Previous Lecture - - - - Next Lecture
Nucleation and Growth
Ohring: Chapter 1, Section 1.7
Can phase diagrams help us in understanding rates ?
Consider cooling a liquid into a solid through a eutectic point:
- Nucleation of new phase
- growth of new phase
- liquid phase instability
- driving force toward equilibrium (as above)
- increases as we move to lower temperatures
- diffusion of atoms into clusters
- increases at higher temperatures
combine these two terms (multiplication) to determine the total nucleation rate
The maximum rate of nucleation is at some T < Te
growth of the phase is diffusion controlled => increases with temperature
total rate of forming solid is product of nucleation rate and growth rate
When moving into a 2 phase region on phase diagram - how does the new phase form ?
vapor --> liquid (solid) for a pure material with NO substrate
Energy minimization involves two terms:
- volume transition
- surface formation
where W is the atomic volume, PS is the pressure above the liquid (solid), and PV is the pressure in the vapor.
We want PV > PS so that ĘG is negative=> supersaturation provides the driving force.
Change in surface energy is always positive when forming surfaces.
Total energy change:
- initial formation of nuclei has increase in G => metastable
- if r < r* then nuclei shrink to lower G
- if r > r* then nuclei grow to lower G
- r* is a critical radius for nuclei
Films will also have an interface term => heterogeneous nucleation (coming soon!)
How fast will the critical nucleus continue to grow ?
Consider the rate at which atoms will join the critical nuclei:
expect nucleation rate to be given byN* = concentration of critical nuclei (nuclei/cm3)
A* = critical surface area of nuclei
w = flux of atom impingement (atoms / cm2sec)
Consider each of these three terms: