Scanning Electron Microscopy SEM Short description Beam parameters

Scanning Electron Microscopy (SEM) Short description Beam parameters influence on image e- gun components filaments lenses Beam-sample interaction electron scattering Image formation

Scanning Electron Microscope (SEM) Field of view: V-shaped Filament 5 x 5 mm 2 – 500 x 500 nm 2 Resolution: down to 1 nm Extractor Beam accelerator Electron Column Scan quadrupole Deflecting Plates Image Display Primary e- Beam e- Detector Backscattered Electrons Sample

How to sweep an electron beam First coil deviate beam from optical axis Optical axis Second coil brings beam back at optical axis on the pivot point Image formation point by point collecting signal at each raster point L S L = raster length on sample W = working distance S = raster length on screen Magnification = S/L L = 10 m, S = 10 cm M depends on working distance

Effect of beam parameters on image V 0 = beam voltage ip = beam current p = beam convergence angle dp = beam diameter at sample

Effect of beam parameters on image High resolution mode Noise on signal Resolution ip = beam current dp = beam diameter Good compromise ip = 1 p. A, dp = 15 nm ip = 320 p. A, dp = 130 nm High current mode Resolution too low ip = 5 p. A, dp = 20 nm

Effect of beam parameters on image Depth of focus If p is small, dp changes little with depth, so features at different heights can be in focus p = 15 mrad p = 1 mrad

Effect of beam parameters on image Electron energy V 0 < 5 k. V, beam interaction limited to region close to surface, info on surface details V 0 15 - 30 k. V, beam penetrates into sample, info on interior of sample V 0 = beam voltage

Electron column e- are produced and accelerated Beam is reduced to increase resolution Beam is focused on sample

Filament Wehnelt: focuses e- inside the gun Controls intensity of emitted e- Grid connected to filament with variable resistor e- exit filament following + lines The equipontential line shape has focussing effect and determines 0 and d 0 e- are accelerated to anode and the hole allows a fraction of this e- to reach the lenses

Filament Equipotential lines Filament head The equipontential line shape has focussing effect and determines 0 and d 0 Electron beam Electron column

Filament types Tungsten hairpin (most common) Lanthanum hexaboride (La. B 6) 0. 120 mm Tungsten wire Operating principle: thermionic electron emission La. B 6 crystal 0. 20 mm

Filament types thermionic electron emission Ac = 120 A/cm 2 K 2 Ew = work function To reduce filament evaporation operate the electron gun at the lowest possible temperature Materials of low work function are desired. Tungsten hairpin Ew = 4. 5 e. V Jc = 3. 4 A/cm 2 at 2700 K Lifetime 50 -150 hours Energy width 0. 7 e. V Operating pressure 10 -5 mbar Lanthanum hexaboride (La. B 6) Ew = 2. 5 e. V Jc = 40 A/cm 2 at 1800 °K Lifetime 200 -1000 hours Energy width 0. 3 e. V Operating pressure 10 -6 mbar

Filament types Operating principle: thermionic electron emission + Tunnelling W-Zr crystal 0. 20 mm I = 1 104 A/cm 2 at 1800 °C Lifetime > 1000 hours Energy width 0. 1 e. V Small source dimension (few nm) Operating pressure 10 -9 mbar Thermal Field Emission

E gun brightness Beam current changes throughout the column Brightness is conserved throughout the column dp R p Tungsten hairpin dp: 30 – 100 m = 105 A/sr cm 2 Lanthanum hexaboride (La. B 6) dp: 5 – 50 m = 106 A/sr cm 2 Thermal Field Emission dp: 5 nm = 108 A/sr cm 2

Electromagnetic Lenses Demagnification of beam crossover image (d 0) to get high resolution (small dp) d 0: 5 – 100 m for filaments High demag needed Beam focussing coils d 0: 5 nm for TFE Low demag needed Fringe field radial parallel

Electromagnetic Lenses Focusing process e- interacts with Br and Bz separately -e (vz x Br) produces a force into screen Fqin giving e- rotational velocity vqin interacts with Bz produces a force toward optical axis Fr = -e (vqin x Bz) f = focal length the distance from the point where an electron first begins to change direction to the point where it crosses the axis. 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 Lenses Lens coil current and focal length I = lens coil current N = number of coils V 0 = accelerating voltage Increasing the strength (current) of the lens reduces the focal distance

