After reviewing the detailed lecture on scanning force microscopy (SFM) and related concepts, here are three key learning objectives to take away:
Understanding the Principles and Challenges of SFM: The SFM operates by detecting forces between a tip and the sample surface, which can be influenced by various interactions such as van der Waals forces, electrostatic forces, and magnetic forces. Recognizing the influence of different forces and how they interact with the measurement process is crucial. The geometry of the cantilever and the tip’s interaction with the sample play significant roles in the accuracy and type of data collected. Differentiating between attractive and repulsive forces is key to avoiding issues like snapping to the surface, which can affect measurement accuracy.
Mastering SFM Operation Modes and Techniques: There are different SFM modes, such as contact mode, tapping mode, and non-contact mode, each suitable for different types of analysis and providing various types of data (e.g., topography, dissipation, electrostatic forces). Choosing the appropriate operation mode and understanding the feedback mechanisms, like AC to DC conversion using a lock-in amplifier, are essential for accurate measurements. The choice of deflection measurement tool—whether optical, capacitive, or piezoresistive—also significantly impacts the measurement outcome and its interpretation.
Recognizing the Impact of Environment and Material Properties: The environment in which SFM is operated, such as vacuum or liquid, and the material properties of the tip and sample, like dielectric constants, can influence the forces measured. For instance, the dielectric constant of the medium can turn attractive van der Waals forces into repulsive forces. Moreover, the force constants of the cantilever and the tip-sample interaction must be balanced to prevent unwanted snapping into the surface. Understanding the physics behind these interactions helps in tailoring the SFM setup and interpreting the results correctly.
These objectives emphasize the complexity of SFM techniques and the necessity of a thorough understanding of the underlying physics to effectively use SFM for material characterization.
Well good morning everyone it’s my pleasure to be here and I would like to really thank also everybody including Rina for this opportunity to be here and really having a fantastic view on the one side but also having this nice public here and it’s my job now to wake you guys up
Right scientifically wake up concerning really that we want to all go for something that is really connecting us which is this kind of very tiny tiny as you see here right so this is basically the starting point of all these actions that we are going here and I’m happy to see that
Also D and everybody has made up this kind of larger project so what qualifies me actually to to talk about scanning Force microscope or AFM in general and the reason is basically okay I had the chance really 35 years back to where it start working together as with B Gan
Rora and Chris of Gerber and these people in Switzerland I’m Swiss from top to the bottom and and this means actually I could really learn from them how to operate such a system and today we just take such a caner lier and we just push buttons right and we believe that what
We see is exactly our near field or our nanophotonics polarons that we have want to measure and so when Ry asked me and then El spec actually to really gave an introduction what can we do wrong with AFM then I said okay I’m happy to really
Actually get you on the same track so I’m from Dron so to say I move as you see from Switzerland down here somewhere into Dron and Dron and that’s a nice connection to what just D I was telling you semiconductor industry and we when we when you guys hear semiconductor you
Always think about the Silicon Valley right now Dron by the way is the Silicon Valley of Europe and in Phan just bought up a they’re just building a new actually manufacturing uh with 5,000 employees new jobs for you guys possibly also neop they do neop itics in fact so
Dressing is one place actually that where we do a lot of stuff and we had the chance you really join into the Excellence of initiative so we’re coming back to Excellence here and in our job actually we want to use this kind of small Gadget this kind kind of Cy L you
Use that for electronics on the one side for magnetism for photonics and you can see it basically here so it’s the in and out it’s our sensing device with which we want to really do that job and in fact to give you just a small glimp of
What we can do with that is a list of of things that I try to cover within this lecture not this one here but also the second one I want to get you back that this scanning Force microscope I’m calling it not Atomic Force microscope
And you will see in the reason why why this scanning for microscope has so many options to measure topography on the one side to go for magnetism to measure electrostatics or Electro yeah time dependent electrostatics to make dissipation on the system because you’re hitting with you can’t leave on your
Surfaces and on top of that also combin with snow so you see there many many different things at the same time happening well to get you back on the same page we are doing also NE Optics and we just have two such NE spec systems uh our specialty is to couple
That system in the terets range to large facilities lasers which is a free electron laser this is about 20 M long and also a super radiant source which gives us the opportunity to go down to wavelength of 3 mm this is 100 GHz so if you’re interested in doing such research
With us then this is a user facility and you can apply for basically beam time so this is really the upper end of the story but we want to start now very simple we want to start at the beginning which is exactly this scanning Force tip
So we need to understand what is it really doing so we take this can back and we see actually there’s a tip we want to see a little bit about history we want to talk about the can properties because that’s essential because what you measure here you see you can go even
Dynamic huh and it’s very important that you stay Dynamic on that we want to see about ctive deflection opportunities the forces that are relevant and finally also different operation modes okay let’s start let me go back 1986 that’s the starting point of everything here because in 1986 three
Things happen at the same time okay a little bit delayed the first thing to mention here is again this one here Santiago deosta not too far off about 600 kilometers to the West here you can walk it actually and it’s a very nice walk on the jackobs way Santiago deosta
Was the very first place in 1986 in July where nio Garcia from the univ aoma Madrid was organizing the very first conference on scanning tonning microscopy I don’t know who was knowing that maybe you you know I know okay okay so this this was the very first starting
Point where the community of STM was growing and um in fact this is actually the first point in 1986 second point a little bit later the same guys hyur G binck were receiving the Noble Prize this is October as you guys know Nobel prizes are always actually contributed or distributed
Actually in October October 1986 and they got the Nobel Prize together with El rusa for electron microscopy so it’s half half as you see one quarter one quarter one half but what is important is that not Hora not gin were really doing the job but that guy on the right
Side which is kristofh Gerber was the guy in the lab doing all the measurements and this is kristofh Gerber he was never at the let’s say awarding actually of the Nobel Prize but he went the same year together with G binik who went to California to call qu’s laboratory ginson laboratory with
