Microelectronics and Quantum Chip Modeling
Overview
Researchers in CCSE have developed several AMReXbased code packages that enable physical modeling and simulation of nextgeneration microelectronic devices.
ARTEMIS  Timedomain electrodynamics solver
FerroX  3D phasefield framework for ferroelectric devices
QuantumeXstatic  coupled electrostatic / quantum transport code for nanoscale transport
MagneX  Magnetostatic solver
Phonon tranport on quantum chips  Ballistic phonon solver for quantum chip design.
Machine learning approaches for predictive design and computational modeling
What is ARTEMIS?
ARTEMIS (Adaptive mesh Refinement Timedomain ElectrodynaMics Solver) is a timedomain electrodynamics
solver developed in CCSE that is fully opensource and portable from laptops to manycore/GPU exascale
systems. The core solver is a finitedifference timedomain (FDTD) implementation for Maxwell's equations
that has been adapted to conditions found in microelectronic circuitry. This includes spatiallyvarying
material properties, boundary conditions, and external sources to model our target problems. In order
to achieve portability and performance on a range of platforms, ARTEMIS leverages the developments of
two DOE Exascale Computing Project (ECP) code frameworks. First, the
AMReX software library is the
product of the ECP codesign center for adaptive, structured grid calculations.
AMReX provides complete
data structure and parallel communication support for massively parallel manycore/GPU implementations
of structuredgrid simulations such as FDTD. Second, the
WarpX accelerator
code is an ECP application code for
modeling plasma wakefield accelerators and contains many features that have been leveraged by ARTEMIS.
These features include core computational kernels for FDTD, an overall time stepping framework, and I/O.
Using the ARTEMIS pythonstyle function interpreter, we can define more advanced structures containing
many different material types using different geometrical configurations. Additionally, the
GPU capability of the code provides extreme speed, as a GPU build offers a 59x speedup over the host on
a nodebynode basis. Thus, using HPC resources will allow for highresolution and rapid prototyping of
various configurations with different geometries and material properties. We also note algorithmic flexibility
for additional physics such as magnetic and superconducting materials.

ARTEMIS is part of the two DOEfunded MicroelectronicsCoDesign programs at Berkeley Lab
(Click here for the full list of awards) .
Overview of the devicelevel modeling capability, the ARTEMIS package.
ARTEMIS bridges the gap between material physics and circuit model of PARADISE, by solving governing PDEs of the physics in devices such as NCFET and MESO.
Since ARTEMIS is based off two ECP products, AMReX and WarpX, it fully functions on GPU supercomputers such as NERSC perlmutter system, providing rapid devicelevel modeling to the codesign workflow.
For more information about ARTEMIS or any of the applications below, contact the
ARTEMIS Team
or visit the ARTEMIS github page.

ARTEMIS for MagnonPhoton Dynamics
The comprehensive simulation of coupled magnonphoton coupling circuits has historically posed challenges due to the significant scale disparity inherent in magnonics and electrodynamics.
Using ARTEMIS, we address this challenge by employing a fully coupled computational approach that simultaneously solves the equations governing ferromagnetic dynamics and electromagnetic dynamics.
we have built the coupled model to include spatial inhomogeneity of materials, containing both magnetic and nonmagnetic regions.
In magnetic regions, our coupled algorithm solves both Maxwell's equations and the LandauLifshitzGilbert equation.
To effectively handle the spatial disparity, we have devised a massively GPUparallelized code package as our computational strategy.
The numerical outcomes from our approach reveal the emergence of an anticrossing spectrum between magnons and photons.
ARTEMIS for Transmission Line Analysis
Modeling and characterization of electromagnetic wave interactions with microelectronic devices to derive network parameters
has been a widely used practice in the electronic industry. However, as these devices become increasingly miniaturized with
finerscale geometric features, computational tools must make use of manycore/GPU architectures to efficiently resolve length and time scales of interest.
Left: A microscale transmission line with a Zdirectional electric field excitation for computing Smatrix between ports (1) and (2). Bottom Right: Components of Smatrix as a function of frequency. Top Right: Weakscaling efficiency of ARTEMIS on NVIDIA A100 GPUs using NERSC's Perlmutter supercomputer.

This has been the focus of our opensource solver, ARTEMIS, which is performant on modern
GPUbased supercomputing architectures while being amenable to additional physics coupling. This work demonstrates its use
for characterizing network parameters of transmission lines using established techniques. A rigorous verification and
validation of the workflow is carried out, followed by its application for analyzing a transmission line on a CMOS chip
designed for a photondetector application. Simulations are performed for millions of timesteps on stateoftheart
GPU resources to resolve nanoscale features at gigahertz frequencies. The network parameters are used to obtain
phase delay and characteristic impedance that serve as inputs to SPICE models. The code is demonstrated to exhibit
ideal weak scaling efficiency up to 1024 GPUs and 84% efficiency for 2048 GPUs, which underscores its use for network
analysis of larger, more complex circuit devices in the future.
The details can be found in the following publication.

