Therefore, in addition to the retarded and advanced green functions, we need the correlation. Nonequilibrium electron transport in twodimensional. We relate the nonequilibrium green s function expressions to the more transparent scheme involving the scattering states. Due to the complexity of the formalism, one should have a deep understanding of. Nonequilibrium greens function negf modeling of phonon transport me 595m wei zhang and t. It has been shown that the phonon nonequilibrium green s function method negf is effective for the investigation of nanoscale quantum transport of. 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.
The formulation of negf which we followed was proposed by keldysh, kadanoff and baym 8, 9. Modeling of electron transport in thin films with quantum. This contradicts todays realistic devices in which contacts are spatially. For these quantities exists a systematic diagrammatic perturbation expansion, both for equilibrium and nonequilibrium systems. This method is mainly used for ballistic conduction but may be extended to include inelastic scattering. In this tutorial paper the negf equations for the current and charge density matrix are derived and explained in a. 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. Modeling of electron transport in thin films with quantum and scattering effects anuradha bulusu. Applications of nonequilibrium greens functions in hunting electronic transport properties of nanoscale materials have been presented. For modeling the transport of carriers in nanoscale devices, a greenfunction formalism is the most. Semiclassical and quantum device modeling and simulation provides a comprehensive overview of the essential techniques and methods. Stefanucci,3 4 1dipartimento di fisica, universita di roma tor vergata, via della ricerca scienti.
Pdf nonequilibrium green functions in electronic device. 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. 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. It is clear that quantitative simulation tools for this new generation of devices will require atomiclevel quantum mechanical models. The nonequilibrium greens function method for nanoscale device simulation computational microelectronics pourfath, mahdi on. Firstprinciples nonequilibrium greensfunction approach to. The nonequilibrium greens function method for nanoscale. Mahdi pourfath for modeling the transport of carriers in nanoscale devices, a green function formalism is the most accurate approach. The inelastic resonant tunneling of single electrons through the. Negf simulation of semiconductor devices at the tight binding or huckel level. They have developed a densityfunctional theory coupled to nonequilibrium green s function theory to calculate the currents through molecular and nanoscopic electronic devices phys.
Densityfunctional method for nonequilibrium electron. The nonequilibrium greens functions formalism negf is a theoretical framework for modeling electron transport through nanoscale devices. Based on nonequilibrium green s function formalism, electronphoton. 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. The nonequilibrium green s function algorithm requires contact selfenergies to model charge injection and extraction. Progresses in nonequilibrium greens functions vii psik. Quantum truansport uand nonequilibrium greens functions. The basic approach developed in the early 1970s has become increasingly popular during the last 10 years. 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. 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.
Nonequilibrium photocurrent modeling in resonant tunneling. Nieminen1 1laboratory of physics, helsinki university of technology, p. 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. Nonequilibrium electron transport in twodimensional nanostructures modeled using green s functions and the. Nonequilibrium definition of nonequilibrium by merriamwebster. Nonequilibrium greens functions for mathematicians claudealain pillet university of toulon abstract.
One of the great successes of the nemo software was its aid in the design. The nonequilibrium greens function negf formalism provides a. Although easily submerged in numerous excitations in macrosystems, quantum behaviors of phonons manifest in nanoscale low. 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. Especially in nanotransport devices, phonons move quasiballistically when the transport length is smaller than their bulk mean free paths. Simulations of semiconductor laser using nonequilibrium. Second quantization, various green s functions, fluctuationdissipation b. This chapter discusses the nonequilibrium greens function negf modeling of the quantum transport of molecular electronic devices.
From the quantum mechanical point of view, the electronic properties. To focus efficiently on the best design, engineers need a tool that predicts electronic characteristics as a function of the device geometry and composition. Modeling transport properties of singlewall carbon. Nonequilibrium electron transport in twodimensional nanostructures modeled using greens functions and the. All the elements of the kinetic equations, which are the device hamiltonian, contact selfenergies, and. The simulation uses the nonequilibrium green s function negf approach to calculate the. Nonequilibrium green functions in electronic device.
Recall lattice dynamics equation of motion for a 1d atomic chain plane wave assumption combine. The nonequilibrium greens function method for nanoscale device. All existing approaches assume infinitely periodic leads attached to a possibly quite complex device. A ballistic calculation of a full quantum mechanical system is presented to study 2d nanoscale devices. The nonequilibrium green function negf formalism sometimes referred to as the keldysh or the kadanoffbaym formalism pro. Contourordered green s functions, analytic continuation b. The nonequilibrium greens function negf formalism provides a sound conceptual ba.
Chapter 7 nonequilibrium greens function modeling of the. Our tb for the interesting 2d transition metal dichalcogenides mos 2 is shown in the figure below. Nonequilibrium green functions in electronic device modeling. Nonequilibrium green functions i joachim keller literature. All the theoretical approaches to the accurate modeling of quantum transport of molecular devices fall into four main categories. The nonequilibrium greens function picture of inelastic.
An efficient quantum mechanical approach is formulated to model electronphoton interactions in nanoscale devices. Box 1100, fin02015 hut, finland 2institute of mathematics, helsinki university of technology, p. We present an overview of electronic device modeling using nonequilibrium green function techniques. Quantum enhancement of a sd tunneling model in a 2d msemc. Distributed nonequilibrium greens function algorithms for the simulation of nanoelectronic devices with scattering stephen cauley, mathieu luisier, venkataramanan balakrishnan, gerhard klimeck, and chengkok koh.
