Lecture‐27
¾
Collision Processes: Collision Cross‐section & Ionization
¾ Ion impact on a target ‐ Sputtering
¾ Sputtering Yield
Ref. :The Materials Science of Thin Films, by Milton Ohring
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Collision Processes
• Collisions between electrons and inert Argon gas atoms could either be elastic or inelastic depending upon whether the internal energy of the colliding species is conserved or not
• Recall that in a billiard‐ball like head on collision, the KE is exchanged (elastic) – momentum & energy are both conserved
• The PE remains constant in such elastic collisions
(The PE basically resides within the electronic structure of the colliding entities) • Increase in PE is manifested by Ionization and Excitation processes (inelastic)
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Elastic and Inelastic Collisions
(H.W.)
Inelastic
Elastic
E2 M 2υ 22 / 2
4M 2 M 1
2
=
=
cos
θ
2
2
E1 M 1υ1 / 2 (M 2 + M 1 )
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M2
ΔU
=
cos 2 θ
E1
M 2 + M1
ΔU = change in internal energy of the struck
particle
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Collision Cross‐section & Ionization
• The mean free path λmfp of gas molecules is related to
collision cross‐section ‘σc ‘ and gas concentration ‘n’ as
σ c ≡ π d c2
• Both λmfp and σc characterize collisions (dc=collision dia.)
λmfp
1
= nσ c
• While λmfp is reserved for elastic collisions, σc has broader applicability as it also include the inelastic collisions
• For ionization of an inert gas atom due to electron impact, the ionization cross‐section σe is a function of electron energy
(see fig, next page)
• The ionization energy threshold (Eth) is the minimum E required to eject the most weekly bound electron; typically, Eth is 15‐20 eV
• Below Eth, σe is zero. As E increases, the σe also increases At Eth , σe is same as molecular cross‐section; Max. σe at ~100 eV
• Above Eth , σe decrease with increase in E because collision time is too short
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Ionization cross sections for various gases plotted as a function of energy
‰ The ionization energy threshold (Eth) is the minimum E required to eject the most weekly electron, Eth is 15‐20 eV, typically
σ0 ≡ π a
2
0
= 8.88 ×10 −17 cm 2
(a 0 = Bohr radius)
‰ Below Eth , σe is zero; as E increases σe also increases; At Eth , σe is same as molecular cross‐section; Max. at ~100 eV
‰ Above Eth , σe decrease with increase in E because collision time is too short
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Elastic & Inelastic electron‐gas atom collisions
E2 M 2υ22 / 2
4M 2 M1
2
=
=
cos
θ
2
2
E1 M1υ1 / 2 (M 2 + M1 )
• Due to large mass difference between them,
the fractional energy transfer ratio γ is ΔU
M2
2
(H.W.)
=
cos
θ
‐4
‐5
very low (~10 ‐10 ). E1 M 2 + M1
Thus electrons continue to gain energy during their drag in the field and undergo several elastic collisions • When the electrons gain sufficient energy, they are able to cause ionization of gas atoms (IE~15‐20 eV) • Actually, on impact with high KE electron, the atom is first excited, and then it may undergo (in order of increasing energy Ee) either:
(i) Relaxation back towards ground state, or
(ii) Dissociation, or
(iii) Ionization 1/4/2016
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Applications in Plasma Enhanced Etching and Chemical Vapor Deposition (CVD) processes
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Physics of Sputtering
Ion‐surface Interactions
Various Energetic‐particle bombardment effects
on surfaces and growing films.
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Ion‐bombardment & its applications ?
