Transmission Electron Microscope_1

Scattering and Diffraction:
1. Elastic scattering usually occurs at relatively low angles (1-10^o), i.e., in the forward direction.
2. At higher angles (>10^o) elastic scattering becomes more incoherent.
3. Inelastic scattering is almost incoherent and relatively low angle (<1^o) forward scattering.
4. As the specimen gets thicker, less electrons are forward scattered and more are backscattered until primarily incoherent backscattering is detectable in bulk, nontransparent specimens.

A convenient definition of a small angle is 10 mrads:
1 mrad = 0.0573^o, 10 mrads is about 0.5^o.

The origin of Kikuchi lines:
Kikuchi patterns are formed by inelastically scattered electrons.
If the specimen is thick enough, we will generate a large number of scattered electrons which travel in all directions, i.e., they have been incoherently scattered but not necessarily in elastically scattered. They are sometimes refered to as diffusely scattered electrons.

• The diffusely scattered electrons have the same λ as the incident electrons since energy losses are small compared to E₀.


• When first formed, most of the diffusely scattered electrons travel close to the direction of the incident beam.


• The ideal specimen thickness will be such that we can see both the spot pattern and the Kikuchi lines. This is one of the few illustrations when thinner is not necessarily better.


• The Kukuchi lines consist of an excess line and a deficient line. In the DP, the excess line is further from the direct beam than the deficient line.


• The Kikuchi lines are fixed to the crystal so we can use them to identify orientation accurately.


• The trace of the diffracting planes is midway between the excess and deficient lines.
  

Resolution and Wavelength:
It is easier to think image resolution in TEM as the smallest distance that can be resolved, the concept is borrowed from the classical optical microscope Raley criterion:

δ=(0.61λ)/μsinβ

μ is the refractive index of the viewing materials;β is the angle of collection of the magnifying lens;
λ is the electron wavelength, which can be calculated in the following simple way ignoring relativistic effects:
λ=1.22/√E

Considering relativistic effects:

Electron Properties as a Function of Accelarating Voltage

Accelerating Voltage(kV)	relativistic wavelength (nm)	Mass(x m0)	Velocity(x108m/s)
100	0.0037	1.196	1.644
200	0.00251	1.391	2.086
300	0.00197	1.587	2.330

Microscopy Related websites:
http://cimewww.epfl.ch/
Scattering and Diffraction:
Diffraction: An interaction between a wave of any kind and an object of any kind.
Scattering: The process in which particles, atoms, etc., are deflected as a result of collision.
So scattering might best apply to particles and diffraction to waves.

Dislocation Density:
The dislocation density is a measure of how many dislocations are present in a quantity of a material. Since a dislocation is a line defect, this is defined as the total length of dislocation per unit volume. Consequently the units are m/m³ = m^-2. Equivalently, it is the number of dislocation lines intersecting a unit area. Dislocation density is usually of the order of 10¹⁰ m^-2 in a metal, increasing to ~10^-15 m^-2 after work hardening.

Relationship Between R and L:
L,Camera Length:distance of the film from the diffraction pattern on the specimen.

....| Incident Beam
..===== Specimen
....| ...L|  ....|   \Diffracted beam
....|    ....o__R__O <- Diffraction spot.

Rd=λL
R is the distance between the diffraction spots.
d is the atomic spacing.
Structure Factors:
F_(hkl)=∑f_ie^{2πi(hx_i+ky_i+lz_i)}
This is the key equation, it is completely general.
BCC:
F=2f if h+k+l is even
F=0 if h+k+l is odd

FCC:
F=4f if h,k,l are all even or all odd
F=0 if h,k,l are mixed even and odd.

HCP:
|F|²=0 if h+2k=3m and l is odd
|F|²=4f² if h+2k=3m and l is even,
|F|²=3f² if h+2k=3m+1 and l is odd,
|F|²=f² if h+2k=3m+1 and l is evn.

NaCl:
F={f_(Na)+f_(Cl)e^πi(h+k+l)}{1+e^πi(h+k)+e^πi(h+l)+e^πi(k+l)}
F=4(f_(Na)+f_(Cl)) if h,k,l are all even,
F=4(f_(Na)-f_(Cl)) if h,k,l are all odd,
F=0, if h,k,l are mixed.

Things to remember

Fermi Level:
Fermi level, E_F, is a chemical energy of a material. It is used to describe the energy level of the electronic state at which the electron has a probability of 0.5 ocuppying that state.
It is given as:
E_F=1/2[E_C+E_V]-(4/3)*KT*ln(m_n^*/m_p^*)

Electron Beam Evaporation Technique Vs. Sputtering

Electron beam evaporation (E-Beam evaporation) and sputtering both can be classified into Physical Vapor Deposition (PVD) category.PVD covers a number of deposition technologies in which material is released from a source and transferred to the substrate. The two most important technologies are evaporation and sputtering.

The choice of deposition method (i.e. evaporation or sputtering) may in many cases be arbitrary, and may depend more on what technology is available for the specific material at the time. In VLSI fabrication, sputtering technology is widely-used for accomplishing thin films.

Evaporation
In evaporation, the substrate is placed inside a vacuum chamber, in which a target (source) material to be deposited is also located. The source material is then heated to the point where it starts to boil and evaporate. This process requires a high vacuum (10^-6 to 10^-7 Torr range)to allow the molecules to evaporate freely in the chamber, and they subsequently condense on all surfaces. This principle is the same for all evaporation technologies, only the method used to heat (evaporate) the source material differs. In E-Beam evaporation, a high kinetic energy beam of electrons is directed at the material for evaporation. Upon impact, the high kinetic energy is converted into thermal energy, heating up and evaporating the target material, on the premise that the heat produced exceeds the heat lost during the process. The rate of mass removal from the source material as a result of such evaporation increases with vapor pressure, which in turn increases with the applied heat. Vapor pressure greater than 1.5 Pa is needed in order to achieve deposition rates which are high enough for manufacturing purposes.

Sputtering
Sputtering is a technology in which the material is released from the source at much lower temperature than evaporation. The substrate is placed in a vacuum chamber with the source material, named a target, and an inert gas (such as argon) is introduced at low pressure. A gas plasma is struck using an RF power source, causing the gas to become ionized. The ions are accelerated towards the surface of the target, causing atoms of the source material to break off from the target in vapor form and condense on all surfaces including the substrate. As for evaporation, the basic principle of sputtering is the same for all sputtering technologies. The differences typically relate to the manor in which the ion bombardment of the target is realized.

Advantages offered by evaporation for PVD
1) high film deposition rates;
2) less substrate surface damage from impinging atoms as the film is being formed, unlike sputtering that induces more damage because it involves high-energy particles; 3) excellent purity of the film because of the high vacuum condition used by evaporation;
4) less tendency for unintentional substrate heating.



Disadvantages of using evaporation for PVD
1) more difficult control of film composition than sputtering;
2) absence of capability to do in situ cleaning of substrate surfaces, which is possible in sputter deposition systems;
3) step coverage is more difficult to improve by evaporation than by sputtering;
4) x-ray damage caused by electron beam evaporation can occur.