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CV profile with different oxide thickness
20 Apr 2010 | Animations | Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
PN junction in forward bias
17 Apr 2010 | Animations | Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
Local density of states
Graphite
Graphene nanoribbon bandstructure
Buckyball C60
16 Apr 2010 | Animations | Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
Diffusion of holes and electrons
15 Apr 2010 | Animations | Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
Fermi-Dirac statistics with temperature
3D wavefunctions
12 Apr 2010 | Animations | Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck
Electronic band structure
Nanoelectronic Modeling nanoHUB Demo 2: RTD simulation with NEGF
09 Mar 2010 | Online Presentations | Contributor(s): Gerhard Klimeck
Nanoelectronic Modeling nanoHUB Demo 1: nanoHUB Tool Usage with RTD Simulation with NEGF
Nanoelectronic Modeling Lecture 25b: NEMO1D - Hole Bandstructure in Quantum Wells and Hole Transport in RTDs
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:
Nanoelectronic Modeling Lecture 23: NEMO1D - Importance of New Boundary Conditions
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.
Nanoelectronic Modeling Lecture 24: NEMO1D - Incoherent Scattering
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.
Nanoelectronic Modeling Lecture 26: NEMO1D -
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]
Nanoelectronic Modeling Lecture 27: NEMO1D -
This presentation provides a very high level software overview of NEMO1D. The items discussed are:
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
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30 Jul 2008 | Teaching Materials | Contributor(s): Dragica Vasileska, Gerhard Klimeck, Mark Lundstrom
Nanoelectronic Modeling Lecture 22: NEMO1D - Motivation, History and Key Insights
07 Feb 2010 | Online Presentations | Contributor(s): Gerhard Klimeck
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:
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.
Nanoelectronic Modeling Lecture 21: Recursive Green Function Algorithm
Nanoelectronic Modeling: Exercises 1-3 - Barrier Structures, RTDs, and Quantum Dots
27 Jan 2010 | Online Presentations | Contributor(s): Gerhard Klimeck
Nanoelectronic Modeling Lecture 20: NEGF in a Quasi-1D Formulation
27 Jan 2010 | Online Presentations | Contributor(s): Gerhard Klimeck, Samarth Agarwal, Zhengping Jiang
Nanoelectronic Modeling Lecture 19: Introduction to RTDs - Asymmetric Structures
Nanoelectronic Modeling Lecture 18: Introduction to RTDs - Quantum Charge Self-Consistency (Hartree)