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Non-equilibrium Steady State & Nano-patterning in Si(001) Homoepitaxy
Wang Xue-sen Department of Physics, NUS Contributors: Hu Yanfang (Fudan U) Xu Maojie & Xue Qikun (Inst. Phys., CAS) Xiao WD, J. Mayandi, S.S. Kushvaha, Yan ZJ (Phys/NUS) Zhang YW, Guo JY (MAS/NUS) (220 nm)2
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Surface Morphology in Homo-epitaxy
Homo-epitaxy: no lattice mismatch, but stress may exist Ideal situation: Layer-by-layer or step-flow growth, which requires sufficient diffusion and step incorporation At high T and low deposition flux F: near-equilibrium growth, surface remains smooth Substrate At lower T and/or higher F: non-equilibrium growth, surface roughness develops
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Non-equilibrium Steady State and Nanoscale patterning in Epitaxy
Non-equilibrium steady-state: surface width w increases initially, but saturate at a finite value after transition period Characteristics of steady state Formation mechanism and characteristic features Scaling of roughness with sampling length Transition to other states Nano-patterning by homoepitaxy What is such pattern good for? Use the characteristic feature/pattern as templates for growing other nano-structures
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Experimental Procedure
UHV STM system: base P ~ 1×10-10 mbar Si(001) substrate: miscut 0.15° E-beam Si source: flux calibrated with STM & AES, ~ 3ML/min Substrate temperature during growth: ºC STM image at RT, artifacts due to tip shape considered (500 nm)2 Starting Si(001)
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Formation of fingers & double steps
3 ML/min 590°C 12 ML (300 nm)2 3 ML/min 590°C 12 ML (500 nm)2 6 ML/min 630°C 120 ML (500 nm)2 3 ML/min 610°C 12 ML (500 nm)2 Influence of initial steps fades away
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Si/Si(001) 2.7 ML/min 650°C Formation of nanoscale void island array
(500 nm)2 (500 nm)2 27 ML, VI depth 2.5 nm 81 ML, VI depth 9 nm Formation of nanoscale void island array 405 ML Void depth 35 nm (2000 nm)2
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Surface Patterning by Homo-epitaxy
Without involving impurities (as by chemisorption) or defects (as in ion sputtering or LTE) Scales adjustable by temperature and flux control Different pattern shape by selecting substrate symmetry, e.g. triangular or hexagonal patterns may form on Si(111) Compatible with micro- electronic processing (220 nm)2 625°C, 2 ML/min, void depth 3 nm
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Unconventional Ge Quantum Structures on Patterned Si(001)
Half pyramids Inverse pyramids (50nm)2
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Roughening in Homo-epitaxy
F At low T and high F: new islands nucleate and grow on incomplete layers Roughening growth: surface width w (<(h - <h>)2>)1/2 increases with deposition time t Scaling: w ~ t , w ~ L & w ~ L f(t/Lz) L: size of sampling area, z = / (Pimpinelli & Villain, 1998) h Substrate (See: Barabási & Stanley, 1995)
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Smooth, roughening & something else (?)
Ag/Ag(100) (Stoldt et al., PRL 2000) Morphology at high T & low F: (near) equilibrium surface At low T and high F: interface width w increases with t, mounds form What happens at intermediate T & F? T On dynamic phase diagram, transition from smooth to roughening should not be abrupt Smooth Roughening F
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Saturation & steady state: Current understanding
Mo et al. proposed the existence of “smooth” interface in homo-epitaxy with ~ 4-5 incomplete layers (Surf. Sci. 219, L551 (1989)) Orr et al. observed decay of RHEED oscillation corresponding to a constant step density in GaAs(001) epitaxy (Sudijono et al. Surf. Sci., 280, 247 (1989)) RHEED in GaAs(001) epitaxy at 555°C Saturation considered as a finite-size effect: Time to reach saturation (tx) increases with system size L as: ξ// ~ tx1/z → L (Family & Vicsek, 1985; also see Barabási & Stanley, 1995)
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Si(001) Surface (2×1) + (1×2) dimer rows SA, SB, DA, DB steps
Anisotropy of atomic diffusion: migration along dimer rows is much faster than across the rows References: Zhang, Wu, Lagally, Annu. Rev. Mater. Sci. 27, 525 (1997) Zandvliet, Rev. Mod. Phys. 72, 593 (2000) Voigtländer, Surf. Sci. Rep. 43, 127 (2001) SB SA [110]
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Current understanding of Si(001) homoepitaxy
Pure step-flow at 775K & 2 ML/hr (but only experimented with < 3ML). (Voigtländer et al, PRL 78, 2164 (1997)) Epitaxial thickness hepi = h0 exp(-Ea/kT), h0 ~ ln(F) or F1/4, Ea ~ 0.45±0.1 eV. (Eaglesham, JAP 77, 3597 (1995)) At ºC & F ~ 13 ML/min, fomation of critical sized {111} facets on side of mounds leads to transition to amorphous growth. Stacking faults, twins and amorphous nucleation occur more easily on {111}. (Karpenko, Yalisove, Eaglesham, JAP 82, 1157 (1997)) Step bunching instability on vicinal Si(001): with 9 ML/min on vicinal Si(001) at C, unstable step-pair flow to form step bunching due to diffusion anisotropy; at T 550C, approaching equilibrium. (Schelling et al, PRL 83, 995 (1999); Myslivecek et al, Surf. Sci. 520, 193 (2002))
