Some Interesting Self-organized nano-structures of Pb/Si(111)

QSEDrivenGrowth Mode

K. Budde, E. Abram, V. Yeh, and M.C. Tringides, PRB 61, 10602 (2000)

Quantum well states of Pb islandsW.B. Su, S.H. Chang, W.B. Jian, C.S. Chang, L.J.Chen, and T.T. Tsong, PRL 86, 5116 (2001)A. Mans*, J.H. Dil, and A. R. H. F. Ettema, H. H.Weitering, PRB 66, 194410 (2002)

Different modes of thin film growthLayer by layerΔγ 0(Volmer-Weber)MixedΔγ < 0, then change sign(Stranski-Kratanov)Newly discovered7-layer high, flat top, steep edgeQuantum size effects (QSE)

Different stable heights with bi-layerdifference under different conditionsM. Hupalo, S. Kremmer, V. Yeh, L. Berbil-Bautista, E. Abram, M.C. Tringides, Surf. Sci. 493 (2001) 526

Comparisonbetweeninterfaces.

Si(111)-7 7θ = 3.3 ML200 nm 200 nmT = 200K3 ×3Pb/Si(111)- -βθ = 3 MLV. Yeh, L. Berbil-Bautista, C.Z. Wang, K.M. Ho, and M.C. Tringides, PRL 85, 5158 (2000)

77Si(111)-77• Wetting layer: from 3 ML at 130Kto 1 ML at RT• 4- to 9-step islands observed• For θ < 6 ML and T between 190Kand 200K, 7-step islands with meansize 90Å• At T = 195K, islands tend to stay at7-step and cover the whole surfaceat θ ~ 8ML, then new islands growon topPb/Si(111)- 3 × 3• First layer used to cover substrateto dense phase• 2-step to 11-step islands observed• For θ < 6 ML and T between190K and 200K, 5-step islandswith mean size 180Å• At T = 195K, islands tend to growhigher, in bi-layer increments,than grow larger for up to 20MLM. Hupalo, S. Kremmer, V. Yeh, L. Berbil-Bautista, E. Abram, M.C. Tringides, Surf. Sci. 493 (2001) 526

E = E 0− E CE 0 : the energy of the Pb film (after subtracting the bulk energy)E C = C(ΔE f ) 2 : energy gain due to the charge transferΔE f = 4.75 eV for 7 7 and 4.98 eV forC = 0.033 eV/Å 2(see Zenyu Zhang, et al, PRL 80, 53813 × 3D.R. Heslina, et al, PRL 64, 1589 and H.H. Weitering, et al, PRB 45, 9126.)Calculated film energyvs film thickness L forthe two interfacesshowing the 3 × 3phase has a lower curveand different minimadue to larger chargetransfer term.V. Yeh, L. Berbil-Bautista, C.Z. Wang, K.M. Ho, and M.C. Tringides, PRL 85, 5158 (2000)

StabilityofQSE driven islands.

Oxygen covered Pb islands retain theirheight to a higher temperatureOxygen suppressedatom diffusion tothe islandsS. Stepanovskyy, V. Yeh, M. Hupalo, and M.C. Tringides, Surf. Sci. 515 (2002) 187

Controlling the Thermal Stability of ThinFilms by Interfacial EngineeringD.A. Ricci, T. Miller, and T.-C. Chiang, PRL 95, 266101 (2005)

Applicabilityofnucleation theory.

For 2D islands and complete saturationnx= η θ⎛⎜⎝( , i)DF⎞⎟⎠−χ⎛exp⎜⎝⎛ ν0 ⎞lnx⎜ ⎟⎝ 4F⎠lnEi⎞⎟( i + 2) kT ⎠χkT( n ) = lnη− χ ln + ( E + E )( n x) ln F + const2miiχ = i + 2= χ Rate dependence( n ) ( E + E ) const.lnx= χm i+kTs = χ ( E ) m+ E ikn ν0lnx 1/⎜T = 0⎝ 4 F⎛ ⎞( ) = lnη− χ ln ⎟⎠Temperaturedependence

STM measurementsS.H. Chang, W.B. Su, W.B. Jian, C.S. Chang, L.J. Chen, and T.T. Tsong, PRB 65, 245401 (2002)W.B. Su, S.H. Chang, H.Y. Lin, Y.P. Chiu, T.Y. Fu, C.S. Chang, and T.T. Tsong, PRB 68, 033405 (2003)

SPA-LEED measurementsn x≈⎛⎜⎝1S⎞⎟⎠2=⎛⎜⎝K1⎞⎟2π⎠2⎛ K=⎜⎝ K110⎞⎟⎠2⎛ 1⎜⎝ a0AssumptionMeasured island density = saturation density⎞⎟⎠2Rate dependenceTemperature dependence

Low θ Structures3 × 3 − β7 ×33 × 3 −HIC43 ×33 × 3 −SICAnything else?

