Investigation of Horizontally Aligned Carbon Nanotubes for Efficient Power Delivery in 3D ICs Aida Todri-Sanial CNRS - LIRMM/University of Montpellier 2 Montpellier, France Email: aida.todri@lirmm.fr Abstract—Carbon nanotubes (CNTs) due their unique me- chanical, thermal, and electrical properties are being investi- gated as promising candidate material for on-chip and off-chip interconnects. The attractive mechanical properties of CNTs, including high Youngs modulus, resiliency and low thermal expansion coefficient offer great advantage for reliable and strong interconnects, and even more so for 3D integration. Through- Silicon-Vias (TSVs) enable 3D integration and implementation of denser, faster and heterogeneous circuits, which also lead to excessive power densities and elevated temperatures. Due to their unique properties, CNTs present an opportunity to address these challenges and provide solutions for reliable 3D integration. In this work, we perform detailed analyses of horizontally aligned CNTs and report on their efficiency to be exploited for 3D power delivery networks. I. I NTRODUCTION Three-dimensional integration technology provides the op- portunity to implement multi-layer circuits for higher density, heterogeneity and small footprint. Utilization of Through- Silicon-Vias (TSVs) as interconnects allows for shorter con- nections with improved delays and increased bandwidths. As wire width continue to shrink, copper interconnects in high- performance systems will suffer from significant increase in resistivity due to surface roughness and grain boundary scatter- ing and from electromigration problems due to the low current densities supported by copper conductors. Hence, despite the advantages of 3D integration, copper (Cu) based interconnects i.e. Cu TSVs will hinder performance and reliability of inter- connects, thus motivating the need for alternative interconnect materials for future process technologies. CNTs are a class of nanomaterials with unique mechanical, thermal and electrical properties [1]. CNTs can be classified into two types: single-wall (SWCNTs) and multi-wall (MWC- NTs). SWCNTs are rolled graphitic sheets with diameters on the order of 1nm. MWCNTs consist of several rolled graphitic sheets nested inside each other and can have diameters as large as 100nm. Depending on their chirality, the CNTs can be metallic or semiconductors. Metallic CNTs (m-CNTs) are ballistic conductors, which show promise for use as intercon- nects in nanoelectronics. On the other hand, semiconducting CNTs (s-CNTs) have a diameter-depended band-gap and do not have surface states that need passivation, thus can be used to make devices such as diodes and transistors [1]–[4]. One essential and most interesting application of the nanotubes in microelectronics is as interconnects using the ballistic (without scattering) transport of electrons and the extremely high thermal conductivity along the tube axis [5]. Electronic transport in SWCNTS and MWCNTS can go over long nanotube lengths, 1μm, enabling CNTs to carry very high currents (i.e. > 10 9 A/cm 2 ) with essentially no heating due to nearly 1D electronic structure. There are many works in literature that investigate CNT interconnects. The first group of works focuses on model- ing aspects of CNT inteconnects [1], [4]–[6]. The second group of works focuses on performance comparison of CNT interconnects versus copper (Cu) interconnects [2], [4], [7], [8]. Almost all these works have considered the application of CNT interconnects for signaling and few works focus on power delivery [3], [9]. Complementary to these efforts, this work aims to investigate the application of horizontally aligned CNTs for power delivery network in 3D ICs while exploiting their unique electrical and thermal properties. The rest of this paper is organized as follows. Section II describes the modeling techniques that we utilize in this work. In Section III we present the analysis of horizontally aligned CNTs for optimal power delivery network. Section IV concludes this paper. II. MODELING OF CARBON NANOTUBES There are many published papers in literature that focus on CNT modeling and understanding its transport properties [1]–[5]. In this section, we provide a brief description of CNT modeling that we utilize in this work. A generalized model for CNT interconnects is depicted in Fig. 1. In Fig. 1a the model of an individual MWCNT is shown with parasitics represent both dc conductance and high-frequency impedance i.e. induc- tance and capacitance effects. Multiple shells of a MWCNT are presented by their individual parasitics. Such model can also be applicable to SWCNTs where only a single shell is represented. Each shell has a lumped ballistic resistance (R i ), and lumped contact resistance (R c ) due to imperfect metal- nanotube contacts. These contacts are typically constructed of Gold, Palladium, or Rhodium [1]. The nanotubes have also a distributed ohmic resistance (R o ), which is dependent on length, l b , and mean free path of acoustic phonon scattering (λ ap ). Overall CNT resistance depends also on the applied bias voltage, R hb = V bias /I o , where I o is the maximum saturation current (I o values 15 to 30μA [6]). Between shells in MWCNTs, there is also an intershell tunneling resistance (R tun ). As the applied bias voltage to each shell is the same, the impact of R tun is relatively small. All the aforementioned ballistic, ohmic and contact resistance depend on the number of 1-D conducting channels, N c . For metallic SWCNTs the number of conducting channels is always N c =2 due to