evolution of micro-structures on silicon substrates by ... · mullins equation for evolution of...
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Evolution of micro-structures on silicon substrates by surface
diffusion diffusion
Koichi SudohKoichi Sudoh
Th I i f S i ifi d I d i l R hThe Institute of Scientific and Industrial ResearchOsaka University
Microstructure Fabrication applying Spontaneous Shape Transformation by Annealing
Collaboration with:Collaboration with:R. Hiruta, H. Kuribayashi, R. Shimizu Fuji Electric Groupj pH. Iwasaki Osaka University
Trench MOSFETSilicon-on-nothing
Useful in fabrication of 3D structures on Si surfacesTrench corner rounding
f
Useful in fabrication of 3D structures on Si surfaces
Formation of empty space in Si
Flattening of Surfacesg
(110) facet formation on id ll f fi t tsidewall of fin structures
T. Tezuka et al., Appl. Phys. Lett. 92, 191903 (2008).
Shape ModificationShape Modification
toroidal structure
M. M. Lee and M. C. Wu: J Microelectromech Sys 15 338 (2006)J. Microelectromech. Sys. 15, 338 (2006).
OutlineOutline
I. Shape transformation of 1D gratingsTrench corner rounding during annealingMass transport mechanism for shape transformation
Analysis based on Mullins’ equation
II. Shpe transformation of high –spect‐ratio hole patternspatterns
Void formation via shape transformationShape change of faceted voidsShape change of faceted voidsModeling of the evolution of faceted structures
Fabrication of 1D gratings on Si(001)g g ( )
1 m
6inchφN Si(100)
<110>
3 mN-Si(100)
2~3Ωcm
OF (1 1 0)-
Fabrication of a 1D trench arrayFabrication of a 1D trench arrayby reactive ion etching on Si(001)
Trench corner ro nding b annealingTrench corner rounding by annealing
for 3 min
1 min 3 min 10 min at 1000 C
Mechanism of Morphological Evolutionec a s o o p o og ca o ut o
Evaporation Condensation(EC)Evaporation‐Condensation(EC)Surface Diffusion (SD)
solid
C t D d f Ch i l P t ti l
Gibbs-Thomson EffectCurvature Dependence of Chemical Potential
(K) = K
KPeq )(
Curvature Dependence of Vapor Pressure: Peq(K)
KkTP
eq
0
)(ln
Mullins Equation for Evolution of Isotropic Surfaces
vapor pressure: p0W. W. Mullins: J. Appl. Phys.
u s quat o o o ut o o sot op c Su aces
1) Evaporation‐Condensation Case
KkT
vn exp10
Vnp(K)
KAAKAAvn 2121 exp1
Curvature
2) Surface Diffusion Case
2
2
2
22
sKB
sK
kTXD
v ssn
s Vn
Predictions from Scaling Argumented ct o s o Sca g gu e t
Time scaling of the trench corner radius: tR
1) Evaporation‐Condensation Case
Time scaling of the trench corner radius: tR
) p
RKvn
1
dR
2/1tR 1 R
dtdR
2) Surface Diffusion Case2Kv
2svn
3 RdR4/1tR
Rdt
Corner Rounding of 1D TrenchesCo e ou d g o e c es
1 min1 min
3 min
10 min
Annealing time dependence of curvatures oftrench corners
4/1tR Surface DiffusiontR Surface Diffusion
Shape Transformation by Mullins Equation for EC and SDS ape a s o at o by u s quat o o C a d S
t = 0 001
t = 0
t = 10
t = 0
t = 0.001
t = 0.01
t = 10
t = 40
Evaporation‐Condensation Surface Diffusion
Difference between EC and SD
evaporation
2/1tR
Evaporation and CondensationEvaporation and Condensation
4/1tR
S f ffSurface diffusion
Simulation using Mullins Equation
2 m2 m
Simulation
Bt = 0.14
SEM Images 4%H /A 760TSEM Images 4%H2/Ar 760Torr 1150 ºC5min
Square Array of Cylindrical Holes
D
P top view
Top ViewTop View3 m
cross section
D = 0.75 m, P = 1.0 m D = 0.75 m, P = 1.8 m
V id F ti b Sh T f ti f H l AVoid Formation by Shape Transformation of Hole Array
Cross section
Top view
Silicon‐on‐Nothing (SON) StructureSilicon on Nothing (SON) Structure
0.8 m
SON structure
33 m
SON structure
Facets on the Void Surface
(111)(101) (011)
(113)
(111)
(113)(011)(101)
(311) (131) (131)(311)(131) (131)(311)(311)
(111)
(110) (010)(100)(110) (010)(100)
(111)
(131)(131)
(311)(311)
(101) (011)
(131)
(111)
(311)
(101) (011)
(131)(311)
(101) (011)(113)(113)
( )
Effects of the adjacent voidsEffects of the adjacent voids
P = 1.8 m P = 1.0 m
Shape change of individual voids occur independently without affected by the neighboring voids.
Evolution of void shape during annealing
at 1100 ºC in 60 Torr H2 gas
5 min 10 min 20 min 40 min
0.70 m3 0.70 m3 0.71 m3 0.72 m3
The volume of a void is preserved during shape change
Mean chemical potential of a facetp
Chemical potential of a faceted crystal(J. E. Taylor, Acta Metall. Mater. 40 (1992) 1475.)(J. E. Taylor, Acta Metall. Mater. 40 (1992) 1475.)
ii K 0i
lfK 1Weighted mean curvature
ij
ijiji
i lfS
K
21/f 21/ ijiijjij ccf
jiijc nn
ij
iji
i JS
vjiijiji
Numerical Simulation of Void Shape Change
Normal velocity of the i-th facet
Area of i-th facet: Si
vi
ijijij
ii Jl
Sv
y
l ij
i
jAtomic current from j-th to i-th facet
j
ij
ijij xkT
DcJ
0
j
jiij SSx M. Kitayama, J. Am. Ceram. Soc. 83(2000) 2561.
Simulation ResultsSimulation Results
0 1500 3000 5000
Annealing time dependence of the height and g p gwidth of voids
1 61.7
1 21.31.41.51.6
e (
m)
W H
0 80.91.01.11.2
Size
HW
0 10 20 30 40 50
0.8
Annealing time (min)
Summaryy
Shape transformation of 1D gratings
Dominant mass transport mechanism for the shape transformation is surface diffusion.
The evolution of trench profiles can be predicted by i l i l ti b d th M lli tinumerical simulation based on the Mullins equation.
Shape transformation of hole arraysEmpty spaces can be created in the bulk Si by annealing of hole arrays.y
Modeling for the evolution of polyhedral crystals reproduces the evolution of a faceted void in Si substrate.reproduces the evolution of a faceted void in Si substrate.