 Welcome back to the lecture series on metrology. Now, let us start lecture number 6 under module number 12. In this lecture, the following topics will be covered. Stage errors, calibration of stages, typical specifications of the microstages and nanostages, and applications and selection of the different kinds of stages. And finally, we will discuss about nanotechnology instrumentation. In the previous lecture, we discussed about different types of stages, linear stages, rotary stages, and what are the different kinds of drives used in the stages. Now, we will understand what are the various errors that occur in the metrology stages. Now, you can see here, they have linear errors and angular errors. So, this picture shows that the table, this is the table surface and the table is moving in the x direction. When it moves, may move like this, that means it will move up and down, the table surface will move up and down, that is known as the flatness error. Similarly, when it moves, it may move like this. In the horizontal, in the vertical plane, it may move like this. So, this is a straightness error. These errors, linear errors occur in all the three axes, in the x-axis movement, in the y-axis movement, as well as in the y-axis movement. And coming to the angular errors, in each axis, there can be error in the y-axis, that means the table is rotating in this fashion. So, this is the y-axis. Similarly, along the pitch axis, it may tilt, the table surface may tilt. And along this x-axis, it may roll, table surface may roll. That is, apart from linear errors in x, y, z direction, there can be roll axis error, y-axis error and pitch axis error. That means while designing and manufacturing these micro nanostages, a lot of care has to be taken so that it is properly designed. Also, in manufacturing, proper care should be taken so that these errors are minimized. Now, these graphs show the repeatability. You can see here, this is the position of the stage and the y-axis shows the deviation in millimeter. Now, after assembling the stage, we have to conduct x-perman performance tests many times and then repeatability should be established. You can see here, the error at each position, the table is moved along the different axis, x-axis, y-axis and z-axis sign. What is the amount of error at different positions? For example, at 25 millimeter position, what is the amount of error? So, multiple readings are taken and then finally we can calculate the average values. That means this line shows the mean error in the forward direction. Similarly, in reverse direction also, we should conduct the experiment to get the bi-directional repeatability performance. So, I can see here this curve shows the error in the forward direction and the yellow line indicates the error in the reverse direction when the table moves in the reverse direction and this blue curve indicates the average of both error in the forward direction and error in the reverse direction. This is the average value. So, this is the zero error line and different positions of the axis, what is the amount of error? So, these experiments should be conducted for all the three axes, x-axis, y-axis and z-axis and then we will come to know what is the repeatability of the stage. Now, there can be errors, the squareness here. That means you can see here we have an x, y table. Now, so this is the x-axis movement and so this is the y-axis movement. So, when the table moves the top surface of the table moves, whether the movement is 90 degree or not, whether the square or not that can be checked by using squares and dial indicators and at proper height the squareness should be measured. So, the squareness is basically the combination of rotational errors and linear errors. Similarly, in stages there can be a big error. You can see this diagram through the surface of the table. So, small angular errors at this stage surface, they produce translation errors at the workpiece. Say we have mounted some workpiece of height h and then this is the workpiece surface. If there is small error at the small angular error at the surface of the table, so it gets amplified at the work surface. So, that is the obey error. So, this obey error delta yes. So, it is nothing but the angle theta times the offset h. So, that gives the obey error. Now, how do we correct correction is given for these errors? So, the different types of errors should be measured and stored as lookup table and as and when necessary we should use these errors, lookup table errors and then correction should be given. So, these lookup table values are meaningful only if we are done at appropriate obey height. Now, how do we calibrate the nanostages and microstages? So, we can use image processing the system software and can use the cameras and also you can use standard specimens for calibrating the nano microstages. Also, you can use linear interferometer for calibration purpose. This picture shows the calibration plate and optical gratings also can be used. So, the calibration plate it has got different contours made in the plate and different holes of different sizes. So, these calibration plates can be used along with the laser system for calibrating to find what is the amount of error and different positions and then the software can be used to calculate what is the amount of error. Now, this picture shows a setup laser based calibration setup. You can see the surface plate on which the xy stage which is to be calibrated is mounted and then there is a laser source and then mirrors are there for reflection of the laser source. Using such a setup we can find, we can determine the different types of errors