Neerav Kharche

Atomistic Simulation of Realistically Sized Nanodevices Using NEMO 3-D—Part I: Models and Benchmarks

Device physics and material science meet at the atomic scale of novel nanostructured semiconductors, and the distinction between new device or new material is blurred. Not only the quantum-mechanical effects in the electronic states of the device but also the granular atomistic representation of the underlying material are important. Approaches based on a continuum representation of the underlying material typically used by device engineers and physicists become invalid. Ab initio methods used by material scientists typically do not represent the band gaps and masses precisely enough for device design, or they do not scale to realistically large device sizes. The plethora of geometry, material, and doping configurations in semiconductor devices at the nanoscale suggests that a general nanoelectronic modeling tool is needed. The 3-D NanoElectronic MOdeling (NEMO 3-D) tool has been developed to address these needs. Based on the atomistic valence force field and a variety of nearest neighbor tight-binding models (e.g., s, sp3s*, and sp3d5s*), NEMO 3-D enables the computation of strain and electronic structure for more than 64 and 52 million atoms, corresponding to volumes of (110 nm)3 and (101 nm)3, respectively. The physical problem may involve very large scale computations, and NEMO 3-D has been designed and optimized to be scalable from single central processing units to large numbers of processors on commodity clusters and supercomputers. NEMO 3-D has been released with an open-source license in 2003 and is continually developed by the Network for Computational Nanotechnology (NCN). A web-based online interactive version for educational purposes is freely available on the NCN portal ( http://www.nanoHUB.org). In this paper, theoretical models and essential algorithmic and computational components that have been used in the development and successful deployment of NEMO 3-D are discussed.

Quasiparticle band gap engineering of graphene and graphone on hexagonal boron nitride substrate.

Graphene holds great promise for post-silicon electronics; however, it faces two main challenges: opening up a band gap and finding a suitable substrate material. In principle, graphene on hexagonal boron nitride (hBN) substrate provides a potential system to overcome these challenges. Recent theoretical and experimental studies have provided conflicting results: while theoretical studies suggested a possibility of a finite band gap of graphene on hBN, recent experimental studies find no band gap. Using the first-principles density functional method and the many-body perturbation theory, we have studied graphene on hBN substrate. A Bernal stacked graphene on hBN has a band gap on the order of 0.1 eV, which disappears when graphene is misaligned with respect to hBN. The latter is the likely scenario in realistic devices. In contrast, if graphene supported on hBN is hydrogenated, the resulting system (graphone) exhibits band gaps larger than 2.5 eV. While the band gap opening in graphene/hBN is due to symmetry breaking and is vulnerable to slight perturbation such as misalignment, the graphone band gap is due to chemical functionalization and is robust in the presence of misalignment. The band gap of graphone reduces by about 1 eV when it is supported on hBN due to the polarization effects at the graphone/hBN interface. The band offsets at graphone/hBN interface indicate that hBN can be used not only as a substrate but also as a dielectric in the field effect devices employing graphone as a channel material. Our study could open up new way of band gap engineering in graphene based nanostructures.

Performance Analysis of a Ge/Si Core/Shell Nanowire Field-Effect Transistor

We ana/lyze the performance of a recently reported Ge/Si core/shell nanowire transistor using a semiclassical, ballistic transport model and an sp3d5s* tight-binding treatment of the electronic structure. Comparison of the measured performance of the device with the effects of series resistance removed to the simulated result assuming ballistic transport shows that the experimental device operates between 60 and 85% of the ballistic limit. For this approximately 15 nm diameter Ge nanowire, we also find that 14-18 modes are occupied at room temperature under ON-current conditions with ION/IOFF = 100. To observe true one-dimensional transport in a 110 Ge nanowire transistor, the nanowire diameter would have to be less than about 5 nm. The methodology described here should prove useful for analyzing and comparing on a common basis nanowire transistors of various materials and structures.

Atomistic Simulation of Realistically Sized Nanodevices Using NEMO 3-D—Part II: Applications

In part I, the development and deployment of a general nanoelectronic modeling tool (NEMO 3-D) has been discussed. Based on the atomistic valence-force field and the sp3d5s* nearest neighbor tight-binding models, NEMO 3-D enables the computation of strain and electronic structure in nanostructures consisting of more than 64 and 52 million atoms, corresponding to volumes of (110 nm)3 and (101 nm)3, respectively. In this part, successful applications of NEMO 3-D are demonstrated in the atomistic calculation of single-particle electronic states of the following realistically sized nanostructures: 1) self-assembled quantum dots (QDs) including long-range strain and piezoelectricity; 2) stacked quantum dot system as used in quantum cascade lasers; 3) SiGe quantum wells (QWs) for quantum computation; and 4) SiGe nanowires. These examples demonstrate the broad NEMO 3-D capabilities and indicate the necessity of multimillion atomistic electronic structure modeling.

Valley splitting in strained silicon quantum wells modeled with 2° miscuts, step disorder, and alloy disorder

Valley splitting (VS) in strained SiGe∕Si∕SiGe quantum wells grown on (001) and 2° miscut substrates is computed in a magnetic field. Calculations of flat structures significantly overestimate, while calculations of perfectly ordered structures underestimate experimentally observed VS. Step disorder and confinement alloy disorder raise the VS to the experimentally observed levels. Atomistic alloy disorder is identified as the critical physics, which cannot be modeled with analytical effective mass theory. NEMO-3D is used to simulate up to 106 atoms, where strain is computed in the valence-force field and electronic structure in the sp3d5s* model.