Comparison to optical lenses Demagnification of beam crossover image (d 0) = object Beam crossover d 0 = tungsten diameter = 50 m Scaling from the figure, the demag factor is 3. 4 so d 1 = d 0/m = 14. 7 m CONDENSER LENSES: the aim is to reduce the beam diameter

Objective Lenses Scope: focus beam on sample Pinhole No B outside Large samples Long working distances (40 mm) High aberrations Snorkel B outside lens Large samples Separation of secondary from backscattered e. Long working distances Low aberrations They should contain: Scanning coil Stigmator Beam limiting aperture They also provide further demagnification Immersion Sample in B field Small samples Short working distances (3 mm) Highest resolution Low aberrations Separation of secondary from backscattered e-

Effect of aperture size Aperture 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 distance Increase in WD increase in q m smaller larger d lower resolution but longer depth of focus

Effect of condenser lens strenght Weak Strong Decrease q 1 and increase p 2 larger m Higher Ibeam Lower dp Lower Ibeam Higher dp Increase in condenser strenght (current) longer q larger m and smaller d Also it brings a beam current reduction, so a compromise between current and resolution is needed

Gaussian probe diameter The distribution of emission intensity from filament is gaussian with size d G d. G = FWHM With no aberrations, keeping d. G constant would allow to increase ip by only increasing p

Spherical aberrations Origin: e- far from optical axis are deflected more strongly e- along PA gives rise to gaussian image plane No aberration e- along PB cross the optical axis in ds So at the focal plane there is a disk and not a point Spherical aberration disk of least confusion Cs = Spherical aberration coefficient f For immersion and snorkel Cs ~ 3 mm For pinholes Cs ~ 20 -30 mm So one need to put an aperture

Aperture diffraction To estimate the contribution to beam diameter one takes half the diameter of the diffraction disk nm sr e. V

Chromatic aberrations Origin: initial energy difference of accelerated electrons Chromatic aberration disk of least confusion For tungsten filament E = 3 e. V At 30 Ke. V E/E 0 = 10 -4 At 3 Ke. V E/E 0 = 10 -3 Cs = Chromatic aberration coefficient f

Astigmatism Origin: machining errors, asymmetry in coils, dirt Result: formation ow two differecnt focal points Effect on image: Stretching of points into lines Can be compensated with octupole stigmator

Astigmatism

Beam-sample interaction Simulation of e- trajectories Backscattered e. Silicon V 0 = 20 KV TFE, = 1 108 A/sr cm 2 dp = 1 nm Ib = 60 p. A Main reason of large interaction volume: Elastic Scattering Inelastic scattering

Beam-sample interaction Elastic Scattering Elastic scattering cross section Elastic mean free path = distance between scattering events 0 Z = atomic number; E = e- energy (ke. V); A = atomic number N 0 = Avogadro’s number; = atomic density Silicon = 2. 33 g/cm 3 Z = 14 A = 28 N 0 = 6. 022 1023

Inelastic Scattering Beam-sample interaction Inelastic scattering energy loss rate Z = atomic number A= atomic number N 0 = Avogadro’s number = atomic density Ei = e- energy in any point inside sample J = average energy loss per event The path of a 20 Ke. V e- is of the order of microns, so the interaction volume is about few microns cube Eb = 20 Ke. V

Beam-sample interaction Interaction volume Energy transferred to sample Simulation 20 Ke. V beam incident on PMMA with different time periods

Influence of beam parameters on beam-sample interaction Beam energy 10 Ke. V 20 Ke. V Fe 30 Ke. V Elastic scattering cross section Longer Lower loss rate Inelastic scattering energy loss rate

Influence of beam parameters on beam-sample interaction Incidence angle Smaller and asymmetric interaction volume 45° Fe surface surf 60° Scattering of e- out of the sample Reduced depth Same lateral dimensions

Influence of sample on beam-sample interaction Atomic number C (Z=6) C, k shell V 0 = 20 ke. V Fe (Z=26) Fe, k shell Elastic scattering cross section 10% to 50% of the beam electrons are backscattered They retain 60% to 80% of the initial energy of the beam Reduced linear dimensions of interaction volume Inelastic scattering energy loss rate