and then we can plot the errors like this. You can see this is the travel of a particular axis of the xyz stage. So, here it is the range is 0 to 285 millimeter travel and y axis indicates the error in terms of micrometer. So, when the stage moves in the forward direction, what is the amount of error that is plotted here? So, the maximum amount of position and accuracy is 8.09 micrometer. So, similarly repeatability can be established. So, in this graph shows the repeatability in the forward direction is 1.02 micrometer. Similarly, the pitch errors and y errors can be determined using such a system calibration system. Now, this table shows typical specifications of nano stages. So, the different models are available. So, this is model 1, model 2, model 3 with different travel ranges you can see and this first model the travel range is up to 10 micrometer and the second model 25 micrometer and third model 40 up to 40 micrometer. This is the travel range of the x, y and z axis. So, normally x axis, y axis range will be greater as compared to the z axis range. So, resolution is 0.05 nanometer in the first model second model 0.1 nanometer and in the third model varying that the travel range is more the resolution is 0.15 nanometer. Also, the linearity ranges with 0.03 percent, 0.02 percent, 0.02 percent are available and bi-directional repeatability of 1.25 nanometer, 1 nanometer and 2 nanometer are available and pitch and y error will be something like 5 micro radians, 5 micro radians and 7.5 micro radians. Now, here you can see some of the stages, nano stage with four axes that will be x axis, y axis, z axis, three linear axis and then fourth rotary axis is available here and this runs with brushless DC 12 and resolution of this table is 20 nanometer such a fine stages are available in the market. Now, this shows six axes a very compact parallel position that means this top surface of the table always moves parallel to the base and this has got six degrees of freedom, three linear axes x, y, z and three axes pitch, roll and y. Load capacity at this particular the position is 10 kg and it can move at a velocity of 25 millimeter per second. The travel range is up to 45 millimeter linear movement and 25 degree rotational movement. The resolution is 7 nanometer such a fine accuracy or positioning accuracy are possible and 300 nanometer minimum incremental motion is available and repeatability is plus or minus 0.1 micrometer and if the range travel range is more and repeatability of plus or minus 2.5 micro radians is possible and standard versions are also available and vacuum compatible versions are also available and DC motors are used in such parallel positioners. Now, this shows a stage used, micro stage used in the micro EDM machine. You can see in my fuel injector where in micro holes are machined for the supply of fuel. So, you can see the micro holes where we can see an amplified microscopic view of a spray nozzle of diameter 100 micro meter. Now, in order to make these fine holes, we have to properly orient the workpieces for that apart from x, y, z motion of the CSE machine the should be possible to rotate the workpiece and it should be possible to tilt the table. So, multiple axis machining systems are needed. So, in order to make these micro holes, we have to position the electrode properly so that these micro holes are made. They should be possible to rotate the workpiece as well as tilt should be possible to tilt the workpiece. Now, in this diagram, you can see regular CXY ZCNC machine 3 axis machine with mounted with a trunnion table to provide two more additional axes. That means, the workpiece can be rotated a rotary axis as well as this table can be tilted. So, totally five axes are possible in this CSE machine. The different sized CSE machines are available, the machine with different table size, different center height, different load capacities etc are possible. Accuracy of such a system is rotary axis accuracy is 15 in the arc second and tilting the accuracy is 20 arc second and repeatability of plus or minus 2 to 3 arc seconds is possible. Now, why normally air bearings are used in micro and nano stages you can see here. If we use linear motors with mechanical air bearings, the positioning accuracy is about plus or minus 5 micrometer. This is a micro stage specification for a micro stage and if we use air bearings, the positioning accuracy can be enhanced to up to plus minus 0.5 micrometer and bidirectional repeatability is plus or minus 0.5 if we use mechanical bearings and if we use air bearings, the repeatability is plus or minus 0.2 micrometer and the straightness and flatness errors also can be reduced very much in case of mechanical bearings. The straightness flatness errors will be 6 to 12 micrometer whereas in the air bearing stages equipped with air bearings, the straightness and flatness error will be as low as 2 micrometer. Also roll error picture and gyro can be reduced from 10 arc second to 2 arc second. That is why normally air bearings are used in micro stages as well as nano stages. Now, what are the different applications of micro and nano stages? These stages are used in lithography tools such as optical steppers and optical scanners, e-beam ratars, laser mask ratars and in the metrology tools such as a mask, wafer and HCD inspection systems, measurement tools, scanning electron microscopes, super resolution microscopy systems. They are also used in the process equipment such as probes, diponders and drilling tools for making very fine drills. These stages are used, you can see the micro drills in the workplace. Such drilling is possible if you use micro stages