|
Symbol |
Description |
Unit |
|
a |
width of a crystal unit cell |
μm |
|
αCO |
production ratio of CO |
1 |
|
b |
height of a crystal unit cell |
μm |
|
B |
parabolic rate coefficient |
m2/s |
|
B/A |
linear rate coefficient |
m/s |
|
C |
initial enhancement parameter |
μm/s |
|
C*, C0 |
concentration of the oxidants in the gas |
cm-3 |
|
Cact |
active dopant concentration |
cm-3 |
|
CC, CCI, CCS |
concentrations of C, C interstitial, and C at the oxide surface |
cm-3 |
|
CC0 |
solubility limit of C |
cm-3 |
|
Cinit |
initial active dopant concentration |
cm-3 |
|
CO, COS |
concentrations of O and O at the oxide |
cm-3 |
|
Cth |
threshold concentration |
cm-3 |
|
Ctot |
total doping concentration |
cm-3 |
|
CS |
concentration of the oxidants at the |
cm-3 |
|
CSi, CSiI, CSiS |
concentrations of Si, Si interstitials, and Si at the oxide surface |
cm-3 |
|
CSi0 |
solubility limit of Si |
cm-3 |
|
Css |
solid solubility |
cm-3 |
|
D |
oxidant diffusion coefficient in the oxide |
m2/s |
|
DC, DO, DSi |
diffusion coefficient of C, O, and Si |
m2/s |
|
E |
energy |
eV |
|
Ea |
activation energy |
eV |
|
EA, ED |
ionization energy of acceptors and donors |
eV |
|
EB |
breakdown field |
MV/cm |
|
EC |
bottom edge of the conduction band |
eV |
|
EF |
Fermi level |
eV |
|
EV |
top edge of the valence band |
eV |
|
Eg |
energy bandgap |
eV |
|
εs |
relative dielectric constant |
1 |
|
η, η’ |
oxidation rate of Si and C interstitials on the oxide surface |
1 |
|
F1-3 |
oxidation fluxes |
cm-2 s-1 |
|
Fact |
empirical scalar parameter |
1 |
|
gA, gD |
spin degeneracy factor of acceptors and donors |
1 |
|
h |
gas-phase transport coefficient |
m/s |
|
H |
inverse Henry’s law constant |
mol/m3Pa |
|
k |
reaction rate coefficient |
cm3 mol-1 s-1 |
|
k0 |
initial interfacial oxidation rate |
m/s |
|
ks |
surface oxidation rate coefficient |
m/s |
|
kSi, km, ka, kC |
oxidation growth rates in direction of the Si-, m-, a-, and C-face |
s-1 |
|
κ |
characteristic reaction rate |
s-1 |
|
κ1/2, κ1/2’ |
oxidation rates of Si and C interstitials on the oxide surface |
m/s |
|
L |
characteristic length |
μm |
|
λ |
thermal conductivity |
W/cm K |
|
MC |
number of equivalent minima in the |
1 |
|
me*, mh* |
effective mass of electrons and holes |
kg |
|
μn |
electron mobility |
cm2/Vs |
|
μp |
hole mobility |
cm2/Vs |
|
n |
electron concentration |
cm-3 |
|
ni |
intrinsic carrier concentration |
cm-3 |
|
N |
number of oxidant species |
cm-3 |
|
NA, ND |
acceptor and donor concentration |
cm-3 |
|
NC, NV |
effective density of states in the conduction and valence band |
cm-3 |
|
νSi, νC |
emission ratio of Si and C |
1 |
|
p |
hole concentration |
cm-3 |
|
px |
partial pressure |
Pa |
|
R1/2 |
half-maximal electrical activation ratio |
1 |
|
Ract |
electrical activation ratio |
1 |
|
Ractn, Ractp |
electrical activation ratio of n-type and |
1 |
|
Rmax, Rmin |
maximal and minimal electrical activation ratio |
1 |
|
ρ |
density of a crystal unit cell |
g/cm-3 |
|
ρC, ρV |
density of states in the conduction and |
cm-3 |
|
t |
time |
s |
|
T |
temperature |
°C |
|
tA |
annealing time |
min |
|
TA |
annealing temperature |
°C |
|
Tip |
temperature at the inflection point |
°C |
|
Tmelt |
melting point |
°C |
|
x, y, z |
direction vector coordinates |
1 |
|
\(\hat{X}\) |
normalized oxide thickness |
1 |
|
X |
thickness of the oxide |
μm |
|
Xinit |
initial thickness of the oxide |
μm |
|
Xmax |
maximal thickness of the oxide |
μm |
|
Z |
pre-exponential factor |
cm-3 |
|
Symbol |
Description |
Value |
|
h |
Planck constant |
6.62607 · 10-34 Js |
|
kB |
Boltzmann constant |
1.38065 · 10-23 JK-1 |
|
m0 |
rest mass of an electron |
9.10938 · 10-31 kg |
|
R |
ideal gas constant |
8.31446 J K-1 mol-1 |