Atif SyedNano Measurement11. Introduction:The introduction and invention of Scanning Tunneling Microscope (STM), Atomic ForceMicroscope (AFM), Magnetic Force Microscope (MFM) and other Scanning ProbeMicroscopes (SPM) (where around 25 types are available currently) bought a wave ofchange in the way we see and study the structures and properties of the surfaces. Withthis development, we are now able to realize novel properties in nanotechnology suchas creation of unique structures by manipulating atoms and molecules. This has alsolead to new developments in the field of electronics, information storage, multicoreprocessors and sensors. There has been a massive interest in this field ever since itsinception in 1982 . One of the main factors behind the rapid development of SPM isthe high availability of commercial instruments, the required conditions which wereavailable easily (like vacuum, liquid and gas from 4 to 700 K) and renewed interestamongst scientist and engineers to be able to manipulate matter at a atomic level andunderstand its properties . From January 1, 2002 to December 31 2003, there werearound 11,000 cited publications solely devoted to the physics and the applications ofSPM . By using STM, one can, with slight modifications to the current technology,image non conductive materials such as DNA and oxides to sub-nanometer level. Theprocesses were observed continuously thanks to the ability of STM and AFM which givesno damage or interference to the sample. One of such example is that the entireprocess of a living cell infected by virus has been seen in detail using AFM .Figure 1: General visual representation of SPM 
Atif SyedNano Measurement22. SPM Techniques (Questions 1 and 2):There are around 25 types of SPM related techniques. Although most of the techniquesare mere modifications of STM or AFM, the following list shows some of frequently usedand widely known SPM techniques:- Atomic Force Microscopy (AFM):AFM is one of the most high resolution type SPM where the resolution isof the order of few nanometers. It was developed in the early 1980s byGerd Binning and Heinrich Rohrer at the IBM Research Labs in Zurich.Since then, AFM has become the foremost tool for nano based imagingand measurements. More detailed explanation of AFM will be discussedfurther in the report.- Scanning Tunneling Microscopy (STM):STM is widely used for imaging surfaces at atomic level. It was inventedat IBM-Zurich by Gerd Binning and Heinrich Rohrer in 1986  and thisearned them a Nobel Prize in 1986 in Physics . The resolution of STM isabout 0.1 nm (lateral) and 0.01 nm (depth) which enables the images tobe viewed at atomic level precision with as low as single atoms can beviewed separately within the materials. STM is based on a quantumphenomenon known as quantum tunneling. This will be explained indetail further in the report.- Near Field Scanning Optical Microscopy (NSOM/SNOM):NSOM/SNOM measures local optical properties by exploiting near fieldeffects which in turn allows the characterization (such as structural,mechanical, optical and electronic) of the material (such as metals,semiconductors, insulators, biomolecules)  with a specific environment(vacuum, liquid, ambient air conditions)  . This is basically done bybreaking the resolution limit through the properties of evanescent wave1.The detector is placed very close to the sample (usually at smallerwavelength) and by using this method, the spatial, and spectral andresolution of the image is highly improved. The resolution is limited bythe size of the detector’s aperture but not by the wavelength of theilluminating light which is usually the case. The lateral resolutionachieved is 20 nm and vertical resolution is 2-5 nm .1Evanescent wave is a near-field standing wave with the intensity having an exponential decay whichstarts from the boundary at which the wave is being formed initially .
Atif SyedNano Measurement3Figure 2: Differences in the probe tip between STM, AFM and SNOM Figure 3: Tip differences in (A)-STM, (B)-AFM, (C)-SNOM, (D)-A probe kept in ambient conditions 
