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Svetlana SanterFreiburg, 06.07.2004
SEM and AFM: SEM and AFM: Complementary Techniques for Complementary Techniques for
High Resolution Surface High Resolution Surface Investigation Investigation
Svetlana Santer
Freiburger Freiburger MaterialforschungszentrumMaterialforschungszentrum
Institut für Institut für MikrosystemtechnikMikrosystemtechnik
Svetlana SanterFreiburg, 06.07.2004
AFM SEMAFM SEM
Svetlana SanterFreiburg, 06.07.2004
ScanningScanning ElectronElectron MicroscopyMicroscopy (SEM)(SEM)
Vacuum: 10-4-10-10 Torr
Svetlana SanterFreiburg, 06.07.2004
Principles Principles of SEM of SEM ImagingImaging
When the electron beam hits the sample,the interaction of the beam electrons from the filament and the sample atoms generates a variety of signals.
•secondary electrons (produced byinteraction of primary e with the looselyheld outer electrons of the sample),
•backscattered electrons (beam electrons from the filament that bounce off nuclei ofatoms in the sample(elastic-interaction of the primary electrons with the nucleus of the atom),
•X-rays, light, heat,
•transmitted electrons (beam electrons that pass through the sample).
Secondary electrons: high spatial resolution, good topographic sensitivity
Backscattered electorns: they have more energy and can escape from greater depths, carry some informartion of sample composition
Svetlana SanterFreiburg, 06.07.2004
Scanning Electron MicroscopyScanning Electron Microscopy (SEM)(SEM)
The SEM uses a beam of electrons to scan the surfaceof a sample to build a three-dimensional image of the specimen.Major Components of the Scanning Electron
Microscope
All scanning electron microscopes consist of:
1. A column which generates a beam ofelectrons.
2. A specimen chamber where the electron beam interacts with the sample.
3. Detectors to monitor the different signals that result from the electron beam/sample interaction.
4. A viewing system that builds an imagefrom the detector signal.
Svetlana SanterFreiburg, 06.07.2004
Generating the beam Generating the beam of of electronselectrons
The electron gun is housed on the top of the column and generates the beam ofelectrons that rushes towards the sample housed in the specimen chamber.
Electrons are very small and easily deflected by gas molecules in the air. Therefore, toallow the electrons to reach the sample, the column is under a vacuum. The vacuum is maintained by two vacuum pumps: a rotary pump and an oil diffusion pump which is housed inside the SEM and is water cooled. Thus, the SEM needs a water cooling line which filters the water before it cools the oil diffusion pump.
Svetlana SanterFreiburg, 06.07.2004
Generating the beam Generating the beam of of electronselectrons
Within the electron gun is the filament which is the source of the beam of electrons.The filament is made of tungsten and is heated to generate a fine beam of electrons.
As the filament gets used, it becomes brittle and coated. If the filament is overheated or too old, it will break.
Svetlana SanterFreiburg, 06.07.2004
Detectors Detectors of of the the SEMSEM
The SEM has several detectors to view the electron signals from the sample.
(1) secondary electron detector looks like a Faraday cage, and detects secondary electrons.
(2) backscattered electron detector (solid state detector) is located above the sample, consists of a diode with a thin gold conductor across the front surface. Backscattered electrons have sufficient energy to pass through the front surface and produce electron hole pairs which produce a curreent in the diode
Svetlana SanterFreiburg, 06.07.2004
Can we see electrons directly by eyeCan we see electrons directly by eye??
The SEM scans its electron beam line by line over the sample.
It's much like using a flashlight in a dark room to scan the room from side to side.
Gradually the image is built on a TV monitor (cathode ray tube or CRT for short). The SEM hasbuttons on the keyboard that control the scan speed. A fast scan which takes a couple of secondsto generate an image can be very grainy - like you're looking at an object in a snow storm. A slow scan is very clear and sharp - but takes a minute or two to get a picture.
Svetlana SanterFreiburg, 06.07.2004
Sample Sample preparationpreparation
Samples have to be prepared carefully to withstand the vacuum inside the microscope. Biological specimens are dried in a special way that prevents them from shriveling. Because the SEM illuminates them with electrons, they also have to be made to conduct electricity.
