Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1,
Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1,
The requirements of the illumination system High electron intensity – Image visible at high magnifications Small energy spread – Reduce chromatic aberrations effect in obj. lens Adequate working space between the illumination system and the specimen High brightness of the electron beam – Reduce spherical aberration effects in the obj. lens
The electron gun The performance of the gun is characterised by: – Beam diameter, d cr – Divergence angle, α cr – Beam current, I cr – Beam brightness, β cr at the cross over Cross over α d Image of source
Brightness Brightness is the current density per unit solid angle of the source β = i e /(πd c α c ) 2 Cross over α d Image of source
The electron source Two types of emission sources – Thermionic emission W or LaB6 – Field emission W ZnO/W Cold FEG Schottky FEG
The electron gun Bias -200 V Ground potential -200 kV Anode Wehnelt cylinder Cathode d cr Cross over α cr Equipotential lines Thermionic gun FEG
Thermionic guns Filament heated to give Thermionic emission -Directly (W) or indirectly (LaB 6 ) Filament negative potential to ground Wehnelt produces a small negative bias -Brings electrons to cross over
Thermionic emission Current density: – Ac: Richardson’s constant, material dependent – T: Operating temperature (K) – φ: Work function (natural barrier that prevents electrons from leaving the solid) – k: Boltzmann’s constant J c = A c T 2 exp(-φ c /kT) Richardson-Dushman Maximum usable temperature T is determined by the onset of the melting/evaporation of material.
Field emission Current density: Fowler-Norheim Maxwell-Boltzmann energy distribution for all sources
Field emission The principle: – The strength of an electric field E is considerably increased at sharp points. E=V/r r W < 0.1 µm, V=1 kV → E = V/m – Lowers the work-function barrier so that electrons can tunnel out of the tungsten. Surface has to be pristine (no contamination or oxide) – Ultra high vacuum condition (Cold FEG) or poorer vacuum if tip is heated (”thermal” FE; ZrO surface tratments → Schottky emitters).
Characteristics of principal electron sources at 200 kV WLaB 6 FEG Schottky (ZrO/W) FEG cold (W) Current density J c (A/m 2 )2-3* *10 4 1*10 7 Electron source size (µm) Emission current (µA) ~100 Brightness B (A/m 2 sr)5*10 9 5* *10 12 Energy spread ΔE (eV) ~0.80.3~0.7 Vacuum pressure (Pa)* Gun temperature (K) * Might be one order lower
Advantages and disadvantages of the different electron sources W Advantages:LaB 6 advantages:FEG advantages: Rugged and easy to handleHigh brightnessExtremely high brightness Requires only moderate vacuum High total beam currentLong life time, more than 1000 h. Good long time stabilityLong life time ( h) High total beam current W disadvantages: LaB 6 disadvantages:FEG disadvantages: Low brightnessFragile and delicate to handle Very fragile Limited life time (100 h)Requires better vacuumCurrent instabilities Long time instabilitiesUltra high vacuum to remain stable
Electron lenses Electrostatic – Require high voltage - insulation problems – Not used as imaging lenses, but are used in modern monochromators or deflectors Magnetic – Can be made more accurately – Shorter focal length F= -eE F= -e(v x B) Any axially symmetrical electric or magnetic field has the properties of an ideal lens for paraxial rays of charged particles.
General features of magnetic lenses Focuses near-axis electron rays with the same accuracy as a glass lens focuses near axis light rays. Same aberrations as glass lenses. Converging lenses. The bore of the pole pieces in an objective lens is about 4 mm or less. A single magnetic lens rotates the image relative to the object. Focal length can be varied by changing the field between the pole pieces (changing magnification).
Electromagnetic lens Bore Soft Fe pole piece gap Cu coil Current in the coil creates A magnetic field in the bore. The magnetic field has axial symmetry, but is inhomogenious along the length of the lens. The soft iron core can increase the field by several thousand times.
Electron ray paths through magnetic fields B See fig 6.9 r θ v v2 v1 The electron spirals through the lens field: A helical trajectory. For electrons with higher keV, we must use stronger lenses (larger B) to get similar ray paths.
