Nonequilibrium green functions in electronic device modeling software

Distributed nonequilibrium green s function algorithms for the simulation of nanoelectronic devices with scattering stephen cauley, mathieu luisier, venkataramanan balakrishnan, gerhard klimeck, and. General atomistic approach for modeling metalsemiconductor. Miloszewski a thesis presented to the university of waterloo in ful llment of the thesis requirement for the degree of doctor of philosophy in physics waterloo, ontario, canada, 2012 c. It is clear that quantitative simulation tools for this new generation of devices will require atomiclevel quantum mechanical models. Although easily submerged in numerous excitations in macrosystems, quantum behaviors of phonons manifest in nanoscale low. The basic approach developed in the early 1970s has become increasingly popular during the. Electron transport based on nonequilibriumgreensfunctions.

Received 24 july 2000 the nonequilibrium greens function negf formalism provides a sound conceptual ba. Starting with the simplest semiclassical approaches and ending with the description of complex fully quantummechanical methods for quantum transport analysis of stateoftheart devices, computational electronics. For modeling the transport of carriers in nanoscale devices, a green function formalism is the most accurate approach. Nonequilibrium electron transport in twodimensional nanostructures modeled using green s functions and the. Progresses in nonequilibrium green s functions vii february 21, 2019 damian jones leave a comment with the advent of nanoscale physics and ultrafast lasers it is now possible to directly probe realtime the correlated motion of electrons and nuclei in excited quantum states.

An efficient implementation of the nonequilibrium green function negf method combined with the density functional theory dft using localized pseudoatomic orbitals paos is presented for electronic transport calculations of a system connected with two leads under a finite bias voltage. Nonequilibrium electron transport in twodimensional nanostructures modeled using greens functions and the. Green function techniques in the treatment of quantum. A brief description of the theoretical basis of nonequilibrium greens function and its application in deducing the current formula for a two probe model are given. Based on nonequilibrium green s function formalism, electronphoton. Second quantization, various green s functions, fluctuationdissipation b.

Nonequilibrium greens function techniques in currentvoltage. Applications of nonequilibrium greens functions in hunting electronic transport properties of nanoscale materials have been presented. This will the basis for the following discussion of nonequilibrium green functions. Negf simulation of semiconductor devices at the tight binding or huckel level. Modeling transport properties of singlewall carbon. Nonequilibrium green functions in electronic device. Nonequilibrium definition is absence or lack of equilibrium or balance.

In the more scientific mode, such a simulator would greatly enhance the understanding of quantum effects that drive the transport process and provide a means to investigate new device. A ballistic calculation of a full quantum mechanical system is presented to study 2d nanoscale devices. Parallelization of nonequilibrium greens function negf. For these quantities exists a systematic diagrammatic perturbation expansion, both for equilibrium and nonequilibrium systems. An efficient quantum mechanical approach is formulated to model electronphoton interactions in nanoscale devices. The nonequilibrium greens function negf formalism provides a sound conceptual ba. Selfenergies are most commonly used in the quantum transport method of nonequilibrium green s functions negf.

Non equilibrium green s function methods are regularly used to calculate current and charge densities in nanoscale both molecular and semiconductor conductors under bias. Green s function negf is a widely used tool for quantum transport simulation, but it is usually expensive for several reasons, among which a huge amount of computational resource is consumed by the recursive green s function rgf algorithm that makes up the central part of the negf method. Thus transiesta 2 an external tool which is a part of the siesta software package was. The retarded and advanced green functions can be obtained from g and g nonequilibrium green s function negf modeling of the quantum transport of molecular electronic devices. This contradicts todays realistic devices in which contacts are spatially. Nonequilibrium green functions in electronic device modeling by roger k. Firstprinciples nonequilibrium greensfunction approach to transient photoabsorption.

Miloszewski a thesis presented to the university of waterloo in ful llment of the thesis requirement for the degree of doctor of philosophy in physics waterloo, ontario, canada, 2012 c jacek m. Mahdi pourfath for modeling the transport of carriers in nanoscale devices, a green function formalism is the most accurate approach. Nonequilibrium greens function formalism sciencedirect. Nonequilibrium green functions i joachim keller literature. We relate the nonequilibrium green s function expressions to the more transparent scheme involving the scattering states.