Sputter coater
Svetlana SanterFreiburg, 06.07.2004
ExamplesExamples
Svetlana SanterFreiburg, 06.07.2004
HistoryHistoryMax Knoll and Ernst Max Knoll and Ernst RuskaRuska --19311931
electron microscopyelectron microscopy
Svetlana SanterFreiburg, 06.07.2004
HistoryHistory
••1938 1938 –– first first SEM SEM by by von Ardennevon Ardenne
••1942 1942 –– first first SEM SEM for bulk samples for bulk samples by Zworkinby Zworkin
••1965 1965 –– first commercila instrument first commercila instrument (Cambridge)(Cambridge)
Resolution:Resolution:
50 nm in 194250 nm in 1942
0.7 nm 0.7 nm todaytoday
Svetlana SanterFreiburg, 06.07.2004
Basics of AFMBasics of AFMAFM provides very high resolution images of various sample properties
50 nm
Piezo
Sample
Cantilever
Tip
PSDLaser
Three basic components:
• Piezoelectric scanner
• Cantilever with a sharp tip
• Position sensitive detector (PSD) coupled with a feed-back system
Digital Instruments (DI) MultiMode Nanoscope IIIa
Svetlana SanterFreiburg, 06.07.2004
Historical steps Historical steps of of developmentdevelopment
•1981-invention of STM
•1985-invention of AFM
•1986-Nobel Price
Christoph GerberChristoph Gerber
It
Vt
1
20
12
−
−
=
=
o
ΑΦ ~h/mk
,eI)z(I kzt
RestrictionRestriction: : conductive samplesconductive samples
IBM‘s Zurich Research Center in Rüschlikon
Svetlana SanterFreiburg, 06.07.2004
General General componentscomponents and and their functionstheir functions
Svetlana SanterFreiburg, 06.07.2004
Control Control of of the cantilever deflectionthe cantilever deflection
Optical Lever
Tunneling sensor (Binnig, Rohrer)
Optical interferometer detection system
Piezoresistive detection
It
Vt
STM tip
•special design of cantilever
•changing of resistivity with the applied stress
Svetlana SanterFreiburg, 06.07.2004
Piezoelectric scannerPiezoelectric scanner•SPM scanners are made from a piezoelectric material that expands and contracts proportionally to an applied voltage
•Whether they expand or contract depends upon the polarity of the applied voltage. Digital Instruments scanners have AC voltage ranges of +220 to –220V
0 V - V + V
No applied voltage Extended Contracted
•In some versions, the piezo tube moves the sample relative to the tip. In other models, the sample is stationary while the scanner moves the tip
Solenoid
Cantilever
PZT
Svetlana SanterFreiburg, 06.07.2004
Piezoelectric scannerPiezoelectric scannerMaterial Material PropertiesProperties
•Piezoelectric ceramics are a class of materials that expand or contract when inthe presence of a voltage gradient
•Lead (plumbum) zicronate titanate (PZT) crystallites exhibit tetragonal or rhombohedric structure
•Due to their permanent electrical and mechanical asymmetry, they exhibit spontaneous polarization and deformation
Poling, an intense electric field (>2000V/mm) is appliedPerovskite-type PZT unit cell (1) in the
symmetric cubic state, (2) distorted
Svetlana SanterFreiburg, 06.07.2004
Geometry Geometry of PZT of PZT scannerscanner
Tube scanner The tripod
Not stable
•The outer electrode is segmented in four equal sectors of 90 degrees
•The inner electrode is driven by the z signal
5 µm125 µm 125 µmJ
2.5 µm10 µm 10 µmE
0.4 µm0.4 µm 0.4 µmA
Vertical RangeScan SizeModel
V/nm~K,VKx 3∆∆ =
Bipolar configuration
Svetlana SanterFreiburg, 06.07.2004
