[Audio] Nanoelectronic Modeling: From Quantum Mechanics and Atoms to Realistic Devices

This presentation demonstrates the OMEN capabilities to perform a multi-scale simulation of advanced InAs-based high mobility transistors.Learning Objectives:Quantum Transport Simulator Full-Band and Atomistic III-V HEMTs Performance Analysis Good Agreement with Experiment Some Open Issues Outlook Improve Models (Contact) Investigate Scaling of Gate Length Scattering?

This presentation the effects of line edge roughness on graphene nano ribbon (GNR) transitors..Learning Objectives:GNR TFET Simulation pz Tight-Binding Orbital Model 3D Schrödinger-Poisson Solver Device Simulation Structure Optimization (Doping, Lg, VDD) LER => Localized Band Gap States LER => Performance Deterioration Outlook and Challenges Ripples Scattering More Accurate Bandstructure Model Dissipative Scattering (Electron-Phonon)

This presentation discusses the motivation for band-to-band tunneling transistors to lower the power requirements of the next generation transistors. The capabilities of OMEN to model such complex devices on an atomistic representation is demonstrated.Learning Objectives:Band-To-Band Tunneling Transistors may be “better” than a superscaled MOSFET because: The subthreshold swing is possibly smaller than the ideal 60mV/dec in the best case MOSFET – i.e the device …

This presentation discusses the consequences of Alloy Disorder in unstrained strained AlGaAs nanowiresRelationship between dispersion relationship and transmission in perfectly ordered wiresBand folding in Si nanowiresTranmisison in disordered wires – relationship to an approximate bandstructreReminder of the origin of bandstructure and bandstructure engineeringLocalization of wavefunctionsLearning Objectives:Alloy wires are NOT smooth“Conduction band edge” flucatuates locallyDispersion changes Transmission and Density of states show localization effects

This presentation discusses the consequences of Alloy Disorder in strained InGaAs Quantum Dots Reminder of the origin of bandstructure and bandstructure engineeringWhat happens when there is disorder?Concept of disorder in the local bandstructureConfiguration noise, concentration noise, clusteringLearning Objectives:Device-to-device fluctuations in nanostructures may be significant even if the shape and size of the quantum dots remain perfectly controlled.Configuration noise, concentration noise and clustering in perfectly size and shape controlled quantum dots can lead to optical transition fluctuations that should be experimentally relevant.

This presentation discusses disorder in AlGaAs unstrained systems in bulk. Bandstructure of an ideal simple unit cellWhat happens when there is disorder?Concept of a supercellBand folding in a supercellBand extraction from the concept of approximate bandstructureComparison of alloy disorder with the virtual crystal approximationConfiguration noise, concentration noiseHow large does an alloy supercell have to be? When does the “bulk” condition occur?Learning Objectives:Bandedges and bandgaps are influenced by: Placement / configuration disorderConcentration noise Clustering System size is very important “bulk” starts at 100,000 atoms=> Nanostructures are not “bulk” => like quantum dots, nanowires, and quantum wells vary locally

This presentation demonstrates the utilization of NEMO3D to understand complex experimental data of embedded InAs quantum dots that are selectively overgrown with a strain reducing InGaAs layer. Different alloy concentrations of the strain layer tune the optical emission and absorption wavelength of the quantum dots. The role of the non-linear strain behavior ovserved in the experimental data is explored in NEMO3D. The simulation engine serves as a virtual microscope to understand the interplay of disorder, strain, and quantum dot shape.Learning Objectives:Objective:Optical emission at 1.5μm without GaNUnderstand experimental data on QD spectra in selective overgrowthApproach: Model large structure60nm x 60nm x 60nm9 million atomsNo changes to the published tight binding parametersResult:Match experiment remarkably well Strain change in quantum dot aspect ratio Quantitative model of complex systemStudied sensitivity to experimental imperfections – small variationsEffective mass theories provided the wrong guidance

