Evolution of micro-structures on silicon substrates by surface. Osaka University

Transcription

1 Evolution of micro-structures on silicon substrates by surface diffusion Koichi Sudoh The Institute of Scientific ifi and Industrial Research Osaka University

2 Microstructure Fabrication applying Spontaneous Shape Transformation by Annealing Collaboration with: R. Hiruta, H. Kuribayashi, R. Shimizu Fuji Electric Group H. Iwasaki Osaka University Silicon-on-nothing Trench MOSFET Useful in fabrication of 3D structures on Si surfaces Trench corner rounding Formation of empty space in Si

3 Flattening of Surfaces (110) facet formation on sidewall of fin structures t T. Tezuka et al., Appl. Phys. Lett. 92, (2008).

4 Shape Modification toroidal structure M. M. Lee and M. C. Wu: J. Microelectromech. Sys. 15, 338 (2006).

5 Outline I. Shape transformation of 1D gratings Trench corner rounding during annealing Mass transport mechanism for shape transformation Analysis based on Mullins equation II. Shpe transformation of high spect ratio hole patterns Void formation via shape transformation Shape change of faceted voids Modeling of the evolution of faceted structures

6 Fabrication of 1D gratings g on Si(001) 1 m <110> 6inchφ N-Si(100) 2~3Ωcm 3 m - OF (1 1 0) Fabrication of a 1D trench array Fabrication of a 1D trench array by reactive ion etching on Si(001)

7 Trench corner rounding by annealing for 3 min 1 min 3 min 10 min at 1000 C

8 Mechanism of Morphological op oogcaevolution outo Surface Diffusion (SD) Evaporation Condensation(EC) solid Gibbs-Thomson Effect Curvature Dependence of fchemical lpotential ti (K) = K Curvature Dependence of Vapor Pressure: P eq (K) ln P eq ( K ) P 0 K kt

9 Mullins Equation for Evolution o of Isotropic op csurfaces W. W. Mullins: J. Appl. Phys. vapor pressure: p 0 1) Evaporation Condensation Case v n 01 exp K kt 1 A K A A K v n A 1 exp ) Surface Diffusion Case p(k) V n Curvature v n D s kt 2 X s 2 s K 2 2 K B 2 s s V n

10 Predictions from Scaling Argument Time scaling of the trench corner radius: R t 1) Evaporation Condensation Case 1 v n K R dr dt 1 R 2) Surface Diffusion Case v n s 2 K 2 1/ 2 R t dr dt R 3 1/ 4 R t

11 Corner Rounding of 1D Trenches es 1 min 3 min 10 min

12 Annealing time dependence of curvatures of trench corners R t 1/ 4 Surface Diffusion

13 Shape Transformation ato by Mullins Equation for EC and dsd t = 0 t=10 t = 40 t = 0 t = t = 0.01 Evaporation Condensation Surface Diffusion

14 Difference between EC and SD evaporation 1/ R t 2 Evaporation and Condensation 1/ R t 4 Surface diffusion

15 Simulation using Mullins Equation Bt = m Simulation SEM Images 4%H 2 /Ar 760Torr 1150 ºC 5min

16 Square Array of Cylindrical Holes D P top view Top View 3 m cross section D = 0.75 m, P = 1.0 m D = 0.75 m, P = 1.8 m

17 VidF Void Formation by Shape Transformation of Hole Array Cross section Top view

18 Silicon on Nothing (SON) Structure 33 m 0.8 m SON structure

19 Facets on the Void Surface (311) (101) (113) (113) (011) (101) (111) (011) (111) (311) (311) (131) (131) (311) (131) (131) (100) (110) (010) (100) (110) (010) (311) (311) (131) (131) (311) (311) (131) (131) (101) (111) (113) (011) (111) (101) (011) (113)

20 Effects 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.

21 Evolution of void shape during annealing at 1100 ºC in 60 Torr H 2 gas 5 min 10 min 20 min 40 min 0.70 m m m m 3 The volume of a void is preserved during shape change

22 Mean chemical potential of a facet Chemical potential of a faceted crystal (J. E. Taylor, Acta Metall. Mater. 40 (1992) 1475.) i 0 K i i Weighted mean curvature K i 1 S i ji f ij l ij v i S i ji J ji 2 / 1 cij 2 f c c ij ij j i ij n n j i

23 Numerical Simulation of Void Shape Change Area of i-th facet: S i i l ij j v Normal velocity of the i-th facet v i S i ji Atomic current from j-th to i-th facet l ij J ij J ji Dc kt 0 j x ij i M. Kitayama, J. Am. Ceram. Soc. 83 (2000) x ij S i S j

24 Simulation Results

25 Annealing time dependence of the height and width of voids 1.7 H W Size (m) W H Annealing time (min)

26 Summary 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 numerical simulation based on the Mullins equation. Shape transformation of hole arrays Empty spaces can be created in the bulk Si by annealing of hole arrays. Modeling for the evolution of polyhedral crystals reproduces the evolution of a faceted void in Si substrate.