Ballistic calculation of nonequilibrium greens function. Quantum enhancement of a sd tunneling model in a 2d msemc. The output is the tb which has a number of useful features for device modeling including orthogonalnonorthogonal basis, various interaction ranges, combination of various types of atoms and orbitals, collinear spin and spinorbit terms. Due to the complexity of the formalism, one should have a deep understanding of. In this work, we present a brief introduction to the nonequilibrium greens function method and discuss two important examples in which nonequlibrium greens functions can be employed. Nonlinear electronic transport in nanoscopic devices. To the simulation of electronic device structures, the transport equations of charge. This chapter discusses the nonequilibrium green s function negf modeling of the quantum transport of molecular electronic devices. Our tb for the interesting 2d transition metal dichalcogenides mos 2 is shown in the figure below. All the theoretical approaches to the accurate modeling of quantum transport of molecular devices fall into four main categories. The nonequilibrium green s function method for nanoscale device simulation. The nonequilibrium greens function method for nanoscale device. Recall lattice dynamics equation of motion for a 1d atomic chain plane wave assumption combine. Specifically, hets is a collection of computer programs to.

The nonequilibrium greens functions formalism negf is a theoretical framework for modeling electron transport through nanoscale devices. Densityfunctional method for nonequilibrium electron transport. Apr 01, 20 read nonlinear electronic transport in nanoscopic devices. The basic approach developed in the early 1970s has become increasingly popular during the last 10 years. Pdf nonequilibrium green functions in electronic device. They have developed a densityfunctional theory coupled to nonequilibrium green s function theory to calculate the currents through molecular and nanoscopic electronic devices phys. Nonequilibrium statistical zubarevs operator and greens functions for an inhomogeneous electron gas p.

Nieminen1 1laboratory of physics, helsinki university of technology, p. Transport properties of the devices formed by interfacing of singlewall carbon nanotube and electrodes are computed using the nonequilibrium green s functional. The main mathematical object in the keldysh formalism is the nonequilibrium green s function negf, which is an twopoint function of particle fields. Greens function, contd the greens function g is the solution that results from the addition of a perturbation to the problem in the present matrix problem, the unperturbed greens function becomes where. The formulation of negf which we followed was proposed by keldysh, kadanoff and baym 8, 9.

To focus efficiently on the best design, engineers need a tool that predicts electronic characteristics as a function of the device geometry and composition. This chapter discusses the nonequilibrium greens function negf modeling of the quantum transport of molecular electronic devices. Pdf ballistic calculation of nonequilibrium greens. Distributed nonequilibrium greens function algorithms for. From the quantum mechanical point of view, the electronic properties. Efficient implementation of the nonequilibrium green. Green s function, cont d the green s function g is the solution that results from the addition of a perturbation to the problem in the present matrix problem, the unperturbed green s function becomes where. Nonequilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of variables nonequilibrium state variables that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Nonequilibrium greens function negf method in thermal. Especially in nanotransport devices, phonons move quasiballistically when the transport length is smaller than their bulk mean free paths. Nonequilibrium green functions in electronic device modeling. Nonequilibrium green functions and the transport problem 1. The quantum mechanics equation describing a semiconductor in equilibrium is.

Opensystem nonequilibrium greens functions and quantum. Stefanucci2,5 1dipartimento di fisica, universita di roma tor vergata, via della ricerca scienti. In this way, it resembles the matsubara formalism, which is based on equilibrium green functions in imaginarytime and treats only equilibrium systems. Pourfath the nonequilibrium greens function method. Therefore, in addition to the retarded and advanced green functions, we need the correlation.

Nonequilibrium green functions jyvaskylan yliopisto. Densityfunctional method for nonequilibrium electron transport mads brandbyge,1, jose. Green functions describe the propagation of manybody states of added or removed particles. At the atomic level a classical description of physical systems gives way to quantum mechanics and in some cases. Densityfunctional method for nonequilibrium electron. Simulations of semiconductor laser using nonequilibrium greens functions method by jacek m. Green s function methods in equilibrium and nonequilibrium problems frontiers in physics on free shipping on qualified orders. Paulsson, non equilibrium greens functions for dummies. The main calculation of this negf method is to compute green s function matrices. This method is mainly used for ballistic conduction but may be extended to include inelastic scattering. We present an overview of electronic device modeling using nonequilibrium green function techniques. Nonequilibrium green s function method choose hamiltonian h for device compute self. Electronic structures have been analyzed using the density functional theory calculator.

For modeling the transport of carriers in nanoscale devices, a greenfunction formalism is the most. Modeling of electron transport in thin films with quantum. Jauho, quantum kinetics in transport and optics of semiconductors j. Nonequilibrium electron transport in twodimensional. Nonequilibrium photocurrent modeling in resonant tunneling. Stefanucci,3 4 1dipartimento di fisica, universita di roma tor vergata, via della ricerca scienti. An electronic state localized in a sphere of radius r has a singleelectron charging energy.

