1
|
Paudel RK, Ren CY, Chang YC. Semi-Empirical Pseudopotential Method for Graphene and Graphene Nanoribbons. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:2066. [PMID: 37513077 PMCID: PMC10383570 DOI: 10.3390/nano13142066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 07/06/2023] [Accepted: 07/11/2023] [Indexed: 07/30/2023]
Abstract
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.
Collapse
Affiliation(s)
- Raj Kumar Paudel
- Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan
- Molecular Science and Technology, Taiwan International Graduate Program, Academia Sinica, Taipei 11529, Taiwan
- Department of Physics, National Central University, Chungli 320, Taiwan
| | - Chung-Yuan Ren
- Department of Physics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan
| | - Yia-Chung Chang
- Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan
- Department of Physics, National Cheng-Kung University, Tainan 701, Taiwan
| |
Collapse
|
2
|
Exploitation of the Maximum Entropy Principle in the Study of Thermal Conductivity of Silicon, Germanium and Graphene. ENERGIES 2022. [DOI: 10.3390/en15134718] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
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.
Collapse
|
3
|
Thakur R, Ahluwalia PK, Kumar A, Sharma R. Strain modulated carrier mobility and optical properties of graphene nanowiggles. NANOTECHNOLOGY 2020; 31:505202. [PMID: 32996468 DOI: 10.1088/1361-6528/abb391] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
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.
Collapse
Affiliation(s)
- Rajesh Thakur
- Department of Physics, Himachal Pradesh University, Summer Hill, Shimla, Himachal Pradesh 171005, India
| | - P K Ahluwalia
- Department of Physics, Himachal Pradesh University, Summer Hill, Shimla, Himachal Pradesh 171005, India
| | - Ashok Kumar
- Department of Physics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab 151001, India
| | - Raman Sharma
- Department of Physics, Himachal Pradesh University, Summer Hill, Shimla, Himachal Pradesh 171005, India
| |
Collapse
|
4
|
Nathawat J, Zhao M, Kwan CP, Yin S, Arabchigavkani N, Randle M, Ramamoorthy H, He G, Somphonsane R, Matsumoto N, Sakanashi K, Kida M, Aoki N, Jin Z, Kim Y, Kim GH, Watanabe K, Taniguchi T, Bird JP. Transient Response of h-BN-Encapsulated Graphene Transistors: Signatures of Self-Heating and Hot-Carrier Trapping. ACS OMEGA 2019; 4:4082-4090. [PMID: 31459617 PMCID: PMC6648290 DOI: 10.1021/acsomega.8b03259] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Accepted: 02/07/2019] [Indexed: 06/10/2023]
Abstract
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.
Collapse
Affiliation(s)
- Jubin Nathawat
- Department
of Electrical Engineering and Department of Physics, University at Buffalo, the State University of New
York, Buffalo, New York 14260, United
States
| | - Miao Zhao
- High-Frequency
High-Voltage Device and Integrated Circuits Center, Institute of Microelectronics of Chinese Academy of Sciences, 3 Beitucheng West Road, Chaoyang District, Beijing 100029, PR China
| | - Chun-Pui Kwan
- Department
of Electrical Engineering and Department of Physics, University at Buffalo, the State University of New
York, Buffalo, New York 14260, United
States
| | - Shenchu Yin
- Department
of Electrical Engineering and Department of Physics, University at Buffalo, the State University of New
York, Buffalo, New York 14260, United
States
| | - Nargess Arabchigavkani
- Department
of Electrical Engineering and Department of Physics, University at Buffalo, the State University of New
York, Buffalo, New York 14260, United
States
| | - Michael Randle
- Department
of Electrical Engineering and Department of Physics, University at Buffalo, the State University of New
York, Buffalo, New York 14260, United
States
| | - Harihara Ramamoorthy
- Department of Electronics Engineering,
Faculty of Engineering and Department of
Physics, Faculty of Science, King Mongkut’s
Institute of Technology Ladkrabang, Bangkok, 10520 Thailand
| | - Guanchen He
- Department
of Electrical Engineering and Department of Physics, University at Buffalo, the State University of New
York, Buffalo, New York 14260, United
States
| | - Ratchanok Somphonsane
- Department of Electronics Engineering,
Faculty of Engineering and Department of
Physics, Faculty of Science, King Mongkut’s
Institute of Technology Ladkrabang, Bangkok, 10520 Thailand
| | - Naoki Matsumoto
- Department
