SPM: Scanning Probe Microscopy

Background

First scanning probe microscope invented in 1981 by Binning and Roher

Wide range of applications

– Topography/Atomic Structure

– Magnetic/Electric fields

– Surface temperatures

Electron tunneling

Typical quantum phenomenon

Wave-particle impinging on barrier

Probability of finding the particle beyond the barrier

The particle have “tunneled” through it

Tunneling definition

Role of tunneling in physics and knowledge development

• Field emission from metals in high E field ( Fowler-Nordheim 1928)• Interband tunneling in solids (Zener 1934)• Field emission microscope (Müller 1937)• Tunneling in degenerate p-n junctions (Esaki 1958)• Perturbation theory of tunneling (Bardeen 1961)• Inelastic tunneling spectroscopy (Jaklevic, Lambe 1966)• Vacuum tunneling (Young 1971)• Scanning Tunneling Microscopy (Binnig and Rohrer 1982)

Electron tunneling

Elastic

Energy conservation during the processIntial and final states have same energy

Inelastic

Energy loss during the processInteraction with elementary excitations

(phonons, plasmons)

1D 3D

Planar Metal-Oxide-Metal junctions Scanning Tunneling Microscopy

Rectangular barriers 3D

Planar Metal-Oxide-Metal junctions Scanning Tunneling Microscopy

Time independent

Matching solutions of TI Schroedinger eq

Time-dependent

TD perturbation approach:(t) + first order pert. theory

ikzikze Re1

22 2

mEk

xzxz BeAe 2

202 )(2

EVmx

ikzTe3

EVdz

d

m 0

2

22

2

Plane-wave of unit amplitude traveling to the right+

plane-wave of complex amplitude R traveling to the left

Region 1

Region 2

exponentially decaying wave

Region 3 plane-wave of complex amplitude T traveling to the right.

The solution in region 3 represents the “transmitted” wave

yprobabilit ontransmissi 2

T

Time independent

20 )(2

EVmsxs

xsexk

xk 2222

22

)(

16

T

Barrier width s = 0.5 nm, V0 = 4 eV T ~ 10-5

Barrier width s = 0.4 nm, V0 = 4 eV T ~ 10-4

Extreme sensitivity to z The transmission coefficientdepends exponentially on barrier width

Exponential dependence of tunneling current

Scanning Tunneling Microscopy (STM)Design and instrumentation

Approach mechanism

Enables the STM tip to be positioned within tunneling distance of the sample

High precision scanning mechanism

Enables the tip to be rastered above the surface

Control electronics

Control tip-surface separationDrive the scanning elements Facilitate data acquisition.

Vibration isolation

The microscope must be designed to be insensitive or isolated from ambient noise and vibrations.

Review of Scientific Instruments 60 (1989) 165Surface Science Reports 26 (1996) 61

Vibration isolation

It is essential for successful operation of tunneling microscopes.

This stems from the exponential dependence of the tunneling current on the tip-sample separation.

Typical surface corrugation is 0.1 0.01 nm or less

tip - sample distance must be maintained with an accuracy of better than 0.001 nm = 1 pm

Dz

STM sensitivity to external and internal vibrational sources:Structural rigidity of the STM itselfProperties of the vibrational isolation system Nature of the external and internal vibrational sources

Design criteria: The system response to external vibrations and internal driving signals is less than the desired tip sample gap accuracy throughout the bandwidth of the instrument.

Scanning Tunneling Microscopy (STM)Design and instrumentation

High precision scanning mechanism

Enables the tip to be rastered above the surface

Typical piezoelectric ceramic is PZT-5H (lead zirconate titanate)Large piezoelectric response (~ 0.6 nm/V).

Tube better than tripodes due to higher m

in-plane tip motionthe outer electrode is sectioned in 4 equal segments x and y directions given by applying differential scan signals (Vx

+, Vx-= - Vx

+; Vy+, Vy

- = - Vy

+)

Z- motioncommon mode signals(Vx

+ = Vx-; Vy

+ = Vy-)

applied to the electrodes allows extension of the tube in the z direction

The voltages are referenced to theconstant potential applied to the electrode located on the inner surface of the tube.

Scanning Tunneling Microscopy (STM)Design and instrumentation

Bimorph cells

Two plates of piezoelectric material glued together with opposite polarization vectors

Applying V one plate will extend, the other will be compressed, resulting in a bend of the whole element

Four sectors for electrodes Allow to move along the Z axis and in the X, Y plane using a single bimorph element

Scanning Tunneling Microscopy (STM)Examples of STM Apparatus

STM scanner

Raster the tip across the surface, and using the current as a feedback signal.