Atif SyedNano Measurement4- Ballistic Electron Emission Microscopy (BEEM):BEEM is a three terminal STM which was invented in 1988 at JetPropulsion Lab by L. Douglas Bell and William Kaiser . BEEM has beenused usually for the study of Metal-Semiconductor Schottky diodes.- Chemical Force Microscopy (CFM):CFM is another variation of AFM. It was developed by Charles Lieber atHarvard University in 1994 . The only difference between them is thatin CFM the interactions between the probes tip and sample is donethrough chemical methods. Typically a gold-coated tip is used with itssurface having R-SH thiols2(where R is any carbon containing atomsfunctional group) . CFM’s main usage is to determine the chemicalnature of surfaces regardless of their morphology and this enables tounderstand the chemical bonding enthalpy and surface energy of thesamples .- Magnetic Force Microscopy (MFM):MFM is another technique derived from AFM. A sharp magnetic tip isused to scan the sample. The interaction between the tip and sample aredetected which in turn are used to reconstruct the magnetic topographyof the material. It’s often used in scanning Magnetic images of HardDrives (or ant recording media), nanowires, Carbon Nanotube (CNT), thinfilms etc. MFM will be discussed in more detail further in the report.Optical SEM/TEM Confocal SPMMagnification 103107104109Price(USD $) $10k $250k $30k $100kTechnology Age 200 years 40 years 20 years 20 yearsApplications Ubiquitous Science andtechnologyNew andUnfoldingCutting EdgeMarket Since1998$800 million $400 Million $80 Million $100 MillionGrowth Rate 10% 10% 30% 70%Table 1: Conventional Microscopes in comparison with SPM techniques 2A thiol is a organosulfur (organic compounds containing sulfur) compound which contains R-SH or C-SHgroup (where R is alkane, alkene or other carbon containing atoms)
Atif SyedNano Measurement5SPL3Method Instruments Environment KeyMechanismTypicalResolutionPatterningMaterialsPossibleApplicationsNanoscalePen WritingDip-PenNanolithographyAFM Ambient ThermalDiffusion ofSoft Solids10nm SAM4,Biomolecules, Sol-Gel,Metal etcBiochip,Nanodevice,Mask RepairetcNanoscalePrinting ofLiquid InkNSOM5Ambient Liquid Flow 100nm EtchingSolution,LiquidMask RepairetcNanoscaleScratchingNanoscaleIndentationAFM Ambient MechanicalForce10nm Solid Mask RepairetcNanografting AFM Liquid Cell MechanicalForce10nm SAM Biochip etcNanoscaleMeltingAFM Ambient MechanicalForce andHeat10nm Low MeltingPointMaterialsMemory etcNanoscaleManipulationAtomic andMolecularManipulationSTM Ultra HighVacuumVan der WaalsorElectrostaticForces0.1nm Metals,OrganicMoleculesetcMolecularElectronics etcManipulation ofNanostructuresAFM Ambient Van der Waalsor MechanicalForce10nm Nanostructures,BiomoleculesMask Repair,NanodevicesetcNanoscaleTweezersAFM Ambient Van der Waalsor MechanicalForce100nm NanostructuresElectricalMeasure etcNanoscaleChemistryNanoscaleOxidationSTM or AFM Humid Air Electrochemical Reaction ina WaterMeniscus10nm Si, Ti etc NanodevicesetcNanoscaleDesorption ofSAMSTM or AFM Humid Air Electrochemical Reaction ina WaterMeniscus10nm SAM NanodevicesetcNanoscaleChemical VaporDepositionSTM Ultra HighVacuum withPrecursor GasNanoscaleChemicalVaporDeposition10nm Fe, W etc MagneticArray etcNanoscaleLightExposureNanoscale LightExposureNSOM Ambient Photoreaction 100nm Photosensitive MaterialsNanodevicesetcTable 2: Applications of SPM related techniques into different SPM Processes and their practical applications .3Scanning Probe Lithography.4Self Assembled Monolayer – It is an organized layer of amphiphilic molecules in which the one end ofthe molecule (named as the “head group”) shows specific affinity for the substrate.5aka SNOM
Atif SyedNano Measurement62.1. Scanning Tunneling Microscope(STM)(Question 3 and 4):During its inception, the STM was the first and one of its kind device which was able toget 3-D images of solid structures with atomic resolution . STM works on theprinciple of quantum tunneling and this was first proposed by I. Giaver .Figure 4: Basic Schematic of a STM According to him if there is a potential difference applied to two metals which areseparated by a thin insulating film, a current will flow due to the ability of electrons topenetrate through the potential barrier. Binning et al. later introduced lateral scanningand vacuum tunneling and also demonstrated that the preferable distance between thetwo metals should be 10nm . Due to the lateral scanning, the resolution laterally isabout 1nm and vertically is about 0.1nm which is sufficient to acquire an image of singleatoms.The working of STM is fairly simple. The metallic tip is bought close to the samplesurface such that after applying a bias voltage (of about 10mV – 1V ), the tunnelingcurrent between the tip and the surface of the sample is measured. The tunnelingcurrent is usually from 0.2nA – 10nA . Figure 5 shows the schematic of the two modes.STM works in two modes; constant current mode and constant height mode.The tunneling current normally gets reduced by a factor of 2 (𝑒2) when the separation(from the tip and the surface) is more than 0.2 nm . This will be explained further inthis section with the introduction of quantum mechanics and the concept of quantumtunneling.
