Graphene Transistor Based on Tunable Dirac Fermion Optics
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Graphene transistor based on tunable Dirac fermion optics Ke Wanga,b, Mirza M. Elahic, Lei Wangd, K. M. Masum Habibc,1, Takashi Taniguchie, Kenji Watanabee, James Honed, Avik W. Ghoshc,f, Gil-Ho Leea,g,2, and Philip Kima,2 aDepartment of Physics, Harvard University, Cambridge, MA 02138; bSchool of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455; cDepartment of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904; dDepartment of Mechanical Engineering, Columbia University, New York City, NY 10027; eResearch Center for Functional Materials, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan; fDepartment of Physics, University of Virginia, Charlottesville, VA 22904; and gDepartment of Physics, Pohang University of Science and Technology, Pohang 37673, South Korea Edited by Tony F. Heinz, Stanford University, Stanford, CA, and accepted by Editorial Board Member Angel Rubio February 12, 2019 (received for review September 18, 2018) We present a quantum switch based on analogous Dirac fermion waveguiding (11–14), beam splitting (15), Veselago lensing (4), optics (DFO), in which the angle dependence of Klein tunneling is and negative refraction (5) in graphene. explicitly utilized to build tunable collimators and reflectors for the The strong angle dependence of Klein tunneling transmission quantum wave function of Dirac fermions. We employ a dual- T has been proposed to realize a type of switching device based source design with a single flat reflector, which minimizes diffu- on DF optics (DFO) (10, 14, 16–19). Fig. 1A shows a simple sive edge scattering and suppresses the background incoherent device scheme utilizing analogous electron optics. Here, a single- transmission. Our gate-tunable collimator–reflector device design layer graphene channel is controlled by several local gates with enables the quantitative measurement of the net DFO contribu- predetermined shapes, dividing up electron-doped (N) and hole- tion in the switching device operation. We obtain a full set of doped (P) regions in the channel. The electrons leaving the transmission coefficients between multiple leads of the device, source electrode pass through the first PN junction orthogonal to separating the classical contribution from the coherent transport the channel direction. This PN junction filters out electrons with contribution. The DFO behavior demonstrated in this work re- an oblique incident angle and collimates electron beams along SCIENCES quires no explicit energy gap. We demonstrate its robustness the channel. The next PN junction, placed at an angle (∼45°), APPLIED PHYSICAL against thermal fluctuations up to 230 K and large bias current blocks the collimated electron beam due to the oblique incidence density up to 102 A/m, over a wide range of carrier densities. to the PN junction and reflects it along a path orthogonal to the The characterizable and tunable optical components (collimator– original. However, in this simplistic device design, the reflected reflector) coupled with the conjugated source electrodes devel- beam hitting the rough physical edge of the device would dif- oped in this work provide essential building blocks toward more fusively scatter (Fig. 1A), leading ultimately to a leakage cur- advanced DFO circuits such as quantum interferometers. The ca- rent into the drain electrode. On top of that, multiple bounces pability of building optical circuit analogies at a microscopic scale of electrons in between collimator and reflector junctions with highly tunable electron wavelength paves a path toward contribute to the leakage current. To circumvent these diffusive highly integrated and electrically tunable electron-optical compo- nents and circuits. Significance graphene | Dirac fermion | electron optics | quantum transport We report an electrically tunable graphene quantum switch based on Dirac fermion optics (DFO), with electrostatically defined – he linear energy momentum dispersion, coupled with pseu- analogies of mirror and collimators utilizing angle-dependent Tdospinors (1), makes graphene an ideal solid-state material Klein tunneling. The device design allows a previously unreported platform to realize an electronic device based on Dirac- quantitative characterization of the net DFO contribution and fermionic relativistic quantum mechanics. Employing local gate leads to improved device performance resilient to abrupt change control, several examples of electronic devices based on Dirac in temperature, bias, doping, and electrostatic environment. The fermion (DF) dynamics have been demonstrated, including electrically tunable collimator and reflector demonstrated in this Klein tunneling (2), negative refraction (3–5), and specular work, and the capability of accurate in situ characterization of Andreev reflection (6, 7). their performance, provide the building blocks toward more While the depletion region of conventional semiconducting complicated functional quantum device architecture such as PN junction blocks the electronic transport across the junction, highly integrated electron-optical circuits. the gapless band structure of the graphene facilitates electrically adjustable PN junctions and enables electronic optics. The Author contributions: K. Wang, L.W., J.H., A.W.G., G.