The tip-surface separation is controlled to be constant by keeping the tunneling current at a constant value.

The voltage necessary to keep the tip at a constant separation is used to produce a computer image of the surface.

Unchanged

Tunneling

Current (nA)

Lower

Tunneling

Current (nA)

Constant height imaging

Dz

Constant current imaging

Higher

Tunneling

Current (nA)

Unchanged

Tunneling

Current (nA)

Typical working mode

Applied only on very flat regions

Spectroscopy

– local variation of can be studied by

taking

the derivative of the current as a function of

the tip distance with lock-in techniques.

I-V curves:

– Stop the feedback loop

– V ramp

– local DOS vs E

– local electronic structure

CITS (Current Imaging Tunneling Spectroscopy)– Local electronic properties– Apparent Topography: Simultaneous measurements of I(V,x,y) and z(x,y)– During the scan: disable the feedback - ramp V and measure I(V)– The ensemble of I values acquired on the surface at a chosen Vi will form acurrent image– Each current image yields a visualization of the electronic density at a selectedenergy

Since you are measuring the electronic states, images of the

same surface can vary!

In prima approssimazione l’immagine STM è quella della densità elettronica delle superficie al livello di Fermi ad una distanza di alcuni A dalla superficie. I calcoli permettono di dimostrare che nel caso dei metalli i punti a più alta densita’ corrispondono alle posizioni dei nuclei mentre nel caso dei semiconduttori dipende dal legame (covalente, ionico…) . Non solo, la presenza del gap di energia rende necessario applicare un potenziale di bias dal cui segno dipende il verso della corrente.Inoltre i calcoli dimostrano che sulle superfici metalliche la corrugazione e’ tale che per avere risoluzione atomica e’ necessario avvicinare molto la punta andando a basse V o alte I. L’approssimazione fatta in prima approssimazione non è più valida le forze punta-campione e la configurazione esatta degli stati della punta non sono più trascurabili.

Quando considero le dimensioni finite della punta è chiaro chel’immagine che ottengo non è direttamente il profilo ma è laconvoluzione tra la superfficie e la punta.Tipici valoridel raggio di curvatura sono 10nm.

Instrumentation details STM tip: atomically sharp needle and terminates in a single atom

Pure metals (W, Au)

Alloys (Pt-Rh, Pt-Ir)

Chemically modified conductor (W/S, Pt-Rh/S, W/C…)

Preparation of tips: cut by a wire cutter and used as is

cut followed by electrochemical etching

Electrochemical etching of tungsten tips. A tungsten wire, typically 0.25 mm in diameter, is vertically inserted in a solution of 2M NaOH. A counter electrode, usually a piece of platinum or stainless steel, is kept at a negative potential relative to the tungsten wire.

The etching takes a few minutes. When the neck of the wire near the interface becomes thin enough, the weight of the wire in electrolyte fractures the neck. The lower half of the wire drops off.

Fe/Cu(111)

Fe/Cu(111)

Sequenza realizzata usando atomi di Xe

su

una superficie di Ni(110)

AFM: Atomic Force Microscopy

La Forza Elastica (legge di Hooke):

F kDxK = costante elastica della molla legata

alla frequenza di vibrazione dalla

relazione:

k m2

Per gli atomi in un solido = 1013 Hz ovvero kAT=10N/m

Un pezzo di Alluminio lungo 4mm ha una k=1N/m < kAT

Katomico=10N/m Kcantilever<1 N/m

The Atomic Force Microscope utilizes a sharp probe moving over the

surface of a sample in a raster scan.

The probe is a tip on the end of a cantilever which bends in response to

the force between the tip and the sample.

La forza che agisce sulla punta puo’ essere repulsiva

(contact mode) oppure attrattiva (non contact

mode).

Nel regime di NON

CONTATTO le

forze sono piu’

deboli, variano

piu’ lentamente,

sono attrattive

tipo forze di Van

der Waals…

Forces can be explained by e.g. van der Waals forces – approximated by Lennard-Jones potential

1. Laser – deflected off cantilever

2. Mirror –reflects laser beam to photodetector

3. Photodetector –dual element photodiode that measures differences in light intensity and converts to voltage

4. Amplifier

5. Register

6. Sample

7. Probe –tip that scans sample made of Si

8. Cantilever –moves as scanned over sample and deflects laser beam

Scanner. The movement of the tip or sample in the x, y, and z-directions is controlled by a

piezo-electric tube scanner, similar to those used in STM.

For typical AFM scanners, the maximum ranges for are 80 mm x 80 mm in the x-y plane

and 5 mm for the z-direction.