Low coverage structuresInconsistent results between different worksKotaro Horikoshi, Xiao Tong, Tadaaki Nagao, Shuiji Hasegawa, PRB 60, 13287 (1999)

STM study on HIC phaseM. Hupalo, T.L. Chan, C.Z. Wang, K.M. Ho and M.C. Tringides, PRB 66 161410 (2002)

αdT 4H 3M. Hupalo, T.L. Chan, C.Z. Wang, K.M. Ho and M.C. Tringides, PRB 66 161410 (2002)

S. Stepanovskyy, M. Yakes, V. Yeh,M. Hupalo and M.C. Tringides, SurfaceScience 600, 1417 (2006)LEED study on HIC phase

Kinematical calculations of LEED patternfor HIC phaseS. Stepanovskyy, M. Yakes, V. Yeh,M. Hupalo and M.C. Tringides, SurfaceScience 600, 1417 (2006)

d ~ 48Åα ~ 5.4∘Three HIC phasesd ~ 53Åα ~ 4.3∘d ~ 61Åα ~ 3.0∘d ~ 47Åα ~ 4.7∘d ~ 53Åα ~ 4.1∘d ~ 59Åα ~ 3.7∘

In Pb/Si(111)Δθ = 0.006MLT dep= 120KHugenumber ofatoms movecollectivelyTwo phasescovers 80%of 0.5mm43 ×50nm3?1.5V, 100nm 100nm

In a tiny change of θθ = 1.2 ML43 ×3(2, 1), θ = 1.231 ML(7, 1) and (5, 1), θ = 1.21 ML(1, 1), θ = 1.25 ML(4, 1), θ = 1.217 ML(1, 1) and (1, 2), θ = 1.263 ML(4, 1) and (3, 1), θ = 1.220 ML(1, 2), θ = 1.27 ML(3, 1), θ = 1.222 ML(1, 2) and (1, 3), θ = 1.28 ML(3, 1) and (2, 1), θ = 1.223 ML(1, 3), θ = 1.285 MLM. Hupalo, J. Schmalian, M.C. Tringides, PRL 90, 216106-1 (2003)STM images of twelve distinct, commensurate phases observedwithin a small coverage range 1.2 ML < θ < 1.3 ML.

Detailedstructures of(3, 1)and(2, 1)phases

What are the detailed structuresof those separations?Smaller separationsΘ = 4/3 MLLarger separationsΘ = 6/5 MLC.Kumpf, etc., Scurf. Sci. 448, L213 (2000)T.L. Chan, etc., Phys. Rev. B 68, 45410 (2003)a = 3.84Å0

Periodicity and coverage of a(n, m) phaseqPeriodicitya0( 5×n + 3 m)2( n , m )= ×For example, (n, m) = (3, 1)θ ( n , m )Coverage==6 n + 4 m5n+ 3mn + m1 +5n+ 3m=1+pqa0q(3,1)= ( 5×3+3×1=18)2θ= 1+( 3+1)= 1( 3,1)+q418θ(3,1)⎛ 22⎜ =⎝ 18⎞⎟⎠⎛ 16 ⎞⊕ θ(2,1)⎜ = ⎟ =⎝ 13 ⎠θ (5,2) = (3,1) ⊕(2,1)⎛⎜ =⎝3831⎟ ⎠⎞

Cantor combCantor functionRational numbersInfinite stepsInfinite steps ina finite intervalAll steps takerational numbershttp://www.mathacademy.com/pr/prime/articles/cantset/

The devil's staircase in Pb/Si(111)reveals itself in θ vs μ stability curveΔ μ12( p / q ) = lq { J ( lq + 2 ) + J ( lq − 2 ) − 2 J ( lq )}∑ ∞l = 1Competing interactionsChemical: immiscibilityElastic: lattice mismatchSteeper steps due todouble separationAdditional 3-foldrotational symmetrygives rise to phases otherthan the DS phases atfinite temperaturesM. Hupalo, J. Schmalian, M.C. Tringides, PRL 90, 216106-1 1 (2003)

Examples of physical systems thatshow a devil's staircase (I)Competing interactionsFerromagnetic for NNAnti-ferromagnetic for NNNPer Bak, J. von Boehm, PRB 21, 5297 (1980)

Examples of physical systems thatshow a devil's staircase (II)Competing interactionsChemical: bulk immiscibilityElastic: lattice mismatchB.D. Krack, V. Ozolins, M. Asta, and I. Daruka, PRL 88, 186101 (2002)

The T-θ phase diagram

Thank youforyour attention.

g(s): Intensity of (00) spot vs electron beam energyd(a)(b)7dΔs n: normal component of momentum of incident wavess = Δs n/ (2π/d)

g(s) definitionA 1A 0

Binary phase diagram Pb vs Si