Back to de Broglie and the electron as a wave

ph mν

h λ ==

We will soon see that the energies (speed for now if you like) of the electronsin the beams in the microscope are high (v is 70% or more of the speed of light)

you will learn more about thisEquation in CHEM* 2060

This definition of mass could be applied in a straightforward way for almost two centuries until Einstein arrived on the scene. In Einstein's theory of motion known as special relativity, the situation became more complicated. When a body is moving, we find that its force–acceleration relationship is no longer constant, but depends on two quantities: its speed, and the angle between its direction of motion and the applied force. If we relate the force to the resulting acceleration along each of the three mutually perpendicular spatial axes, we find that in each of the three expressions a factor of γ m appears, where the gamma factor γ = (1–v2/c2) –1/2 is a common quantity in special relativity, and m is the body'srest mass. The new quantity γ m is traditionally called the body's relativistic mass.

( Is called the Lorentz factor (see page 123 of text)

Bottom line: this will change the wavelength of the electron 3-1

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So we modify the wavelength according to

8 = h/p = h/(mv

8 = (h/mv)* r(1- v2/c2)The wavelength is also given by a somewhat simpler ploy…..

KE = ½ mv2 = EBut h/8 = mv and so (h/8)2 = (mv)2 = p2

2mE = m2v2 = p2

h2/82 = 2mE

82 = h2/2mE

8 = h / r(2mE)See eqn 3.24

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Electrons and their interaction with matter

• electrons interact with matter in many ways• can be scattered once or more that once• elastic or inelastic effects• can be used for imaging or to get other info (see later)

Exactly what you wantor what you see depends on manExperimental factors

Lets see what this all means

Types of electrons that come off the sample and how they are useful

1. Secondary Electrons

Secondary electrons are electrons generated as ionization products. They are called 'secondary' because they are generated by other radiation (the primary radiation). This radiation can be in the form of ions, electrons, or photons with sufficiently high energy, i.e. exceeding the ionization potential.

Mean free path of low-energy electrons. Secondary electrons are generally considered to have energies below 50 eV. The rate of energy loss for electron scattering is very low, so most electrons released have energies peaking below 5 eV(Seiler, 1983). Secondary electrons are also the main means of viewing images in the SEM. The range of secondary electrons depends on the energy. The distance they originate from is on the order of a few nanometers in metals and tens of nanometers in insulators This small distance allows such fine resolution to be achieved in the SEM.

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Notice how the depth from which the electrons originate is small

Usually gives large depth of field

-image is “clean” 3-5

2. Backscattered ElectronsBackscattered electrons (BSE) consist of high-energy electrons originating in the electron beam, that are reflected or back-scattered out of the specimen interaction volume by elastic interactions with specimen atoms. Since heavy elements (high atomic number) backscatter electrons more strongly than light elements (low atomic number), and thus appear brighter in the image, BSE are used to detect contrast between areas with different chemical compositions.

The image illustrates two different scanning modes of a scanning electron microscope (SEM). In the lower part of the image, we can see the relief of the sample. This is obtained using the detection of secondary electrons. In the upper part of the image, we can see light spots surrounded by darker areas. The light spots correspond to the zirconium aggregates in an aluminum matrix. This is obtained using the detection of backscattered electrons.

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3. Surface Plasmons: don’t worry about these: not used in SEM

4. Auger Electrons: also we will not learn about the Auger effect here5. Bremsstrahlung Radiation

The word Bremsstrahlung is retained from the original German to describe the radiation which is emitted when electrons are decelerated or "braked" when they are fired at a metal target. Accelerated charges give off electromagnetic radiation, and when the energy of the bombarding electrons is high enough, that radiation is in the x-ray region of the electromagnetic spectrum. It is characterized by a continuous distribution of radiation which becomes more intense and shifts toward higher frequencies when the energy of the bombarding electrons is increased.

Considered to be “background radiation3-7

6. Cathode Ray Luminescence -- cathodoluminescence

Cathodoluminescence occurs when a beam of electrons (30kV or so) impacts on a luminescent material such as a phosphor causing the material to emit visible light. The most common example is the screen of a tv. In geology, mineralogy and materials science SEM with specialized optical detectors, or an optical is used to examine internal structures of semiconductors, rocks, ceramic, glass etc. in order to get information on the composition, growth and quality of the material.

CL image of a granite sample

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7. Transmitted unscattered electronsThis is the basis for TEM (see a bit later). There is no interaction between the electrons and the sample.The acceleration voltages (see electron guns soon) are about 100kV. Transmission efficiency is Inversely proportional to thickness (so thin samples are best). Light elements transmit better and appear Light on detection screen –and the reverse is true for heavy elements.

Highest resolution – good for nano!!3-9

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Scanning Electron Microscopy (SEM)As we know the Scanning Electron Microscope (SEM) is a microscope that uses electrons rather than light to form an image.Advantages: SEM instead of a light microscope.SEM has a large depth of field, which allows a large amount of the sample to be in focus at one time. produces images of high resolution, which means that closely spaced features can be examined at a high magnification.

Preparation of the samples is relatively easy since most SEMs only require the sample to be conductive. The combination of higher magnification, larger depth of focus, greater resolution, and ease of sample observation makes the SEM one of the most heavily used instruments in research areas today.

Amorphous SiOx nanowirebundles have an uncanny ability to self-assemble into various shapes, including one that strikingly resembles a sunflower. Each nanowire is about 10 nm in diameter

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First we look at the instrument itself

Electrons are produced by a hot “filament” – like a flashlight bulb

Tungsten filament

Electrodes connect to power

Ceramic insulator

heated wire gives electrons enough thermal energy to overcome work function of the source, with an electric potential to give electrons a direction and velocity. materials used for source are Tungsten (has a very high melting temp), so more thermal energy LaB6; and Ce6 (have a low work function and a high melting temp.). source is usually held at some potential (anywhere from ~500V to maybe 100kV) negative relative to ground, so that a sample (as well as the rest of the microscope) can be kept at ground.

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Electron optics (also see Fig 3.6)

Sample goes here

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Image Generation

Images are collected by rastering the electron beam (spot size 50 microns or less)Across the sample.

The electrons that “bounce off” the sample are sent to a detector

This signal is sent to a display which is scanned synchronously

Detectors collect these X-rays, backscattered electrons, and secondary electrons and convert them into a signal that is sent to a screen similar to a television screen.

Images are photographed or stored digitally

SEM-EDX (Electron Probe Microanalysis)

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image

X Ray Fluorescence Spectrum

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X-Ray emission

When very energetic (fast) electrons hit a sample X –rays are given off

sampleIncoming electrons

Electrons knocked out of atoms