This presentation demonstrates the importance of long-range strain in quantum dotsNumerical analysis of the importance of the buffer around the central quantum dot - local band edges – vertical and horizontal extension of the bufferControlled overgrowth can tune the electron energies in the systemLearning Objectives:Strain is the source of the creation of the InAs QDs on GaAsStrain is a long range phenomenonStrain reaches further vertically than horizontallyQuantum dots will grow on top of each otherElectron wavefunctions are confined to the central quantum dots and can be computed in a smaller domain

This presentation provides a very high level software overview of NEMO3D. The items discussed are:Modeling Agenda and MotivationTight-Binding Motivation and basic formula expressionsTight binding representation of strainSoftware structureNEMO3D algorithm flow NEMO3D parallelization scheme – original 1D spatial decompositionNEMO3D scaling on parallel computes from the year 2000 til 2007New 1D, 2D, and 3D spatial decomposition scheme and parallel performance52 million atom simulation demonstrationLearning Objectives:Convey a broad overview of the NEMO3D simulation engine. Student shall learn about the algorithmic coponents of geometry construction, atom position computaion, and electronic structure calculation.Student shall learn the need and usefulness of parallel computers to solve the NEMO3D problems.Student shall learn a demonstration of a software capability and validation.

This presentation provides a very high level software overview of NEMO1D.Learning Objectives:This lecture provides a very high level overview of quantum dots. The main issues and questions that are addressed are:Length scale of quantum dotsDefinition of a quantum dotQuantum dot examples and ApplicationsSingle electronicsNeed for quantum dot modelingModel requirements – what are the physical effects that need to be included?Overview of some of the existing theories and modelsTight binding approach

(quantitative RTD modeling at room temperature)

This presentation provides a very high level software overview of NEMO1D. The items discussed are:User requirementsGraphical user interfaceSoftware structureProgram developer requirementsDynamic I/O design for batch and GUIResonance finding algorithmInhomogeneous energy meshingInformation flow, code modularityCode documentation systemRevision control systemLearning Objectives:Convey the complexity of a large software package in its various components –User requirementsGraphical user interface requirements and examplesSoftware structureProgram developer requirementsDynamic I/O design for batch and GUIResonance finding algorithm – numerical and analytic advantagesInhomogeneous energy meshing – computational savingsInformation flow, code modularityCode documentation systemRevision control system

NEMO1D demonstrated the first industrial strength implementation of NEGF into a simulator that quantitatively simulated resonant tunneling diodes. The development of efficient algorithms that simulate scattering from polar optical phonons, acoustic phonons, alloy disorder, and interface roughness were critical in testing the theory towards its general capability to deliver quantitative matches to experimental data for low temperature devices. That quantitative agreement at low temperature devices and disagreement at room temperature led to a significant conclusion on the importance of full bandstructure models for devices which have material and potential variations on the order of 5nm.This presentation oveviews the computational flow of the various scattering models implemented in NEMO1D: single sequential scattering, multiple sequential scattering, multiple sequential scattering at coupled energies, and self-consistent first Born approximations. For the derivations of the equations and further detail I just refer here to the Journal of Applied Physics publication in 1997 [1].This presentation is NOT intended to teach anyone NEGF. It is merely a computational flow overview. For true NEGF teaching material I refer to Datta's NEGF topic page on nanoHUB [2]Learning Objectives:Understand the general concept of sequential scattering, multiple sequential scattering, and self-consistent first Born approximationAppreciate the complexity of of the the flow of computational objects in a large scale simulation engine

One of the key insights gained during the NEMO1D project was the development of new boundary conditions that enabled the modeling of realistically extended Resonant Tunneling Diodes (RTDs). The new boundary conditions are based on the partitioning of the device into emitter and collector reservoirs which are assumed to be in local equilibrium with a local quasi Fermi level and a central non-equilibrium region. In the reservoirs the electrostatic potential generally varies spatially due to non-uniform doping and possibly heterostructures. The introduction of an empirical scattering relaxation rate in the reservoirs enabled the modeling of phase-breaking and relaxation in the equilibrium reservoirs and the elimination of un-realistically narrow resonance states. With these new boundary conditions one can reduce dramatically the spatial region in which the non-equilibrium problem is being computed. This allowed for the efficient simulation of scattering effects inside the central RTD under non-equilibrium conditions at low temperature, and avoided the need to compute explicitly the computation of the equilibrating scattering in the high electron density contacts.The presentation closes with the challenge that the boundary conditions alone are not sufficient to completely explain the valley current of resonant tunneling diodes. It leads into the discussion of incoherent scattering inside the central RTD for the next lecture.Learning Objectives:Comprehension of the major concept of device partition into reservoirs and central non-equilibrium regionConprehension of the associated reduction in computational cost due to device partitioningComprehension of the physical effects of relaxation in the reservoirs and the broadening of the resonance states