Simple ray diagrams Electron lenses act like a convex glas lens Thin lens β: variable giving the fraction of rays collected by the lens ~ 10 m rad ~0.57 o β α Point obj Point image Never a perfect image
Changing the strength of the lens The further away rays are from the optical axis the stronger they are bent by a convex lens. What happens to the focal and image plane when the strength of the lens is changed? What happens to the image?
Under conditions normally found in the TEM, strong lenses magnify less and demagnify more (not in VLM). When do we want to demagnify an object? The strength of the lens
Spherical aberration d s = 0.5MC s α 3 (disk diameter, plane of least confusion) d s = 2MC s α 3 (disk diameter, Gaussian image plane) M: magnification C s :Spherical aberration coefficient α: angular aperture/ angular deviation from optical axis r1r1 r2r2 Plane of least confusion α Gaussian image plane 2000FX: C s = 2.3 mm 2010F: C s = 0.5 nm Highest intensity in the Gaussian image plane
Chromatic aberration v v - Δ v Diameter for disk of least confusion: d c = C c α ((ΔU/U) 2 + (2ΔI/I) 2 + (ΔE/E) 2 ) 0.5 C c : Chromatic aberration coefficient α: angular divergence of the beam U: acceleration voltage I: Current in the windings of the objective lens E: Energy of the electrons 2000FX: C c = 2.2 mm 2010F: C c = 1.0 mm Thermally emitted electrons: ΔE/E=kT/eU, LaB 6 : ~1 eV Disk of least confusion The specimen will introduce chromatic aberration. The thinner the specimen the better!! Correcting for Cc effects only makes sense if you are dealing with specimens that are thin enough.
Lens astigmatism Loss of axial symmetry y-focus x-focus y x This astigmatism can not be prevented, but it can be corrected! Disk of least confusion Diameter of disk of least confusion: d a : Δfα Due to non-uniform magnetic field as in the case of non-cylindrical lenses. Apertures may affect the beam if not precisely centered around the axis.
Depth of focus and depth of field (image) Imperfections in the lenses limit the resolution but give a better depth of focus and depth of image. – Use of small apertures to minimize aberrations. The depth of field (Δb or D ob ) is measured at, and refers to, the object. – Distance along the axis on both sides of the object plane within which the object can move without detectable loss of focus in the image. The depth of focus (Δa, or D im ), is measured in, and referes to, the image plane. – Distance along the axis on both sides of the image plane within which the image appears focused.
α im D ob D im d ob d im Depth of focus and depth of field (image) β ob Ray 1 and 2 represent the extremes of the ray paths that remain in focus when emerging ± D ob /2 either side of a plane of the specimen. α im ≈ tan α im = (d im /2)/(D ob /2) β ob ≈ tan β ob = (d ob /2)/(D im /2) Angular magnification: M A = α im / β ob Transvers magnification: M T = d im / d ob M T = 1/M A Depth of focus: D im =(d ob / β ob )M T 2 Depth of field: D ob = d ob / β ob α im ≈ tan α im = (d im /2)/(D ob /2) β ob ≈ tan β ob = (d ob /2)/(D im /2) Angular magnification: M A = α im / β ob Transvers magnification: M T = d im / d ob M T = 1/M A Depth of focus: D im =(d ob / β ob )M T 2 Depth of field: D ob = d ob / β ob
Depth of field: D ob = d ob / β ob Carefull selection of β ob Thin sample: β ob ~10 -4 rad Thicker, more strongly scattering specimen: β ob (defined by obj. aperture) ~10 -2 rad Depth of field Example: d ob / β ob = 0.2 nm/10 mrad = 20 nm Example: d ob / β ob = 2 nm/10 mrad = 200 nm D ob = thickness of sample all in focus D ob = thickness of sample all in focus
Depth of focus Depth of focus: D im =(d ob / β ob )M T 2 Example: To see a feature of 0.2 nm you would use a magnification of ~ x (d ob / β ob )M 2 = 20 nm *(5*10 5 ) 2 = 5 km Example: To see a feature of 0.2 nm you would use a magnification of ~ x (d ob / β ob )M 2 = 20 nm *(5*10 5 ) 2 = 5 km Example: To see a feature of 2 nm you would use a magnification of ~ x (d ob / β ob )M 2 = 200 nm *(5*10 4 ) 2 = 500 m Example: To see a feature of 2 nm you would use a magnification of ~ x (d ob / β ob )M 2 = 200 nm *(5*10 4 ) 2 = 500 m Focus on the wieving screen and far below! Focus on the wieving screen and far below!
