Short description

Beam parametersinfluence on imagee- gun componentsfilamentslenses

Beam-sample interactionelectron scatteringImage formation

Scanning Electron Microscopy (SEM)

Scanning Electron Microscope (SEM)V-shaped FilamentExtractorDeflecting PlatesBackscatteredElectronse- DetectorPrimarye- BeamSampleImage DisplayElectronColumnField of view:5x 5 mm2 500 x 500 nm2Resolution: down to 1 nm Scan quadrupoleBeam accelerator

How to sweep an electron beamFirst coil deviate beam from optical axisSecond coil brings beam backat optical axis on the pivot pointImage formation point by pointcollecting signal at each raster pointL = raster length on sampleW = working distanceS = raster length on screenMagnification = S/LLL = 10 m, S = 10 cmM depends on working distance

Effect of beam parameters on imageV0 = beam voltageip = beam currentp = beam convergence angledp = beam diameter at sample

High resolution modeNoise on signalEffect of beam parameters on imageip = 1 pA, dp = 15 nmip = 320 pA, dp = 130 nmHigh current modeResolution too lowip = 5 pA, dp = 20 nmGood compromiseip = beam currentdp = beam diameterResolution

Depth of focusEffect of beam parameters on imageIf p is small, dp changes little with depth, so featuresat different heights can be in focusp = 15 mradp = 1 mrad

Effect of beam parameters on imageV0 < 5 kV, beam interaction limited to region close to surface, info on surface detailsV0 15 - 30 kV, beam penetrates into sample, info on interior of sampleV0 = beam voltageElectron energy

Electron columne- are produced and acceleratedBeam is reduced to increase resolutionBeam is focused on sample

Filamente- are accelerated to anode and the hole allowsa fraction of this e- to reach the lenses Wehnelt: focuses e- inside the gunControls intensity of emitted e-Grid connected to filamentwith variable resistore- exit filament following + linesThe equipontential line shapehas focussing effect anddetermines 0 and d0

FilamentElectron columnFilament headThe equipontential line shapehas focussing effect anddetermines 0 and d0Equipotential linesElectron beam

Filament typesTungsten hairpin(most common)Lanthanumhexaboride (LaB6)0.120 mm Tungsten wireLaB6 crystal 0.20 mmOperating principle: thermionic electron emission

Filament typesTungsten hairpinLanthanum hexaboride (LaB6)Ew = 4.5 eVJc = 3.4 A/cm2 at 2700 KLifetime 50-150 hoursEnergy width 0.7 eVOperating pressure 10-5 mbar Ew = 2.5 eVJc = 40 A/cm2 at 1800 KLifetime 200-1000 hoursEnergy width 0.3 eVOperating pressure 10-6 mbar thermionic electron emissionAc = 120 A/cm2K2 Ew = work functionTo reduce filament evaporation operate the electron gun at the lowest possible temperature

Materials of low work function are desired.

Filament typesThermal FieldEmissionW-Zr crystal 0.20 mmI = 1 104 A/cm2 at 1800 CLifetime > 1000 hoursEnergy width 0.1 eVSmall source dimension (few nm)Operating pressure 10-9 mbarOperating principle: thermionic electron emission +Tunnelling

E gun brightnessTungsten hairpinLanthanum hexaboride (LaB6)Thermal Field Emission = 105 A/sr cm2Brightness is conserved throughout the column = 106 A/sr cm2 = 108 A/sr cm2Beam current changes throughout the columndp: 30 100 mdp: 5 50 mdp: 5 nm

Electromagnetic Lenses Demagnification of beam crossover image (d0)to get high resolution (small dp) Beam focussingHigh demagneededd0: 5 100 mfor filamentsd0: 5 nmfor TFELow demagneededcoilsFringe fieldradialparallel

Electromagnetic Lensesf = focal length the distance from the point where an electron first begins tochange direction to the point where it crosses the axis.Focusing processe- interacts with Br and Bz separately-e (vz x Br) produces a force into screen Fqin giving e- rotational velocity vqinvqin interacts with Bzproduces a force toward optical axisFr = -e (vqin x Bz)The actual trajectory of the electron will be a spiral The final image shows this spiraling action as a rotation of the image as the objective lens strength is changed.