Which is torn down at the moment so you can’t really visit anymore and they said okay let’s develop something which is called Atomic Force microscope or scanning Force microscope published exactly in this kind of PRL in 1986 because they said okay we are really bit bored off of our STM because
Our STM is very nice because our STM can really measure currents through our xyc scanning of this Paso but that’s electrostatics tuning measurements and so on what about insulin s can we also do the same thing when we go for insulating surfaces and the answer is they developed exactly this kind of
Cartoon it’s a lever where you have a tip attached that is sensitive to any kind of forces and they said okay simply we need a sensor this is actually from g b a slide he was really presenting at the Nobel Prize talk so that was exactly the starting
Point the scanning for this kind of Gadget basically was developed exactly 1986 and you see in the first publication 1986 they said okay let’s take such a can here you see schematically and you put it on a sample which is on the left side you have a scanner for the sample
Which is called a feed back here on AFM and on the right side they said okay we need a mimic to measure this okay they didn’t have anything already so they said okay why don’t you take an STM so make a tandem and in fact that’s why actually they came up with
The idea to measure Atomic forces and that’s exactly the point where the branding name name AFM Atomic forces was delivered well it caused a couple couple of confusion because some people thought in communities AFM is atomic Force you’re going for nuclear physics and it’s not it’s solid solid state phys
Physics I rather like to really name it scanning Force because we measuring generally forces in total Atomic force is one type of forces and you will see in a second there’s more so let’s turn page we need to know a little bit actually on this C Li before we can really start doing
Measurements we need to know what are the static and what are the dynamic properties of this cany liver and you see first of all we take such kind of a cany lver well here it’s a very nice silicon based can lver in the early days
I can tell you what we did we went into the kitchen you know there’s aluminum foil that you wrap up your sandwich in you took a scissors and you cut actually actually C leaves out of an aluminum foil very tiny tiny ones it was working okay not so Splendid but it was really
Actually a good approach now we take this Canter L and you see nicely basically you have a certain deflection of this caner L let’s call this z z that’s exactly my deflection and this is so tiny that we can apply hook slope which means that the force is really
Linear on z0 we don’t have to go for non developments of these forces and even more if you take a feedback that keeps actually the deflection constant you’re better off actually with this hook slw so that means the can of a force constant the spring constant K is
Exactly what you have here now if you go for math you see okay well this spring constant is something that is related to the material constant the young modus as well as the geometry lens times width and so on and moreover the lens you see L power three so the longer the can
Lever the smaller the spring constant if I go short okay you see basically I get a much much stronger this goes with power three low now the moment of inertia e is important because that’s a cross-section you can quasi calculate that if it’s really square like you see here then you
Go basic for width time thickness power three and you get exactly this which ends up in my Force depending on the deflections Z here exactly in this manner so this is the static point we keep the cter L like this you basically stay there you go into your sample possibly and you stay
Wonderful now let’s go dynamic because that’s much more important in life H you want to be be dynamic well everybody knows here harmonic oscillated which means if you take a pendulum right you guys know what the solution to this kind of dynamic prop property is because it’s a harmonic oscillator which
Has ion states that are spaced equally which means we go up exactly by H bar Omega always Grand State first order State second order and so on this is just quantum physics right and this is basically simply because we have a harmonic oscillator where we have a mass
A concentrated mass at the end and we say well my spring here basically or my yeah my rope has no M at all so what about actually if you go really for this kind of C lever now we have two options how we can calculate that one thing is
Actually we could say exactly the same way like we go for energy potential energy basically is the same like the dynamic energy which means they have a deformation okay which means this is a deformation energy which is exactly proportional to my deflection z0 or under have the Dynamic one which is
Basically the velocity or in other words it’s the frequency Omega Z that comes in the I frequency which is the lowest ion state of the system equate these two things balance off forces or or energies which means my ion resence frequency is simply a geometry Factor again EI times
A and row a is the cross-section W * T huh you see that basically here and row the density of the material the beta is a so soal normal IED constant and you see nicely it’s a fact of 1.8 788 keep this in mind I will ask you later okay
1.87 A8 okay so this is one way to approach by energy and that’s exactly the poor man’s version because we miss half of the world or even even more than that what we should do rather is actually we should really go and really solve the equation of motion of this can
So we go Dynamic we have a dynamic illation and you see nicely that if you go and do the math right we have this kind of equation to solve you say well it’s an harmonic oscillation but what we’re doing is actually we say already that we want to have higher order
Excitation modes not only the fundamental one but also higher orders see n is an index number going from zero 1 2 3 and so on so similar like my ground state we have a zero first second third exited state so it’s really quantum physics that we do here so if
You plug this in basically your solution or let’s say your equation comes up actually in a fourth order differential equation that we have to solve with some kind of uh really normalized really frequencies again and we can now make an approximation that means we take any solution that is possible so you see
Basically it’s a harmonic oscillation so why not to take s and cosine ways we don’t know what is really the right one that just pH shift at 90° but on the other side you see also if I’m going to excited it’s going to have a damping right so there’s
Basically a damping of the system which means we take s hyperbolic and cosine hyperbolic at the same time which means we get four Solutions here we need four boundary conditions which is clamping by hand which means first order second order is really zero and the open end
Also has the third and the fourth order to be zero which means in the end we get four Solutions which ends up in this solution of my can solation that’s what we want to see and this gives a solution which is not only one solution but we
See nicely uhhuh the higher orders the first one is actually 1.875 so remember how much how much was the beta before exactly fantastic so very close to that value but nevertheless we see higher orders so if you plug in 4.69 4 this solution is also fulfilled we could
Go for 7.8 so in fact you see we get higher orders for the solution this is fundamental mod Omega Omega 0 first order second order third order and so on and they’re not equidistant so it’s not 0 1 2 3 4 it’s not H bar Omega it’s more
