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In this paper, electrothermal modeling and simulation of thermoelectric cooling (TEC) in the package design of VLSI systems are performed by solving coupled heat conduction and current continuity equations. We propose a new analytical solution to the coupled partial differential equations which describe temperature and voltage with the reduction from 3D to 1D. In addition to this, we derive new analytic expressions for two key performance metrics for TEC devices: the maximum temperature difference and the maximum heat-flux pumping capability, which can be guided for the optimal design of thermoelectric cooler to achieve the maximum cooling performance. Further, for the first time, we observe that when the dimensionless figure of merit ZT0 value is larger than 1, there is no maximum heat-flux value, which means the heat dissipation due to Peltier and Fourier transfer effects is larger than the heat generation caused by Joule heating effect, which can lead to more efficient TEC cooling design. The accuracy of the proposed 1D formulas is verified by 3D finite element method using COMSOL software. The compact model delivers many orders of magnitude speedup and memory saving compared to COMSOL with marginal accuracy loss. Compared with the conventional simplified 1D energy equilibrium model, the proposed analytical coupled multiphysics model is more robust and accurate.

In this article, we present a novel post-silicon approach to locating the dominant heat sources on commercial multicore processors using heatmaps measured via an infrared (IR) thermal imaging setup. To locate the heat sources, 2-D spatial Laplacian transformation is performed on the heatmaps followed by $K$ -means clustering to find the dominant power/heat-source clusters. This is an exclusively post-silicon approach that does not require any knowledge of the underlying design of the commercial chips other than the information that is publicly available. Since the identified clusters are the thermally vulnerable areas on the die, we then propose a machine-learning-based framework to deriving a thermal model capable of estimating their temperatures during online use. Our approach involves collecting transient temperature data of the aforementioned heat sources and synchronized high-level performance metrics from the chip, and training a long-short-term-memory (LSTM) neural network (NN) that uses the performance metrics as inputs to estimate the temperatures of the identified heat sources in real time. Since the model is meant for real-time use, we explore methods of reducing the performance overhead and inference time of the model. This includes a novel power correlation-based approach to identifying the thermally irrelevant performance metrics and eliminating them in order to reduce the input dimensionality of the model, and an analysis on network sizing to determine the ideal NN configuration for the problem at hand. The model is trained and tested exclusively using measured thermal data from commercial multicore processors. The experimental results from two Intel multicore processors (i5-3337U and i7-8650U) show that the proposed approach achieves very high accuracy (root-mean-square error: 0.55 °C–0.93 °C) in estimating the temperatures of all the identified heat sources on the chip.

For practical testing and detection of electromigration (EM) induced failures in dual damascene copper interconnects, one critical issue is creating stressing conditions to induce the chip to fail exclusively under EM in a very short period of time so that EM sign-off and validation can be carried out efficiently. Existing acceleration techniques, which rely on increasing temperature and current densities beyond the known limits, also accelerate other reliability effects making it very difficult, if not impossible, to test EM in isolation. In this paper, we propose novel EM wear-out acceleration techniques to address the aforementioned issue. First, we show that multisegment interconnects with reservoir and sink structures can be exploited to significantly speedup the EM wear-out process. Based on this observation, we propose three strategies to accelerate EM induced failure: 1) reservoir-enhanced acceleration; 2) sink-enhanced acceleration; and 3) a hybrid method that combines both reservoir and sink structures. We then propose several configurable interconnect structures that exploit atomic reservoirs and sinks for accelerated EM testing. Such configurable interconnect structures are very flexible and can be used to achieve significant lifetime reductions at the cost of some routing resources. Using the proposed technique, EM testing can be carried out at nominal current densities, and at a much lower temperature compared to traditional testing methods. This is the most significant contribution of this paper since, to our knowledge, this is the only method that allows EM testing to be performed in a controlled environment without the risk of invoking other reliability effects that are also accelerated by elevated temperature and current density. The simulation results show that using the proposed method, we can reduce the EM lifetime of a chip from ten years down to a few hours (about ${10^{5}} \times $ acceleration) under the 150 °C temperature limit, which is sufficient for practical EM testing of typical nanometer CMOS ICs.

