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

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

3. Optical axis How to sweep an electron beam First coil deviate beam from 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 = raster length on sample W = working distance S = raster length on screen Magnification = S/L L S L = 10  m, S = 10 cm M depends on working distance

4. Effect of beam parameters on image V 0 = beam voltage i p = beam current  p = beam convergence angle d p = beam diameter at sample

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

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

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

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

9. Filament e - are accelerated to anode and the hole allows a fraction of this e - to reach the lenses 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

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

11. Filament types Tungsten hairpin (most common) Lanthanum hexaboride (LaB 6 ) 0.120 mm Tungsten wire LaB6 crystal 0.20 mm Operating principle: thermionic electron emission

12. Filament types Tungsten hairpin Lanthanum hexaboride (LaB 6 ) E w = 4.5 eV J c = 3.4 A/cm 2 at 2700 K Lifetime 50-150 hours Energy width  0.7 eV Operating pressure 10 -5 mbar E w = 2.5 eV J c = 40 A/cm 2 at 1800 °K Lifetime 200-1000 hours Energy width  0.3 eV Operating pressure 10 -6 mbar thermionic electron emission A c = 120 A/cm 2 K 2 E w = work function To reduce filament evaporation  operate the electron gun at the lowest possible temperature Materials of low work function are desired.

13. Filament types Thermal Field Emission W-Zr crystal 0.20 mm I = 1 10 4 A/cm 2 at 1800 °C Lifetime > 1000 hours Energy width  0.1 eV Small source dimension (few nm) Operating pressure 10 -9 mbar Operating principle: thermionic electron emission + Tunnelling

14. E gun brightness Tungsten hairpinLanthanum hexaboride (LaB 6 )Thermal Field Emission  = 10 5 A/sr cm 2 Brightness is conserved throughout the column R pp dpdp  = 10 6 A/sr cm 2  = 10 8 A/sr cm 2 Beam current changes throughout the column d p : 30 – 100  m d p : 5 – 50  m d p : 5 nm

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

16. Electromagnetic Lenses f = focal length the distance from the point where an electron first begins to change direction to the point where it crosses the axis. Focusing process e - interacts with B r and B z separately -e (v z x B r ) produces a force into screen F  in giving e - rotational velocity v  in v  in interacts with B z produces a force toward optical axis F r = -e (v  in x B z ) 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.

17. Electromagnetic Lenses I = lens coil current N = number of coils V 0 = accelerating voltage Lens coil current and focal length Increasing the strength (current) of the lens reduces the focal distance

18. Comparison to optical lenses 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 Demagnification of beam crossover image (d 0 ) = object

19. Objective Lenses Scope: focus beam on sample Pinhole No B outside Large samples Long working distances (40 mm) High aberrations 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 - 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

20. 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

21. Effect of working distance Increase in WD  increase in q  m smaller  larger d  lower resolution but longer depth of focus

22. Effect of condenser lens strenght 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 Weak Strong Higher I beam Lower I beam Lower d p Higher d p Decrease q 1 and increase p 2  larger m

23. 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 i p by only increasing  p

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

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

26. Origin: initial energy difference of accelerated electrons For tungsten filament  E = 3 eV Chromatic aberrations Chromatic aberration disk of least confusion At 30 KeV  E/E 0 = 10 -4 At 3 KeV  E/E 0 = 10 -3 C s = Chromatic aberration coefficient  f

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

28. Astigmatism

29. Beam-sample interaction Backscattered e - Silicon V 0 = 20 KV TFE,  = 1 10 8 A/sr cm 2 d p = 1 nm I b = 60 pA Simulation of e - trajectories Main reason of large interaction volume: Elastic Scattering Inelastic scattering

30. Beam-sample interaction Elastic scattering cross section Z = atomic number; E = e - energy (keV); A = atomic number N 0 = Avogadro’s number;  = atomic density Elastic Scattering Elastic mean free path = distance between scattering events Silicon  = 2.33 g/cm 3 Z = 14 A = 28 N 0 = 6.022 10 23 00

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

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

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

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

35. 10% to 50% of the beam electrons are backscattered They retain 60% to 80% of the initial energy of the beam Atomic number C (Z=6) C, k shell Fe (Z=26) Influence of sample on beam-sample interaction Fe, k shell V 0 = 20 keV Reduced linear dimensions of interaction volume Elastic scattering cross section Inelastic scattering energy loss rate

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

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

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

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

40. Energy distribution BSE dependence 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 Lateral spatial distribution Region good for high resolution Gives rise to loss in lateral resolution At low Z the external region increases

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

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

43. Origin: electron elastic and inelastic scattering Secondary electrons SURFACE SENSITIVE SE 1 = secondary due directly to incident beam 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 Low backscattering cross section High backscattering cross section Beam resolution BSE resolution SE Intensity angular distribution: cos 

