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Film Formation I
Ohring: Chapter 5, sections 1 - 3
We can characterize the process of getting atoms onto a surface with
We will examine each of these steps in turn.
impinging atoms must lose enough energy thermally to stay on surface
assume that E = kT so we can talk about energy or temperature equivalently
thermal accommodation coefficient (aT)
Examine energy transfer to lattice:one dimensional model from B.McCarrol and G. Ehrlich, J. Chem. Phys. 38, 523 (1963).
consider a chain of atoms connected by springs:
if rebound is strong enough - atom escapes
if not - atom is trapped - oscillates and loses energy to lattice
- atom is trapped if Ev < 25 Edesorb
- Edesorb is typically 1-4 eV
- trapped if Ev < 25 - 100 eV
- equivalently Tv < 2500 - 10,000 K
- most deposition processes have Ev < 10 eV
- MOST ATOMS ARE TRAPPED
- thermal accommodation is very fast
- around 10-14 seconds
two broad types of surface bonds:
Can we keep the atoms on the surface ?
competition between impinging atoms (deposition) and desorption of atoms
deposition: determined by deposition rate (atoms/cm2sec) =
desorption: determined by
- ĘGdes = free energy of desorption
- TS = temperature of substrate
- no = frequency of adsorbed atom attempting to desorb = lattice vibration frequency
- heat up substrate => lower coverage
- stop depositing => lower coverage until not film
- films are not stable !!!
What is wrong with this model ?
missing surface diffusion
allows clusters of adsorbed atoms to form
clusters are stable => film forms
How far do they diffuse ?from random walk analysis [see F. Reif "Fundamentals of Statistical and Thermal Physics" p. 486]
diffusion distance (X) is given by
Consider two cases:
How do clusters form ? => nucleation
Two competing processes in cluster formation
- clusters have a condensation energy per unit volume (ĘGV) which lowers the desorption rate (higher barrier)
- clusters have a higher surface energy than individual atoms
- clusters want to break up to minimize energy
Capillarity Model (= heterogeneous nucleation)nucleation on a substrate
assume nuclei are spherical caps
as with homogeneous nucleation, we can plot ĘG against r and determine a critical nucleus size:
Substrates are NOT flatsteps, kinks, etc. have higher Edes barrier => longer residence time on surface
=> preferred sites for nucleation
How quickly do nuclei form ?
(similar analysis to homogeneous nucleation rate from earlier)
Combining all these expressions:
What can we learn from the capillarity model about effects of deposition rate and substrate temperature on nucleation ?
To see how the lab variable (deposition rate, substrate temperature) change the basic physics examine the derivatives (and plug in some typical values):
Summary:high T and/or low deposition rate => large crystal grains
low T and/or high depostion rate => small polycrystalline structure
Problem: Can we apply macroscopic thermodynamics to nuclei of 2-100 atoms ?
Walton - Rhodin Theory
treat clustes of atoms like molecules rather than solid caps
consider the bonds between atoms
similar to capillarity model, but now include Ei* = energy to break apart a critical cluster of i* atoms into individual atoms.
- Ni* = concentration of critical clusters per unit area
- N1 = concentration of single atoms per unit area
- no = total density of adsorption sites on surface
advantages of this model:
[Section 5.3.2 has other film growth models]