Atif SyedNano Measurement7Figure 5: The two modes of the STM; constant current and constant height mode are illustrated in the above image.The concept of Quantum Tunneling can be explained through classical mechanics; let’sassume an electron has an energy E and having a Potential Energy U(x), then thefollowing can be deduced:𝒑 𝒙𝟐𝟐𝒎+ 𝑼( 𝒙) = 𝑬 1Where m = 9.1 𝑋10−28𝑔 which is the electron mass. This can be further elaborated intotwo cases. If E > U(x) the electron has a non zero momentum and if E < U(x) thenelectron cannot penetrate into any region and hence creating a potential barrier. This isbetter described by using the wave function Schrödinger’s Equation:−ℏ 𝟐𝟐𝒎𝒅 𝟐𝒅𝒙 𝟐 𝝍( 𝒙) + 𝑼( 𝒙) 𝝍( 𝒙) = 𝑬𝝍( 𝒙) 2
Atif SyedNano Measurement8Image 1: Difference between classical and quantum physics .In the image above, there is a constant energy and a piece-wise constant potential. Inthe first half of the above image, classical physics allowed region E > U, then equation 1has solutions of the wave function which is also a wave vector and can be representedas:𝝍( 𝒙) = 𝝍(𝟎)𝒆±𝒊𝒌𝒙3Where k is:𝒌 =√𝟐𝒎(𝑬−𝑼)ℏ4The electron is moving in positive/negative direction having a constant momentum 𝑝 𝑥 =ℏ𝑘 = √2𝑚(𝐸 − 𝑈) with a constant velocity which can be derived from the momentumequation 𝑣 𝑥 =𝑝 𝑥𝑚. When the electron is in the classically forbidden/impenetrableregion then equation 2.2 becomes:𝝍( 𝒙) = 𝝍(𝟎)𝒆−𝒌𝒙5
Atif SyedNano Measurement9Where k becomes:𝒌 =√𝟐𝒎(𝑼−𝑬)ℏ6The U-E is present which signifies a decay of electron in positive x direction (+x). Theprobability density of finding an electron which is having a non-zero value near the pointx is proportional to |𝜓(0)|2𝑒−2𝑘𝑥and if the decay is in negative direction then theprobability is 𝜓(0)𝑒 𝑘𝑥which signifies the decay stage.Image 2.2: Grey Scale Images. The two images are of Si (111) -7X7 with dimensions 100X125Å 𝟐taken from a STMUsing the concepts above, we can now prove the metal-vacuum-metal tunneling. Wecan now include the concept of work function which states that it’s the minimum energyrequired to remove an electron from the surface of the metal. The work function of ametal depends on two things; the material itself and on the crystallographic orientationof the surface (or lattice arrangement). Table 2.1 shows all commonly used metals inSTM based experiments. Assuming that the work function of the tip and the sample inthe STM are the same, then the electron can tunnel from the sample to the tip  .Element Al Au Cu Ir Ni Pt Si W𝝓(𝒆𝑽) 4.1 5.4 4.65 5.6 5.2 5.7 4.8 4.8Table 3.1: Typical work function values of metals commonly used in STM experiments 
Atif SyedNano Measurement10- Derivation and equations the tunneling current acting within the STM:Figure 2.5: A 1-D barrier between two metals. A bias voltage is applied in between two electrodes Let’s assume a 1-D barrier and a vacuum barrier in between two electrodes as shown inthe above image where the two electrodes’ work functions are the same and hencehaving a same barrier height Φ, bias voltage V and barrier width d, then according toquantum physics’ first order perturbation theory , the tunneling current can bewritten as:𝑰 =𝟐𝝅𝒆ℏ∑ 𝒇( 𝑬 𝝊)[ 𝟏 − 𝒇( 𝑬 𝝊 + 𝒆𝑽)]|𝑴 𝝁,𝝊|𝟐𝜹(𝑬 𝝁 − 𝑬 𝝊)𝝁,𝝊 7Where 𝑓( 𝐸) is the Fermi function, 𝑀𝜇,𝜐 is the tunneling matrix element between thequantum states 𝜓 𝜇 𝑎𝑛𝑑 𝜓 𝜐 of the electrodes. 𝐸𝜇and 𝐸𝜐 are the energies within thestates 𝜓 𝜇 𝑎𝑛𝑑 𝜓 𝜐. If we assume that we are working at cryogenic temperatures andsmall voltages, then the equation 7 can be simplified to as follows:𝑰 =𝟐𝝅𝒆 𝟐ℏ𝑽 ∑ |𝑴 𝝁,𝝊|𝟐𝜹(𝑬 𝝊 − 𝑬 𝑭)𝜹(𝑬 𝝁 − 𝑬 𝝊)𝝁,𝝊 8Under certain conditions , the tunneling matrix element can be expressed as:𝑴 𝝁𝝊 =ℏ 𝟐𝟐𝒎∫ 𝒅𝑺⃑⃑⃑⃑⃑ . ( 𝝍 𝝁 𝛁∗⃑⃑⃑⃑⃑ 𝝍 𝝊 − 𝝍 𝝊 𝛁∗⃑⃑⃑⃑⃑ 𝝍 𝝁) 9The integral mentioned in equation 9 is the integral over the entire barrier region .Now we will estimate the magnitude of 𝑀𝜇𝜐.
