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Physics of Thin Films

PES 449 / PHYS 549

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

polycrystalline solid

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

grain boundary

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:

simple model of cubic grains

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

equation for ratio of surface to volume atoms

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).


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.

  • 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)

edge dislocation

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

    point defects


    in principle you can eliminate all of these except vacancies

    vacancies arise from thermodynamics (entropy)

    entropy higher with vacancy

    fraction of vacancies (f)

    • equation for fraction of vacancies

      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

film roughness

in the worst case:

equation for roughness

generally observed less roughness

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