The influence of ion-beam divergence on surface sputtering

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The influence of ion-beam divergence on surface sputtering

Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surfacesputteringTaha YasseriInstitut für ong>Theong>oretische PhysikUniversität GöttingenJanuary 16th 2008A. K. Hartmann, E. O. Yewande, R. KreeTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


OutlineSurface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooks1 Surface sputtering experiments2 Linear theory3 Monte Carlo simulatong>ionong>4 Ion-ong>beamong> ong>divergenceong>5 Summery and outlooksTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


OutlineSurface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooks1 Surface sputtering experiments2 Linear theory3 Monte Carlo simulatong>ionong>4 Ion-ong>beamong> ong>divergenceong>5 Summery and outlooksTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksDotsRipplesDesirable to have such patterns in nano scale:20nm Ripples on Silicon20nm Q.D. on InGaAsTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksSputtering: Shooting energetic ong>ionong>(keV) onto the surface.Different morphologies depend on θ, ong>ionong>s energy, substrate, ... .11 2 keV Xe + on Ge. (Ziberi et. al. 2006)Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksOrientatong>ionong> ong>ofong> ripples depends on θ22 5 keV Xe + on Graphite. (Habenicht et. al. 1999)Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksGrowth equatong>ionong> (only linear terms)∂ t h ∼ = −v 0 (θ)+v ′ 0(θ)∂ x h+f ×[Γ 1 (θ)∂ 2 xh+Γ 2 (θ)∂ 2 yh]−B∇ 2 ∇ 2 h3 Sigmund 1969Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksGrowth equatong>ionong> (only linear terms)∂ t h ∼ = −v 0 (θ)+v ′ 0(θ)∂ x h+f ×[Γ 1 (θ)∂ 2 xh+Γ 2 (θ)∂ 2 yh]−B∇ 2 ∇ 2 h⇑erosong>ionong> rate ong>ofong> planer surface3 Sigmund 1969Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksGrowth equatong>ionong> (only linear terms)∂ t h ∼ = −v 0 (θ)+v ′ 0(θ)∂ x h+f ×[Γ 1 (θ)∂ 2 xh+Γ 2 (θ)∂ 2 yh]−B∇ 2 ∇ 2 h⇑erosong>ionong> rate ong>ofong> planer surface⇑ ⇑curvature dependent terms⇑surface diffusong>ionong>3 Sigmund 1969Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksGrowth equatong>ionong> (only linear terms)∂ t h ∼ = −v 0 (θ)+v ′ 0(θ)∂ x h+f ×[Γ 1 (θ)∂ 2 xh+Γ 2 (θ)∂ 2 yh]−B∇ 2 ∇ 2 h⇑erosong>ionong> rate ong>ofong> planer surface⇑ ⇑curvature dependent terms⇑surface diffusong>ionong>Solutong>ionong>: h(x,y,t) = −v 0 (θ)t + A exp[i(k 1 x + k 2 y − ωt) + rt]3 Sigmund 1969Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksGrowth equatong>ionong> (only linear terms)∂ t h ∼ = −v 0 (θ)+v ′ 0(θ)∂ x h+f ×[Γ 1 (θ)∂ 2 xh+Γ 2 (θ)∂ 2 yh]−B∇ 2 ∇ 2 h⇑erosong>ionong> rate ong>ofong> planer surface⇑ ⇑curvature dependent terms⇑surface diffusong>ionong>Solutong>ionong>: h(x,y,t) = −v 0 (θ)t + A exp[i(k 1 x + k 2 y − ωt) + rt]r = −f [Γ 1 (θ)k 2 1 + Γ 2(θ)k 2 2 ] − B(k2 1 + k2 2 )2 .3 Sigmund 1969Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksGrowth equatong>ionong> (only linear terms)∂ t h ∼ = −v 0 (θ)+v ′ 0(θ)∂ x h+f ×[Γ 1 (θ)∂ 2 xh+Γ 2 (θ)∂ 2 yh]−B∇ 2 ∇ 2 h⇑erosong>ionong> rate ong>ofong> planer surface⇑ ⇑curvature dependent terms⇑surface diffusong>ionong>Solutong>ionong>: h(x,y,t) = −v 0 (θ)t + A exp[i(k 1 x + k 2 y − ωt) + rt]r = −f [Γ 1 (θ)k 2 1 + Γ 2(θ)k 2 2 ] − B(k2 1 + k2 2 )2 .To calculate v 0 ,Γ 1 ,Γ 2 , asfunctong>ionong>s ong>ofong> θ, a Gaussianenergy distributong>ionong> 3 is used.3 Sigmund 1969Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksΓ 1 and Γ 2 are like negativesurface tensong>ionong>s.|Γ 1 |/|Γ 2 | determines theripples directong>ionong>.θ c : Orientatong>ionong> is changed.44 Bradley et. al. 1988Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksΓ 1 and Γ 2 are like negativesurface tensong>ionong>s.|Γ 1 |/|Γ 2 | determines theripples directong>ionong>.θ c : Orientatong>ionong> is changed.4initial fluctuatong>ionong>s areamplified by ong>ionong> flux andsmoothed by diffusong>ionong>.4 Bradley et. al. 1988Ion flux and Diffusong>ionong>constant select the fastestgrowing mode like λ ∼ √ B/fTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