ARTEMIS for Superconducting Resonators
In collaboration with
Richard Lombardini of Saint Mary's University,
we have implemented a new London equation
module for superconductivity in the GPUenabled ARTEMIS framework, and coupled it to a finitedifference
timedomain solver for Maxwell's equations. We applied this twofluid approach to model a superconducting
coplanar waveguide (CPW) resonator and validated our implementation by verifying that the theoretical skin
depth and reflection coefficients can be obtained for several superconductive materials,
with different London penetration depths, over a range of frequencies. Our convergence studies show that
the algorithm is secondorder accurate in both space and time. In our CPW simulations, we leverage the GPU
scalability of our code to compare the twofluid model to more traditional approaches that approximate
superconducting behavior and demonstrate that superconducting physics can show comparable performance
to the assumption of quasiinfinite conductivity as measured by the Qfactor. The details can be found
in this recent publication.
On the left is an illustration of a CPW resonator structure found in quantum readout applications with superconducting films sitting atop a silicon substrate.
The right depicts the spatial variation of electric field along an xz slice passing through the transmission lines. The dark shaded regions indicate metal
(either conducting or superconducting). The red and blue shading indicates the magnitude of the Ex field (blue/red = +/0.001 V/m) near the end of the simulation,
illustrating the fundamental mode. The inset is an xz slice with normal in the ydirection extract at the front of the resonator line,
y = 300 microns, with vectors illustrating the electric field.
FerroX
FerroX is a massively parallel 3D phasefield simulation framework for modeling and design of
ferroelectricbased microelectronic devices. Due to their switchable polarization in response
to applied electric fields, ferroelectric materials have enabled a wide portfolio of innovative
microelectronics devices, such as ferroelectric capacitors, nonvolatile memories, and
ferroelectric field effect transistors (FeFET). FeFETs, in particular, are designed to
overcome the fundamental energy consumption limit (the "Boltzmann's Tyranny") associated
with individual semiconductor components, allowing for the design of ultra lowpower logic
technologies. The goal of FerroX is to provide an indepth insight into the underlying
physics and to facilitate researchers with a reliable design tool for novel microelectronic
devices. One of the key challenges in the modeling of devices such as FeFETs is the intrinsic
multiphysics nature of the multimaterial stacks. Typical ferroelectric devices involve at
least three coupled physical mechanisms: ferroelectric polarization switching, semiconductor
electron transport, and classical electrostatics, each of which includes rich underlying
physics. FerroX selfconsistently couples the timedependent Ginzburg Landau (TDGL) equation
for ferroelectric polarization, Poisson's equation for electric potential, and charge equation
for carrier densities in semiconductor regions. We discretize the coupled system of partial
differential equations using a finite difference approach, with an overall scheme that is
secondorder accurate in both space and time. The algorithm is implemented using the AMReX
software framework, which provides effective scalability on manycore and GPUbased supercomputing
architectures. We have demonstrated the performance of the algorithm with excellent scaling
results on NERSC multicore and GPU systems, with a significant (15x) speedup on the GPU using
a nodebynode comparison. Additional details can be found
in this recent publication. Our ongoing efforts include implementation of the capability to
quantify the effect of tetragonal/orthorhombic phase mixtures in the negative capacitance
stabilization and effective oxide thickness lowering. In addition, we are adding features to
model carrier transport in semiconductor region to enable first full 3D simulation of FeFETs.
MFISM stack with 5 nm thick HZO on top, followed by 1 nm thick SiO2, and a 10 nm thick Si as the ferroelectric, dielectric, and semiconductor layers, respectively. Vertical direction represents the thickness of the device (z). For an applied voltage, V app = 0 V (a) Polarization distribution showing multidomain formation in HZO (b) Potential distribution induced in the semiconductor (c) Electric field vector plot in semiconductor.
QuantumeXstatic
QuantumeXstatic
is an exascale electrostaticquantum transport framework currently supporting the modeling of carbon nanotube fieldeffect transistors (CNTFETs). It is developed as part of a DOEfunded project called 'Codesign and Integration of Nanosensors on CMOS.' One of the applications of CNTFETs is their use as sensors in advanced photodetectors, where carbon nanotubes are particularly attractive due to their high surfacetovolume ratio, making them highly sensitive to their environment. Such sensing applications require modeling arrays of nanotubes on the order of hundreds of nanometers in length, which may be functionalized with photosensing materials such as quantum dots. The goal of QuantumeXstatic is to model such systems, making efficient use of CPU/GPU heterogeneous architectures.
The framework comprises three major components: the electrostatic module, the quantum transport module, and the part that selfconsistently couples the two modules. The electrostatic module computes the electrostatic potential induced by charges on the surface of carbon nanotubes, as well as by source, drain, and gate terminals, which can be modeled as embedded boundaries with intricate shapes. The quantum transport module uses the nonequilibrium Green's function method to model induced charge. Currently, it supports coherent (ballistic) transport, contacts modeled as semiinfinite leads, and Hamiltonian representation using the tightbinding approximation. The selfconsistency between the two modules is achieved using Broyden's modified second algorithm, which is parallelized on both CPUs and GPUs.
