Electron Optics Two essential components: 1)Electron source (gun) 2)Focusing system (lenses) Add scanning apparatus for imaging Electron gun Cathode Anode Alignment coils Lenses condensers objective Objective aperture assembly sample

Electron Lenses Principle of electromagnetic focusing Interaction of electromagnetic field on moving charge (electron) Vector equation Magnitude of F will be F = -eVBsinθ where θ is the smaller of two angles between V and B Direction of F determined by “right hand rule” F = Force on electron V = electron velocity B = Magnetic field strength (rotationally symmetric) e = charge of electron → → → F = -e(VxB)

Axially symmetric electromagnetic lens Fe shielding to prevent flux leakage from solenoid Lens strength:intensity of field in gaps proportional to (NxI)N = # turns of solenoid winding I = current flowing through windings

Focal Length (f): Point on Z axis where initially parallel rays cross the axis after passing through the lens HIGHER LENS STRENGTH = SHORTER FOCAL LENGTH B = vector parallel to field B r = radial component of field (vector perpendicular to axis) B z = axial component of field (vector parallel to axis) B varies depending on position in lens Results: Force strongest in the center of the gap Actual electron paths spiral through lens Low lens strength = long focal length High lens strength = short focal length Upper polepiece Lower polepiece

Usually two-stage condenser system Purpose: 1)Further demagnification of the gun crossover image 2)Control amount of beam entering objective major effect on beam current at sample High Lens strength Small crossover image Less current entering the objective Low Lens strength Large crossover image More current entering the objective

Sample Objective Condenser Electron gun f (low condenser lens strength) f (high condenser lens strength) Low condenser strength Long focal length Small divergence angle High current into objective High condenser strength Short focal length Large divergence angle Low current into objective

Objective lens Purpose: control the size and shape of the final beam spot Considerations: Produce small beam diameter Magnetic field must not hinder detector system from collecting low eV electrons Must allow clear path from sample to detectors Bore must be large Contain scan coils and Stigmators Beam-limiting apertures Aberrations usually increase with focal length – minimize aberrations For quantitative analysis long focal length = long working distance high takeoff angle and low absorption

For objective Increase demagnification by increasing lens strength to produce small spot size →Short working distance due to short focal length →Short depth of field Objective lens, therefore, Controls image focus = beam size

Objective lens design Pinhole lens Snorkel lens Immersion lens

Depth of field

Sample Objective Condenser Electron gun f (high objective lens strength) = short working distance f (low objective lens strength) = long Working distance Effective beam diameter High objective strength Short focal length Large divergence angle Short working distance Short depth-of-field High resolution Low objective strength long focal length Small divergence angle Long working distance Large depth-of-field Low resolution

Current in final beam spot is a function of: 1)Condenser lens strength 2)Objective aperture size Objective aperture affects: 1)Current reaching sample 2)Beam size passing through objective 3)Depth of field Tradeoff: Best image resolution with smallest spot size (smaller aperture) Direct cutting of current compromises signal produced as current reduced in final spot

Depth of field Plane of focus D Region of image in effective focus Long working distance Sample surface Short working distance Insert smaller objective aperture to improve D Pixel size

Objective aperture assembly = beam regulating assembly Sense current drift on aperture and adjust condenser lens strength to compensate Beam current regulation Feedback to condensers

Production of minimum beam size Magnification: M c = S 0 /S i = magnification of condenser S 0 = distance from gun crossover to lens gap S i = distance from gap to where imaged (related to focal length) Diameter of beam after passing through condenser d i = d 0 /M c S 0 is constant, so Increase condenser current → decrease in focal length and increase in demagnification (smaller crossover diameter) Note that divergence angle also increases so less current enters objective Sample Objective Condenser Electron gun S0S0 S1S1

For objective: Increase demagnification to produce small beam diameter, results in: - short working distance - short depth of field Final beam size: d f = d 0 / (M c M obj ) Current in final beam is a function of: - condenser lens strength - objective aperture size Minimum beam size (and highest resolution) achieved by increasing lens strength – sacrifice current (and signal / noise) Quality of final beam at the sample will be affected by: - lens aberrations - vacuum quality - sample effects

