Pseudopotential-based studies of electron transport in graphene and graphene nanoribbons

Semi-Empirical Pseudopotential Method for Graphene and Graphene Nanoribbons

We implemented a semi-empirical pseudopotential (SEP) method for calculating the band structures of graphene and graphene nanoribbons. The basis functions adopted are two-dimensional plane waves multiplied by several B-spline functions along the perpendicular direction. The SEP includes both local and non-local terms, which were parametrized to fit relevant quantities obtained from the first-principles calculations based on the density-functional theory (DFT). With only a handful of parameters, we were able to reproduce the full band structure of graphene obtained by DFT with a negligible difference. Our method is simple to use and much more efficient than the DFT calculation. We then applied this SEP method to calculate the band structures of graphene nanoribbons. By adding a simple correction term to the local pseudopotentials on the edges of the nanoribbon (which mimics the effect caused by edge creation), we again obtained band structures of the armchair nanoribbon fairly close to the results obtained by DFT. Our approach allows the simulation of optical and transport properties of realistic nanodevices made of graphene nanoribbons with very little computation effort.

Exploitation of the Maximum Entropy Principle in the Study of Thermal Conductivity of Silicon, Germanium and Graphene

In this paper, we review the application of a recent formula for the lattice thermal conductivity to silicon and germanium, which are two of the most commonly used materials in electronic devices, and to graphene, one the most promising new materials. The formula, which is based on a hierarchy of macroscopic models that generalize the Cattaneo equation, is capable of reproducing the results achieved by means of the well-known Callaway formula. In semiconductors, energy transport is largely due to acoustic phonons, therefore one can choose suitable moments of their occupation numbers as variables of the models. Equations determining the time evolution of these state variables are derived from the Boltzmann–Peierls transport equation by integration, while the maximum entropy principle (MEP) is used to obtain closure relations for the extra variables. All relevant phonon scattering mechanisms are taken into account. We present numerical results regarding the steady-state and dynamical thermal conductivities of silicon, germanium, and graphene, showing their main characteristics and how these are affected by the various scatterings. The results are in good qualitative and quantitative agreement with those in the literature, confirming that MEP is a valid method for developing macroscopic models of charge and energy transport in semiconductor materials.

Strain modulated carrier mobility and optical properties of graphene nanowiggles

Recently, synthesized Chevron graphene nanoribbons (CGNRs) and its laterally extended counterpart known as extended CGNRs (ECGNR) are constructed by making alternated regular cuts in pristine graphene nanoribbons (GNRs). First-principles calculations demonstrate that these GNRs are super-ductile and possess width-dependent mechanical properties. The Young's modulus is calculated to be 389.4 GPa and 414.6 GPa for CGNR and ECGNR, respectively. The bandgap of these nanoribbons decreases on the application of tensile strain. The carrier effective masses are found to be highly sensitive towards mechanical strains. The holes (electrons) mobility of ECGNR is calculated to be 7.68 × 10⁴ cm² V^-1 s^-1 (1.69 × 10⁴ cm² V^-1 s^-1), which is higher than that of CGNR can be further enhanced by elongation. The prominent peaks of the imaginary part of dielectric function and electron energy loss spectra show redshift on increasing the tensile strain. The electron energy loss spectra show intense plasmonic structure in low energy spectrum indicating GNRs to be more sensitive to the visible region than ultra violet spectrum. Our results provide insight about the possible applications of GNRs in the fields of high-speed transistors, sensors, photonics, and optoelectronics.

Transient Response of h-BN-Encapsulated Graphene Transistors: Signatures of Self-Heating and Hot-Carrier Trapping

We use transient electrical measurements to investigate the details of self-heating and charge trapping in graphene transistors encapsulated in hexagonal boron nitride (h-BN) and operated under strongly nonequilibrium conditions. Relative to more standard devices fabricated on SiO₂ substrates, encapsulation is shown to lead to an enhanced immunity to charge trapping, the influence of which is only apparent under the combined influence of strong gate and drain electric fields. Although the precise source of the trapping remains to be determined, one possibility is that the strong gate field may lower the barriers associated with native defects in the h-BN, allowing them to mediate the capture of energetic carriers from the graphene channel. Self-heating in these devices is identified through the observation of time-dependent variations of the current in graphene and is found to be described by a time constant consistent with expectations for nonequilibrium phonon conduction into the dielectric layers of the device. Overall, our results suggest that h-BN-encapsulated graphene devices provide an excellent system for implementations in which operation under strongly nonequilibrium conditions is desired.