The quantum mechanics equation describing a semiconductor in equilibrium is. Specifically, hets is a collection of computer programs to. Paulsson, non equilibrium green s functions for dummies. 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. Since the pioneering work of schwinger, baym and kadano, and keldysh in the early 60, the greens function formalism became an invaluable tool for the calculation of nonequilibrium properties of manybody systems. 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.
The nonequilibrium green s function method for nanoscale device simulation. Nonequilibrium green functions in electronic device modeling by roger k. Modeling of nanoscale devices using nonequilibrium green s function. Transport properties of the devices formed by interfacing of singlewall carbon nanotube and electrodes are computed using the nonequilibrium green s functional. Nonequilibrium greens function negf modeling of phonon.
We present an overview of electronic device modeling using non equilibrium green function techniques. Green function techniques in the treatment of quantum. Pdf nonequilibrium green functions in electronic device modeling. Stefanucci2,5 1dipartimento di fisica, universita di roma tor vergata, via della ricerca scienti. 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. Introduction to the one particle negf equations, condmat0210519 2002. Nonequilibrium statistical zubarevs operator and greens. 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.
Distributed nonequilibrium greens function algorithms. This will the basis for the following discussion of nonequilibrium green functions. Green s function methods in equilibrium and nonequilibrium problems frontiers in physics on free shipping on qualified orders. Distributed nonequilibrium green s function algorithms for the simulation of nanoelectronic devices with scattering stephen cauley, mathieu luisier, venkataramanan balakrishnan, gerhard klimeck, and. 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. Read nonlinear electronic transport in nanoscopic devices. Nonequilibrium greens function negf method in thermal. Nonequilibrium greens function techniques in currentvoltage.
Electronic structures have been analyzed using the density functional theory calculator. Nonlinear electronic transport in nanoscopic devices. An electronic state localized in a sphere of radius r has a singleelectron charging energy. Pourfath the nonequilibrium greens function method.
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 green functions jyvaskylan yliopisto. Nonequilibrium statistical zubarevs operator and greens functions for an inhomogeneous electron gas p. Received 24 july 2000 the nonequilibrium greens function negf formalism provides a sound conceptual ba. Jauho, quantum kinetics in transport and optics of semiconductors j. A full quantum mechanical simulation of device transport is commonly done using the nonequilibrium green s function negf calculation.
Rudavskii1 1 national university lvivska politekhnika 12, bandera str. Thus transiesta 2 an external tool which is a part of the siesta software package was. Firstprinciples nonequilibrium greensfunction approach to transient photoabsorption. From the green functions a wealth of experimental data can be obtained. The greens function for systems under equilibrium and nonequilibrium conditions are. Apr 27, 2018 thermal engineering of quantum devices has attracted much attention since the discovery of quantized thermal conductance of phonons. Nonequilibrium greens function formalism sciencedirect. The basic approach developed in the early 1970s has become increasingly popular during the.
Nonequilibrium green s function approach made fast s. Abstract we present an overview of electronic device modeling using nonequilibrium green function techniques. Selfenergies are most commonly used in the quantum transport method of nonequilibrium green s functions negf. Densityfunctional method for nonequilibrium electron transport mads brandbyge,1, jose. Paulsson, non equilibrium greens functions for dummies. The effect of the finite bias including selfconsistency and the solution of the electrostatic problem is taken into account using nonequilibrium green s functions. 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. For modeling the transport of carriers in nanoscale devices, a green function formalism is the most accurate approach. Electron transport based on nonequilibriumgreensfunctions. 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.
Nonequilibrium greens function negf method is a popular and. Efficient implementation of the nonequilibrium green. Nonequilibrium definition is absence or lack of equilibrium or balance. Opensystem nonequilibrium greens functions and quantum. Green functions describe the propagation of manybody states of added or removed particles.
To the simulation of electronic device structures, the transport equations of charge. Quantum transport and phasefield modeling for next generation. Distributed nonequilibrium greens function algorithms for. Parallelization of nonequilibrium greens function negf. Compared to ballistic nonequilibrium greens function negf. We point out common approximations and open questions of which one finds little discussion in the literature. Apr 01, 20 read nonlinear electronic transport in nanoscopic devices. Nonequilibrium green functions and the transport problem 1. Densityfunctional method for nonequilibrium electron transport. The main calculation of this negf method is to compute green s function matrices. Pdf ballistic calculation of nonequilibrium greens. Received 24 july 2000 the nonequilibrium green s function negf formalism provides a sound conceptual ba. 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.
General atomistic approach for modeling metalsemiconductor. Most device simulation is based on models that neglect interactions or at best treat them to first order, for which simple treatments are adequate. At the atomic level a classical description of physical systems gives way to quantum mechanics and in some cases. Nonequilibrium green s function method choose hamiltonian h for device compute self. 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. In this way, it resembles the matsubara formalism, which is based on equilibrium green functions in imaginarytime and treats only equilibrium systems. The main mathematical object in the keldysh formalism is the nonequilibrium green s function negf, which is an twopoint function of particle fields. This chapter discusses the nonequilibrium green s function negf modeling of the quantum transport of molecular electronic devices. Ballistic calculation of nonequilibrium greens function. Nonequilibrium statistical zubarevs operator and green s functions for an inhomogeneous electron gas p.