Dr. Kasra Etemadi September 14, 2011 Lecture Notes on Principles of Plasma Processing

Part A: III Gas Discharge Fundamentals 11-24 Part B2: III Collision Dynamics 119 Elastic Collisions 129 Inelestic Collisions 130 Part B3 II Atomic Collisions 126 III Elestic Collisions 129 IV Inelestic Collisions 130 Part B4 III Electron Collision with Molecules 140 IV Heavy Particle Collisions 142

Handbook of Advanced Plasma Processing Techniques

2.3 Collision Process 38

Definition Collision means the action of bodies striking or coming together (touching). When two particle pass each other and some measurable change in their path occurs, collision has taken place

Collisions involve forces (there is a change in velocity). Collisions can be elastic, meaning they conserve energy and momentum, inelastic, meaning they conserve momentum but not energy

. 1- Type of Collisions a- Elastic Collisions b- Inelastic Collisions

2- Collision Parameters

3- A Simple Example Binary Collisions

atom atom

+ + ion ion

electron electron photon Major Types of Atomic Processes (see the handout) Particle Type Symbol

Photon o Examples: Electron e A++B A+B+ Ground State atom or molecule 0 Electronically excited-one electron 0’ 10/01 Charge Transfer

two electrons 0’’ metastable state 0m +ABA+B*A+B + Vibrationally excited molecules 0v Rotationally excited molecules r 0 ’ o(00)/00 /00o Photo Dissociation Positive ion ; singly, doubly, … 1, 2, …

Negative ion 1 e + A  A+ + 2e Ionization e +A  A* e + A + h Excitation e + A*  2e + A+ Penning Ionization e + A  e + A Elastic Scattering e + AB  e + A + B Dissociation e +AB  2e + A+ + B Dissociative Ionixation e +AB  A- + B Dissociative Attachment e + A+ + B  A + B Recombination A+ + B  A + B+ Charge Exchange A+ + B  A+ + B Elastic Scattering A+ + B  A+ + B+ + e Ionization A+ + B  A+ + B* A+ B +  Excitation A+ + e + B  A + B Recombination A+ + BC  A+ + B + C Dissociation A + BC  C + AB Chemical Reaction  + A  A* Photo Excitation  + AB  A + B Photo Dissociation  + A  A+ + e Photo Ionization

A + B  A + B Elastic Scattering A + B  A + B+ + e Ionization A + BC  A + B + B Dissociation A*  A +  Photo Emission Energy [eV]

 e  N2  N2  e  e 15.6  e  H 2  H 2  e  e 15.4 Ionization energy:  e  SiH 4  SiH 4  e  e 11.4 e  H  H   e  e 13.6

H   H  e 0.75 OH   OH  e 18  O3  O3  e 2.0 Electron Affinity:  O2  O2  e 0.44 O  O  e 1.5

 SiH 3  SiH 3  e 2.7 Formation of multicharged negative ions is much less possible See: “Plasma Physics and Engineering; Chapter 2 & 3; pp. 15-155

Particle Type Sy mb ol Photon o Electron e Examples: Ground State atom 0 or molecule Electronically 0’ e(00)’/e0’0’ Electron impact dissociation excited-one electron

0’’ two electrons e1/e1Ф Bremsstrahlung, or free-free emission metastable state 0m Vibrationally 0v excited molecules 0v0/00v Vibrational excitation exchange Rotationally excited molecules 0r e(01)/ee11 Electron impact dissociative ionization Positive ion ; 1, singly, doubly, … 2, … Negative ion Collision Parameters

1- Impact Parameter (b):

Scattering angle 1

a Impact parameter  a tan( )  2 b 2 2- Total Collision Cross Section Q12(v):

Field Number of test Particle particles colliding with the field particles per Test Particle Beam unit time (J1=njv) Q12(v) = Flux Density J1

elastic nonelastic Q12 = Q12 + Q12

Elastic Collision: no changes in internal energy

Inelastic Collision: with internal energy exchange 3- Nonelastic Collision Cross Section Q12(v):

