evolution of micro-structures on silicon substrates by ... · mullins equation for evolution of...

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.