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# Physics of Thin Films

## Structure of Solids: defects in solids

Ohring: Chapter 1, Section 1.3

### Classification of Defects in Crystalline solids

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.

### Three types of defects:

1. Planar defects - grain boundaries
interfaces 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 Angstroms

about 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 atoms

distorts 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

### Surface Roughness

films always have some statitistical distribution of thickness across the film

in the worst case:

generally observed less roughness

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