Number of test particles causing a (12) excitation of the field particles per unit time (12) Q12 (v) = Flux Density J1

In an electron atom collision, kinetic energy of the electron needs to be above the energy of the first excited level in order to have an inelastic collision. x 4- Differential Cross Sections I12(,) : d   J Z 1 2

y

Number of test particles scattered by the field particles into the solid angle d per unit time I12(,) d = J1

Q12=4 I12(,)d Total Cross Section m 5- Cross section for momentum transfer Q12 (v): x d   J Z 1 2 y Qm (v)  (1 cos )I elastic(,)d 12  12 4

m (m1vJ1)Q12 (v) is the total loss in the z-component of momentum of the beam per unit time

m elastic Q12 /Q12 the average fraction of momentum lost by the test particle in elastic collisions. Binary Hard-sphere Collision

Collision Cross a a Section, 

2a

Collisional Cylinder

Collision Cross Section, 

Number of Collisions = n .  . v . t Reaction Rate Coefficient:

Reaction: A + B → C Collision Cross Section

Velocity Velocity distribution function 1  v   (v)vf (v)dv n 

Collision Frequency Density of the target

 c  n v Interaction Rate

Density of the beam

* * R  n  c  n n v

Average distance covered by a particle (photon, atom or molecule) between Mean Free Path successive impacts. Distance at which the intensity of particles drops by 1/e.

v 1    n v n Before the collision After the collision

v2=0 v1 m2 m1

E1

Conservation of Momentum: E2

m1v1  m1V1  m2V2

Conservation of energy: U=0 elastic collision

m v2 mV 2 m V 2 1 1  1 1  2 2 U U 0 inelastic collision 2 2 2 Elastic Collision ( U=0)

Elastic collision of equal masses

Elastic collision of masses in a system with a moving frame of reference

Elastic collision of unequal masses Elastic Collision ( U=0)

m1v1 = m1V1 + m2V2 m v2 mV 2 m V 2 1 1  1 1  2 1 2 2 2

Fraction of energy E2 transferred in an  ? elastic collision E1 E2

Answer:

E 2 4  m1  m2  2 E1 (m1  m2) Inelastic Collision ( U=0)

m1v1 = m1V1+ m2V2 2 2 2 m v m V m V 1 1 = 1 1 + 2 2 +U 2 2 2

First eliminate V2 from the above equations Assume v1 is constant Maximum fraction U U Max  0 = ? of energy E1 transferred in an U V1 elastic collision

Answer:

m2 UMax   E1 m1  m2 Elastic Collision ( U=0) Inelastic Collision ( U=0)

E 2 4  m1  m2 m2 UMax   E1  2 E1 (m1  m2) m1  m2

m1=m2= me Case 1- m1=m2  E1 = E2 Umax~0.5E1 m1=m2=ma or mi

m1= me Case 2- m2 >> m1  E2~0 Umax~E1 m2= ma or mi Power Supply

Anode Cathode ion

electron

Lorentz Force  F=eE  Fi = Fe

F=ma Electrons accelerate faster a >> a mi>>me e i and travel longer distances

F =F and electrons travel longer distances i e Electrons pick Energy=Force x Distance up more energy from the power source Electrons pick up energy from the power supply

Electrons transfer energy to ions because of large collision cross sections (Coulomb interaction) compared to the atoms

Ions transfer energy to the neutral because of their approximately equal mass • Every week at the end of my lecture, we will discuss for ½ hour about the project.

• You will be randomly asked to present your most recent project activities and you will be graded.

1-The objective (or importance) of your plasma application

2- At least two recent (max 1 year) activities (such as publication, Links to other research activities, …) in your project area.

+ + + + + + + + +

Coupling Breakdown Maintenance DC, AC, RF, MW Power Supplies Solid (e.g. iron, copper, …) Man-Made Capacitors Liquid (Mercury, …) Plasmas

Focused Laser Gas (Ar, H2, SF6, …) Beam

Electron and ion beams