The transmission electron microscope Additional web resources http

The transmission electron microscope

Additional web resources • http: //nanohub. org/resources/3777 – Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1, http: //nanohub. org/resources/3907

Simplified ray diagram Parallel incoming electron beam 3, 8 Å Si Sample 1, 1 nm Objective lense Diffraction plane Objective aperture (back focal plane) Image plane MENA 3100 V 08 Selected area aperture

Illumination system JEOL 2000 FX Mini-lens screws Specimen Intermediate lens shifting screws Projector lens shifting screws Wehnelt cylinder Filament Anode Electron gun 1. and 2. beam deflectors 1. and 2. condenser lens Condenser aperture Condenser lens stigmator coils Condenser lens 1. and 2. beam deflector Condenser mini-lens Objective lens pole piece Objective aperture Objective lens pole piece Objective lens stigmators 1. Image shift coils Objective mini-lens coils (low mag) 2. Image shift coils 1. , 2. and 3. Intermediate lens Projector lens beam deflectors Projector lens Screen

Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1, http: //nanohub. org/resources/3907

Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1, http: //nanohub. org/resources/3907

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, dcr Divergence angle, αcr Beam current, Icr Beam brightness, βcr at the cross over d Cross over α Image of source

Brightness • Brightness is the current density per unit solid angle of the source • β = ie/(πdcαc)2 d Cross over α Image of source

The electron source • Two types of emission sources – Thermionic emission • W or La. B 6 – Field emission • W Cold FEG Zn. O/W Schottky FEG

The electron gun Thermionic gun FEG Wehnelt cylinder Bias -200 V Cathode -200 k. V Equipotential lines Anode Ground potential dcr Cross over αcr

Thermionic guns Filament heated to give Thermionic emission -Directly (W) or indirectly (La. B 6) Filament negative potential to ground Wehnelt produces a small negative bias -Brings electrons to cross over

Thermionic guns

Thermionic emission • Current density: Jc= Ac. T 2 exp(-φc/k. T) Richardson-Dushman – – 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 Maximum usable temperature T is determined by the onset of the melting/evaporation of material.

Field emission • Current density: Maxwell-Boltzmann energy distribution for all sources Fowler-Norheim

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 k. V → E = 1010 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; Zr. O surface tratments → Schottky emitters).

Characteristics of principal electron sources at 200 k. V W La. B 6 FEG Schottky (Zr. O/W) FEG cold (W) Current density Jc (A/m 2) 2 -3*104 25*104 1*107 Electron source size (µm) 50 10 0. 1 -1 0. 010 -0. 100 Emission current (µA) 100 20~100 Brightness B (A/m 2 sr) 5*109 5*1010 5*1012 Energy spread ΔE (e. V) 2. 3 1. 5 0. 6~0. 8 0. 3~0. 7 Vacuum pressure (Pa)* 10 -3 10 -5 10 -7 10 -8 Gun temperature (K) 2800 1800 300 * Might be one order lower

Advantages and disadvantages of the different electron sources W Advantages: La. B 6 advantages: FEG advantages: Rugged and easy to handle High brightness Extremely high brightness Requires only moderate vacuum High total beam current Long life time, more than 1000 h. Good long time stability Long life time (500 -1000 h) High total beam current W disadvantages: La. B 6 disadvantages: FEG disadvantages: Low brightness Fragile and delicate to handle Very fragile Limited life time (100 h) Requires better vacuum Current instabilities Long time instabilities Ultra high vacuum to remain stable

Electron lenses Any axially symmetrical electric or magnetic field has the properties of an ideal lens for paraxial rays of charged particles. • Electrostatic F= -e. E – 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= -e(v x B)

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). http: //www. matter. org. uk/tem/lenses/electromagnetic_lenses. htm

Electromagnetic lens Bore Current in the coil creates A magnetic field in the bore. Soft Fe pole piece The magnetic field has axial symmetry, but is inhomogenious along the length of the lens. gap Cu coil The soft iron core can increase the field by several thousand times.

Electron ray paths through magnetic fields r The electron spirals through the lens field: A helical trajectory. θ v B v 2 v 1 For electrons with higher ke. V, we must use stronger lenses (larger B) to get similar ray paths. See fig 6. 9

Simple ray diagrams • Electron lenses act like a convex glas lens • Thin lens Point obj • β: variable giving the fraction β of rays collected by the lens ~ 10 m rad ~0. 57 o α 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?

