SEM magnetic lenses

Question 1

The Electron Column Contains the:

Answer 1

a. Electron Gun,
b. Magnetic Lenses,
c. Scan Coil, and
d. Apertures

Question 2

Electromagnetic Lenses

Answer 2

• The path of an electron can be altered by exposure to a magnetic field.
• Electromagnetic lenses create a circular magnetic field that demagnify (condense) the electron beam as it passes through.
• The strength of the lenses can be changed by varying the current supplied to the lens. Changing the lens current changes the focal length of the lens.
• Magnetic lens consists of a coil of copper wires inside the iron pole pieces.
• A current through the coils creates a magnetic field in the bore of the pole pieces.
• The rotationally symmetric magnetic field is inhomogeneous in such a way that it is weak in the center of the gap and becomes stronger close to the bore.
• Electrons close to the center are less strongly deflected than those passing the lens far from the axis.
• The overall effect is that a beam of parallel electrons is focused into a spot (called cross-over).

Question 3

Right hand rule:

Answer 3

F  = - e (v X B)
e  = electron charge
v  = electron velocity
B = magnetic flux density

Question 4

Focal Length

Answer 4

Focal length, f, of the lens is the distance along optic axis from the point where an electron first changes direction to the point where the electron cross the axis.
Electron travels in spiral path, that is why image rotates when objective lens strength changes.

N = No. of turns in the lens coil
V0= accelerating voltage
I = lens current
Magnetic lenses influence electrons in a similar way as convex glass lenses do with light. Thus, very similar diagrams can be drawn to describe the respective ray paths.
Consequently, the imaginary line through the centers of the lenses in an electron microscopes is called optical axis as well.
The lens equation of light optics is also valid in electron optics, and the magnification is defined accordingly:
(look at equation)

Question 5

Problems in Electromagnetic Lenses

Answer 5

There are some problems inherent in electromagnetic lenses. They are:
• Spherical Aberration
• Chromatic Aberration
• Diffraction and
• Astigmatism.
It is possible to correct for these problems, once one understands them.

Question 6

Spherical Aberration

Answer 6

Spherical aberration concerns the path of the electron in respect to its position within the electromagnetic lens. The strength of the magnetic field is the strongest near the surface of the lens.
Therefore, the electrons that travel through a lens close to its surface will have their paths altered more than an electron which travels through the center of the lens and results in a loss of electrons from the beam.
Electrons that strike the interior surface of the electron column are absorbed.

Question 7

Chromatic Aberration

Answer 7

• Chromatic aberration relates to the varying energy of the electrons that comprise the beam.
• Not all electrons generated at the gun assembly have the same energy.
• Electrons with different energies have different wavelengths.
• A magnetic field will have more of an influence on a longer wavelength electron.
• Thus, due to a variance in the energies of the electrons in the beam, it is not focused to a discrete focal point.

Question 8

Diffraction

Answer 8

• Diffraction is caused by the electrons wavelengths being out of phase. Thus, a lens will focus electrons of different phase to a different point depending upon the position of an electron in its wavelength when it passed through the lens.
• Diffraction is of most importance at the final probe forming lens.
• To correct diffraction, the electrons would have to be monochromatic and coherent. If these conditions were met, the lens could focus the stream of electrons to a point rather than to a disk of confusion.

Question 9

Astigmatism

Answer 9

• Astigmatism occurs because of manufacturing imperfections within the electromagnetic lens. It is extremely difficult to manufacture an electromagnetic lens that forms a perfectly even magnetic field.
• It happens when a lens field is not symmetrical in strength, but weaker in one plane than another.
• Variances in the strength of the magnetic field around the circumference of the lens causes an elliptical focal spot.
• This problem can be overcome by segmenting the lens into many parts and being able to adjust the excitation to each part. In this manner, weak portions of the lens can be strengthened.