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Physics of Thin Films

PES 449 / PHYS 549

Film Formation I

Ohring: Chapter 5, sections 1 - 3

Competing Processes

  • adding to film:
    • 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

impinging and reflected atoms

thermal accommodation coefficient (aT)

thermal accommodation coeffiecient equations

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:

one dimensional lattice

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:
  • physisorption (physical adsorption)
    • Van der Waals type
    • weak bonds
    • 0.01 eV
  • chemisorption (chemical adsorption)
    • 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) = R dot

desorption: determined by

  • ĘGdes = free energy of desorption
  • TS = temperature of substrate
  • no = frequency of adsorbed atom attempting to desorb = lattice vibration frequency

equations: desorption rate and substrate coverage

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 equation for diffusion distance

Consider two cases:

surface diffusion to form clusters

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

 capillarity model and free energy equation

as with homogeneous nucleation, we can plot ĘG against r and determine a critical nucleus size:

critical radius graph and equations

How do nuclei grow initially ?

initial growth is by surface diffusion

 

Substrates are NOT flat

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

=> preferred sites for nucleation

steps and kinks

Nucleation Rate

How quickly do nuclei form ?

(similar analysis to homogeneous nucleation rate from earlier)

equations for nucleation rate on surface

Combining all these expressions:

equation for total nucleation rate on surface

Capillarity Model - applications

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

from before:

equations for capillarity model and inert substrate

To see how the lab variable (deposition rate, substrate temperature) change the basic physics examine the derivatives (and plug in some typical values):

equations of derivatives

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

equations for Walton-Rhodin model

advantages of this model:

  • depends on microscopic parameters
  • includes crystalographic information
    • since bonds between atoms are included
  • critical size (i*) depends on substrate temperature
    • model shows transitions in growth modes
    • preferred i* increases with T

    [Section 5.3.2 has other film growth models]

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