and nano stages. They are also used in calibration equipment, measurement and calibration of high resolution or high frequency mechanical motion systems and these stages are also used in magnetic levitation positioners. Now, this picture shows a ultra high precision positioning system with sub nanometer resolution. Now, how do we select these metrology stages? The primary characteristics by selecting a stage or linearity sensitivity that is resolution, stability, bandwidth and cost these factors are considered by selecting the stages. For shorter travel ranges normally PGO drives with frictionless flanger guidance are used for better accuracies and PGO drives combined with fast response, extreme guide guiding precision, very long maintenance free service life and they can be easily used where some nanometer step sizes are needed. Due to high stiffness and low inertia, PGO flexor stages can achieve extremely fast step and certain times in a millisecond or microsecond range. PGO drives have high scanning rates with hundreds of thousands of hertz. This high scanning rate is very important in optics alignment and semiconductor testing and manufacture and for longer travel ranges positioning stages with frictionless air bearings and linear motors are used. Frictionless bearings avoid the bearing rumble caused by balls and rulers to provide vibration free motion and highly constant velocity. Another option to go frictionless is known as magnetic levitation that is magnetic bearings. Position feedback for closed-loop controls such as capacitive sensor strain gauges and PRS strain gauges are available and whenever low inertia improved dynamics and smaller package size and higher stiffness required we can go for micron nanostages and also another important requirement to use these stages is thermal and mechanical stability. Also we should look for the viability of user-friendly software to run these stages and the stage should have low maintenance requirements and the controllers and interfacing circuitry should be available and rotation requirement whether the rotary stages are needed that also we should see. With this we will stop the discussion on nano and micro stages. Let us begin our discussion on nanotechnology instrumentation. So under this topic we will be discussing about the measurement instrumentation used in nanotechnology. So we will discuss about the need for nanotechnology and various building blocks of nanotechnology. And what are the various measurement instrumentations used in nanotechnology for measuring the nano sizes and then the resolution aspect of various devices and how do we select the nano instrumentation. And then we will discuss in some detail about atomic force microscopy and this we will be discussing about the probe tip used in atomic force microscopy and working details of AAFM and applications of AAFM. What are the various limitations and challenges of AAFM and then we will move on to the discussion on large area atomic force microscope and then how to calibrate the atomic force microscope. Now let us discuss what is the need for nanotechnology. Now this nanotechnology it is a new scientific field evolving from material specific individualities of presently available elements when their sizes become nanometric. The nanotechnology manipulates matter at atomic level. Presently the nanotechnology is dealing with the creation and utilization of new functional materials, new devices and systems based on innovative functions and properties of nanometric sized elements and ultra small sensors communication and navigation systems with very low mass low volume and low power consumption are very much needed in the present day scientifically and technologically advanced systems. So in this aspect nanotechnology helps us to create the ultra small sensors and navigation systems. Now what are the building blocks of nanotechnology. You can see here we have a work piece this is the base material with very rough surface and now we want to change the characteristic of the surface of this base material. So we can always apply ultra thin nano layers that is nanometric sized layers can be applied onto the surface so that the desired properties of the surface can be achieved. You can see here this diagram by applying a ultra thin layer of the work piece surface. The surface is converted into hydrophobic surface. Now nano structures can be built using the nanotechnology and analytical instrumentations can be built and used for measuring the performance of nano structures and other important area in the nanotechnology is integration of nano materials and molecular sized structures. Now in this picture we can see very small nano sized disks are made and here we can see a nano sized round part and here again a nano sized cubic or rectangular shaped work pieces. All these are made using the nanotechnology. Now how do we measure the nano sizes? Different instrumentations are currently available and some of them are listed below. We can measure the nano sizes using scanning electron microscopy or atomic force microscopy, optical microscopes with very high resolution, transmission electron microscope, agar electron spectroscopy, scanning tunneling microscope, x-ray photo electron spectroscopy. So these devices can be used for measurement of nano sizes of the work pieces. Now let us try to understand the range of lateral and vertical resolutions of various nano instrumentation. I can see here the x-axis is a lateral resolution and y-axis is a vertical resolution. Now I can see we have the scanning electron microscopy. It has a very wide area, it is covering a very wide area. The lateral resolution