Revolutionizing Semiconductor Development With GPU-Enhanced Atomistic Modeling

There are many challenges in the development of a modern semiconductor chip, from front-end architecture simulation to final signoff. Volume manufacturing has its own set of challenges, while silicon lifecycle management (SLM) extends into field deployment and aging concerns. Underlying this entire development flow, however, lie the materials used to build the actual chips. Guiding the exploration of new materials, discovering them, understanding and analyzing them, and supporting and extending their use is the domain of materials engineering. Atomistic modeling plays a major role in this process, with graphics processing units (GPUs) now emerging as a key enabler to reduce the turnaround time of the simulations and to increase the size of the systems that can be modeled and simulated.

Overview of atomistic simulation

Traditional investigation of new materials has involved physically building the compounds and evaluating them in the lab. This requires developing synthesis methods, dealing with sourcing and cost challenges, and handling toxicity issues. Even if the materials can be created, only limited extrinsic properties can be measured in the lab.

Atomic-scale modeling provides a solution to these challenges in three ways. First, engineers can screen large amounts of possible materials for specific properties and select promising candidates for deeper analysis. This saves time and money since simulations can be massively parallelized and there are no limitations on the materials that can be studied—literally any element in the periodic table, and combinations thereof, can be considered.

Atomistic simulations also provide a detailed picture of internal properties such as band offsets at interfaces and defect levels, which are hard to measure. This enables a “what if” approach to turn on and off certain effects, or move atoms around, in ways that are not possible in lab experiments, to better understand the underlying causes for the observed results. Finally, atomistic simulations are used to parametrize higher level mesoscopic continuum calculations, for example in cases where there is not enough experimental data available, or to calibrate a particular model.

The predictive power and flexibility of atomistic simulation stems from the fact that no input is needed other than the positions and elements of the atoms in the system, plus a model for how the atoms interact. Such models generally fall into two categories: quantum mechanics-based, and force field methods that rely on classical Newtonian mechanics; a previous blog post provides more details on this topic.

GPU acceleration of electronic structure models

There are two main categories of quantum-mechanical models: density functional theory (DFT) and semiempirical models. DFT is based on first principles—solving the fundamental equations of nature—and therefore is very accurate and predictive, but time-consuming. Semiempirical models are faster, but require parameters, which can be taken from DFT or lab experiments.

Materials engineers prefer the accuracy and transparency of DFT, but historically, they have been severely limited by runtime. With central processing units (CPUs), reasonable simulation times can be obtained only for small systems of low complexity, such as basic crystalline materials. As in so many other fields, GPUs are now proving to be an attractive platform to accelerate these calculations. The graphs below show the actual speedup attained by the Synopsys QuantumATK atomistic simulation platform running on GPUs versus CPUs, for both DFT and semiempirical calculations.

Fig. 1: Speedup of GPU vs. CPU for running large-scale models with Synopsys QuantumATK. The two examples on the left-hand side used the generalized gradient approximation (GGA) and a medium size basis set within the linear combination of atomic orbitals (LCAO) approach to DFT. The top right example was run with a non-orthogonal tight-binding model, while the lower right calculation was performed with a single-zeta polarized basis set and the HSE06 hybrid functional, considered to be the most accurate but also very time-consuming way to correctly describe the band structure of semiconductors within DFT.

The measured speedup ranges from roughly 5X to more than 10X. This will bring a week-long simulation down to well under one day, which can mean the difference between a simulation that is worthwhile to run versus one that is not. Faster turnaround time enables many more “what if” runs and, therefore, more thorough investigations of new materials. The speedup actually increases as the number of atoms grows, which is ideal since the goal is to enable simulation of larger models. Note how the systems simulated ranged from 8,000 to 25,000 atoms, far beyond traditional limitations of electronic structure software. It is also worth highlighting that the two examples on the right-hand side are non-equilibrium Green’s function (NEGF) transport simulations, a unique feature in Synopsys QuantumATK that yields some of the most impressive runtime reductions.

GPU acceleration of machine-learned potentials

Static atomistic electronic structure calculations using DFT, especially when accelerated with GPUs, solve many problems in materials engineering. However, many material properties of interest, including thermal ones, require that the system evolves in time. Although it is possible to run such dynamic calculations using DFT, the task is so time-consuming that such efforts are generally reserved for special cases or very small systems. Another option is to use classical force fields, for which molecular dynamics (MD) simulations can readily be performed for even millions of atoms. The problem is that parameters for such force fields, or potentials, only exist for select materials, and are often not accurate enough for chemical reactions or high-temperature simulations.

Recently, a new type of force fields, based on AI or machine learning (ML), have emerged to very successfully close this gap. Machine-learned potentials (MLPs) address system size limitations by learning the energies and interactions in atomic-scale systems directly from DFT calculations. When trained sufficiently, MLPs can model the dynamic evolution of large systems much faster than DFTs and with more accuracy than conventional force field models. MLPs thus provide a modern, data-driven approach to atomistic simulation for virtually any kind of material. More information is available in another recent blog post.

Synopsys QuantumATK offers a general platform for a variety of different MLPs, with a library of high-quality, ready-to-use potentials, both general-purpose neural network models that cover the entire periodic table, and high-accuracy moment tensor potentials (MTPs) for complex materials such as InGaZnO (IGZO). Users can also develop their own high-accuracy MLPs based on MTP or neural networks for specific materials, interfaces, and surface processes. Simulation accuracy with MLPs (in particular MTPs) is nearly identical to that of DFT, but 1,000-100,000X faster. In one example, a DFT simulation of 270 atoms took 21,500 hours and the MTP simulation of 6,144 atoms ran for only seven hours, a speedup of roughly 120,000. These simulations were executed entirely on CPUs, but even greater speedup can be obtained using GPUs; the training phase can usually be accelerated by 10-20X and the execution phase by 5-15X.

The following graph shows an MD simulation for a very large cobalt disilicide model with nearly 200,000 atoms. The speedup using four GPUs was greater than 10X, achieving around ten MD steps per second. With 1 fs time steps, this means that materials engineers can run about 1 ns per day of high-accuracy simulations.

Fig. 2: Synopsys QuantumATK is first to introduce the ability to accelerate MTP calculations (and other MLPs like MACE) on multiple GPUs, with excellent scaling, as demonstrated in this example.

Conclusion

GPUs are providing dramatic speedups and enabling new modes of operation for many parts of the semiconductor development flow. GPU acceleration is a piece of the puzzle to democratize atomistic simulations, turning them from research adventures only available to experts into engineering tools with broad applicability by maintaining accuracy while reducing runtime and increasing the return on investment (ROI). Newer generations of GPUs will offer even more speed and memory, which is important as model complexity continues to grow, while simulation tools continuously are being improved to benefit from the massively parallel GPU architecture in more parts of the simulation flow. AI and ML are two other key components in the ongoing evolution of materials engineering, to which can be added improvements in usability and integration with higher-level tool chains within EDA and Integrated Computational Materials Engineering (ICME). Synopsys is actively working at the forefront of tool development in all these areas, and future blog posts will cover all the exciting developments ahead.