Nonequilibrium greens function negf method is a popular and. Distributed nonequilibrium greens function algorithms for the simulation of nanoelectronic devices with scattering stephen cauley, mathieu luisier, venkataramanan balakrishnan, gerhard klimeck, and chengkok koh. Nonequilibrium statistical zubarevs operator and greens. Firstprinciples nonequilibrium greensfunction approach to. It has been shown that the phonon nonequilibrium green s function method negf is effective for the investigation of nanoscale quantum transport of. Compared to ballistic nonequilibrium greens function negf. Chapter 7 nonequilibrium greens function modeling of the. We derive the equations of motion for the retarded green function gr and the correlation function g electron density and the current that are in widespread use.

Nonequilibrium green s function approach made fast s. We point out common approximations and open questions of which one finds little discussion in the literature. Box 1100, fin02015 hut, finland 2institute of mathematics, helsinki university of technology, p. Simulations of semiconductor laser using nonequilibrium. In this tutorial paper the negf equations for the current and charge density matrix are derived and explained in a. General atomistic approach for modeling metalsemiconductor interfaces using density functional theory and nonequilibrium green s function daniele stradi,1, 2 umberto martinez, anders blom, mads brandbyge,1 and kurt stokbro2 1center for nanostructured graphene cng, department of micro and nanotechnology dtu nanotech. One of the great successes of the nemo software was its aid in the design. The greens function for systems under equilibrium and nonequilibrium conditions are. Nonequilibrium statistical zubarevs operator and green s functions for an inhomogeneous electron gas p. The simulation uses the nonequilibrium green s function negf approach to calculate the.

General atomistic approach for modeling metalsemiconductor interfaces using density functional theory and nonequilibrium greens function daniele stradi,1, 2 umberto martinez, anders blom, mads brandbyge,1 and kurt stokbro2 1center for nanostructured graphene cng, department of micro and nanotechnology dtu nanotech. The nonequilibrium green function negf formalism sometimes referred to as the keldysh or the kadanoffbaym formalism pro. The nonequilibrium greens function negf formalism provides a. Contourordered green s functions, analytic continuation b. Nonequilibrium greens functions for mathematicians claudealain pillet university of toulon abstract. The rise in popularity was driven first by the experimental investigations of mesoscopic physics made possible by high quality semiconductor heterostructures grown by. All existing approaches assume infinitely periodic leads attached to a possibly quite complex device. In this talk, it will be shown how the concept of selfenergies can be used to interface all these fields into the same nanotechnology modeling framework. Quantum transport and phasefield modeling for next generation. The nonequilibrium greens function picture of inelastic. From the green functions a wealth of experimental data can be obtained. The effect of the finite bias including selfconsistency and the solution of the electrostatic problem is taken into account using nonequilibrium green s functions. Rudavskii1 1 national university lvivska politekhnika 12, bandera str. Paulsson, non equilibrium green s functions for dummies.

Received 24 july 2000 the nonequilibrium green s function negf formalism provides a sound conceptual ba. All the elements of the kinetic equations, which are the device hamiltonian, contact selfenergies, and. Quantum truansport uand nonequilibrium greens functions. Introduction to the one particle negf equations, condmat0210519 2002. Progresses in nonequilibrium greens functions vii psik. Simulations of semiconductor laser using nonequilibrium green s functions method by jacek m.

We present an overview of electronic device modeling using non equilibrium green function techniques. Apr 27, 2018 thermal engineering of quantum devices has attracted much attention since the discovery of quantized thermal conductance of phonons. The nonequilibrium greens function method for nanoscale. Read nonlinear electronic transport in nanoscopic devices. Nonequilibrium greens function negf modeling of phonon transport me 595m wei zhang and t. Most device simulation is based on models that neglect interactions or at best treat them to first order, for which simple treatments are adequate. Distributed nonequilibrium greens function algorithms. Nonequilibrium greens function negf modeling of phonon. Abstract we present an overview of electronic device modeling using nonequilibrium green function techniques. A full quantum mechanical simulation of device transport is commonly done using the nonequilibrium green s function negf calculation. Green function techniques in the treatment of quantum transport 217 electronvibron model can be solved exactly by the socalled polaron or langfirsov transformation 9597, the coupling to the leads produces a true manybody problem. Due to the complexity of the formalism, one should have a deep understanding of the underlying principles and use smart approximations and numerical methods for solving the kinetic equations at a reasonable computational time. Semiclassical and quantum device modeling and simulation provides a comprehensive overview of the essential techniques and methods. Modeling of nanoscale devices using nonequilibrium green s function.