This paper investigates whether the self-heating effect in short intra-block wires will become apparent with technology scaling. These wires seem to have good thermal radiation characteristics, but we validate that the self-heating effect in local signal wires will be greater than that in optimal repeater-inserted global wires. Our numerical experiment shows that the maximum temperature increase from the silicon junction temperature will reach 40.4 in a steady state at a 14-nm process. Our attribution analysis also demonstrates that miniaturizing the area of wire cross-section exacerbates self-heating as well as using low-κ material and increased power dissipation in advanced technologies below 28 nm. It is revealed that the impact of self-heating on performance in local wires is limited, while underestimating the temperature may cause an unexpected reliability failure.

As VLSI process node continue to shrink, chemical mechanical planarization (CMP) process for copper interconnect has become an essential technique for enabling many-layer interconnection. Recently, Edge-over-Erosion error (EoE-error), which originates from overpolishing and could cause yield loss, is observed in various CMP processes, while its mechanism is still unclear. To predict these errors, we propose an EoE-error prediction method that exploits machine learning algorithms. The proposed method consists of (1) error analysis stage, (2) layout parameter extraction stage, (3) model construction stage and (4) prediction stage. In the error analysis and parameter extraction stages, we analyze test chips and identify layout parameters which have an impact on EoE phenomenon. In the model construction stage, we construct a prediction model using the proposed multi-level machine learning method, and do predictions for designed layouts in the prediction stage. Experimental results show that the proposed method attained 2.7∼19.2% accuracy improvement of EoE-error prediction and 0.8∼10.1% improvement of non-EoE-error prediction compared with general machine learning methods. The proposed method makes it possible to prevent unexpected yield loss by recognizing EoE-errors before manufacturing.

We propose a transistor sizing method that downsizes MOSFETs inside a cell to eliminate redundancy of cell-based circuits as much as possible. Our method reduces power dissipation of detail-routed circuits while preserving interconnects. The effectiveness of our method is experimentally evaluated using 3 circuits. The power dissipation is reduced by 75% maximum and 60% on average without delay increase. Compared with discrete cell sizing, the proposed method reduces power dissipation furthermore by 30% on average.

This paper discusses performance limitation of on-chip interconnects. On-chip global interconnects are considered to be a bottleneck of high-performance LSIs. To overcome this issue, high-speed signaling and large throughput interconnection using electrical wires have been studied. However the limitation of on-chip interconnects has not been examined sufficiently. This paper reveals the maximum performance of on-chip global interconnects based on derived analytic expressions and detailed circuit simulation. We derive trade-off curves among bit rate, interconnect length, and eye opening both for single-end and for differential signaling. The results show that differential signaling improves signaling performance several times compared with conventional single-end signaling, and demonstrate that 80 Gbps differential signaling on 10 mm interconnects is promising.

This paper discusses a statistical effect of performance optimization to uncertainty in circuit delay. Performance optimization has an effect of balancing the delay of each path in a circuit, i.e. the delay times of long paths are shortened and the delay times of short paths are lengthened. In these path-balanced circuits, the uncertainty in circuit delay, which is caused by delay calculation error, manufacturing variability, fluctuation of operating condition, etc., becomes worse by a statistical characteristic of circuit delay. Thus, a highly-optimized circuit may not satisfy delay constraints. In this paper, we demonstrate some examples that uncertainty in circuit delay is increased by path-balancing, and we then raise a problem that performance optimization increases statistically-distributed circuit delay.

This paper evaluates impact of self-heating in wire interconnection on signal propagation delay in an upcoming 32 nm process technology, using practical physical parameters. This paper examines a 64-bit data transmission model as one of the most heating cases. Experimental results show that the maximum wire temperature increase due to the self-heating appears in the case where the ratio of interconnect delay becomes largest compared to the driver delay. However, even in the most significant case which induces the maximum temperature rise of 11.0, the corresponding increase in the wire resistance is 1.99% and the resulting delay increase is only 1.15%, as for the assumed 32 nm process. A part of the impact reduction of wire self-heating on timing comes from the size-effect of nano-scale wires.