• Ion bombardment on a target results in: Back reflection, sticking or adsorption, scattering, ejection or sputtering of surface atoms, or ion getting buried in subsurface layers (ion implantation)
• Other manifestation ‐ Surface heating, chemical reactions, atom mixing, and alteration of surface topography
• Ion bombardment is exploited in 2 ways in materials processing: At cathode, sputtering ejects atoms required for thin film deposition; At anode, the bombardment of growing film can alter film properties
• Other important applications: Ion milling (used in patterning/etching
in chip fabrication industry) & Ion implantation (in controlled doping)
• Release of the assorted charged particles (e‐s & ions), neutrals and photon of varying energies and abundances. The analysis of later yields useful information about the surface – structure and composition (This is how RBS and SIMS characterization tools work)
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Particle sticking probability – vs. – KE of incident ion
Sputtering
20 eV
↓
~3 regimes of influence of incident ion energy can be identified
25 meV
(RT Energy)
No. of deposited ions
Particle sticking probability =
~1 if E=10‐2 eV
No. of incident ions (thermal E at RT)
Other important parameters : Type, mass, charge of the impinging ions, nature of the surface, its crystallography/ texture
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Sputtering : What happens at the time of impact ?
‰ When ion and the target atom are angstroms apart, the electron exchange occurs (within ~10‐15 s), and result in electronic excitations
As work functions of solids (3‐6 eV) < the ioniz. potentials for most gases (15 ‐ 20 eV), the ions capture e‐s from the target atoms. Thus, the scattered & recoiled species with keV energies are largely neutral
‰ At further small distance during the ion‐solid encounter, the separate atoms of atomic number Z1 (ion) and Z2 (target) evolve into molecular orbitals of a quasimolecule and finally into the atomic orbitals of an unstable but united atom of atomic number Z1+ Z2
Subsequently, the Pauli exclusion principle begins to dominate, resulting in atomic separation and collisional reionization of neutrals. This may be viewed as the moment of collision ‰ During the collision, several processes are possible depending on what is impacted and with what energy, e.g., if an ion strikes an atom of a molecule, the latter may dissociate or sputter out.
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Sputter Yield • Sputtering is a momentum transfer process, often dubbed as billiard of “atomic pool” wherein the incident ion (~cue ball) breaks up the close‐packed rack of atoms (~billiard balls), scattering some of them in backward direction (i.e., toward the player)
• This process is characterized by an important parameter, known as sputter yield (S), which is defined as:
Sputter yield, S ≡ No. of sputtered atoms per incident particle
•
•
•
•
S depends on energy of incident ion
S is a measure of efficiency of sputtering
Experimental values of S range from 10‐5 to 103
But for thin films by sputtering, the narrower range of S of 0.1‐10 is useful 1/4/2016
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Three energy regimes of sputtering Single Knock‐on
(Low energy)
Linear cascade
Spike
(High Energy)
o Ion impact sets atoms into motion →separate knock‐on events
o Eth required : 5‐40 eV (Eth depends on BE of surface atoms Us~2‐5 eV)
o Either, Eth=4Us (0.08 <M1/M2<1 or Eth=Us/γ ; γ=energy transfer fn.
(γ essentially magnifies the value of Us by accounting for the fraction of the ion energy transferred during the collision process)
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Sputtering Yield Data for Metals (Atoms/Ion)
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Here S varies from 0.01 to 4
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Linear collision‐cascade
‰ At further higher KE of incident ion: The density of recoils is sufficiently low so that most collisions involve one moving and one stationary particle (rather than 2 moving particles as in Single knock‐on process) ‰ This is the usual sputtering regime in which ejection of target atoms occurs
‰ S is a function of energy, S = Λ FD (E )
(Sigmund Theory)
o Λ = materials constant, related to the BE of surface atoms Us, the range of displaced target atoms, and the number of recoil atoms that overcome the surface barrier of the solid and escape.
o FD(E) accounts for energy deposited into the surface, and depends upon type, energy, and incident angle of the ion, and on target parameters (e.g., temperature)
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Sputter‐yield values for Al as a function of energy
Λ ~ 1 / NU S
N=Target’s atomic density
Us=Heat of sublimation, ΔHs
FD ( E ) = αNS n ( E )
α=f(Mt/Mi ,θ) ~0.1 – 1.4
NSn(E)=nuclear stopping power in eV.nm2/atom
Widely applicable simple formula for S:
4.2α S n ( E )
S=
US
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