Recently, many physics-based electromigration (EM) models have been proposed to mitigate the over-conservativeness of existing Black–Blech-based EM models. To assess EM failures, one needs to estimate how the void grows after the nucleation phase. As a result, it is important to estimate the saturation volume of a void, which is important for EM mortality check. The existing saturation void volume model only works for a single wire segment. In this paper, we propose a new model for fast estimation of the void’s saturation volume for general multisegment interconnect wires. The new model is based on the fundamental atom conservation at the steady-state condition of void growth phases. The new formula agrees with the existing saturation void volume formula for the single-segment wire case and is a natural extension of the single-segment case to general multisegment wires. In addition, we consider the impacts of the void volume on final stress distributions of the wire to further improve the accuracy of the proposed formula. Based on the new formula, we propose a new EM immortality check flow, which considers both the recently proposed EM immortality in the void nucleation phase and the void saturation volume in the growth phase. The new flow can further reduce the conservativeness of the existing EM failure effect analysis. The numerical results show that the proposed formula agrees well with a published work for two-segment cases, which are supported by experimental data. The formula is also validated by the recently proposed physics-based 3-D finite-element (FEM) analysis tool for general multisegment interconnect wires. We also demonstrate new EM immortality check flow to quickly identify the new type of immortal wires, which are nucleated but with smaller-than-critical voids.

In recent years the concern over Hardware Trojans has come to the forefront of hardware security research as these types of attacks pose a real and dangerous threat to both commercial and mission-critical systems. One interesting threat model utilizes semiconductor physics, specifically aging effects such as Electromigration (EM). However, existing methods for EM-based Trojans rely on empirical Black's models can easily lead to performance degradation and less accuracy in Trojan activation time prediction. In this article, we study the EM-based Trojan attacks based on recently developed physics-based EM models. We propose novel EM attack techniques in which the EM-induced hydrostatic stress increase in a wire is caused by wire structure or layer changes without changing the current density of the wires. The proposed techniques consist of sink/reservoir insertion or sizing and layer switching techniques based on the early and late failure modes of EM wear-out effects. As a result, the proposed techniques can have minimal impact on circuit performance, which is in contrast with existing current-density-based EM attacks. The proposed techniques can serve as a trigger for the EM attack on power/ground networks and signal and clock networks. Furthermore, we also present two potential EM attack mitigation techniques, namely, the split fabrication and burn-in testing.

This paper proposes a new power–ground (P/G) network sizing technique based on the recently proposed fast electromigration (EM) immortality check method for general multisegment interconnect wires and a new physics-based EM assessment technique for more accurate time to failure analysis. This paper first shows that the new P/G optimization problem, subject to the voltage IR drop and new EM constraints, can still be formulated as an efficient sequence of linear programing problem, where the optimization is carried out in two linear programing phases in each iteration. The new optimization will ensure that none of the wires fail if all the constraints are satisfied. However, requiring all the wires to be EM immortal can be overconstrained. To mitigate this problem, the first improvement is by means of adding reservoir branches to the mortal wires whose lifetime cannot be made immortal by wire sizing. This is a very effective approach as long as there is a sufficient reservoir area. The second improvement is to consider the aging effects of interconnect wires in the P/G networks. The idea is to allow some short-lifetime wires to fail and optimize the rest of the wires while considering the additional resistance caused by the failed wire segments. In this way, the resulting P/G networks can be optimized, such that the target lifetime of the whole P/G networks can be ensured and will become more robust and aging-aware over the expected lifetime of the chip. Numerical results on a number of IBM and self-generated power supply networks demonstrate that the new method can effectively reduce the area of the networks while ensuring immortality or enforcing target lifetime for all the wires, which is not the case for the existing current-density-constrained optimization methods.