Atif SyedNano Measurement11To estimate, we will expand the wave function of 𝜓 𝜐 in a plane-wave form which is asfollows:𝝍 𝝊 =𝟏√𝛀 𝑺∑ 𝒂 𝑮 𝒆[√ 𝒌 𝟐+|𝒌 𝑮⃑⃑⃑⃑⃑ |𝟐𝒛]𝑮 𝒆[𝒊𝒌 𝑮⃑⃑⃑⃑⃑ .𝒙⃑⃑ ]10Where Ω 𝑆 is the volume of the sample, 𝑘 =√2𝑚ϕℏis the decay constant/rate, ϕ is thework function of the electrodes, 𝑘 𝐺⃑⃑⃑⃑ = 𝑘||⃑⃑⃑⃑ + 𝐺⃑⃑ where 𝑘||⃑⃑⃑⃑ is the surface component ofthe Bloch vector6and 𝐺 is the surface reciprocal vector .Figure 6: If we assume the radius of the edge of the tip to be R, the distance from the sample to the tip to be d,then the position of the centre of the sphere will be 𝒓 𝟎 .Using the principle mentioned in the Figure 6 above, the wave function of the tip can beexpressed as:𝝍 𝝁 =𝟏√𝛀 𝒕𝒄𝒕 𝒌𝑹𝒆 𝒌𝑹( 𝒌| 𝒓⃑ − 𝒓 𝟎⃑⃑⃑⃑ |)−𝟏𝒆−𝒌|𝒓⃑ −𝒓 𝟎⃑⃑⃑⃑ |11where 𝜓 𝜇 is the voltage of the tip, 𝑐𝑡 is the sharpness of the tip which is a constant.6Bloch vector is a unit vector which is used to represent points in a Bloch Sphere.SampleR𝑟0Tip
Atif SyedNano Measurement12In this case we will be focusing only on s-wave function of the tip7and this due to:𝟏𝒌𝒓⃑𝟏𝒆−𝒌𝒓⃑ = ∫ 𝒅 𝟐𝒒𝒃( 𝒒⃑⃑ ) 𝒆^[−√𝒌 𝟐 + 𝒒 𝟐| 𝒛|] 𝒆𝒊𝒒⃑⃑ .𝒙⃑⃑12𝒃( 𝒒) =𝟏𝟐𝝅 𝒌𝟐√ 𝟏+𝒒 𝟐𝒌 𝟐13Substituting 12 and 13 into 9 we get:𝑴 𝝁𝝊 =ℏ 𝟐𝟐𝒎𝟒𝝅𝒌√𝛀 𝒕𝒌𝑹𝒆 𝒌𝑹𝝍 𝝊(𝒓 𝟎⃑⃑⃑⃑ ) 14Substituting 8 into 2 we get:𝑰 = 𝟑𝟐𝝅 𝟑 𝟏ℏ𝒆 𝟐𝑽𝝓 𝟐𝑫𝒕( 𝑬 𝑭) 𝑹 𝟐 𝟏𝒌−𝟒𝒆 𝟐𝒌𝑹 ∑ | 𝝍 𝝊( 𝒓 𝟎)| 𝟐𝜹(𝑬 𝝊 − 𝑬 𝑭)𝝊 15where 𝐷𝑡( 𝐸 𝐹) is the local density of states at Fermi level for the tip . By substitutingtypical values for metals for density of states in 15, we get:𝑰𝜶𝑽𝑫𝒕( 𝑬 𝑭) 𝒆 𝟐𝒌𝑹𝝆( 𝒓 𝟎, 𝑬 𝑭)𝝆( 𝒓 𝟎, 𝑬 𝑭) = ∑| 𝝍 𝝊( 𝒓 𝟎)| 𝟐𝜹(𝑬 𝝊 − 𝑬 𝑭) 16Equation 11 shows that the STM tip would only measure 𝜌(𝑟0, 𝐸 𝐹).Since,|𝜓 𝜐(𝑟0)⃑⃑⃑⃑⃑ |2𝛼 𝑒−2𝑘(𝑅+𝑑), ℎ𝑒𝑛𝑐𝑒 𝐼 𝛼 𝑒−2𝑘𝑑This proves that the tunneling current depends on the tunneling gap distance d. Thisallows the resolution to be around 0.1 Å. This makes STM have atomic resolution andthis will be discussed further in this section with examples.7It is a type of elastic wave also known as the secondary wave.
Atif SyedNano Measurement13Another very important issue in STM is the noise level requirements. This is a big burdenfor STM manufacturers to decide whether a huge amount of money should be put in tocreate a vibration isolated room which can be very expensive. But this has to bedetermined depending on the use of the STM. Preamplifiers can also be used and placedat low cryogenic temperatures. There are two ways of reducing noise: Noise Calculations:- Mechanical Noise Cancellation Method (Vibration Control):In Mechanical Noise cancellation method, a suspension spring withmagnetic damping is used. This is done due to the fact that the tunnelingcurrent is extremely sensitive to height of the tip. In other words, if thetip-sample separation has an offset of a few angstroms then there wouldbe a big deviation in the images taken from the STM and there would behardly any useful/meaningful data acquired due to the noise generated.- Electronic Noise:There are three major form of electronic noise namely; Johnson noise,shot noise and 1/f noise (or time period dependent noise). Johnson noiseacross a resistor is given by:∆𝑽 = √ 𝟒𝒌𝑻𝑹∆𝒇 17The noise increases with resistance and since 𝑉 = 𝐼𝑅, having largerresistor values will result in less noise ratio. The rms Johnson currentnoise through the resistor is given by:𝑰 = √𝟒𝒌𝑻∆𝒇𝑹18Using the above equations 2.7 and 2.8, we can calculate the noise levelrequired for the STM, assuming the work function to be 4eV and thevertical mapping distance to be 0.01Å. Note that at low cryogenictemperatures, the tunneling current is proportional to the exponential ofthe decay constant (k) and vertical mapping distance (d) which can beexpression as follows:𝑰 ∝ 𝒆−𝟐𝒌𝒅19
Atif SyedNano Measurement14Where the decay constant is given by:𝒌 =√ 𝟐𝒎𝚽ℏ20Then we can do the calculation as follows:𝑘 =√2𝑋9.1𝑋10−31 𝑋6.4𝑋10−191.05𝑋10−34= 1010Hence, the decay constant is 1010. Using this we can calculate the noiselevel by using equation 2.8:𝐼 = 𝑒−2𝑋0.01𝑋1010 𝑋10−10= 0.98 𝐴 ≈ 1𝐴∆𝐼𝐼= −2𝐾𝑑 = −2 ∗ 1010∗ 10−12= 0.02 = 2%STM offers atomic resolution in every clean surface of metals andsemiconductors. Normally to achieve atomic scale resolution, a lateralresolution of 2Å is required. If we assume that each point on the tip thetunneling current density follows the equation for 1-D quantum tunnelingcase then the current distribution is and by using the experiment done byQuate et al :𝐼 = 𝐼0 𝑒−2𝑘∆𝑥22𝑅Where 𝑘 = 1Å−1, 𝑅 = 1000Å, ∆x = 45Å(∆x is current column) , thecurrent drops by a factor of 𝑒−2. If 𝑅 = 100Å, the current stays at around R=14 Å which enables atomic precision. Hence a high lateral resolution isachieved . The following images show a good example of some imagesachieved through STM with atomic level precision.
