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.

Cl 2 O + + H + O 2 2 Which one is elementary?

2HCl O + O 2 +

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

R

  1

j dn j dt

n j = volume density (m -3 ) of molecules of the j:th substance α j = stoichiometric coefficient

A A+B K 1 K 2

Kinetics

products 

R

 

dn A dt



K

1

n A

products 

R

 

dn A dt

 

dn B dt



K

2

n A n B

A+B+C K 3 products 

R

 

dn A dt

 

dn B dt

 

dn C dt



K

3

n A n B n C

The quantities K 1

first-

,

second-

(s and -1 ), K 2 (m 3 /s) and K 3 (m 6 /s) are the

third- order rate constants

Kinetics

• Relation to equilibrium constants A+B K 2 K -2 C+D K 2 n A n B =K -2 n C n D Thermal equilibrium  n C n D n A n B 

K

2

K

 2   (

T

)

First order consecutive reactions

A K A B K B C

dn A dt dn B dt dn C dt

 

K A n A



K A n A



K B n B



K B n B

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.

A + + e  A A +  + e A + S + S S - 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

Condition for emission:  iz > 2   Kinetic energy:  max  min =  iz =  iz 2   2   2  F  iz ionization energy    F - work function - fermi energy

Case 2

Atom/Ion impact on surface

Sputtering Adsorption, desorption Molecules split into atoms Implantation Low energies ~10 V ~100 V ~1000V

Dissociative chemisorption

Adsorption: Lennard-Jones diagram

Physisorption Molecular chemisorption

Adsorption

Physisorption

• Van der Waal •  H ads < 35 kJ/mol • No energy barrier • Never dissociative • Many monolayers • Not dependent on surface coverage

Chemisorption

• Chemical bond •  H ads > 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  

p h ys o r ch em K desor



K

0

e T

Associative desorption

• Opposite to associative adsorption K 0 ~ the number of attempted escapes per second from the adsorption well K 0 ~ the number of collisions per second per unit area on the surface between two adsorbed atoms

Equations

Surface coverage (Täckningsgrad) :

 

Number of adsorbed Total number of species sites

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

  1  

ads n



A

:

S ads n A

:

S

Sticking coefficient :

S

 

E



S

0

e k B T

( 1   )

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

 sput  0.06



t Z t

( 

i

 Z t  thr – Average atomic number of target – Threshold energy for an ion to sputter target  t  i – Average energy for atoms in collision  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 ( i ) 

thr

) ( t )

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

K b K a K f K g K c K h K e K d Ka – flow to the surface Kb – adsorbation rate Kc – reaction rate Kd – desorption rate Ke – flow rate into gas phase Kf – normal desorption Kg – associative desorption Kh – adsorption of products