# Scanning Electron Microscope

### An Extensively Brief History

The Scanning Electron Microscope (SEM) was first introduced commercially in 1965. However, the principles behind the electron microscope were first theorized by Louis de Broglie (1925) saying that the electron had wave-like characteristics with substantially smaller wavelength than visible light. In 1927, the Davisson & Germer group and the Thomson & Reid group independently carried out electron diffraction experiments that demonstrated electron’s wave-like behavior. In 1932, Knoll & Ruska published a paper describing electron lenses and first used the term electron microscope. Ruska would, much later, win the Nobel Prize for his later findings. By 1933, the resolution of the electron microscope had exceeded that of the light microscope.

### Equations and Theory

To understand the difference between light microscopes and electron microscopes, one must first understand the difference between magnification and resolution. Magnification of an object occurs when the image is increased or expanded in size. The magnification range of an SEM is large, from about 10X to over 500,000X. Resolution of an object describes the ability to distinguish between objects. Thus, a microscope’s maximum magnification is defined by its maximum amount of resolution. At some point during the magnification process, the resolution of the image fades and the magnified objects become an indiscernible blob of black and white. The equation for the smallest distance that can be resolved (the Rayleigh criterion) is:

δ = 0.61λ/(μsin(β))

where λ is the wavelength of the radiation, and μsin(β) is collectively the numerical aperture (dependent on the microscope and lenses) which can usually be approximated to unity. Thus, as the wavelength of the radiation decreases, so does the resolving distance.

The equation for the wavelength of an electron follows:

λ ~ 1.22/(Ε^(1/2)) where Ε is the energy of the electrons in electron volt (eV) and ranges from 0.5 to 40 keV depending on the current of the electron gun, and λ is in nanometers.

This is the principal reason that electron microscopes can resolve magnitudes higher than light microscopes. Since the wavelength of the electron (1.7 nm to 6.1 pm)  is about three orders of magnitude smaller than that of light (380 nm to 750 nm), the smallest distance objects can be resolved decreases three fold. The SEM can resolve images at the 5 to 10 nm range, but there are often other factors that inhibit this maximum resolution being achieved.

As a side note, the term resolution in electron microscopy is rather imprecise. In light microscopy, the resolution of the microscope is the ability to display fine detail in the image. The resolving power of a microscope is its ability to make closely adjacent objects distinguishable in the image. The minimum distance on the object that distinguishable items appear in the image is known as the "minimum resolvable distance". Thus, since electron microscopists talk about the resolution of the microscope in terms of distance in the object, the term minimum resolvable distance should be used, but all the same, resolution is well understood.

### Mechanism of the SEM

Electron microscopes image by emitting a beam of electrons that pass through a series of electromagnetic lens, strike the substance, and use detectors to create an image. While this may sound similar to a visible light microscope (VLM), there are many fundamental differences that must be discussed. Both electron and optical light microscopes emit a beam of particles (electrons or photons, respectively), both use lenses to focus the beam, and both strike the sample and detect the reflected particle. However, the paths that the particles take are different in the two cases.

In the SEM, electrons are generated in the gun at the top of the microscope. The gun is a hairpin filament cathode, usually made of tungsten for its high melting point and low vapor pressure, that is heated by an applied current. The heat supplies the electrons sufficient energy to overcome the natural barrier that prevents them from leaking out. An anode, towards the base of the machine, accelerates the electrons towards itself and the sample by its applied positive voltage relative to the cathode. This voltage is known as the accelerating voltage and ranges between 0.2 and 40 KV (I too think it should be a kV rather than KV, but arguing with a scientist is futile).

Before starting up the electron gun, the machine must be pumped down to nearly vacuum pressure. Why is a vacuum required? First, if the filament were exposed to air, it would burn out very quickly. Second, without a vacuum, the electrons would collide with the particles in the chamber and create a distorted image. Lastly, if gas molecules react with the sample, different compounds could form and condense on the sample. A pressure of about 10^-6 torr is sufficient in most cases. Once the electrons begin accelerating towards the sample, a series of three condenser lenses are used to focus the beam (I will go into more detail if desired in a later node). Condenser lens 1 (C1) is used to control the beam current (the amount of electrons striking the specimen). C2 is used to control the size of the beam spot on the surface of the specimen. C3 is used primarily to focus the beam onto locations on the sample using deflector coils and stigmator coils. The deflector coils position the beam along the sample in a scanning raster pattern (thus giving the SEM its scanning nature). The stigmator coils are used to make the beam as circular, or symmetrical, as possible to avoid stretching of the created image.

