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The density of states of a nanowire exhibits peaks at energies in which the individual transverse modes begin to propagate. Under ideal conditions these modes are eigenstates solely determined by the cross sectional size and shape of the nanowire. However, for realistic nanowires, which are grown on semiconductor substrates, the density of states of the subsrate-nanowire structure is dependent on the distance from the nanowire endpoints. Near the substrate, the density of states is is nonzero far below the energy corresponding to the first eigenstate of the ideal nanowire. This initial increase in the density of states occurs at energies near the conduction and valence band edges of the semiconductor substrate on which the nanowire is grown. Away from the substrate, the density of states begins to acquire ideal nanowire characteristics. In the present work this effect is captured by imposing boundary conditions, with properties of bulk material, at the nanowire base. The calculations utilize a first neighbor sp 3 s*d 5 orbital basis within the non-equilibrium Green function formalism.

Full-band simulations of indirect, phonon assisted, interband tunneling are used to calculate the current–voltage response of a low-temperature molecular-beam-epitaxy-grown silicon tunnel diode with delta-doped contacts. Electron confinement in the contacts results in weak structure in the current–voltage characteristic. The structure is lost when finite lifetime effects are included. The approach uses the nonequilibrium Green function formalism in a second-neighbor sp3s* planar orbital basis.

We present an overview of electronic device modeling using non-equilibrium Green function techniques. The basic approach developed in the early 1970s has become increasingly popular during the last 10 years. The rise in popularity was driven first by the experimental investigations of mesoscopic physics made possible by high quality semiconductor heterostructures grown by molecular beam epitaxy. The theory has continuously been adapted to address current systems of interest moving from the mesoscopic physics of the late 1980s to single electronics to molecular electronics to nanoscaled FETs. We give an overview of the varied applications. We provide a tutorial level derivation of the polar optical phonon self-energy [1]. Then, focusing on issues of a non-orthogonal basis used in molecular electronics calculations, we derive and the basic Green function expressions starting from their definitions in second quantized form in a non-orthogonal basis. We derive the equations of motion for the retarded Green function G R and the correlation function G < , and we derive the standard expressions for the electron density and the current that are in widespread use. We point out common approximations and open questions of which one finds little discussion in the literature. II. INTRODUCTIONThe applications of nonequilibrium Green functions [2, 3] have been extensive including quantum optics [4], quantum corrections to the Boltzmann transport equation [5,6], high field transport in bulk systems [7], and electron transport through nanoscaled systems. Our interest has been in this last category of electron transport through nanoscaled materials under a finite applied bias. Below, we review the work in this area and then provide tutorial derivations of the standard expressions.Over the last decade, non-equilibrium Green's function (NEGF) techniques have become widely used in corporate, engineering, government, and academic laboratories for modeling high-bias, quantum electron and hole transport in wide variety of materials and devices: III-V resonant tunnel diodes [1, and inter-band phonon scattering, alloy disorder and interface roughness scattering in Born type approximations [1, 9,11,13,15,20,21,25,26,27], photon absorption and emission [25], energy and heat transport [16] , single electron charging and nonequilibrium Kondo systems [75,76,77,78,79,80,81], shot noise [14,17,82], A.C. [10, 83, 84, 85, 86, 87, 88], and transient response [85,89]. Time-dependent calculations are described further in [90]. General tutorials can be found in [91,92].The general formalism for NEGF calculations of current in devices was first described in a series of papers in the early 1970s [71,93,94,95]. The partitioning of an infinite system into left contact, device, and right contact, and the derivation of the open boundary self-energies for a tight-binding model was presented in [71]. This theory was re-derived for a continuum representation in [93], tunneling through localized impurity states was treated in [94], and a treatment of phonon ass...

The current of a molecular beam epitaxially grown Sb and B delta-doped Si tunnel diode is simulated in all regions of tunneling: peak, valley, and post-valley turn-on. All three regions of the I-V are qualitatively captured by the calculations. The inclusion in the model of bandtail states gives rise to the excess current and the post-valley turn on of the tunnel current. This excess current is dominated by the direct coherent tunneling component of the current tunneling from gap state to gap state. The crossover between phonon-assisted and direct occurs immediately after the valley minimum. The calculated voltages quantitatively match the experimental measurements. The magnitude of the calculated current is approximately a factor of 5.4 too small. Sources of error are analyzed. The current calculations use a second neighbor sp 3 s* planar orbital basis within the nonequilibrium Green function formalism.