of scanning electron microscopy, it starts from one nanometer, it goes up to few millimeters and the vertical resolution of scanning electron microscopy, it starts from few micrometers or few nanometers up to few millimeters and then the lateral resolution of optical microscopy is, it starts from one micrometer, it goes up to few millimeters and vertical resolution, it starts from approximately one micrometer and it goes up to a few hundred micro meters. Now you can see here we have this atomic force microscopy which is having very very low lateral resolutions of fraction of nanometers to up to few hundred micrometers and vertical resolution of AFM is very very low, it is less than nanometer, fraction of nanometer vertical resolutions can be obtained by using atomic force microscopy. Now how do we select the nano instrumentation? Now very first thing is we should understand what is the resolution requirement vertical resolution and horizontal resolution and also we should understand what is the observation environment. So by considering these two we can select the nano instrument. You can see here atomic force microscopy and STM they can provide the fractional nanometric resolution. So horizontal resolution is less than one nanometer is possible and vertical resolution of one thousandth of an nanometer is possible and the observations environment is normal atmosphere it can be our pieces can be measured gas, vacuum, liquid. So a different observation environments we can use the AFM and STM. Now if you see scanning electron microscopy the resolution vertical resolution of the order of eight nanometers and horizontal resolution of the order of five nanometers is possible and the work pieces should be placed in the vacuum. So like this by knowing the observation environment and resolution requirement we can select the appropriate the instrument nano instrument. Now here we have compared the atomic fire force microscopy with SCM and DEM sample preparation very little preparation is required for AFM when compared to SM and TEM. The fractional nanometric resolution is possible in AFM and the cost is relatively low and sample environment any sample environment it can be in the gaseous medium or liquid medium or normal atmosphere whereas when we want to use SEM a vacuum is required similarly for measurement purpose in TEM vacuum environment is required. Only drawback of AFM is the depth of field is very poor and the work piece sample can be conductive or even insulating work pieces can also be measured using AFM whereas in SEM and TEM the work piece should be conductive. And another drawback of AFM is the time of imaging or measurement time is it takes longer time when compared to SEM and TEM and maximum field of view is under the micrometer whereas here in SEM it is a little bit more maximum sample size is unlimited whereas in SEM and TEM it is very much limited. Nowadays large area AFM are available so that any area can be measured using AFM and the very important benefit or advantage of AFM is three-dimensional characteristics can be obtained it can measure the height information whereas in SEM and TEM there would be two dimensional measurements. Now let us discuss about atomic force microscope in some detail this atomic force microscope is a very powerful surface analytical technique which can be used in different working environments like air, liquid or a vacuum and it generates a very high resolution topographic images of the work piece surface down to atomic resolution and depending upon the sharpness of the tip it gives the spatial resolutions of 1 to 20 nanometer and records topographic images. You can see here we have the cantilever attached to the basic body of the atomic force microscope and which is having a very sharp tip and you can see there is a stage on which the work piece is placed the stage is mowed under the tip and the tip records the topographic details of the work piece. The AFM can also be used for force spectroscopy that means it applies force on to the work piece surface varying from 5 to 50 picot newtons to analyze mechanical or electrical and chemical properties of surfaces it either drives into the surface to measure mechanical properties such as modulus stiffness and adhesion or the tip is pulled away from the surface to investigate bond rupture and molecular pooling. So this method of using the AFM is known as tapping mode. Now the AFM basically has a cantilever with its tip you can see the image this is the cantilever portion of the cantilever portion and this is the tip attached to the cantilever the material of cantilever and tip is normally silicon, silicon nitride metal or diamond coated levers and tips. Diamond tips are also sometimes used chemically functionalized probe tips are also used and the geometry of cantilever is it can be single beam cantilever or v-shaped cantilever that means the cantilever can be of this shape single beam cantilever with some length and width and this is the thickness of the cantilever or it can be v-shaped cantilever like this. So at the end the tip is attached like this the normally the cantilever length will be it will vary from 50 to 400 micro meters and tip shape this tip shape it can be pyramidal with opening angle varying from 50 degree to 35 degree and inclination angle of tip that means the this is the cantilever the tip can be like this or sometimes tip can be like this so this is the inclination angle of tip and tip position on cantilever so the position also vary it can be somewhere here it can be at the tip and then relevant physical parameters such as length of cantilever width of cantilever thickness of the