Atif SyedNano Measurement15- Some Interesting Images from STM showing atomic scale resolution:Image 2: This image shows the atomic resolved image of Cu (111). The atomic distance of Cu here is 2 Å 
Atif SyedNano Measurement16Image 3: STM images of evaporated 𝑪 𝟔𝟎 film on a gold coated mica Image 4: In the image above, individual atoms and their electronics structure can be seen clearly. This is the firstSTM image of Si (111) achieved by Binnig et al . The height of each step is 12 Å .Image 5: In the first image from the STM of Si(111)[-7X7] surface, the individual atomic bonds can be clearly seen.The above images were taken in the first year of the inception of the STM. The individual nearest-neighbor bond
Atif SyedNano Measurement17distance in the first image is 7.68 Å. The second image above is taken after the Si substrate is evaporated withChlorine. After this the bond distance is 3.84 Å Image 6: In the above STM image, defects in the Si(100) topographic image are revealed 
Atif SyedNano Measurement18Image 7: The above image is of Gi(111) surface as seen through the STM. Individual dangling atomic bonds can beclearly seen Image 8: STM image of GaAs (001) with bias voltage = -1.8V and tunneling current = 40pA 
Atif SyedNano Measurement19Image 9: STM images of Au (001) Image 10: Atomically resolved image of carbon nanotube taken through an STM. T represents the tube axis and Hrepresents the nearest neighbor hexagon rows Image 11: (A) – STM image of 𝑪 𝟐 𝑯 𝟐 molecule (left) and 𝑪 𝟐 𝑫 𝟐, the imaged area is 48 Å X 48 Å. The same imageswere recorded at (B) – 358 mV, (C) – 266 mV, (D) – 311mV with tunneling current 1nA DC 
Atif SyedNano Measurement20Image 12: “Quantum Coral” created by using 48 Fe atoms on top of Cu (111) surface and seen through an STM Image 13: STM imaged of patterns generated by (A) dodecanethiol and (B) decanethiol 
Atif SyedNano Measurement212.2. Atomic Force Microscopy/Scanning ForceMicroscopy(AFM/SFM)(Question 5):AFM relies on 3-D scanning same as the STM. AFM measures ultra-small forces betweenthe tip and the surface of the sample (a force of around 1nN ).One big differencebetween STM and AFM is that STM requires the surface of the sample to be electricallyconductive in nature but AFM can scan conductive and isolators with atomic scaleprecision. The sample is generally is generally scanned instead of the tip because AFMmeasures the relative displacement between the cantilever surface (shown in the imagebelow) and the tip surface (also known as the reference surface).Figure 7: Schematic of the operation of AFM There are typically three methods or variations of AFM:- Contact Mode- Non-Contact Mode- Tapping ModeIn the contact mode/static mode/Repulsive Force mode, the tip is bought in contactwith the surface of the sample. The atoms at the end of the tip experience a weakrepulsive force due to the orbital overlap8on the surface of the sample. The cantilever is8Orbital Overlap is a concept first introduced by Linus Pauling which states that the s orbital are special inshape and p orbitals have a 90 degree orientation which means that bonds are created due to the overlapof adjacent atomic orbitals. If the overlap is greater, the resulting bonds are much stronger than theindividual orbitals .
Atif SyedNano Measurement22then dragged across the surface of the sample. The force on the tip makes the cantileverdeflect and this is measured by tunneling, capacitive or optical detectors. Typically thedetectors can detect if the deflection is about 0.02nm and the spring constant of thecantilever is about 10 N/m with a force of 0.2 nN . The reason cantilevers are used inthe contact mode of AFM is because the static signal is prone to noise.In Non-Contact mode/Dynamic mode/Attractive Force mode, the tip is bought veryclose to the sample surface but the tip is not allowed to made contact with the surface.The cantilever is on purpose vibrated in Amplification Modulation  or FrequencyModulation     just above its resonant frequency. Weak Vanderwallattractive forces (which are strongest from 1 nm to 10 nm above the surface of thesample) are seen between the tip and the sample. This makes the resonant frequencydrop. Unlike the static method, dynamic method’s measurement is done by thevibration in AM or FM and due to this a force gradient is obtained which in turn allowsto measure the resonant frequency of the cantilever. The tip-sample distance iscaptured by the software which recreates the topographic image of the surface of thesample. If the vibration is done in Frequency Modulation (FM), the changes in thefrequency of the oscillation give the tip to sample information. If Amplitude Modulation(AM) is used, then the phase of the oscillation can be measured and by using thisinformation the sample’s material can be identified and more information about thematerial itself can be given. This method is very slow and time consuming and usuallythis type of AFM techniques are only used in research based laboratory rather thancommercial. Major differences in two of the techniques can be seen in the table below:AFM Static Mode AFM Dynamic ModeThe interaction force between the tip andthe sample is measured by the deflectionof the cantileverThe force gradient between the tip and thesample is measured due to the deflectionof the cantilever by vibrating the cantileverin AM or FMHas comparatively lower resolution Have comparatively higher resolutionResolution is about 0.02 nm (lateral) Resolution is about 0.01 nm (lateral)Assuming the spring constant of thecantilever is 10 N/m, the measurable forceis about 0.02nNAssuming the spring constant of thecantilever is 10 N/m, the measurable forceis about 1nNTable 4: Major differences between Static and Dynamic modes of AFMTypically in the contact mode, the friction acts as a major role and disadvantage becauseit can vastly affect the accuracy of the topographic images . To overcome this, thethird technique of AFM known as the tapping method is used.
Atif SyedNano Measurement23In tapping method, the friction is reduced substantially and it can also get topographicimages of soft materials as well. The working principle is similar to dynamic mode hencethis is called Dynamic Force Mode. The cantilever is vibrated by a piezoelectric on top ofthe cantilever. The tip, which is oscillating, slightly taps the surface of the sample with afrequency of 70-400Hz and amplitude of 20-100nm in a vertical direction9.Image 14: AFM image of Au(111) evaporated gold on mica .9The scanning angle is usually not important but it has been seen that if the scanned vertically, thetopographic images are much clearer as compared to parallel scanning. This is due to the frictiongenerated between the tip and the sample surface by the cantilever.
Atif SyedNano Measurement24Image 15: AFM image of Au(111) after exposed to air for sometime Image 16: A 3-D AFM image of Platinum .
