Electrostatic lens
Encyclopedia
An electrostatic lens is a device that assists in the transport of charged particles. For instance, it can guide electron
s emitted from a sample to an electron analyzer, analogous to the way an optical lens
assists in the transport of light in an optical instrument. The recent development of electron spectroscopy
makes it possible to reveal the electronic structures of molecule
s. Although this is mainly accomplished by electron analysers, electrostatic lenses also play a significant role in the development of electron spectroscopy.
An electrostatic lens can also be used to focus
an ion beam, for example to make a microbeam
for irradiating individual cells
.
Since electron spectroscopy detects several physical phenomena from the electrons emitted from samples, it is necessary to transport the electrons to the electron analyser. Electrostatic lenses satisfy the general properties of lenses. Systems of electrostatic lenses can be designed in the same way as optical lenses, so electrostatic lenses easily magnify or converge the electron trajectories.
There are several types of electrostatic lenses:
As an example, the principle of the cylinder lenses is explained.
A cylinder lens consists of several cylinders whose sides are thin walls. Each cylinder lines up parallel to the optical axis into which electrons enter. There are small gaps put between the cylinders. When each cylinder has a different voltage, the gap between the cylinders works as a lens. The magnification is able to be changed by choosing different voltage combinations. Although the magnification
of two cylinder lenses can be changed, the focal point is also changed by this operation. Three cylinder lenses achieve the change of the magnification while holding the object and image positions because there are two gaps that work as lenses. Although the voltages have to change depending on the electron kinetic energy
, the voltage ratio is kept constant when the optical parameters are not changed.
While a charged particle is in an electric field force acts upon it. The faster the particle the smaller the accumulated impulse. For a collimated beam the focal length is given as the initial impulse divided by the accumulated (perpendicular) impulse by the lens. This makes the focal length of a single lens a function of the second order of the speed of the charged particle. Single lenses as known from photonics are not easily available for electrons.
Usually the dependency is given for the kinetic energy itself depending on the power of the velocity.
So for an electrostatic lens the focal length varies with the second power of the kinetic energy,
while for a magnetostatic lens the focal length varies proportional to the kinetic energy.
And a combined quadrupole can be achromatic around a given energy.
If a distribution of particles with different kinetic energies is accelerated by a longitudinal electric field, the relative energy spread is reduced leading to less chromatic error for example in the electron microscope
.
Multipoles beyond the quadrupole can correct for spherical aberration and in particle accelerators the dipole bending magnets are really composed of a large number of elements with different superpositions of multipoles.
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s emitted from a sample to an electron analyzer, analogous to the way an optical lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
assists in the transport of light in an optical instrument. The recent development of electron spectroscopy
Electron spectroscopy
Electron spectroscopy is an analytical technique to study the electronic structure and its dynamics in atoms and molecules. In general an excitation source such as x-rays, electrons or synchrotron radiation will eject an electron from an inner-shell orbital of an atom...
makes it possible to reveal the electronic structures of molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s. Although this is mainly accomplished by electron analysers, electrostatic lenses also play a significant role in the development of electron spectroscopy.
An electrostatic lens can also be used to focus
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
an ion beam, for example to make a microbeam
Microbeam
A microbeam is a narrow beam of radiation, of micrometer or sub-micrometer dimensions. Together with integrated imaging techniques, microbeams allow precisely defined quantities of damage to be introduced at precisely defined locations...
for irradiating individual cells
Cell (biology)
The cell is the basic structural and functional unit of all known living organisms. It is the smallest unit of life that is classified as a living thing, and is often called the building block of life. The Alberts text discusses how the "cellular building blocks" move to shape developing embryos....
.
Since electron spectroscopy detects several physical phenomena from the electrons emitted from samples, it is necessary to transport the electrons to the electron analyser. Electrostatic lenses satisfy the general properties of lenses. Systems of electrostatic lenses can be designed in the same way as optical lenses, so electrostatic lenses easily magnify or converge the electron trajectories.
There are several types of electrostatic lenses:
- Einzel lensEinzel lensAn einzel lens is a charged particle lens that focuses without changing the energy of the beam. It consists of three or more sets of cylindrical or rectangular tubes in series along an axis...