Feedback control. The forces that are exerted between the tip and the sample are

measured by the amount of bending (or deflection) of the cantilever.

By calculating the difference signal in the photodiode quadrants, the amount of

deflection can be correlated with a height .

Because the cantilever obeys Hooke's Law for small displacements, the

interaction force between the tip and the sample can be determined.

Feedback control is used to maintain a set force between the probe and the sample.

AFM: modalità altezza costante (misura ad anello aperto)

Durante scansione se mantengo punto V ad un’altezza costante deformazioni del supporto seguono profilo della superficie analizzata

Corrente in uscita dal rivelatore di posizione del fascio dipende da forza agente sulla punta.Posso usare la corrente per ricostruire l’immagine della superficie del campione.Questo metodo di acquisizione fornisce una mappa del profilo della superficie del campione (vale per piccole deformazioni).

Confronto tra modalità «altezza costante» e «forza costante»

Metodo «forza costante»:Permette maggiore dinamica (non c’è limitazione alla deformazione massima consentita) ed una maggiore linearità (quella dello scanner non dipende da dipendenza della formula).Per contro minore velocità e minore sensibilità.

Possibili due modalità regime di «contatto» e regime di «non contatto»:In non contatto devo usare punta con maggiore forza elastica (devo evitare che punta sia «risucchiata») quindi minore sensibilità

Possibile soluzione è l’uso di tecniche di risonanza

Metodo di rivelazione a forza costante (tecnica non risonante)

Metodo di rivelazione in regime non contatto: tecnica di risonanza

Metto leva in oscillazione intorno a frequenza di risonanza propria del sistema (0) e misurare:

• Variazione di ampiezza A• Variazione frequenza di risonanza 0

In assenza di gradiente

In presenza di gradiente

In altre parole…la cantilever viene messa inoscillazione ad una frequenza vicina a quella propria di risonanza da un elementopiezoelettrico, e avvicinata alla superfice del campione. Il segnale ottenuto dal sensore di deflessione viene analizzato con la tecnica lockin. Un circuito di retroazione agisce in modo da mantenere costante o la differenza di fase o di ampiezza fra il segnale del sensore e quello di eccitazione. Questa modalità di acquisizione mantiene costante la frequenza di risonanza e non la deflessione della cantilever, e si ottengonolinee di gradiente di forza costante.

La punta non tocca il campione durante la misura, in questo modo si minimizzano deformazioni e forze laterali. Poiché la distanza di lavoro dalla superfice può variare da alcuni nanometri a decine o centinaia, si possono acquisire immagini associate a forze a lungo range come quelle elettrostatiche e magnetiche assieme all’immagine topografica

Se definisco Q come fattore di merito

La variazione dell’ampiezza ad una frequenza prossima ad una frequenza laterale

In alternativa si può misurare agganciamento in frequenza.

Tipici valori di A sono 10-10 m.

Accessible via TappingMode

Oscillate the cantilever at its resonant frequency. The amplitude is used as a feedback signal. The phase lag is

dependent on several things, including composition, adhesion, friction and viscoelastic properties.

Identify two-phase structure of polymer

blends

Identify surface contaminants that are

not seen in height images

Less damaging to soft samples than

lateral force microscopy

Metodo di rivelazione in regime non contatto: tecnica di risonanza caratteristiche della misura

Essendo F più deboli nel modo di misura in non contatto posso misurare campioni soffici.Ho però maggiore distanza punta-campione, ciò significa che sono necessarie punte più sottili.

Contact ModeAdvantages:

High scan speeds

The only mode that can obtain “atomic resolution” images

Rough samples with extreme changes in topography can sometimes be scanned more easily

Disadvantages:Lateral (shear) forces can distort features in the image

The forces normal to the tip-sample interaction can be high in air due to capillary forces from the adsorbed fluid layer on the sample surface.

The combination of lateral forces and high normal forces can result in reduced spatial resolution and may damage soft samples (i.e. biological samples, polymers, silicon) due to scraping

TappingMode AFMAdvantages:

Higher lateral resolution on most samples (1 to 5nm)

Lower forces and less damage to soft samples imaged in air

Lateral forces are virtually eliminated so there is no scraping

Disadvantages:Slightly lower scan speed than contact mode AFM

The probe is scanned sideways. The degree of torsion of the cantilever is used as a relative measure of

surface friction caused by the lateral force exerted on the probe.

Identify transitions between different components in a polymer blend, in composites or other mixtures

This mode can also be used to reveal fine structural details in the sample.