Electromagnetic LensesI = lens coil currentN = number of coils V0 = accelerating voltageLens coil current and focal lengthIncreasing the strength (current) of the lens reduces the focal distance

Comparison to optical lensesBeam crossoverd0 = tungsten diameter = 50 mScaling from the figure, the demag factor is 3.4 so d1 = d0/m = 14.7 mCONDENSER LENSES: the aim is to reduce the beam diameterDemagnification of beam crossover image (d0) = object

Objective LensesScope: focus beam on samplePinholeNo B outsideLarge samplesLong working distances (40 mm)High aberrationsThey also providefurther demagnificationImmersionSample in B fieldSmall samples Short working distances (3 mm)Highest resolutionLow aberrationsSeparation of secondaryfrom backscattered e-SnorkelB outside lensLarge samplesSeparation of secondaryfrom backscattered e-Long working distancesLow aberrationsThey should contain:Scanning coilStigmatorBeam limiting aperture

Effect of aperture sizeAperture size: 50 500 m

Decrease 1 for e- entering OL to a

a determines the depth of focus

Determines the beam current

Reduces aberrations

Effect of working distanceIncrease in WD increase in q m smaller larger d lower resolution but longer depth of focus

Effect of condenser lens strenghtIncrease in condenser strenght (current) longer q larger m and smaller dAlso it brings a beam current reduction, so a compromise between current and resolution is neededWeakStrongHigher IbeamLower IbeamLower dpHigher dpDecrease q1 and increase p2 larger m

Gaussian probe diameterThe distribution of emission intensity from filament is gaussian with size dGdG = FWHMWith no aberrations, keeping dG constant would allow to increase ip by only increasing p

Spherical aberrationsOrigin: e- far from optical axis are deflected more strongly So at the focal plane there is a disk and not a pointe- along PA gives rise to gaussian image planeNo aberratione- along PB cross the optical axis in dsSpherical aberration disk of least confusionCs = Spherical aberration coefficient fFor immersion and snorkel Cs ~ 3 mmFor pinholes Cs ~ 20-30 mmSo one need to put an aperture

Aperture diffractioneVTo estimate the contribution to beamdiameter one takes half the diameterof the diffraction disknmsr

Origin: initial energy difference of accelerated electronsFor tungsten filament E = 3 eVChromatic aberrationsChromatic aberration disk of least confusionAt 30 KeV E/E0 = 10-4At 3 KeV E/E0 = 10-3Cs = Chromatic aberration coefficient f

Origin: machining errors, asymmetry in coils, dirtAstigmatismResult: formation ow two differecntfocal pointsEffect on image:Stretching of points into linesCan be compensated with octupole stigmator

Astigmatism

Beam-sample interactionBackscattered e-SiliconV0 = 20 KVTFE, = 1 108 A/sr cm2dp = 1 nmIb = 60 pASimulation of e- trajectoriesMain reason of large interaction volume:Elastic ScatteringInelastic scattering

Beam-sample interactionElastic scattering cross sectionZ = atomic number;E = e- energy (keV);A = atomic numberN0 = Avogadros number; = atomic densityElastic ScatteringElastic mean free path =distance between scattering eventsSilicon = 2.33 g/cm3Z = 14A = 28N0 = 6.022 1023

Beam-sample interactionInelastic scattering energy loss rateInelastic ScatteringZ = atomic numberA= atomic numberN0 = Avogadros number = atomic densityEi = e- energy in any point inside sampleJ = average energy loss per eventEb = 20 KeVThe path of a 20 KeV e- is of theorder of microns, so the interaction volumeis about few microns cube

Beam-sample interactionSimulationEnergytransferredto sampleInteraction volume20 KeV beam incident on PMMA with different time periods

Influence of beam parameters on beam-sample interactionBeam energy10 KeV20 KeV30 KeVFeLonger Lower loss rateElastic scatteringcross sectionInelastic scatteringenergy loss rate

Incidence angleInfluence of beam parameters on beam-sample interaction4560FeSmaller and asymmetric interaction volumeScattering of e- out of the sampleReduced depthSame lateral dimensionssurfacesurface

10% to 50% of the beam electrons are backscatteredThey retain 60% to 80% of the initial energy of the beamAtomic numberC (Z=6)C, k shellFe (Z=26)Influence of sample on beam-sample interactionFe, k shellV0 = 20 keVReduced linear dimensions of interaction volumeElastic scatteringcross sectionInelastic scatteringenergy loss rate

Atomic numberAg (Z=47)Ag, k shellU (Z=92)Influence of sample on beam-sample interactionU, k shellV0 = 20 keVMore spherical shape of interaction volume

Backscattered electronsSignal from interaction volume (what do we see?)Secondary electronsBackscattered e-

