Subband Engineering in n-Type Silicon Nanowires using Strain and Confinement

Abstract We present a model based on k · p theory which is able to capture the subband structure effects present in ultrathin strained nanowires. The effective mass and valley minima are calculated for different crystal orientations thicknesses and strains. The results show that transport enhancement can be achieved by both confinement and strain which is in agreement with recent experimental findings. Motivation Nanowire based gate-all-around transistors offer a perspective for further device size reduction in microelectronics. Apart from the enhancement of electrostatic control over the channel due to a high surface to volume ratio, nanowires exhibit transport properties which deviate significantly from what is observed in bulk silicon or inversion layers. In a recent experimental study Modeling To understand the transport properties in wires below 10 nm one must carefully take quantization effects into account. A simple treatment using effective masses fails to satisfactorily describe the subband structure of such thin devices. This is due to the energy of the lowest subband already being of the order of 100 meV where nonparabolicity effects become noticeable. In this work we investigate the effects of both two dimensional confinement and strain using a two band k · p model for the conduction band V denotes the conduction band edge; m l = 0.91m e are the longitudinal and m t = 0.19m e the transversal effective mass and a amounts to the distance between a X point and the nearest ∆ valleys; ε l-l and ε t1-t2 are uniaxial and shear strain components and Ξ u and Ξ u the deformation potentials; σ x,z denote the Pauli matrices and I the identity matrix. The Hamiltonian is rotated according to the nanowire axis and quantized in the cross section plane to obtain the subband structure

Study of Thermal Properties of Graphene-Based Structures Using the Force Constant Method

The thermal properties of graphene-based materials are theoretically investigated. The fourth-nearest neighbor force constant method for phonon properties is used in conjunction with both the Landauer ballistic and the non-equilibrium Green's function techniques for transport. Ballistic phonon transport is investigated for different structures including graphene, graphene antidot lattices, and graphene nanoribbons. We demonstrate that this particular methodology is suitable for robust and efficient investigation of phonon transport in graphene-based devices. This methodology is especially useful for investigations of thermoelectric and heat transport applications.Comment: 23 pages, 9 figures, 1 tabl

Numerical study of the thermoelectric power factor in ultra-thin Si nanowires

Low dimensional structures have demonstrated improved thermoelectric (TE) performance because of a drastic reduction in their thermal conductivity, {\kappa}l. This has been observed for a variety of materials, even for traditionally poor thermoelectrics such as silicon. Other than the reduction in {\kappa}l, further improvements in the TE figure of merit ZT could potentially originate from the thermoelectric power factor. In this work, we couple the ballistic (Landauer) and diffusive linearized Boltzmann electron transport theory to the atomistic sp3d5s*-spin-orbit-coupled tight-binding (TB) electronic structure model. We calculate the room temperature electrical conductivity, Seebeck coefficient, and power factor of narrow 1D Si nanowires (NWs). We describe the numerical formulation of coupling TB to those transport formalisms, the approximations involved, and explain the differences in the conclusions obtained from each model. We investigate the effects of cross section size, transport orientation and confinement orientation, and the influence of the different scattering mechanisms. We show that such methodology can provide robust results for structures including thousands of atoms in the simulation domain and extending to length scales beyond 10nm, and point towards insightful design directions using the length scale and geometry as a design degree of freedom. We find that the effect of low dimensionality on the thermoelectric power factor of Si NWs can be observed at diameters below ~7nm, and that quantum confinement and different transport orientations offer the possibility for power factor optimization.Comment: 42 pages, 14 figures; Journal of Computational Electronics, 201

Hierarchically nanostructured thermoelectric materials: challenges and opportunities for improved power factors

Abstract: The field of thermoelectric materials has undergone a revolutionary transformation over the last couple of decades as a result of the ability to nanostructure and synthesize myriads of materials and their alloys. The ZT figure of merit, which quantifies the performance of a thermoelectric material has more than doubled after decades of inactivity, reaching values larger than two, consistently across materials and temperatures. Central to this ZT improvement is the drastic reduction in the material thermal conductivity due to the scattering of phonons on the numerous interfaces, boundaries, dislocations, point defects, phases, etc., which are purposely included. In these new generation of nanostructured materials, phonon scattering centers of different sizes and geometrical configurations (atomic, nano- and macro-scale) are formed, which are able to scatter phonons of mean-free-paths across the spectrum. Beyond thermal conductivity reductions, ideas are beginning to emerge on how to use similar hierarchical nanostructuring to achieve power factor improvements. Ways that relax the adverse interdependence of the electrical conductivity and Seebeck coefficient are targeted, which allows power factor improvements. For this, elegant designs are required, that utilize for instance non-uniformities in the underlying nanostructured geometry, non-uniformities in the dopant distribution, or potential barriers that form at boundaries between materials. A few recent reports, both theoretical and experimental, indicate that extremely high power factor values can be achieved, even for the same geometries that also provide ultra-low thermal conductivities. Despite the experimental complications that can arise in having the required control in nanostructure realization, in this colloquium, we aim to demonstrate, mostly theoretically, that it is a very promising path worth exploring. We review the most promising recent developments for nanostructures that target power factor improvements and present a series of design ‘ingredients’ necessary to reach high power factors. Finally, we emphasize the importance of theory and transport simulations for materialoptimization, and elaborate on the insight one can obtain from computational tools routinely used in the electronic device communities. Graphical abstract: [Figure not available: see fulltext.]