-H.L., and P.K. designed research; transmission probability (T) across the PN junction is unity for K. Wang, L.W., and G.-H.L. performed research; L.W. contributed new reagents/analytic normal incident electrons due to the pseudospin conservation of tools; K. Wang, M.M.E., L.W., K.M.M.H., A.W.G., G.-H.L., and P.K. analyzed data; K. Wang, M.M.E., L.W., K.M.M.H., T.T., K. Watanabe, J.H., A.W.G., G.-H.L., and P.K. wrote the paper; DFs. This startling phenomenon known as Klein tunneling (8, 9) and T.T. and K. Watanabe provided hBN crystals. was first demonstrated in a graphene PNP junction (2). For the The authors declare no conflict of interest. DFs with an oblique incident angle (θ), a PN junction exhibits ’ This article is a PNAS Direct Submission. T.F.H. is a guest editor invited by the Snell s law like an electron beam path with a negative refraction Editorial Board. – medium (3 5) for incoming Dirac electron wavefunctions. Published under the PNAS license. However, T is exponentially suppressed with θ as T ∼ exp 1 2 Present address: Technology Computer Aided Design, Intel Corporation, Santa Clara, [−π(kF(d/2))sin θ] for the symmetric potential of P and N re- CA 95054. k d gions, where F is Fermi momentum and is characteristic 2To whom correspondence may be addressed. Email: [email protected] or pkim@ length scale of potential change across the junction (8, 9). A physics.harvard.edu. generalized equation for arbitrary junctions is in ref. 10. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. Depending on the value of kFd, the junction can be transparent 1073/pnas.1816119116/-/DCSupplemental. or reflective, a result that has been employed for electron www.pnas.org/cgi/doi/10.1073/pnas.1816119116 PNAS Latest Articles | 1of5 Downloaded by guest on September 23, 2021 V A B gate region (controlled by gate 2) turns into the opposite carrier polarities of source and drain regions (controlled by gate V1), carriers injected from each source will either reflect back to the same source (oblique incident angle) or travel ballistically to the other source contact (perpendicular incident angle). This collimation–reflection results in suppressed conduction be- tween the source and the drain, and the device is in “off” state. When V1 and V2 are at the same polarity, the carriers flow ballistically to the drain, and the device is in “on” state. This device operation scheme has an advantage compared with the aforementioned single-source collimator–reflector scheme (Fig. 1A) or a sawtooth-shaped gate structure (18, 20, 21), as there is no significant channel edge contribution and only one reflection can be used for the off operation. Even with a nonideal reflector, we thus expect considerably enhanced DFO of the switch. CDFig. 1B shows electron microscope image of the local gates used for the dual-source device before the integration of gra- phene channel with two-source and one-drain electrodes in place. Switching operation of our device can be demonstrated by measuring two terminal resistance RT between the drain elec- trode (1) and source electrodes (2 and 3). A common bias voltage VD is applied to the source electrodes while the drain electrode is grounded. Two gate regions, collimation gates and the central gate, are controlled by applied gate voltages V1 and V2, respectively. Fig. 1C shows the measured RT as a function of V1 and V2. The resistance map in (V1, V2) plane can be divided into four quadrants separated by the peak region of RT ∼ 8kΩ, corresponding to the charge neutral Dirac point, V1, V2 ∼ 0. These four distinctive quadrants represent the source collima- tion/central gate/drain collimation regions in the NNN, NPN, Fig. 1. Graphene quantum switch. (A) Schematics of the device in the off PPP, and PNP regimes, respectively. We note that the NNN V V mode. Central green area (gate voltage, 1) and the blue areas ( 2)are R ∼ Ω V ·V < regime has the lowest resistance T of 500 , while the PPP doped in different polarity ( 1 2 0). The collimated electron beams regime exhibits considerably larger resistance of ∼1.5 kΩ.Inan through vertical and horizontal junctions are reflected toward the device ideal device, we expect a P/N symmetry in the device gate op- edge in one-source geometry or back to the source in two-source geometry. – (B) Atomic force microscope image of bottom gates was taken before eration due to the particle hole symmetry in the graphene band transferring a stack of hBN/graphene/hBN. Overlaid broken lines guide the structure. However, the graphene channel can exhibit asymmetry boundaries of graphene. (C) Color-coded total resistance (RT) as a function of in contact resistance due to the metal-induced contact doping V V D 1 and 2.( ) Slide cut of the resistance shows the on/off ratio of 6 at fixed (22), which prefers N channel to have lower contact resistance in V = 2 5 V.