, - cylinder lenses,
- aperture lenses,
- quadrupole lensMagnetic lensA magnetic lens is a device for the focusing or deflection of charged particles, such as electrons or ions. Charged particles are deflected based upon the strength of the magnetic field, which can be varied by controlling the current flowing through several electromagnets...
es.
As an example, the principle of the cylinder lenses is explained.
A cylinder lens consists of several cylinders whose sides are thin walls. Each cylinder lines up parallel to the optical axis into which electrons enter. There are small gaps put between the cylinders. When each cylinder has a different voltage, the gap between the cylinders works as a lens. The magnification is able to be changed by choosing different voltage combinations. Although the magnification
Magnification
Magnification is the process of enlarging something only in appearance, not in physical size. This enlargement is quantified by a calculated number also called "magnification"...
of two cylinder lenses can be changed, the focal point is also changed by this operation. Three cylinder lenses achieve the change of the magnification while holding the object and image positions because there are two gaps that work as lenses. Although the voltages have to change depending on the electron kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
, the voltage ratio is kept constant when the optical parameters are not changed.
While a charged particle is in an electric field force acts upon it. The faster the particle the smaller the accumulated impulse. For a collimated beam the focal length is given as the initial impulse divided by the accumulated (perpendicular) impulse by the lens. This makes the focal length of a single lens a function of the second order of the speed of the charged particle. Single lenses as known from photonics are not easily available for electrons.
- The cylinder lens consists of defocusing lens, a focusing lens and a second defocusing lens, with the sum of their refractive powers being zero. But because there is some distance between the lenses, the makes three turns and hits the focusing lens at a position farther away from the axis and so travels through a field with greater strength. This indirectness leads to the fact that the resulting refractive power is the square of the refractive power of a single lens.
- The quadrupole lens consists of two single quadrupoles turned 90° with respect to each other. Let z be the optical axis then one can deduce separately for the x and the y axis that the refractive power is again the square of the refractive power of a single lens.
- A magnetic quadrupole works very similar to an electric quadrupole. But the Lorentz forceLorentz forceIn physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
increases with the velocity of the charged particle. In spirit of a wien filterWien filterA Wien filter is a device consisting of perpendicular electric and magnetic fields that can be used as a velocity filter for charged particles, for example in electron microscopes and spectrometers. It is named for Wilhelm Wien who developed it in 1898 for the study of anode rays. It can be...
a combined magnetic, electric quadrupole is achromatic around a given velocity. BohrBohrBohr may refer to:People:* Niels Bohr , Danish atomic physicist, Nobel Prize in physics 1922* Aage Bohr , Danish nuclear physicist, Nobel Prize in physics 1975, son of Niels Bohr...
and PauliWolfgang PauliWolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...
claim that this lens leads to aberration when applied to ions with spin (in the sense of chromatic aberration), but not when applied to electrons, which also have a spin. See Stern-Gerlach experiment.
- The magnetic lens consists of three parts. A radial field with a flux decreasing towards the optical axis, which makes particles at the outer rim perform a spiraling motion. A homogeneous magnetic field along the optical axis which leads to the focusing Lorentz forceLorentz forceIn physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
. And a second part with a radial field undoing the spiraling. Again the indirectness leads to the fact that the resulting refractive power is the square of the refractive power of a single lens.
Usually the dependency is given for the kinetic energy itself depending on the power of the velocity.
So for an electrostatic lens the focal length varies with the second power of the kinetic energy,
while for a magnetostatic lens the focal length varies proportional to the kinetic energy.
And a combined quadrupole can be achromatic around a given energy.
If a distribution of particles with different kinetic energies is accelerated by a longitudinal electric field, the relative energy spread is reduced leading to less chromatic error for example in the electron microscope
Electron microscope
An electron microscope is a type of microscope that uses a beam of electrons to illuminate the specimen and produce a magnified image. Electron microscopes have a greater resolving power than a light-powered optical microscope, because electrons have wavelengths about 100,000 times shorter than...
.
Multipoles beyond the quadrupole can correct for spherical aberration and in particle accelerators the dipole bending magnets are really composed of a large number of elements with different superpositions of multipoles.