Electro-thermal Transport through Graphene & CNT at Nano-second Time Scales and its Implications on Device Reliability

Abstract

The prospects of using Graphene and MWCNT as a channel material for RF transistors and interconnects, respectively, have recently garnered much attention. E orts are being made for improvements at the material and device fronts. The development of a technology platform for devices based on these materials demands consideration of two crucial factors - 1) comprehensive understanding of time evolution of electro-thermal transport, so that the associated mechanisms can be modelled for deterministic operation of devices at di erent time scales (frequency); 2) understanding the physical limits of operation by assessment of reliability against electro-thermal transport induced instantaneous or catastrophic failure and long-term material degradation. In this work, a comprehensive investigation of time-evolution of electro-thermal transport is presented, and its implications on operational reliability is explored. Various time-scales and associated events discussed in the thesis are shown in figure 1. When an electron enters a channel, it undergoes collision at the rate estimated by Fermi's Golden Rule. The state of collision is a near-adiabatic process, which lasts for few pico-seconds, during which the collision-induced thermal energy remains localised to the site of collision. Gradually, the collision-induced thermal energy or heat diffuses in the entire device, due to which the device enters a state of electro-thermal non-equilibrium. The state is prone to catastrophic events like EOS/ESD. The non-equilibrium state is succeeded by a state of electro-thermal equilibrium, during which the temperature and excess energy transients settle down, and further elongated operation results in degradation of the material. Given the low-dimensional nature of the materials chosen for this thesis and their extraordinary electrical and thermal properties, the devices so fabricated demand deployment of novel techniques for the investigation of time-evolution of transport and assessment of reliability. A measurement setup employing a synergetic utilization of a transmission line pulse generator, DC SMUs, current sensor, high frequency oscilloscope and a Raman spectrometer is developed for such investigations. To comprehend the temporal nature of transport, it's time evolution is investigated during the process of redistribution of thermal energy after inelastic collisions. The process, governed by diffusion of heat across the device, happens at the time scale corresponding to characteristic thermal diffusion time of the device, which, owing to high thermal conductivity of graphene, MWCNT and high thermal mass of dielectric substrate, is of the order of nano-seconds. The time response is captured during a state of electro-thermal non-equilibrium, which exists in a window between near-adiabatic and steady state of the device. The response is interpreted by studying the corresponding effects on metal-graphene contact resistance, conductivity near the Dirac point, conduction through higher sub-bands and inner shells of a MWCNT. The parameters were found to show a temporal behaviour during the electro-thermal non-equilibrium state, followed by a saturation during the steady state. Having developed an understanding of electro-thermal transport through graphene and MWCNT, an assessment of operational reliability is done for electro-thermal transport induced instantaneous or catastrophic failures and long-term material degradation. The instantaneous failures correspond to damage during energy redistribution (non-equilibrium state) or post energy redistribution (equilibrium or steady state) across the device. The former failure conditions are emulated by electro-static discharge (ESD), while the latter corresponds to electrical over-stress (EOS). The degradation of material is studied at a longer time scale, while capturing the changes in chemical state of the material. The reliability assessment is done while considering the possible heat sinks in the device - metal contacts and substrate. Breakdown behaviour corresponding to shell-by-shell ablation and defect-by-defect unzipping are investigated as possible failure routes in a MWCNT and graphene, respectively. In graphene, the phonon transport due to high electric-field was found to impart a transient nature to contact resistance and conduction near Dirac point [1], both of which have previously been assumed to be time-independent parameters. Their transient nature was captured during the non-equilibrium state of the transport, which, in turn, was found to persist for few nano-seconds. Such a transient behaviour of contact resistance highlights the elusive role of metal-graphene interface in dissipation of excessive heat in 2D-material based devices, which has been captured here by monitoring it at the time-scale of thermal diffusion time. The role of contacts in removing heat is further substantiated by breakdown voltage, which was found to scale with contact resistance. The electric-field induced breakdown was found to follow two different pathways. A field-dependent defectby- defect breakdown was observed at high electric-fields, particularly under electro-static discharge (ESD) and electrical over-stress (EOS) conditions. At low electric-fields, a time-dependent defect-by-defect breakdown was captured, where the oxidation of defects (captured through Raman map) was dictated by time for which the electric-field was applied. The graphene channel, instead of showing a complete and abrupt breakdown, was found to fail in steps, captured through discrete fall in current through the channel. Overall, the breakdown was found to follow a cascade of two-step process -(1) excessive scattering and eventual heat dissipation at the defect site and (2) oxidation at the defect site, resulting in emergence of more defects [2]. A similar set of investigations were carried out on MWCNT-based interconnects. Interestingly, under high-fields, the electro-thermal transport was found to cause shell-by-shell breakdown of a MWCNT [3]. The current due to electro-thermal transport through a suspended MWCNT was found to increase with time due to rise in temperature of the cold electrode, followed by saturation due to attainment of equilibrium [4]. The tubes supported by a polar dielectric were found to break at higher voltages than the suspended tubes, which, in turn, is attributed to remote Joule heating of the polar dielectric via surface polar phonons [5,6,]. Moreover, at high currents, in addition to melting of the hot contact, flow of heat from this end to the cold contact, through a bundle of MWCNTs, was found to cause a melt of cold contact as well [7]. Further, a controlled technique to anneal the contacts and channel is explored, which enables a lever to achieve a precise control on resistance of the MWCNT-based devices at the time scale of nano-seconds and provides insights into the process of current annealing [8]. In a nutshell, the mechanism behind time-evolution of electro-thermal transport through graphene and MWCNT-based devices has been investigated, and its manifestation as a potential reliability and aging issue has been explored. It is found that the electrical transport is a time-function of intrinsic heating (scattering) of the device. A maximum change of 50% in metal-graphene contact resistance was captured over a time-span of 8 ns. Further, it is found that the low-dimensional nature of 1D and 2D materials amplifies the effect of various interfaces and defects on the electro-thermal transport through the devices based on these materials. Consequently, their reliable operation demands engineered interfaces and low-defect density, for efficient phonon transport across the interface and delayed oxidation of the lattice, respectively. Contrary to bulk semiconductors, which break only above a critical field, the time-dependent failure behaviour of graphene has been discovered, which precludes the existence of failure threshold and manifests as a potential defect-assisted aging issue for graphene and other 2D material-based devices