Basic Concepts Rubn Prez Nanomechanics & SPM Theory Group - PowerPoint PPT Presentation

Dynamic Atomic Force Microscopy: Basic Concepts Rubén Pérez Nanomechanics & SPM Theory Group Departamento de Física Teórica de la Materia Condensada http://www.uam.es/spmth Curso “Introducción a la Nanotecnología” Máster en física de la materia condensada y nanotecnología

References R. García and R. Pérez, Surf. Sci. Rep. 47, 197 (2002) F.J. Giessibl, Rev. Mod. Phys. 75, 949 (2003) W. Hofer, A.S. Foster & A. Shluger , Rev. Mod. Phys. 75, 1287 (2003) C. J. Chen. “Introduction to Scanning Tunneling • Microscopy”. 2nd Edition. (Oxford University Press, Oxford, 2008). S. Morita, R. Wiesendanger, E. Meyer (Eds ). “Noncontact • Atomic Force Microscopy”. (Springer, Berlin, 2002). S. Morita, F.J. Giessibl R. Wiesendanger (Eds). • “Noncontact Atomic Force Microscopy”. Vol. 2 (Springer, Berlin, 2009).

Outline • Static vs Dynamic AFM: AM-AFM & FM-AFM. • Amplitude Modulation AFM • Frequency Modulation AFM

Static vs Dynamic AFM: Amplitude Modulation (AM) & Frequency Modulation (FM).

ATOMIC FORCE MICROSCOPY (AFM) G. Binnig, C. Gerber & C. Quate, PRL 56 (1986) 930 2nd most cited PRL: +5000 citations !!! http://monet.physik.unibas.ch/famars/afm_prin.htm

AM-AFM Fixed excitation frequency constant oscillation Cantilever amplitude Piezo oscillator Electronics and feedback: constant amplitude Tip 5  m Sample Scanner Piezo XYZ Computer and display

Limitations of static AFM Contact Non-contact F F  Deformation, Friction  Detection of small forces:  No point defects observed soft cantilevers.  “Jump to contact” : Atomic Resolution? stiff cantilevers AFM: G. Binnig, C. Gerber & C. Quate, PRL 56 (1986) 930

Dynamic AFM http://monet.physik.unibas.ch/famars/afm_prin.htm

Dynamic AFM: Our Goal Why changes observed in the dynamic properties of a vibrating cantilever with a tip that interacts with a surface make possible to: AM-dAFM • Obtain molecular resolution • Resolve atomic-scale defects images of biological samples in UHV. FM-dAFM in ambient conditions. R. García and R. Pérez, Surf. Sci. Rep. 47, 197 (2002)

Dynamic description Cantilever-tip ensemble as a point mass spring described by a non- linear 2nd order differential equation   2          2 2    0 0 z (t) z (t) z(t) F z z(t) A (t) 0 ts c 0 exc Q k Amplitude link the dynamics of a Resonance Frequency vibrating tip to the tip-surface F ts interaction. Phase shift

Why do A and  f (  ) depend on F ts ? (simple quasi-harmonic argument) -kz F ts For small amplitudes and large distances    d F k k Δω    k  ω ts ts k z z  k  ts k ts c d z m ω ts 2k 0 New   new resonance curve  New amplitude for given  exc BUT: Large amplitudes  Force gradient varies considerably during oscillation  Non-linear features in the dynamics

Two major modes: AM-AFM and FM-AFM Amplitude Modulation Frequency Modulation AFM AFM Excitation with constant Constant oscillation • • amplitude A exc and frequency amplitude at the current  exc close or at its FREE resonance frequency resonance frequency  0 . (depends on F ts ). Frequency shift  f as Oscillation amplitude A as • • feedback for topography. feedback for topography. Phase shift  between Excitation amplitude A exc • • excitation and oscillation: provides atomic-scale compositional contrast. information on dissipation. Air and liquid environments. UHV (now also liquids !) • • Y. Martin et al, JAP 61, 4723 (1987) T.R. Albrecht et al, JAP 69, 668 (1987) Q. Zhong et al, SS 290, L688 (1993) F.J. Giessibl, Science 267, 68 (1995)

Amplitude Modulation (AM) AFM

Outline: AM-AFM (or Tapping mode AFM) • Operation Parameters. • Non-linear dynamics: Existence of two oscillation states (L & H): implications for imaging. • Understanding amplitude reduction. • Imaging materials properties: phase shifts and dissipation. • Summary: things to remember...

