Thermodynamics of Materials
19th Lecture 2007. 5. 27 (Monday)
CVD Diamond
P = 20 ~ 100 Torr Tf= 1900~2200oC Ts= 800~1100oC CH4 – H2: 100 sccm CH4 : 1 ~ 3%
Atomic Hydrogen Hypothesis Atomic Hydrogen Hypothesis
graphite C
gas
C
μ
μ <
Graphite Etching
gas diamond
C C
μ < μ
Diamond Etching
gas graphite
C C
μ > μ
Graphite Deposition
gas diamond
C C
μ > μ
Diamond Deposition
Apply thermodynamics to etching or deposition.
Graphite vs Diamond
μ
Cgraphite< μ
CdiamondAtomic Hydrogen Hypothesis Atomic Hydrogen Hypothesis
Thermodynamics of simultaneous graphite etching and diamond deposition
gas graphite
C C
μ < μ
Graphite Etching and Diamond Deposition
graphite diamond
C C
μ < μ
gas diamond
C C
μ > μ
and
graphite gas diamond
C C C
μ > μ > μ
The inequalities do not satisfy
Fig. 4
The simultaneous CVD of diamond and gasification of graphite is recognized as the vapor-phase transport of carbon from graphite to diamond. Summing Eqs. (5) and (6) to obtain an overall process gives
o
graphite diamond
y m
( y +m )H +C → + H2 +C (7) 2
which, if separated into independent reactions, is simply the recombination of atomic hydrogen with the conversion of graphite into diamond, i.e.,
o
graphite diamond
y m
(Y M )H H
C C
(8) (9) + → +
→
2 2
Equation (9) conflicts with the accepted phase diagram for carbon, and the paradox that has disturbed the early skeptics becomes apparent.
Thus, there must be an error either in re(in fact) or in voce(in discourse or logic), and there has been much debate as to the proper synthetic paradigm for the CVD of diamond.
Atomic hydrogen hypothesis is not an hypothesis
but an experimental fact!
Diamond Deposition on the Etch Pit of Graphite Substrate
A.R. Badzian et al., Mat. Res. Bull., 23 (1988) 531
Weight Change of Graphite Ring
M. C. Salvadori et al, J. Electrochem. Soc., 139 (1992) 558 0.5%CH4-H2, 80 Torr. Tsub= 870oC
Deposition Time (h)
before experiment after experiment 37.06 mg
43.21 mg (6.15 mg)
TF : 2100oC, Ts: 1050oC, 1% CH4 - H2, 2h
Simultaneous Diamond Deposition and Graphite Etching
Two irreversible processes of deposition and etching take place simultaneously in opposite directions!
Contradiction between Experimental Facts and the 2nd Law of Thermodynamics
Which should we believe, experimental facts or the 2nd law of thermodynamics?
What should we do in this situation?
Do we understand it clearly?
How about thermodynamics of CVD?
Simultaneous Deposition and Etching Simultaneous Deposition and Etching
→ Simultaneous condensation & evaporation
→ Simultaneous Si deposition by SiH4 and its etching by HCl in Si CVD.
What is the thermodynamic meaning?
Condensation → HvaporO HliquidO
2
2
μ
μ
>Evaporation →
2 2
vapor liquid
H O H O
μ
<μ
Simultaneous condensation & evaporation
liquid O H vapor
O
H2
μ
2μ
> and2 2
vapor liquid
H O H O
μ
<μ
Lower Limit of Deposition Temperature of CVD Diamond in the C-H-O System
Hwang, J. Crystal Growth, 135 (1994) 165
Hwang et al. Diamond Relat. Mater., 3 (1993) 163
Hwang, J. Crystal Growth, 135 (1994) 165
Bachmannet al, Diamond Relat. Mater. 1 (1991) 1 Petherbridge et al. J. Appl. Phys., 89 (2001) 5219
CVD Diamond
P = 20 ~ 100 Torr Tf= 1900~2200oC Ts= 800~1100oC CH4 – H2: 100 sccm CH4 : 1 ~ 3%
Anybody can make CVD diamond.
Nobody knows why!
