A Novel SPM System for Determining Quantum Electronic Structure at the Nanometer-scale Joseph A. Stroscio, NIST Fellow Electron Physics Group 2011 Nanoelectronics Metrology, May 25, 2011
Presentation Outline Microscopy Honeycomb Lattices Magnetic Fields B Graphene Devices Graphene“Quartet” 2
Some History of Microscopy Occhiolino “Little Eyes” – 16 th Century First microscope was the optical microscope Compound microscopes end of 16 century Galileo Galilei's compound microscope in 1625 Occhiolino “Little Eyes” Wikipedia 18th century microscopes Musée des Arts et Métiers, Paris http:/www.eatechnology.com 3
Some History of Microscopy: Scanning Tunneling Microscope a “Quantum” Microscope Invented by Gerd Binnig and Heinrich Rohrer in 1981 Nobel Prize in Physics in 1986 with Ersnt Ruska (electron microscope) Quantum Mechanical Tunneling 2 d I e Current Distance from Wikipedia 4
Scanning Tunneling Microscopy A “Quantum” Microscope STM is an electron probe, sensitive to the energy resolved local density of electron states (LDOS) – seeing in “color” E V F I ( , r E T E V dE ) ( , ) t E F 2 ( , r E ) ( ) r ( E E ) t t dI ( , r E ) ,B ,V g t dV J. A. Stroscio, R. M. Feenstra, and A. P. Fein, PRL 57 , 2579 (1986) GaAs(110) R. M. Feenstra, J. A. Stroscio, J. Tersoff, and A. P. Fein, PRL 58 , 1192 (1987) 5
Evolution of Cryogenic Scanning Tunneling Microscopes Exponential tunneling transmission selects out the last atom on the probe tip Allows to “see”, “feel”, and “hear” in the nanometer scale world 6
Evolution of Cryogenic Scanning Tunneling Microscopes Desire stability and higher energy resolution Resolution limited by the thermal Fermi-Dirac distribution ~ 3k B T T = 10 mK Solution: Go to lower temperatures T = 0.6 K Not so easy! T = 4 K T = 295 K 2010 1990 2004 1981 7
Competing Requirements to Achieve High Resolution at Low Temperatures Tunneling current changes by x10 with 1 Å change < 1 picometer displacement fluctuation is required Isolate from the environment to achieve small fluctuations Poor thermal transport Bond strongly to environment to achieve good thermal contact Poor isolation Solution is to do both! 8
Developing High-Energy Resolution SPM Measurements ULTSPM Lab at NIST Processing Lab Vibration Isolation Stage 3 Stage 2 Stage 1 9
Developing High-Energy Resolution SPM Measurements Refrigeration to 10 mK using 3He-4He mixture 3 He- 4 He Gas Handling System (GHS) 3 He 3 He Pump 3 He Pumping Comp Station 4 K 4 LHe IVC 1.5 K UHV E3 E1 1K pot Z3 Z1 STILL E2 ≈700 mK 700 m K Z2 STILL E4 50 mK Shield ≈50 mK E5 ICP 10 m K Shield 3 He rich ≈10 mK 3 He dilute Mixing Chamber Silver rods Vladimir Shvarts Zuyu Zhao Magnet Y. J. Song et al . RSI (2010) STM 10
Developing High-Energy Resolution SPM Measurements Young Jae Song Alexander F. Otte Young Kuk Joseph A. Stroscio 11
Developing High-Energy Resolution SPM Measurements Excellent performance down to lowest temperatures JT is better than 1K pot Z noise < 1 pm Hz 1/2 I noise < 100 fA Hz 1/2 Er atoms on CuN Graphene/SiC T=13 mK 5 nm 8 nm Y. J. Song et al . RSI (2010) 12
Presentation Outline Microscopy Honeycomb Lattices Magnetic Fields B Graphene Devices Graphene“Quartet” 13
From Honeycombs to the Dirac Hamiltonian Graphene – Light-like Electrons From Pencil Drawings to High Speed Transistors to iPAD? Or Galaxy Tab? Nature Nanotech. (2010) SKKU, Korea Savage, N., "Researchers pencil in graphene transistors." IEEE Spec. 45, 13 (2008). IBM and HRL GHz Transistors 14
New Materials and State Variables Graphene, TIs; Spin and Pseudo-Spin as State Variables Electron spin Graphene sub-lattice pseudo-spin Graphene bilayer – layer pseudo-spin Topological Insulator – spin locked to momentum 15
Graphene Dirac Fermions Graphene Basics Carbon with 4 valence electrons Two atom basis in the unit cell → pseudo -spin Top View (real space) 16
From Honeycombs to the Dirac Hamiltonian Wallace (1947) Energy K’ K Figure from droid-life.com k y k y ' k x ' k x Energy is linear with Figure from P. Kim momentum massless particles 17
