Fast Multipole Method (FMM) : A disadvantage of a typical particle-based device simulation experiment is that the 3-D Poisson equation must be solved repeatedly in order to properly describe the self-consistent fields, which consumes more than 80% of the total simulation time. Instead, we used a 3-D Fast Multi-Pole Method (FMM) to accelerate simulations even further. The FMM calculates the field and potential in a system of n particles connected by a central force within operations of a certain precision. The FMM is based on the concept of condensing the information generated by point sources in truncated series expansions. After calculating appropriate expansions, the long range part of the potential is calculated by evaluating the truncated series at the point of interest, and the short range part is calculated by direct summation. At the start of the simulation, the field due to the applied boundary biases is obtained by solving the Poisson equation. As a result, the total field on each electron is equal to the sum of this constant field and the contributions from electron-electron and electron-impurity interactions handled by the FMM calculations. The method of images handles the image charges that arrive as a result of the dielectric discontinuity. The approach's correctness is demonstrated through simulations of the doping dependence of low-field electron mobility in a 3-D resistor and comparison with available theoretical and experimental data.

Event-biasing for statistical enhancement in the Monte-Carlo device simulations : Enhancement algorithms are especially useful when the device behavior is governed by rare events in the carrier transport process. It is shown that the weight of the particles, as obtained by biasing the Boltzmann equation, survives between the successive steps of solving the Poisson equation. Particular biasing techniques are applied to the simulations of subthreshold conduction in a 15 nm n-channel MOSFET and the convergence of both the terminal current and the channel current is analyzed.  It is found that event-biasing experiments recover precisely the physical averages and the self-consistent field and reduces the time necessary for computation of the desired device characteristics.

Parallel computation. Parallel programming and algorithms are parts and parcels in our group and routinely used. Parallel applications like LAMPS and NEMO 3-D are the core components in the software developed by the group. LAMMPS is a classical molecular dynamics code that models an ensemble of particles in a liquid, solid, or gaseous state. It can model atomic, polymeric, biological, metallic, granular, and coarse-grained systems using a variety of force fields and boundary conditions. LAMMPS is designed to be easy to modify or extend with new capabilities, such as new force fields, atom types, boundary conditions, or diagnostics. Excellent parallel scaling exceeding 120,000 cores has recently been performed by our group on ORNL Jaguar XT5, maximum number of atoms simulated being ~3.84 billion! Also, In the self consistent quantum simulations, the most computationally expensive part is the Green’s function calculation at every energy point. For example, the size of the Hamiltonian can be up to 7000×7000, block-tri-diagonal. Depending on the required energy resolution, the equations may need to be solved 1000 times for every Poisson iteration. In order to reduce the computational burden, the MPI (message passing interface) parallelization scheme has been implemented in most of the quantum transport solvers in the independent computation of Green’s function at each point along the energy spectrum.

Electronic structure of realistically-sized quantum dots : The theoretical knowledge of the electronic structure of nanoscale semiconductor devices is the first and most essential step towards the interpretation and the understanding of the experimental data and reliable device design at the nanometer scale. Electronic band structure of a solid originates from the wave nature of particles and depicts the allowed and forbidden energy states of electrons in the material. Recently we have studied symmetry breaking and energy level splitting in self-assembled Zincblende and Wurtzite quantum dots through atomistic simulations. The symmetry in quantum dots realized from III-V materials is lowered due to two fundamental symmetry breaking mechanisms: (a) the underlying crystal, which lacks inversion symmetry, (2) the presence of strain, and (3) strain induced piezoelectric potential. In III-N materials, in addition to piezoelectric field, there exists a pyroelectric contribution as well. Results show a significant dependence of the dot states and optical polarization on the geometry (Box/Dome/Pyramid) and size of the QDs. NEMO 3-D, a versatile and open source electronic structure code that can handle device domains relevant for realistic large devices, is used in this work. Realistic devices containing millions of atoms can be computed with reasonably, easily available cluster computers. NEMO 3-D employs a VFF Keating model for strain and the 20-band sp3d5s* empirical tight-binding model for the electronic structure computation. It is released under an open source license and maintained by the NCN at Purdue University, West Lafayette under the supervision of Professor Gerhard Klimeck.