Gas Gas
Diamond
Diamond GraphiteGraphite
Austenite
Fe3C
Graphite
Gas Liquid
Tetra. ZrO2
Mono. ZrO2
Examples of Dominant Formation Examples of Dominant Formation of Metastableof Metastable PhasePhase
Gas
Diamond
Graphite
3
4 2
3 4
gas solid
G πr f → π σr
Δ = Δ +
2 2
(3.7 / ) (3.1 / )
dia gra
J M J M
σ σ
gas dia gas gra
f → f →
Δ Δ
Comparison of stability and nucleation barrier Comparison of stability and nucleation barrier
Plot ΔG vs r
for diamond and graphite.
( ) ( )
3 2
2 / 3 2 / 3
1/ 3 2 / 3
4 4
3
4 3
π π σ
μ η σ
μ η σ
η π
→
→
→
Δ = Δ +
Δ = Δ +
Δ = Δ +
= Ω
gas solid
dia vol
gas dia
dia dia dia
gas gra
gra gra gra
G r f r
G n n
G n n
for sphere
Derive n*.
( )
( ) ( )
( )
{ }
2 / 3 2 / 3
2 / 3
1/ 3
μ η σ μ η σ 0
μ μ η σ η σ
μ μ η σ η σ
→ →
→ →
→ → −
Δ + − Δ + =
= Δ − Δ + −
= Δ − Δ + −
gas gra gas dia
gra gra dia dia
gas gra gas dia
gra gra dia dia
gas gra gas dia
gra gra dia dia
n n n n
n n
n n
2 / 3 2 / 3 3
* 36 σ σ
π μ →
⎛Ω − Ω ⎞
= ⎜⎜⎝ Δ ⎟⎟⎠
gra gra dia dia
gra dia
n
3 3
*
2 / 3 2 / 3 3
36
η σ η σ η σ η σ
σ σ
π μ
→ → →
→
− −
⎛ ⎞ ⎛ ⎞
=⎜⎝Δ − Δ ⎟⎠ =⎜⎝ Δ ⎟⎠
⎛Ω − Ω ⎞
= ⎜⎜⎝ Δ ⎟⎟⎠
gra gra dia dia gra gra dia dia
gas dia gas gra gra dia
gra gra dia dia
gra dia
n u u u
2 / 3 2 / 3
(8.38) (9.55)
dia dia gra gra
V σ ≺ V σ
0 500 1000 1500 2000
-10 -5 0 5 10
graphite diamond
Gibbs free energy, 10-20 KJ
Number of carbon atoms Size Dependence of Clusters on
Stability between Diamond and Graphite
Hwang et al.
Diamond Relat. Mater.
1 (1992) 9
No Gas Activation
→ Graphite Gas Activation
→ Diamond
n* > 1,000,000 for other metastable phases such as Fe3C and t-ZrO2
→Dominant nucleation of a metastable phase is a rule rather than exception.
In the case of carbon,
Surface Energy is the only one that can be varied by the processing condition
n* = 36 π ( σdia (Ωdia)3_
2
_σgra (Ωgra)3
2
)3 f fgra dia
Role of the Gas Activation is to
modify the surface energy in the way favoring the stability of diamond over that of graphite
essential to the dominant formation of diamond over graphite
0 500 1000 1500 2000 -10
-5 0 5 10
20%
10% graphite diamond
Gibbs free energy, 10-20 KJ
Number of carbon atoms Size Dependence of Clusters on
Stability between Diamond and Graphite
Hwang et al.
J. Crystal Growth 172 (1997) 416
Capillary Pressure in the Nucleation Capillary Pressure in the Nucleation
Stage of Diamond or Graphite Stage of Diamond or Graphite
r
P2 P1
P r P
P 2σ
1
2 − =
= Δ
Cluster of 1 nm in radius
2 9
2 2 3.7 / 10
J M
r M
σ
−
= × = 7400 MPa
1/ 3
3 1/ 3
r 4 n
π
⎛ Ω⎞
= ⎜ ⎟
⎝ ⎠
Find n, where
dia , c C gra , c
C μ
μ =
2 / 3 2 / 3 3
* 36
σ σ
π μ
→⎛Ω − Ω ⎞
= ⎜⎜⎝ Δ ⎟⎟⎠
gra gra dia dia gra dia
n