cantilever spring constant of the material used to make the cantilever resonance frequency tip radius normally it varies from 5 to 15 nanometer and tip height varies from 10 to 25 micro meter now you can see a scanning electron microscope image of AFM cantilever and probe tip so this is the cantilever with a length of about 50 to 100 micro meter and this is the probe tip attached to the cantilever and you can see another double beam type of cantilever with probe tip attached at the end of the cantilever and this has got a piezo resistive sensor attached at other end of the cantilever now we can see the two types of cantilevers v-shaped cantilevers and the tip there will be probe tip and this is a single beam cantilever with the tip attached at the end and these are micro fabricated pyramidal tips of the pyramid base width is about 4 micrometer and the height of the tip is about 6 to 10 micro meter now I can see the different probe tips special probe tips so this is probe tip with 870 nanometer tip radius and here the tip radius is 150 nanometer and in this case it's a very sharp probe tip with 20 nanometer tip radius and here this is a thermal probe tip which senses the temperature of the workpiece surface and this is a double beam type cantilever with the tip attached at the end and this is a special probe having this is a ball probe diameter varies from 10 to 13 nanometer 40 to 60 nanometer like this balls with different diameters are available now so these are tetrahedral pyramid shapes so this is the width of the cantilever and this is the top view of the cantilever and in the side view and the thickness of the cantilever is the length and here we can see the tip attached at the end and this is the closer view of the tip of the AFM tip probe tip and this is the height and this is the offset from the end what is the distance so this is the offset with different angle angles 9 degree angle this is that t1 degree angle okay and from different view you can see the angles 80 degree and 80 degree the height of the probe ranges from 14 to 16 micrometer and tip offset ranges from 15 to 25 micrometer and these are triangular pyramid tips the height range is 14 to 16 micrometer is the height 14 to 16 micrometer and apex angle apex of one angle is 11 degree tip material is n-type antimony doped single crystal silicon material is used to fabricate these tips now let us study how the AFM works we can see this schematic diagram this is the stage scanner stage which moves in x y and z directions and these stages are normally piezoelectric stages with nanometric resolution and this is the cantilever with tip attached to it now there is a laser source which is incident laser falling on the cantilever surface the sharp micro fabricated tip is attached to the cantilever and this is used this tip is used to scan the workpiece surface this is the sample placed on the scanner stage now when the tip is moved nearer to the surface it deflects the cantilever deflects because of the force developed the van der Waal force developed between the tip and the sample and this deflection of the cantilever so the cantilever will deflect like this because of the attraction or if the force is repulsive it will move back now this deflection is monitored using a laser and photo diode and the reflected light will fall on the photo diode and this will generate the image of topographic image of the surface now AFM can be can image the AFM can image in a number of ways using either contact mode wherein the tip will be in contact with the sample surface and the surface will be moved under the probe or the another mode is oscillating technique where the tip taps the surface now either tip or workpiece table moves by using piezoelectric positioning systems having nanometric resolutions the cantilever is designed with a very low spring the constant material so that it is very very sensitive to forces it is sensitive to even force as low as pico newtons the laser is focused to reflect off the cantilever and on to the sensor we can observe here the laser is falling on the back surface of the cantilever a mirror will be placed here so that the laser incident ring is reflected back and then it falls on the photo diode the position of the beam in the sensor measures the deflection of the cantilever the position of the reflected beam of laser in the photo diode measures the deflection of the cantilever and then in turn the force between the tip and the sample is measured I can see here depending upon the material combination material of tip and material of sample there can be repulsive force or attractive force and even the small forces as well as a few micro newtons and pico newtons can be sensed and here you can see the displacement of the XYZ scanner piezoelectric scanners are used for moving the workpiece under the probe AFM probe the AFM scanners are normally made of piezoelectric material which expands and contracts proportionally to an applied voltage this we discussed in detail in the stage version the metrology we can see here a piezoelectric stage when the voltage is applied it expands our contracts depending upon the voltage that is applied and this is the XYZ scanner on which the sample is motor and this shows the cantilever with probe distal instrument scanners have AC voltage ranges of plus 220 volts to minus 220 volts in some versions the piezo actuator moves the sample relative to the tip that means tip will be constant it will move in the up and down and the sample the stage on which the sample is mounted will be moved using the piezoelectric device in some other models the sample is stationary by the piezo actuator moves the