Atomistic electronic structure of ZB and WZ nanowires : In the last decade, nanowires (NWs) made from a wide variety of materials have drawn considerable interest because of their potential applications in various optoelectronic and high-mobility electronic devices. Using NWs in these devices, the performance is enhanced due to increased charge localization and reduction in the defect density. In this work, electronic bandstructure of [0001]-oriented Wurtzite nanowires with square cross sections is calculated using sp3s*d5 and sp3s* tight-binding models and then used to parameterize the bandgap and Gamma-valley effective masses. The materials used include: group III-V, group III-nitrides, group II-VI (CdSe, ZnSe, CdS and ZnS) and 2H-SiC.

Carbon nanotubes. The electronic behavior of metallic carbon nanotubes under the influence of atomistic vacancy defects present in the channel is theoretically investigated using the Non-Equilibrium Green’s function (NEGF) method self-consistently coupled with three-dimensional (3D) electrostatics. A nearest neighbor tight binding model based on a single pz orbital is used for the device Hamiltonian. A single vacancy defect in the channel of a small diameter metallic carbon nanotube can decrease its conductance by a factor of two. More than one vacancy in the channel can further drastically decrease the conductance. Larger diameter nanotubes suffer less from the presence of vacancy defects. The presence of a single vacancy locally modulates the LDOS significantly in the device. More importantly, regardless of the chirality of the nanotube, the transmission is reduced throughout the entire energy spectrum (by one quantum unit in some regions). The work is done in collaboration with Neophytos Neophytou and Gerhard Klimeck at Purdue University.

Quantum simulations of nanoscale dual-gate MOSFETs. There is a virtual consensus that the most practically scalable variety of all novel MOSFETs, that are in the focus of many researchers’ study today, are the double-gate SOI MOSFETs with a sub-10 nm gate length, ultra-thin, intrinsic channels and highly doped (degenerate) bulk electrodes. In such transistors, short channel effects typical for their bulk counterparts are minimized, while the absence of dopants in the channel maximizes the mobility and hence drive current density. Such advanced MOSFETs may be practically implemented in several ways including planar, vertical, and FinFET geometries. However, several design challenges have been identified such as a process tolerance requirement of within 10% of the body thickness and an extremely sharp doping profile with a doping gradient of 1 nm/decade. The SIA forecasts that this new device architecture may extend MOSFETs to the 22 nm node (9-nm physical gate length) by 2016. Intrinsic device speed may exceed 1 THz and integration densities will be more than 1 billion transistors/cm2.This work focused mainly on the modeling and simulations of the size-quantization effect within a fully quantum mechanical Non-equilibrium Green’s Function (NEGF) approach and a quantum-corrected Monte Carlo transport framework for 2-D MOSFET structures and presents benchmark results of three software packages namely nanoFET, nanoMOS and QuaMC 2-D.

Unintentional /discrete dopant effects in Si nanowires : Numerical simulations are performed to study the single-charge-induced ON-current fluctuations (random telegraphic noise) in silicon nanowire field-effect transistors. A 3-D fully atomistic quantum-corrected particle-based Monte Carlo device simulator (MCDS 3-D) has been used in this work. Our study confirms that the presence of single channel charges modifies the electrostatics (carrier density) and dynamics (mobility) of the device, both of which play important roles in determining the magnitude of the current fluctuations. The relative impact (percentage change in the ON-current) depends on an intricate interplay of device size, geometry, channel (crystal) orientation, gate bias, and energetics and spatial location of the charge.

Bandstructure and crystal orientation effects in III-V MOS devices.  : Nanoscale double-gate n-MOSFETs with silicon and III-V (GaAs and InAs) channels are studied using numerical simulation. The device structures are based on the ITRS 14nm node (year 2020), and are simulated using the program nanoMOS, which utilizes the NEGF technique for treating ballistic electron transport in the channel. The effective masses used are obtained by extraction from the full band structure using the sp3d5s* empirical tight-binding method. This process returns effective mass values for all valleys which are far more accurate than bulk values for the ultra-thin-body MOSFET. The results indicate that for digital logic applications, III-V materials offer little or no performance advantage over silicon for ballistic devices near the channel length scaling limit. 