Incoherent processes due to phonons, interface roughness and disorder had been suspected to be the primary source of the valley current of resonant tunneling diodes (RTDs) at the beginning of the NEMO1D project in 1994. The modeling tool NEMO was created at Texas Instruments to fundamentally understand the valley current in RTDs. With the common understanding that scattering is the source of the valley current and with the early successes in NEGF significant resources were invested to model incoherent scattering. A full NEGF transport model implemented in NEMO1D enabled an analysis of various scattering mechanisms. Important incoherent scattering mechanisms that affect the operation of a GaAs/AlGaAs RTD are alloy disorder, interface roughness, acoustic and polar optical phonon scattering. A thorough analysis of each of these scattering mechanisms has shown that the effects of alloy and acoustic phonon scattering are small compared to those of interface roughness and polar optical phonon scattering. It is found from the analysis performed with NEMO1D tool that incoherent scattering affects the valley current of the RTD particularly at low temperatures. These scattering effects are, however not strong enough to explain the valley current in high performance, high temperature devices. Two other key elements are needed to explain the valley current in RTDs: 1) scattering in the contact/emitter and 2) the proper modeling of excited states through full band material representations.This presentation provides an overview of the physical scattering mechanisms and tries to convey some intuition of what is to be expected from these scattering mechanisms. Quantitative agreement of NEMO1D simulations with experimental data at low temperatures proves that NEMO1D indeed models the critical scattering mechanisms inside the central RTD properly. Experimental data for the same device at room temperature that scattering is not enough to expain the valley current at room temperature.Learning Objectives:Overview scattering mechanisms inside a resonant tunneling diode, polar optical phonons, acoustic phonons, interface roughness, and alloy disorder.Demonstrate that NEMO1D can model scattering quantitatively at low temperatures and match experimental data.Demonstrate that scattering is not enough to explain room temperature data.

Heterostructures such as resonant tunneling diodes, quantum well photodetectors and lasers, and cascade lasers break the symmetry of the crystalline lattice. Such break in lattice symmetry causes a strong interaction of heavy-, light- and split-off hole bands. The bandstructure of holes and the transport through these states is of very current interest to the semiconductor industry. As semiconduction devices are scaled down to a nanometer level and as holes are confined to very thin triangular or square quantum wells.A resonant tunneling diode is used as a vehicle to study the bandstructure in thin quantum wells and hole transport in heterostructures including the subband dispersion transverse to the main transport direction. Four key findings are demonstrated: (1) the heavy and light hole interaction is shown to be strong enough to result in dominant current flow off the Gamma zone center (more holes flow through the structure at an angle than straight through), (2) explicit inclusion of the transverse momentum in the current integration is needed, (3) most of the current flow is due to injection from heavy holes in the emitter, and (4) the dependence on the angle φ of the transverse momentum k is weak. Two bandstructure models are utilized to demonstrate the underlying physics: (1) independent/uncoupled heavy-, light- and split-off bands, and (2) second-nearest neighbor sp3s* tight-binding model. Current–voltage (I–V ) simulations including explicit integration of the total energy E, transverse momentum |k| and transverse momentum angle φ are analyzed. Three independent mechanisms that generate off-zone-center current flow are identified: (1) nonmonotonic (electron-like) hole dispersion, (2) different quantum well and emitter effective masses, and (3) momentum-dependent quantum well coupling strength. The methodologies and physical mechanism explained here provide a critical guidance to the treatment of hole transport in ultra-thin bodies or shallow channel transistors. Since the tight binding model intrinsically comprehends strain and crystal distortions, the methodology is immediately applicable to strain engineering methods.Learning Objectives:Understand the approximate construction of hole dispersions in quantum wells from simple effective mass theories.Understand the consequences of band mixing in full band theories.Understand the correlation between transverse dispersion in a quantum well and transmission coefficents.Understand physical mechanisms that can cause hole transport to be highly momentum dependent.Appreciate the relevance to modern ultra-thin body devices.