Atif SyedNano Measurement25Image 17: An AFM image of protein surface layer .Image 18: (a) – AFM image taken by tapping mode with carbon probe of polydiacetylene crystal. (b) – Moleculararrangement of polydiacetylene crystal. (c) – Contact mode image of the bc-plane of the polydiacetylene crystal.(d) – Tapping mode image of the bc-plane of the polydiacetylene Image 19: (A) – Dual height and (B) dual amplitude image of multiphase film structure in films of 𝟐 𝟑. (𝑫𝑬𝑩 𝟏𝟐) onHOPG [nanorod (a), crystal (b), granular (c), and gas/liquid phase (d)] 
Atif SyedNano Measurement26Image 20: Multiwalled Nanotube attached to a silicon tip image taken through an AFM 
Atif SyedNano Measurement27Image 21: Creation of a deflated bacterium because of high vertical forces. (A), (C), (E), and (G) are height images,whereas (B), (D), (F), and (H) are deflection images. The bacterium is deflated in (C) and (D) at the dotted line. Asimilar deflated bacterium is shown in (G) and (H) Image 22: Image of a living S. cerevisiae [(height = 6 X 6 𝝁m and z range = 1 𝝁m)] immobilized on a porous polymermembrane Image 23: von Willebrand factor adsorption onto OTS. Atomic force microscopy image (2 mm 2 mm scan) of VWFmultimers adsorbed on hydrophobic OTS and imaged under PBS. Most VWF multimers display the characteristiccompact ball of yarn structures observed by electron microscopy. Each VWF multimer is closely packed withintramolecular overlap and crossover of chains. Intramolecular structural features of the VWF multimer chain areresolved. However, the compact arrangement of the chain makes it difficult to discern the structural features
Atif SyedNano Measurement28belonging to neighboring repeat units. In some multimer chains, short sections are not as compact and appearextended (arrows). Completely extended chains are rare. None are seen in this image area. The average lateraldimensions of the VWF multimers are 256 X 74nm and 152 X 62 nm in dimensions  Image 24: IC-1000 polishing pad surface imaged by using an AFM  Image 25: AFM image of DNA on top of Mica surface 
Atif SyedNano Measurement29- Experimental Work using AFM on Silicon Solar Cell:The AFM experiment was carried out by using silicon based solar cell. The solar cell iskept on the AFM’s sample stage/holder and the tip is added as well. After the initial setup the laser beam is aligned in such a way that the focus of the beam is that the top ofthe tip. The laser beam reflected back is detected by a photodiode. In the figure below,the screw C and D are used to adjust the position of the laser and the screws E and F areused to adjust the position of the photodiode.Figure 8: Left-(www.ems.psu.edu/~ryba/coursework/..../class%20slides/AFM.ppt), where 1-Laser Source, 2- Laserreflection Mirror, 30 Sample stage, 4- Laser reflection mirror (fixed), 5-Photodiode, Right- Experimental setup ofthe AFM in the JEOL Nanocentre York.Screws A and B are used to move the position of the sample stage. A computer aidedmovement can also be employed for precise measurements. Once the setup iscompleted and the working distance is acquired and set, the line by line scan can bedone. In the demonstration we have used the tapping mode method of the AFM (whichis also described above in this section). The scan speed can be controlled; slower scanwill result in high resolution images and better clarity which is seen in the image nextpage.
Atif SyedNano Measurement30Image 26: Computer output of the AFM image
Atif SyedNano Measurement312.3. Magnetic Force Microscopy(MFM)(Question 7 and 8):The concept of MFM is similar to AFM. The tip is magnetically coated and the differenceis that the static cantilever deflection due to magnetic force on the tip is detected. Thisallows the MFM images of the material to be produced. The sensitivity can be handledby vibrating the cantilever to near resonant frequency. When the tip encounters amagnetic field, the magnetic gradient along with the resonant frequency is shifted .The magnetic field gradient image is created by measuring the oscillation amplitude asthe tip is scanning over the surface of the sample .The topography of the sample is usually taken by a method called as the lift mode whichis done by separating the magnetic gradient from the magnetic field images. Themeasurements taken during the lift mode is done by scanning twice over the sample.During the first scan, the topographic information of the sample is recorded by using thetapping method where the tip is oscillating and the oscillating tip slightly taps thesurface of the sample. During the second scan, the tip is lifted up and the distance of thelift between the tip and surface of the sample is upon the discretion of the user (butideally 20nm-200nm is preferred ). At this stage, the image taken from the first scanis used as a reference rather than the standard feedback hereby making the separationconstant. This height allows the cantilever amplitude to be sensitive to electric fieldgradients without being influenced by topographic features . The two scanningmethod allows the two different kinds of images to be produced; topographic andmagnetic force images .Figure 9: Flow chart of the electronics for constant electronic frequency scanning 
Atif SyedNano Measurement32Figure 10: The block controller scheme of the MFM. This figure is the illustration of the working principle of theMFM Image 27: The image on the left is obtained after the first scan is performed. After the first scan, the image isstored. The image on the right is taken after the second scan of the MFM image. The second scan is made aftertaking the first image as reference rather than the conventional standard feedback system (the block diagram isshown in Figure 9) .