From Honeycombs to the Dirac Hamiltonian Low Energy Expansion: Dirac Hamiltonian Real space: For behavior away from Dirac point, make an expansion: y 4 K K K 0, k , k y x a 3 x 3 a v F nn 2 Reciprocal space: k ik 0 x y σ k H v v E K F F k ik 0 x y i /2 1 e k E v k ( ) k F , K i /2 e 2 k k x ' k y ' k x arctan k k Paul Dirac y 18
The Independent Two Valleys E 0 k ik x y H v K K F k ik 0 k x ' x y k y ' E Leads to additional degeneracy 0 k ik x y K’ H v K F k ik 0 k x ' k y ' x y 19
Consequences of Dirac Hamiltonian Pseudo-spin; reduced Klein tunneling; backscattering transmission through potential barriers E k x ' k y ' Katsnelson et al. Nature Physics 2006 20
Presentation Outline Microscopy Honeycomb Lattices Magnetic Fields B Graphene Devices Graphene“Quartet” 21
Landau Quantization in Graphene Cyclotron motion in a magnetic field Quantized orbits and energy levels Scattering in the graphene landscape Effects of disorder and B interactions Lev Landau 1908 - 1968 Graphene Landau level spacing “Standard” Landau level spacing 1000 K@10 T 10 K@10 T Relativistic: Standard Model: e 2 E E B n E n e c n B ( 1/ 2) sgn( ) 2 n n * m Geim & Novoselov Nature 2007 22
Landau Quantization in Graphene The Graphene Quartet Four-fold degenerate due to spin and valley symmetries STS provides direct measure of energy gaps and interaction effects 23
STS vs Transport Measurements STS Transport Wide energy spectrum Localized states in the mobility gaps Spatial properties of extended and localized states Energy gaps when degeneracies are lifted Correlation effects http://en.wikipedia.org/wiki/Quantum_Hall 24
Presentation Outline Microscopy Honeycomb Lattices Magnetic Fields B Graphene Devices Graphene“Quartet” 25
Epitaxial Graphene on C-face SiC – Weak Disorder Induction Furnace Method C-Face termination Graphene layers 4 - 100 ML n~10 10 /cm 2 (0001) SiC SiC SiC E n~10 12 /cm 2 SiC 1 - 5 ML E (0001) J. Hass et al., PRL 100 , 1255504 (2008) Si-Face termination Berger et al., J. Phys. Chem B 108, 19912 (2004) Berger et al., Science 312, 1191 (2006) de Heer et al., Sol. St. Commun., 143 , 92 (2007) 26
Magnetic Quantization C-face Graphene at 4K Direct measurement of graphene quantization Weak disorder 5 B= 5 T Quantization obeys -2 -1 4 graphene scaling n =0 Full quantization of DOS -4 3 dI/dV (nS) -5 into Landau levels -7-6 1 -3 2 3 4 5 6 2 Very sharp LLs 7 High mobility 1 0 -300 -200 -100 0 100 200 300 Sample Bias (meV) D. L. Miller, et al ., Science 324 , 924 (2009). 27
Resolving the Graphene Quartet Tunneling Spectroscopy at ~10 mK 300 B=0 T E N -E 0 (meV) Linear Fit 30 B=2 T B=2 T 200 B=3 T B=3 T B=4 T B=4 T 100 dI/dV (nS) 0 20 N=1 0 2 4 6 1/2 (NB) N=0 10 0 -200 -100 0 100 200 Sample Bias (mV) Graphene on C-face SiC Zero field Dirac point is at -125 meV indicating a doping of ~1 x 10 12 cm -2 Y. J. Song et al . Nature (2010) 28
Resolving the Graphene Quartet Tunneling Spectroscopy at ~10 mK Weak disorder in graphene 3 on C-face SiC allows fine B= 2 T N =1 features to be observed 2 dI/dV (nS) 5 B = 11.5 T 4 1 3 dI/dV (nS) 0 2 -200 -100 0 100 200 Sample Bias (mV) 1 Δ V rms = 1 mV 0 -1 -25 -20 -15 -10 -5 0 5 Δ V rms = 50 μ V Sample Bias (mV) Y. J. Song et al . Nature (2010) 29
Resolving the Graphene Quartet Tunneling Spectroscopy at ~10 mK Smaller peak separation Weak disorder in graphene – electron spin? on C-face SiC allows fine features to be observed 2.0 5 B = 11.5 T 1.5 4 g S = 2.26 0.05 E S (meV) 3 1.0 dI/dV (nS) 2 0.5 1 0.0 0 0 2 4 6 8 10 12 14 Magnetic Field B (T) -1 -25 -20 -15 -10 -5 0 5 Δ V rms = 50 μ V Sample Bias (mV) Y. J. Song et al . Nature (2010) 30
Resolving the Graphene Quartet Tunneling Spectroscopy at ~10 mK Valley splitting is ten Weak disorder in graphene times larger than on C-face SiC allows fine smaller energy splitting features to be observed 5 B = 11.5 T 4 dI/dV (nS) 3 ~1 meV/T 2 1 0 -1 -25 -20 -15 -10 -5 0 5 Δ V rms = 50 μ V Sample Bias (mV) Y. J. Song et al . Nature (2010) 31
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