Preliminary studies have demonstrated that the electrostatic and quantum transport modules can compute the potential on billions of grid cells and compute the Green's function for a material with millions of site locations within a couple of seconds, respectively.
A scalable approach to modeling CNTFETs using the 3D exascale electrostaticquantum transport framework.
The lower left figure shows the variation in the selfconsistently computed electrostatic field in a gateallaround CNTFET due to variation in the userdefined gatesource voltage for a fixed drainsource bias of 0.1 V.
The lower right figure shows the magnitude of the drainsource current as a function of gatesource voltage for the same CNTFET, along with a comparison to the results of Léonard and Stewart (2006). The subthreshold swing of 69 mV/decade is calculated from this plot.
MagneX
For classes of micromagnetic problems where the electromagnetic fields are slowly varying, the magnetostatic approximation offers huge computational savings.
We are developing a new micromagnetics code, MagneX for modeling ferromagnetic materials using the magnetostatic approximation.
MagneX incorporates many different physical phenomena, such as exchange coupling, anisotropy, Dzyaloshinskii Moriya interaction (DMI), and demagnetization.
The GPUcapabilities provided by the AMReX library makes MagneX a powerful tool for simulating a wide range of micromagnetic applications, including magnetic storage and memory devices.
phononeX: Phonon Transport on Quantum Chips
We have recently developed a modeling package, phononeX, to simulate the dynamics of ballistic phonons to apply to the design of quantum chips in support of the DOEACCELERATE project,
"Phonon control for nextgeneration superconducting systems and sensors."
The code employs a Monte Carlo approach to solving the Boltzmann transport equation, using the relaxation time method to account for phonon scattering.
Phonons are generated stochastically from an equilibrium source via the Planck distribution.
At low temperatures, low phonon density and energy allow for very simple phonon transport models, i.e. the Debye model.
Arbitrary geometries can be simulated, including effects such as surface roughness and inhomogeneous temperatures.
PhononeX capitalizes on AMReX, which ensures its portability across various supercomputers and PCs.
It is highly scalable on GPUs/CPUs, allowing for massive parallelization, and its algorithmic flexibility facilitates future advancements in modeling new physical mechanisms.
Machine Learning
We are working on two machine learning projects that leverage simulation efforts described above.
First, we are using the FerroX framework to enable design of NCFET gate stack with machine learning.
In collaboration with Jorge Munoz of UTEP, we are employing multilayer perceptrons (MLP) to directly map input variables (e.g., the thickness of ferroelectric, dielectric, and Landau free energy coefficients) to the output variables (e.g., semiconductor voltage).
We are also testing the convolutional neural network (CNN) as a means of establishing a mapping from the field quantities to semiconductor voltage.
Also, we are using Gaussian Process Regression (GPR) to discern the significance of the input parameters.
Using the Radial Basis Function (RBF) kernel, the model was trained to comprehend the influence of parameters such as ferroelectric (FE) and dielectric (DE) thicknesses on capacitance at a given applied voltage.
Second, we are developing highly performant MLaugmented models, that integrate neural networks directly into multiphysical mechanistic models to capture the coupling mechanisms between different physics.
This project focuses on the capabilities of the ARTEMIS framework to model spintronic devices, a thriving technique that utilizes magnetic spins to control and manipulate electric signals with remarkable scalability and low power dissipation.
We are using neural networks as a universal approximator to model the coupling phenomena, which can alleviate stiffness in multiple PDEs and significantly enhance the efficiency of scientific modeling.
The core approach is that we will solve the governing PDE of magnetic spins and incorporate neural networks to represent the coupling torque term coming from the electric field.
This enables us to fully utilize the immense computational power of modern manycore/GPU exascale supercomputers (this approach surpasses the capabilities of popular PINNs models), while taking advantage of the acceleration offered by machine learning techniques.
Publications
P. Kumar, M. Hoffmann, A. Nonaka, S. Salahuddin, and Z. Yao,
3D ferroelectric phase field simulations of polycrystalline multiphase hafnia and zirconia based ultrathin films,
submitted for publication.
[arxiv]
R. Jambunathan, Z. Yao, R. Lombardini, A. Rodriguez, and A. Nonaka,
TwoFluid Physical Modeling of Superconducting Resonators in the ARTEMIS Framework,
Computer Physics Communications, 291, 2023.
[link]
P. Kumar, A. Nonaka, R. Jambunathan, G. Pahwa, S. Salahuddin, and Z. Yao,
FerroX: A GPUaccelerated, 3D PhaseField Simulation Framework for Modeling Ferroelectric Devices,
Computer Physics Communications, 108757, 2023.
[link]
S. Sawant, Z. Yao, R. Jambunathan, and A. Nonaka,
Characterization of Transmission Lines in Microelectronics Circuits using the ARTEMIS Solver,
IEEE J. on Multiscale and Multiphysics Comp. Tech., 8, 2022.
[link]
Z. Yao, R. Jambunathan, Y. Zeng, and A. Nonaka,
A Massively Parallel TimeDomain Coupled ElectrodynamicsMicromagnetics Solver,
International Journal of High Performance Computing Applications, 10943420211057906, 2021.
[link]
