STM: Scanning Tunneling Microscope Basic idea STM working principle
Schematic representation of the sample-tip tunnel barrier Assume tip and sample described by two infinite plate electrodes Φ t +Φ s = 2Φ Sample work function Φ s Φ t Energy diagram Wave function ψ s ψ t Plane wave Exponential decay Electron tunneling DOS 4 e 2 I = π f ( E, T)[1 f ( E + ev, T)] M δ( E E ev ) t s s t bias ts t s bias ts, occupied sample states unoccupied tip states tunneling matrix elements elastic tunneling DOS: Density of State
I = I I = 4π e t s s t ts, Electron tunneling [ f( E, T) f( E + ev, T)] M δ( E E ev ) t s bias ts t s bias 2 Moving to the continuous t deρ ( E), deρ ( E) t s s 4π e 2 I = [ f( EF+ ε) f( EF+ ev+ ε) ] ρs( EF+ ev+ ε) ρt( EF+ ε) M( ε) dε sample and tip DOS For small kt, f(e) step function ev 4π e 2 I = ρs( EF + ev + ε) ρt( EF + ε) M( ε) dε 0 2 4π e I = VρS( EF) ρt( EF) M 2 And for small V bias di dv 2 4π e = ρs( EF + ev ) ρt( EF) M 2 The tunneling current is a function of the tip and sample density of state close to the Fermi level
STM vertical resolution Assuming the electron wave functions for tip and sample described by plane waves, the quantum mechanics predicts an exponential decay in the vacuum gap following ( Φ ) 2m ev ψ ( z) = ψ ( 0 ) e κ z, κ = t t ( d z) ( ) = ψ ( 0) ψs z e κ s For small T and V 2 z I VρS( EF) ρt( EF) e κ N.B.: if the tip (sample) is an insulator -> ρ t (E F ) (ρ s (E F )) = 0 implying I = 0 The STM is useless in this case I Vρ ( E ) ρ ( E ) e S F T F 1.025 Φd Φ in [ev] d in [Å] Typically Φ = 5 ev Atomic step Δd = 2 Å Δ I 1.025 ΦΔd e I 1 100 Easy to measure ΔI/I = 0.1 -> Δd = Φ -0.5 ΔI/I = 0.05 Å
STM lateral resolution J. Tersoff and D.R. Hamann. Phys. Rev. B. 31, 805 (1985). Spherical apex tip ψ t r r κre ( ) 0 κ exp r r R κ r r ( κ 0 ) 0 M r Re r 1 ρ ψ δ EF 2 s ( E, r0) = s( r0) E Es V E = E ev s ts κ R ( ) κ ψ ( ) F 0 0 s ( ) Bardeen matrix element Local density of states For small kt, f(e) > step function; for small V > ρ = constant, one gets z IrV (, ) Rρ ( E) ρ ( r, E) Ve κ 2 2 0 t F s 0 F The tunneling current depends on the tip position (ρ s (r 0,E F )) respect to the surface Tersoff calculated a resolution function which is a Gaussian with an RMS width of L = R+ d 2κ atomic tip R = 2 Å d = 2-3 Å L ~ 1 Å Actually can be better depending on the tip wave function
Not for free Table-top STM 10 K 100 K >0.5 M Home made UHV 3 He cryo-stm UHV STM
N. Weiss, EPFL PhD thesis My STM (UHV)
After electro-erosion Tip preparation
1) Imaging and topography feedback Basic concepts of STM imaging. Tunneling current is exponentially dependent on distance between tip and sample (< 1 nm). As the tip is moved from x 1 to x 2, the current increases as the tip-to-sample distance decreases due to the change in sample height. The increase in current causes the control loop to move the tip away from the sample until the error signal is again zero. Recording the value of the tip height (z) as a function of position (x,y) allows the 3-dimensional topography to be reconstructed. Constant current image of a stepped Pt surface covered by 1 monolayer Ag (I = 2.7 na, V bias = 10 mv) P. Gambardella, EPFL PhD thesis (2000)
Å Å Å Å H. Brune PhD thesis
Warning!!! I Vρ ( E ) ρ ( E ) e S F T F 1.025 Φd Remember: the tunneling current is a measure of the Local Density of States (at the Fermi level) of tip and sample
Atomic Force Microscopy (AFM) Technique enabling atomic-scale imaging of insulating surfaces. The tip is mounted on a cantilever and is brought into contact with the sample surface. The force on the cantilever is related to its deflection via Hooke s law: F = -kx, where k is the spring constant of the cantilever and x is the deflection. (1) Non-contact AFM Van der Waals attraction 10-100 Å tip-surface separation (2) Contact AFM e - -e - repulsion <5 Å tip-surface separation (3) Intermittent contact AFM (tapping mode AFM) 5-20 Å tip-surface separation
Optical detection The attractive or repulsive force between the tip and the sample causes a deflection of the cantilever towards or away from the sample. The deflection is measured by a laser beam directed at the back of the cantilever. As the cantilever deflects, the angle of the reflected beam changes, and the spot falls on a different part of the photodetector. The signals from the four quadrants of the detector are compared to calculate the deflection signal. Piezo motor for x,y mapping
(1) In contact mode: F(x) = -k x Hooke's Law Spring constant of cantilever is less than surface, cantilever bends. Typical atom-atom k ~ 10 N m -1, typical cantilever k 0.1-1 N m -1 Total force on sample 10-6 to 10-8 N If spring constant of cantilever is greater than surface, surface deformed. This mode can be used for very high resolution imaging, such as atomic resolution (3) In intermittent contact (tapping) mode: Similar to non-contact AFM using vibrating cantilever except at one extent tip "taps" into contact mode Useful for soft surfaces - less prone to external vibration/noise than non-contact Less destructive than contact AFM and can image rougher samples DNA acquired in tapping mode
(2) In non-contact mode: Very small force on surface (~ 10-12 N) - tip-surface distance 10-100 Å - best for soft or elastic surfaces - least contamination - least destructive - long tip life In non-contact mode the cantilever oscillates close to the sample surface, but without making contact with the surface : AC driven oscillating cantilever (100-1000 Hz frequency, 10-100 Å amplitude) - resonant frequency ν =1/(2 π) sqrt(k/m) - k varies with external force gradient (df(x)/dx) so frequency changes with external force - electronics adjust tip-surface distance to keep resonant frequency constant -> constant tip force Contact and non-contact show similar topography except for soft/deformable materials