Triangular patternTriangular pattern
Slow
sca
n di
rect
ion
Fast scan speed
Slow scan speed
Hzf lvv 2=
Nvl
v Hzs
⋅=
Fast scan direction
Svetlana SanterFreiburg, 06.07.2004
Feedback Feedback looploop
Svetlana SanterFreiburg, 06.07.2004
AFM Probe ConstructionAFM Probe Construction
Low spring constant (k - 10-2 to 102 N/m)
Sharp protruding tip (r=5-50 nm)
High resonance frequency mk
πω
21
=
Three common types of AFM tip
normal normal supertip ultraleversupertip ultralever
Svetlana SanterFreiburg, 06.07.2004
A A few requisites for cantileversfew requisites for cantilevers
1. Must be soft zkF ∆= Minimize k
For rectangular cantilevers
Example: t=10 µm, w=1mm, l=4mm k~1N/m
k (C-C stretch.)~500N/m k (C-C-H bend)~50 N/m
2. Must be insensitive to external vibrations Maximize eigenfrequencies
mk=ω Minimize m
Ex: Si or Si3N4 L=140µm, w=40µm, t=1.5 µm, k~0.7 N/m, ~60 kHz
Svetlana SanterFreiburg, 06.07.2004
Common Common types types of of cantileverscantilevers
Si3N4 Si
Diamond
Svetlana SanterFreiburg, 06.07.2004
Fabrication Fabrication of of cantileverscantilevers
Svetlana SanterFreiburg, 06.07.2004
Calibration Calibration of of cantilevercantilever
Theoretical method
E=300 GPa
E=238 GPaStatic method Dynamic method•Measuring of thermal responseof the cantilever
•Measuring of the change of resonance frequency caused by the addition of known masses
( ) ctstt kZkZZ ' =⋅−
Svetlana SanterFreiburg, 06.07.2004
Superposition of Superposition of two geometriestwo geometries
Svetlana SanterFreiburg, 06.07.2004
Reconvolution Reconvolution of of the tip shapethe tip shape
D=dreal
IIIIII
r
d
D
rDd4
2=
Svetlana SanterFreiburg, 06.07.2004
DeconvolutionDeconvolution of of the tip shapethe tip shape
Tobacco Mosaic Virus (TMV)
d~18 nm
r-?
Svetlana SanterFreiburg, 06.07.2004
AFMAFM Tip ArtifactsTip Artifacts
We start off with an example of a „good“ AFM image of 300 nm
polystyrene spheres.....
Svetlana SanterFreiburg, 06.07.2004
AFMAFM Tip ArtifactsTip Artifacts
Similar spheres imaged with asupposedly sharp tip
Svetlana SanterFreiburg, 06.07.2004
AFMAFM Tip ArtifactsTip Artifacts
This image should only contain images of large polysterene spheres
Svetlana SanterFreiburg, 06.07.2004
Blind Blind ReconstructionReconstruction
AFM profile of a single „bump“
What does this single scan line tell us about the topography of the tip and sample?
The tip geometry can be no bigger than the obtained profile
Svetlana SanterFreiburg, 06.07.2004
Blind Blind ReconstructionReconstruction
Line scan having two „bumps“
What does this tell us about the shape of the tip?
Case 1: Tip with single apex
Svetlana SanterFreiburg, 06.07.2004
Case 2: double tip
Svetlana SanterFreiburg, 06.07.2004
True threeTrue three--dimensional dimensional scanningscanning??
One of the drawbacks of typical AFM is that the images obtained are not truely three-dimentional. No matter how sharp the tip, the data collected can never access the underside of the sample.
„Petticoat“ effect-all images of objects having steep walls or undercut regions appear to have flared sides
Svetlana SanterFreiburg, 06.07.2004
Method for imaging sidewalls by Method for imaging sidewalls by AFMAFM
Martin, Wickramasinghe, Appl. Phys Lett 1994, 64, 2498
Can we get a similar image using a typical AFM and the boot-shaped tip?
No!No!