Influence of sample on beam-sample interaction Atomic number Ag (Z=47) Ag, k shell V 0 = 20 ke. V U (Z=92) U, k shell More spherical shape of interaction volume

Signal from interaction volume (what do we see? ) Backscattered electrons Secondary electrons Backscattered e-

BSE dependence Backscattered electron coefficient Monotonic increase Relationship between and a sample property (Z) This gives atomic number contrast 60° If different atomic species are present in the sample Ci = weight concentration

BSE dependence Incidence angle n = intensity at normal Line length: relative intensity of BSE Strong influence on BSE detector position 60°

BSE dependence Energy distribution Lateral spatial distribution The energy of each BSE depends on the trajectory inside sample, hence different energy losses Region I: E up to 50 % Becomes peaked with increasing Z Region good for high resolution Gives rise to loss in lateral resolution At low Z the external region increases

BSE dependence Sampling depth Percent of Fraction of maximum e- penetration (microns) RKO defines a circle on the surface (center in the beam) spanning the interaction volume Sampling depth is typically 100 -300 nm for beam energies above 10 ke. V

Signal from interaction volume (what do we see? ) Energy distribution of electrons emitted by a solid Secondary electrons Energy: 5 – 50 e. V Probability of e- escape from solid = e- mean free path

Secondary electrons Origin: electron elastic and inelastic scattering SURFACE SENSITIVE SE 1 = secondary due directly to incident beam Beam resolution SE 2 = secondary generated by backscattered electrons Carbon: SE 2 /SE 1 = 0. 18 Aluminum: SE 2 /SE 1 = 0. 48 Copper: SE 2 /SE 1 = 0. 9 Gold: SE 2 /SE 1 = 1. 5 BSE resolution Low backscattering cross section High backscattering cross section SE Intensity angular distribution: cos

Image formation Backscattered e- Volume sensitive Sampling depth ~ 100 -300 nm Secondary e- Surface sensitive

Image formation Many different signals can be extracted from beam-sample interaction So the information depends on the signal acquired, is not only topography

Image formation The beam is scanned along a single vector (line) and the same scan generator is used to drive the horizontal scan on a screen Signals to be recorded For each point the detector collects a current and the intensity is plotted or the intensity is associated with a grey scale at a single point A one to one correspondence is established between a single beam location and a single point of the display Magnification M = LCRT/Lsample But the best way is to calibrate the instrument

Image formation Digital image: array (x, y, Signal) Signal: output of ADC Pixel = picture element Resolution = 2 n 8 bits = 28 = 256 gray levels 16 bits = 216 = 65536 gray levels Pixel is the size of the area on the sample from which information is collected Considering the matrix defining the: Pixel edge dimension Actually is a circle Length of the scan on sample number of steps along the scan line The image is focused when the signal come only from a the location where the beam is addressed At high magnification there will be overlap between two pixel

Image formation For 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 size beam Area producing BSe- V 0 = 10 ke. V, d. B = 50 nm on Al, d. BSE = 1. 3 m deff = 1. 3 m on Au d. BSE = 0. 13 m deff = 0. 14 m 10 x 10 cm display There is overlapping of pixel signal intensity Different operation settings for low and high magnification

Depth of field D = distance along the lens axis (z) in the object plane in 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 broadened Broadening means adjacent pixel overlapping The vertical distance required to broaden a beam r 0 to a radius r (causing defocusing) is For small angles

Depth of field How much is r? On 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 divergence Beam divergence is defined by the beam defining aperture

Depth of field Optical SEM

Detector Everhart-Thornley Secondary + BSE Grid Positive: BSE+SE Grid negative: only BSE The bias attracts most of SE solid angle acceptance: 0. 05 sr Geometric efficiency: 0. 8 %

Topographic contrast Intensity of SE and BSE depends on beam/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 contrast Negative bias cage to exclude secondary e- Detector is on one side of sample anysotropic view - Small solid angle of acceptance small signal - High tilt angle Dierctional view High contrast due to orientation of sample surfaces Analogy to eye view

Topographic contrast Contributions: Direct BSE+SE SE distribution intensity I ~ sec Positive bias cage to accept secondary e- Variation in SE signal between two surfaces with different d. I = sec tan d So the contrast is given by d. I/I = tan d The SE are collected from most emitting surfaces since the positive bias allows SE to reach the detector Analogy to eye view

