Nanomanufacturing by Bottom-up Growthacg.cs.tau.ac.il/courses/computational-geometry/... ·...
Transcript of Nanomanufacturing by Bottom-up Growthacg.cs.tau.ac.il/courses/computational-geometry/... ·...
Nanomanufacturing by Bottom-up Growth
An Application of Voronoi Diagrams
Karl F Böhringer University of Washington
Seattle, WA, USA
Lectures on Computational Geometry Tel Aviv University
Tel Aviv, Israel, 26 March 2012
Manufacturing
• “Top-down” subtractive manufacturing:
– Milling, drilling, turning, boring, broaching, sawing, shaping, cutting, planing, reaming, tapping, grinding, etching, molding, …
• “Bottom-up” additive manufacturing
– Assembly, synthesis, growth, …
26 March 2012 © Karl F Böhringer
Some Useful Terms and Definitions
• MEMS: microelectromechanical systems – tiny mechanisms made of silicon, such as accelerometers in cell phones and cars. – milli: 10–3 , micro: 10–6 , nano: 10–9
• Electrodeposition: common technique to coat objects with metals; dissolved metals (positive ions) deposit on negatively charged electrodes from a solution (electrolyte).
• Isotropic: having properties that are identical in all directions. 26 March 2012 © Karl F Böhringer
Desired Object Seed Planting
Software Seed Positions
Output Object Electrodeposition
Growth Electron Beam Lithography Patterning
20 μm
Bottom-up Nanomanufacturing
Automated synthesis of product:
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Orchestrated Structure Evolution
Automated OSE process:
A. Enter desired pattern (CAD)
B. Generate seeds (algorithms, models)
C. “Plant” (by electron beam or dip-pen) and grow seeds (electrolyte)
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How Does Growth Proceed?
Positive ions move towards negative electrodes
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How Does Growth Proceed?
Positive ions move towards negative electrodes
26 March 2012 © Karl F Böhringer
Top View of Growth Regions
• Voronoi diagram: decomposition of space into cells; a Voronoi cell is the set of all points whose distance to a given object is not greater than their distance to the other objects – Note: distance metric does not
need to be Euclidean
Image source: wikipedia.org
26 March 2012 © Karl F Böhringer
Growth of Simple Structures by Electrodeposition
• Disks and squares
• Place seeds across areas
• Grow structures until areas are covered
• How accurate is coverage?
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Bottom-up Nanomanufacturing
Orchestrated structural evolution – results:
- 10m
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0%
5%
10%
15%
20%
25%
30%
e are
a
Pitch ratio
C 1:2 1:5 1:10
Time and quality trade-off
Deposited at -350mV vs. SEC in 0.5M CuSO4 and 0.5M H2SO4
Growth error (area)
Pitch ratio (Seed size : Pitch distance)
0%
5%
10%
15%
20%
25%
30%
e pe
rim
ete
r
Pitch ratio C 1:2 1:5 1:10
Growth error (perimeter)
0
5
10
15
20
25
C 1:2 1:5 1:10
Tim
e (
s)
Growth Time
Write Time
We can reduce process time with small quality tradeoff
Conventional
No CMP
No CMP
Orchestrated Structure Evolution
Growth models for OSE:
Structure evolution may be limited by
• charge transfer (surface)
• mass transfer (bulk)
26 March 2012 © Karl F Böhringer
OSE Design Challenges
• Forward problem: what is end result of OSE?
– Look at Voronoi diagram!
• Inverse problem: how to choose seeds and process conditions, given a desired outcome?
– Solution for simplified case see [Thiyanaratnam et al. SIAM’09]
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Anisotropic growth
Space-filling growth
Solution for Simplified Problem
26 March 2012 © Karl F Böhringer
P. Thiyanaratnam et al., SIAM J. APPL. MATH. Vol. 69, No. 4, pp. 1043–1064
General Solution of Seed Layout Problem
• Solution by P. Thiyanaratnam et al. assumes isotropic growth with constant growth rate
• In practice, growth rate is not isotropic and time-varying
• Seeds compete for ions during electrodeposition ( Voronoi regions)
• General solution is inverse design problem with complex underlying physics
• Numerical solutions: S. Abbasi et al. Nanotech. 2011
26 March 2012 © Karl F Böhringer