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

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

46. The beam is scanned along a single vector (line) and the same scan generator is used to drive the horizontal scan on a screen A one to one correspondence is established between a single beam location and a single point of the display 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 Signals to be recorded Image formation Magnification M = L CRT /L sample But the best way is to calibrate the instrument

47. Image formation Pixel = picture element Pixel is the size of the area on the sample from which information is collected 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 Digital image: array (x,y,Signal) Signal: output of ADCResolution = 2 n 8 bits = 2 8 = 256 gray levels 16 bits = 2 16 = 65536 gray levels Considering the matrix defining the: Pixel edge dimension

48. 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 keV, d B = 50 nm on Al, d BSE = 1.3  m  d eff = 1.3  m on Au d BSE = 0.13  m  d eff = 0.14  m There is overlapping of pixel signal intensity 10x 10 cm display Different operation settings for low and high magnification

49. Depth of field 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 The vertical distance required to broaden a beam r 0 to a radius r (causing defocusing) is For small angles Broadening means adjacent pixel overlapping

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

51. Depth of field OpticalSEM

52. Detector Everhart-Thornley Secondary + BSE Grid negative: only BSE solid angle acceptance: 0.05 sr Geometric efficiency: 0.8 % Grid Positive: BSE+SE The bias attracts most of SE

53. 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

54. Topographic contrast Negative bias cage to exclude secondary e - High contrast due to orientation of sample surfaces - Detector is on one side of sample  anysotropic view - Small solid angle of acceptance  small signal - High tilt angle Analogy to eye view Dierctional view

55. Topographic contrast Positive bias cage to accept secondary e - Contributions: Direct BSE+SE SE distribution intensity I ~ sec  Variation in SE signal between two surfaces with different  dI = sec  tan  d  So the contrast is given by dI/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

57. High resolution imaging High resolution signal if selected in energy High resolution signal generated by BSE 1, SE 1 Separation of signal is necessary to obtain high resolution 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

58. Silicon V 0 = 30 KV TFE,  = 1 10 8 A/sr cm 2 d p = 1 nm I b = 60 pA SE 1 - BSE 1 width = about 2 nm Beam penetration depth = 9.5  m Emission area = 9.5  m Scan width at 10000 X = 10x10  m 2 image 1024x1024, pixel width 10 nm Low mag 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 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 Scan width at 100000 X = 1x1  m 2 image 1024x1024, pixel width 1 nm High mag FWHM = 2 nm

59. Carbon nanotubes

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

61. SEM in FOOD 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 ‘‘bloomed’’ chocolate.

62. 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 20 μm

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

64. Two-Hole Final State One-Hole Initial State Ground State De-Excitation Auger Process Auger Spectroscopy L 1 2s e-e- e-e- K 1s L 2,3 2p M 1 3s M 2,3 3p VB E vac EFEF E kin E K (XYZ)= E B (X)-E B (Y)-E B (Z)-  XYZ Auger Process One-Particle Scheme Energy Conservation E K (XYZ) = KE of Auger electron E B (X) = BE of X level E B (Y) = BE of Y level E B (Z) = BE of Z level

65. Usually additional terms must be included accounting for the two-hole final state correlation interaction and the relaxation effects F Two-Hole Final State Correlation Energy R Two-Hole Relaxation Energy E b One electron binding energy E K (XYZ)= E B (X)-E B (Y)-E B (Z)-F+R-  K L1L1 M1M1 VB E vac EFEF E kin L 2,3 M 2,3

66. Auger Process Nomenclature KL 1 M 2 Auger Process L 1 L 2 M 1 Coster-Kronig Process (the initial hole is filled by an electron of the same shell) CCCCore-Core-Core Transition CCVCore-Core-Valence Transition CVVCore-Valence-Valence Transition K L1L1 M1M1 VB E vac EFEF E kin L 2,3 M 2,3 KL 1 M 2 K L1L1 M1M1 VB E vac EFEF E kin L 2,3 M 2,3 L1L2M1L1L2M1

67. 3d M 4,5 3p M 2,3 Electron Auger X-Ray Fluorescence 3s M 1 2p L32p L3 1s K1s K 2s L12s L1 2p L22p L2 EFEF Photon Competitive processes Relative Probabilities of Relaxation by Auger Emission and by X-Ray Fluorescence Emission For lines originating from shell L and M the Auger yield remains much higher than X-ray emission

68. Principal Auger Lines while Spanning the Periodic Table of the Elements CHEMICAL SENSITIVITY

69. 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

70. Chemical environment sensitivity Gas Solid

71. Auger Electron Spectroscopy Quantitative Analysis In analogy to what developed for XPS, one can determine the atomic concentration (C i ) of the atomic species present in the near-surface region of a solid sample C i Atomic Concentration of the i-th species s i Orbital Sensitivity Factor of the i-th species I i Spectral Intensity Related to the i-th species

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

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