Iteration scheme for the solution of the two-dimensional Schrödinger-Poisson equations in quantum structures

Trellakis, A.; Galick, A. T.; Pacelli, A.; Ravaioli, Umberto

doi:10.1063/1.365396

Cited by 260 publications

(179 citation statements)

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“…The NEGF equations are solved self-consistently with the Poisson equation for electrostatics in three dimensions. Our simulator solves the nonlinear Poisson equation using the predictor-corrector scheme described by Trellakis et al using a semiclassical approximation for the charge density 30 . The geometry of the system is modeled using a tetrahedral finite element mesh generated with the SALOME package 31 .…”

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confidence: 99%

Negative Differential Resistance and Steep Switching in Chevron Graphene Nanoribbon Field-Effect Transistors

Smith

Llinas

Bokor

et al. 2018

IEEE Electron Device Lett.

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Ballistic quantum transport calculations based on the non-equilbrium Green's function formalism show that field-effect transistor devices made from chevron-type graphene nanoribbons (CGNRs) could exhibit negative differential resistance with peak-to-valley ratios in excess of 4800 at room temperature as well as steepslope switching with 6 mV/decade subtheshold swing over five orders of magnitude and ON-currents of 88 µA µm −1 . This is enabled by the superlattice-like structure of these ribbons that have large periodic unit cells with regions of different effective bandgap, resulting in minibands and gaps in the density of states above the conduction band edge. The CGNR ribbon used in our proposed device has been previously fabricated with bottom-up chemical synthesis techniques and could be incorporated into an experimentally-realizable structure.In 1970, L.Esaki and R. Tsu predicted 1 that in an appropriately made superlattice, it should be possible to obtain very narrow width bands, which could then lead to negative differential resistance. The remarkable property of these superlattices is in the fact that, unlike the Esaki diodes, this negative differential resistance does not need any tunneling, rather it comes from the direct conduction of electrons. Nonetheless, significant difficulty in synthesizing atomically precise, eptiaxial heterostructures has made it very challenging to realize such superlattice structures 2-8 . Much work has been done on modeling graphene nanoribbon heterostructures and superlattices which could exhibit NDR 9-15 . Other work has been done on steep slope devices based on GNR and CNT heterojunctions 16,17 . Gnani et al. showed how superlattices could be used in a III-V nanowire FET to achieve steep slope behavior by using the superlattice gap to filter high energy electrons in the OFF state 18 . Here, we show that the recently synthesized chevron nanoribbons 19 provides a natural, monolithic material system where narrow-width energy bands and negative differential resistance (NDR) can be achieved. Our atomistic calculations predict that the NDR behavior should manifest at room temperature along with sub-thermal steepness (<60 mV/decade at room temperature). Such NDR behavior could lead to completely novel devices for next generation electronics.Unlike a graphene sheet, a narrow strip etched out of graphene, often called a graphene nanoribbon (GNR), can provide a sizeable bandgap. As a result, GNRs could lead to devices with good ON/OFF ratio at the nanoscale. However, a number of studies have also shown the deleterious effect of edge roughness on the device performance 20,21 . Recent breakthroughs in bottom-up chemical synthesis can produce GNRs with atomistically pristine edge states and overcome this shortcoming 19 . In fact, a recent experimental work demonstrated working transistors with 9-and 13-AGNRs made with these techniques 22 . The methods used to synthesize these ribbons can also be used to generate complex periodic structures beyond simply armchair and zigzag nanoribbon...

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confidence: 99%

Negative Differential Resistance and Steep Switching in Chevron Graphene Nanoribbon Field-Effect Transistors

Smith

Llinas

Bokor

et al. 2018

IEEE Electron Device Lett.