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Diffusion anisotropy, mistakes & roughening
Fingers & vacancy islands (400 nm)2 (From YW Mo)
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Si/Si(001) 2.7 ML/min 650°C (500 nm)2 (500 nm)2
27 ML, VI depth 2.5 nm 81 ML, VI depth 9 nm 135 ML VI depth 20 nm 243 ML VI depth 29 nm (1500 nm)2 (1000 nm)2
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Si/Si(001) 2.7 ML/min 650°C 243 ML VI depth 29 nm (1500 nm)2
405 ML Void depth 35 nm 675 ML (2000 nm)2 (2000 nm)2
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Characteristics of Steady-state Surface
Connected flat top surface plus isolated vacancy islands: Height of top surface is correlated because of connected fast diffusion channel, the surface roughness is limited In mound-dominated roughening growth, the height of growth front is not correlated (even with flat-top mounds) Steady state Increasing roughening Isolated vacancy islands vs. mounds Ge(001) epitaxy at 175°C (Nostrand et al., PRB 57 (1998)) (700 nm)2
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Transition between different modes
Smooth (500 nm)2 Roughening F At higher T & lower F: Small deviation from equilibrium
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From steady-state to roughening
Break points block the communication (correlation) across top flat areas Break points (300 nm)2 (2000 nm)2 Si/Si(001), 2 ML/min at 600ºC Such a steady state cannot exist in (1+1)D system
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Universal Existence of Steady State
Because smooth and roughening states are general, the steady state corresponding to the transition should be commonly observable (?) in (2+1)D systems T Smooth Roughening F Modeling & simulation studies can provide more insight The details of nano-patterns depend on material properties Ordering of nano patterns: need other driving forces
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Relaxation & ordering of pattern
Pattern ordering due to anisotropies in step/surface energies, mass transport and elasticity = C11- C C44 = -1 = 40 mJ/m2 = 1 = 57 mJ/m2 Ordering = 0.21 = 0.35 (See: Seul & Andelman, Science 267, 476 (1995); L. Proville, PRB 64, (2001); W. Lu & Z. Suo, PRB 65, & (2002))
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Pattern evolution under 600ºC annealing
As-grown Sample [100] Two types of voids decay in different rates (2000 nm)2 [110] 15 min 60 min (2000 nm)2 (1500 nm)2
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Summary Existence of non-equilibrium steady-state in Si(001) homoepitaxy(?) (and also in the epitaxy of other materials?) Key factors: balance between driving forces to equilibrium and instability (flux fluctuation, diffusion anisotropy, Ehrlich-Schwoebel barrier): Errors occur but are limited Morphology characteristics: Connected flat top surface (the smooth part) with isolated vacancy islands (the roughening part) Pattern shape and ordering: interplay between anisotropies in step/surface energies (faceting), transport length scale and elastic relaxation As templates for fabrication of other nanostructures
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Roughening in model systems
(Ft) = 4000 Random deposition, no relaxation = ½, = Random deposition, with relaxation (1D) = 1/4, = 1/2 (Barabási & Stanley, Fractal concept in surface growth)
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Study of Roughening Growth
Roughening epitaxy normally is not desirable, but inevitable sometime. Example: Growth of diluted magnetic semiconductor In1-xMnxAs (x0.18) at 300°C (Munekata et al., PRL 63, 1849 (1989)) Similar phenomena: Wetting of paper Fire front Bacteria colony (See: Barabási & Stanley, Fractal concept in surface growth)
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Current understanding of Si(001) homoepitaxy
Pure step-flow at 775K & 2 ML/hr (but only experimented with < 3ML). (Voigtländer et al, PRL 78, 2164 (1997)) Epitaxial thickness hepi = h0 exp(-Ea/kT), h0 ~ ln(F) or F1/4, Ea ~ 0.45±0.1 eV. (Eaglesham, JAP 77, 3597 (1995)) At ºC & F ~ 13 ML/min, fomation of critical sized {111} facets on side of mounds leads to transition to amorphous growth. Stacking faults, twins and amorphous nucleation occur more easily on {111}. (Karpenko, Yalisove, Eaglesham, JAP 82, 1157 (1997)) Step bunching instability on vicinal Si(001): with 9 ML/min on vicinal Si(001) at C, unstable step-pair flow to form step bunching due to diffusion anisotropy; at T 550C, approaching equilibrium. (Schelling et al, PRL 83, 995 (1999); Myslivecek et al, Surf. Sci. 520, 193 (2002))
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Ge(001) LT-MBE Vicinal Si(001) MBE
Ripples formed on 0.66°-miscut Si(001) in MBE (From: Mysliveček et al., Surf. Sci. 520 (2002)) (700 nm)2 At 175°C, Ft = 1000 nm From: Nostrand et al., PRB 57 (‘98)
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