Atif SyedNano Measurement33Figure 11: Illustration of the two modes of MFM. dZ signifies the cantilever being lifted up at a height z which achange of height denoted by dZ. Due to the height dZ, the cantilever is only sensitive to long-ranged forces(magnetic forces will be explained in detailed further in this section) .As described above in this section, we will further elaborate the different modes ofoperation of MFM and how it relates to the force acting upon the cantilever due to themagnetic field and magnetic field gradients. Just as in AFM there are two modes:- Static Mode:In this mode the force acting upon on the cantilever follows the Hook’s Law and is givenby:𝑭 = −𝒌∆𝒛 21∆𝑧 is the displacement of the cantilever measured.- Dynamic Mode:In this mode, the cantilever is kept close to its resonant frequency. Since it’s in aresonant frequency, the harmonic oscillator can be expressed as:𝒇 =𝟏𝟐𝝅√𝒌 𝒆𝒇𝒎22Where m is the effective mass of the system and 𝑘 𝑒𝑓 is the effective spring constant. The effective spring constant can be also expressed as:= 𝒌 −𝝏𝑭𝝏𝒛23
Atif SyedNano Measurement34k is the cantilever’s spring constant (not to be confused with 𝑘 𝑒𝑓 which is the effectivespring constant),𝝏𝑭𝝏𝒛is the force gradient 10.Figure 12: Illustration of Tip-Sample interaction in a MFMBy substituting equation 23 into 22 we get:𝒇 = 𝒇 𝟎√ 𝟏 −𝝏𝑭𝝏𝒛𝒌24Where 𝑓0 is the free resonant frequency of the cantilever when there is no tip-sampleinteraction.10This will be explained further in this section.z𝝏𝑭𝝏𝒛k𝑧0
Atif SyedNano Measurement35- Magnetic Interaction in the MFM:MFM displays magnetic force and magnetic gradient based on the fluctuations on top ofthe magnetic samples. One of the biggest factors in determining the topographic imageis the tip-sample distance as mentioned before. The forces acting on top of themagnetic tip are not magnetic forces but in fact many other forces such as electrostatic,Van der Waals (some examples given in Table 2), quantum mechanical or capillary forcesact upon the tip. The magnetic force however can take effect only if the recommendedtip-sample distance is maintained which in turn depict the magnetic image (throughmagnetic contrast).Let’s assume that the magnetic element is exposed to magnetic stray field of the surfaceof the sample. Then the magnetic potential is given by:𝑬 = −𝝁 𝟎 ∫ 𝑴𝒕𝒊𝒑𝑽. 𝑯 𝒔𝒂𝒎𝒑𝒍𝒆 𝒅𝑽𝒕𝒊𝒑 25where 𝑀𝑡𝑖𝑝 𝑎𝑛𝑑 𝐻𝑠𝑎𝑚𝑝𝑙𝑒 are the tip magnetization and sample stray field respectivelyand the integration is done over one period of V (tip volume) . The magnetic force(gradient) can be expressed as:𝑭 = −𝛁𝑬 = ∫ 𝛁(𝑴𝒕𝒊𝒑𝑽. 𝑯 𝒔𝒂𝒎𝒑𝒍𝒆)𝒅𝑽𝒕𝒊𝒑 26Some alterations have been made to the current method where the magnetic field isallowed to alternate and the field mechanism is dependent on the shape of the tip  and the magnetic tip-sample interaction .Figure 13: MFM tip-sample interaction and also resembling magnetic spin of electrons 
Atif SyedNano Measurement36To better explain the concept in Figure 13, we need to understand a method commonlyused in the magnetic recording theory known as the spatial frequency domain method.According to the method, 𝑴𝒕𝒊𝒑 is transformed into its Fourier derivatives into 𝑀̂ (x,y)plane (2-D) and leaving the third plane (z) unchanged, we then get :𝑴̂ (𝒌 𝒙, 𝒌 𝒚, 𝒛) = ∫ ∫ 𝑴⃑⃑⃑ ( 𝒙, 𝒚, 𝒛) 𝒆−𝒊(𝒙𝒌 𝒙+𝒚𝒌 𝒚)𝒅𝒙𝒅𝒚∞−∞∞−∞27The relation between the wavelength of a certain magnetic component and its Fouriercomponent is given by :𝒌⃑⃑ = (𝒌 𝒙, 𝒌 𝒚) 28𝒌 𝒙(𝒚) =𝟐𝝅𝝀 𝒙(𝒚)29The stray field of the sample can be calculated by using Laplace transforms :(𝑯 𝒙̂ (𝒌 𝒙, 𝒌 𝒚, 𝒛)𝑯 𝒚̂ (𝒌 𝒙, 𝒌 𝒚, 𝒛)𝑯 𝒛̂ (𝒌 𝒙, 𝒌 𝒚, 𝒛)) =(−𝒊𝒌 𝒙|𝒌⃑⃑ |−𝒊𝒌 𝒚|𝒌⃑⃑ |𝟏 )𝟏𝟐(𝟏 − 𝒆−|𝒌⃑⃑ |𝒕) 𝒆−|𝒌⃑⃑ |𝒛𝝈 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆(𝒌⃑⃑ ) 30where 𝝈 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 is the effective surface charge distribution. According to Laplace’sproperty, we can safely say that the stray field at height z above the sample isdetermined by the stray field at height z = 0. If the sample is perpendicular (i.e. 𝑀𝑥 =0 𝑎𝑛𝑑 𝑀 𝑦 = 0) then the surface charge distribution will be:𝝈 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆(𝒌⃑⃑ )̂= 𝑴 𝒛̂ (𝒌⃑⃑ ) = 𝝈̂(𝒌⃑⃑ ) 31If the magnetization is constant and the only volume we have is the charge volumedenoted by 𝜌(𝑥, 𝑦), the effective surface charge equals:𝝈 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆(𝒌⃑⃑ )̂=𝒊𝒌⃑⃑|𝒌⃑⃑ |. 𝑴 𝒛̂ (𝒌⃑⃑ ) =𝝆̂(𝒌⃑⃑ )|𝒌⃑⃑ |32The energy of the tip and the sample can be calculated by combining the equations 25and 30.
