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MSE 550 . Presentation #2. What is a thin film? Science background overview of film growth crystal structure and defects (dislocations, grain boundaries) diffusion properties of vacuum Film formation Thermal accommodation Sticking and surface diffusion nucleation of film

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mse 550

MSE 550

Presentation #2

What is a thin film?

Science background

overview of film growth

crystal structure and defects (dislocations, grain boundaries)


properties of vacuum

Film formation

Thermal accommodation

Sticking and surface diffusion

nucleation of film

growth modes (island, layer by layer, mixed)

coalescence of film

continued growth (zone models)

other factors

energetic deposition

amorphous films

epitaxial growth

Deposition parameters and techniques

(relate the knobs on equipment to what happens on the film)


Vacuum Arc Deposition

Sputter Deposition



Chemical Vapor Deposition

Ion Beam assisted deposition

plasma enhanceddeposition (PECVD, ECR . . .

How are thin films made?

What are the basic parts of deposition systems?


transport region

substrate - deposition region

What parameters can we control?


deposition rate

deposition energy

Within the framework established above, examine each of the following deposition methods in detail:


cathodic arc vaporization

sputter deposition



Molecular Beam Epitaxy

Chemical Vapor Deposition

Ion Beam assisted deposition / ion implantation

plasma enhanced deposition (PECVD, ECR . . . )

Spin coating


What is a "thin film" ?

thin = less than about one micron ( 10,000 Angstroms, 1000 nm)

film = layer of material on a substrate

(if no substrate, it is a "foil")


microelectronics - electrical conductors, electrical barriers, diffusion barriers . . .

magnetic sensors - sense I, B or changes in them

gas sensors, SAW devices

tailored materials - layer very thin films to develop materials with new properties

optics - anti-reflection coatings

corrosion protection

wear resistance

Typical steps in making thin films:

emission of particles from source ( heat, high voltage . . .)

transport of particles to substrate (free vs. directed)

condensation of particles on substrate (how do they condense ?)

Simple model:


thermodynamics and kinetics

phase transition - gas condenses to solid


growth kinetics

activated processes



allowed processes and allowed phases

Kinetics and Diffusion

Kinetics= how fast it will happen

we will concentrate on mass transport

= atoms diffusing through a solid

Diffusion in one dimension - Fick's 1st and

Fick's 1st Law = "stuff moves from where you have lots to where you have little"

There is always a potential energy barrier to diffusion (activation energy).

What do we expect mathematically for the flux to the right (from position1 to 2):

Similarly we can find the flux to the left:

(note: if we had used the gas constant, R, instead of Boltzmann constant, k, then the energy would be the diffusion energy/mole)

nucleation and growth
Nucleation and Growth
  • Connection to Phase Diagrams
  • Can phase diagrams help us in understanding rates ?
  • Consider cooling a liquid into a solid through a eutectic point:
  • at point A: solid is not stable so will not form
  • at point B: solid and liquid are both stable so no driving force to solid
  • at point C: liquid is unstable - will form solid
  • at point D: liquid is unstable - will form solid
    • further from equilibrium => greater driving force to form solid

depends on:

  • 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
  • Transformation rate:
  • total rate of forming solid is product of nucleation rate and growth rate
nucleation details
Nucleation details
  • When moving into a 2 phase region on phase diagram - how does the new phase form ?
  • Two issues:
  • Thermodynamics: Is nucleation possible ? (energy minimization)
  • Kinetics: How fast does it happen ? (nucleation rate)
  • Homogeneous Nucleation
  • vapor --> liquid (solid) for a pure material with NO substrate
Energy minimization involves two terms:

volume transition

surface formation

volume transition:

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 ÆG is negative

=> supersaturation provides the driving force.


surface formation:

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
Nucleation rate
  • 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 by

N* = 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:

Film Formation I
  • 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
  • thermal accommodation
  • binding
  • surface diffusion
  • nucleation
  • island growth
  • coalescence
  • 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)


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
  • 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) = desorption: determined by DGdes = 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
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 (DGV) 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 ÆG 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 ?

  • Nucleation Rate
  • 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):


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 clusters 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


advantages of this model:

  • depends on microscopic parameters
  • includes crystallographic 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
Film Formation II

5. Island Growth

observe 3 growth modes experimentally

1. Island growth (Volmer - Weber)

form three dimensional islands


film atoms more strongly bound to each other than to substrate

and/or slow diffusion

2. Layer by layer growth (Frank - van der Merwe)

generally highest crystalline quality


film atoms more strongly bound to substrate than to each other

and/or fast diffusion

3. Mixed growth (Stranski - Krastanov)

initially layer by layer

then forms three dimensional islands

=> change in energetics

When would we expect to see each of these ?

The layer growth condition with cosine greater than 1 looks odd. This is the case where the angle theta is undefined because for layer growth there really is no point where the substrate, vapor and film come together and therefore, no way to define the angle.

6. Island Coalescence

three common mechanisms:

1. Ostwald ripening

atoms leave small islands more readily than large islands

more convex curvature => higher activity => more atoms escape

2. Sintering

reduction of surface energy

3. Cluster migration

small clusters (<100 Å across) move randomly

some absorbed by larger clusters (increasing radius and height)

7. Thick films - zone models

Further growth depends on:

bulk diffusion

surface diffusion



shadowing (line of sight impingement)

  • Relative importance of these processes depends on
  • substrate temperature (T)
  • deposition rate

these variables to find regions with similar film structure (similar properties)

Columnar structures

very common

from limited atomic mobility

often oriented slightly toward source

  • Films are typically lower density than bulk
    • more porosity at macro, micro and nano scales.
  • Grain size dependence on deposition rate and substrate temperature
    • grain size typically increases with increasing film thickness, increasing substrate temperature, increasing annealing temperature, and decreasing deposition rate.
Other factors affecting film growth

1. Substrate

not really a featureless plane

atomic structure => epitaxy

relationship of film crystal structure to substrate crystal structure


nucleation sites

2. Contamination


poor background pressure

impure deposition source

dirty substrate

changes the energies (surface energies, desorption energy, surface diffusion energy)

3. Impinging particle energy

0.5 eV -------------------> 10 - 20 eV --------> 100-1000 eV

thermal evaporation ----- sputtering --------- accelerated (bias)

interactions of incident particles with film/substrate produce:

sputter removal of surface atoms

insertion of particles into film or substrate

increased local temperature


shock (pressure) waves