= 6 (1/ nm) So what is probability of finding electron tunneled into a barrier 3 ev high?

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2 STM

3 STM With a scanning tunneling microscope, images of surfaces with atomic resolution can be readily obtained. An STM uses quantum tunneling of electrons to map the density of electrons on the surface of a sample. The STM works by bringing a metal wire with a sharp tip very close to a conducting surface. The distance is generally on the order of m, a distance corresponding to a few atomic diameters

4 STM This equation predicts that the tunneling current I t decreases exponentially with distance d and increases linearly with voltage potential V t. The function A(E) represents the density of electrons with energy E in the sample

5 Probability goes as Ψ (x) 2 so chance of electron tunneling distance x is: Probability (x) = e -2 k x where k = [2 m (V-E) / ħ 2 ] What would a typical (V-E) " work function barrier" be? Work function energies are typically ~ a few electron-volts (ev = q x Volt = 1.6 x Joules) k ~ [2 m (3 ev) / ħ 2 ] = 6 (1/ nm) So what is probability of finding electron tunneled into a barrier 3 ev high? Probability (x) = e -2 k x e - 2 x (6 / nm) = e -12 x / (1 nm) if x = 0.1 nm then P = e -1.2 = 30% if x = 1 nm then P = e -12 = % if x = 10 nm then P = e -120 = 7 x % So electron tunneling is only measurable up to scales of ~ 1 nm

6 The STM operates in the regime of extremely small distances between the tip and the surface of only 0.5 to 1.0 nm, i.e. 2 to 4 atomic diameters. Feedback The STM tip is attached to a piezo-electric element. This is a piece of material with the useful property that it changes its length a little bit, when it is put under an electrical voltage. By adjusting the voltage on the piezo element, the distance between the tip and the surface can be regulated. In most STMs, the voltage on the piezo element is adjusted such, that the tunneling current always has the same value, for example 1 na. In this way, the distance between the last atom on the tip and the nearest atoms in the surface is being kept constant. This distance regulation is performed automatically, by socalled feedback electronics, which continually measure the deviation of the tunneling current from the desired value e.g. 1 na and retract the tip when the current is too high or advance it when the current is too low.

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9 Electronics The circuit that is used for the feedback electronics schematically looks as follows. The tunneling current It, which is typically 1 na, is converted by a so-called pre-amplifier to an ordinary voltage Vt. Often the conversion is such that a current It of 1 na at the input of the preamplifier results in a voltage Vt of 1 V at the output. In the next step, this voltage Vt is amplified logarithmically. Because the tunneling current and therefore also the voltage Vt is an exponential function of the distance d between the tip and the surface, the logarithm of the voltage Vt is a measure for the distance between the tip and the surface. We refer to the result of the logarithmic conversion as Vlog. The relation between Vlog and the distance d is then Vlog=a + b d, where a and b are constants. From this voltage Vlog we subtract a reference voltage Vref. This reference value can be chosen at will. It forms a measure for the tip-surface distance that we want to work at. When the difference voltage between Vlog and Vref is equal to zero, the tip-surface distance is precisely right. When the difference is positive, the distance is too small; and when it is negative, the distance is too large. This difference voltage forms the input for a high-voltage amplifier, which amplifies it very strongly and passes it on to the piezo element, with which we control the height of the tip. This closes the feedback loop and makes the system complete. Many extra elements are necessary to make the feedback circuit work in practice. Examples are appropriate filters, to avoid spontaneous ringing of the STM, and combinations of linear, integrating and differentiating amplifiers, in order to obtain a more ideal response.

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13 The Interaction of a Tip and the Sample Lennard-Jones potential The forces in SFM in the absence of added magnetic or electrostatic potentials are governed by the interaction potentials between atoms. The interaction is attractive at large distances due to the van-der-waals interaction. At short distances repulsion originates between electrons when one atom tries to penetrate another. The repulsive forces have their origin in the quantum mechanical exclusion principle, which states that no two fermions can be in exactly the same state, that is to say have the same spin, angular momentum, z-component of the angular momentum and location

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19 (Note: all samples unless in a controlled UHV or environmental chamber have some liquid adsorbed on the surface).

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28 Diffraction limits

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33 Bright field

34 Dark field

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40 TEM - The transmission electron microscope can be compared with a slide projector. In the latter, light from a light source is made into a parallel beam by the condenser lens; this passes through the slide (object) and is then focused as an enlarged image onto the screen by the objective lens. - In the electron microscope, the light source is replaced by an electron source (a tungsten filament heated in vacuum), the glass lenses are replaced by magnetic lenses and the projection screen is replaced by a fluorescent screen which emits light when struck by electrons. - The whole trajectory from source to screen is under vacuum and the specimen (object) has to be very thin to allow the electrons to penetrate it. - Typically, the specimen must be no thicker than a few hundred nanometres

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42 Electron Density How many electrons impinge on the specimen? A typical electron beam has a current of about 1 picoampere (10 12 A). One ampere is 1 coulomb/sec. The electron has a charge of 1.6 x coulomb. Therefore approximately 6 million electrons per second impinge on the specimen.