tip AC signals are applied to conductive areas of the piezo mass to create micro or nano-level movement along the XYZ answers now these pictures show the external appearance of AFM and here we can see the schematic diagram of AFM so we have this white box is the XYZ linearized piezo scanner on which the sample to be tested is mounted and this is the XY sample translation stage we can see two micrometers are provided for X moment and Y moment the initial adjustment of the sample initial positioning of the sample can be made using these manual micrometers and then the scanning is carried out by moving by using this XYZ linearized piezo scanner and here we can see there is a column to support this high resolution video microscope which captures the images and then all the electronic circuitry will be placed in this box now this schematic diagram shows the internal structure of AFM you can see the this is the area where the sample is mounted this is the motorized XY stage so here we have manual XY stage for initial positioning whereas here for initial positioning the motorized XY stage is used and this is the surface stage surface on which the sample is mounted and we can see the probe the zoomed view we can see here the probe we can see and this is the incident laser and this is the reflected laser and this housing the carries laser diode and the optical lenses and the laser is made to fall on the back surface the cantilever and the laser is reflected back and this mirror which is adjustable mirror will deflect the laser and it falls on the fixed mirror and again it is reflected back on to the split diode photo detector the position of the laser on this detector decides the bending of the scanner cantilever and here the camera lens is provided for viewing the measurement or to capture the images now the work stage workpiece tail of AFM is very very important where it should be free from any vibration it should have very very finer linear and horizontal and vertical resolutions so that very fine topographic image can be captured the sample size normally varies from 50 mm 50 mm and up to 20 mm thickness workpieces can be mounted sample weight can be up to 500 grams and XY stage travel is 20 mm by 20 mm so for initial adjustments this XY stage man it can be manually or motorized and also the cantilever is moved up and down for initial adjustment for which there is a jet stage and focusing stage travel is up to 15 mm accurate XY scanning is to be carried out for that closed loop XYZ flexor scanners are provided and the flat and orthogonal XY scanning is very very essential the out of plane motion of the uh XY stage there should be less than one nanometer over the total scan range the jet scanner linearity error is less than 0.015 percent of the overall scanning range accurate height measurements without any software is possible in some AFMs accurate topography with low noise as low as 0.05 to 0.07 nanometer jet detectors are used for topographic sensing now let us move to the applications of atomic force microscope there are many biological applications of AFM the AFM is used for getting the images of biological samples we can see here an image of human chromosome obtained from AFM so many microbiological applications AFM can be used and when we use some personal care products like gel, soil, space there will be changes in the hair, teeth and skin in the nano scale level so what is the amount of change in these things in these items at nano scale for measurement of that we can use AFM and you can see here sometimes the nanoparticle coating will be there on some surfaces and we need to remove the nanoparticles from the surface and to study what is the amount of force required to remove nanoparticles we can use AFM and for topographical studies of surfaces and to get the nanomechanical properties of coatings we can use AFM now the normal AFM resolutions will be like this if the moment of XY stage is something like 100 micrometer or 200 micrometer then the resolution of X axis and Y axis will be 1 nanometer whereas the vertical resolution will be 0.1 nanometer and if the scanning range is limited to say 50 micrometer and 50 micrometer in such cases AFMs are available with ultra fine resolution that is resolution as low as 0.003 nanometer and if the Z axis moment is limited to 15 micrometer then a resolution of 0.001 nanometer is possible and these AFMs can be used for studying the subunstrom deflection of cantilevers and they can be used for measurement of very small forces in the pico Newton level now with this we will conclude the Martial 12 lecture number 6 in this lecture we discussed the following topics we studied about the micro nanostage errors, linear errors as well as angular errors in micro stages and nanostages and how do we calibrate the micro nanostages what are the facilities available like interferometry laser based systems and what are the typical specifications of micro nanostages also we discussed about the various applications and selection of stages then we discussed on nanotechnology instrumentation we discussed the need for nanotechnology and what are the various building blocks of nanotechnology and then nanotechnological metrological instrumentation and we also discussed about resolution and how to select nano metrological instrumentation then we also discussed in some length about atomic force microscopy in which we discussed about cantilever and probe tips used in AFM how the AFM works and the stage details of AFM and some applications of AFM with this we will conclude this lecture we will continue continue the discussion in the next lecture on atomic force microscopy thank you