Diffusion

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Diffusion

• ?This animation illustrates the process of
  diffusion in which particles move from a region
  of higher concentration to a region of lower
  concentration by random motion

• Related LOs
• gt Prior Viewing -
• gt Future Viewing -
• Course Name VLSI Technology
  Level(UG/PG)UG
• Author(s) Raghu Ramachandran
• Mentor Prof Anil Kottantharayil

The contents in this ppt are licensed under
Creative Commons Attribution-NonCommercial-ShareAl
ike 2.5 India license
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Learning objectives
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• After interacting with this Learning Object, the
  learner will be able to
• Explain the process of diffusion

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Master Layout
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Container
After Diffusion
Particles
Before Diffusion
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Definitions and Keywords
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• 1 Diffusion is the process of motion of particles
  from regions of higher concentration to regions
  of lower concentration by random motion
• 2 Container could be a vessel containing gas
  molecules, or a piece of semiconductor containing
  particles such as electrons or dopant atoms
• 3 Particles could be dopant atoms, gas molecules,
  electrons etc.

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Step 1
T1 Random Motion of Particles in a Box?
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Audio Narration (if any)?
Instructions to Animator Initially the particles
are collected together inside a rectangular box
moving randomly and undergoing collisions amongst
themselves and with the walls of the container.
There is an outer boundary that is not visible to
the user that encloses the box.

• For User
• Particles collected together in a rectangular box
  moving randomly and undergoing collisions amongst
  themselves and with the walls of the container.

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Step 1
T1 Random Motion of Particles in a Box?
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Audio Narration (if any)?
Instructions to Animator Continue with random
particle motion in the box while text on the left
is displayed

• For User
• In a gas, pressure is caused by collision of the
  molecules with the walls of the container
• In a gas or a semiconductor, the mean free path
  of a molecule or a charge carrier is the average
  distance travelled between collisions with
  another similar moving particle

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Step 2
T1 Remove Rectangular Boundary?
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Audio Narration (if any)?
Instructions to Animator After the collision
counter reaches a suitable value, remove the
walls of the rectangular box. Undergoing
collisions with each other the particles move
outward beyond their region of confinement. Stop
the animation when any particle hits the outer
boundary.

• For User
• Upon removal of the barrier the particles spread
  out into space resulting from collisions and
  random motion.

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Step 3
T1 Diffusion Mechanisms in Solids?
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v
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Audio Narration (if any)?
Instructions to Animator Atoms vibrate randomly
about their mean positions.

• For User
• In a perfect lattice with no defects the atoms
  vibrate about their stable positions due to
  thermal energy.
• Since there are no defects the atoms cannot move
  from one site to another.

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(No Transcript)
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Step 4
T1 Substitutional Diffusion due to Vacancy?
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Audio Narration (if any)?
Instructions to Animator Atoms vibrate randomly
about their fixed positions, however, two atoms
are missing from the lattice

• For User
• In a real material there are defects such as the
  vacancies. Atoms can then move within the
  structure from one atomic site to another.

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Step 5
T1 ? Substitutional Diffusion due to Vacancy
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Audio Narration (if any)?
Instructions to Animator Atom shifts into the
vacant site

• For User
• There is an energy barrier for the movement of
  atoms into the vacant sites.
• At a high enough temperature some of the atoms
  gain enough energy to move into the vacant sites.
  
• The rate of diffusion is determined by the
  density of vacancies.

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Step 6
T1 ? Substitutional Diffusion due to Vacancy
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Audio Narration (if any)?
Instructions to Animator Only change in text
displayed to user

• For User
• The probability of any atom in a solid to move
  is the product of
• The probability of finding a vacancy in an
  adjacent lattice site and
• The probability of thermal fluctuation necessary
  to overcome the thermal barrier

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Step 7
T1 ? Substitutional Diffusion due to Vacancy
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where Qd is the activation energy for diffusion
(J/mol)
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Audio Narration (if any)?
Instructions to Animator Only change in text
displayed to user
For User The diffusion coefficient which is a
measure of mobility of the diffusing species is
given by
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where Qd is the activation energy for diffusion
(J/mol)
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Step 8
T1 Interstitial Diffusion
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Audio Narration (if any)?
Instructions to Animator An atom occupies an
interstitial position and all atoms vibrate
randomly about their mean positions

• For User
• When the atom is not on a lattice site but on an
  interstice, it is free to move to an adjacent
  unoccupied interstitial position.
• The probability of an atom in an interstitial
  to diffuse is controlled by the probability of
  its overcoming the thermal barrier, since there
  are a lot of vacant interstitial sites

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Step 9
T1 Interstitial Diffusion
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Audio Narration (if any)?
Instructions to Animator The interstitial atom
pushes the lattice atoms out of the way to move
to the adjacent interstitial position

• For User
• The atom on the interstice pushes the lattice
  atoms out of the way to move to the adjacent
  vacant interstitial position, thus overcoming the
  energy barrier

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Step 10
T1 Interstitial Diffusion
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Audio Narration (if any)?
Instructions to Animator The atom moves into an
adjacent interstitial position

