Making Functional Surfaces and Thin Films: Where are the Atoms?

Making Functional Surfaces and Thin Films: Where are the Atoms? K. Ludwig, A. DeMasi, J. Davis and G. Erdem Department of Physics Materials Science and Engineering Program Why x-rays? λ ~10-10 m ~ distance between atoms

X-ray Scattering (Diffraction) θ images-mediawikisites.thefullwiki.org The momentum transfer to an elastically scattered photon is:

X-ray Scattering (Diffraction) In the Born Approximation, the intensity of x-ray scattering is equal to the structure factor S(q) of atom positions:

Thanks to synchrotron x-ray sources, available x-ray brightness has been growing fast faster than computer speeds!

National Synchrotron Light Source (NSLS) and NSLS-II Brookhaven National Laboratory (Long Island)

National Synchrotron Light Source (NSLS) and NSLS-II Brookhaven National Laboratory (Long Island)

Facility for Real-Time Studies of Surface and Thin Film Growth Processes NSLS insertion device beamline X1 back hutch Experimental conditions can be optimized in ultra-high vacuum (UHV) chambers at the home laboratory the chambers can then be rolled onto the base diffractometer permanently installed at NSLS

Surface Modification and Characterization Instrumentation System installed on base diffractometer with UHV chamber, surface modification and characterization equipment

Facility for Real-Time X-ray Studies of Thin Film and Surface Processes National Synchrotron Light Source (NSLS) X1 Brookhaven National Laboratory Detector Exit X-rays Incoming X-rays Flight Path Incoming X-rays Physical Electronics PHI ion gun x 10 1 ions/cm s Sample manipulator Sample

Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) Z X q z detector X-rays ω α f q y α i θ Y q x

Grazing-Incidence Small-Angle X-ray Scattering (GISAXS)

BU Research Program - Spontaneous Nano-Patterning of Surfaces during Ion Bombardment Aziz group (Harvard) - III-V Nitride Semiconductor Growth (lasers, detectors, solar cells) T. Moustakas (BU), O. Malis (Purdue) - Solid Oxide Fuel Cell (SOFC) Cathodes S. Basu, S. Gopalan, U. Pal (BU) - Fundamental Processes in Thin Film Growth Headrick group (UVM)

Spontaneous Nanopatterning of Semiconductor Surfaces by Ion Bombardment Off-Axis Bombardment Ripples: Normal Incidence Bombardment Smoothening: Dots: ion direction Si(100) Si(100) GaSb (100) Facsko et al., Science 85, 1551 (1999)

Off-Axis Bombardment Normal Incidence Bombardment Ripples: Smoothening: Dots: ion direction Facsko et al., Science 85, 1551 (1999) Si(100) Si(100) GaSb (100) Importance of understanding patterning during bombardment: - Hyperthermal bombardment is a ubiquitous technological process (e.g. sputter deposition, ion-assisted deposition, PLD, sputter cleaning, plasma etching) - Potential route for inexpensive nanopatterning of surfaces Fundamental questions: What physical processes cause nanopattern formation? How can we control it?

Formation of ripple structures on surfaces during ion bombardment reported as early as 1960: Key early observations: Semiconductor surfaces are amorphized by ion bombardment at RT Wavelengths can be much longer than penetration depths of ions At low bombardment angles, ripple wavevector parallel to projected direction of ion beam At high bombardment angles, ripple wavevector perpendicular to projected direction of ion beam Ar + θ 5 kev Xe+ on graphite: Habenicht et al. PRB 60, R00 (1999).

Theoretical treatment of Sputter Erosion 1973: Model of sputter erosion process: Energy deposited by incident ion assumed to be a Gaussian ellipsoid Sputter rate from a given point on the surface assumed to be proportional to energy deposited there Chan and Chason, JAP 101, 11301 (007)

Theoretical treatment of Sputter Erosion 1973: Surface Instability to Ion Bombardment due to curvature-dependent sputter erosion rate Chan and Chason, JAP 101, 11301 (007)

Theoretical treatment of Sputter Erosion 1973: Surface Instability to Ion Bombardment due to curvature-dependent sputter erosion rate Key Questions Not Addressed by Sigmund Mechanism: Chan and Chason, JAP 101, 11301 (007) - What determines ripple wavelength? - Why determines ripple orientation?

These are potentially answered by the Bradley-Harper Model primary paradigm for last 0 years: Calculate local surface height evolution from Sigmund model to first order in (ion penetration depth/surface radius of curvature): 0 1 1 ), ( y h S x h S x h v t t r h y x + + + Γ = r Average sputter erosion rate

These are potentially answered by the Bradley-Harper Model primary paradigm for last 0 years: Calculate local surface height evolution from Sigmund model to first order in (ion penetration depth/surface radius of curvature): h( r, t) t = v 0 h + Γ x + 1 S x h x + 1 S y h y Average sputter erosion rate Slope-dependent erosion rate causes motion of ripples across surface