How much well let’s see so we do that we calculate exactly Omega n and we go for the normalized Omega n over Omega 0 Omega 0 means the fundamental resonance frequency basically about two Herz here and that means the higher order mode obviously must be six times three times
Larger so let’s try to excite it ooh maybe you can see it now huh you see there’s a note here okay if I go for 12 Herz 12.56 Herz I have a note there which means that my Solutions now are higher order modes we get the fundamental mode here we get the first
Order mode here we get the second aut mode and so on so you can’t Del has more than one mode to go so if you go Dynamic you can excite any of these modes in your can deliv it’s not at two Omega 0 but it’s at 6.3 * Omega 0 the third
Order is at 70.5 Omega 0 okay and so on so that means if you buy a lock in look that it has enough bandwidth okay so we see ahuh the comparison between energy conservation and equation of motion is quite close for the fundamental mode and in fact if you plug
This all together we can find uhuh that my Omega 0er which is now exactly the k0 or D Capa 0 this is the full formula goes exactly to K Over m * 24 in the denomination well that means my effective Omega 0 is about twice as
Large as K Over M so it’s much larger than a free oscillator that we had my pendulum before K Over M right it’s a factor of two off question for you why why is that if you take the same mass at the front end of my
Pendum huh and I take the same cand mass why do we have a different so you say oscillation frequency question to you why well the difference is clear here we have a distributed mass the mass is not at the front end it’s not a concentrated Mass but it’s really distributed which
Means in average uhuh half of it basically is not really contributing yeah so just hand waving argument you can really see you go for a concrete calculation which is this one here it’s just a factor of two if you add some concentrated bass in the front we because of my tip here then
I just adding this one here to the front Jesus I’m just adding this to the front end and you see nicely that we can really calculate the effective resonance frequency so when you calculate or when you measure your resonance frequency be aware that this is all in it so the
Concentrated Mass plus that actually lever Mass weighted has to be respected and then only you can really calculate your Force constant your spring Conant of you can Delver here’s a table basically of involed in the things that we need to know only two things need to be known
Actually the geometry that’s clear but also the Young modelist on the one side if you take silicon it’s 1.79 if you take Row the density it’s a 2.3 fine okay this is all clear and we can turn page and say okay now let’s go and try to measure this candy deflection and
I would like to really briefly strive historically whatever has been proposed to that which are electrical measurements on the one side here on the left side using an STM on the back side capacitive or pH or resistive and on the right side are the ones more modern type
Which are Optical measurement you see beam deflection which is the most known one to you guys you adjust your knobs to four knobs in order to get the beam deflection right but there are better ones concerning sensitivity right homod and heterodon interferometry and also one very very special technique called
Differential polarization well let’s see how we go go in time um and we were going to really strive that historically said binck Gerber and quate said well let’s take this can lver and put the S10 behind well this means we need to really collect the tunneling current you see
The tuning current here the density is proportional to my exponential value with see the distance between the tip and my cter L well this is good this is bad well I have this picture here for you this is a real picture how your STM tip looks on the back side if you can
Deliver and you see how dramatically impacting is so we have some pros it’s a very accurate measure with the tip and is very historical but there are tons of cons actually as you see you need a backside is that is really conductive on the one side it has a certain roughness
Because you evaporating gold or show on on the backside which means the surface Topography of that one matters then you need stronger forces because that’s an electrostatic interaction finally you get adhesion of your tape and so on the feedback loop is twice for the STM and for the
AFM and then we have a very low bandwidths typically below 1 Kilz which is really low and hence it’s not very suited for Dynamics remember these kind of dynamic modes higher orders you can forget about that so no way so that’s why it was abundant people thought well
Let’s go Dynamic and let’s go for a capacitive sensing and is actually at zsm they have done this so to say in in in Switzerland with ygen Brooker and others and Jim Jimi saying okay why not you take a capacitor from the backside of my c l in order to detune as you
Nicely see here my capacitor when I’m vibrating the counter lever so you have a oscillation you’re LC circuit as you see nicely and you have a certain frequency and you Dune that by simply vibrating your c l what is needed for that is a ful integration and it’s very
Nice but you need an extra electrode on the back side you need a conductive back electrode this was be in the ’90s people tried to do that it has been a bond as well but it’s a very nice Revival these days at least for let’s say yeah
Environments which are let’s say uhv or or let’s say low temperatures next thing we want to look on P resistive and that’s a really nice thing that people are thinking of these days again to Revival specifically also for going for uhb or low temperature measurements including also snum what is
A pH resistive measurement well we take the can now and make two wires we take two of them one and second one that are connected but we dope the surface with a p doping of silicon we change the resistivity by T do p doping and hence when a current is passing through that
Wire here as you see and we’re deflecting the the cania either tensile or compressive you change the resistance so basically what you have to do in the end is just to measure measure the resistance change Delta R upon deflection which means you take a w stone bridge and you balances off and
You get a certain resistance change so that’s a very nice actually possibility in fact there are tons of Pros it’s fully integrated it’s electrical sensing it’s static and dynamic it’s and amm mode possible it’s low temperature compatible but there also cons every Pio coefficient whether P resistive p Electric is always
Temperature dependent that means if you work at room temperature or you work basically at low temperature the coefficients are much much much diverse so you have to keep the temperature very constant there might be cross torque because we measuring electrically and hence this is not really what you want
Here also the issue of tip integration and noise is very one well yes sure what is the noise increasing noise compared to the normal deflection okay so the increasing noise is basically because you have always an active feedback loop so that means basically you have Electronics in order
To measure that in order to make this very sensitive you say I take an AC current okay you pass an AC current and this gives you a noise flow that goes above the1 so I can you show figures on that you larger basically than one F noise for this
Measurement typically about 10 DB okay at 1 khz okay factor of what Square two yeah okay France Gible has tried that 1994 and they said okay I take exactly that tip for doing STM fantastic you see high resolution silicon one 1 7×7 Atomic resolution and then also doing the same