Svetlana SanterFreiburg, 06.07.2004
Calibration Calibration of of the tip shapethe tip shape
hL
2rL
rLR4
2= h
LR2
2=
Svetlana SanterFreiburg, 06.07.2004
OxideOxide--Sharpened TipsSharpened Tipsincreasing aspect ratio
reducing tip radius
•Aspect ration- 10:1
•Radius r~1nm
HF
etchingSiO2
Svetlana SanterFreiburg, 06.07.2004
Electron beam deposition Electron beam deposition (EBD)(EBD)High-aspect-ratio tips
L=(1-5)µm
R=(20-40)nm
Carbon materials are deposed by the dissociation of background gases in the SEM vacuum chamber
Svetlana SanterFreiburg, 06.07.2004
Carbon Nanotube TipsCarbon Nanotube Tips•Single-walled carbon nanotubes (SWNT), d=(0.7-3)nm
•Multiwalled carbon nanotubes (MWNT) (nested, concentrically arrangedSWNT, d=(3-50)nm
•High-aspect-ration AFM probes
•Very stiff, E=1012 Pa (the stiffest known materials)
•Buckled nanotubes
Labor intensive
Not amenable to mass production
Svetlana SanterFreiburg, 06.07.2004
PickPick--up up TipsTips
d=0.9nm d=2.8nm
Svetlana SanterFreiburg, 06.07.2004
Chemical Vapor deposition Chemical Vapor deposition (CVD)(CVD)Direct grow nanotubes onto AFM tip
•Heating of nanocatalyst particle (r~3.5 nm)
•Presipitates carbon nucleates a grow of nanotube
Svetlana SanterFreiburg, 06.07.2004
Direct grow Direct grow of of nanotubesnanotubes
•2 nm in diameter
•2µm in length
Alumina/iron/molybdenum-powdered catalyst
Labor intensive
Not amenable to mass production
Svetlana SanterFreiburg, 06.07.2004
Modes Modes of of operationoperation
Svetlana SanterFreiburg, 06.07.2004
The common The common AFM AFM modesmodes
contact mode
tapping mode
Contact mode
Non-contact mode
Intermittent mode
Svetlana SanterFreiburg, 06.07.2004
Contact Contact mode AFMmode AFM
•A tip is scanned across the sample while a feedback loop maintains a constant cantilever deflection (and force)
•The force on the tip is repulsive ~ a few nN
•The tip senses lateral and normal forces
•The tip contacts the surface through the adsorbed fluid layer
•Forces range from nano to micro N in ambient conditions and even lover (0.1 nN or less) in liquid
Svetlana SanterFreiburg, 06.07.2004
Force Force curvecurve
Svetlana SanterFreiburg, 06.07.2004
ContactContact modemode
Force
Oscillation amplitude
Probe-sample distance, z
AABB
CCDD
Static mode
Dynamic mode
pN~Fnm.z
,m/N..k,kzF
110
10010=
÷==
C"" contact to a into jump is B""at
,kzF>
∂∂
Svetlana SanterFreiburg, 06.07.2004
Problems of Problems of the contact the contact modemode
Large deformation forces ~ 100 nN
Capillary forces
nN~cosRFcap 224 1 θγπ=
To solve the problem operation in liquid
Elimination of capillary forces
Reduction of van der Waals forces
Svetlana SanterFreiburg, 06.07.2004
Different Different types types of of forces forces relevant to AFMrelevant to AFM
2
3
3
89251
34
sec/m.gnmr
cm/g
grmgFg
=
=≈
==
ρ
ρπ
nmrnm.D
JAD
rAFvdW
2530
10619
2
===
⋅=
−( )
energysurfacepolymermJ/mγ
energysurfacesilicamJ/mγ
/γγγ
γπradhF
p
s
ps
225
2100
212
4
=
=
=
⋅=
nNFg910−≈
nN~FvdW 5nN~Fadh 30
nN~cosRFcap 224 1 θγπ=(d) Deformation forces
(a)
(b) Capillary forces
radiuscontact typical thenm, 5 ~a 63
,nN~R
KaFd =
Svetlana SanterFreiburg, 06.07.2004
Problems ofProblems of the contactthe contact modemode
Large lateral (shear) forces ~ 100 nN
To solve the problem non-contact mode
Svetlana SanterFreiburg, 06.07.2004
Problems ofProblems of the contactthe contact modemode
Svetlana SanterFreiburg, 06.07.2004
NonNon--contactcontact Mode AFMMode AFM
Highly unstable mode Ultra high vacuum at low temperature
Svetlana SanterFreiburg, 06.07.2004
Tapping Tapping mode AFMmode AFM
•A cantilever with attached tip is oscillated at its resonant frequency and scanned across the sample surface
•A constant oscillation amplitude (and thus a constant tip-sample interaction) are maintained during scanning. Typical amplitudes are 20-100 nm
•Forces can be 200 pN or less
•The amplitue of the oscillations changes when the tip scans over bumps or depressions on a surface
Svetlana SanterFreiburg, 06.07.2004
TappingTapping mode AFMmode AFM
nmAkHz
1001050050
0
0
÷≈÷≈ω
Svetlana SanterFreiburg, 06.07.2004
TappingTapping mode AFMmode AFM
Force
Oscillation amplitude
Probe-sample distance, zAABB
CC
DD
Static modeDynamic mode
Svetlana SanterFreiburg, 06.07.2004
TappingTapping mode AFMmode AFM
0AA
r spsp =Three regimes of tapping mode:
(i) Light tapping
(ii) Moderate tapping
(iii) Hard tapping
170 ≤≤ spr.