These are potentially answered by the Bradley-Harper Model primary paradigm for last 0 years: Calculate local surface height evolution from Sigmund model to first order in (ion penetration depth/surface radius of curvature): h( r, t) t Average sputter erosion rate = v 0 h + Γ x + 1 S Slope-dependent erosion rate causes motion of ripples across surface x h x + 1 S y h y Curvaturedependent erosion rate

h( r, t) t = 1 S x h x + 1 S y h y 1 B 4 h Bradley- Harper: Add relaxation at short lengthscales due to diffusion or viscous flow Stability or instability of surface for a ripple of a given wavelength is determined by tradeoff between curvaturedependent erosion rate and surface smoothening by diffusion/viscous flow

Lateral mass redistribution (CV) effect smoothens at low incidence angles Magnitude proportional to cos(θ) h = t v j h v j h t = α h q

More General Linear Theory Formalism ),, ( 1 1 1 4 t y x h B h S h S t h y y x x η + + = Linear theory growth or decay of local surface height fluctuations: Curvature coefficients S x and S y can include both curvature-dependent Bradley- Harper erosion instability and stabilization due to lateral mass redistribution Uncorrelated Noise: 0 ),, ( = t y x η ') ( ') ( ') ( ') ', ', ( ),, ( t t y y x x n t y x t y x = δ δ δ η η Ensemble-averaged height-height structure factor evolution: [ ] t q R t q R e q R n q I e t q h t q h t q I ) ( 0 ) ( 1 ) ( ) ( ), *( ), ( ), ( + = = ( ) 4 ) ( Bq q S q S q R y y x x + + = Amplification Factor:

Linear Theory of Surface Stability/Instability: Amplification Factor Amplification Factor: ( 4 S q + S q ) R( q) = Bq x x y y + If R(q) > 0, surface is unstable: I(q,t) If R(q)< 0, surface is stable: I(q,t) I(q,t) t S 0( q) > n R( q) t S q) < 0 ( n R( q) t

1 kev Ar + on Si: For each ion bombardment angle θ use real-time GISAXS to measure I(q x,y,t) Madi, Anzenberg, Ludwig and Aziz, PRL 106, 066101 (011) Anzenberg, Madi, Aziz and Ludwig, PRB 84, 14108 (011) GISAXS evolution during hours of 1 kev Ar + bombardment of Si (100) At each wavenumber, fit I(q x,y,t) to determine Amplification Factor R(q x,y )

Measured Amplification Factor R(q x,y ) as a function of incident angle in x- and y-directions Transition from smoothening to ripple formation at ion bombardment angle θ ~45.

Measured Amplification Factor R(q) as a function of incident angle in x- and y-directions Simultaneously fit all R(q x,y ) to form: R(q x ) = -(S x (θ)q x + Bq x4 ) R(q y ) = -(S y (θ)q y + Bq y4 ) to determine curvature coefficients S x,y (θ)

Angular Dependence of Curvature Coefficients S x,y (θ) Fits show dominance of mass redistribution both for smoothing at low angles and for creating ripples. Consistent also with simulations. (Kalyanasundaram et al., APL 9, 131909 (008); Norris et al., Nature Comm. 10.1038/ncomms180 (011))

Data show dominance of Lateral Mass Redistribution through most of angular range Above 45 ion incidence angle, roughening caused by ion momentum knocking surface atoms uphill! Recoils Ion Ions also knock atoms downhill when hitting downhill slope, but effective ion flux density is lower because of the slope

In these studies, structure evolution has been on seconds time scale. Can we use x-rays to look at much faster time scales (e.g. motion of atoms in liquids)? X-ray Free-Electron Laser (XFEL) Self Amplified Spontaneous Emission (SASE) Femtosecond (10-15 s) x-ray laser pulses!

X-ray Free-Electron Laser (XFEL)

X-ray Photon Correlation Spectroscopy (XPCS) Study evolution of x-ray scattering speckle pattern to learn about motion of atoms, molecules transversely coherent X-ray beam sample t 1 monochromator t g (Δt) I(t) I(t + Δt) I t 3 g 1 τ Δt τ 1 (Q) = Rate(Q) movie of speckle recorded by CCD I(Q,t)

XPCS at LCLS using Split Pulse Mode Femtoseconds to nanoseconds time resolution Uses high peak brilliance splitter sample transversely coherent X-ray pulse from FEL Contrast τ variable delay Δt 10 ps 3mm Analyze contrast as f(delay time) sum of speckle patterns from prompt and delayed pulses recorded on CCD I(Q,Δt) Δt

XPCS of Non-Equilibrium Dynamics using Pumped Mode Femtoseconds to seconds time resolution Uses high peak brilliance transversely coherent X-ray beam monochromator sample before Δt after pump Pump sample e.g. with laser, electric, magnetic pulse Correlate a speckle pattern from before pump to one at some Δt after pump

Key Problem: High peak x-ray beam intensity can damage sample (e.g. vaporize it!) Damage to Ni-Pd-P samples by single pulse of LCLS x-ray beam

First Experiments Show Success is Possible X-ray scattering from liquid Gallium

Conclusions Goal of condensed matter physics research is to understand how materials behave and how new materials or material structures can be developed to meet societal needs The behavior of materials depends on the atomic structure and evolution X-ray scattering is a uniquely powerful tool for determining atomic structure (both static and evolving) Available x-ray intensities have been increasing dramatically due to development of new sources (synchrotrons, FEL s) X-ray scattering can give crucial information enabling us to understand and control materials behavior