Quantum Confinement of Electrons at Surfaces Robert A. Bartynski Department of Physics and Astronomy Laboratory for Surface Modification and NanoPhysics Lab Rutgers University Piscataway, NJ 08854 NPL 203 bart@physics.rutgers.edu 732-445-5500 x4839 Laboratory for Surface/Interface Science Course (Phys 627/Chem 542) 25 March2013 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS NanoPhysics Laboratory
Quantum Confinement Interference of Electron Waves M.F. Crommie, C.P. Lutz, D.M. Eigler. Confinement of electrons to quantum corrals on a metal surface. Science 262, 218-220 (1993) M.F. Crommie, C.P. Lutz, D.M. Eigler, E.J. Heller. Waves on a metal surface and quantum corrals. Surface Review and Letters 2 (1), 127-137 (1995) STM rounds up electron waves at the QM corral. Physics Today 46 (11), 17-19 (1993).
Electronic Quantum Size Effects: Dimensionality...... y(z) y(x) Y(z) y(z) y(x) 2-d structure (thin film, quantum well) confinement in 1-d 1-d structure (atomic chain, quantum wire) confinement in 2-d 0-d structure (cluster, quantum dot) confinement in 3-d Electron density acquires nodal structure along confinement direction. Energy spectrum acquires discrete character.
Scanning Tunneling Microscopy/Spectroscopy
Photoelectron Spectroscopy KE KE Valence Band Photoemission Core level Photoemission hu 1 hu 2 > hu 1 E V Intensity Intensity VB E F Auger Electron Emission CL S CL B
Complementary Spectroscopic Techniques Photoemission (Occupied Inverse Photoemission (Unoccupied States) e - States) e - e - e - E F E initial e - e - E final E V E F Electron Counts E V E F Photon Counts E F X X k Vertical transitions in the reduced Brillioun Zone k
Angle Resolved Photoelectron Spectroscopy Direct transition in solid k in = k o Periodicity in plane of surface k -in = k -out + G k -out = k -o k = (2mE/h 2 ) 1/2 sinq Map E(k ) k -in k in k out q k -out For 2d system obtain all information about energy bands k o Surface Crystal Vacuum
1-d confinement: Quantum Wells
Metallic Quantum Well (MQW) States 5 ML C u(100) f c c F e C u Fe Cu Surf. 2 15ML 200 x 200 nm 200 x 200 nm 300 x 300 nm Cu(100) Fe/Cu(100) Cu/Fe/Cu(100)
Effect of Confinement on Electronic States 1) Free electron bands E k 2 2) Continuous paraboloid shown as grid [Dk x = 2p/Na] 3) Confinement allows only fixed values of k^ Energy 4) Projected on E axis: sub-bands E(k )= E n + h 2 k 2 /2m For square well: E n = n 2 h 2 /8mL 2 k_parallel k_perpendicular k_perpendicular
Typical MQW Behavior: Cu/fccFe/Cu(100) Binding Energy (ev) 0.0 0.2 0.4 0.6 0.8 Photoemission (occupied states) q Cu 19 ML 10 ML Inverse Photoemission (unoccupied states) 1.0 0 10 20 Thickness (ML) 30 @ALS w/ M. Hochstrasser, D. Arena, J. Tobin (LBL) Cu Fe 3 ML 0 1 2 3 4 Energy above E F (ev) Cu Fe All spectra here obtained at k = 0 MQW states disperse up with increasing Cu overlayer thickness!
Since E = n 2 h 2 /8mL 2 down when you increase the width of the well? n + 1 n + 1 n n d d + D they do, but by how much? u - 1 n + 1 n + 2 u - 1 u = (m n) n n + 1 u n u + 1 ma (m + 1)a
But the Electrons are NOT in a Square Well e - V in Fe V in Cu Fe Cu We must include the effect of the atomic potential
Quantum Well States in a Band Bohr-Summerfeld Approx. (Phase Accumulation Model) 2k^ma + Df c +Df s = n 2p Phase accumulated in well Phase shift on reflection Existence from condition vacuum crystal 0 5 10 15 20 Phase/2p 2k^ma = n 2p - Df c - Df s u = m - n
MQW states disperse up with increasing Cu overlayer thickness Electron Energy (ev) 10 8 6 4 2 0-2 -4 0 k ^ p /a 4 3 2 1 0 States near BZB k 2 p a a n nodes m ML m+1 ML (n+1) nodes Add a layer, add a node (MQW states are characterized by the quantum number u = m - n)
Sorting out n and n for MQW states of Ag/Fe(100) T.C. Chiang n+1 n n + 1 n
Do MQW state disperse discretely or continuously with film thickness? T.C. Chiang Yes, they move discretely!