The primary objective of the NEMO-1D tool was the quantitative modeling of high performance Resonant Tunneling Diodes (RTDs). The software tool was intended for Engineers (concepts, fast turn-around, interactive) and Scientists (detailed device anaysis). Therefore various degrees of sohphistication have been built into the tool which allow the users to trade off accuracy and completeness of the models against computation time and memory usage.The Nanoelectronic Modeling tool (NEMO) is a 1-D device design tool for the quantum mechanical simulation of electron (and hole) states in semiconductor heterostructures. A variety of material systems such as GaAs, InP and Si can presently be analysed. A graphical user interface enables the simple enrty of the heterostructure, the entry of the simulation parameters, the simulation control, and the analysis of the data. The code consists presently of approximately 255,000 lines of code written in C, FORTRAN, F90 and yacc.The four key modeling aspects that resulted in the accurate modeling of RTDs are:Proper treatment of extended contacts. Contacts typically contain resonance states which modify the injection of carriers into the central RTD structure.Proper treatment of the quantum mechanical charging in the central RTD AND the contacts.Proper treatment of the material bandstructure properties, such as non-parabolicity, band-warping, and Gamma-X transistions, andat low temperatures the proper treatement of electron scattering due to optical phonons, acoustic phonons, and interface roughness...NEMO was developed at the Applied Research Laboratory of Raytheon (formerly known as the Central Research Lab of Texas Instruments) with U.S. government funding. The tool was delivered to the U.S. government and it was available to the U.S. research community.Learning Objectives:General NEMO 1D modeling challenge – understanding valley current.Overview of the state-of-the art knowledge of resonant tunneling diode simulation before the NEMO project in 1994High level overview of alternative modeling methodologies available in 1994Key simulation results for room temperature, high performance RTDsSoftware overviewState-of-the-art knowledge in 1998 / 2000

The Recursive Green Function (RGF) algorithms is the primary workhorse for the numerical solution of NEGF equations in quasi-1D systems. It is particularly efficient in cases where the device is partitioned into reservoirs which may be characterized by a non-Hermitian Hamiltonian and a central device region which is Hermitian. Until now (2009) it also appears to be the only scalable algorithm that enables the rapid computation of incoherent transport with NEGF.

Exercises:Barrier StructuresUses: Piece-Wise Constant Potential Barrier ToolResonant Tunneling DiodesUses: Resonant Tunneling Diode Simulation with NEGF • Hartree calculation • Thomas Fermi potentialQuantum DotsUses: Quantum Dot Lab • pyramidal dot

This lecture will introduce a spatial discretization scheme of the Schrödinger equation which represents a 1D heterostructure like a resonant tunneling diode with spatially varying band edges and effective masses.

This lecture explores this effect in more detail by targeting an RTD that has a deliberate asymmetric structure. The collector barrier is chosen thicker than the emitter barrier. With this set-up we expect that the tunneling rate into the RTD from the emitter is faster than the tunneling rate from the RTD into the collector.

In this semi-classical charge and potential model the quantum mechanical simulation is performed once and the quantum mechanical charge is in general not identical to the semi-classical charge.

Realistic RTDs will have nonlinear electrostatic potential in their emitter. Typically a triangular well is formed in the emitter due to the applied bias and the emitter thus contains discrete quasi bound states.

Realistic RTDs need extremely high doping to provide enough carriers for high current densities. However, Impurity scattering can destroy the RTD performance. The dopants are therefore typically spaced 20-100nm away from the central double barrier structure.

