Manetic Lenses Manetic fields can displace electrons Manetic field can be produced by passin an electrical current throuh coils of wire Manetic field strenth can be increased by usin a soft ferromanetic core like Fe. Current in coil ~ 0 1 A Iron core/shroud F = e (v x B) Electron initially unaffected by B ax, but feels force B rad ev pushes it into a helix. Now v has component perpendicular to axis B ax pushes it into tihter helix. Imae rotates! Manetic field nearly parallel to electron trajectory It is impossible to produce a perfect EM lens only approximates to Maxwell lens when electrons are close to axis. B ax rows as electron approaches middle of ap path narrows and focuses about optic axis Electrons Interactions with Matter N = number of scatterin particles per unit volume Scatterin cross section, σ: area which the scatterin particle appears to present to the electron p = N σdx p = probability of scatterin N = number of particles per unit volume dx = distance throuh specimen Mean free path, λ: averae distance an electron will travel before bein scattered in a particular way λ = 1/(N σ) p (n) = (1/n! )(x/λ) n exp(-x/λ) Poisson equation - Assumes multiple scatterin by same process not very accurate Interaction volume: reion into which the electrons penetrate the specimen
Electrons Interaction Volume Incident (primary) beam d SEM 1µm Secondary electrons Backscattered electrons X-rays TEM (d +b ) ½ 100nm Numerous scatterin events widen diameter of interaction volume Depth increases as Voltae increases Depth decreases as Z increases b = 0.00807(Z /E )(N v ) 1/ t 3/ (TEM) b [nm], Z [atomic number], E [kev], N v [atoms/nm 3 ], t [nm] Electron Scatterin Inelastic Scatterin: Any process which causes the primary electron to lose a detectable amount of enery Elastic Scatterin: Any scatterin process which results in no measurable chane to the enery of the primary electron Characteristic x-ray or Backscattered electron primary electrons cathodoluminescence Auer electron ejected secondary electron ejected secondary electron primary electron primary electron
Inelastic Scatterin Phonon scatterin ~ 1 ev per interaction, but heatin can be considerable, especially at hih kv. Not a problem in ood conductors ( T ~ 10 C), but can melt Al O 3 (T m > 000 C) Lare deflection (hih-anle) of electron (~10 ) diffuse intensity. Plasmon scatterin ~ 5 30 ev per interaction and small mean free path (very common) Contributes some diffuse intensity around transmitted spot. Important in Auer and EELS studies. Phonon: quantum of atomic vibration Plasmon: wave in the sea of conduction-band electrons Sinle valence-electron excitation ~ 1 ev per interaction, but very lare mean free path (microns) and small scatterin anle Primary electron transfers enery to a sinle conduction-band electron rather than entire sea Not exploited in electron microscopy Inner shell excitation leadin to characteristic x-ray production 100s 1000s ev per interaction, lare mean free path (µm) Primary electron transfers enouh enery to an inner electron (K, L) to knock it out Outer electron drops down to fill the hole releasin a characteristic quantum of enery λ increases as V increases (more likely to pass throuh without interactin) λ increases as Z increases (critical enery, E c, required to produce an x-ray increases) 83 ev for Carbon K (Z = 6), 69,508 ev for Tunsten K (Z = 74) Produced throuhout interaction volume, and virtually all escape from the surface Smallest reion which can be analysed by SEM ~ 1 µm. σ α 1 E c E o Fluorescence yield, w = Z 4 / (Z 4 + c) Much hiher for lare Z c ~ 10 6 for K Inelastic Scatterin Cont Inner shell excitation leadin to characteristic (Auer) electron production Alternative to x-ray emission Primary electron loses some enery to inner-shell electron, which is knocked out of the atom One outer electron falls into the hole left behind Another outer electron carries off E as kinetic enery Yield increases for low