Backscattered electron coefficient60Relationship between and a sample property (Z)This gives atomic number contrastIf different atomic species are present in the sampleCi = weight concentrationBSE dependenceMonotonic increase

Incidence angle60BSE dependencen = intensity at normalLine length: relative intensity of BSEStrong influence on BSE detector position

Energy distributionBSE dependenceThe energy of each BSE depends on the trajectory inside sample, hence differentenergy lossesRegion I: E up to 50 %Becomes peaked with increasing ZLateral spatial distributionRegion good forhigh resolutionGives rise to loss in lateral resolution At low Z the external region increases

Sampling depthBSE dependenceSampling depth is typically 100 -300 nmfor beam energies above 10 keVFraction of maximume- penetration(microns)Percent of RKO defines a circle on the surface (center in the beam) spanning the interaction volume

Energy distribution of electrons emitted by a solidSignal from interaction volume (what do we see?)Secondary electronsEnergy: 5 50 eVProbability of e- escape from solid = e- mean free path

Origin: electron elastic and inelastic scatteringSecondary electronsSURFACESENSITIVESE1 = secondary due directly to incident beamSE2 = secondary generated by backscattered electronsCarbon: SE2 /SE1 = 0.18Aluminum: SE2 /SE1 = 0.48Copper: SE2 /SE1 = 0.9Gold: SE2 /SE1 = 1.5Low backscattering cross sectionHigh backscattering cross sectionBeam resolutionBSE resolutionSE Intensity angular distribution: cos

Image formationBackscattered e-Secondary e-Volume sensitiveSurface sensitiveSampling depth ~ 100 -300 nm

Image formationMany different signals can be extracted from beam-sample interactionSo the information depends on the signal acquired, is not only topography

The beam is scanned along a single vector (line) and the same scan generatoris used to drive the horizontal scan on a screenA one to one correspondence is established betweena single beam location and a single point of the displayFor each point the detector collects a current and the intensity is plottedor the intensity is associated with a grey scale at a single pointSignals to be recordedImage formationMagnification M = LCRT/LsampleBut the best way is to calibrate the instrument

Image formationPixel = picture elementPixel is the size of the area on the sample from which information is collectedActually is a circleLength of the scan on samplenumber of steps along the scan lineThe image is focused whenthe signal come only from athe location where the beamis addressedAt high magnification therewill be overlap between two pixelDigital image: array (x,y,Signal)Signal: output of ADCResolution = 2n8 bits = 28 = 256 gray levels16 bits = 216 = 65536 gray levelsConsidering the matrix defining the: Pixel edge dimension

Image formationFor a given experiment (sample type) and experimental conditions (beam size, energy)the limiting magnification should obtained by calculating the area generating signal taking into account beam-sample interactions and compare to pixel sizebeamArea producing BSe-V0 = 10 keV, dB = 50 nmon Al, dBSE = 1.3 m deff = 1.3 mon Au dBSE = 0.13 m deff = 0.14 mThere is overlappingof pixel signal intensity10x 10 cm displayDifferent operation settingsfor low and high magnification

Depth of fieldDepth of field D = distance along the lens axis (z) in the object planein which an image can be focused without a loss of clarity. To calculate D, we need to know where from the focal plane the beam is broadenedThe vertical distance required to broaden a beam r0 to a radius r (causing defocusing) isFor small anglesBroadening means adjacent pixel overlapping

Depth of fieldOn a CRT defocusing is visible when two pixels are overlapped r = 1 pixel (on screen 0.1 mm)But 1 pixel size referred to sample depends on magnification To increase D, we can either reduce M or reduce beam divergenceHow much is r?Beam divergence is defined by the beam defining aperture

Depth of fieldOpticalSEM

DetectorEverhart-ThornleySecondary + BSEGrid negative: only BSEsolid angle acceptance: 0.05 srGeometric efficiency: 0.8 %Grid Positive: BSE+SEThe bias attracts most of SE

Topographic contrastIntensity of SE and BSE depends onbeam/sample incidence angle ()and on detector/sample angle ()BSE coefficient increase with

BSE emission distribution ~ cos

SE emission distribution ~ sec Detector position and electron energy window are important

Topographic contrastNegative bias cage to exclude secondary e-High contrast due to orientation ofsample surfaces- Detector is on one side of sample anysotropic view- Small solid angle of acceptance small signal- High tilt angleAnalogy to eye viewDierctional view

Topographic contrastPositive bias cage to accept secondary e-Contributions:Direct BSE+SESE distribution intensity I ~ sec

