Frank Tseng

Diluted chirality dependence in edge rough graphene nanoribbon field-effect transistors

We investigate the role of various structural nonidealities on the performance of armchair-edge graphene nanoribbon field effect transistors (GNRFETs). Our results show that edge roughness dilutes the chirality dependence often predicted by theory but absent experimentally. Instead, GNRs are classifiable into wide (semimetallic) versus narrow (semiconducting) strips, defining thereby the building blocks for wide-narrow-wide all-graphene devices and interconnects. Small bandgaps limit drain bias at the expense of band-to-band tunneling in GNRFETs. We outline the relation between device performance metrics and nonidealities such as width modulation, width dislocations and surface step, and nonideality parameters such as roughness amplitude and correlation length.

Monolithically Patterned Wide–Narrow–Wide All-Graphene Devices

We investigate theoretically the performance advantages of all-graphene nanoribbon field-effect transistors (GNRFETs) whose channel and source/drain (contact) regions are patterned monolithically from a 2-D single sheet of graphene. In our simulated devices, the source/drain and interconnect regions are composed of wide GNR sections that are semimetallic, while the channel regions consist of narrow GNR sections that open semiconducting bandgaps. Our simulation employs a fully atomistic model of the device, contact, and interfacial regions using tight-binding theory. The electronic structures are coupled with a self-consistent 3-D Poissons equation to capture the nontrivial contact electrostatics, along with a quantum kinetic formulation of transport based on nonequilibrium Greens functions. Although we only consider a specific device geometry, our results establish several general performance advantages of such monolithic devices (besides those related to fabrication and patterning), namely, the improved electrostatics, suppressed short-channel effects, and Ohmic contacts at the narrow-to-wide interfaces.

Graphene devices, interconnect and circuits — challenges and opportunities

Graphene has recently emerged as a serious contender for the post Silicon era. Graphene NanoRibbon (GNR) devices have similar performance characteristics to Carbon Nano Tube (CNT) ones. However, lithographic patterning methods applied to graphene can avoid the degree of chirality control and alignment issues typical of CNTs, and GNR devices and GNR interconnect can in principle be seamlessly obtained by patterning single graphene sheets, thus leading to monolithically device-interconnect structures. Electrically doped GNR devices in series and in parallel can be used for creating complex GNR FET digital circuits. There are also several important challenges facing the graphene “brave new world,” but many of the difficulties hopefully will have tractable solutions. This paper examines the topic of GNR FET circuit design from a bottom-up theoretical perspective, starting with GNR device and interconnect modeling and simulation, while trying to reconcile theory with some recent experimental results.

Atomistic deconstruction of clear performance advantages of a monolithically patterned wide-narrow-wide all-graphene FET

Experiments show that wide GNRs are all metallic while ultra thin ribbons (<10 nm in width) are all semiconducting [1] and the bandgap increases as the width get narrower. This leads us to design an all a graphene nanoribbon field effect transistor (GNRFET) and atomistically simulate its transport properties. We expect this system to benefit from the unique 2-D electrostatics of the source-drain regions and the covalent bonding at the contact-channel interfaces. Our device model is unique compared to standard treatments of all graphene nanoribbons with side gates [2], because our drain/source contacts and the channel are patterned from a single graphene sheet template. Also our top gate geometry is superior compared to the side gates that act through fringing fields and are susceptible to tunneling due to the absence of an interfacing oxide film. Simulations were conducted using orthogonal tight-binding (TB) and the bandstructures coupled with non-equilibrium Greens Function [3] (NEGF)-based quantum transport formalism. The simulated geometry includes a metallic gate approximately three times wider than the channel placed 1nm above it. A wide, finite, and grounded substrate is placed 3nm below the channel region to control the device I–V characteristics. We used HfO2 (k=16) as a high-k top-gate dielectric and SiO2 (k=3.9) as the substrate dielectric with grounded substrate contact.

Physics-based GNRFET compact model for digital circuit design

Graphene has attracted significant interest as a possible candidate for future transistors because of its high carrier mobility and current density [1]. The biggest setback of intrinsic graphene in digital applications is the absence of a bandgap, needed for digital logic to distinguish between high and low current states. Experiments demonstrated the opening of a bandgap by either applying an interlayer electrical field on bilayer graphene [2], or quantum confinement in narrow graphene nanoribbons (GNRs) (<10 nm in width) [3], which ushered in the design of wide-narrow-wide GNR field-effect transistors (GNRFET) [4]. However, such a bandgap comes at the expense of mobility [5]. Goal of this paper is to show the architectural ramifications of small bandgap graphene, using physics based compact model benchmarked with experiment.

