Scanning Probe Microscopies (SPM) Nanoscale resolution af objects at solid surfaces can be reached with scanning probe microscopes. They allow to record an image of the surface atomic arrangement in direct space avoiding complicated calculations to invert the experimental result from reciprocal space measurements. All SPM have in common the necessity to place a tip placed at atomic distances from a surface using piezoelectric elements. The observed quantities may be: -Tunneling current (Scanning tunnelling Microscope, STM) - Photon emission (single molecule Raman spectroscopy) - Deflection of a cantilever (Atomic Force Microscope, AFM) - Local work function (Kelvin Probe) - Optical response (Scanning Near Field optical microscope, SNOM)
STM: working principle What is imaged is the convolution of the density of electronic states of surface and tip, making use of the tunneling current between the metallic tip and a conductive substrate. If a metallic tip, terminated ideally with one single atom, is brought to a distance of few Å from a surface and polarized by a bias voltage, electrons may tunnel through the vacuum. Since the process is strongly localized what matters is the density of states at tip and surface and lateral resolutions of just a few Å can be achieved (atomic resolution). Mapping the tunneling current vs x-y coordinates gives an image of the electronic state density at the surface (either empty or filled depending on the direction of the current).
STM: images Atomic resolution at Ag(110) Atomic resolution of adsorbates at Ag(110) a 0 b 0 Glutamic acid at Ag(100) Ice cluster on Cu(111)
The tunneling effect had been known for decades but STM was invented only in 1981 by Binning e Roher (Physics Nobel Prize winners in 1986). Why did mankind need so long to move this step forward? Solution was needed for non trivial problems
STM: stability Mechanical stability - Compact design; -The microscope is fixed to the apparatus with springs with risonance frequency of just few Hertz; - Permanent Magnets attenuate vibrations generating eddy currents ; - Pneumatic feet decouple the apparatus from the pavement. Createc STM apparatus at the University of Genoa
STM: feedback circuit
STM: scanner designs
STM: scanning methods Dz Constant current (na). The feedback is active and the tip is elongated or retracted during the scanning. Constant height (~5 Å). Feedback inactive. Quicker, but works only on atomically flat surfaces
STM: Theory The tunnelling current is determined by the superposition of the wave function of tip and surface electronic states in the junction region. F S F S Filled Electronic Valence Band States d F T Filled Electronic Valence Band States d e - F T Potential Barrier Quantum tunnelling off (no superposition) Potential Barrier Quantum tunnelling on (superposition)
STM: Theory The tunnelling current is determined by the superposition of the wave function of tip and surface electronic states in the junction region. Within Bardeen s formalism we can write: I M 2e 2 2m f ( E )[1 f ( E ds ( where: f(e ) and f(e -ev) are the occupation factors of the Fermi-Dirac distribution; M matrix element of the tunnelling process; e the wavefunctions of the electronic states of the two electrodes ev )] ( E ) E ) M 2
STM: Theory One dimensional barrier (we neglect the electric field in the junction and assume that both electrons have the same work function f). For a barrier width s we get: e 0 e 0 kz k ( sz) with k 2mf 2 1.1 Å -1 for f=4.5 ev So that M I 2 2m 0 2 0 0 ds 2k( ) e 0 2 e 2ks ks Sum over all energy states of energy and occupation number such to be involved in the tunneling process - 0 2 and 0 2 are the local density of states at tip and surface, respectively -Removing the dependence on z the current I can be estimated. -I depends exponentially on barrier width. For k=1.1 Å -1, I varies by one order of magnitude per Å. High sensitivity to the surface corrugation!
STM: scheme of the energy bands Sample Tip Sample Tip Negative Bias Positive Bias Positive Bias Negative Bias F S F T Filled Electronic Valence Band States e - F T 1eV F S e - d d
STM: spatial resolution Tersoff-Hamann model: The tip is described by a sphere of radius R (R0) placed in r 0. I ( r ) ( E E ) 2 0 F I is proportional to the local density of states of the sample in r 0. The formula can be rewritten for a spatially extended tip, considering R+d the tip-surface distance. (large R smaller sensitivity to surface corrugation). Analitic form for the corrugation amplitude: ne superficiale Δd unta Where: h s = corrugation amplitude; a = periodicity along the surface; Δd = apparent observed corrugation; R = radius of the tip; d = tip surface distance a = lattice spacing
STM: Examples - surface reconstructions O-Ag(110) added row reconstruction Si(111)-(7x7) Surface STM Image Sticks-and-Balls Model
How complicated can be a simple system? O adsorption on Ag(110) for low temperature dissociation
a b <0-11>. 5. Coexistence of flower-like and square-like structures upon Glu deposition on Ag(100) at T=350 K. The two arrangements are present either as well separated island with defined structure (panel a) or as small aggregates in which they are intermixed (panel b). a) Image size 188 Å x 188 Å, V=0.17 V, I=0.3 na; b) image size 94 Å x 94 Å, V=-1.0 V, I=0.3 na (L. Savio et al. 2012)
STM: manipulation Manipulation of weakly bound atoms/molecules adsorbed at a solid surface allows to organise them in particular arrangments. The STM tip is used to lift and put down the atomic units or to move them by pushing or pulling.