43 When electrons impinge on the specimen, a number of things can happen: a. Some of the electrons are absorbed as a function of the thickness and composition of the specimen; these cause what is called amplitude contrast in the image. b. Other electrons are scattered over small angles, depending on the composition of the specimen; these cause what is called phase contrast in the image. c. In crystalline specimens, the electrons are scattered in very distinct directions which are a function of the crystal structure; these cause what is called diffraction contrast in the image. d. Some of the impinging electrons are reflected (these are called backscattered electrons). e. The impinging electrons can cause the specimen itself to emit electrons (these are called secondary electrons). f. The impinging electrons cause the specimen to emit X-rays whose energy and wavelength are related to the specimen s elemental composition. g. Finally, electrons which have lost an amount of energy because of interaction with the specimen can be detected by an Energy Loss Spectrometer which is the equivalent of a prism in light optics. h. Some of the electrons lose energy when they travel through the specimen. This loss of energy can be measured with an Electron Energy Loss Spectrometer (EELS). This detector is mounted under the projection chamber of the TEM. In a standard TEM the first two phenomena contribute to the formation of the normal TEM image for non-crystalline (biological) specimens, while for crystalline specimens, phase contrast and diffraction contrast are the most important factors in image formation It is necessary to add accessories or peripheral equipment in order to exploit the additional information which can be obtained by studying the last four interactions listed above.

44 SEM A scanning electron microscope, like the TEM, consists of an electron optical column, a vacuum system and electronics. The column is considerably shorter because there are only three lenses to focus the electrons into a fine spot (< 10 nm) onto the specimen; in addition there are no lenses below the specimen. The specimen chamber, on the other hand, is larger because the SEM technique does not impose any restriction on specimen size other than that set by the size of the specimen chamber The most important differences between TEM and SEM are: a. the beam is not static as in the TEM: with the aid of an electromagnetic field, produced by the scanning coils, the beam is scanned line by line over an extremely small area of the specimen s surface; b. the accelerating voltages are much lower than in TEM because it is no longer necessary to penetrate the specimen; in a SEM they range from 200 to volts. c. specimens need no complex preparations.

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48 Electron Gun - The electron gun comprises a filament, a so-called Wehnelt cylinder and an anode. - These three together form a triode gun which is a very stable source of electrons. - The tungsten filament is hairpin-shaped and heated to about 2700 O C. - By applying a very high positive potential difference between the filament and the anode, electrons are extracted from the electron cloud round the filament and accelerated towards the anode. - The anode has a hole in it so that an electron beam in which the electrons are travelling at several hundred thousand kilometres per second emerges at the other side. - The Wehnelt cylinder which is at a different potential, bunches the electrons into a finely focused point. Electron Velocity The higher the accelerating voltage, the faster the electrons. 80 kv electrons have a velocity of km/s (1.5 x 10 8 m/s) which is half the speed of light. This rises to m/s for 300 kv electrons (2.3 x 10 8 m/s more than three-quarters the speed of light).

49 Apply a small negative bias between the filament and the Wehnelt cap which houses the filament. With no bias (i) there is high emission current, but that current has a high divergence angle or spread. A very high bias (iii) will actually retard the emission of electrons. The optimum bias level (ii) will take the emitted electrons and produce a crossover point (gun source) of small diameter -- a saturated electron cloud Producing a small gun source or crossover has several benefits: An electron beam emanating from a small source size is said to have high spatial coherency. That is, the waves emanating from the source point are in phase with one another. High spatial coherence of the illuminating beam will enhance the contrast producing mechanisms in the TEM. Also, by using the bias to form a small source size we are putting the emission current into a smaller area and thus maximizing the brightness of the electron beam. With greater brightness we can have a smaller diameter beam on the specimen and still have adequate current for signal production. The result is higher magnification imaging capabilities. Brightness, unlike current, is conserved down the column. Brightness increases linearly with accelerating voltage.

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51 The brightness equation

52 Resolution and brightness

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56 Thermal emission Field emission

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64 Cross-section of an electromagnetic lens.

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67 Lens Aberrations Aperture diffraction aberration

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72 What happens in the specimen during electron bombardment? When discussing the TEM, it was seen that when electrons strike the specimen several phenomena occur. In general, five of these phenomena are used in an ordinary SEM. a. The specimen itself emits secondary electrons. b. Some of the primary electrons are reflected (backscattered electrons). c. Electrons are absorbed by the specimen. d. The specimen emits X-rays. e. The specimen sometimes emits photons (= light). All these phenomena are interrelated and all of them depend to some extent on the topography, the atomic number and the chemical state of the specimen. The number of backscattered electrons, secondary electrons and absorbed electrons at each point of the specimen depends on the specimen s topography to a much greater extent than the other properties mentioned. It is for this reason that these three phenomena are exploited primarily to image the specimen s surface. Detectors for backscattered electrons and secondary electrons are usually either a scintillation detector or a solid state detector

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79 Illustration of the universal curve for electron attenuation in solids as a function of electron kinetic energy

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