Chemical kinetics

Lecture IV

Jenny Frodelius & Jonas Lauridsen

References

• Principles of Plasma Discharges and Materials Processing, 2nd Edition

M. A. Lieberman & A. J. Lichtenberg

• Surface Chemistry and Catalysis

G. A. Somorjai

Outline

• Kinetics – – What’s our interest? – Terms, Basic kinetics (rate constants)

• Surface Processes -

• Surface Kinetics -

Kinetics

The study of how fast processes occur

We are interested in...

...kinetics for

the gas phase , between the gas-phase and surface

and on the surface.

Kinetics

• Elementary reactions – a reaction that proceeds in one step in a simultaneous collision of all reactant molecules.

Cl2 + H2 2HCl

O+ + O2 O + O2+

Which one is elementary?

Kinetics

• The most important elementary reactions– Unimolecular A products– Bimolecular A+B products

• In low-pressure termolecular are complex

Kinetics

• The reaction rate (R) for gas-phase reaction

nj= volume density (m-3) of molecules of the j:th substance

αj= stoichiometric coefficient

dt

dnR j

j1

Kinetics

A products

A+B products

A+B+C products

The quantities K1 (s-1), K2 (m3/s) and K3 (m6/s) are the first-, second- and third- order rate constants

AA nKdt

dnR 1

BABA nnKdt

dn

dt

dnR 2

CBACBA nnnKdt

dn

dt

dn

dt

dnR 3

K1

K2

K3

Kinetics

• Relation to equilibrium constants

A+B C+D

K2nAnB=K-2nCnD

Thermal equilibrium

K2

K-2

)(nn

nn

2

2

BA

DC TK

K

First order consecutive reactions

A B CKA KB

BBC

BBAAB

AAA

nKdt

dn

nKnKdt

dn

nKdt

dn

Outline

• Kinetics• Surface Processes -

– Positive ion neutralization & secondary electron emission

– Atom/Ion impact on surface• Adsorption Desorption• Fragmentation• Sputtering• Implantation

• Surface Kinetics

Surface processes

Surface processes

Neutralization in the gas-phase is a

forbidden reaction, but on the surface a

fast three-body reaction occurs.

AA++ + e + e-- A A

AA++ + e + e-- + S + SA + SA + S

S - surfaceS - surface

Neutralization of positive ions and secondary electron emission

• Case 1: Ion pick up electron, becomes excited and release an photon to reach atomic state

• Case 2: Ion pick up electron, becomes an atom, release excess energy that will cause the surface to release an Auger electron.

• Case 3: Upon ion impact kinetic energy is transfered to surface so that the surface can release an Auger electron

Case 2

Condition for emission:

iz > 2

Kinetic energy:

max = iz - 2

min = iz - 2 - 2F

iz - ionization energy

- work function

F - fermi energy

Atom/Ion impact on surface

Low ~10 V ~100 V ~1000V energies

Sputtering

Adsorption,desorption

Molecules splitinto atoms

Implantation

Adsorption: Lennard-Jones diagram

Dissociativechemisorption

Physisorption

Molecularchemisorption

Adsorption

Physisorption• Van der Waal

• -Hads < 35 kJ/mol

• No energy barrier• Never dissociative• Many monolayers• Not dependent on surface

coverage

Chemisorption• Chemical bond

• -Hads > 35kJ/mol

• Varying energy barriers• Often dissociative• One monolayer• Dependent on surface

coverage

Desorption

Desorption• Reverse reaction to adsorption• Must be in balance with

adsorption at thermal equilibrium

• First order desorption rate constant

K0 ~ the number of attempted escapes per second from the adsorption well

Associative desorption• Opposite to associative adsorption

K0 ~ the number of collisions per second per unit area on the surface between two adsorbed atoms

Tdesor

chemorphys

eKK

0

Equations

Surface coverage (Täckningsgrad) :

Langmuirs adsorption isotherm :Equilibrium surface coverageas a function of pressure at fixed temperature.

Sticking coefficient : )1(0 Tk

E

BeSS

SAads

SAads

n

n

:

:

1

sitesofnumberTotal

speciesadsorbedofNumber

Fragmentation (~10 V)

• Ionic and neutral molecules fragment into atoms

• Atoms are reflected or adsorbed

• Energy must be in the range of atomic bonds (1-10 V)

• When energy is 4-5 times higher than the threshold energy, over half of the molecules split into atoms

Sputtering (~100 V)

• Heavy particles, usually ions, bombard and transfer energy to many target atoms which collide with other atoms in the solid.

• Most atoms are trapped in solid but one or several escape from the surface.

• Threshold energy (thr) 20-50 V

• Distribution of atom energies is isotropic with mean energy (t) of the surface binding energy.

Sputtering yield

Zt – Average atomic number of target thr – Threshold energy for an ion to sputter targett – Average energy for atoms in collisioni N(t)(i) N – Number of atoms in the collision cascade having t

(i) – Range of ion penetration into the target (t) – Surface depth from where atoms can escape

)(0.06

sput thritt

Z

ti

Sputtering yield

Sputtering yield

as a function of

angle of incidence for

different metals

Outline

• Kinetics

• Surface Processes

• Surface Kinetics– Equations– Equations

• ...and more equations...

Surface kinetics

Surface kinetics

Ka

Kb

KfKg

KhKd

Ke

Kc

Ka – flow to the surfaceKb – adsorbation rateKc – reaction rateKd – desorption rate

Ke – flow rate into gas phaseKf – normal desorptionKg – associative desorptionKh – adsorption of products