Previous Lecture - - - - Next Lecture

# Physics of Thin Films

## Film Formation I

Ohring: Chapter 5, sections 1 - 3

### Competing Processes

• impingement (deposition) on surface
• removing from film:
• reflection of impinging atoms
• desorption (evaporation) from surface

We can characterize the process of getting atoms onto a surface with

• sticking coefficient = mass deposited / mass impinging

### Steps in Film Formation

1. thermal accommodation
2. binding
3. surface diffusion
4. nucleation
5. island growth
6. coalescence
7. continued growth

We will examine each of these steps in turn.

### 1. Thermal accommodation

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

RESULTS:

• 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

### 2. Binding

two broad types of surface bonds:
• Van der Waals type
• weak bonds
• 0.01 eV
• chemical bonds
• strong bonds
• 1 - 10 eV

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

Consequences:

• 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

### 3. 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:

### 4. Nucleation

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:

### How do nuclei grow initially ?

Substrates are NOT flat

steps, kinks, etc. have higher Edes barrier => longer residence time on surface

=> preferred sites for nucleation

### Nucleation Rate

How quickly do nuclei form ?

(similar analysis to homogeneous nucleation rate from earlier)

Combining all these expressions:

### Capillarity Model - applications

What can we learn from the capillarity model about effects of deposition rate and substrate temperature on nucleation ?

from before:

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 ?

### Atomistic (Statistical) Nucleation Model

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.

other terms:

• Ni* = concentration of critical clusters per unit area
• N1 = concentration of single atoms per unit area
• no = total density of adsorption sites on surface