Thing at room temp temperature on Mo and disulfide a very modern material as you guys know and also getting Atomic resolution this is one of the rare works but as I said this about 30 years back and now there’s a Revival coming back the issue is exactly that you want to
Integrate these things for low temperature for instance and uhv so let’s change page we discussed all these electronic properties and they’re not too much paying off at the moment and in fact actually these side this side on optical deflection sensing is much much more appropriate let’s go for the first one a
Homod dine interferometry all you guys know what Michaelson interferometry is right we take a beam we just split it up into two beams which is a reference arm and a signal arm and then we just add these two beams in reflection which means we take two frequencies the one
From the reference one from the signal let’s say from your can L backside for instance and this means we’re going to add Omega plus Omega or we rather do Omega minus Omega so the sum of these two things goes at zero frequency again thank you for the question we are at at
Zero Hertz which means we’re totally in the noise level so measuring at zero Hertz which means we have the maximum noise ever which is bad H homod is nice because it can be also be integrated here you see a version that you go with a fiber optic to The Bitter End for
Instance low temperature after Cube has that and then actually you go and go for the reflection the C and you go backwards and go with your signal here so the interference comes here from the back side from the interface of your cany lver on the one side and from the
Ending of your fiber so you have the glass fiber my Feast this is my can L CH and then in the end I keep you awake huh thank you Monica um and then basically we have the two signals one actually back reflected from my my fiber and the
One from the can so this is very nice you can make fabric par compatible actually measurements you can make a robust and vence independent system it’s fully integrated it’s low temperature compatible there are some cons on it we measuring the power rather than actually the electric field here so that’s one of
The points because you go for E * e which is e^ squ which is power and we need a zero position when I put my can here or here matters because as you know from standing waves we get a face shift H can we do better and the answer is yes
We can because we go heterodon so we do the same thing like Michaelson but now we split up the two beams the one beam which is the reference beam and the signal Beam by modulating one of these beams you see nicely basically that we have now two frequencies the bra cell is
An acusta optical modulator which shifts us from the zero frequency in the sum now out by the frequency we apply here which is about 80 mahz so we get out of the one over ref noise but this is one of the nice things that we can really now work zero position independent we
Get an excellent sign to noise ratio a very high bandwidths for Dynamics because we are already modulating and we have so to say ultral noise there a couple of noise it’s Dynamic only that we can really measure not static and we need a mehz modelator which is
Costly well I can only say that this is a very good measurement and we do that also at low temperatures second last is now actually theorization and I want to keep this very small or short you guys know if you take an optical beam it’s polarized let’s say linear polarization let’s turn
45° and now shoot with that laser onto the can deliv you see the can here and we do that basic basically by putting a so-called cul side C window in between which splits up the beam into two oral beams one vertical and one horizontal
Let’s say S and P okay the S goes on the back side the p goes on the front side which means we make a differential measurement it’s the best differential measurement ever that you say here on the back side and the front side we can really measure what is the relative
Deflection of my can Li so that means what we’re doing is exactly what you know from ellipsometry we’re shooting with a laser on it and we want to know what is the signal that comes out we don’t know what a sample is what it does to the signal but what we measuring is
Basically the Turning of this polarization we start with let’s say spherical let’s say s SMP same magnitude and then we get an elliptical polarization and we turn this ellipses these are the two values in the end that you measure and detector that’s the same thing here you measure this with two
Photo diets one and two very very very bulky because of discrete elements very costly but the best resolution ever that you can really see for common mode rejection here now we come last but not least to the one actually that is really the one everybody’s using these days at Rel leas
At room temperature this is something that you can really do even in vacuum you go for beam deflection that means we take c l take a laser point on the back side as you can see nicely here and then we go basically bouncing off this beam
Left and right right or top and down which means we measuring simply the differential image differential uh let’s say um yeah Reflection by two photo diets on on it or you go for four quadrants which also means that we can go for both in plain lateral forces and
Vertical forces I think you familiar with that most of you are familiar with that if not you can ask me the nice thing about that it’s very simple cheap accurate robust so that’s why also companies most companies have really implemented that one actually in their gadgets cons are really for low
Temperatures and for vacuum applications because that’s the issue so let’s compare that yes please it’s not for low it does work for low temp temperatures the question is okay you need a detector possibly if you take a fiber to get out it’s fine if you take a semiconductor
Basically it’s closing up so the sensitivity let’s say is is really bad for the semiconductor at low temperatures if you cool it down 77k is working fine we’re doing that but if you want to go for liquid helium it’s difficult that’s right yeah yeah because if you want to have a for Quadrant
Basically it’s down there I mean you can say okay I’m going for macroscopic Optics out of of the low temperature and they go really macroscopic so the question was why doesn’t it not work actually at low temperatures yeah okay good so we see basically in this comparison table actually that we have
All these five or these seven systems with all pros and cons if it comes to really sensitivity then hetero dining is fantastic I can only really cope for that one if it goes for inplane poo we really really thin there there only so the beam deflection there right um if
You go for uh LT you have seen actually what where we go okay so this is all about deflection and you have the choice to couple this ctive now to the measurement detection of your choice you can say well I can elaborate that this was basically the time in early AFM
Where everybody was sign trying out to do something today you buy the gadget and you cannot change too much but what I want you to take home is actually that you can take a lot of information by steering all the system you can look on the polarization you can really look on
The noise that your laser diet has and so on there many many supp things that you should really keep in mind let’s turn page we come to forces so we have this cver and we want to measure forces with this Cana and this guy is fantastic because it’s sensitive to all type of