Other System: Cu/fccNi/Cu(100) Anomalous behavior above E F Binding Energy (ev) Binding Energy (ev) 0.0-0.2-0.4-0.6-0.8 Photoemission (occupied states) But 12 ML Cu Inverse Photoemission (unoccupied states) 0 10 20 30 40 10 20 30 Cu Thickness (ML) Cu Thickness (ML) Cu Ni 2 ML Cu Energy 0 Above 2 E 4 F (ev) 6 Cu Ni Similar to Cu/Ni(100) [Himpsel and Rader, APL 67, 1151 (1995)]
Behavior of electronic states depends on band alignment Ni Cu Fe E F d bands d bands d bands C C C Ni 4sp Cu 4sp Cu 4sp Fe 3d
Dispersion with k Energy Energy T.C. Chiang k = (2mEh 2 ) 1/2 sinq k_parallel k_perpendicular Free electron-like dispersion of sub-bands k
Dispersion with k Flat dispersion!! Projected bands of Cu and Co Downward dispersion!! Nearly parabolic Upward dispersion 0 2 4 6 Energy (ev)
Quantum Size Effects and Materials Properties Mediate oscillatory magnetic coupling GMR Kawakami et al. PRL, 82, 4098 (1999) MQW Intensity at E F (belly) Low High MQW Intensity at E F (neck) MXLD Calculation
MQW state-induced layer stability Ag/Fe(100) Pb/Si(111) T.C. Chiang Expt. Theory Weitering et al. Theory Quantum size effects stabilize island height Low T = 6 ML High T = 5 & 7 ML Low T = 3 ML High T = 2 & 4 ML
Chemisorption on MQW s 5 ML O C C u(100) f c c F e C u C C O O O C 2 15ML Quantization of Cu sp band results in MQW states Cu sp electrons play a role in CO chemisorption (A. Nilsson et al.) Changing Cu thickness modifies electronic levels without changing geometric structure Corresponding modification in CO chemisorption?
Measuring Bonding Strength Temperature Programmed Desorption (Bond Strength) Mass Spec -C-O -C-O -C-O Mass 28 signal (Arb. Units) T P (th) TPD of CO/Cu(100) 150 200 250 Temperature (K) 300
CO TPD from MQWs CO/Cu/fccCo/Cu(100) CO/Cu/fccFe/Cu(100) q Cu (ML) Mass 28 Intensity (Arb. Units) Cu(100) q Cu 15 ML 10 ML Mass 28 Intensity (Arb. Units) 13.75 10 5 5 ML 2.5 ML 2.5 120 160 200 Temperature (K) 240 120 160 200 Temperature (K) 240
IPE Intensity and Desorption Temperature (Arb. Units) Intensity at E F 0 CO/Cu/fccCo F T d Cu(100) IPE Intensity at E 10 20 Cu Film Thickness (ML) F 172 170 168 166 164 162 T d (K) Intensity at E F (Arb. Units) 0 CO/Cu/fccFe 10 20 Cu(100) T d IPE Intensity at E F Cu Film Thickness (ML) 30 185 180 175 170 165 160 T d (K)
Low Dimensionality and Hard Superconductivity Weitering et al., Nature Physics (March 06)
2-d confinement: Quantum Wires
How to make quantum wires (and dots) CaF/Si as mask Highly regular steps on Si(111) (Himpsel et al.)
Electronic structure of quantum wires Si Au Si Metallic Au wires Semiconducting Au film Si(557) - Au (Himpsel et al.)
Fermi surface of quantum wires (and dots) 2D Energy E_F F Energy k x k_x k_y k y 1D
Other routes to quantum wires (and dots) Sprunger, Kurtz Self-assembly Ag/Cu(110) Atom-by-atom construction (Au/NiAl) N. Nilius, T. M. Wallis, and W. Ho, Science 297, 1853-1856 (2002).
Scanning tunneling spectroscopy of quantum wires (and dots) di/dv ~ N(E) W. Ho Y(x) = Sc n sin(npx/l)
CDW within an atomic wire Competing periodicities in fractionally filled one-dimensional bands, P.C. Snijders, S. Rogge, H.H. Weitering Physical Review Letters (February 24, 2006)
Summary Direct and Inverse Photoemission spectroscopies are powerful techniques for exploring the electronic structure of nanometer scale structures. 2-d structures show discrete electronic structure ^ to plane of the film, but band-like structure parallel to plane. Square well model NOT sufficient, must take into account electronic structure of overlayer AND substrate to fully describe. 1-d structures can be fabricated and photoemission shows that metallic behavior is possible (undoubtedly owing to interaction with substrate). Fermi surface mapping shows closed or open curves as expected for 2-d and 1-d structures, respectively. Scanning tunneling spectroscopy (STS) is powerful tool for fabricating and characterizing 1-d and 0-d structures. Can use STS to map electronic states of small (i.e. several atom long) 1-d structures to reveal dispersion with length.