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Physics of Thin Films

PES 449 / PHYS 549

Thermodynamics and Phase Diagrams

Ohring: Chapter 1, Section 1.5


tells us what can happen - - - not how fast it will happen

free energy change

G = Gfinal - Ginitial = H - T S

where H = enthalpy change, T = temperature, S = entropy change

  • G < 0 => process is allowed
  • G > 0 => process is forbidden
  • G = 0 => equilibrium

    nature will minimize free energy

Chemical Reactions

aA + bB <=> cC

We can relate the free energy change for this reaction to the activity, a, (kind of concentration).

It can be shown:

equation for free energy change

where R = gas constant = 1.987 cal/(mole K)

note if ai > ai(eq) you have supersaturation

often G is about the same as Go which is the free energy change in standard state

example: Ellingham diagrams

oxide formation

Ellingham diagram of Ni, Si and Al oxidation

if Al and Al2O3 are in contact with Si and SiO2:
  • Al will be oxidized to Al2O3
  • SiO2 will be reduced to Si

No information about rate.

if you have a Ni-Al alloy

Al oxidizes preferentially => may end up with Al2O3 film on top

Ni-Al alloy oxidation model

another example is stainless steel (Cr, Fe, Ni) which forms a Cr + Fe oxide layer

Phase Diagrams

arise from minimizing free energies for each phase

use for

  • gas - liquid - solid transitions
  • structural changes (graphite <--> diamond)
  • stable alloys


example: Carbon

Carbon phase diagram

the two phases (diamond and graphite) can coexist on the line that separates them

example: Iron

iron phase diagram showing triple point

triple point has three phases coexisting (very well defined point)


examples: alloys such as GaAs, NiCr, WSi

variables: P, T, and composition => 3 dimensional diagrams

typically we fix the pressure at one atmosphere

draw diagrams of Temperature vs. composition

Examine several common types of two component phase diagrams:

Binary Solid Solutions:

completely soluble in liquid and solid state at all compositions

SiGe phase diagram

phases and compositions:

at I: liquid with composition Co (about 30% Si, 70% Ge)

at II: liquid with composition Co and solid with composition CS(II)

at III: liquid with composition Cl(III) and solid with composition CS(III)

at IV: solid with composition Co

How much (mole fraction) is in each phase ?

at III:

equation of fraction in each phase

examples of other systems with binary solid solution phase diagrams:

Cu-Ni, Pt-Rh, NiO-MgO, FeO-MgO

components have same crystal structure

Binary Eutectic diagrams:

limited solubility in the solid state

eutectic phase diagram of PbSn

two solid phases: a, b

a = fcc substitutional solid of Sn in Pb

b = tetragonal substitutional solid of Pb in Sn

(note the reduced melting points of the alloys from either Pb or Sn)

phases and compositions:

at I: liquid of composition Co (about 35% Sn and 65% Pb)

at II: liquid of composition Co and solid a of composition Ca(II) and no solid b

at III: liquid of composition Cl(III) and solid a of composition Ca(III) and no solid b

at IV: solid a of composition Ca(IV) and solid b of composition Cb(IV)

How much of each phase:

same rule as above for binary solid solutions

examples of other systems having binary eutectic phase diagrams:

Bi-Cd, Al-Si, CaO-MgO


These phase diagrams are equilibrium phase diagrams.

Thin Films are generally NOT equilibrium growth processes.

(usually T is too low or deposition rate is too high.)

=> we can form other structures

Remember these examples have been at atmospheric pressure.

phase diagram does change at other pressures (like inside a vacuum system)

[HANDOUT: Si-Ge phase diagrams at other presssures]

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