Characteristics of quasi-ballistic heat conduction in a multiple materials system based on the solution of the Boltzmann transport equation
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Ballistic conduction
Boltzmann constant
Ballistic transport of electrons at room temperature in top-gated InAs nanowire (NW) transistors is experimentally observed and theoretically examined. From length dependent studies, the low-field mean free path is directly extracted as ∼150 nm. The mean free path is found to be independent of temperature due to the dominant role of surface roughness scattering. The mean free path was also theoretically assessed by a method that combines Fermi's golden rule and a numerical Schrödinger–Poisson simulation to determine the surface scattering potential with the theoretical calculations being consistent with experiments. Near ballistic transport (∼80% of the ballistic limit) is demonstrated experimentally for transistors with a channel length of ∼60 nm, owing to the long mean free path of electrons in InAs NWs.
Ballistic conduction
Ballistic limit
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In this study, we simulate double-gate MOSFET using a 2-D direct Boltzmann transport equation solver. Simulation results are interpreted by quasi-ballistic theory. It is found that the relation between average carrier velocity at virtual source and back-scattering coefficient needs to be modified due to the oversimplified approximations of the original model. A 1-D potential profile model also needs to be extended to better determine the kT-layer length. The key expression for back-scattering coefficient is still valid, but a field-dependent mean free path is needed to be taken into account.
Ballistic conduction
Boltzmann constant
Solver
Convection–diffusion equation
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Abstract The Boltzmann equation is at the heart of the semiclassical Bloch–Boltzmann theory of electronic transport in solids. The kinetic theory of gases based on the Boltzmann equation, originally developed for dilute classical gases, has since been applied successfully to the electron gas in metals and in semiconductors, despite of the fact that this latter gas is neither classical (except in non-degenerate semiconductors) nor dilute.
Semiclassical physics
Boltzmann constant
Kinetic Theory
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Phonon scattering
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This paper describes the information for quantitative simulation of weakly ionized plasma. In previous paper, we calculated the electron transport coefficients by using two-term approximation of Boltzmann equation. But there is difference between the result of the two-term approximation of the Boltzmann equation and experiments in pure CF$_4$ molecular gas and in CF$_4$ +Ar gas mixture. Therefore, In this paper, we calculated the electron drift velocity (W) in pure CF$_4$ molecular gas and CF$_4$ +Ar gas mixture (1 %, 5 %, 10 %) for range of E/N values from 0.17～300 Td at the temperature was 300 K and pressure was 1 Torr by multi-term approximation of the Boltzmann equation by Robson and Ness. The results of two-term and multi-term approximation of the Boltzmann equation have been compared with each other for a range of E/N.
Boltzmann constant
Torr
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Abstract In Chapter 4, we examined the classical and quantum mechanical generalizations of the Boltzmann equation needed for the treatment of transport and relaxation phenomena in a gas of rotating molecules.
Boltzmann constant
Lattice Boltzmann methods
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Abstract Unlike classical heat diffusion at macroscale, nanoscale heat conduction can occur without energy dissipation because phonons can ballistically travel in straight lines for hundreds of nanometres. Nevertheless, despite recent experimental evidence of such ballistic phonon transport, control over its directionality, and thus its practical use, remains a challenge, as the directions of individual phonons are chaotic. Here, we show a method to control the directionality of ballistic phonon transport using silicon membranes with arrays of holes. First, we demonstrate that the arrays of holes form fluxes of phonons oriented in the same direction. Next, we use these nanostructures as directional sources of ballistic phonons and couple the emitted phonons into nanowires. Finally, we introduce thermal lens nanostructures, in which the emitted phonons converge at the focal point, thus focusing heat into a spot of a few hundred nanometres. These results motivate the concept of ray-like heat manipulations at the nanoscale.
Ballistic conduction
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Brillouin zone
Phonon scattering
Dispersion relation
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We present a direct solution method to the Bloch‐Boltzmann‐Peierls equations governing the transport of carriers and optical phonons in semiconductors. This approach is based on a multigroup formulation of the original equations, which still contains both the full quantum statistics of carriers and phonons and a very general description of the carrier band structure. It allows the investigation of the particle distributions of arbitrary anisotropies with respect to a main direction. Concerning the mathematical properties of the deduced transport model, we prove a Boltzmann H‐theorem for the obtained evolution equations. The equilibrium solution of the multigroup model is compared with that of the original Bloch‐Boltzmann‐Peierls equations. Numerical results are given for relaxation processes of hot electrons and hot phonons.
Boltzmann constant
Convection–diffusion equation
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