The strength of the lens • 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?

Spherical aberration Gaussian image plane r 2 α r 1 Highest intensity in the Gaussian image plane Plane of least confusion ds = 0. 5 MCsα 3 (disk diameter, plane of least confusion) ds = 2 MCsα 3 (disk diameter, Gaussian image plane) M: magnification Cs : Spherical aberration coefficient α: angular aperture/ angular deviation from optical axis 2000 FX: Cs= 2. 3 mm 2010 F: Cs= 0. 5 nm

Chromatic aberration Diameter for disk of least confusion: dc = Cc α ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0. 5 v v - Δv Cc: 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 Thermally emitted electrons: ΔE/E=k. T/e. U, Disk of least confusion La. B 6: ~1 e. V The specimen will introduce chromatic aberration. 2000 FX: Cc= 2. 2 mm 2010 F: Cc= 1. 0 mm 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 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. This astigmatism can not be prevented, but it can be corrected! y • Loss of axial symmetry x y-focus x-focus Disk of least confusion Diameter of disk of least confusion: da: Δfα

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 Dob) 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 Dim), 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.

Depth of focus and depth of field (image) 1 dob 1 2 βob dim 2 αim Dob Ray 1 and 2 represent the extremes of the ray paths that remain in focus when emerging ± Dob/2 either side of a plane of the specimen. αim≈ tan αim= (dim/2)/(Dob/2) βob≈ tan βob= (dob/2)/(Dim/2) Angular magnification: MA= αim/ βob Transvers magnification: MT= dim/ dob MT= 1/MA Depth of focus: Dim=(dob/ βob)MT 2 Depth of field: Dob= dob/ βob

Depth of field: Dob= dob/ βob Carefull selection of βob • Thin sample: βob ~10 -4 rad • Thicker, more strongly scattering specimen: βob (defined by obj. aperture) ~10 -2 rad Example: dob/ βob= 0. 2 nm/10 mrad = 20 nm Example: dob/ βob= 2 nm/10 mrad = 200 nm Dob= thickness of sample all in focus

Depth of focus: Dim=(dob/ βob)MT 2 Example: To see a feature of 0. 2 nm you would use a magnification of ~500. 000 x (dob/ βob)M 2= 20 nm *(5*105)2= 5 km Example: To see a feature of 2 nm you would use a magnification of ~50. 000 x (dob/ βob)M 2= 200 nm *(5*104)2= 500 m 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)=Io(JI(πu)/ πu)2 http: //en. wikipedia. org/wiki/Airy_disk

Strengths of lenses and focused image of the source http: //www. rodenburg. org/guide/t 300. html 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 http: //www. rodenburg. org/guide/t 300. html 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

The objective lens • 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)

Apertures

Apertures 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.

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). A. E. Gunnæs MENA 3100 V 08

Objective aperture: Contrast enhancement Bright field (BF) hole glue (light elements) Ag and Pb Objective aperture Si BF image All electrons contribute to the image. Only central beam contributes to the image.

Small objective aperture Bright field (BF), dark field (DF) and weak-beam (WB) Objective aperture BF image Diffraction contrast Weak-beam Dissociation of pure screw dislocation In Ni 3 Al, Meng and Preston, J. Mater. Scicence, 35, p. 821 -828, 2000.

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 Parallel incoming electron beam Specimen with two crystals (red and blue) Objective lense Pattern on the screen Diffraction pattern Image plane Selected area aperture

Diffraction with no apertures Convergent beam and Micro diffraction (CBED and µ-diffraction) Convergent beam Focused beam C 2 lens Convergent beam Illuminated area less than the SAD aperture size. Small probe CBED pattern Diffraction information from an area with ~ same thickness and crystal orientation µ-diffraction pattern

Shadow imaging (diffraction mode) Parallel incoming electron beam Sample Objective lense Diffraction plane (back focal plane) Image plane

Magnification and calibration Resolution of the photographic emulsion: 20 -50 µm Magnification depends on specimen position in the objective lens Microscope Lens Mode Magnification JEM-2010 Objective MAG 2 000 -1 500 000 LOW MAG 50 - Twin TEM 25 - 750 000 Super twin TEM 25 - 1 100 000 Twin SA 3 800 - 390 000 Super twin SA 5 600 - 575 000 Philips CM 30 6 000 Magnification higher than 100 000 x can be calibrated by using lattice images. Rotation of images in the TEM.