The Univ. of Toledo’s Jacques Amar, PhD, leveraged Ohio Supercomputer Center systems to test an accelerated approach to simulating thin film growth. Using two different models (fcc and SOS), Amar compared the regular Kinetic Monte Carlo method (figures A and C) with a first-passage-time approach coupled with the KMC method (figures B and D). |
A Toledo,
Ohio, physicist has implemented a
new mathematical approach that accelerates some complex computer calculations
used to simulate the formation of micro-thin materials.
Jacques Amar, PhD, professor of physics at the Univ. of
Toledo (UT), studies the modeling and growth of materials at the atomic level.
He uses Ohio Supercomputer Center (OSC) resources and Kinetic Monte Carlo (KMC)
methods to simulate the molecular beam epitaxy (MBE) process, where metals are
heated until they transition into a gaseous state and then reform as thin films
by condensing on a wafer in single-crystal thick layers.
“One of the main advantages of MBE is the ability to control
the deposition of thin films and atomic structures on the atomic scale in order
to create nanostructures,” explained Amar.
Thin films are used in industry to create a variety of
products, such as semiconductors, optical coatings, pharmaceuticals, and solar
cells.
“Ohio’s
status as a worldwide manufacturing leader has led OSC to focus on the field of
advanced materials as one of our areas of primary support,” noted Ashok
Krishnamurthy, co-interim co-executive director of the center. “As a result, numerous
respected physicists, chemists and engineers, such as Dr. Amar, have accessed
OSC computation and storage resources to advance their vital materials science
research.”
Recently, Amar leveraged the center’s powerful
supercomputers to implement a “first-passage time approach” to speed up KMC
simulations of the creation of materials just a few atoms thick.
“The KMC method has been successfully used to carry out
simulations of a wide variety of dynamical processes over experimentally
relevant time and length scales,” Amar noted. “However, in some cases, much of
the simulation time can be ‘wasted’ on rapid, repetitive, low-barrier events.”
While a variety of approaches to dealing with the
inefficiencies have been suggested, Amar settled on using a first-passage-time
(FPT) approach to improve KMC processing speeds. FPT, sometimes also called
first-hitting-time, is a statistical model that sets a certain threshold for a
process and then estimates certain factors, such as the probability that the
process reaches that threshold within a certain amount time or the mean time
until which the threshold is reached.
“In this approach, one avoids simulating the numerous
diffusive hops of atoms, and instead replaces them with the first-passage time
to make a transition from one location to another,” Amar said.
In tests run on Ohio Supercomputer Systems, Jacques Amar, PhD, compared the surface simulations of thin film copper growth using regular (a) Kinetic Monte Carlo methods (KMC) and (b) first-passage-time distribution KMC simulations. |
In particular, Amar and colleagues from the UT department of
Physics and Astronomy targeted two atomic-level events for testing the FPT
approach: edge-diffusion and corner rounding. Edge-diffusion involves the “hopping”
movement of surface atoms—called adatoms—along the edges of islands, which are
formed as the material is growing. Corner rounding involves the hopping of
adatoms around island corners, leading to smoother islands.
Amar compared the KMC-FPT and regular KMC simulation
approaches using several different models of thin film growth: Cu/Cu(100), fcc(100)
and solid-on-solid (SOS). Additionally, he employed two different methods for
calculating the FPT for these events: the mean FPT (MFPT), as well as the full
FPT distribution.
“Both methods provided ‘very good agreement’ between the
FPT-KMC approach and regular KMC simulations,” Amar concluded. “In addition, we
find that our FPT approach can lead to a significant speed-up, compared to
regular KMC simulations.”
Amar’s FPT-KMC approach accelerated simulations by a factor
of approximately 63 to 100 times faster than the corresponding KMC simulations
for the fcc(100) model. The SOS model was improved by a factor of 36 to 76
times faster. For the Cu/Cu(100) tests, speed-up factors of 31 to 42 and 22 to
28 times faster were achieved, respectively, for simulations using the full FPT
distribution and MFPT calculations.
Amar’s research was supported through multiple grants from
the National Science Foundation, as well as by a grant of computer time from
OSC. A paper co-authored by Amar and UT colleagues Giridhar Nandipati and
Yunsic Shim, “First-passage time approach to kinetic Monte
Carlo simulations of metal (100) growth,” appeared in Physical Review B.