Bipolaron Dynamics in Graphene Nanoribbons

Graphene nanoribbons (GNRs) are two-dimensional structures with a rich variety of electronic properties that derive from their semiconducting band gaps. In these materials, charge transport can occur via a hopping process mediated by carriers formed by self-interacting states between the excess charge and local lattice deformations. Here, we use a two-dimensional tight-binding approach to reveal the formation of bipolarons in GNRs. Our results show that the formed bipolarons are dynamically stable even for high electric field strengths when it comes to GNRs. Remarkably, the bipolaron dynamics can occur in acoustic and optical regimes concerning its saturation velocity. The phase transition between these two regimes takes place for a critical field strength in which the bipolaron moves roughly with the speed of sound in the material.

High-Velocity Saturation in Graphene Encapsulated by Hexagonal Boron Nitride

We measure drift velocity in monolayer graphene encapsulated by hexagonal boron nitride (hBN), probing its dependence on carrier density and temperature. Due to the high mobility (>5 × 10⁴ cm²/V/s) of our samples, the drift velocity begins to saturate at low electric fields (∼0.1 V/μm) at room temperature. Comparing results to a canonical drift velocity model, we extract room-temperature electron saturation velocities ranging from 6 × 10⁷ cm/s at a low carrier density of 8 × 10¹¹ cm^-2 to 2.7 × 10⁷ cm/s at a higher density of 4.4 × 10¹² cm^-2. Such drift velocities are much higher than those in silicon (∼10⁷ cm/s) and in graphene on SiO₂, likely due to reduced carrier scattering with surface optical phonons whose energy in hBN (>100 meV) is higher than that in other substrates.

Imperfect two-dimensional topological insulator field-effect transistors

To overcome the challenge of using two-dimensional materials for nanoelectronic devices, we propose two-dimensional topological insulator field-effect transistors that switch based on the modulation of scattering. We model transistors made of two-dimensional topological insulator ribbons accounting for scattering with phonons and imperfections. In the on-state, the Fermi level lies in the bulk bandgap and the electrons travel ballistically through the topologically protected edge states even in the presence of imperfections. In the off-state the Fermi level moves into the bandgap and electrons suffer from severe back-scattering. An off-current more than two-orders below the on-current is demonstrated and a high on-current is maintained even in the presence of imperfections. At low drain-source bias, the output characteristics are like those of conventional field-effect transistors, at large drain-source bias negative differential resistance is revealed. Complementary n- and p-type devices can be made enabling high-performance and low-power electronic circuits using imperfect two-dimensional topological insulators.

A challenge of using 2D materials for nanoelectronic devices is the need for defect-free lattice supporting efficient carrier transport. Here, the authors show theoretically that 2D topological insulators enable high-performance, low-power field-effect transistors without requiring defect-free materials.

Validity criteria for Fermi's golden rule scattering rates applied to metallic nanowires

Fermi's golden rule underpins the investigation of mobile carriers propagating through various solids, being a standard tool to calculate their scattering rates. As such, it provides a perturbative estimate under the implicit assumption that the effect of the interaction Hamiltonian which causes the scattering events is sufficiently small. To check the validity of this assumption, we present a general framework to derive simple validity criteria in order to assess whether the scattering rates can be trusted for the system under consideration, given its statistical properties such as average size, electron density, impurity density et cetera. We derive concrete validity criteria for metallic nanowires with conduction electrons populating a single parabolic band subjected to different elastic scattering mechanisms: impurities, grain boundaries and surface roughness.

Thermoelectric effects in graphene nanostructures

The thermoelectric properties of graphene and graphene nanostructures have recently attracted significant attention from the physics and engineering communities. In fundamental physics, the analysis of Seebeck and Nernst effects is very useful in elucidating some details of the electronic band structure of graphene that cannot be probed by conductance measurements alone, due in particular to the ambipolar nature of this gapless material. For applications in thermoelectric energy conversion, graphene has two major disadvantages. It is gapless, which leads to a small Seebeck coefficient due to the opposite contributions of electrons and holes, and it is an excellent thermal conductor. The thermoelectric figure of merit ZT of a two-dimensional (2D) graphene sheet is thus very limited. However, many works have demonstrated recently that appropriate nanostructuring and bandgap engineering of graphene can concomitantly strongly reduce the lattice thermal conductance and enhance the Seebeck coefficient without dramatically degrading the electronic conductance. Hence, in various graphene nanostructures, ZT has been predicted to be high enough to make them attractive for energy conversion. In this article, we review the main results obtained experimentally and theoretically on the thermoelectric properties of graphene and its nanostructures, emphasizing the physical effects that govern these properties. Beyond pure graphene structures, we discuss also the thermoelectric properties of some hybrid graphene structures, as graphane, layered carbon allotropes such as graphynes and graphdiynes, and graphene/hexagonal boron nitride heterostructures which offer new opportunities. Finally, we briefly review the recent activities on other atomically thin 2D semiconductors with finite bandgap, i.e. dichalcogenides and phosphorene, which have attracted great attention for various kinds of applications, including thermoelectrics.