7030 .r. sp ≤≤
30010 .r. sp ≤≤
Svetlana SanterFreiburg, 06.07.2004
TappingTapping mode AFMmode AFM
Phase Phase ImagingImaging
Driven force
Actual responce
Different characteristics of the sample different offset the phase
Svetlana SanterFreiburg, 06.07.2004
Svetlana SanterFreiburg, 06.07.2004
Svetlana SanterFreiburg, 06.07.2004
Examples Examples of Phase Images AFMof Phase Images AFM
Svetlana SanterFreiburg, 06.07.2004
Svetlana SanterFreiburg, 06.07.2004
Svetlana SanterFreiburg, 06.07.2004
Advantages and Advantages and DisadvantagesDisadvantagesContact Mode
Advantages
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 images
the forces normal to the tip-sample interction 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 spatials resolution and may damage soft samples (i.e. biological samples, polymers) due to scraping
Svetlana SanterFreiburg, 06.07.2004
Advantages and Advantages and DisadvantagesDisadvantages
Tapping mode
Advantages
higher lateral resolution on most samples (1 to 5 nm)
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
Svetlana SanterFreiburg, 06.07.2004
Cantilevers used Cantilevers used in in contact contact and and tapping modestapping modes
m/N.k 1010 ÷−
m/N~k 50
Svetlana SanterFreiburg, 06.07.2004
Contact vs Tapping modesContact vs Tapping modes
Svetlana SanterFreiburg, 06.07.2004
ScanningScanning ProbeProbe MicroscopeMicroscope (SPM)(SPM)
•A family of microscopy forms where a sharp probe is scanned across a surface and some tip/sample interactions are monitored
•Scanning Tunneling Microscopy (STM)
•Atomic Force Microscopy (AFM)
contact mode
non-contact mode
tapping mode
•Other forms of SPM
lateral force
magnetic or electric force
thermal scanning
phase imaging
Svetlana SanterFreiburg, 06.07.2004
Comparison Comparison of of TechniquesTechniques: AFM : AFM vs vs SEMSEM
Surface structureSurface structure::
••atomically smooth surfacesatomically smooth surfaces
TM-AFM image of 0.14 nm monoatomic steps on epitaxial silicon deposited on (100) Si. 1 µm scan, RMS=0.07 nm
On a On a sample this smoothsample this smooth, , the the SEM has SEM has difficulty resolving difficulty resolving these features due these features due to to the the subtle variations subtle variations in in heightheight
Svetlana SanterFreiburg, 06.07.2004
Comparison Comparison of of TechniquesTechniques: AFM : AFM vs vs SEMSEM
Surface structureSurface structure::
••Thin filmsThin films
Polysilicon thin film at approximately the same lateral magnification. But they differ in the other types of information
AFM provides with roughness and height
SEM provides a large area view
On On most thin filmsmost thin films, , the the SEM SEM and AFM and AFM produce produce a a similar similar representation representation of of the sample the sample surfacesurface
SEMSEM
AFMAFM
Svetlana SanterFreiburg, 06.07.2004
Comparison Comparison of of TechniquesTechniques: AFM : AFM vs vs SEMSEM
Surface structureSurface structure::
••Thin filmsThin films: : interpretation interpretation of of heightheight
In In the the SEM image, SEM image, it can be it can be sometimes be difficult sometimes be difficult to to determine whether the feature determine whether the feature is sloping is sloping up up or or downdown
GaP on Si during chemical beam epitaxy deposition
Svetlana SanterFreiburg, 06.07.2004
Comparison Comparison of of TechniquesTechniques: AFM : AFM vs vs SEMSEM
Surface structureSurface structure::
••High High Aspect Aspect Ration Ration StructuresStructures
With With AFM AFM one can measure the one can measure the structure nondestructivelystructure nondestructively, , but but without details without details on on the sides
