Optical Microscope Plan Lenses In an "ideal" single-element lens system all planar wave fronts are focused to a point at distance f from the lens; therefore: Image near the optical axis will be in perfect focus on a flat image sensor/screen. Non-axial rays will come into focus before the image sensor. This problem is reduced when the imaging surface is curved, as in the eye. φ Most current photographic lenses are designed to minimize field curvature (plan lenses), and so effectively have a focal length that increases with ray angle. f = f 0 /cosφ
Achromatic Lenses f (focal length) = f(µ) µ blue > µ red (dispersion) Chromatic aberration means that a lens will not focus different colors in exactly the same place because the focal length depends on refraction and the index of refraction for blue light (short λ) is larger than that of red light (long λ). The amount of chromatic aberration depends on the dispersion of the glass. Image Formation Three ways to form an image: Projection (shadow) Optical (with lenses) } all parts of image simultaneously Scanning Three requirements for image formation: Brightness Contrast Resolution
Visible Spectrum Electrons vs Light Electron Optics 4000 nm λ 7000 Å Wavelength of a photon is inversely proportional to its energy, λ = ch/e hν e- 100 Å λ 2000 Å X-Rays Wavelength of an electron is dependent on its energy (accelerating voltage) JEOL 2100-HR TEM: Hitachi 4500 SEM: λ = 0.0251 Å (200 kv) 5 orders of magnitude } smaller than for visible light! λ = 0.0859 Å (20 kv) Electrons Electrons are much more strongly scattered by matter (EM operates in vacuum) Lenses are magnetic fields (n = 1) Electrons carry a charge r d = 0.61λ α Electrons vs Light Electron Optics hν e- Compared to optical microscopy, electron microscopy offers the following advantges: Higher resolution Higher magnification Greater depth of field Crystallographic information Chemical analysis
Electron Generation β - The illumination system in an EM consists of a source of electrons (electron gun) and a lens system to focus and control emitted electrons. Electron guns overcome the work function of the electrons by either resistive heating or a strong electric field (or both). Thermionic Emission: A heated wire or crystal is given enough thermal energy to overcome work function (Edison Effect) plus an electric potential (0.5 300 kv) to accelerate the electrons. Tungsten (hairpin) W has very high T m (3422 C) so can have more thermal energy But work function still high (φ = 4.5 ev) even at operating T 2500 C Cheap ($30) Hitachi S-3400N SEM LaB 6 /CeB 6 Lower work function (φ = 2.5 ev) than W at operating T 1500 C, so it is easier to pull electrons off and can have beams 30 times brighter than with W hairpin. Require high vacuum, suffer from thermal shock, and are expensive ($1000). Higher T causes increased volatilisation and premature failure. T m (LaB 6 ) = 2530 C, T m (CeB 6 ) = 2540 C. JEOL 2100 HR TEM, CAMECA SXFive EPMA Electron Generation Field Effect Emission: The field effect gun (FEG) uses a W single crystal and high field (> 10 9 V/m), which lowers the height of the potential barrier via the Schottky effect. In addition, if the field is sufficiently high, the width of the potential barrier becomes small enough to allow electrons to escape via tunnelling (field emission). Field reduces the work function by φ = 3.8x10-5 F ½ ev Cold FEG operates at room temperature, but requires flashing Thermally-Assisted FEG (Schottky emitter) pointed W crystal (coated with ZrO 2 ) is welded to V-shaped W filament and heated to 1500 C ZrO 2 lowers work function (φ = 2.8 ev) improved stability and no flashing enhanced emission by giving some thermal energy, which reduces tunneling distance (really a field-assisted thermionic source) FEI Teneo F-SEM
Thermionic Emission Current density at filament surface: j = AT 2 e -φ/kt [A/m 2 ] A = 1.20173x10 6 [A/m 2 /K 2 ] (Richardson s constant) T = absolute temperature [K] increases rapidly as T increases & φ decreases (so use high-t m low-φ material W) Brightness: B = j/(πα 2 ) (j = beam current density, α = convergence semi-angle) Example: (at cross-over: Langmuir equation): B = (jv)/(πkt) [A/m 2 /sr] V = voltage [V] k = 8.617x10-5 ev/k For W (φ = 4.5 ev) operating at T = 2500 K and V = 100 kv: j = (1.20173x10 6 A/m 2 K 2 )(2500 K) 2 exp(-4.5 ev/[(8.617x10-5 ev/k)(2500 K)] = 6364 A/m 2 B = (6364 A/m 2 )(100000 ev)/[(π sr)(8.617x10-5 ev/k)(2500 K)] = 9.4035x10 8 A/m 2 /sr ~9x10 4 A/cm 2 /sr Field Effect Emission Current density = j = 6.2x10-10 (E f /φ) ½ F 2-6.8x10 exp 9 φ 3/2 Acm -2 E f + φ F Temperature-independent E f 5 ev for W at R.T. For a field F > 5x10 9 V/m, field emission exceeds thermionic emission. To apply such a high field, W has to be prepared as a sharp point of diameter 100 nm, which makes it very delicate; therefore, ultra-high vacuum systems (10-8 10-9 torr) are necessary adds cost (JEOL 2100 LaB 6 TEM operates at 10-7 torr). Low energy spread (δe 0.3 ev) for improved resolution and better interpretation of EELS data More coherence Highly sensitive to contamination - cold FEG must be flashed every few hours
Brightness increases linearly with voltage. Electron Generation A comparison of electron emission characteristics of W, LaB 6, CeB 6 and FEG guns W wire LaB 6 <100> CeB 6 <100> FEG (cold) FEG (Schottky) Operating temperature ( C) 2500 1500 1500 27 1500 Work function (ev) 4.5 2.7 ~2.5 4.5 2.8 Emission current density (A/cm 2 ) 3 30 30 17,000 5,300 Brightness (A cm -2 sr -1 ) 10 4 10 5 10 5 2x10 7 10 7 Crossover diameter (mm) 30 10 10 0.01 0.02 Short-term beam current stability (%RMS/hr) <1 <1 <1 3-5 <1 Energy spread at 100 kv (ev) 2 1.5 1.5 0.2-0.4 0.5 Typical service life (hr) 30-100 1000 1,500 10 3 10 4 10,000 Operating vacuum (torr) 10-5 10-7 10-7 10-10 10-9 Evaporation rate (g cm -2 s -1 ) NA 2.2 x 10-9 1.6 x 10-9 NA NA Resolution determined largely by diameter of beam and δe Thermionic guns have large areas of emission beam is demagnified x10-4 very stable and insensitive to contamination Cold FEG has small area of emission beam is reduced just 5-10x to 1 nm unstable and very sensitive to contamination, but nearly coherent End of Lecture Yes, in your face! I found Waldo! Goodfellow Cartoon Caption Contest, September 2012 First place: Daniel Glover, Ohio