STM: manipulation Cu(111) surface state electrons form a 2Dim, quasi-free electron gas. Their scattering off point defects, steps, adsorbates etc. generates standing wave patterns in the electron density, which can be investigated by STM. Fe/Cu(111) Confinement of electrons in quantum corrals at a metal surface. Standing waves - Interference patterns
STM: manipulation Vertical manipulation V,I F. Moresco et al., PRL 86, 672 (2001) Porfirin on Cu(111) behaves like a molecular switch if tension pulses are applied to it via the STM tip
17Å esa-tert-butil-pirimido-pentafenilbenzene (HB-NPB) benzene Marker: pyrimidine N N Lateral phenyl ring tert-butilic group (leg) 19Å
STM: manipulation Cu HB-NPB single HB-NPB molecules on Cu F. Moresco et al Nature nanotech 2006 Dim.: 32 nm x 32 nm; STM parameters: I = 110 pa; V = 2,2 V 20 Å
STM: manipulation
STM: manipulation Electrical contacts Lander molecule on Cu(111). Column A: at (111) terrace; columns B and C: contact to (100) step. The molecular board is either parallel (B) or orthogonal (C) to the step. Only in the latter case an influence becomes visible on the upper terrace. In (C2) and (C3), an additional bump corresponding to the contact point of the wire to the step appears and in (C4) a modification of the upper terrace standing wave patterns is visible. Row1: Sphere models of optimized molecular structures. Row 2: Calculated STM images, corresponding to the models above. Row 3: STM measurements. Black to white distance 3.5 A, V=0.8 V, I=0.2 na, T=8 K. Line 4: Pseudo-three-dimensional STM measurements visualizing the standing wave patterns. V=0.1 V, I=0.2 na, T=8 K. F. Moresco et al., PRL 91, 036601 (2003).
Tip induced OH dissociation on Ag(110)
Scanning Tunnelling Spectroscopy I eu 0 nt ( eu ) ns ( ) T(, eu ) d Differentiating with respect to U Where: n t, n s = density of states of tip and sample; U = bias voltage; T = transmission coefficient (tunnelling matrix) di du ( U) en (0) n ( eu ) T( eu, eu ) t s (considering T(,eU) constant) The measured property (conducibility) is in good approximation proportional to the density of states of the sample. In the limit of small bias voltage (a few V), when the junction has an ohmic behavior, one plots usually (di/du)/(i/u). In this way one eliminates the exponential dependence of the current on the barrier thickness.
Scanning Tunnelling Spectroscopy Experiment Si(111)-(2x1) Unoccupied States Occupied States Theory
Scanning Tunnelling Spectroscopy Carbon Nanotubes Measurement of the gap of the nanotubes The magnitude of the gap depends on the diameter of the nanotubes
Inelastic ElectronTunnelling Spectroscopy For bias values ev>h, the excitation of a vibrational mode of frequency of an adsorbed molecule or of the substrate becomes possible. The opening of the inelastic channel implies an increase of the total tunnelling current, causing a jump in the conducitivity and a peak in the second derivative (d 2 I/dV 2 ). Single molecule vibrational spectroscopy. The chemical sensitivity allows for an additional contrast in the STM images.
Inelastic ElectronTunnelling Spectroscopy 29 Å x 29 Å STM topographical images (bare tip, V=70 mv, I=1 na) showing the manipulation of a CO molecule toward two O atoms co-adsorbed on Ag(110) at 13 K. (A) A single CO molecule and two O atoms. (B) The CO is moved toward O atoms by applying sample bias pulses (1240 mv) after positioning the tip over it. (C) The CO was moved to the closest distance from the two O atoms to form the O-CO-O complex. (D) A CO 2 molecule is desorbed by an additional voltage pulse and the remaining O atom is imaged. (E) STM- IETS Spectra over the CO along the reaction pathways (I, II, and III). The peak (dip) at positive (negative) bias is assigned to the hindered rotation mode. The vibrational assignment is supported by isotopic shift. The voltage position of the peak is 2 mv higher than that of the dip, due to changes in the interaction between the CO and the surface under different bias polarities. No significant differences in the line shape and position of the peak or dip are observed between spectra I and II as well as for isolated CO molecules. The mode shows an up-shift of 4 mev, a decrease in intensity, and a line shape broadening for the O-CO-O complex (III). The spectra displayed are averages of multiple scans from -70 mv to +70 mv and back down and subtracting the background spectra taken over clean Ag(110). Dwell time of 300 ms per 2.5 mv step and 7 mv rms bias modulation at 200 Hz were used for recording the spectra. W. HO, PLR 87, 166102 (2001)
Inelastic ElectronTunnelling Spectroscopy Acetylene on Cu(100) a) I V curves recorded with the STM tip directly above the center of a C 2 HD molecule (1) and above the bare copper surface (2). The difference curve (1 2) is also shown. Each scan took 10 s. b) di/dv curves recorded directly above the center of the molecule (1) and above the bare surface (2). The difference spectrum (1 2) shows two sharp increases (arrows). c) d 2 I / dv 2 recorded simultaneously with the data in b) directly above the molecule (1) and above the bare surface (2). The difference spectrum shows peaks at 269 and 360 mv, resulting from the C D and C H stretch excitations, respectively.