SEM SEM provides measuring the provides measuring the undercuts undercuts of of these linesthese lines
the sides
Svetlana SanterFreiburg, 06.07.2004
Comparison Comparison of of TechniquesTechniques: AFM : AFM vs vs SEMSEM
Surface structureSurface structure::
••Rough surfacesRough surfaces
SEM has a SEM has a large depth large depth of of fieldfield::
Ability to image Ability to image very rough very rough surfacessurfaces
Svetlana SanterFreiburg, 06.07.2004
Comparison Comparison of of TechniquesTechniques: AFM : AFM vs vs SEMSEM
EnvironmentEnvironment::
SEM SEM is conducted is conducted in a in a vacuum vacuum environmentenvironment
AFM AFM is conducted is conducted in in vacuumvacuum, , gas, liquid, gas, liquid, vapourvapour, and in an , and in an ambient ambient environmentenvironment
Liquid cell AFM
Svetlana SanterFreiburg, 06.07.2004
ComparisonComparison ofof TechniquesTechniques: AFM: AFM vsvs SEMSEM
Although Although SEM and AFM SEM and AFM appear very appear very different , different , they they share share a a number number of of similaritiessimilarities
Both techniques raster Both techniques raster a probe a probe across the surfaceacross the surface
Similar Similar lateral lateral resolutionresolution
Both techniques can produce artifactsBoth techniques can produce artifacts
AFM AFM can provide measurements can provide measurements in all in all three three dimensionsdimensions, , with with a a vertical resolution vertical resolution of <0.05 nmof <0.05 nm
SEM has SEM has the ability the ability to image to image very rough surfacesvery rough surfaces
SEM and AFM SEM and AFM are complementary techniques that are complementary techniques that provide provide a a more complete representation more complete representation of a of a surface surface
when used together than if each were the only when used together than if each were the only technique availabletechnique available
Svetlana SanterFreiburg, 06.07.2004
ReviewReview ofof Harmonic OscillatorsHarmonic Oscillators
Summing the forces, we get the equation for damped, driven oscillators:
)tcos(Fdtdxkz
dtzdm
)tcos(FdtdzkzFFFF drivingdampingspring
ωγ
ωγ
02
2
0
+−−=
+−−=++=∑
γωω
γ 00 mQ,
Qm
==Using expresion for Using expresion for quality factor:
)cos(00
2
2
tFdtdz
Qmkz
dtzdm ωω
+−−=
)tcos(mF
dtdz
Qz
dtzd
mk
ωω
ω
ω
00202
2
20
+−−=
≡
Svetlana SanterFreiburg, 06.07.2004
Modeling the Modeling the AFM AFM cantilevercantileverthe cantilever is essentially a driven damped oscillator
)z,z(F)tcos(Fdtdz
Qm
zkdt
zdm cc ++−−= ωω
00
2
2
kkcc
zzcc
zz
S>aS>a00 S<aS<a00
zz
Z=0Z=0F(zc,z) term inserted to account for the surface interactions. This term depends on whether or not the tip in contact with the surface (i.e., zc+z <ao)
or not (zc+ z > ao)
002/3
0220
02
,)()(33
46
),(
,)(6
),(
azzdtdzzza
hRzzaRE
aARzzF
azzzz
ARzzF
cccc
cc
c
≤+−−−−−−
+−=
>++
−=
πην
Svetlana SanterFreiburg, 06.07.2004
Modeling theModeling the AFM AFM cantilevercantilever
,dtdz)zza(
hR)zza(RE
aAR)tcos(F
dtdz
Qm
zkdt
zdm c/
cc −−−−−−
+−+−−= 023
0220
00
2
2
334
6πη
νω
ω
Svetlana SanterFreiburg, 06.07.2004
RestrictionsRestrictions
The direct asignment of the phase contrast is hadly possible:
(i) The abrupt transition from an attractive force regime to strong repulsion which acts for a short moment of the oscillation period
(ii) Localisation of the tip-sample interaction in a nanoscopic contact area
(iii) The non-linear variation of both attractive forces and mechanical compliance in the repulsive regime
(iv) The interdependence of the material properties (viscoelasticity, adhesion, friction) and scanning parameters (amplitude, frequency, cantilever position)
The interpretation of the phase and amplitude images becomes especially intricate for viscoelastic polymers