Physics of Giga Scale Integration

SEM view of 6 levels of IBM Cu interconnect [ref]

Moore's law has been an important benchmark for developments in microelectronics for over three decades. Reversing early limitations on Moore's law, on-chip interconnects have become one of the main determinants of chip performance. My research interests lie broadly in modeling and studying problems associated with gigascale integration (GSI) interconnects at smaller dimensions and higher frequencies. The solutions to these problems vary from new interconnect-centric design parigms to the applications of new technologies such as Carbon nanotubes.

Surface Scattering, Surface Roughness, Anomalous Skin Effect
The International Technology Roadmap for Semiconductors projects that for the year 2018 (18 nm node), interconnects will be as narrow as 21 nm.  For a wire with such dimensions, the collision rate of the electrons with the surfaces will be a significant fraction of the total number of collisions, causing an increase in the total resistance of the wire. At the same time, interconnections operate at higher frequencies, such that electrons are confined to a sheet near the surface; therefore, the effective cross-sectional area of the conductor decreases and the effective resistance increases. For a wire that operates at ultra-high frequencies, such that skin depth and the mean free path of the electrons are in the same order, skin effect and surface scattering should be considered at the same time. This is known as the anomalous skin effect (ASE). My primary research shows that while ASE has limited impact on delay and bit-rate limit of GSI chips operated at room temperature, it should be considered for sub-ambient cooling applications.

Compact Model for Bit-Rate Limit
As digital circuits approach gigascale integration, the demand for transmitting data at very high rates grows rapidly. Electrical interconnects have been conventionally used for on-chip and chip-to-chip interconnection, and because of the simplicity of the transmitters and receivers that they need, they will remain an attractive solution for GSI interconnection. Although electrical wires are relatively very simple, various effects including surface scattering and skin effect simultaneously affect their bandwidth, and make it difficult to accurately determine the bit-rate of electrical wires. Physical models that accurately determine bit-rate limit of electrical wires are very helpful in determining their capabilities at various generations. Such models can also help optimize the cross-sectional dimensions of wires to maximize aggregate bandwidth.

Impact of Size Effects on the Design and Performance of Metal Interconnect Networks

Size effects have been subject of many studies in the past, and currently many research groups are investigating techniques that can potentially mitigate size effects to improve copper conductivity for the future technology generations. However, a multi-level interconnect network consists of interconnects with a wide range of lengths that are routed in metal levels with different pitches and thicknesses. The impact of size effects on the design of multilevel interconnect networks has not been studied, and it is not clear how much overall chip performance will be degraded due to size effects. Such quantitative analyses can be very helpful for any kind of cost/performance analysis for various size effect mitigation techniques.

Design and Optimization for Nanoscale Power Distribution Networks in Gigascale Systems
As technology advances, it becomes more and more challenging to design on-chip power distribution networks. This is because, power supply voltage and hence the noise margin scale down with technology while the number of devices in a die and the current per unit area of a die scale up. At the global level, power and ground lines are routed in the top metal levels with relatively large cross-sectional dimensions, and size effects do not affect them. At the local level, however, power and ground lines are routed in the first two metal levels to deliver power and ground to each individual gate. Due to their small dimensions, these interconnects are vulnerable to size effects. It is therefore critical to model and optimize power distribution networks at the local level and to quantify the impact of size effects on the design and performance of local power distribution networks.

Performance Comparison between Carbon Nanotube and Copper Interconnects
Carbon nanotubes have received tremendous research interest as they have many unique mechanical, electrical, thermal, and chemical properties. A single-walled carbon nanotube (SWCN) is a graphene roll with a diameter of 0.5 to a few nanometers that, depending on its chirality, can be either metallic or semiconductor. Multiwall carbon nanotubes (MWCNs), on the other hand, are concentric graphene tubes that may have diameters from a few to a hundred nanometers. Copper wires are facing many challenges as on-chip interconnects, including their delay, power dissipation, noise, jitter, and electromigration. Carbon nanotubes can potentially address these challenges if they are optimally utilized.