Laboratorio de Fuerzas y Túnel Forces in AFM Restoring force cantilever 40 F c =-kz Force (nN) 0 PM - 40 van der Waals forces ts - 80 HR  0 2 4 6 8 10 F vdw 2 6 d Separation (nm) Excitation force F 0 cos  t Capillary forces Hidrodynamic forces Adhesion forces  m dz  F a =4  R 0 F h Q dt Short range repulsive forces (DMT)   * 3 / 2 F E R DMT Instituto de Microelectrónica de Madrid

Forced damped harmonic oscillator k mQ          m z (t) z (t) kz(t) kA cos( t ) 0 m  exc exc 0  Q  Quality factor (cantilever damping)   0 2 Q          z t C exp( t ) cos(  t ) (transient)  2 A     0 exc cos( t )     exc 2       2 2 2 / Q 0 0 exc exc  0 =  exc  A = QA exc (resonance)   exc Q   0 tan    BUT F ts is nonlinear 2 2 0 exc  anharmonic effects

16 14 EXPERIMENT 12 Amplitude (nm) 10 Silicon, A 0 =15 nm, A=13 nm, f 0 =295.64 kHz 8 6 Low to high 4 high to low 2 0 0 1 2 3 4 5 1.2 1.1 A/z c 1.0 0.9 SIMULATION R= 10 nm, A 0 =10 nm, z c =8 0.998 1.000 1.002 nm, E=1 GPa, k=40 N/m, f 0 =325 kHz  /  0

AM-AFM: Two stable oscillation states      ( ) cos( ) z t z A t ( ) ( ) ( ) H L c H L exc H L (two steady state solutions) A exc = 10 nm H: high amplitude state A set L: low amplitude state Amplitude curves: A H(L) vs z c • Collection of L and H solutions gives rise to L and H branches. • A H(L) decreases linearly with z c for both branches. • Ambiguity in the operation: both branches can match the set amplitude A set .

Experimental implications of the coexistence of states (I): Noise and stability Sample: InAs quantum dots 18 Amplitude (nm) A 1 15 L A 2 12 H A 3 9 6 6 9 12 15 18 21 24 z piezo displacement (nm) 40 nm A 1 low amplitude branch A 2 A 3 high amplitude branch García, San Paulo, PRB 61, R13381 (2000)

∙ Are both solutions 18 equally accessible ? 15 Amplitude (nm) Phase space diagrams: 12 Representation of the tip final 9 state as a function of the initial García and San Paulo, Phys. Rev. B low oscillation solution (L) high oscillation solution (H) 61, R13381 (2000) 6 velocity and positions ∙ 6 9 12 15 18 Tip-surface separation (nm) Z c =7.5 nm Z c =16 nm Z c =14.5 nm 1.0 (c) 1.0 1.0 0.5 0.5 0.5 z/A 0  z/A 0  V/A 0 ω 0.0 0.0 0.0 ∙ -0.5 -0.5 -0.5 -1.0 -1.0 -1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 z/A 0 Z/A 0 Phase space diagram with Phase space dominated by Phase space diagram significant H and L the L state=stable operation dominated by the H contributions=unstable state basin of operation attraction=stable operation Tip should stay always on the same branch (deterministic) BUT…

NOISE: Implications for scanning Mechanical, electronical,thermal and feedback perturbations... Finite time response of the V scan  feedback (   10 -4 s) Change in separation can lead to transitions before the feedback takes over • AM-AFM would operate properly if initial (unperturbed) and intermediate state belong to the same branch, otherwise instabilities and image artifacts will appear. • Stable operation when one of the states dominates the phase space (tip oscillates in the state with the largest attraction basin).

Characterizing the physical properties of the two states.... Amplitude (nm) (a) 10 8 H and L states have 6 different properties 4 2 High amplitude solution Low amplitude solution 0 (b) 1.0 > (nN) 0.5 1   0.0 F F ( t ) dt int <F ts ts -0.5 T -1.0 (c) 1.0 Contact time 0.5 Simulation data: R=20 nm f 0 =350 kHz, Q=400, H=6.4x10 -20 , E * =1.52 GPa 0.0 0 2 4 6 8 10 12 Tip-surface separation (nm) García, Pérez, Surf. Sci. Rep. 47, 197 (2002)

a-HSA Does resolution depend on antibody the oscillation state chosen? on mica Morphology and dimensions of fragments clearly resolved L state No domain structure H state Irreversible deformation after imaging on H state