
Graphite
17 Apr 2010  Animations  Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
Graphene is a oneatomthick planar sheet of sp2bonded carbon atoms that are densely packed in a honeycomb crystal lattice. Graphene sheets are weakly bonded to other graphene layers above and below to form Graphite. The difference between two layers is approximately 0.335 nm [1].
Graphite can conduct electricity due to the vast electron delocalization within the carbon layers (a phenomenon called aromaticity). …

Graphene nanoribbon bandstructure
17 Apr 2010  Animations  Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
Graphene nanoribbons (often abbreviated as GNR) are planar strips of graphene with a thickness of approximately one atom. Carbon atoms in graphene are sp2hybridized with a carboncarbon bond length of approximately 0.142 nm. As an electronic material, graphene exhibits many desirable properties, such as high carrier mobility, a thin body and compatibility with top down fabrication.
A graphene nanoribbon can be either a zigzag or armchair type. Both zigzag and armchair type GNR are shown …

Buckyball C60
16 Apr 2010  Animations  Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
A fullerene is any molecule composed entirely of carbon, and can take the form of hollow spheres, ellipsoids, or tubes. Spherical fullerenes (often referred to as "buckyballs") are one of the known structurally different form of carbon. C60 are the most common of buckyball structures. …

Diffusion of holes and electrons
15 Apr 2010  Animations  Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
Diffusion is a process of particles distributing themselves from regions of high to low concentrations. In semiclassical electronics these particles are the charge carriers (electrons and holes). The rate at which a carrier can diffuse is called diffusion constant with units of cm2/s. The image shows the process of steady state diffusion in an intrinsic semiconductor bar with different light shining intensity (different carrier generations rates /cm3) at the center of the bar. …

FermiDirac statistics with temperature
15 Apr 2010  Animations  Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
FermiDirac statistics is applied to identical particles with halfinteger spin (such as electrons) in a system that is in thermal equilibrium. Since particles are assumed to have negligible mutual interactions, this allows a multiparticle system to be described in terms of singleparticle energy states. FermiDirac statistics are commonly used in semiconductors to find the distribution of electrons as a function of energy. …

3D wavefunctions
12 Apr 2010  Animations  Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
In quantum mechanics the timeindependent Schrodinger's equation can be solved for eigenfunctions (also called eigenstates or wavefunctions) and corresponding eigenenergies (or energy levels) for a stationary physical system. The wavefunction itself can take on negative and positive values and could be complex.
The square magnitude of the wavefunction is the probability density of finding the particle in space at that particular energy level.
A quantum dot is a physical system that …

Electronic band structure
12 Apr 2010  Animations  Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
In solidstate physics, the electronic band structure (or simply band structure) of a solid describes ranges of energy in which an electron is "forbidden" or "allowed". The band structure is also often called the dispersion or the E(k) relationship. It is a mathematical relationship between the electron wave energy and its momentum.
The valence band edge is generally at the 'Gamma' point. This is at zero momentum in the graph below. If the conduction band edge minimum also lies …

Nanoelectronic Modeling nanoHUB Demo 2: RTD simulation with NEGF
09 Mar 2010  Online Presentations  Contributor(s): Gerhard Klimeck
Demonstration of resonant tunneling diode (RTD) simulation using the RTD Simulation with NEGF Tool with a Hartree potential model showing potential profile, charge densities, currentvoltage characteristics, and resonance energies. Also demonstrated is a RTD simulation using a ThomasFermi potential model showing the effects of eta.

Nanoelectronic Modeling nanoHUB Demo 1: nanoHUB Tool Usage with RTD Simulation with NEGF
09 Mar 2010  Online Presentations  Contributor(s): Gerhard Klimeck
Demonstration of running tools on the nanoHUB. Demonstrated is the RTD Simulation with NEGF Tool using a simple leveldrop potential model and a more realistic device using a ThomasFermi potential model.

Nanoelectronic Modeling Lecture 25b: NEMO1D  Hole Bandstructure in Quantum Wells and Hole Transport in RTDs
09 Mar 2010  Online Presentations  Contributor(s): Gerhard Klimeck
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 splitoff 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 splitoff bands, and (2) secondnearest neighbor sp3s* tightbinding 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 offzonecenter current flow are identified: (1) nonmonotonic (electronlike) hole dispersion, (2) different quantum well and emitter effective masses, and (3) momentumdependent quantum well coupling strength.
The methodologies and physical mechanism explained here provide a critical guidance to the treatment of hole transport in ultrathin 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 ultrathin body devices.

Nanoelectronic Modeling Lecture 23: NEMO1D  Importance of New Boundary Conditions
09 Mar 2010  Online Presentations  Contributor(s): Gerhard Klimeck
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 nonequilibrium region. In the reservoirs the electrostatic potential generally varies spatially due to nonuniform doping and possibly heterostructures. The introduction of an empirical scattering relaxation rate in the reservoirs enabled the modeling of phasebreaking and relaxation in the equilibrium reservoirs and the elimination of unrealistically narrow resonance states. With these new boundary conditions one can reduce dramatically the spatial region in which the nonequilibrium problem is being computed. This allowed for the efficient simulation of scattering effects inside the central RTD under nonequilibrium 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 nonequilibrium region
 Conprehension of the associated reduction in computational cost due to device partitioning
 Comprehension of the physical effects of relaxation in the reservoirs and the broadening of the resonance states

Nanoelectronic Modeling Lecture 24: NEMO1D  Incoherent Scattering
09 Mar 2010  Online Presentations  Contributor(s): Gerhard Klimeck
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.