Variation in SE signal between two surfaces with different dI = sec tan dSo the contrast is given by dI/I = tan d

The SE are collected from most emitting surfaces sincethe positive bias allows SE to reach the detectorAnalogy to eye view

High resolution imagingHigh resolution signal if selected in energyHigh resolution signalgenerated by BSE1, SE1Separation of signal is necessary to obtain high resolutionSE1 : e- directly generated by beam BSE1 : low energy loss (

SiliconV0 = 30 KVTFE, = 1 108 A/sr cm2dp = 1 nmIb = 60 pASE1 - BSE1 width = about 2 nmBeam penetration depth = 9.5 mEmission area = 9.5 m Scan width at 10000 X = 10x10 m2image 1024x1024, pixel width 10 nmLow magScanning at low M means field of viewlarger than SE2 emission areaSo there is large overlap between pixelAnd the changes are due only to SE2 variationsScanning at high M means field of viewsmaller than SE2 emission areaSo as the beam is scanned, no changes inSE2 but changes are due to SE1SE2 gives large random noiseScan width at 100000 X = 1x1 m2image 1024x1024, pixel width 1 nmHigh magFWHM = 2 nm

Carbon nanotubes

SEM in FOODSchematic representation of gaseous SEDthe role of imaging gas in VP-SEM

SEM in FOOD50mBlades of cocoa butter present on the surfaceImage taken with sample at 5 C using nitrous oxide at ~ 100 Pa (0.8 torr)as imaging gasbloomed chocolate.

SEM in FOODVP-SEM image of commercially produced mayonnaise. Image taken with sample at 5.0C using water vapor at around 670Pa (5.0torr) as imaging gas. Light continuous phase is water mid grey discrete phase is oil. Darkest grey areas are air bubblesDisadvantages of conventional SEM techniques insulating specimens impossibility of examining hydrated samples without altering their state (drying or freezing)Sample preparation treatments introduce artifacts No studies of dynamic processes for such samples20m

Two-HoleFinal StateOne-HoleInitial StateGround StateDe-ExcitationAuger ProcessAuger SpectroscopyL1 2se-e-K 1sL2,3 2pM1 3sM2,3 3pVBEvacEFEkinEK(XYZ)= EB(X)-EB(Y)-EB(Z)-XYZ Auger ProcessOne-Particle SchemeEnergy ConservationEK(XYZ) = KE of Auger electronEB(X) = BE of X levelEB(Y) = BE of Y levelEB(Z) = BE of Z level

Usually additional terms must be included accounting for the two-hole final state correlation interaction and the relaxation effectsF Two-Hole Final State Correlation EnergyR Two-Hole Relaxation EnergyEb One electron binding energyEK(XYZ)= EB(X)-EB(Y)-EB(Z)-F+R-

Auger ProcessNomenclatureKL1M2Auger ProcessL1L2M1Coster-Kronig Process(the initial hole is filled by an electronof the same shell)CCCCore-Core-Core TransitionCCVCore-Core-Valence TransitionCVVCore-Valence-Valence TransitionK L1M1VBEvacEFEkinL2,3M2,3KL1M2K L1M1VBEvacEFEkinL2,3M2,3L1L2M1

3d M4,53p M2,3ElectronAugerX-RayFluorescence3s M12p L31s K2s L12p L2EFPhotonCompetitive processesRelative Probabilities of Relaxationby Auger Emission and by X-Ray Fluorescence EmissionFor lines originating from shell L and M the Auger yield remains much higher than X-ray emission

Principal Auger Lines while Spanning the Periodic Table of the Elements

CHEMICAL SENSITIVITY

Electron distribution spectrumPulse Counting ModeDerivative ModeSince Auger emission lines are often very broad and weak, their detectability is enhanced by differentiating of the spectrum

Chemical environment sensitivityGasSolid

Auger Electron SpectroscopyQuantitative AnalysisIn analogy to what developed for XPS,one can determine the atomic concentration (Ci) of the atomic species present in the near-surface region of a solid sampleCi Atomic Concentration of the i-th speciessi Orbital Sensitivity Factor of the i-th speciesIi Spectral Intensity Related to the i-th species

Auger Spectra as Measured at Selected Points of the Self-organized Agglomerated Au/Si(111) InterfaceFlat regionIslandSi L2,3VVAu N6,7VV

Si L2,3VV Auger Line Shape as Measured at Selected Points of the Self-organized Agglomerated Au/Si(111) InterfaceFlat regionIsland