Graphene Field Effect Transistor

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  1. 1. GRAPHENE FIELD EFFECT TRANSISTORS Prepared By: Ahmed Nader Al-Askalany Sumit Mohanty Mohamed Atwa Faraz Khavari Supervisor: Jan Linnros 4/14/2015
  2. 2. AGENDA I. Introduction II. Theory of Graphene III. GFET IV. Conclusion
  3. 3. INTRODUCTION
  4. 4. HISTORY OF GRAPHENE Theoretically predicted 50 years ago 2004 making 2- D sheet Andre Geim www.observation-science.com
  5. 5. MONOLAYER AND BILAYER GRAPHENE Monolayer single layer of Graphite zero band gap semiconductor or a semimetal Linear dispersion relation Hassan Raza, Hassan, Graphene nanoelectronics: Metrology, synthesis, properties and applications, Springer Science & Business Media, 2012. E. L. Wolf, Applications of Graphene, SPRINGER BRIEFS IN MATERIALS, Springer, ISBN 978-3-319- 03945-9, 2014.
  6. 6. MONOLAYER AND BILAYER GRAPHENE Bilayer Graphene same methods to grow bilayer Graphene Semimetal, high carrier mobility, parabolic Hassan Raza, Hassan, Graphene nanoelectronics: Metrology, synthesis, properties and applications, Springer Science & Business Media, 2012.
  7. 7. POTENTIAL APPLICATION tolerating tension, bending heat and electricity conductors Tunable Fermi Single velocity of 106m/s high electron mobility, chemically inert very large area of 2600m2/g 1. organic and CdTe based solar cells 2. transparent electrodes in Touch Screens 3. FET switches& Tunneling FET Devices 4. High Frequency FET 5. Flash memories
  8. 8. THEORY OF GRAPHENE
  9. 9. SUB-AGENDA 2. Monolayer Graphene A. Real Space Structure B. Reciprocal Lattice C. Electronic Structure 1. The Tight Binding Approximation 2. Results of Tight Binding 3. Bilayer Graphene A. Real Space Structure B. Reciprocal Lattice C. Electronic Structure 1. The Tight Binding Approximation 2. Results of Tight Binding Again For: 1. Synthesis of Graphene Reduction of Intercalated GO
  10. 10. SYNTHESIS OF GRAPHENE Deceptively Simple?
  11. 11. RESULTING NUMBER OF LAYERS Monolayer Graphene Micromechanical cleavage of High-Purity Graphite CVD on metal surfaces Epitaxial growth on an insulator (SiC) Intercalation of graphite Dispersion of graphite in water, NMP Reduction of single-layer graphene oxide Bi/Multi-Layer Graphene Chemical reduction of exfoliated graphene oxide (26 layers) Thermal exfoliation of graphite oxide (27 layers) Aerosol pyrolysis (240 layers) Arc discharge in presence of H2 (24 layers) C. N. R. Rao, Ajay K. Sood. Graphene: Synthesis, Properties, and Phenomena. John Wiley & Sons, 2013 .
  12. 12. HIGHLIGHTED METHOD: REDUCTION OF EXFOLIATED GRAPHENE OXIDE 1. Oxidation of graphite with strong oxidizing agents such as KMnO4 and NaNO3 in H2SO4 /H3PO4 2. Oxygen atoms interleave between the layers increasing the atomic spacing from 3.7 to 9.5 3. Ultrasonication and reduction in dimethyl fluoride or water yields bilayer Boya Dai, Lei Fu, Lei Liao, Nan Liu, Kai Yan, Yongsheng Chen, Zhongfan Liu. "High-quality single- layer graphene via reparative reduction of graphene oxide." Nano Research, 2011: 434-439
  13. 13. GRAPHENE: A FAMILIAR STRUCTURE REVISITED
  14. 14. MONOLAYER GRAPHENE Real Space Lattice Reciprocal Lattice: 1 2 3 , 2 2 3 , 2 2 a a a a a a 2.46 1.42 3cc a aa 1 2 2 2 , 3 2 2 , 3 b a a b a a Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
  15. 15. ELECTRONIC STRUCTURE OF MONOLAYER GRAPHENE sp2 Hybridization: 2s +2px+2py sp2 hybridization three sp2 orbitalsCarbon atoms each possess six electrons: Two 1s core electrons Four valance electrons: 1 2s 1 2px 12py 1 2pz 3 sp2 Orbitals Adjacent pz orbitals combine orbitals Magazine, Paintings & Coatings Industry. Graphite: A Multifunctional Additive for Paint and Coatings. October 1, 2003. http://www.pcimag.com/a rticles/83004-graphite-a- multifunctional-additive- for-paint-and-coatings
  16. 16. THE TIGHT BINDING APPROXIMATION orbitals One 2pz orbital per atom is the orbital binding energy 0 is the nearest-neighbor hopping energy s0 is a factor accounting for the non- orthogonality of orbitals on adjacent atomic sites and are the structure factor and its complex conjugate describing nearest neighbor hopping 0 1 0 2 2 ( ) *( ) p p f H f k k 0 1 0 1 ( ) 1*( ) s f S s f k k Transfer integral matrix Overlap integral matrix 2 p 0 ( )s f k 0 *( )s f k Relation between H and S: j j jH E S Solving the secular equation Ej det 0jH E S
  17. 17. SOLVING THE SECULAR EQUATION FOR MONOLAYER GRAPHENE Around the Brillouin zone edges K+ and K- : 2 0 0 ( ) 1 ( ) p f E s f k k E p is the mean electron velocity: 03 2 a p is the canonical momentum: p k K Effective Hamiltonian: Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012 1 = 0 + 0
