Interconnect modeling plays an important role in design and verification of VLSI circuits and packages. For low frequency circuits, great advances for parasitic resistance and capacitance extraction have been achieved and wide varieties of techniques are available. However, for high frequency circuits and packages, parasitic inductance and impedance extraction still poses a tremendous challenge. Existing algorithms, such as FastImp and FastHenry developed by MIT, are slow and inherently unable to handle multiple dielectrics and magnetic materials. In this research, we solve three problems in interconnect modeling for high frequency circuits and packages. 1) Multiple dielectrics are common in integrated circuits and packages. We propose the first Boundary Element Method (BEM) algorithm for impedance extraction of interconnects with multiple dielectrics. The algorithm uses a novel equivalentcharge formulation to model the extraction problem with significantly fewer unknowns. Then fast matrix-vector multiplication and effective preconditioning techniques are applied to speed up the solution of linear systems. Experimental results show that the algorithm is significantly faster than existing methods with sufficient accuracy. 2) Magnetic materials are widely used in MEMS, RFID and MRAM. We present the first BEM algorithm to extract interconnect inductance with magnetic materials. The algorithm models magnetic characteristics by the Landau Lifshitz Gilbert equation and fictitious magnetic charges. The algorithm is accelerated by approximating magnetic charge effects and by modeling currents with solenoidal basis. The relative error of the algorithm with respect to the commercial tool is below 3%, while the speed is up to one magnitude faster. 3) Since traditional interconnect model includes mutual inductances between pairs of segments, the resulting circuit matrix is very dense. This has been the main bottleneck in the use of the interconnect model. Recently, K = L-1 is used. The RKC model is sparse and stable. We study the practical issues of the RKC model. We validate the RKC model and propose an efficient way to achieve high accuracy extraction by circuit simulations of practical examples.

Modeling approaches are developed to optimize emerging on-chip and off-chip electrical interconnect technologies and benchmark them against conventional technologies. While transistor scaling results in an improvement in power and performance, interconnect scaling results in a degradation in performance and electromigration reliability. Although graphene potentially has superior transport properties compared to copper, it is shown that several technology improvements like smooth edges, edge doping, good contacts, and good substrates are essential for graphene to outperform copper in high performance on-chip interconnect applications. However, for low power applications, the low capacitance of graphene results in 31\% energy savings compared to copper interconnects, for a fixed performance. Further, for characterization of the circuit parameters of multi-layer graphene, multi-conductor transmission line models that account for an alignment margin and finite width of the contact are developed. Although it is essential to push for an improvement in chip performance by improving on-chip interconnects, devices, and architectures, the system level performance can get severely limited by the bandwidth of off-chip interconnects. As a result, three dimensional integration and airgap interconnects are studied as potential replacements for conventional off-chip interconnects. The key parameters that limit the performance of a 3D IC are identified as the Through Silicon Via (TSV) capacitance, driver resistance, and on-chip wire resistance on the driver side. Further, the impact of on-chip wires on the performance of 3D ICs is shown to be more pronounced at advanced technology nodes and when the TSV diameter is scaled down. Airgap interconnects are shown to improve aggregate bandwidth by 3x to 5x for backplane and Printed Circuit Board (PCB) links, and by 2x for silicon interposer links, at comparable energy consumption.

<p dir="ltr">Interconnects pose severe performance bottlenecks in advanced technology nodes due to multiple scaling challenges. To understand such problems and explore potential solutions, it is important to develop advanced models. This is particularly relevant for modern interconnects (especially vias) with complex structures with non- trivial current paths. In this dissertation, we develop a comprehensive physics-based interconnect models to capture surface and grain boundary scattering. We further analyze the circuit implications of 2D transition metal dichalcogenide (TMD)-augmented interconnects, which show potential in mitigating some of the scalability concerns of state-of-the-art interconnects. First, we propose a 2D spatially resolved model for surface scattering in rectangular interconnects based on the Fuchs-Sondheimer (FS) theory. The proposed spatially resolved FS (SRFS) model offers both spatial dependence and explicit relation of conductivity to physical parameters. We also couple the SRFS model with grain boundary scattering based on the Mayadas−Shatzkes (MS) theory. The SRFS-MS model is exact for diffusive surface scattering and offers a good approximation for elastic surface scattering. Furthermore, we develop a circuit-compatible version of the SRFS-MS model and show a close match with the physical SRFS-MS model (error < 0.7%). Moreover, we integrate temperature dependency, confirming that surface scattering has a negligible temperature-dependence. Second, we analyze the circuit implications of 2D TMD augmented interconnects and show the effective clock frequency of an AES circuit is boosted by 2%-32%. We also establish that the vertical resistivity of the TMD material must be below 22 kΩ-nm to obtain performance benefits over state-of-the-art interconnects in the worst-case process-temperature corner.</p>

Clustered architecture processors are preferred for embedded systems because centralized register file architectures scale poorly in terms of clock rate, chip area, and power consumption. Although clustering helps by improving clock speed, reducing energy consumption of the logic, and making the design simpler, it introduces extra overheads by way of inter-cluster communication. This communication happens over long wires having high load capacitance which leads to delay in execution and significantly high energy consumption. Inter-cluster communication also introduces many short idle cycles, therby significantly increasing the overall leakage energy consumption in the functional units. The trend towards miniatrurization of devices (and associated reduction in threshold voltage) makes energy consumption in interconnects and functional units even worse and limits the usability of clustered architectures in smaller technologies. In the past, study of leakage energy management at the architectural level has mostly focused on storage structures such as cache. Relatively, little work has been done on architecture level leakage energy management in functional units in the context of superscalar processors and energy efficient scheduling in the context of VLIW architectures. In the absence of any high level model for interconnect energy estimation, the primary focus of research in the context of interconnects has been to reduce the latency of communication and evaluation of various inter-cluster communication models. To the best of our knowledge, there has been no such work in the past from the point of view of enegy efficiency targeting clustered VLIW architectures specifically focusing on smaller technologies. Technological advancements now permit design of interconnects and functional units With varying performance and power modes. In thesis we people scheduling algorithms that aggregate the scheduling slack of instructions and communication slack of data values to exploit the low power modes of interconnects and functional units . We also propose a high level model for estimation of interconnect delay and energy (in contrast to low-level circuit level model proposed earlier) that makes it possible to carry out architectural and compiler optimizations specifically targeting the inter connect, Finally we present synergistic combination of these algorithms that simultaneously saves energy in functional units and interconnects to improve the usability of clustered architectures by archiving better overall energy-performance trade-offs. Our compiler assisted leakage energy management scheme for functional units reduces the energy consumption of functional units approximately by 15% and 17% in the context of a 2-clustered and a 4-clustered VLIW architecture respectively with negligible performance degradation over and above that offered by a hardware-only scheme. The interconnect energy optimization scheme improves the energy consumption of interconnects on an average by 41% and 46% for a 2-clustered and a 4-clustered machine respectively with 2% and 1.5% performance degradation. The combined scheme options slightly better energy benefit in functional units and 37% and 43% energy benefit in interconnect with slightly higher performance degradation. Even with the conservative estimates of contribution of functional unit interconnect to overall processor energy consumption the proposed combined scheme obtains on an average 8% and 10% improvement in overall energy delay product with 3.5% and 2% performance degradation for a 2-clustered and a 4-clustered machine respectively. We present a detailed experimental evaluation of the proposed schemes using the Trimaran compiler infrastructure.