Modeling and Simulation for the NanoDefect Community - Sematech
Modeling and Simulation for the NanoDefect Community - Sematech
Modeling and Simulation for the NanoDefect Community - Sematech
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<strong>Modeling</strong> <strong>and</strong> <strong>Simulation</strong> <strong>for</strong> <strong>the</strong><br />
This work is funded in<br />
part by <strong>Sematech</strong><br />
project #LITH143<br />
<strong>NanoDefect</strong> <strong>Community</strong><br />
Peter Stoltz, Tech-X Corp.<br />
Collaborators: Alex Likhanskii, Chu<strong>and</strong>ong Zhou – Tech-X Corp.<br />
Vibhu Jindal, Pat Kearney - <strong>Sematech</strong><br />
Tech-X Corporation
Tech-X is a computational science<br />
company headquartered in Boulder<br />
- Founded in 1994<br />
- 70 employees in 2012<br />
- Offices in US (Boulder & Buffalo) UK, <strong>and</strong> Taiwan<br />
- Main focus is computational plasma science<br />
- Especially focused on multi-core computing<br />
Tech-X Corporation
Scale of meters!<br />
Inspiration <strong>for</strong> this work came from<br />
<strong>the</strong> lunar science community<br />
Depending on <strong>the</strong> angle of solar wind, lunar craters can<br />
charge negatively. So, charged dust particles (defects) are<br />
eventually repelled from <strong>the</strong> surface.<br />
Tech-X Corporation
Vorpal is a 3D, FDTD PIC code<br />
with MCC to model plasmas<br />
Self-consistent treatment of particles <strong>and</strong> fields includes<br />
Monte Carlo collisions <strong>for</strong> excitation, ionization, secondary<br />
emission<br />
Tech-X Corporation
Vorpal solves Poisson's equation<br />
<strong>and</strong> particle motion toge<strong>the</strong>r<br />
e<br />
e<br />
e<br />
e<br />
Area weighting preserves momentum exactly<br />
e<br />
Tech-X Corporation
Particle-in-cell has <strong>the</strong> advantage that it<br />
scales to large numbers of particles<br />
• Particle nature of plasma can be important<br />
– E.g. non-<strong>the</strong>rmal phase-space distributions<br />
• Particle-particle interaction too time consuming<br />
– Compute Coulomb <strong>for</strong>ces between particles<br />
– Computationally too dem<strong>and</strong>ing<br />
• O(N 2 ) algorithm<br />
– Some projects may require it<br />
• Strongly coupled plasmas<br />
• Particle-in-cell algorithm<br />
– Particles: anywhere<br />
– Fields: discretized in space<br />
– Particle only interact with fields<br />
• Collective effects correct<br />
– O(N) algorithm -> Feasible!<br />
Tech-X Corporation
e<br />
Incident<br />
electron, inc,e<br />
e<br />
Incident<br />
electron, inc,e<br />
Cu<br />
Neutral<br />
atom,<br />
0,Cu<br />
Elastic scattering<br />
Cu<br />
Neutral<br />
atom, 0,Cu<br />
Ionization<br />
Vorpal supports Monte Carlo<br />
Electron - Neutral Collisions<br />
e<br />
e<br />
e<br />
Scattered<br />
electron, sc,e<br />
Ejected<br />
electron, ej,e<br />
Cu+<br />
Scattered<br />
electron, sc,e<br />
Ionized<br />
atom,<br />
+,Cu<br />
e<br />
Incident<br />
electron, inc,<br />
e<br />
Cu<br />
Wall Surface<br />
e<br />
Neutral<br />
atom, 0,Cu<br />
Incident<br />
electron, inc,e<br />
Excitation<br />
X-ray photon<br />
emitted, h<br />
Tech-X Corporation<br />
e<br />
Cu*<br />
Scattered<br />
electron, sc,e<br />
Excited<br />
atom, ex,Cu<br />
e<br />
Secondary<br />
electron, ej,e<br />
Bremsstrahlung X-Ray emission
PIC is computationally expensive compared to<br />
o<strong>the</strong>r approaches (fluids, lumped circuit)<br />
● Time step must resolve plasma frequency<br />
● Cell size must resolve Debye length<br />
● Often requires parallel computing <strong>for</strong> industrial plasmas<br />
● Monte Carlo is only as good as <strong>the</strong> cross sections<br />
Tech-X Corporation
We are modeling a simplified version<br />
of a mask blank chamber geometry<br />
-400 to 0 V @ 60 MHz<br />
Mask blank<br />
Ar (0.1 mT)<br />
20 cm<br />
Ion Source<br />
Target<br />
Tech-X Corporation
We monitor Ar plasma quantities in<br />
steady state<br />
Potential v. position<br />
Electron Temperature<br />
Ion x-vx phase space<br />
Tech-X Corporation
We observe repelling of defects due<br />
to plasma sheath<br />
t=0 t=3 us<br />
t=6 us<br />
t=10 us<br />
Defect charge<br />
-1<br />
-5<br />
-10<br />
-20<br />
Defect<br />
free<br />
region<br />
near<br />
mask!<br />
Tech-X Corporation
Phase space shows defects repelled<br />
from surface by sheath<br />
t=0 us t=3 us<br />
t=6 us<br />
t=10 us<br />
Defect<br />
free<br />
region<br />
near<br />
mask!<br />
Tech-X Corporation
Potential<br />
contours<br />
Vorpal also can model kinetic processes<br />
in etch <strong>and</strong> deposition systems<br />
Anode (grounded)<br />
Cathode (-2500 V peak, 13.56 MHz)<br />
AVS, Nashville, TN, Nov 4 2011<br />
Hot electrons (10-20eV)<br />
Blue – 10 eV<br />
Green – 15 eV<br />
Red – 20 eV
We can correlate high energy electrons<br />
with ion density <strong>and</strong> energy<br />
r (m)<br />
Energy (eV)<br />
AVS, Nashville, TN, Nov 4 2011<br />
Cathode<br />
Change in ion<br />
density<br />
EE<br />
DF<br />
Anode<br />
Z<br />
Negative values are (m) small <strong>and</strong> are due to ion motion
17eV<br />
We can correlate high energy electrons<br />
with ion density <strong>and</strong> energy<br />
AVS, Nashville, TN, Nov 4 2011<br />
Increasing time<br />
Enhanced ionization due to hot electrons
This work is funded in<br />
part by <strong>Sematech</strong><br />
project #LITH143<br />
Thanks <strong>for</strong> your attention...<br />
Peter Stoltz, Tech-X Corp.<br />
Collaborators: Alex Likhanskii, Chu<strong>and</strong>ong Zhou – Tech-X Corp.<br />
Vibhu Jindal, Pat Kearney - <strong>Sematech</strong><br />
Tech-X Corporation
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