GPU-Enabled Exascale Quantum Transport Modeling of Carbon Nanotube Devices

Abstract

The work will describe our efforts to develop an exascale electrostatic-quantum transport framework, Quantum-eXstatic (https://github.com/AMReX-Microelectronics/eXstatic), currently supporting the modeling of carbon nanotube field-effect transistors (CNTFETs). The framework is capable of modeling realistic three-dimensional structures, efficiently, using CPU/GPU heterogeneous architectures of state-of-the-art supercomputers. It is built on top of the AMReX library, which is a GPU-enabled software library containing functionality for writing particle-mesh applications on structured grids. The Quantum-eXstatic framework comprises three major components: the electrostatic module, the quantum transport module, and the part that self-consistently couples the two modules. The electrostatic module using a finite-volume multigrid solver to compute 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 using an embedded boundary approach to allow for intricate shapes. The quantum transport module uses the Nonequilibrium Green's Function (NEGF) method to model induced charge. Currently, it supports coherent (ballistic) transport, mode-space approximation for subbands of nanotube, contacts modeled as semi-infinite leads, and Hamiltonian representation using the tight-binding approximation. Special features are being included for accurate modeling of long nanotubes, such as adaptive refinement of integration contours to resolve van Hove singularities in long channels. Particular attention is paid to overlap computations with communication to optimize GPU performance. The self-consistency between the two modules is achieved using Broyden's modified second algorithm, which is parallelized using CPUs and GPUs. Preliminary scaling studies show that the code exhibits ~77% weak-scaling efficiency on 512 NVIDIA A100 GPUs of Perlmutter supercomputer for modeling gate-all-around CNTFETs with a channel length of 13.5 microns at equilibrium conditions. This case involved computations of electrostatic potential in 14.5 billion computational cells and Green’s function computation for a Hamiltonian of size 131,072 x 131,072. For problems of this large size, the code takes about 5 min to reach self-consistency. Figure 1