We propose an optimization method for power distribution network that explicitly deals with timing. We have found and focused on the facts that decoupling capacitance (decap) does not necessarily improve gate delay depending on the switching timing within a cycle and that power wire expansion may locally degrade the voltage. To resolve the above facts, we devised an efficient sensitivity calculation of timing to decap size and power wire width for guiding optimization. The proposed method, which is based on statistical noise modeling and timing analysis, accelerates sensitivity calculation with an approximation and adjoint sensitivity analysis. Experimental results show that decap allocation based on the sensitivity analysis efficiently minimizes the worst-case circuit delay within a given decap budget. Compared to the maximum decap placement, the delay improvement due to decap increases by 3.13% even while the total amount of decaps is reduced to 40%. The wire sizing with the proposed method also efficiently reduces required wire resource necessary to attain the same circuit delay by 11.5%.

Adaptive voltage scaling is a promising approach to overcome manufacturing variability, dynamic environmental fluctuation, and aging. This paper focuses on error prediction based adaptive voltage scaling (EP-AVS) and proposes a mean time to failure (MTTF) aware design methodology for EP-AVS circuits. Main contributions of this work include (1) optimization of both voltage-scaled circuit and voltage control logic, and (2) quantitative evaluation of power saving for practically long MTTF. Experimental results show that the proposed EP-AVS design methodology achieves 38.0% power saving while satisfying given target MTTF.

This paper proposes a simple yet sufficient Si-substrate modeling for interconnect resistance and inductance extraction. The proposed modeling expresses Si-substrate as four filaments in a filament-based extractor. Although the number of filaments is small, extracted loop inductances and resistances show accurate frequency dependence resulting from the proximity effect. We experimentally prove the accuracy using FEM (Finite Element Method) based simulations of electromagnetic fields. We also show a method to determine optimal size of the four filaments. The proposed model realizes substrate-aware extraction in SoC design flow.

This work proposes a design methodology that saves the power dissipation under voltage over-scaling (VOS) operation. The key idea of the proposed design methodology is to combine critical path isolation (CPI) and bit-width scaling (BWS) under the constraint of computational quality, e.g., Peak Signal-to-Noise Ratio (PSNR) in the image processing domain. Conventional CPI inherently cannot reduce the delay of intrinsic critical paths (CPs), which may significantly restrict the power saving effect. On the other hand, the proposed methodology tries to reduce both intrinsic and non-intrinsic CPs. Therefore, our design dramatically reduces the supply voltage and power dissipation while satisfying the quality constraint. Moreover, for reducing co-design exploration space, the proposed methodology utilizes the exclusiveness of the paths targeted by CPI and BWS, where CPI aims at reducing the minimum supply voltage of non-intrinsic CP, and BWS focuses on intrinsic CPs in arithmetic units. From this key exclusiveness, the proposed design splits the simultaneous optimization problem into three sub-problems; (1) the determination of bit-width reduction, (2) the timing optimization for non-intrinsic CPs, and (3) investigating the minimum supply voltage of the BWS and CPI-applied circuit under quality constraint, for reducing power dissipation. Thanks to the problem splitting, the proposed methodology can efficiently find quality-constrained minimum-power design. Evaluation results show that CPI and BWS are highly compatible, and they significantly enhance the efficacy of VOS. In a case study of a GPGPU processor, the proposed design saves the power dissipation by 42.7% with an image processing workload and by 51.2% with a neural network inference workload.

We propose an estimation method of crosstalk noise for generic RC trees. The proposed method derives an analytic waveform of crosstalk noise in a 2-π equivalent circuit. The peak voltage is calculated from the closed-form expression. We also develop a transformation method from generic RC trees with branches into the 2-π model circuit. The proposed method can hence estimate crosstalk noise for any RC trees. Our estimation method is evaluated in a 0.13 µm technology. The peak noise of two partially-coupled interconnects is estimated with the average error of 11%. Our method transforms generic RC interconnects with branches into the 2-π model with 14% error on average.

Capacitive and inductive crosstalk noises are expected to be more serious in advanced technologies. However, capacitive and inductive crosstalk noises in the future have not been concurrently and sufficiently discussed quantitatively, though capacitive crosstalk noise has been intensively studied solely as a primary factor of interconnect delay variation. This paper quantitatively predicts the impact of capacitive and inductive crosstalk in prospective processes, and reveals that interconnect scaling strategies strongly affect relative dominance between capacitive and inductive coupling. Our prediction also makes the point that the interconnect resistance significantly influences both inductive coupling noise and propagation delay. We then evaluate a tradeoff between wire cross-sectional area and worst-case propagation delay focusing on inductive coupling noise, and show that an appropriate selection of wire cross-section can reduce delay uncertainty at the small sacrifice of propagation delay.