OutlineSurface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooks1 Surface sputtering experiments2 Linear theory3 Monte Carlo simulatong>ionong>4 Ion-ong>beamong> ong>divergenceong>5 Summery and outlooksTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooks(2+1)-d discrete SOSmodelPeriodic boundaryconditong>ionong> [256 × 256]5˘Smilauer et. al. 1993Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooks(2+1)-d discrete SOSmodelPeriodic boundaryconditong>ionong> [256 × 256]Erosong>ionong>: P ∝ received E5˘Smilauer et. al. 1993Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooks(2+1)-d discrete SOSmodelPeriodic boundaryconditong>ionong> [256 × 256]Erosong>ionong>: P ∝ received EDiffusong>ionong>: P ′ ∝ e −E ′ /k B TE ′ = E s + nnE NN + E SB5Chosen among different models.5˘Smilauer et. al. 1993Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksObtained surfacesfor different energy distributong>ionong>widths.θ = 50 ◦ , t = 3ong>ionong>/atom6 Yewande et. al. 20066Taha Yasseriong>Theong> only model wcich produceall different patterns.ong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


OutlineSurface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksmotivatong>ionong>Generic resultsSpecific results1 Surface sputtering experiments2 Linear theory3 Monte Carlo simulatong>ionong>4 Ion-ong>beamong> ong>divergenceong>5 Summery and outlooksTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksmotivatong>ionong>Generic resultsSpecific resultsIn reality ong>ionong>s are not completely parallel.Different ong>ionong> prong>ofong>iles lead to different surfaces. 7θ = 0 ◦(rotating sample)7 Ziberi et. al. 2004Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksmotivatong>ionong>Generic resultsSpecific resultsIn reality ong>ionong>s are not completely parallel.Different ong>ionong> prong>ofong>iles lead to different surfaces. 7θ = 0 ◦(rotating sample)what is material specific? what is generic?7 Ziberi et. al. 2004Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksmotivatong>ionong>Generic resultsSpecific resultsSimulatong>ionong>:Draw a random θ from[θ 0 − ∆θ ∆θ, θ0 + ]2 2Results:Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksmotivatong>ionong>Generic resultsSpecific resultsSimulatong>ionong>:Draw a random θ from[θ 0 − ∆θ ∆θ, θ0 + ]2 2Results:Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksmotivatong>ionong>Generic resultsSpecific resultsSimulatong>ionong>:Draw a random θ from[θ 0 − ∆θ ∆θ, θ0 + ]2 2Results:Slower dynamicsTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksmotivatong>ionong>Generic resultsSpecific resultsLooking at solutong>ionong>s ong>ofong> growth equatong>ionong>:h(k 1 ,k 2 ,t) ∝ e r(k 1,k 2 ,θ)×t Averaging:〈h(k 1 ,0,t)〉 P(θ) = ∫ P(θ)dθe (r×(k 1,0,θ)t)Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksSputtering at critical angle (θ c )motivatong>ionong>Generic resultsSpecific resultsθ 0 = 65 ◦ ∆θ = 0 ◦ /20 ◦ θ c : Orientatong>ionong> is changed.2-d structure factor has picks inboth directong>ionong>s.combinatong>ionong> ong>ofong> crossed ripples.Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksSputtering at normal incidencemotivatong>ionong>Generic resultsSpecific results∆θ = 0 ◦ /32 ◦ - rotating sampleWhere does the size scale come from?Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksSputtering at normal incidencemotivatong>ionong>Generic resultsSpecific results∆θ = 0 ◦ /32 ◦ - rotating sampleWhere does the size scale come from?Size scale holds for rotating caseTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


OutlineSurface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooks1 Surface sputtering experiments2 Linear theory3 Monte Carlo simulatong>ionong>4 Ion-ong>beamong> ong>divergenceong>5 Summery and outlooksTaha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Surface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooksSlowing down the process by ong>ionong>-ong>beamong> ong>divergenceong>.Obtaining crossed ripples by sputtering at critical angle.Controlling the size scale in normal sputtering by ong>ionong>-ong>beamong>ong>divergenceong>.OutlooksLocal effects ong>ofong> thermal spikes (better approach to surfacediffusong>ionong>).Taking redepositong>ionong> ong>ofong> sputtered atoms into account.More realistic energy distributong>ionong> by studying the cascades ong>ofong>single ong>ionong> shooting.Sputtering ong>ofong> subsurface atoms.Dynamics ong>ofong> atoms-vacancies using binary systems.Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering


Thanks toSurface sputtering experimentsLinear theoryMonte Carlo simulatong>ionong>Ion-ong>beamong> ong>divergenceong>Summery and outlooks◮ Alexander Hartmann,Reiner Kree◮ AudienceNordsee - June 2007Taha Yasseriong>Theong> ong>influenceong> ong>ofong> ong>ionong>-ong>beamong> ong>divergenceong> on surface sputtering

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