Details of the non contact mode (NC-AFM) First, the tip is vibrated at its resonant frequency (ω 0 ) using a piezoelectric element while far from the surface (assuming no interaction). As the tip is moved towards the surface, the presence of a force gradient modifies the spring constant of the cantilever so that k eff = k F where k is the spring constant of the cantilever in the absence of a tip-sample interaction. The key point is that this modification of the spring constant will produce a shift of the resonant frequency of the cantilever given by: ω = = = ω k eff m k m 1 0 = F' 1 k F' k k F' m where ω is the new resonant frequency of the cantilever due to its interaction with the surface. In practice, the user first selects an operating resonant frequency, ω sp. As the tip moves towards the surface both the shift in resonance frequency and the damping of the cantilever s oscillation due to tip-surface interactions will produce a corresponding change in the amplitude of oscillation at ω sp. To generate a NC- AFM image the user chooses a set-point amplitude, A sp. As the tip is scanned across the surface the feedback loop controls the tip-sample separation so as to maintain the oscillation amplitude constant at A sp. A NC-AFM image therefore represents a map of a constant force gradient (defined by A sp ) due to the tipsample interaction.
The method in theory: The result in image: Contact mode topography (left) and non contact mode image (right) of a two-phase block copolymer.
Mechanical characteristics of the AFM cantilever SEM images Dimensions 5 μm
Magnetic Force Microscopy (MFM) Topography Magnetism
Scanning near-field optical microscopy (SNOM) The diffraction limit of spatial resolution. It is not possible to spatially resolve details that are located closer together than approximately half the probing wavelength. For optical microscopy, typically operating at a wavelength of 500 nm (the visible spectrum ranges from 400 nm to 700 nm), the lateral resolution is thus limited to about 250 nm. Scanning Near-Field Optical Microscopy (SNOM), brings a small optical probe very close to the sample surface, in the region called "near-field (opposed to conventional microscopy which are far-field microscopes). Here, at distances smaller than the wavelength away from the surface, also those waves can be probed that do not propagate, but rather decay exponentially perpendicular to the surface. In this evanescent field the k-vectors parallel to the surface can be fairly large, corresponding to small lateral (spatial) dimensions. Broadly speaking, if the aperture-specimen separation is kept roughly less than half the diameter of the aperture, the source does not have the opportunity to diffract before it interacts with the sample and the resolution of the system is determined by the aperture diameter as oppose to the wavelength of light used. An image is built up by raster-scanning the aperture across the sample and recording the optical response of the specimen through a conventional far-field microscope objective Spatial resolution = 50 nm
SNOM is a technique based on the STM. In a SNOM experiment, a fiber tip is scanned in close proximity across a sample, and optical information like reflectivity, fluorescence, luminescence or polarization can be derived with subwavelength resolution. In addition, topographical information can usually be obtained, since a local interaction (e.g. the lateral force between tip and sample surface) is used for control of the tip-sample distance, in a similar way as in an atomic force microscope (AFM) A typical instrument consists illumination (laser, fiber coupler) and collection optics (objectives, filters, photomultipliers for moderate light levels or photon counters of very low intensities), fiber tip holder with shear force feedback (oscillator and lock-in amplifier), an approach scheme (mechanical or motorized), and a scanner (piezo tubes or stacks, it is often advantageous to scan the sample rather than the probe). Digital data acquisition and anti-vibration damping (optical tables, actively or passively dampened) completes the equipment. The microscope shown here sits on a conventional (inverted) light microscope, which allows to localize the sample with low resolution prior to SNOM operation.
SNOM ways of operation Most common today is the use of aperture probes for transmission microscopy, either in illumination (a) or in collection (b). However, many samples or substrates are opaque, so that working in reflection is necessary (c). The reflected light can be collected by optics close to the tip, or by the fiber probe itself, in which case often uncoated fiber tips are used (d). The probe tip acts as a scatterer of the evanescent field, leading to homogeneous waves which can be easily detected.. Of high interest is this arrangement with inverted light path, Tunnel Near-Field Optical Microscope (TNOM) or forbidden light near-field optical microscope. Light can be scattered from the evanescent field by other probe tips, such as a force microscope tip on a cantilever (e). In the Plasmon Near-Field microscope, surface plasmons are generated at the surface of a sample on a thin film metallic substrate, and scattered by a probe tip (f). See also FSB/IPMC/LPMV or FSB/IPMC/LPRX/LPFM