The infinite periodic structure Kroenig Penney model is often used to introduce students to the concept of bandstructure formation. It is analytically solvable for linear potentials and shows critical elements of bandstructure formation such as core bands and different effective masses in different bands.

This presentation shows that double barrier structures can show unity transmission for energies BELOW the barrier height, resulting in resonant tunneling. The resonance can be associated with a quasi bound state, and the bound state can be related to a simple particle in a box calculation.

One of the most elemental quantum mechanical transport problems is the solution of the time independent Schrödinger equation in a one-dimensional system where one of the two half spaces has a higher potential energy than the other. The analytical solution is readily obtained using a scattering matrix approach where wavefunction amplitude and slope are matched at the interface between the two half-spaces. Of particular interest are the wave/particle injection from the lower potential energy half-space.

This presentation provides a brief overview of the concepts of bandstructure engineering and its potential applications to light detectors, light emitters, and electron transport devices. Critical questions of the origin of bandstructure and its dependence on local atom arrangements are raised to create awareness of the need of atomistic materials and device models at the nanometer scale.

This presentation serves as a reminder about basic quantum mechanical principles without any real math. The presentation reviews critical properties of classical systems that can be described as particles, propagating waves, standing waves, and chromatography.

The rapid deployment of over 150 simulation tools in just over 4 years has been enabled by 2 critical software developments: 1) Maxwell's Daemon: a middleware that can deploy at a production level UNIX based codes in web browsers, and 2) Rappture: a software system that enables the rapid development of graphical user interfaces and data management to new and legacy softwares.

Impact on research is often measured by the number of publications in the scientific literature. The nanoHUB support team has identified 430 citations to nanoHUB.org and/or nanoHUB tools and seminars in the time frame leading up to May 2008 the 430 citations in the scientific literature. 52% of these papers are authored by persons outside of the Network for Computational Nanotechnology (NCN) which created and hosts nanoHUB.org. Social network of usage and collaboration are developing and documented in social network maps. nanoHUB.org can show usage on nanoHUB and subsequent publications and several testimonials of research use are given. Use by experimentalists can be demonstrated through publications and through testimonials.

This presentation will provide a few highlights of how nanoHUB.org is being used in education and what kind of impact it has had so far. Tools and seminars are indeed being used as instructional materials. nanoHUB has been used in over 290 classes in the past few years in over 90 institutions for class room instruction. New developments are under way to provide one-stop-shops for tool-powered classes / curricula, which aggregate tools, homework assignments, and other teaching materials into one single resource.

This presentation provides a brief overview of the nanoHUB capabilites, compares it to static web page delivery, highlights its technology basis, and provides a vision for future cyberinfrastructures in a system of federated HUBs powered by the HUBzero.org infrastructure.

Fundamental device modeling on the nanometer scale must include effect of open systems, high bias, and an atomistic basis. The non-equilibrium Green Function Formalism (NEGF) can include all these components in a fundamentally sound approach and has been the basis for a few novel device simulation tools.

The goal of this series of lectures is to explain the critical concepts in the understanding of the state-of-the-art modeling of nanoelectronic devices such as resonant tunneling diodes, quantum wells, quantum dots, nanowires, and ultra-scaled transistors. Three fundamental concepts critical to the understanding of nanoelectronic devices will be explored: 1) open systems vs. closed systems, 2) non-equilibrium systems vs. close-to-equilibrium systems, and 3) atomistic material representation vs. continuum matter representation.

The transfer matrix approach is analytically exact, and “arbitrary” heterostructures can apparently be handled through the discretization of potential changes. The approach appears to be quite appealing. However, the approach is inherently unstable for realistically extended devices which exhibit electrostatic band bending or include a large number of basis sets.

Tunneling and interference are critical in the understanding of quantum mechanical systems. The 1D time independent Schrödinger equation can be easily solved analytically in a scattering matrix approach for a system of a single potential barrier. The solution is obtained by matching wavefunction values and derivatives at the two interfaces in the spatial domain. This simple example shows the extended nature of wavefunctions, the non-local effects of local potential variations, the formation of resonant states through interference, and quantum mechanical tunneling in its simplest form.