Inelastic ElectronTunnelling Spectroscopy Octanedithiolate (-SC8H16S-) bonded to gold electrodes.
Atomic Force Microscopy The parameter is the force between tip and surface
AFM: tip-surface interactions Repulsive region positive deflection of the cantilever Interaction energy U(s) = 4ε[(σ/s) 12 (σ/s) 6 ] where: s = distance tip sample; σ = distance at which U(σ) = 0; ε = energy at the equilibrium position No interaction no deflection of cantilever attractive region negative deflection of cantilever The derivative du/ds is in first approximation the force between tip and sample
AFM: the cantilever The mechanical parameters of the cantilever are critical for sensitivity and resolution. Elastic constant k resonance frequency Physical dimensions k between 0.01 N/m and 1 N/m - contact k>1 N/m - tapping. Length: from 100 to 200μm Width: from 10 to 40μm Thickness: from 0,3 to 2 μm. The cantilever must be soft minimization of k (at given force, larger displacements)
AFM: the cantilever The tip must be sharp to evidence the irregularities of the surface and must be tight for not breaking when it comes in contact with the surface. =45 -The radius of curvature determines the lateral resolution on a flat surface. More recent techniques allowed to prepare tips with r 5nm. - The half-angle θ corresponds to the largest inclination of a wall reproduced by the tip. Typically 10 <θ<45. - The height h determines the capability to probe deep valleys. The highest vertical extension is usually smaller than 10 μm. =10
STM vs AFM: tip surface interaction STM In AFM images more than one atom contributes to the image. Since they are in different positions, the global signal consists of the sum of such dephased contributions. Atomic resolution may result all the same AFM
AFM: measurement methods Contact mode measurement -The tip touches the sample, i.e. the tip sample distance is smaller than one atomic radius. - The electrostatic forces acting on the tip are repulsive and have an average value of 10-9 N. - This mode is used to investigate the friction force at the nanoscale by evaluating the lateral deflections of the tip. Constant height quicker large friction forces Constant force Slower (feedback on) Small friction forces
AFM: measurement methods No-contact mode - Tip- surface distance: 5-15 nm. - Van der Waals forces, electrostatic and capillar forces. Tapping mode The tip is maintained in a forced oscillation at a frequency close to resonance and kept constant by a feedback system. The deviation from the resonance frequency due to the Van der Waal forces between tip and sample allow to perform an image the surface Amplitude of the oscillation of the tip: 1-10 nm. Sample tip distance : 1-40 nm Resonance frequency: 50-500 khz; depending on the sample characteristics. Narrow resonance peak under vacuum conditions, larger for AFM measurement in air.
AFM: measurement methods Amplitude modulation (AM) The cantilever is put at a fixed vibrational frequency close to resonance and the variation of the vibrational amplitude is recorded. The amplitude of the modulation of the cantilever depends on the elastic properties of the sample. Amplitude of the vibration Frequency shift at resonace shift in amplitude frequency
Measurement of dephasing AFM: measurement methods This method is used to determine differences in the chemical composition of the surface. The dephasing depends on the energy dissipation (viscosity, friction, adhesion) and is affected by the following parameters: - Forcing frequency ω 0 - Forcing amplitude A 0 - Surface topography - Elastic properties of the material
AFM: examples Graphite surface The AFM image shows all atoms within the hexagonal unit cells. Steps on a Si (111) surface (10 m x 10 m) 2 2 nm 2 From http://www.physik.uni-regensburg.de/forschung/giessibl.shtml
AFM: examples Chromosomes can "self-assemble" into some amazing structures. The application of scanning force microscopy (SFM) has been used to provide high-resolution, three-dimensional images of uncoated and unstained human chromosomes in which surface features of less than 50 nm have been resolved. This technique has applications in the imaging and analysis of chromosome structure. TJ McMaster et al., CANCER GENETICS AND CYTOGENETICS, 76(2), 93 (1994).
STM vs AFM STM AFM Measurement of current; Conducting and semiconducting surfaces; Atomic resolution; Allows manipulation; Allows electronic and vibrational spectroscopy of individual molecules (chemical sensitivity); Vacuum is not necessary; The interaction may damage the sample. Measurement of force; Any surface; Good resolution, sometimes at atomic level; Allows manipulation; Topographic information and measurement of friction forces; Chemical sensitivity in the tapping mode (Kelvin microscopy) No necessity for vacuum except to keep surface in controlled state; Non destructive, allows to investigate biological samples
Near Field Scanning Optical Microscopy NSOM Light microscopes are limited in resolution to half the wavelength of light (Abbe) i.e. 200 nm for visible light. This isn t true, however, in the near field. Ash and Nichols demonstrated in 1972 that /60 can be reached with 3 cm microwaves.