Lens aberrations Spherical Chromatic Diffraction Astigmatism Coma Electrons moving in trajectories further from optic axis are focused more strongly than those near the axis Causes image enlargement (disk = d s ) Diameter of d s = ½ C s α 3 C s = spherical aberration coefficient α = angle of outer ray through lens C s minimized in short focal length lenses (e.g., immersion) For pinhole lenses, can decrease spherical aberration by decreasing α using aperture

Lens aberrations Spherical Chromatic Diffraction Astigmatism Coma If energies of electrons passing through the lens differ, they will follow different ray paths Diameter of d c = C C α (ΔE / E 0 ) C c = chromatic aberration coefficient α = convergence angle Directly related to focal length Much less significant at high E 0 Always some spread in initial electron energies as leave cathode W ~ 2 eV LaB 6 ~ 1 eV FE ~ 0.2 to 0.5 eV Minimize by decrease in α

Lens aberrations Spherical Chromatic Diffraction Astigmatism Coma Diameter of d d = 0.61 λ / α λ electrons = 1.24 / (E 0 ) 1/2 Larger divergence angle (α) = smaller contribution of d d Wave nature of electrons

Spherical aberration disk d s and aperture diffraction disk d d vs. aperture angle

Lens aberrations Spherical Chromatic Diffraction Astigmatism Coma Magnetic lenses have imperfect symmetry Enlarges beam diameter and changes shape Use stigmators in objective lens supplies weak correcting field typically use octupole arrangement

Lens aberrations Spherical Chromatic Diffraction Astigmatism Coma Different focal lengths of electron paths with different incidence angles Generally eliminated by proper lens alignment

Aberrations most significant in objective Final probe size = quadrature sum of disk diameters… d p = (d g 2 + d s 2 + d d 2 + d c 2 ) 1/2 Importance: At 30 kV, tungsten filament i max = 1.64 x A diameter d d = 1.4 nm d s = 2.5 nm chromatic aberration especially significant for W sources where ΔE ~ 2-3 eV Increase effective diameter 1) 30 kVd p 5nm → 6.5nm 2) 15 kV→ 9.5 nm lower energy spread will make a big difference… d g = gaussian probe size

Elstar electron column Key design elements: Large travel/tilt stage compatible “DualBeam” SEM-FIB Minimum lens aberrations Automated aperture selection Default small beam current Small gun apertures High current for analytics >20 nA Thermal & environmental stability Constant power lenses Double magnetic shielding Electrostatic scanning

Magellan XHR SEM: three beam modes available Schottky- FEG extractor, 2 apertures segmented gun lens aperture and slit deflector Standard High current Monochromated (UC)

Performance improvement with monochromator Beam voltage 1 kV Improved resolution More current (better S/N) Chromatic Spherical UC allows larger α therefore lower diffraction (d d ) Diffraction effects dominate everything at low aperture angles… The chromatic and spherical aberration contributions dominate at high aperture angles…

Magellan: Resolution improvement UC off and on 1 kV, no beam deceleration 256 nm HFW in both cases UC offUC on

Beam deceleration: enhancing resolution and contrast If Bias=0 (no BD): Landing V = HV What is beam deceleration? New optics mode enabling high resolution imaging and high surface sensitivity at very low kV BD specifications: Landing energy range: 30 keV down to 50 eV The deceleration (Bias) can be continuously adjusted by the user Benefits: Enhances the resolution Provides additional contrast options Greatest benefit at 2kV and below Bias HV Landing V Beam vCD Sample TLD 2-mode final lens

Extending low kV resolution via UC and BD 50 V with 1 kV beam deceleration 850 nm HFW 50 V

Practical considerations: Must optimize:  Instrument alignment (gun, lenses, apertures)  Minimum vibration  Minimum stray fields  Specimen contamination  Clean apertures Then go for minimum spot size if resolution is the goal However, ultimate resolution depends on the detected signal, a function of: Minimum spot size AND Emission volume of signal…beam-specimen interactions

SEM variables and secondary electron imaging – essential tradeoffs Res. DOF S/N charge Higher Voltage (kV) Higher Current Longer WD Larger Obj. Aperture decrease increase Arrows illustrate result (increase or decrease) on increasing kV, current, working distance, or objective aperture diameter Metal coat C-coat Res. = resolution DOF = Depth-of-Field S/N = Signal/noise Charge = propensity for charging Complex