Quantum Monte Carlo at Exascale Could Be Key to Finding New Semiconductor Materials

By Linda Barney

September 27, 2021

Researchers are urgently trying to identify possible materials to replace silicon-based semiconductors. The processing power in modern computers continues to increase even as the size of the silicon on which components are placed shrinks. The silicon chip size continues to decrease from 14 nanometers (nm) to 10nm, to 7nm and even smaller. The laws of physics suggest that there is a limit to the number of transistors that can fit on silicon-based chips. As this limit is reached, processing gains will decrease and there will be electron interactions between the components on the chip.

This is one of the research challenges being pursued by scientists preparing for the upcoming Intel-HPE exascale supercomputer, Aurora, which will be housed at the U.S. Department of Energy’s (DOE) Argonne National Laboratory. Supported by the Argonne Leadership Computing Facility’s (ALCF) Aurora Early Science Program, an Argonne team is performing Quantum Monte Carlo research to help locate a new material that could replace silicon-based semiconductors. ALCF computational scientist Anouar Benali is the Primary Investigator on the project.

Anouar Benali

Benali explains, “The search for the next semiconductor material will require high-performance computers (HPC) at exascale. Simulations can only be done on very small prototypes of semiconductor materials with current supercomputers. Using an exascale supercomputer, such as the future Aurora system, will allow us to expand simulations of more materials to help find a viable semiconductor material. Our team is also working with ALCF and the Intel Parallel Computing Center in modifying codes to run on the Aurora supercomputer. We have already seen a 20x processing speedup on the ALCF’s Theta supercomputer, which will allow us to run larger and more realistic compounds in our search for a new semiconductor material.”

What is Quantum Monte Carlo?

The Quantum Monte Carlo (QMC) calculation is a quantum calculation that provides some of the most accurate solutions to quantum mechanical problems. QMC provides theoretical predictions for many problems at the forefront of research—from materials science to complex biological systems. The main power of the QMC method is that instead of trying to solve analytically the Schrödinger equation, describing and predicting all interactions in nature, QMC generates millions of random solutions. QMC then accepts all the solutions that solve the equation or rejects all the ones that don’t to save research time and improve prediction accuracy.


Semiconductor Quantum Chemistry Research

Predicting the properties of materials, or designing materials based on desired properties, is one of the most important goals of material science simulations. Benali states, “Most of the phenomena driving these properties occur at very small scales that are ruled by the laws of quantum mechanics.” For example, knowing if a material will be a good semiconductor or fine tuning the composition of a material to generate the perfect semiconductor requires solving the many-body problem of interacting particles in a quantum system. Researchers often use density functional theory (DFT) equations for organic molecules to determine the properties of a many-electron system. DFT simulations are less computationally expensive than QMC, but the predictions are not as accurate.

Benali’s team developed the open-source simulation code QMCPACK, software which contains Monte Carlo algorithms and uses the Schrödinger equation in calculations. Benali explains, “By solving the Schrödinger equation using statistical methods, large and complex systems can be studied to unprecedented accuracy—including systems where other electronic structure methods have difficulty. The Schrödinger equation can predict all behavior of almost everything in the universe. However, solving the equation for a system as small as a hydrogen molecule is impossible without a significant number of approximations using computer simulations. When simulating properties of more complex materials such as semiconductors, the number of approximations becomes significant, with a tradeoff of a loss of accuracy.”

“The team can significantly reduce the number of quantum approximations that can be simulated using an exascale system such as the future Aurora supercomputer. Using an exascale system will allow us to run calculations on larger systems as well as increase the accuracy of the simulation result to help identify a new semiconductor material to replace silicon-based semiconductors,” states Benali.

Scientific Case Study

The team’s research involves searching for a substitute for silicon (Si) complementary metal-oxide-semiconductor (CMOS) based computing materials. In locating a suitable material to replace silicon, the team must address a fundamental materials problem that current can leak through a hafnium(IV) oxide (HfO2) gate dielectric. Hafnium is used in optical coatings, and as a high-κ dielectric in Dynamic Random-Access Memory (DRAM) capacitors and in advanced metal-oxide-semiconductor devices. Researchers have found evidence that impurities like nitrogen and fluorine are able to reduce leakage currents. However, current computational studies are limited to DFT which do not provide the necessary accuracy to test this theory.

The team is using QMCPACK software to study the energetics of point defects near a HfO2 interface. QMCPACK is funded by the DOE Exascale Comupting Project. Due to the large number of electrons in these simulations, calculations can only be made possible by the large aggregate memory and performance offered by an exascale system such as the future Aurora supercomputer. Benali states, “Our research seeks to prove that adding the right amount of the right impurities can enable the properties we are looking for in the next generation of semiconductors. But mostly, our research is trying to demonstrate that with enough computer power, quantum simulations can be fully predictive and provide significant support to experimental research.”