Fraunhofer and Fresnel diffraction Fraunhofer diffraction: far-field diffraction – The electron source and the screen are at infinite distance from the diffracting specimen. Flat wavefront Fresnel diffraction: near-field diffraction – Either one or both (electron source and screen) distances are finite. Electron diffraction patterns correspond closely to the Fraunhofer case while we ”see” the effect of Fresnel diffraction in our images.
Airy discs (rings) Fraunhofer diffraction from a circular aperture will give a series of concentric rings with intensity I given by: I(u)=I o (J I (πu)/ πu) 2
Strengths of lenses and focused image of the source If you turn up one lens (i.e. make it stronger, or ‘over- focus’ then you must turn the other lens down (i.e. make it weaker, or ‘under-focus’ it, or turn its knob anti-clockwise) to keep the image in focus.
Magnification of image, Rays from different parts of the object If the strengths (excitations) of the two lenses are changed, the magnification of the image changes
The Objective lens Often a double or twin lens The most important lens – Determines the resolving power of the TEM All the aberations of the objective lens are magnified by the intermediate and projector lens. The most important aberrations – Astigmatism – Spherical – Chromatic
Astigmatism Can be corrected for with stigmators
Cs can be calculated from information about the shape of the magnetic field – Cs has ~ the same value as the focal length (see table 2.3) The objective lens is made as strong as possible – Limitation on the strength of a magnetic lens with an iron core (saturation of the magnetization Ms) – Superconductiong lenses (give a fixed field, but need liquid helium cooling) The objective lens
We use apertures in the lenses to control the divergence or convergence of electron paths through the lens which, in turn, affects the lens aberrations and controls the current in the beam hitting the sample.
A.E. GunnæsMENA3100 V08 Use of apertures Condenser apertures: Limit the beam divergence (reducing the diameter of the discs in the convergent electron diffraction pattern). Limit the number of electrons hitting the sample (reducing the intensity). Objective apertures: Control the contrast in the image. Allow certain reflections to contribute to the image. Bright field imaging (central beam, 000), Dark field imaging (one reflection, g), High resolution Images (several reflections from a zone axis).
BF image Objective aperture Objective aperture: Contrast enhancement All electrons contribute to the image. Si Ag and Pb glue (light elements) hole Only central beam contributes to the image. Bright field (BF)
Small objective aperture Bright field (BF), dark field (DF) and weak-beam (WB) BF image Objective aperture DF imageWeak-beam Dissociation of pure screw dislocation In Ni 3 Al, Meng and Preston, J. Mater. Scicence, 35, p , Diffraction contrast
Large objective aperture High Resolution Electron Microscopy (HREM) HREM image Phase contrast
Use of apertures Condenser aperture: It limits the beam divergence (reducing the diameter of the discs in the convergent electron diffraction pattern). It limits the number of electrons hitting the sample (reducing the intensity). Objective aperture: It controls the contrast in the image. It allows certain reflections to contribute to the image. Bright field imaging (central beam, 000), Dark field imaging (one reflection, g), high resolution images (several reflections from a zone axis). Selected area aperture: It selects diffraction patterns from small (> 1µm) areas of the specimen. It allows only electrons going through an area on the sample that is limited by the SAD aperture to contribute to the diffraction pattern (SAD pattern).
Selected area diffraction Objective lense Diffraction pattern Image plane Specimen with two crystals (red and blue) Parallel incoming electron beam Selected area aperture Pattern on the screen
Diffraction with no apertures Convergent beam and Micro diffraction (CBED and µ-diffraction) Convergent beam Focused beam Convergent beam Illuminated area less than the SAD aperture size. CBED pattern µ-diffraction pattern C2 lens Diffraction information from an area with ~ same thickness and crystal orientation Small probe
Magnification and calibration MicroscopeLensModeMagnification JEM-2010ObjectiveMAG LOW MAG Philips CM30TwinTEM Super twinTEM TwinSA Super twinSA Resolution of the photographic emulsion: µm Magnification depends on specimen position in the objective lens Magnification higher than x can be calibrated by using lattice images. Rotation of images in the TEM.