### Detectors

#### Electron Detectors

As the electron beam strikes the sample, the electrons will disperse within the sample in a given volume coined the interaction volume. Some low energy electrons scatter inelastically, in a sense, from the surface of the sample upwards towards the detector; these are called secondary electrons (SE). Only secondary electrons that are emitted near the surface of the sample will reach the detector since the others lost too much energy and are absorbed into the sample. Some high energy electrons elastically strike at and below the surface of the sample’s atoms, which generate ionization products due to exceeding the ionization potential of the material. These are called backscattered (BS) electrons. There are detectors for each of these types of electrons.

A Faraday Cage is set up above and to the side of the sample and surrounds the SE detector. A small positive voltage is applied to the cage so the cage will exert a pulling force on the electrons towards the SE detector. Since BS electrons are of such high energy, the faraday cage will have little effect on the BS electrons and will attract most of the low energy secondary electrons.

The BS detector is a donut shaped detector that is inserted directly above the sample and has a concentric hole through the middle to allow the beam to pass through. Due to the conservation of momentum, BS electrons are scattered more strongly off of heavier atoms. This intensity can be measured by the detector and will show a difference of contrast on the image when the atomic number between atoms differs by three or more. The BS electrons can thus be used to develop a scheme of the different chemical compositions in a sample, but it does not give enough information to show what type of elements make up the sample (that is done by X-ray microanalysis).

#### X-Ray Detector

X-Ray emission is the most important secondary signal generated in the specimen. X-rays can tell us what elements and the amount of that element constitute a specific spot on the sample.

So how are X-rays generated? A high-energy electron must penetrate through the outer shell (valence electrons)of an atom and interact with the inner shell electrons (core electrons). If the beam electron is high enough energy, it will eject the inner shell electron leaving a hole in the inner shell. This creates a higher energy state atom (ionized), basically a very unhappy atom. The atom can return to its lower energy state by refilling its inner shell with an electron from the outer shell. When this occurs, it is accompanied by the emission of an X-ray, or an Auger electron but that is out of the scope of this article. This X-ray is termed a characteristic X-ray.

Since the energy of the emission is relative to the difference in energy of the two electron shells involved, the energy of the X-ray is "characteristic" and unique to the atom. Using Energy-Dispersing X-ray Spectroscopy (EDS or usu. EDX), a spectrum of the X-ray energy can be created for the spot on the sample. Microscopists use this spectrum for elemental analysis.

### Image Creation

Most articles explaining SEM function fail when explaining the formation of an image. It’s frustrating I know, but don’t worry. I’ll feed you baby birds.

Remember that the SEM scans the electron beam across the sample in a raster pattern. The time that the beam hitting the sample, the electrons being scattered or emitted, and the time it takes for the detectors to detect the stream of electrons is so small that it can be approximated to instantaneous for the purpose of explanation. When the beam hits the sample and the instantaneous process occurs, the detectors measure the charge density (the number of electrons per area per unit time). For any given sample, the beam hits the sample on a non-even surface. When the surface dips down below the rest of the sample, some of the electrons are shielded and refracted away from the detector, resulting in a decreased current density. When the beam strikes a peak, more electrons are refracted towards the detector and an increased current density results. This means that as more electrons scatter off of a given point on the sample, the intensity (charge density) is increased. The magnitude of intensity translates to contrast difference on the created image. High intensity creates a “brighter” spot while lower intensity creates a “darker” spot. Combining the scanned portions of the sample creates a contrasted black and white image of the sample.

Once the images have been created, they are saved to a hard disk and analyzed.

All of this information came from either my notes while working in the lab or from knowledge I have accumulated over the past year working in the microscopy lab.