Most crystalline materials have many defects.
Some (like Silicon) can be grown with relatively few defects.
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Structure of Solids: defects in solids
Ohring: Chapter 1, Section 1.3
polycrystalline solid - contains several crystalline regions which are randomly oriented
Most crystalline materials have many defects.
Some (like Silicon) can be grown with relatively few defects.
1. Planar defects - grain boundariesinterfaces between two single crystal regions of different orientation
atoms at grain boundaries tend to be loosely bound
=> more reactive (corrosion) and accelerated diffusion along grain boundaries
typical grain sizes: 0.01 mm - 100 mm (micron)
How many atoms in a solid are at grain boundaries ?
rough model:
assume grains are all cubes with sides of length l
l = grain size
a = atomic lattice parameter
n = number of atoms in one row of the grain
then, l = na
What would be the result for spherical grains of diameter, l ?
A somewhat better argument using truncated octahedra leads to the fraction being about 3.35 (a/l). (See Christian "Theory of Transformations in Metals and Alloys", p. 332).
example:
for l = 0.1 micron (1000 Angstroms) and a = 3 Angstromsabout 10 atoms out of 1000 are at grain boundaries (1 %)
Number of grain boundaries in film (grain size) depends on deposition rate and substrate temperature.
generally:
- lower T => smaller grains => many boundaries
- hight T => larger grains => fewer boundaries
grain size is often proportional to film thicknes
(thinner films tend to have smaller grains)
2. line defects - dislocations
example: edge dislocation - from inserting an extra row of atomsdistorts lattice => stresses (compression and tension)
very common: often 1010 - 1012 dislocations/ cm2 in films
form from:
- film growth process
- dislocations in substrate continuing into film
- contamination on substrate
3. point defects
- self interstitial - extra atom
- vacancy - missing atom
- substitutional impurity - impurity atom in lattice
- interstitial impurity - impurity atom not in regular lattice site
in principle you can eliminate all of these except vacancies
vacancies arise from thermodynamics (entropy)
fraction of vacancies (f)
where kB = Boltzmann's constant = 1.381 x 10-23 J/K
typically Ef is about 1 eV
at room temperature, f is about 10-17
point defects often arise from
- fast deposition
- low substrate temperatures
=> no time for atoms to move to crystal lattice sites
films always have some statitistical distribution of thickness across the film
in the worst case:
generally observed less roughness
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