Nanoelectronic Modeling Tool Research Articles

Spin–orbit splittings in Si/SiGe quantum wells: from ideal Si membranes to realistic heterostructures

We present a calculation of the wavevector-dependent subband level splitting from spin–orbit coupling in Si/SiGe quantum wells. We first use the effective-mass approach, where the splittings are parameterized by separating contributions from the Rashba and Dresselhaus terms. We then determine the inversion asymmetry parameters by fitting tight-binding numerical results obtained using the quantitative nanoelectronic modeling tool, NEMO-3D. We describe the relevant coefficients as a function of applied electric field and well width in our numerical simulations. Symmetry arguments can also predict the behavior, and an extensive analysis is also presented in this work. Using vast computational resources, we treat alloy disorder at the atomistic scale. We obtain first-time results for realistic Si/SiGe heterostructures. Our numerical data are in very good agreement with experimental results, both qualitatively and quantitatively. We conclude that effects of alloy disorder have a crucial influence on the spin–orbit parameters.

Development of a Nanoelectronic 3-D (NEMO 3-D ) Simulator for Multimillion Atom Simulations and Its Application to Alloyed Quantum Dots

Material layers with a thickness of a few nanometers are common-place in today's semiconduc- tor devices. Before long, device fabrication methods will reach a point at which the other two device dimensions are scaled down to few tens of nanometers. The total atom count in such deca-nano devices is reduced to a few million. Only a small finite number of free electrons will operate such nano-scale devices due to quantized electron energies and electron charge. This work demon- strates that the simulation of electronic structure and electron transport on these length scales must not only be fundamentally quantum mechanical, but it must also include the atomic granularity of the device. Various el- ements of the theoretical, numerical, and software foun- dation of the prototype development of a Nanoelectronic Modeling tool (NEMO 3-D) which enables this class of device simulation on Beowulf cluster computers are pre- sented. The electronic system is represented in a sparse complex Hamiltonian matrix of the order of hundreds of millions. A custom parallel matrix vector multiply al- gorithm that is coupled to a Lanczos and/or Rayleigh- Ritz eigenvalue solver has been developed. Benchmarks of the parallel electronic structure and the parallel strain calculation performed on various Beowulf cluster com- puters and a SGI Origin 2000 are presented. The Be- owulf cluster benchmarks show that the competition for memory access on dual CPU PC boards renders the util- ity of one of the CPUs useless, if the memory usage per node is about 1-2 GB. A new strain treatment for the

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, sp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s*, and sp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> s*), 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) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> and (101 nm) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> , 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.

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 sp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> s* 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) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> and (101 nm) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> , 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

A theory based on localized-orbital approaches is developed to describe the valley splitting observed in silicon quantum wells. The theory is appropriate in the limit of low electron density and relevant for quantum computing architectures. The valley splitting is computed for realistic devices using the quantitative nanoelectronic modeling tool NEMO. A simple, analytically solvable tight-binding model reproduces the behavior of the splitting in the NEMO results and yields much physical insight. The splitting is in general nonzero even in the absence of electric field in contrast to previous works. The splitting in a square well oscillates as a function of S, the number of layers in the quantum well, with a period that is determined by the location of the valley minimum in the Brillouin zone. The envelope of the splitting decays as S−3. The feasibility of observing such oscillations experimentally in Si/SiGe heterostructures is discussed.

Diagonal parameter shifts due to nearest-neighbor displacements in empirical tight-binding theory

Nanoscale heterostructures are generally characterized by local strain variations. Because the atoms in such systems can be irregularly positioned, theroretical models and parameterizations that are restricted to hydrostatic and uniaxial strain are generally not applicable. To address this shortcoming, a method that enables the incorporation of general distortions into the empirical tight binding model is presented. The method shifts the diagonal Hamiltonian matrix elements due to displacements of neighboring atoms from their ideal bulk positions. The new, efficient, and flexible method is developed for zincblende semiconductors and employed to calculate gaps for GaAs and InAs under hydrostatic and uniaxial strain. Where experimental and theoretical data are available our new method compares favorably with other methods, yet it is not restricted to the cases of uniaxial or hydrostatic strain. Because our method handles arbitrary nearest-neighbor displacements it permits the incorporation of diagonal parameter shifts in general, three-dimensional nanoscale electronic structure simulations, such as the nanoelectronic modeling tool (NEMO 3D).

Parallelization of the Nanoelectronic Modeling Tool (NEMO 1-D) on a Beowulf Cluster

NEMO's main task is the computation of current-voltage (I-V) characteristics for resonant tunneling diodes (RTDs). The primary model for high performance RTDs is the full band sp3s* tight binding simulation, which is based on a numerical double integral of energy and transverse momentum over a transport kernel at each bias point. A full charge self-consistent simulation invoking this model on a single CPU is prohibitively expensive, as the generation of a single I-V curve would take about 1–2 weeks to compute. Simplified charge self-consistent models, eliminating the numerical momentum integral for the quantum mechanical charge self-consistency, followed by a single pass double integration for the current, have been used in the past. However, Computation on a parallel computer now enables the thorough exploration of quantum mechanical transport including charge self-consistency effects within the entire Brillouin zone based on the double integral. Various parallelization schemes (fine, coarse, and mixed) are presented and evaluated in their performance. Finally a comparison to experimental data is given.

Genetically Engineered Nanostructure Devices

AbstractMaterial variations on an atomic scale enable the quantum mechanical functionality of devices such as resonant tunneling diodes (RTDs), quantum well infrared photodetectors (QWIPs), quantum well lasers, and heterostructure field effect transistors (HFETs). The design and optimization of such heterostructure devices requires a detailed understanding of quantum mechanical electron transport. The Nanoelectronic Modeling Tool (NEMO) is a general-purpose quantum device design and analysis tool that addresses this problem. NEMO was combined with a parallelized genetic algorithm package (PGAPACK) to optimize structural and material parameters. The electron transport simulations presented here are based on a full band simulation, including effects of non-parabolic bands in the longitudinal and transverse directions relative to the electron transport and Hartree charge self-consistency. The first result of the genetic algorithm driven quantum transport calculation with convergence of a random structure population to experimental data is presented.