Z, so have low eneries and only escape from top ~1 nm of specimen Important surface analysis technique, but require very hih vacuum sytem Auer electrons are outer electrons and so contain information about bondin Auer yield = 1 - w Outer shell excitation leadin to cathodoluminescence (CL) Similar to inner-shell excitation, but enery of resultin photon is lower (typically visible or UV) Emission from semiconductors and insulators is modified by presence of defects (e.., dislocations) Excitation of outer electrons leadin to emission of low-enery secondary electrons Eneries < 50 ev, so can escape from top ~ 10 nm of specimen - toporaphical either primary electrons multiply scattered or (more probably) electrons created by a process above Edes, corners, and areas tilted towards detector appear briht yield can be > 1 hih yield primary beam low yield specimen shadowin
Inelastic Scatterin Bremsstrahlun x-rays (bremsen = to brake, Strahlun = radiation) primary electrons are decelerated and deflected by Coloumb field of atoms in specimen KE transformed into x-rays Mixture of x-rays with many wavelenths no use in microanalysis unwanted backround radiation Inelastic Scatterin Absorption Penetration depth/mean free path determines depth of specimen sampled Varies with kev and material, but typically shorter than for x-rays s = s + 1 When specimen is very thick, you won t see an imae. Have electrons been absorbed?? πvc θ Extinction distance: = cos λ F = 1+ s (s = 0) Kinematic: Dynamical: sin (πts) (πs) sin (πts ) (πs ) for s = 0, increases as t sinusoidal variation t Define imainary component of extinction distance: 1 1 1 = + i ~ 10 Dynamical + Absorption: sin (πts ) (πs ) Fude factor! Usable thickness limited to ~5
Inelastic Scatterin Absorption Penetration depth/mean free path determines depth of specimen sampled Varies with kev and material, but typically shorter than for x-rays When specimen is very thick, you won t see an imae. Have electrons been absorbed?? 0 0 = Linear absorption (overall decrease in intensity with increased t) = Anomalous absorption (selective absorption of certain electron waves) Kinematical ( s >> 0): frines are closely spaced and limited to thin reions near the hole. Frines are stroner in the DF than in BF (i.e., they are non-complimentary), and the contrast from defects is low. Dynamical (s = 0): frines are broader with reasonably complimentary BF and DF imaes. Defect contrast is stron and the best defect imaes occur just as frines damp out. Rockin Curve sin (πts ) (πs ) πvc = cosθ λ F s = s + 1 (s = 0) Intensity of Diffracted Beam t/ = 1.5 / ' = 0.1 / o' = 0.1-0.04-0.0 0 0.0 0.04 Deviation Parameter (nm -1 ) I is periodic in t and s. If t is constant and s is varied bend contours Dark-Field bend contours in Pb 3 Nb O 8
Thickness Frines If s is constant and t is varied thickness frines sin (πts ) (πs ) s = s + 1 Intensity of Diffracted Beam 0 100 00 300 400 Thickness (nm) = 100 nm / ' = 0.1 / o' = 0.1 w = 0 (s = 0) Effective extinction distance w = w= s 1+ w When other diffracted beams are present, the ective is reduced. Elastic Scatterin Rutherford Scatterin Coulombic interactions between primary electrons and atoms in specimen Probability (per unit area) of scatter: n = atoms per unit volume in taret L = thickness of taret Z = atomic number of taret e = electron chare k = Coulomb s constant, 1/(4πε o ) r = taret-to-detector distance E = kinetic enery θ = scatterin anle Stronly forward-peaked (small-anle scatter much more probable than lare-anle scatter)
Electron Microscopes All have electron un (source), condenser lens system, and sinal detection SEM also has scannin coils Add EDS and possibly WDS it becomes an analytical SEM Hitachi 4500 SEM Add several WDS spectrometrs and it becomes a Microprobe (EPMA) TEM also requires objective and projector lenses Add scan coils and it becomes a scannin TEM (STEM) Add EDS/EELS and it becomes an analytical TEM/STEM JEOL 100 HR TEM