Forces so basically you can really tap around basically and see are there forces somewhere or not well that’s very nice on the one side but on the other side it’s sensitive to all forces which means who is the right Force which is the right Force which force do I really want we
Have tons of forces as you guys see we have for instance vaval forces we have magnetic electrostatic long range forces we have adhesion bonding forces so to say you have even elastic and plastic information forces think of you go on a membrane or you go basically on graphine
Or graphite you compress in the system completely by applying a force of one nanon so this is all true what I I’m seeing can I believe what I’m seeing so this is the Holy Grail that we can that we are able to discriminate between these forces by using the
Different measurement techniques I was just telling you so in fact what we come up can come up we say okay we can take the tip and we can basically say okay this tip is the one that we need to really have a look on where is exactly the coupling to
Every of my forces I want to see we can say starting really at the front end because we always believe that’s the front end that does the job well this is not really true because we have tons of forces like for instance electrostatic forces but the front end might be in
Fact relevant but possibly it’s much more like a dipole or a quadrupole sitting somewhere here that is doing the job so the front end nanal tape as I’m calling it is only relevant for instance if you start really thinking about chemical forces so really coent B
Binding if you go want to go for measuring local density of states right there’re more long range forces even the Fise Force doesn’t care too much about what is really the front and because it’s a more integral as we will see in a second actually force and also if you go
For optically induced forces we know and there will couple of talks coming then where we induce a dipole or even a higher order mode into the tip and this dipole then couples to mamp so we need to really respect that so what I want to really get you home here
Is that the different origins of these kind of forces is not the one and the same always that means by comparison of different modes we have to really think hard what I’m doing I’m comparing a chemical bond at the front Nano end with an induced dipo Force at this position
Of my radius here of my tip so this is something to keep in mind when you interpret your data let’s continue and if you take all these forces we can simply state that we start now by simply approaching this tip certain distances closer closer closer and look with snapshots what is going on
Really so we start above 10 nanometers let’s go far away so my tip is far away okay much ways above my Surface and well that far away we have very weak funerals forces so there’s a small attractive Force and if you say okay we can even include some bias
Voltage we apply a voltage to my can L then what could possibly happen is naturally that we can even have at certain voltages at certain Fields so-called electron emission I’m far away you apply a voltage above the work function which means you get an emission of electrons so imagine you have a 10
Kilt or let’s say even 10 volt on your can the tips shall be conductive for this and you apply a voltage you’re far away bang you get electrons out okay possibly they they don’t arrive on your sample because you are working in air so you get dissipation you get possibly
Even sparking huh but nevertheless this is something you have to keep in mind it’s called the fou and or time tuning because it’s a field emission current right now even if you don’t apply a bias voltage my tip here metallic my sample silicon are two different materials
Which means we inherently have a soil certain bias voltage because chemically they’re not the same so we have a chemical potential difference and Rhino was already saying about Kelvin that comes up basically on Thursday and we will see then actually what is exactly this giving us so let’s go and now
Approach we go smaller with the distance D we go smaller between 1 and 10 nanometers we come down okay what happens at this inter we have still long range interactions we have thunder walls but but no tunneling so that means even the electrons they stay actually but
They should be and we get actually already some kind of wave function has been modified on the atomic scale the density of states that we are really taking as an integral for measuring the interaction is already modified if you go closer clearly we get so to say a
Taling current this is exactly where STM then is really relevant 3 to 1 nanometer we get strong attractive forces and there’s an electron transfer now if you go closer we go even to3 which is quite the diameter of let’s say one atom we get strong repulsive forces powery and the atoms might even
Touch now what you do when you take an AFM for instance in most cases and you go for instance for this famous let me call it tapping mode is you go basic and you go into it and you go out of it again you go into it and you go out of
Per cycle which means imagine what happens these start up here and they go into it and they go back out of it they go into it and out of it so you see many things happen at the same time and you’re not aware of possibly electrons can really change
Positions they can B basically transfer from tip to sample simply because we have different biases we have different electrochemical potentials and hence everything of that can really happen here on the other side you can even have emissions of electrons down here then we going through a whole zoo of
Forces so it’s not as easy as we think in the in the beginning so let’s see how we can really cut this down into something doable and we start basically with the most famous forces which are also branded in the so-called Lenard Jones potential we just take one
Attractive shorter range Force which is defund ofas and we take the repulsive so Force which is the power repulsion principle and this is all um brought together by Lena Jones here as that you see him here so let’s start with the greenish one which is the fondas attractive forces fondas generally is
Thought of as an attractive one over potential six Force but there are three contributions be aware of that there are three contributions which have three names keam Dubai and London what are they you see nicely here we have dipoles these are dipoles imagine we have two diol talking to each other they can
Orient and basically one makes a field electric field the other one is actually orienting in his field coupling to this kind of field and hence giving us a orientational factor Z Orient which is goes 1/ power R6 there says well we take a dipole but we take the second partner to be not
Being polarized yet so it’s an atom for instance and we see we know atoms have electrons they have ions we have a core which means this field of my dipole here is producing an electric field at the position of my second atom which is polar inducing a polarization called
Polarizability that’s exactly what Alpha is the polarizability we polarizing inducing a dipole it’s an induced dipole that’s why the factor is called induced dipolar the third and last one is basically this kind of where we have two polarizabilities alpha 1 Alpha 2 nothing is a diple yet and due to random Fields
Electrons made pivot and so on this kind of randomized actually field on the alpha 1 is producing a field at position Alpha 2 this one is talking back to Alpha 1 and hence we get two induced dios talking to each other again if you just omit retardation it’s a one over
Power Six law and if you put this all together as you see we end up exactly in the total fer walls the force so to say naturally is a derivative of this one and to give you some numbers the founder W Force typically that we are looking at an AFM