Modeling droop in solid-state lighting devices : III-nitride solid-state lighting (SSL) has the potential, by 2025, to decrease electricity consumed by lighting by >50%, cut ~28 million metric tons of carbon emission annually, and benefit general illumination, transportation, communication, automobiles, imaging, agriculture, and medicine. SSL will revolutionize semiconductor market and can reestablish U.S. manufacturing leadership. The objective of this research is to computationally investigate: i) how efficiency droop and color degradation in III-nitride SSL devices are governed by an intricate interplay of crystal atomicity, built-in structural fields, and charge and phonon transport processes, and ii) how tuning the basic physical properties at nanoscale can create transformative solution paths. [Supported by NSF]

Multiscale Design of Nanostructured Thermoelectric Coolers : Here, our objective is to deploy a multiscale simulator for thermoelectric cooler devices, where the material parameters are obtained atomistically using a combination of molecular dynamics and tight-binding simulations and then used in the system level design. In a recently published work [Afsana Sharmin, Mohammad Rashid, Vamsi Gaddipati, Abu Sadeque, and Shaikh Ahmed, “Multiscale Design of Nanostructured Thermoelectric Coolers: Effects of Contact Resistances,” IEEE/TMS Journal of Electronic Materials, vol. 44, no. 6, pp. 1697–1703, 2015], after benchmarking the simulator against a recent experimental work [I. Chowdhury, R. Prasher, K. Lofgreen, G. Chrysler, S. Narasimhan, R. Mahajan, D. Koester, R. Alley and R. Venkatasubramanian, “On-chip cooling by superlattice-based thin-film thermoelectrics”, Nature Nanotechnology, vol. 4, pp. 235–238, 2009], we carried out a detailed numerical investigation of the performance of Bi2Te3 nanowire based thermoelectric devices for hot-spot cooling. The results suggest that active hotspot cooling of as much as 23 ºC with a high heat flux is achievable using such low-dimensionality structures. However, it has been observed that thermal and electrical contact resistances, which are quite large in nanostructures, play a critical role in determining the cooling range and lead to significant performance degradation that must be addressed before these devices can be deployed in such applications. Besides applications in embedded and potable coolers, thermoelectric devices are used as power sources for remote telecommunication, navigation, and radioisotope generator for space vehicles, and show great promise in heat scavenging in vehicle exhaust system. Recently, within a sp3d5s* tight-binding scheme, we have determined the bandstructure of Bi2Te3 nanowire for use in high-temperature thermoelectric devices. Previously, we worked on bulk Bi2Te3 material (left panel of the below Figure). Right panel of the Figure shows (inset) a rectangular (atomistic) Bi2Te3 nanowire having dimensions of Lx = 0.8 nm Ly = 0.8 nm, and Lz = 3.045 nm, and the energy bandgap vs. nanowire dimension (side-length) plot where a decrease in bandgap with the reduction of nanowire dimension is due to the quantum-mechanical size-quantization effect. [Supported by NSF] 

Atomistic Modeling of Degradation Mechanisms in Nanoscale HEMT Devices. Through atomistic numerical simulations, we investigate how performance degradation of state-of-the-art AlGaN HEMTs is governed by an intricate coupling of the underlying thermo-electro-mechanical processes while operating at high power and/or high-temperature. The polarization induced charge density is shown to be strongly dependent on the thickness of the AlN barrier layer. This further demonstrates that the degradation in these HEMT devices is related to the reduction of the effective thickness of the AlN barrier layer, which, during operation at high device temperature, could arise from the diffusion of gate metal into the barrier material matrix. This finding has been validated using the massively parallel LAMMPS molecular dynamics tool and available experimental data. We have also demonstrated that the polarization fields alone can induce channel carriers at zero external bias and lead to a significant increase in the ON current. [Supported by NSF]

This work aims to develop a multiscale Quantum Atomistic Device Simulator (QuADS 3-D) where: a) material parameters are obtained atomistically using first-principles, b) structural relaxation and phonon dispersions are studied via molecular mechanics/dynamics, c) a variety of tight-binding models (s, sp3s*, sp3d5s*) are used for the calculation of electronic bandstructure and interband transition rates, and d) coupled charge-phonon transport is simulated using a combined Monte Carlo-NEGF framework. The atom-by-atom simulation capability in QuADS 3-D exposes new degrees-of-freedom at nanoscale (such as engineering the stress, hybrid crystal cuts, composition, surface polarization, and electrostatics) and creates transformative design routes for boosting performance and reliability of novel nanoelectronic devices. QuADS 3-D uses several novel, memory-miserly, parallel and fast algorithms [5], and incorporates state-of-the-art fault-tolerant software design approaches, which enables the simulator to assess the reliability of available petaflop computing platforms (TeraGrid, NCCS, NICS). A web-based online inter¬active version for educational purposes will soon be available on http://www.nanoHUB.org.