  18. 18. CHIRALITY: NOT ALL FIELD IS EQUAL Pseudospin: H and Eigenstates near each K point Two values Called Psudospins Deg. of freedom for the relative amplitude of the wavefunction on each sublattice: All electrons on sublattice A: Pseudospin Up All electrons on sublattice B: Pseudospin Down Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
  19. 19. ANGULAR DEPENDENCY OF SCATTERING Rotating the Pseudospin Degree of Freedom Changing of the wavefunction on A or B Rewriting the Hamiltonian: 1 = ( + = Where: = cos, sin, 0 Angular dependence of scattering: ( = cos2 ( 2 No backscattering! Klein tunneling, anisotropic scattering at potential barriers in monolayers Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012 Berrys phase: Angular range of the scattering probability of the chiral wavefunction in monolayer
  20. 20. BILAYER GRAPHENE Real Space Lattice B1 and A2, are directly below or above each other (dimer sites) A1 and B2, do not have a counterpart in the other layer (Bernal Stacking, AB-Stacking) 0 3.033 eV 1 0.39 eV Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
  21. 21. ELECTRONIC STRUCTURE OF BILAYER GRAPHENE Four atoms per unit cell One pz orbital in tight binding model per atomic site We expect 4 bands near zero energy Solving the Secular Equation: 2 2 ( 1) 2 1 4 1 1 2 p E At low energies: 2 2 2 ( 1) 1 4 2 p p E m Quadratic, Chiral and Massive Separation between each two bands is 1 Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
  22. 22. CHIRALITY IN BILAYER GRAPHENE Berrys Phase: 2 Forward and backward scattering! 2 ( ) cos ( )w Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
  23. 23. KEY TAKE-AWAYS Comparison Monolayer Graphene Bilayer Graphene E-k relation Around the K points Linear Dispersion Number of Bands One Conduction, One Valance Two Conduction, Two Valance, Split by 1 Bandgap at zero bias No-(opened via additional confinement) No-(opened via doping, sandwiching or application of field) Scattering Anisotropic forward scattering (Berrys Phase ) Anisotropic forward and backward scattering (Berrys Phase 2)
  24. 24. GFET
  25. 25. AGENDA I. Introduction II. Theory of Graphene III. GFET I. Bilayer Graphene Field Effect Transistor II. Graphene Nanoribbon Field Effect Transistor IV. Conclusion
  26. 26. BILAYER GRAPHENE FET 1.Breaking the Symmetry 2.BLG Electrostatics 3.Actual Device 4.Charge Neutrality and Bandgap Tunability 5.Optical Absorption Spectra of BLGFET 6.I-V Characteristics
  27. 27. BREAKING THE SYMMETRY? A1 and B2 symmetry Zero bandgap at K point Perpendicular E breaks symmetry A1 and B2 at different energies Bandgap opened Fermi level position (effective doping)
  28. 28. BLGFET ELECTROSTATICS Bottom Gate Top Gate 0 Interlayer Separation top gate Dielectric constant bottom gate Dielectric constant interlayer separation dielectric constant top gate potential bottom gate potential 1 2 charge density0 bottom gate distance top gate distance
  29. 29. BLGFET ELECTROSTATICS Asymmetry parameter Electric fields
  30. 30. BLGFET ELECTROSTATICS Both layers Top layer Electronic Density Asymmetry parameter
  31. 31. BLGFET ELECTROSTATICS At low screening Characteristic Density (Screening) Dimensionless Screening Parameter Layers Densities in presence of Asymmetr
  32. 32. BLGFET ELECTROSTATICS
  33. 33. ACTUAL DEVICE Dual-Gated BLGFET Gate dielectrics Channel: W=1.6m L=3m Organic seed layer: 9 nm (HfO2 growth, enhanced mobility) HfO2: 10 nm SiO2: 300nm Max. bandgap: 250 mV Ion/Ioff=100 at RT and 2000 at LT
  34. 34. CHARGE NEUTRALITY AND BANDGAP TUNABILITY Electrical Displacement Fields 0 at CNP Bandgap and CNP position
  35. 35. OPTICAL ABSORPTION SPECTRA FOR BLGFET
  36. 36. BLGFET I-V CHARACTERISTICS Output characteristics: (Vds Ids) Vb = -100V Vd = 0 50mV Vt = -2 6V
  37. 37. AGENDA I. Introduction II. Theory of Graphene III. GFET I. Bilayer Graphene Field Effect Transistor II. Graphene Nanoribbon Field Effect Transistor IV. Conclusion
  38. 38. GRAPHENE CONFIGURATIONS Electronic Confinement Zigzag Metallic Edge State formation Armchair Metallic or Semiconductor (bandgap) Fraternal to Carbon Nanotubes [6] Reddy, Dharmendar, et al., Graphene field-effect transistors, Journal of Physics D: Applied Physics 44.31 (2011): 313001, 2011. [7] Chung, H. C., et al., Exploration of edge-dependent optical selection rules for graphene nanoribbons, Optics express 19.23: 23350-23363, 2011.
  39. 39. TIGHT BINDING APPROXIMATION DOS (low energy) near these Dirac points: Remember? Hamiltonian Dirac-like-Hamiltonian [7] Raza, Hassan, Graphene nanoelectronics: Metrology, synt