Or scanning force is typically on the one nanon and this means that the distance then for that one nton is already on the your about 0.25 no it’s 2.5 angstrom it’s 0.25 nanometers if you go further away if you go one nanometer apart that Force goes
Down to below .1 M electron volt so very low it’s a very steep so to say attractive interaction the second very important important force that we are looking at are the repulsive forces and you see nicely there are different models being proposed for repulsive forces on the one
Side heart sphere you take two spheres until they touch and once they touch the force the repelling the repelling Force goes up infinitely that means my n goes up to Infinity you see it’s a potential law that has really a straight value we can take a power law where the N is not
Infinite but something between 9 and 16 and in fact Len Jones said okay let’s take 12 because it’s just in the middle that’s why we all talk about the 612 potential right but it can be anything in between there then the exponential law is the final one that is
Also uh describing the uh repulsive repulsive forces this is very nice for everybody who does computer uh qu calculations because the derivative of an exponential is an exponential and hence basically the best that you can really use there right so long story short we take the power force which is
Exactly one/ power 12 and if you put these two things now together as you see nicely we have the attractive contribution which is the right thing here on the one over power R six negative as you see that’s attractive and we have the repelling Force the
Bluish one which is actually the PO in total we get so you say exactly this kind of curve with a minimum at a certain point right here well one thing is very important at this point what we did so far is exactly we take a point of my tip the front end
Really the front end atom and I take one atom in my sample one atom okay so it’s a pair potential that’s what we did it’s pair pair nothing else it’s not a sample that is extended with many atoms it’s not a tip which has many atoms as I have
Here so we have to respect for that well the other forces that we will really talk also later which means on Thursday electrostatic forces come in at energies as you see 100 to four electron volts really large energies we cannot forget about those ones because they matter in our small interactions they
Magnetic interactions also from 10 m electron volts up to one electron WT if you want to measure scare Neons or so then you have to respect that or if you go now for induced Optical dipoles like we do in snum then actually our energies
Go from point .1 to 2 e so you see again actually in the energy scape actually what that means we have tons of energies that we are adding up and possibly we not knowing what we’re doing so I just said we have pair potentials one atom here one atom here
In the sample now we do see that this is a finite distribution of my tip it is a finite distribution of my sample how do we cope with that so we need two corrections to do you see the two Corrections called in the lifshits theory and you can really read it up
Also in the jackobs isra’s book which is very nice on that let’s start simple and take the two things separate a sample and a tip if I take a sample let’s say that’s my sample here I take a tip atom my Feast I need to do this integral of pair
Potential over all atoms that I have in my sample which means that my tip so to say goes not only to this surface point but every point in my sample including subsurface interactions for instance so you make an integral laterally and Into the Depths and you end up with something that is
Reducing your power LW second point my tip the same thing my sample is extended my tip is extended I have to now integrate also over my tip because it’s not a single point in my Center we always think about the dipole possibly sitting in the center fine but
Nevertheless if you take really my real tip and that’s a real tip here then you see nice we have to integrate over all tip atoms so this is the big big question how relevant is this distribution and they come back to the different forces that we had we have different relevance radii
For different that’s interaction lens if you go for an atomic lens calent interaction it’s just the front end atom we finished by a pair potential if you go for a dipole then you have to really integrate over the whole system this means in the end that our fantastic 612
Potential that we just had from the pair potential ends up in a 1 to7 so we’re losing five orders of magnitude in the funerals we’re losing five4 of magnitude repulsive so that means my Lenard Jones potential is not as steep as I think it’s ways less Steep and you’re going to
Basically approach your ctive exactly into this very soft potention now huh it’s not as steep as you think this is the first correction the finite size of tip and example second Point there’s an environmental impact most of you work for instance in air Oro or in vacuum that’s fine because then my
Medium has a dialectric constant of exactly one now if you compare that to the dialectric concept of my tip let’s say silicon question to you guys what is the Epsilon of silicon so four okay more exactly so how does it go together from four to 16 huh so four is the
Refractive index so it’s basically between 3.5 and and four and if you go basically you have to do n Square for Epsilon which means we go something between 12 or 11.7 and 16 so let’s take 10 because we can calculate easier with 10
Okay okay so if I take 10 for my tip and I take a medium of one which is basically my medium which is air we get so to say for my funas attractive Force you 10 – 1 is 9 10 + 1 is 11 so we get
So you say yeah roughly one okay now let’s go for water we go the same experiment you want to do snam in water we take a AFM we put it on the water we go for a medium that is 80 uh water dialectric constant DC is 80 I go from
10 – 80 which is – 70 I go 10 + 80 which is 90 two things you see I’m changing sign my fun was who is attractive becomes repulsive interesting huh so in water basically and changing the medium means you can basically change the effective sign of your
Foundables the other thing is the waiting how strongly does it impact actually on it and you see uhhuh it it’s really a matter so these two things keep them in mind they have to do exactly the way you operate the medium and the size of your system so jackob Isel was really doing
That and he said okay let’s go from Pair potential developing into so to say one tip so to say in front of a surface and then go from this one to a finite size and he was even developing an instrumentation called the surface Force apparates because he found out that this
Tip roundish tip spherical in front of a flat surface is exactly the same thing like two cross cylinders so if you take two cylinders you cross them you get exactly the same topology of the system it’s also 1 overd for funa was one over def for fun was and that’s why he was
Using two mic sheets bent them a little bit coat them and measure the interaction his surface fores on the liquids so this goes together and this was in the 70s already so much much earlier than STM okay now let’s go for sfm operation modes we need to now really work with
This kind of potential and we start really simple I’m going back to the 612 potential because you can develop it much easier so the first thing we have is really the potential as you nicely see we have again this potential curve 612 now we want to measure forces and
That means in the end we need to take the derivative so this really minimum in the potential gives us the zero Crossover at this point in the force and hence the deflection Turning Point at this point gives us the minimum in the force we go from the force here to my