Nanoelectronic Modeling Lecture 26: NEMO1D 
09 Mar 2010  Online Presentations  Contributor(s): Gerhard Klimeck
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 selfconsistent 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 selfconsistent first Born approximation
 Appreciate the complexity of of the the flow of computational objects in a large scale simulation engine
 Roger Lake, Gerhard Klimeck, R. Chris Bowen and Dejan Jovanovic, "Single and multiband modeling of quantum electron transport through layered semiconductor devices", J. of Appl. Phys. 81, 7845 (1997).
 Supriyo Datta maintains an excellent web page on nanoHUB.org which contains tutorials, OnLine seminars, Ph.D. theses, and tool examples.

Nanoelectronic Modeling Lecture 27: NEMO1D 
09 Mar 2010  Online Presentations  Contributor(s): Gerhard Klimeck
This presentation provides a very high level software overview of NEMO1D. The items discussed are:
 User requirements
 Graphical user interface
 Software structure
 Program developer requirements
 Dynamic I/O design for batch and GUI
 Resonance finding algorithm
 Inhomogeneous energy meshing
 Information flow, code modularity
 Code documentation system
 Revision control system
Learning Objectives:
 Convey the complexity of a large software package in its various components –
 User requirements
 Graphical user interface requirements and examples
 Software structure
 Program developer requirements
 Dynamic I/O design for batch and GUI
 Resonance finding algorithm – numerical and analytic advantages
 Inhomogeneous energy meshing – computational savings
 Information flow, code modularity
 Code documentation system
 Revision control system

ECE 694A: Professional Development Seminar Series
17 Feb 2010  Series  Contributor(s): Gerhard Klimeck
The ECE Graduate Seminar, ECE 694, is designed to provide opportunities for professional development of graduate sudents, raise their awareness of various other issues that they may face in their professional careers, and provide them opportunities to survey research seminars of their interest.

Semiconductor Device Theory Exercises
30 Jul 2008  Teaching Materials  Contributor(s): Dragica Vasileska, Gerhard Klimeck, Mark Lundstrom
This collection of problems should help the students to better understand Semiconductor Device Physics on a fundamental and more complex level.
Crystal lattices and Miller indicies
From 1 well to 2 wells to 5 wells to periodic potentials
Periodic potentials and bandstructure
Bandstructure exercise
Simplified bandstructure model
Can we define unique effective masses in Si nanowires?
Density of states function calculation
Dopants and semiconductor statistics
General tool construction ...

Nanoelectronic Modeling Lecture 22: NEMO1D  Motivation, History and Key Insights
07 Feb 2010  Online Presentations  Contributor(s): Gerhard Klimeck
The primary objective of the NEMO1D tool was the quantitative modeling of high performance Resonant Tunneling Diodes (RTDs). The software tool was intended for Engineers (concepts, fast turnaround, 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 1D 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 nonparabolicity, bandwarping, and GammaX transistions, and
 at 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 stateofthe art knowledge of resonant tunneling diode simulation before the NEMO project in 1994
High level overview of alternative modeling methodologies available in 1994
Key simulation results for room temperature, high performance RTDs
Software overview
Stateoftheart knowledge in 1998 / 2000

Nanoelectronic Modeling Lecture 21: Recursive Green Function Algorithm
07 Feb 2010  Online Presentations  Contributor(s): Gerhard Klimeck
The Recursive Green Function (RGF) algorithms is the primary workhorse for the numerical solution of NEGF equations in quasi1D systems. It is particularly efficient in cases where the device is partitioned into reservoirs which may be characterized by a nonHermitian 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.

Nanoelectronic Modeling: Exercises 13  Barrier Structures, RTDs, and Quantum Dots
27 Jan 2010  Online Presentations  Contributor(s): Gerhard Klimeck
Exercises:
 Barrier Structures
Uses: PieceWise Constant Potential Barrier Tool
 Resonant Tunneling Diodes
Uses: Resonant Tunneling Diode Simulation with NEGF
• Hartree calculation
• Thomas Fermi potential
 Quantum Dots
Uses: Quantum Dot Lab
• pyramidal dot

Nanoelectronic Modeling Lecture 20: NEGF in a Quasi1D Formulation
27 Jan 2010  Online Presentations  Contributor(s): Gerhard Klimeck, Samarth Agarwal, Zhengping Jiang
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.

Nanoelectronic Modeling Lecture 19: Introduction to RTDs  Asymmetric Structures
27 Jan 2010  Online Presentations  Contributor(s): Gerhard Klimeck
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 setup we expect that the tunneling rate into the RTD from the emitter is faster than the tunneling rate from the RTD into the collector.

Nanoelectronic Modeling Lecture 18: Introduction to RTDs  Quantum Charge SelfConsistency (Hartree)
27 Jan 2010  Online Presentations  Contributor(s): Gerhard Klimeck
In this semiclassical charge and potential model the quantum mechanical simulation is performed once and the quantum mechanical charge is in general not identical to the semiclassical charge.

Nanoelectronic Modeling Lecture 17: Introduction to RTDs  Relaxation Scattering in the Emitter
27 Jan 2010  Online Presentations  Contributor(s): Gerhard Klimeck
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.

Nanoelectronic Modeling Lecture 16: Introduction to RTDs  Realistic Doping Profiles
27 Jan 2010  Online Presentations  Contributor(s): Gerhard Klimeck
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 20100nm away from the central double barrier structure.

Nanoelectronic Modeling Lecture 14: Open 1D Systems  Formation of Bandstructure
27 Jan 2010  Online Presentations  Contributor(s): Gerhard Klimeck, Dragica Vasileska
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.