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Worked Examples for a PN Diode

01 Jun 2010 | Teaching Materials | Contributor(s): Dragica Vasileska, Gerhard Klimeck

InAs: Evolution of iso-energy surfaces for heavy, light, and split-off holes due to uniaxial strain.

25 May 2010 | Animations | Contributor(s): Abhijeet Paul, Denis Areshkin, Gerhard Klimeck

Carbon nanotube bandstructure

22 Apr 2010 | Animations | Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck

Threshold voltage in a nanowire MOSFET

22 Apr 2010 | Animations | Contributor(s): Saumitra Raj Mehrotra, SungGeun Kim, Gerhard Klimeck

Resonant Tunneling Diode operation

Nanotechnology Animation Gallery

22 Apr 2010 | Teaching Materials | Contributor(s): Saumitra Raj Mehrotra, Gerhard Klimeck

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