High resolution imaging High resolution signal if selected in energy SE 1 : e- directly generated by beam BSE 1 : low energy loss (<2%) e- from beam SE 2 : e- generated by BSE into sample BSE 2 : higher energy loss e- from beam High resolution signal generated by BSE 1, SE 1 Separation of signal is necessary to obtain high resolution

Silicon V 0 = 30 KV TFE, = 1 108 A/sr cm 2 dp = 1 nm Ib = 60 p. A SE 1 - BSE 1 width = about 2 nm Beam penetration depth = 9. 5 m Emission area = 9. 5 m FWHM = 2 nm Low mag Scan width at 10000 X = 10 x 10 m 2 image 1024 x 1024, pixel width 10 nm Scanning at low M means field of view larger than SE 2 emission area So there is large overlap between pixel And the changes are due only to SE 2 variations High mag Scan width at 100000 X = 1 x 1 m 2 image 1024 x 1024, pixel width 1 nm Scanning at high M means field of view smaller than SE 2 emission area So as the beam is scanned, no changes in SE 2 but changes are due to SE 1 SE 2 gives large random noise

Carbon nanotubes

SEM in FOOD Schematic representation of gaseous SED the role of imaging gas in VP-SEM

SEM in FOOD ‘‘bloomed’’ chocolate. 50 μm Blades of cocoa butter present on the surface Image taken with sample at 5 °C using nitrous oxide at ~ 100 Pa (0. 8 torr) as imaging gas

20 μm SEM in FOOD VP-SEM image of commercially produced mayonnaise. Image taken with sample at 5. 0 °C using water vapor at around 670 Pa (5. 0 torr) as imaging gas. Light continuous phase is water mid grey discrete phase is oil. Darkest grey areas are air bubbles Disadvantages 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 samples

V-shaped Filament Scanning Auger Microscopy (SAM) Extractor Deflecting Plates Primary e- Beam Electron Energy Analyzer e- Detector Backscattered Electrons Chemical Map Sample Auger Spectrum

Auger Spectroscopy Ekin Evac EF VB M 2, 3 3 p M 1 3 s e- e- L 2, 3 2 p L 1 2 s K 1 s Ground State XYZ Auger Process One-Particle Scheme Energy Conservation EK(XYZ) = KE of Auger electron EB(X) = BE of X level EB(Y) = BE of Y level EB(Z) = BE of Z level One-Hole Initial State De-Excitation Auger Process EK(XYZ)= EB(X)-EB(Y)-EB(Z)- Two-Hole Final State

Usually additional terms must be included accounting for the two-hole final state correlation interaction and the relaxation effects EK(XYZ)= EB(X)-EB(Y)-EB(Z)-F+R- F Two-Hole Final State Correlation Energy R Two-Hole Relaxation Energy Eb One electron binding energy Evac VB M 2, 3 M 1 L 2, 3 L 1 K Ekin EF

Auger Process Nomenclature KL 1 M 2 L 1 L 2 M 1 Auger Process Coster-Kronig Process (the initial hole is filled by an electron of the same shell) Core-Core Transition Core-Valence Transition CCC CCV CVV L 1 L 2 M 1 KL 1 M 2 Ekin Evac VB M 2, 3 Evac EF VB M 2, 3 M 1 L 2, 3 L 1 K K EF

Competitive processes Auger Electron X-Ray Fluorescence EF 3 d M 4, 5 3 p M 2, 3 3 s M 1 2 p L 3 2 p L 2 2 s L 1 Relative Probabilities of Relaxation by Auger Emission and by X-Ray Fluorescence Emission Photon 1 s K For 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 spectrum Pulse Counting Mode Derivative Mode Since Auger emission lines are often very broad and weak, their detectability is enhanced by differentiating of the spectrum

Chemical environment sensitivity Gas Solid

Auger Electron Spectroscopy Quantitative Analysis In 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 sample Ci Atomic Concentration of the i-th species si Orbital Sensitivity Factor of the i-th species Ii Spectral Intensity Related to the i-th species

Au N 6, 7 VV Si L 2, 3 VV Auger Spectra as Measured at Selected Points of the Self-organized Agglomerated Au/Si(111) Interface Island Flat region

Si L 2, 3 VV Auger Line Shape as Measured at Selected Points of the Self-organized Agglomerated Au/Si(111) Interface Island Flat region