For each block still using full-transistor description, the current waveform for each device is recorded, and the device currents are later used for corresponding devices of each instance of this block. Post-layout LVS ( Layout versus Schematic ) results are used to back-annotate the device currents to the correct locations in the design layout and simulated using the commercial PI tool. III.2.4. AC Analysis Maturity Some of the information necessary for this device-level dynamic IR drop analysis are available very late in the design process. In order to get an earlier first look into AC noise levels and distributions, block-level current waveform assignments can be extracted and assigned earlier in the design cycle and the current extraction and assignment

19 continuously is then refined to the final device level current assignment while the design matures. Table 1 shows the different stages of dynamic AC noise analysis and the continuous improvement of analysis accuracy as the design is maturing. Design stage Current assignment strategy Analysis results Early analysis Single toplevel current Total amount of decaps Block-level analysis Block-level currents Amount and placement of decaps Sign-off Individual device currents Power grid and decap sign-off Noise distribution, noise spectrum Table 1: AC Noise Analysis Steps during Design Maturity In the early stage of the design, as soon as the design schematic is available, the supply current waveforms for the entire design is extracted and used to determine the amount of on-chip decoupling capacitors necessary for each supply rail. Since no layout is available at this stage, the analysis assumes a perfect distribution of the capacitors over the design. Once the layout is largely stable, a block-level AC noise analysis can be used to verify the amount and the distribution of on-chip decoupling capacitors. At this stage, most issues meeting the AC noise budget will be revealed and can be addressed. Finally, when the layout is finished and the design passes the LVS check, device-level currents are used to sign-off the on-chip power supply grid as well as capacitor amount and placement. This analysis also provides the supply noise distribution over the design and the noise spectrum seen by sensitive circuits that is used for the estimation of PSIJ. III.2.5. AC Noise Analysis Result Example Figure 15 shows an example of AC noise analysis results. The analysis tool provides a map of color-coded peak-peak IR drop results and a listing of noise results sorted by noise amplitude. For each location in the design the noise waveform can be shown. The noise waveform can then be exported and the spectrum of the supply noise at this location can be calculated using FFT.

20 IV. Figure 15: Example results of Dynamic AC Noise Analysis Correlation Results In order to verify our supply noise analysis methodology we correlated the predicted supply noise with measurements using on-chip noise monitor circuits. For details of the noise monitor circuits please see [4], [5]. Figure 16 shows a comparison of simulated and measured supply noise in time domain and in frequency domain. Figure 16: Correlation of Simulated and Measured Supply Noise

21 The comparison shows excellent correlation between simulated and measured noise levels, in time domain as well as in frequency domain. This demonstrates the accuracy of AC noise prediction that can be achieved using the presented analysis flow. V. Summary The analysis of on-chip power integrity and reliability is a requirement for any silicon design. High-speed I/O interfaces have a particular high requirement for the accuracy of such an analysis. At the same time, the design style of high-speed interface designs poses serious challenges for the supply noise analysis, making it difficult to meet and verify the supply noise requirements necessary for multi-gigabit operation. We have presented an on-chip power integrity analysis and reliability flow that addresses these challenges. This flow is well suited for a full-custom mixed-signal design methodology typically used for high-speed I/O interfaces and provides a path to gradually improve the accuracy of the analysis as the design matures. Special attention was given to the device current extraction and distribution in the design. Using a combination of external simulations and refinement strategies for internal current distribution we achieve a device-level accurate current assignment for design sign-off, providing accurate supply noise information for any location in the design. A comparison of simulated and measured supply noise shows excellent correlation in time domain as well as in frequency domain. VI. References [1] R. Schmitt, X. Huang, L. Yang, C. Yuan, System Level Power Integrity Analysis and Correlation for Multi-Gigabit Designs, DesignCon 2004, Feb. 6-9, 2004, Santa Clara [2] R. Schmitt, X. Huang, L. Yang, X. Yuan, Modeling and Hardware Correlation of Power Distribution Networks for Multi-Gigabit Designs, Proceedings 54th Electronic Components & Technology Conference 2004, Las Vegas, June 2004 [3] R. Schmitt, H. Lan, C. Madden, and C. Yuan, Analysis of supply noise induced jitter in Gigabit I/O interfaces, DesignCon, Jan. 29-Feb. 1, 2007, Santa Clara, CA [4] H. Lan, R. Schmitt, C. Yuan, Prediction and Measurement of Supply Noise Induced Jitter in High-Speed I/O Interfaces, DesignCon 2009, Santa Clara, CA, 2009 [5] E. Alon, V. Stojanovic, and M. Horowitz, Circuits and Techniques for High- Resolution Measurement of On-Chip Power Supply Noise, IEEE J. Solid-State Circuits, vol. 40, no. 4, April 2005, pp