HfO2 semiconductor (Hf in blue, Oxygen in red) between Pt connectors (white) Courtesy of Dr. Benali, Argonne National Laboratory.

Reducing Calculations with Future Exascale Supercomputers

Increased compute power enables the research team to use QMC to significantly reduce the number of approximations in the resolution of the Schrödinger equation. “The more solutions we try, the more accurate our results become. The greatest value of using the Monte Carlo approach resides in the fact that each random solution is independent from another, meaning that the resolution can be distributed on as many processing units as are available,” indicates Benali.

How Long Does Semiconductor Research Take?
If the accuracy of the answer requires simulating one million random solutions and simulating one solution takes one second on one processing unit, the team’s simulation will end in one million seconds (277 days). However, because the evaluations of the random solutions are independent, on a machine like Argonne’s Theta supercomputer, the evaluation takes about 3.55 seconds. In a more realistic simulation, some operations of initialization and collection of data cannot be parallelized and increase the cost of the computation, but overall the method remains extremely parallel.


Updating QMCPACK Software: Exascale Systems Require a New Approach to Software

The open-source QMCPACK code used by the team in their in the semiconductor research is maintained by Argonne National Laboratory, Oak Ridge National Laboratory, Lawrence Livermore National Laboratory and several universities. Benali is one of the co-owners and co-developers of QMCPACK. Intel has been working with this group since 2016 and provides access to multiple experimental computer systems along with tools such as the Intel Math Kernel Library (MKL) and Intel compilers. The ALCF team maintains the software and code stacks on test machines. In addition, ALCF staff aids researchers in creating or modifying code so that it performs the desired chemistry functions and is designed to run on the future Aurora exascale system.

Coding software for an exascale system requires a new approach to software design and coding. Hardware on an exascale system is not a heterogenous system. In an exascale system, there is not one single Central Processing Unit (CPU) but many components such as CPUs, Graphic Processing Units (GPUs), Field Programmable Gate Arrays (FPGAs), or expanded memory that performs different tasks. The team is breaking the program functions into various modules that perform calculations for a component such as a CPU, multiple CPUs, a GPU as well as calculations based on memory. Coding for an exascale system requires that the programmer is more aware of the varied architecture of the system when writing code. In addition, the team’s semiconductor research can do millions of simulations that are running completely separately. So modifying QMCPACK code to optimize running on GPUs is a priority.

Challenges for Future Quantum Materials Research

“In our current research, our team uses quantum material science simulations to try to predict the behavior and structure of materials to help locate a suitable material to replace silicon in semiconductors. Our team uses QMCPACK on large scale HPC in our quantum chemistry research. “With the advent of the exascale era, a machine like Aurora will allow simulating more realistic and complex materials, replicating what experimentalists do in-situ. Such leaps will allow to orders of magnitude speed up in the pace of discoveries” indicates Benali.

The ALCF is a DOE Office of Science User Facility. Primary support for QMCPACK is via the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, as part of the Computational Materials Sciences Program and Center for Predictive Simulation of Functional Materials, and also the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.

References

  • “QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo” , P. R.C. Kent, A Annaberdiyev, A Benali et. al. J. Chem. Phys. 152 (17), 174105 (2020)
  • ”Defect energetics of cubic hafnia from quantum Monte Carlo simulations”, Raghuveer Chimata, Hyeondeok Shin, Anouar Benali, and Olle Heinonen, Phys. Rev. Materials 3, 075005 – (2019)
  • “Zirconia and hafnia polymorphs: Ground-state structural properties from diffusion Monte Carlo” H. Shin, A. Benali, Y. Luo, E. Crabb, A. Lopez-Bezanilla, L.E. Ratcliff, A. M. Jokisaari and O. Heinonen, Phys Rev. Mat 2 (7), 075001 (2018)
  • “QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids”, J. Kim, A. Baczewski , T. D. Beaudet, A. Benali , M C. Bennett, M. A Berrill , N. S Blun, M. Casula, D. M Ceperley, S. Chiesa, B. K Clark, R. C Clay III, K. T Delaney, M. Dewing, K. P Esler, H. Hao, O. Heinonen, P. R C Kent, J. T Krogel, I. Kylänpää, Y. Wai Li, M G. Lopez, Y. Luo, R. M Martin, A. Mathuriya, J. McMinis, C. A Melton, L. Mitas, M. A Morales, E. Neuscamman, W. D Parker, S. D Pineda Flores, N. A Romero, B. M Rubenstein, J. A R Shea, H. Shin, L. Shulenburger, A. Tillack, J. P Towsend, N. M. Tubman, B. Van Der Goetz, J. E Vincent, S. Zhang, L. Zhao, Y. Yang. J. Phys. Cond. Mat. 30 195901 (2018)

Linda Barney is the founder and owner of Barney and Associates, a technical/marketing writing, training, and web design firm in Beaverton, Ore.

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