Force derivative because we want to make also gradients later and I do the same thing I take this point so to say the M goes to my deflection point my zero cross over here and this one here why do I’m doing this here well what okay what you see here with
This bottom curve since this is the interaction potential is exactly that we see with this curve here this is the spring constant of my interaction we know this can has spring constant K right now what about my interaction I want to interact with my tip to my
Surface my measurement I want to do and we see nicely that this is not a constant spring constant A4 so to say minus F Prime is something derivative F divid DF over DZ which is a spring constant this is the spring con of my interaction kts tip sample and you see
Nicely that spring constant sometimes is negative and that spring con sometimes is positive and we coupling with my spring here to that spring of my interaction so we’re making two Springs interaction that’s exactly what the force is about so let’s see how we can really do that
And for that we need the full potential we have again the 62 potential as we see here and we take so to say the potential of this can lever which is again then as you see the harmonic potential so we have a deflection out of Z z0 here this
Is my harmonic potential we have to couple now to actually this one here and we take this as a normalized version Za is a distance at which the potential is zero so you see basically this one is Za which means exactly here my potential crosses zero bang at this point let’s
Take this as a norm Za and so what we do now is the following I take a sample I take my can lever and I’m looking at different distances what kind of interactions in my potential curve do we see so let’s start we take again this formula and we start basically in the
First picture at a distance far away four time CA so far away so you can imagine uhhuh this tip now feels an attractive Force maybe it’s bend a little bit okay but in fact if you solve this equation here we get a saddle point we get a minimum here at this point close
To the four which is a stable point if you go closer to Z three times z z we go here a little bit more shifted below the three but still something which is in the potential the minimum here but you nicely see that this Saddle Point here comes down already the point
E and G and if you continue with this you see basically we go to 2.3 we suddenly drop into a minimum here we goes below below zero although my can stands at 2.3 which is here it feels an attractive force and says bang I want to snap in it goes
Directly to the surface you can’t prevent that it goes to the surface that’s exactly the snap into contact although the tip stand here it goes exactly at this point 1.4 and if you go for 1.5 it’s even more dramatic it’s down here so you see actually what happens is that the
Attraction of this can due to the different Force constants kts and K makes my can snap into the surface you can really imagine this the are these are the four plots at the same way imagine you take a small bead or small ball and you just roll that down
You put it in here at the ball and and you just wait until it’s rolling down into the minimum you will find it actually in the end here right that’s the minimal position do thees the same thing here maybe might stay here it’s a quasi equilibrium position we don’t know
And here it will definitely roll bang into the minimum so that’s exactly what happens the system automatically finds the minimum by really wanting to go into this snapping position this is not good and the question is can we prevent that well let’s do the math first let’s go for the
Math solution of this equation again we have this full potential and we want to look on the minimum of this potential which means we have to put the zero which means that this tip s interaction has to balance off with the force that we have here and
In fact the tip sample force is balanced by the counter L Force finished at the same time and that’s now the important thing is we need also a certain deflection which means the second derivative needs to be positive which ends up that my force const of my can
Here this K needs to be larger than the force constant of my tip sample raction that’s exactly the kts if I want to prevent the system to snap in I need a force constant K that is ways larger than my tip sample interaction well in the beginning we
Don’t know the tip sample interaction right you never measure that possibly so here is actually the whole snaping process in a nutshell we start basically here and you see that’s not the potential but that’s the force now we see basically the tip sample force in redish
I take my can lever spring constant as you see this is force this is distance the greenish one is the force constant K of my can L and so if I’m going to approach now my can here as you see I can do that we coming in basically and
If F the force and then bang he goes right into this minimum and the reason is that my Force constant that we have here as you nicely see we can do that mathematically or geometrically approaching the point C and hence we get from C to D so take two points which are
Connected that means basically the system does not know whether to stay at Point C or D because they’re on equ let’s say force and in the end this one is the lower one because it’s a lower Force so it’s snaps into D on the way back if you’re in
Here the same procedure we want to go back so we go backwards we are down here I’m pulling back my tip stands stands stands until I’m here and then bang it snaps down here up here to the a point so you can take the K value you plot
This this Force actually as you have it here oh sorry wrong you plot this Force as you have it here and you go and basically draw this so you get basically a hysteresis between a to c to D to F to a this is an energy because it’s force
Times distance right this is energy this is dissipation this is aesan energy so at every cycle when you go down with your tip your tip snaps in and then you pulling back because we for instance go for a tapping or so and hence you have a dissipation of energy at any of these
Oscillations and you can see how much that is it’s just a hatched area between AC CD so you can hatch that and you see quantitatively how much energy is gone this means now we can really differentiate between the different let’s say modes on the one side we can
Say well contact is then exactly when we left of this snapping point we want to just go only into the repulsive regime huh we are then really working the repulsive regime if you want to go really on the other side of the snaping we go attractive only and if you go over
That point of snapping it’s exactly what we do with tapping or intermittent contact you name it they different names on that so you see actually we have to really look on the force constant with relation to the tip samp interaction there so put this into figures means that we have now the repulsive
Interaction on this side as you see we have forces which are really strong and we mostly go for static measurements that means the deflections really statically my bending is exactly this way we have a large Ates a large contact area we can use one of the deflection methods that we just were discussing
Before and in order to measure that and scan if I go basically for attractive I want to stay at this Rim at never want to really go basically Beyond this point which means I need a force constant DF over DC which is large enough in order
To avoid that snap in and hence I can then beas take a mimic to really dynamically mostly really measure that we do that dynamically simply because if you go statically I says I was just really sh before okay now maybe so you basically see actually if I go Dam I have a much