Compositepolymerimbedded in a matrix

1 micron scan

Bond pad on anintegrated circuit

Contamination

1.5 micron scan

MoO3 crystalliteson a MoS2 substrate

6 micron scan

Special probes are used for MFM. These are magnetically sensitized by sputter coating with a ferromagnetic material.

The cantilever is oscillated near its resonant frequency (around 100 kHz).

The tip is oscillated 10’s to 100’s of nm above the surface

Gradients in the magnetic forces on the tip shift the resonant frequency of the cantilever .

Monitoring this shift, or related changes in oscillation amplitude or phase, produces a magnetic force image.

Many applications for data storage technology

Overwritten tracks on a textured hard disk, 25 micron scan

Domains in a 80 micron garnet film

Effect of Shape of Tip

Details of Parts of AFM

Property Typical Value Desired Quality

Material Silicon, Silicon Nitride, Silicon Oxide

Hard, Unreactive

Tip Radius < 10 nm Small

Tip Height 15-20 µm Mechanically stable

Cantilever Length

100-250 µm Appropriate reach

Mean Width 20 – 70 µm Mechanically stable

Half Cone Angle 25° Sample dependent

Base Shape configurable Sample dependent

Apex Shape configurable Sample dependent

Resonant Frequency

Several kHz, depends on shape

Matching piezo’sresonant frequency

Coating None, Gold, Platinum, Diamond

Experiment dependent

Cantilever and Tip

Details of Parts of AFMShapes of AFM Tip

Details of Parts of AFMShapes of AFM Tip

Protruding from the Very

End

Positioned at the Very End

Square-Based Pyramid

Rectangular-based

Pyramid

Circular Symmetric

Spike

Details of Parts of AFMHigh Aspect Ratio

Spike AFM Tips

Focused Ion Beam

Electron Beam Deposited

Carbon Nanotube

Plateau Rounded Sphere

Critical Dimension

Details of Parts of AFMScanner

In most AFMs piezoelectric materials are used to achieve this. These change dimensionswith an applied voltage. The diagram below shows a typical scanner arrangement.

Details of Parts of AFMScanner

The presence of electrical resonances and anti-resonances make the piezoelectricimpedance unique. The resonances result from the electrical input signal exciting amechanical resonance in the piezo element.

Equivalent Circuit Model

Details of Parts of AFMFeedback

The feedback system is affected by three mainparameters:

1. Setpoint2. Feedback gains3. Scan rate

Optical AFM• Advanced Surface Topography technique avoids cantilever mechanism by use of optical

fiber based tips and using Fabry–Pérot Interferometry (or Etalon):

There is only one limitation of such an approach: surface of the sample should be smooth enough and homogeneously reflecting.

Artefacts in AFMScanner Related

Hysteresis

The piezoelectric’s response to an applied voltage is not linear. This gives rise to hysteresis.

Artefacts in AFMScanner Related

Scanner creep

If the applied voltage suddenly changes, then the piezo-scanner’s response is not all at once. It moves the majority of the distance quickly, then the last part of the movement is slower. This slow movement will cause distortion, known as creep.

Change in x-offset Change in y-offset Change in size

Artefacts in AFMScanner Related

Bow and Tilt

Because of the construction of the piezo-scanner, the tip does not move in a perfectly flat plane. Instead its movement is in a parabolic arc (scanner bow). Also the scanner and sample planes may not be perfectly parallel (tilt). Both of these artefacts can be removed by using post-processing software.

Artefacts in AFMTip Related

Blunt tip: Use Feedback Mode

Tip picks up debris: Cleaning the sample with compressed air or N2 before use

Artefacts in AFMFeedback Related

Poor tracking due to high scan rate

Gains are set too high, then the feedback circuit can begin to oscillate. This causes high frequency noise

AFMs are very sensitive to external mechanical vibrations, which generally show up ashorizontal bands in the image. These can be minimised by the use of a vibrationalisolation table, and locating the AFM on a ground floor or below.Acoustic noise such as people talking can also cause image artefacts, as can drafts ofair. An acoustic hood can be used to minimise the effects of both of these.

Artefacts in AFMVibration Related

Beyond just surfaceSeeing the atomic orbital

Beyond just surfaceSeeing the atomic orbital

Ref: Minghuang Huang, Martin Cuma, and Feng Liu. (27 June, 2003). Seeing the Atomic Orbital: First-Principles Study of the Effect of Tip Termination on Atomic Force Microscopy. Physical Review Letters. Volume 90, Number 25.

Beyond just surfaceSeeing the reactionWork done by Franz J. Giessibl at the Department of Physics, University of Regensburg have been success to image chemical reaction using AFM by having a carbon monoxide molecule at the tip to obtain high spatial resolution.