Performance Comparisons of III–V and Strained-Si in Planar FETs and Nonplanar FinFETs at Ultrashort Gate Length (12 nm)

The exponential miniaturization of Si complementary metal-oxide-semiconductor technology has been a key to the electronics revolution. However, the downscaling of the gate length becomes the biggest challenge to maintain higher speed, lower power, and better electrostatic integrity for each following generation. Both industry and academia have been studying new device architectures and materials to address this challenge. In preparation for the 12-nm technology node, this paper assesses the performance of the In0.75Ga0.25As of III-V semiconductor compounds and strained-Si channel nanoscale transistors with identical dimensions. The impact of the channel material property and the device architecture on the ultimate performance of ballistic transistors is theoretically analyzed. Two-dimensional and three-dimensional real-space ballistic quantum transport models are employed with band structure nonparabolicity. The simulation results indicate three conclusions: 1) the In0.75Ga0.25As FETs do not outperform strained-Si FETs; 2) triple-gate Fin-shaped Field Effect Transistor (FinFET) surely represent the best architecture for sub-15-nm gate contacts, independently from the material choice; and 3) the simulations results further show that the overall device performance is very strongly influenced by the source and drain resistances.

Approximate bandstructures of semiconductor alloys from tight-binding supercell calculations

Alloys such as AlGaAs, InGaAs, and SiGe find widespread usage in nanoelectronic devices such as quantum dots and nanowires. For these devices, in which the carriers probe nanometre-scale local disorder, the commonly employed virtual crystal approximation (VCA) is inadequate. Although the VCA produces small-cell E(k) relations it fails to include local disorder. In contrast, random-alloy supercell calculations do include local disorder but only deliver band extrema and supercell (not small cell) E(k) relations. Small-cell E(k) relations are, however, needed to interpret transport parameters such as effective masses. This work presents a method to extract the necessary approximate small-cell E(k) relations from the disordered supercell states. The method is applied to AlGaAs and gives significantly improved energy gaps versus the VCA, as well as approximate effective masses. The results illuminate the bowing of the Γ-valley gap and the good agreement with bulk experimental data shows that this method is well suited for nanodevices.

Controlled Sculpture of Black Phosphorus Nanoribbons

Black phosphorus (BP) is a highly anisotropic allotrope of phosphorus with great promise for fast functional electronics and optoelectronics. We demonstrate the controlled structural modification of few-layer BP along arbitrary crystal directions with sub-nanometer precision for the formation of few-nanometer-wide armchair and zigzag BP nanoribbons. Nanoribbons are fabricated, along with nanopores and nanogaps, using a combination of mechanical-liquid exfoliation and in situ transmission electron microscopy (TEM) and scanning TEM nanosculpting. We predict that the few-nanometer-wide BP nanoribbons realized experimentally possess clear one-dimensional quantum confinement, even when the systems are made up of a few layers. The demonstration of this procedure is key for the development of BP-based electronics, optoelectronics, thermoelectrics, and other applications in reduced dimensions.

Accurate Six-Band Nearest-Neighbor Tight- Binding Model for the π-Bands of Bulk Graphene and Graphene Nanoribbons

Accurate modeling of the π-bands of armchair graphene nanoribbons (AGNRs) requires correctly reproducing asymmetries in the bulk graphene bands, as well as providing a realistic model for hydrogen passivation of the edge atoms. The commonly used single-pz orbital approach fails on both these counts. To overcome these failures we introduce a nearest-neighbor, three orbital per atom p/d tight-binding model for graphene. The parameters of the model are fit to first-principles density-functional theory –based calculations as well as to those based on the many-body Green’s function and screened-exchange formalism, giving excellent agreement with the ab initio AGNR bands. We employ this model to calculate the current-voltage characteristics of an AGNR MOSFET and the conductance of rough-edge AGNRs, finding significant differences versus the single-pz model. These results show that an accurate band structure model is essential for predicting the performance of graphene-based nanodevices.

Effect of Layer Stacking on the Electronic Structure of Graphene Nanoribbons

The evolution of electronic structure of graphene nanoribbons (GNRs) as a function of the number of layers stacked together is investigated using ab initio density functional theory (DFT), including interlayer van der Waals interactions. Multilayer armchair GNRs (AGNRs), similar to single-layer AGNRs, exhibit three classes of band gaps depending on their width. In zigzag GNRs (ZGNRs), the geometry relaxation resulting from interlayer interactions plays a crucial role in determining the magnetic polarization and the band structure. The antiferromagnetic (AF) interlayer coupling is more stable compared to the ferromagnetic (FM) interlayer coupling. ZGNRs with the AF in-layer and AF interlayer coupling have a finite band gap, while ZGNRs with the FM in-layer and AF interlayer coupling do not have a band gap. The ground state of the bilayer ZGNR is nonmagnetic with a small but finite band gap. The magnetic ordering is less stable in multilayer ZGNRs compared to that in single-layer ZGNRs. The quasiparticle GW corrections are smaller for bilayer GNRs compared to single-layer GNRs because of the reduced Coulomb effects in bilayer GNRs compared to single-layer GNRs.