Mechanisms of Probe-Sample Multistability in Tapping-Mode AFM Imaging Santiago D. Solares*, Ian R. Shapiro, Maria J. Esplandiu, Yuki Matsuda*, Lawrence A. Wade, C. Patrick Collier and William A. Goddard III* Division of Chemistry and Chemical Engineering *Materials and Process Simulation Center California Institute of Technology Multi-Scale Modeling Approach A (Ao, Zc) AFM IMAGING ALG. Image AFM Par.,Zc(t),F(Ri) CD: AFM Cantilever Motion A (Ao,t,Zc) Par., Mod., Trj. MD (QEQ): Tip-Sample Interactions F(Ri) Elements QM: Force Field Optimization MD Par. Probe Resolution A. TEM image of a SWNT tip attached to the silicon support tip B. Close-up of SWNT tip showing its dimensions C D C. AFM image of a sample carbon nanotube taken with the above probe in tapping mode D. Cross-section AFM trace of the sample carbon nanotube at the location shown on figure C Note that the probe resolution (full measured width minus sample height) is less than the probe diameter (5.4 nm) Ideal rigid sample – rigid probe model: The full measured width is equal to the sum of the probe and sample diameters (the probe’s resolution is equal to its diameter) We seek an explanation to the observed Sub-diameter probe resolution A Tip-Sample Interaction Energy Scan Point 5 C Energy, kcal/mol 48000 47000 46000 45000 -2 -1 0 1 2 3 4 3.0 4.0 Tip Position,nm Tip-Sample Interaction Force Scan Point 5 D 35 B Force, nN 25 15 5 -2.0 -1.0 -5 0.0 1.0 2.0 Tip Position, nm mω0 dz d2z + Fts + F0 cos(ωt ) m 2 = −kz − dt Q dt AFM Tapping Amplitude Vs. Tip Position Scan Point 5 A. Schematic of the atomistic tip-sample models and scan points B. Illustration of the SWNT approaching the sample and slipping past it due to elastic deformation C. Energy Vs. tip position curve for one of the scan points D. Force Vs. tip position curve (obtained by differentiation of C) E. AFM amplitude Vs. tip rest position (obtained by integration of the AFM tip equation of motion at various tip rest positions for each scan point) Tapping amplitude, nm E 50 40 30 20 10 0 0 10 20 30 T ip position, nm 40 50 Construction of the AFM scan from the AFM amplitude Vs. tip rest position curves. The simulation explains the observed sub-diameter probe resolution as a result of elastic deformations of both the probe and the sample. Tip-Sample Interaction Force Scan Point 5 35 Force, nN 25 15 5 9 -1.0 -2.0 -5 0.0 1.0 2.0 3.0 4.0 Tip Position, nm Measu red h eight relative to the surface , n m 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 -1 9 10 11 12 13 Sim ulated AFM Scan Lateral Tip Position, nm Ideal Probe Scan Reconciliation of theory and experiment: physical insight Imaging Stability CANTILEVER OSCILLATION PHASE CANTILEVER OSCILLATION AMPLITUDE Phase, degrees Amplitude, nm 90 60 40 20 0 0 20 40 60 60 30 0 -30 0 20 40 -60 -90 Zc, nm Zc, nm Force, nN 20 1 -1 -20 2 Zc, nm 3 60 Experimental Observations (b) 33 0 50 0 33 -90 Phase, degrees Phase, degrees 90 0 90 0 Zc, nm 50 90 0 -90 0 75 0 Zc, nm -90 0 75 Zc, nm Zc, nm 0 50 0 Phase, degrees 0 (c) Amplitude, nm 33 Amplitude, nm Amplitude, nm (a) Zc, nm 75 0 Zc, nm SWNT TIP SLIDING SWNT TIP SNAPPING 1 nm SWNT Tip Sliding Silicon Tip 1 2 -20 3 -1 Down Up 20 1 2 -20 3 Force, nN -1 20 Force, nN Force, nN 20 SWNT Tip Snapping 1 -1 2 -20 Ti p position, nm Ti p position, nm Ti p position, nm (a) (b) (c) 3 Inclusion of Adhesion Forces AMPLITUDE 40 PHASE 90 Repulsive 20 45 0 0 50 -20 25 50 25 0 Attractive SNAPPED UNSNAPPED AU RS 40 AS 15 -2 0 2 4 20 0 -15 -30 RS 90 0 0 25 50 -90 AS AU 0 25 50 Inclusion of Friction (b) 33 0 50 0 90 33 -90 0 90 0 50 Zc, nm 90 0 -90 0 75 0 Zc, nm -90 0 75 Zc, nm Phase, degrees Phase, degrees Zc, nm 0 50 0 Phase, degrees 0 (c) Amplitude, nm 33 Amplitude, nm Amplitude, nm (a) Zc, nm 75 0 Zc, nm mω0 dz d z m 2 = −kz − + Fts + F0 cos(ω t ) Q dt dt 2 500 Force, nN 1000 Energy Kcal/mol Multistability for Other Geometries B C D 2 B 1 D C A A -2 4 2 -2 6 2 4 6 -1 Tip position, nm E 90 D 0 5 C B 10 15 -90 Zc, nm A 20 Amplitude, nm Phase, degrees Tip position, nm 10 C D A B 5 0 E 0 5 10 Zc, nm 15 20 Conclusions • Elastic deformations of SWNT probes and samples can decrease the imaging resolution (as currently defined) causing a loss of structural information • Multiple solutions to the oscillation amplitude are possible when tip-sample sliding occurs • Single-regime imaging with multiple solutions is possible when using SWNT AFM probes in the presence of tip-sample adhesion and friction forces References • Shapiro, I.R.; Solares S.D.; Esplandiu, M.J.; Goddard, W.A.; Collier, C.P.; “Influence of Elastic Deformation on Single-Wall Carbon Nanotube Atomic Force Microscopy Probe Resolution”, J. Phys. Chem. B 2004, 108, 13613. • Solares, S.D.; Esplandiu, M.J.; Goddard, W.A.; Collier, C.P.; “Mechanisms of SWNT ProbeSample Multistability in Tapping-Mode AFM Imaging” J. Phys. Chem. B 2005, 109, 11493. • Solares, S.D.; Matsuda, Y.; Goddard, W.A. III; “Influence of the Carbon Nanotube Probe Tilt Angle on the Effective Probe Stiffness and Image Quality in Tapping-Mode Atomic Force Microscopy”, J. Phys. Chem. B 2005, asap web article.