Atif SyedNano Measurement37o Interesting Facts and Development in Magnetic Recording Media:IBM has recently managed to make the world’s smallest bit by using only12 atoms. The illustration below shows the Atomic-Scale MagneticMemory .Image 28: A infograph about Atomic-Scale Magnetic Memory by IBM 
Atif SyedNano Measurement383. Photovoltaic Solar Cells(Question 6):Advancement in the field of renewable energy technology has gained the center ofattention all over the world. The solution lies within Solar Cells; or precisely photovoltaicSolar Cells.Figure 14: Photovoltaic Devices progress in terms of efficiency achieved One of the highest solar cells’ efficiency has been achieved in multijunction cells basedon III-V compound semiconductors as each of them have different band gaps andmultiple absorbing layers  which in turn should allow higher efficiencies. Tounderstand this better we need to analyze the atomic microstructures within the solarcell. In this section we will focus on organic-based solar cells which are developingrapidly as the future of solar cells.
Atif SyedNano Measurement39- Charge Transportation within organic semiconductors used in organic-basedsolar cells:Organic semiconductors can be classified into two different categories namely; smallmolecules (having molecular weight less than a 1000 AMU11) or polymers (havingmolecular weight between 1000 AMU-1 Million AMU) . This is highly important indetermining the lithography process required for the making of thin films and based onthis related morphologies are obtained . These mechanisms are the basis of lightabsorption, exciton12diffusion and charge carrier motion within the solar cell. Theproperties are primarily governed by molecular orbital which are built from 𝜋-electronswhich in turn are delocalized across the molecules .Figure 15: Molecular structures of some semiconductors which are usually used in photovoltaic devices such assolar cells The charge transfer between organic molecules can be better understood by the theoryof Marcus . Using the theory, the rate of electron transfer between two moleculescan be expressed as:𝒌 𝑬𝑻 =𝟒𝝅 𝟐ℏ𝟏√𝟒𝝅𝒌 𝑩 𝒕𝒕 𝟐 𝒆−𝝀𝟒𝒌 𝑩 𝑻3311Atomic Mass Unit12It is a bound state of an electron and hole which are attracted to each other by electrostatic CoulombForce
Atif SyedNano Measurement40where ℏ is the Planck’s constant, 𝑘 𝐵 is the Boltzmann’s constant, T is temperature, t isthe transfer integral describing the strength of interaction between the two molecules,𝜆 is the reorganization energy that describes the strength of the electron-phononinteraction . For a highly ordered system, single or polycrystalline molecular films ofmaterials are sufficient in terms of interaction strength for band transport to be seen  . Similarly by using Poole-Frenkel behavior , the charge carrier mobilityfor organic semiconductors can be derived as:𝝁(𝑬, 𝑻) 𝜶 𝝁 𝟎( 𝑻) 𝒆 𝜸(𝑻)√𝑬34where 𝛾( 𝑇) is the coefficient of the stretched exponential that describes thetemperature dependence of the field activation, 𝜇0 is the zero-field mobility. Thisbehavior has been successfully modeled and developed by B𝑎̈ssler . Another muchrecent development in this area has been done by Novikov et al.  and this one takesthe account of spatial correlations in site energies which turn out to be:𝝁 = 𝝁∞ 𝒆[(𝟑𝝈̂ 𝒅𝟓)𝟐+𝑪 𝟎(𝝈̂ 𝒅𝟑𝟐−𝚪)√𝒆𝒂𝑬𝝈̂ 𝒅]35Where 𝜇∞ is the mobility at limit T → ∞, 𝜎̂ 𝑑 is the width of the Gaussian distribution thesite energies divided by 𝑘 𝐵 𝑡, 𝐶0 is the empirical constant, Γ describes the geometricdisorder and a is the intersite spacing .Image 29: Difference between semiemperical calculations and highest occupied molecular orbitals ofrepresentative organic semiconductors with extended 𝝅-electron delocalization 
Atif SyedNano Measurement41Using the basic concept above, the light absorption in inorganic semiconductor normallyleads to an electron-hole pair while in organic semiconductor light absorption leads toexciton. For a free carrier to be generated, the exciton has to be dissociated . Forthis to happen, a very high electric field should be present at the defect site of thematerial or at the interface between two materials that have a sufficient mismatch oftheir energetic levels. We can fabricate a device as such with the structure positiveelectrode/donor/acceptor/negative electrode . One of the first experiments done byusing this method was by using copper phthalocyanine layer as the donor and perylenederivate as acceptor and was done by Tang . This particular device achieved anefficiency of about 1% in terms of solar illuminations and light absorption . Thebiggest obstacle in this method is that due to a lot of short exciton diffusion lengths, theexciton that are generated at around 10nm contribute to photocurrent, the rest pose aserious limitation to the device itself. To overcome this, research has been done todevelop a device which I an amalgamation of donor and acceptor molecules and theyare collectively called as “bulk heterojunction” solar cell . Photoinduced electrontransfer from a conjugated polymer-fullerene was used and the transfer rate wasaround 45fs and the recombination rate being 300ns-1ms  . The exciton nowproduce a conjugated polymer having lifetimes of 100’s of pico seconds. The freeelectrons now have sufficient time to be transported before recombining. This producesa more light-absorbed solar cell having high carrier mobility and large optical density. Some latest improvements include using nanorods, nanofibers and nanorods whichlead in using these structures in 3-D. Some images are shown on the next page takenfrom an SEM .Figure 16: Diagram of conjugated polymer-fullerene bulk heterojunction photovoltaic device 
Atif SyedNano Measurement42Image 30: Scanning electron microscopic image of TiO2 nanofibers grown from an aqueous solution at 150 C .Image 31: Scanning electron microscopic image of ZnO microcrystallites grown from an aqueous solution at 95 C.
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