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“…The CBR quantum transport is selfconsistently coupled with the Poisson equation in the CBR3D simulator to satisfy the charge self-consistency. The self-consistent convergence is achieved by adopting the predictor-corrector algorithm 15 to open systems. 13,16 Surface and interface roughness are included with the real-space treatment, 17 inelastic scattering processes are emulated with an analog of relaxation time approximation or "Buttiker probes."…”

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confidence: 99%

The fundamental downscaling limit of field effect transistors

Mamaluy

Gao

2015

Applied Physics Letters

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We predict that within next 15 years a fundamental down-scaling limit for CMOS technology and other Field-Effect Transistors (FETs) will be reached. Specifically, we show that at room temperatures all FETs, irrespective of their channel material, will start experiencing unacceptable level of thermally induced errors around 5-nm gate lengths. These findings were confirmed by performing quantum mechanical transport simulations for a variety of 6-, 5-, and 4-nm gate length Si devices, optimized to satisfy high-performance logic specifications by ITRS. Different channel materials and wafer/channel orientations have also been studied; it is found that altering channel-source-drain materials achieves only insignificant increase in switching energy, which overall cannot sufficiently delay the approaching downscaling limit. Alternative possibilities are discussed to continue the increase of logic element densities for room temperature operation below the said limit.

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“…1. The electron states in such a structure can be found by solving the Schrodinger equation which in this case takes the form [10] …”

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confidence: 99%

“…Potentials and h V xc V were treated similarly to [12]. The potential φ can be found from the Poisson equation [1,10,11] ( )…”

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confidence: 99%

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Self‐consistent calculations of phonon scattering rates in the GaAs transistor structure with one‐dimensional electron gas

Borzdov

Pozdnyakov

Galenchik

et al. 2005

Physica Status Solidi (b)

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Self-consistent calculations of acoustic and polar optical phonon scattering rates in GaAs quantum wire transistor structures were carried out with account of collisional broadening. The influence of the gate bias on the scattering rates was examined, too. It was shown that in order to treat the scattering rates rigorously it is important to search for electron energy levels by means of the self-consistent solution of Schrodinger and Poisson equations and to take into account the collisional broadening.Modern technologies in micro-and nanoelectronics allow different semiconductor device structures of very small sizes and various geometry to be created. In particular, high-speed field effect GaAs transistors with one-dimensional electron gas (1DEG) or, in other words, quantum wire transistors [1,2] have been successfully created and actively investigated. It is supposed that on the basis of these transistors a new generation of high-speed GaAs ULSI circuits can be produced.It is known that the efficient design of such devices today is a very hard problem without numerical simulation of their electrical characteristics. In this regard, one of the most promising simulation methods is the Monte Carlo one [3]. Its correct implementation is possible when the rigorous expressions for the scattering rates for all dominant scattering mechanisms in the simulated structure are known. In this connection it is necessary to note that acoustic and polar optical phonon scattering are two of the important scattering mechanisms in GaAs structures with 1DEG [4][5][6][7].Several works were devoted to the calculation of acoustic and polar optical phonon scattering rates (A&POPSR) in quantum wires. Particularly, in the papers [5,7] expressions for the A&POPSR in the rectangular quantum wires were proposed taking into account the collisional broadening (in case of intersubband scattering being the same as the broadening of the energy levels) in the first order approximation. It was shown that the functions of A&POPSR versus electron kinetic energy have not any singularity points. The latter is especially important for the direct use of the derived expressions in Monte Carlo procedures as it naturally eliminates the tendency to infinity of A&POPSR in singularity points related to the features of the density of states in quantum wires. Besides, the rigorous incorporation of the phonon scattering into the charge transport simulation by means of Monte Carlo method requires the exact knowledge of electron subband energy levels in the considered quantum well as they directly enter into the expressions for A&POPSR. These energy levels in real device structures with an arbitrary quantum well can be found only by means of numerical self-consistent solution of the corresponding Schrodinger and Poisson equations.In this work we present the results of calculation of A&POPSR in the GaAs-transistor structure (see Fig. 1), with taking into account the collisional broadening caused by only acoustic and polar optical phonon scattering, and exa...

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Iteration scheme for the solution of the two-dimensional Schrödinger-Poisson equations in quantum structures

Cited by 260 publications

References 5 publications

Negative Differential Resistance and Steep Switching in Chevron Graphene Nanoribbon Field-Effect Transistors

Negative Differential Resistance and Steep Switching in Chevron Graphene Nanoribbon Field-Effect Transistors

The fundamental downscaling limit of field effect transistors

Self‐consistent calculations of phonon scattering rates in the GaAs transistor structure with one‐dimensional electron gas

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