Graphene Nanoribbons: From Chemistry to Circuits

The Y-chart is a powerful tool for understanding the relationship between various views (behavioral, structural, and physical) of a system, at different levels of abstraction, from high-level, architecture and circuits, to low-level, devices and materials. We thus use the Y-chart adapted for graphene to guide the chapter and explore the relationship among the various views and levels of abstraction. We start with the innermost level, namely, the structural and chemical view. The edge chemistry of patterned graphene nanoribbons (GNRs) lies intermediate between graphene and benzene, and the corresponding strain lifts the degeneracy that otherwise promotes metallicity in bulk graphene. At the same time, roughness at the edges washes out chiral signatures, making the nanoribbon width the principal arbiter of metallicity. The width-dependent conductivity allows the design of a monolithically patterned Wide–Narrow–Wide (WNW) all graphene interconnect-channel heterostructure. In a three-terminal incarnation, this geometry exhibits superior electrostatics, a correspondingly benign short-channel effect and a reduction in the contact Schottky barrier through covalent bonding. However, the small bandgaps make the devices transparent to band-to-band tunneling. Increasing the gap with width confinement (or other ways to break the sublattice symmetry) is projected to reduce the mobility even for very pure samples, through a fundamental asymptotic constraint on the bandstructure. An analogous trade-off, ultimately between error rate (reliability) and delay (switching speed) can be projected to persist for all graphitic derivatives. Proceeding thus to a higher level, a compact model is presented to capture the complex nanoribbon circuits, culminating in inverter characteristics, design metrics, and layout diagrams.

Conductance of graphene: Role of metal contact, charge puddles and differential gating

We demonstrate how several experiments on graphene transport can be explained semi-quantitatively within a Non-Equilibrium Greens Function (NEGF) formalism. The key features are controlled by-(i) the boundary potential established at a metal-graphene interface,(ii) charge puddles that help the conductivity in the ballistic limit and hurt in the diffusive limit and (iii) alignment of the local Dirac points in a multiply gated segment. Simulations reveal that at the ballistic limit, the conductance depends on the aspect ratio which controls tunneling from source to drain and across the metal-graphene interface. We show that the boundary potential VB at the interface together with Metal Induced Doping (MID) are critical to graphene transport-specifically, the maximum conductance achievable with a given metal contact, the electron-hole asymmetry (EHA) and the peak device resistance. The boundary potential is formed due to in-plane charge transfer from metal covered graphene to graphene on substrate [1] and may produce an additional smooth pn junction, typically ignored in existing models. In the experiments however, the contact resistance heavily depends on the fabrication procedure [2], varying from hundreds of Ω- μm to several thousands of Ω- μm [3]. A rigorous model of the performance limits of several contacts and change of carrier transport from ballistic to diffusive regime is lacking. We report the upper limit of the performance of various metal-graphene contacts and compare with the best available experimental values. To reach experimental dimensions, we use tight-binding real space calculations as well as the powerful KSF-RGFA approach (combination of K Space Formalism (KSF) and Recursive Greens Function Algorithm (RGFA) [4]), which allows us to simulate devices as large as microns in size.

Can we engineer current saturation in narrow gap graphitic FETs without hurting mobility

While a wide bandgap material with poor mobility can saturate the output current, we demonstrate a way to achieve clear current saturation in the output characteristics using narrow-bandgap, high mobility graphitic-channels(Fig.4b, 4c) without hurting the mobility. Using gate engineering alone, we preserve the intrinsic narrow bandgap but locally cascade them along the channel. This filters intermediate conduction and valence bands and widens the gap in the tranmission (Fig.3) without sacrificing mobility. A widen transmission gap delays the onset of band-to-band tunneling, which normally plagues devices with a narrow bandgap channel. Results are verified using an optimized fully atomistic non-equilibrium Greens Function(NEGF) solver with complex 3-D Poisson1. A graphitic channel is used as a template but is one of many possible narrow-bandgap materials with high mobility. Without hurting mobility, the improved current saturation is expected to enhance gain for radio frequency(RF) and potentially digital switching applications by significantly decreasing output conductance(gds)2.

Switching limits in nano-electronic devices

Present day CMOS transistors operate by thermionic emission of electrons over a gate tunable barrier. The fundamental switching energy for each such switching event can be derived from equilibrium thermodynamic considerations. While clever ways can sometimes mitigate the power budget, more often than not, this involves trade-offs with short channel effects (variability), on-off ratio (reliability) and mobility (switching speed). We discuss switching paradigms that venture beyond the near-equilibrium operation of transistors involving the absence or presence of charges as the digital switching bits. To this end, a few case studies are presented. Dipolar switching is invoked as an example to show how gating non-electronic degrees of freedom can reduce the subthreshold swing below the textbook limit by acting as an added cut-off filter on the current. We discuss how new state variables may be engineered into a CMOS platform to enable such non-electronic switching. Another, completely different direction involves non-equilibrium switching, such as a ratchet that allows us to move charges unidirectionally without a drain bias, by using instead an always present AC clock signal adiabatically coupled with the gate.

Absolute control of chirality unnecessary for wide-narrow-wide graphene field effect transistor

In contrast with carbon nanotubes, graphene nanoribbons (GNRs) suffer from edge roughness that dilutes its chirality dependence, creating a single inverse power law curve relating energy-bandgap and width. Thus all narrow nanoribbons (>10nm) are semiconducting while all wide nanoribbons are metallic. Our model which combines well-benchmarked semi-empirical Extended Huckel Theory (EHT)-based electronic structure with an atomistic theory for quantum transport to illustrate this dilution of chirality dependence not-predicted by simplified tight-binding theory with ideal GNRs, but observed in experiments (Fig.1) [1, 2].