Length Scales in Step-Bunch Self- Organization during Annealing of Patterned Vicinal Si(111) Surfaces

Transcription

1 Length Scales in Step-Bunch Self- Organization during Annealing of Patterned Vicinal Si() Surfaces T. Kwon, H.-C. Kan, and R. J. Phaneuf Nonequilibrium Interface and Surface Dynamics: Theory, Experiment and Simulation from Atomistic to Continuum Scales CSCAMM, April 3, 7

2 Silicon Surfaces Flat, Stepped & Patterned D. Lee, et al., MRS Sym Proc. 648 () 5 μm Spin Coating Resist Photolithography Mask Si() Reactive Ion etching Liftoff Developing Solvents, O Plasma

3 Patterned Silicon Surfaces Relaxation Kinetics Relaxation of Patterned Si() Annealing of Patterned Vicinal Si() T. Ogino, Surf. Sci 386, 37 (997) S. Tanaka, et al, PRL 78, 334 (997)

4 Lithographically Patterned Surface Combinatorial Length Scale Investigation Diameter (um) Spacing (um) 35 nm Si ().5 off toward [- ] Si()

5 Effect of Annealing (73 ºC) Small Period Limit.4 μm Diameter x.8 μm Pitch Before Anneal t = 3 s t = 65 s Up hill Down hill

6 Effect of Annealing (73 ºC) Intermediate Period Regime 4 μm Diameter x 8 μm Pitch t = 3 s t = 65 s t = 4 s Up hill Down hill

7 Effect of Annealing (73 ºC) Large Period Limit 8 μm Diameter x 6 μm Pitch t = 3 s t = 65 s t = 4 s Up hill Down hill

8 In-Plane Corrugation Step Bunch Waviness In-plane Corrugation (um) um.8um 4um 8um 5.6um. 3 4 Anneal Time (sec)

9 Out-of-Plane Corrugation- Step Bunch Height.8 um Diameter x 5.6 um Spacing Height (nm) s Height (nm) s 5 5 Distance (μm) 5 5 Distance (μm) RMS Amplitude (A) um Dia 5.6 um Pitch Time (s) 3 4

10 Evolution: Effects of length scale & Annealing time Pattern Length Scale.4um dia x.8 um spa 4um dia x 8 um spa 8 um dia x 6 um spa 3 73 C 65 sec In-plane Corrugation (um) RMS Amplitude (A) um.8um Time (s) 4um 3.4 um Dia.8 um Pitch Out of Plane 4 8um 5.6um In Plane Annealing Time 8 min. Decay Time Constant OOP IP Pit Diameter (um) τ ~ D Anneal Time (sec)

11 Step Stiffness- Steps And Kinks Produce Extra Broken Bonds.4 μm Diameter x.8 μm Pitch Kink Kink Step Surface Free Energy/Area 4 μm Diameter X 8 μm Pitch β gh f = f l l β = β + β φ

12 Step-Step Interaction 8 μm Dia. x 6 μm Pitch : 3 73 C On uphill side of the pit, Repulsive step-step interaction On downhill side of the pit, Bowed downhill wall possible sign of attractive step-step interaction β f = f + + l gh 3 l Bowed downhill wall

13 Step Motion Due to Sublimation Step profile on a patterned vicinal surface [] [] Loop Steps Vicinal Steps Up-hill Down-hill

14 ( ) = dt y x d n n, n w w gh R kt ˆ ~ Γ β ( ) n w k w k ˆ + + Mesoscopic Model for Step Kinetics* Attraction, g - g z x x y (xn(s),yn(s)) w w R n^ + k k *J.D. Weeks et. al. Dynamics o f Crystal Surfaces and Interfaces, Plenum Press 996

15 .7um.8um

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18 Simulated Length scale dependence on Pit Evolution t=s.4 um 4. um 8. um 3s Norm. In Plane Corrugation Time (sec) 6s Norm. OOP Corrugation Time (sec) 8

19 Time constant (sec) Pit Diameter (μm) OOP IP Exp Sim In-Plane and Out-of-Plane Corrugation Decay Time Constant Experiment vs. Simulation Γ=9x 9 A 3 /s; β = 8.35x - mev/a; g =.78 mev/a ~ m g d L d A L A r w h g r μ β θ π θ π β 5.5 ~ sin,, ~ 3 3 > < m g h L w A L A r w h w h g r μ β θ π π θ θ β. ~, tan, ~ 3 3 < = > ) sin( = = L A r y L A x π π.7 um 5.6um

20 Step Kinetic Parameters for Simulation d ( x, n yn ) = dt Γ ~ 3 gh nˆ 3 3 kt β + R w w ( + k w k w ) n ˆ + Γ (A 3 /sec) 9 8 Step Mobility Step Stiffness Step-Step Interaction (mev/a) β~ T ( K) T ( K) g (mev/a ) T ( K) ( π kt ) 4 A [] N.C. Bartelt et. al., PRB 48, 5453 (993) g = 3 ~ + + [] S.D. Cohen et. al., PRB 66, 53 () h β ( kt ) [3] J.M. Bermond, et. al. Surf. Sci. 46, 43 (998) [4] J.J. Metois et. al. Surf. Sci. 486, 95 () k + = k - =.5 BL/s * / ~ β 4

21 Effect of Step-Step interaction on Corrugation Decay Time Constants g= Time constant (sec) Exp Sim OOP IP Pit Diameter (μm)

22 Publications Sublimation on Patterned Vicinal Si() Characteristic Length Scales In Evolution Of Patterned Step Structure On Vicinal Si() Surface During High Temperature Annealing, H-C.Kan, T. Kwon and R. J. Phaneuf, in preparation (7). Length-Scale Dependence of the Step Bunch Self-Organization on Patterned Vicinal Si() Surfaces, T. Kwon, H-C. Kan and R. J. Phaneuf, Appl. Phys. Lett. 88, 794 (6). Growth on Patterned GaAs() Temperature-Driven Change in the Unstable Growth Mode on Patterned GaAs(), T. Tadayyon-Eslami, H.-C. Kan, L. C. Calhoun and R. J. Phaneuf, Phys. Rev. Lett. 97, 6 (6). Evolution of Patterned GaAs() during Homoepitaxial Growth: Size vs. Spacing, H.-C. Kan, R. Ankam, S. Shah, K.M. Micholsky, T. Tadayyon-Eslami, L. Calhoun, and R. J. Phaneuf, Phys. Rev. B 73, 954 (6). Transient evolution of surface roughness on patterned GaAs() during homoepitaxial growth, H.-C. Kan, S. Shah, T.T. Tadyyon-Eslami and R.J. Phaneuf, Phys. Rev. Lett., 9, 46 (4).