scholarly journals Efficient Ab-Initio Electron Transport Calculations for Heterostructures by the Nonequilibrium Green’s Function Method

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hirokazu Takaki ◽  
Nobuhiko Kobayashi ◽  
Kenji Hirose
Keyword(s):  
Electron Transport ◽  
Ab Initio ◽  
Green’S Function ◽  
Green's Function ◽  
Density Functional ◽  
Green's Functions ◽  
Green’S Functions ◽  
Computational Techniques ◽  
Nonequilibrium Green's Function ◽  
Nonequilibrium Green’S Function

We present an efficient computation technique for ab-initio electron transport calculations based on density functional theory and the nonequilibrium Green’s function formalism for application to heterostructures with two-dimensional (2D) interfaces. The computational load for constructing the Green’s functions, which depends not only on the energy but also on the 2D Bloch wave vector along the interfaces and is thus catastrophically heavy, is circumvented by parallel computational techniques with the message passing interface, which divides the calculations of the Green’s functions with respect to energy and wave vectors. To demonstrate the computational efficiency of the present code, we perform ab-initio electron transport calculations of Al(100)-Si(100)-Al(100) heterostructures, one of the most typical metal-semiconductor-metal systems, and show their transmission spectra, density of states (DOSs), and dependence on the thickness of the Si layers.

NONEQUILIBRIUM GREEN'S FUNCTION BASED QUANTUM TRANSPORT SIMULATION FOR STRAINED-ENGINEERED NANOSCALE TRANSISTORS IN THE PRESENCE OF ELECTRON–PHONON INTERACTIONS

2010 ◽  
Vol 09 (04) ◽  
pp. 327-333
Author(s):  
T. K. MAITI ◽  
C. K. MAITI
Keyword(s):  
Ab Initio ◽  
Green’S Function ◽  
Quantum Transport ◽  
Green's Function ◽  
Electronic Transport ◽  
Phonon Scattering ◽  
Local Density ◽  
Nonequilibrium Green's Function ◽  
Nonequilibrium Green’S Function ◽  
Nanoscale Transistors

Based on ab initio formulation and using nonequilibrium Green's function (NEGF) formalism, electronic transport in the presence of electron–phonon interactions in strained-engineered nanoscale transistors is presented. Ab initio methods are applied to treat the metal/semiconductor interface properly. NEGF formalism is applied as quantum transport and phonon scattering are the dominant factors in devices under realistic operating voltages. Local self-energy functions for electron–phonon scattering have been obtained using deformation potential theory. This approach is applied to the study of electronic transport in strain-engineered nanowire transistors. Electron–phonon interactions on broadening of local density of states are also reported.

Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Random Phase ◽  
Integration Contour ◽  
Differential Formulation ◽  
Variational Relations ◽  
Potential Perturbation ◽  
Non Equilibrium

Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.

Thermodynamic Green’s Functions and Spectral Structure

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spectral Weight ◽  
Statistical Thermodynamic ◽  
Spectral Structure ◽  
Imaginary Time ◽  
Translational Invariance ◽  
The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

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