More much larger sensitivity for doing so so this is the way we can really differentiate between these different modes now I would like to break the eyes really for actually Dynamic modes we need for that an AC to DC conversion what means I’m excited my can L as we
Have it here and hence I have to really measure the deflection and I want to really use something like a locket amplifier or something which is really giving me a conversion from the AC signal into a DC signal in order to feed that back actually into my system I
Don’t know whether you guys are really familiar what the lockin is doing uh just a quick sketch here which I borrowed here from Zurich lockin Zurich instrument you just take a signal in and you compare so to say with a certain reference signal and then you say okay I’m going
To do that once at 0o degree and I’m going to do it once at 90 deges you guys are familiar with Transformers 50 HZ for instance in the power lines you take basically and you want to make a DC out of that which means you always go this
Way this is very important thing this kind of mixing because you get two signals out and you can do that now for my amplitude of oscillation you can do it for the phase of my oscillation but you can also do it for the frequency and this is the Holy Grail how
Actually you to operate it say most people take that phase and now this phase contains any kind of force interaction the mechanical phase the optical phase everything that is acting on my can lever I can’t really say and that’s really the the point where you have now to think of how can
We differentiate because the goal is now to take this non-con Mode Shake it here take any kind of deflection the back side and then say from that oscillation can I take that as a frequency shift I’m looking on Delta F the frequency shift and just use that as
Topography well at the same time when we do this as you guys know we already said I’m going to oscillate that and there’s a certain damping right so we’re having a losses in the amplitude now we could also take say okay why not to take this oscillation amplitude and keep this
Constant if I’m keeping this oscillation amplitude constant I have to feed in here on the back side with a certain feedback loop that that my drive is always the same I can use this as a signal in order to measure directly the dissipation stdm dissipated power I can really have a feeling on
That I can also at the same time use the same lock in or let’s say the same signal in order to go for Kelvin and so on in the end and that’s exactly what we want to discuss actually then on Thursday we will use about three four five different feedback loops in order
To disentangle whatever you have in here in order to make different modes of measurement you get topography you get dissipation you get signals like the electrostatic you get capacitance and so on further all if you have your illumination with snum then you need another lock in and also there’s a phase
But you should be aware of that not to really mix is up well what I would like to do for the end of this lecture is now the following in order to really make this kind of thing happening I have brought an experiment here and I would
Like to invite you basically do that after the lecture here in front because I cannot show this really too much what this is is actually nothing else than an oscillating c l you see basically it’s a small can lever and I have basically
Here a sample and you see 1 2 3 4 5 six and what I want to show you and I will do that basically for the people in the camera not for you is actually that you see actually this this tip is oscillating and there’s an attractive
Force which is increasing now which is decreasing the frequency and if I go basically for a repulsive Force we’re going to have basically a higher frequency we looking on frequency mode FM and you can really play with that hopefully you saw that you can play down with that I’m going to put
It right here don’t break the tip okay why is this disspation important why do we need to disentangle this and the reason is B because of the physics this is nothing else than my harmonic oscillator that we have here right now we have dissipation which means my gamma
Zer is non zero that’s the point otherwise this would be really out we solve we can go home finished this is basically my oscillation here and this is the drive my hand is driving it and we do have a couple of interactions like tip sample now to solve this kind of
Differential equation means we need to do the following we need to really apply again the same same formalism as shown before cosine sine wave sinus holus cosine holus most people if you do that and you did that in school you solve basically one of the equations you say I’m going
For that solution which means I’m using cosine solution because this is what we call in physics the so-called conservative forces we’re not looking on the imaginary part the solution contains cosine plus I sign right there’s a complex number as well because this is a complex Sim if you take cosine make derivative you
Get S so there are two equations that you have to solve the first one which is the conservative forces and the second one this is at the damping as you see this are these are the losses which is the dissipation for the sine waves most people forget about and I
Would like to break the ice that you can do that in a very very concise way you can go down to measure dissipations down to one at what which means you tip so to say on one cycle this Ates 10 to- 18 Watts which is very small and I’ve done
This basically for now 10 100 let’s say um thousand uh Q values and that 100,000 Kilz for 100 khz sorry now if you go for room temperature where your Q is lower and your resonance might be different and your illation might be larger you plug in different values and you end up
With the patient on about 1 to 10 nano wats per cycle so imagine that’s exactly the energy that goes a into your sample or in your tip or whatever you you name it so you see in the end this is very important that we know what we are doing
By this kind of oscillation because we’re hitting the surface we’re coupling to the sample and to make it even more complicated these are all the sources for this kind of dissipation and you see you can write up tons of projects on that if you want to uh it’s not solved
Because very very few people are really working on that I like like to finish this this lecture now with the following take home messages first of all the geometry is really the important thing that determines my K of my counter lever we saw actually that the higher order resonances are very important and
We can solve them by going for the equation of motion then it’s very important that you select the deflection measurement tool of your choice that does a the bandwidths B the sensitivity and C the approp for your measurement like say a low temperature vacuum now be aware of this here our tip
Is really stupid because it measures all forces I unless you say Okay I want to be really measuring one type of forces only and you can choose between that by using different operation modes the distance at which you operate the amplitude at which you operate so the
Operate allows to disc between those and be aware of that when you interpret your data that we don’t have a point too interaction I don’t know how many people really know that but it’s really an assumption to take Lenard Jones only but in reality it’s much more complicated there is snap
In be aware of that and you have I hopefully I showed you how to really do this without act and last but not least dissipation matters and with this thank you very much [Applause]