With increase of clock frequency, on-chip wire inductance starts to play an important role in power/ground distribution analysis, although it has not been considered so far. We perform a case study work that evaluates relation between decoupling capacitance position and noise suppression effect, and we reveal that placing decoupling capacitance close to current load is necessary for noise reduction. We experimentally show that impact of on-chip inductance becomes small when on-chip decoupling capacitance is well placed according to local power consumption. We also examine influences of grid pitch, wire area, and spacing between paired power and ground wires on power supply noise. When effect of on-chip inductance on power/ground noise is significant, minification of grid pitch is more efficient than increase in wire area, and small spacing reduces power noise as we expected.

This paper proposes a closed-form eye-diagram model for on-chip distortionless transmission lines with intentionally inserted shunt conductance. We derive expressions of eye-opening both in voltage and time, by assuming a piece-wise linear waveform model. The model is experimentally verified with various length, shunt conductance and resistive termination. We also apply the proposed model to design space exploration, and demonstrate that the proposed model helps estimate the optimal shunt conductance and resistive termination according to required signaling length and throughput.

FPGA that exploits via-switches, which are a kind of non-volatile resistive RAMs, for crossbar implementation is attracting attention due to its high integration density and energy efficiency. Via-switch crossbar is responsible for the signal routing in the interconnections by changing on/off-states of via-switches. To verify the via-switch crossbar functionality after manufacturing, fault testing that checks whether we can turn on/off via-switches normally is essential. This paper confirms that a general differential pair comparator successfully discriminates on/off-states of via-switches, and clarifies fault modes of a via-switch by transistor-level SPICE simulation that injects stuck-on/off faults to atom switch and varistor, where a via-switch consists of two atom switches and two varistors. We then propose a fault diagnosis methodology for via-switches in the crossbar that diagnoses the fault modes according to the comparator response difference between the normal and faulty via-switches. The proposed method achieves 100% fault detection by checking the comparator responses after turning on/off the via-switch. In case that the number of faulty components in a via-switch is one, the ratio of the fault diagnosis, which exactly identifies the faulty varistor and atom switch inside the faulty via-switch, is 100%, and in case of up to two faults, the fault diagnosis ratio is 79%.

PMOS stress (ON) probability has a strong impact on circuit timing degradation due to NBTI effect. This paper evaluates how the granularity of stress probability calculation affects NBTI prediction using a state-of-the-art long term prediction model. Experimental evaluations show that the stress probability should be estimated at transistor level to accurately predict the increase in delay, especially when the circuit operation and/or inputs are highly biased. We then devise and evaluate two annotation methods of stress probability to gate-level timing analysis; one guarantees the pessimism desirable for timing analysis and the other aims to obtain the result close to transistor-level timing analysis. Experimental results show that gate-level timing analysis with transistor-level stress probability calculation estimates the increase in delay with 12.6% error.

This paper proposes an approach to cope with temporal power/ground voltage fluctuation for static timing analysis. The proposed approach replaces temporal noise with an equivalent power/ground voltage. This replacement reduces complexity that comes from the variety in noise waveform shape, and improves compatibility of power/ground noise aware timing analysis with conventional timing analysis framework. Experimental results show that the proposed approach can compute gate propagation delay considering temporal noise within 10% error in maximum and 0.5% in average.

This paper discusses how to cope with dynamic power supply noise in FF timing estimation. We first review the dependence of setup and hold times on supply voltage, and point out that setup time is more sensitive to supply voltage than hold time, and hold time at nominal voltage is reasonably pessimistic. We thus propose a procedure to estimate setup time and clock-to-Q delay taking into account given voltage drop waveforms using an equivalent DC voltage approach. Experimental results show that the proposed procedure estimates setup time and clock-to-Q delay fluctuations well with 5% and 3% errors on average.

VLSIs that perform signal processing near infrared sensors cooled to ultra-low temperature are demanded. Delay test of those chips must be executed at ultra-low temperature while functional test could be performed at room temperature as long as hold timing errors do not occur. In this letter, we focus on the hold timing violation and evaluate the feasibility of functional test of ultra-low temperature circuits at room temperature. Experimental evaluation with a case study shows that the functional test at room temperature is possible.

Body-biasing is expected to be a common design technique, and then area efficient implementation in layout has been demanded. Body-biasing outside standard cells is one of possible layouts. However in this case body-bias controllability, especially when forward bias is applied, is a concern. To investigate the controllability, we fabricated and measured a ring oscillator in a 90 nm technology. Our measurement result and evaluation of area efficiency reveal that body-biased circuits can be implemented with area overhead of less than 1% yet with sufficient speed controllability.