• For User
• The atom moves into an adjacent interstitial
  position

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Step 11
T1 Ficks First Law
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constant
concentration

constant


concentration
Flux Jx
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Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user
For User For a flux of diffusing particles
(atoms, molecules or ions) diffusing in one
dimension Ficks first law can be written as
where D is the diffusivity, Jx is the flux
of particles (diffusion flux) and C is their
number density (concentration). Ficks first law
can only be used to solve steady state diffusion
problems
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Step 12
T1 Ficks First Law
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constant


constant
concentration


concentration Low Temp


HighTemp
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Flux Jx
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Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user
For User In the above graph, diffusivity changes
as Ficks first law holds even if diffusivity
changes with position
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Step 13
T1 Ficks Second Law Finite Source
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Impurity
Bar
Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user
For User In one dimension Ficks second law is
Consider a semi-infinite bar with a small
fixed amount of impurity diffusing in from one
end.
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Step 14
T1 Ficks Second Law Finite Source
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Bar
Impurity
Bar
Impurity
After Diffusion
Before Diffusion
Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user
For User Boundary Conditions 1. Since the
amount of impurity in the system must remain
constant where B is a constant and C is the
concentration of impurity in the bar. 2. The
initial concentration of impurity in the bar is
zero, therefore
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Step 15
T1 Ficks Second Law Finite Source
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Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user
For User The solution for C(x,t) is The
diffusion of impurity material into the bar with
time is shown above.
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Step 16
T1 Ficks Second Law Infinite Source
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Bar
Bar
Infinite Source
Infinite Source
Before Diffusion
After Diffusion
Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user
For User Consider a semi-infinite bar with a
constant concentration of impurity material
diffusing in from one end. Boundary
conditions 1. Since there are no impurity atoms
in the bar at the start 2. Since the
concentration at x0 is constant
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Step 17
T1 Ficks Second Law Infinite Source
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Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user
For User The solution for C(x,t) is The
diffusion of impurity material into the bar with
time is shown above.
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Step 18
T1 Ficks Second Law Non-Zero Boundary
Conditions
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Infinite Source
Bar
Infinite Sink
Before Diffusion
After Diffusion
Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user

• For User
• Consider a bar of length L such that impurity
  material enters at one end of the bar and leaves
  at the other end. The concentrations at either
  end of the bar are held constant. The boundary
  conditions are
• Since there are no impurity atoms in the bar at
  the start
• 2. Since the concentration at x0 is constant

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Step 19
T1 Ficks Second Law Infinite Source
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Graph Here
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Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user

• For User
• 3. Consider the case where the concentration at x
  L is
• Since there are no sources or sinks in the bar
  and the concentration at the ends is fixed, the
  concentration distribution eventually stabilizes
  and no longer depends on time. This is shown
  above.

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Step 20
T1 Ficks Second Law Non-Zero Boundary
Conditions
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Infinite Source
Bar
Infinite Sink
Before Diffusion
After Diffusion
Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user

• For User
• Consider a bar of length L such that impurity
  material enters at one end of the bar and leaves
  at the other end. The concentrations at either
  end of the bar are held constant. The boundary
  conditions are
• Since there are no impurity atoms in the metal at
  the start
• 2. Since the concentration at x0 is constant

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Step 21
T1 Ficks Second Law Infinite Source
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Graph Here
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Audio Narration (if any)?
Instructions to Animator Display the figure and
text for user

• For User
• 3. Consider the case where the concentration at x
  L is
• Since there are no sources or sinks in the bar
  and the concentration at the ends is fixed, the
  concentration distribution eventually stabilizes
  and no longer depends on time. This is shown
  above.

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Questionnaire
APPENDIX 1

• For an ideal gas at constant volume and pressure,
  how does the mean free path of gas molecules
  change with increasing temperature?
• a) Increases b) Decreases c) Remains the same
• For an ideal gas at constant volume and
  temperature, how does the mean free path of gas
  molecules change with increasing pressure?
• a) Increases b) Decreases c) Remains the same
• For a doped solid semiconductor, how does the
  mean free path of electrons change with
  increasing temperature?
• a) Increases b) Decreases c) Increases and then
  decreases

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Questionnaire
APPENDIX 1

• The minus sign in Ficks first law signifies
  the fact that the flux is
• a) in the direction of decreasing impurity
  concentration b) in the direction of increasing
  impurity concentration
• Pre-deposition and drive-in are cases of
• a) diffusion from finite and infinite sources
  respectively b) diffusion from infinite and
  finite sources respectively

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APPENDIX 2
Links for further reading

• Reference websites
• Books James D. Plummer, Michael D. Deal, Peter
  B. Griffin, Silicon VLSI Technology
• Ben G. Streetman, Sanjay Banerjee, Solid
  State Electronic Devices
• Research papers

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APPENDIX 3
Diffusion is a process in which particles move
from a region of higher concentration to a region
of lower concentration by random
motion Impurities diffuse through solids by
substitutional diffusion due to the presence of
vacancies or interstitial diffusion where the
impurity atom occupies an interstitial
position For diffusing particles, Ficks first
law is and Ficks second law is

Summary