of Materials Science, Chiba University, Inage-ku, Chiba 263-8522, Japan
| | - Kohei Sakanashi
- Department
of Materials Science, Chiba University, Inage-ku, Chiba 263-8522, Japan
| | - Michio Kida
- Department
of Materials Science, Chiba University, Inage-ku, Chiba 263-8522, Japan
| | - Nobuyuki Aoki
- Department
of Materials Science, Chiba University, Inage-ku, Chiba 263-8522, Japan
| | - Zhi Jin
- High-Frequency
High-Voltage Device and Integrated Circuits Center, Institute of Microelectronics of Chinese Academy of Sciences, 3 Beitucheng West Road, Chaoyang District, Beijing 100029, PR China
| | - Yunseob Kim
- School
of Electronic and Electrical Engineering and Sungkyunkwan Advanced
Institute of Nanotechnology (SAINT), Sungkyunkwan
University, Suwon 16419, Korea
| | - Gil-Ho Kim
- School
of Electronic and Electrical Engineering and Sungkyunkwan Advanced
Institute of Nanotechnology (SAINT), Sungkyunkwan
University, Suwon 16419, Korea
| | - Kenji Watanabe
- Advanced
Materials Laboratory, National Institute
for Materials Science, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Advanced
Materials Laboratory, National Institute
for Materials Science, Tsukuba 305-0044, Japan
| | - Jonathan P. Bird
- Department
of Electrical Engineering and Department of Physics, University at Buffalo, the State University of New
York, Buffalo, New York 14260, United
States
- Department
of Materials Science, Chiba University, Inage-ku, Chiba 263-8522, Japan
| |
Collapse
|
5
|
Silva GG, Ribeiro Junior LA, Pereira Junior ML, Fonseca ALDA, de Sousa Júnior RT, Silva GME. Bipolaron Dynamics in Graphene Nanoribbons. Sci Rep 2019; 9:2909. [PMID: 30814607 PMCID: PMC6393677 DOI: 10.1038/s41598-019-39774-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2018] [Accepted: 01/28/2019] [Indexed: 11/18/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Gesiel Gomes Silva
- Goiás Federal Institute of Education, Science and Technology, Luziania, Goias, 72.811-580, Brazil
| | - Luiz Antonio Ribeiro Junior
- Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83, Linkoping, Sweden.
- International Center for Condensed Matter Physics, University of Brasília, P.O. Box 04513, 70910-900, Brasília, Brazil.
- University of Brasília, PPG-CIMA, Campus Planaltina, 73345-010, Brasília, DF, Brazil.
| | | | - Antonio Luciano de Almeida Fonseca
- International Center for Condensed Matter Physics, University of Brasília, P.O. Box 04513, 70910-900, Brasília, Brazil
- University of Brasília, PPG-CIMA, Campus Planaltina, 73345-010, Brasília, DF, Brazil
| | | | | |
Collapse
|
6
|
Yamoah MA, Yang W, Pop E, Goldhaber-Gordon D. High-Velocity Saturation in Graphene Encapsulated by Hexagonal Boron Nitride. ACS NANO 2017; 11:9914-9919. [PMID: 28880529 DOI: 10.1021/acsnano.7b03878] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
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.
Collapse
Affiliation(s)
- Megan A Yamoah
- Department of Physics, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
| | - Wenmin Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences , Beijing 100190, China
| | | | | |
Collapse
|
7
|
Imperfect two-dimensional topological insulator field-effect transistors. Nat Commun 2017; 8:14184. [PMID: 28106059 PMCID: PMC5263869 DOI: 10.1038/ncomms14184] [Citation(s) in RCA: 63] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2016] [Accepted: 12/07/2016] [Indexed: 11/09/2022] Open
Abstract
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.
Collapse
|
8
|
Moors K, Sorée B, Magnus W. Validity criteria for Fermi's golden rule scattering rates applied to metallic nanowires. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:365302. [PMID: 27400727 DOI: 10.1088/0953-8984/28/36/365302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
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.
Collapse
Affiliation(s)
- Kristof Moors
- Institute for Theoretical Physics, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Imec, Kapeldreef 75, B-3001 Leuven, Belgium
| | | | | |
Collapse
|
9
|
Dollfus P, Hung Nguyen V, Saint-Martin J. Thermoelectric effects in graphene nanostructures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:133204. [PMID: 25779989 DOI: 10.1088/0953-8984/27/13/133204] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
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.
Collapse
Affiliation(s)
- Philippe Dollfus
- Institut d'Electronique Fondamentale (IEF), Université Paris-Sud, CNRS, UMR 8622, Orsay, France
| | | | | |
Collapse
|