Longer Mean Free Path Research Articles

Topology optimization for near-junction thermal spreading of electronics in ballistic-diffusive regime

Hotspots in electronic devices can cause overheating and reduce performance. Enhancing the thermal spreading ability is critical for reducing device temperature to improve the reliability. However, as devices shrink, phonon ballistic effects can increase thermal resistance, making conventional optimization methods less effective. This paper presents a topology optimization method that combines the phonon Boltzmann transport equation with solid isotropic material with penalization method to optimize high thermal conductivity (HTC) material distributions for thermal spreading problems. Results show that the contraction-expansion structure can effectively reduce thermal resistance. Optimal distributions differ from that based on Fourier's heat conduction law, and only the trunk structure appears in optimized layouts due to the size effect. Additionally, HTC material with longer mean free paths tends to be filled around the heat source with a gap in a ballistic-diffusive regime. This work deepens understanding of thermal spreading and aids in thermal optimization of microelectronic chips.

Phason-Dominated Thermal Transport in Fresnoite.

Fast-propagating waves in the phase of incommensurate structures, called phasons, have long been argued to enhance thermal transport. Although supersonic phason velocities have been observed, the lifetimes, from which mean free paths can be determined, have not been resolved. Using inelastic neutron scattering and thermal conductivity measurements, we establish that phasons in piezoelectric fresnoite make a major contribution to thermal conductivity by propagating with higher group velocities and longer mean free paths than phonons. The phason contribution to thermal conductivity is maximum near room temperature, where it is the single largest contributing degree of freedom.

Impurity leakage and radiative cooling in the first nitrogen and neon seeding study in the closed DIII-D SAS configuration

A comparative study of nitrogen versus neon has been carried out to analyze the impact of the two radiative species on power dissipation, SOL impurity distribution, divertor and pedestal characteristics. The experimental results show that N remains compressed in the divertor, thereby providing high radiative losses without affecting the pedestal profiles and displacing carbon as dominant radiator. Neon, instead, radiates more upstream than N thus reducing the power flux through the separatrix leading to a reduced ELM frequency and compression in the divertor. A significant amount of neon is measured in the plasma core leading to a steeper density gradient. The different behavior between the two impurities is confirmed by SOLPS-ITER modeling which for the first time at DIII-D includes multiple impurity species and a treatment of full drifts, currents and neutral–neutral collisions. The impurity transport in the SOL is studied in terms of the parallel momentum balance showing that N is mostly retained in the divertor whereas Ne leaks out consistent with its higher ionization potential and longer mean free path. This is also in agreement with the enrichment factor calculations which indicate lower divertor enrichment for neon. The strong ionization source characterizing the SAS divertor causes a reversal of the main ions and impurity flows. The flow reversal together with plasma drifts and the effect of the thermal force contribute significantly in the shift of the impurity stagnation point affecting impurity leakage. This work provides a demonstration of the impurity leakage mechanism in a closed divertor structure and the consequent impact on pedestal. Since carbon is an intrinsic radiator at DIII-D, in this paper we have also demonstrated the different role of carbon in the N vs Ne seeded cases both in the experiments and in the numerical modeling. Carbon contributes more when neon seeding is injected compared to when nitrogen is used. Finally, the results highlight the importance of accompanying experimental studies with numerical modeling of plasma flows, drifts and ionization profile to determine the details of the SOL impurity transport as the latter may vary with changes in divertor regime and geometry. In the cases presented here, plasma drifts and flow reversal caused by high level of closure in the slot upper divertor at DIII-D play an important role in the underlined mechanism.

Evaluation of PBMR-400 Core Design Steady State Condition with Serpent and AGREE

The significant recent advances in computer speed and memory have made possible an increasing fidelity and accuracy in reactor core simulation with minimal increase in the computational burden. This has been important for modeling some of the smaller advanced reactor designs for which simplified approximations such as few groups homogenized diffusion theory are not as accurate as they were for large light water reactor cores. For narrow cylindrical cores with large surface to volume ratios such the Ped Bed Modular Reactor (PBMR), neutron leakage from the core can be significant, particularly with the harder neutron spectrum and longer mean free path than a light water reactor. In this paper the core from the OECD PBMR-400 benchmark was analyzed using multigroup Monte Carlo cross sections in the HTR reactor core simulation code AGREE. Homogenized cross sections were generated for each of the discrete regions of the AGREE model using a full core SERPENT Monte Carlo model. The cross sections were generated for a variety of group structures in AGREE to assess the importance of finer group discretization on the accuracy of the core eigenvalue and flux predictions compared to the SERPENT full core Monte Carlo solution. A significant increase in the accuracy was observed by increasing the number of energy groups, with as much as a 530 pcm improvement in the eigenvalue calculation when increasing the number of energy groups from 2 to 14. Significant improvements were also observed in the AGREE neutron flux distributions compared to the SERPENT full core calculation.

Nonequilibrium phonon transport induced by finite sizes: Effect of phonon-phonon coupling

In heat conduction through a homogenous nanomaterial, various phonons may exhibit diverse temperatures even at the same location at a steady state, known as the local phonon nonequilibrium phenomenon. Different phonons are often considered to behave independently, and the phonons with longer mean free paths (MFPs) have smaller temperature gradients. That is, the temperature gradient exhibits the following order: ballistic phonons semiballistic phonons \ensuremath{\approx} lattice (average) temperature gradient diffusive phonons, where ballistic phonons have MFPs much larger than the characteristic length, semiballistic phonons have MFPs like the characteristic length, and diffusive phonons have MFPs much smaller than the characteristic length. However, in this paper, we reveal that the effect of phonon-phonon coupling leads nonequilibrium phonon temperature gradients to the following trend: diffusive phonon temperature gradients will decrease to the lattice temperature, and temperature gradients of some semiballistic phonons even surpass that of diffusive phonons. The diffusive phonon temperature is merged onto the lattice temperature since they have large scattering rates and can be equilibrated quickly to the lattice temperature after traveling for a short distance away from the boundaries into the nanomaterial. The semiballistic phonons have large scattering rates but not large enough to bring them down to the lattice temperature. To obtain a further understanding of the nonequilibrium phonon temperatures, we have also derived a simple analytical model which can accurately predict the temperature profiles of all individual phonons given their MFPs. Using this model, we find that, near the boundary, phonon temperatures decay with position exponentially (instead of linearly), with a rate inversely proportional to their MFPs. Our findings offer insight for the understanding and prediction of phonon nonequilibrium temperatures within nanodevices.

Variation of Plasma Properties in Cylindrical Inertial Electrostatic Confinement Device by Changing the Anode Transparency

Inertial electrostatic confinement (IEC) is investigated in terms of direct-current discharge in a cylindrical configuration using nitrogen gas in the pressure range between 0.028 and 0.09 Torr. Discharge characteristics are determined for different anode transparencies of 84%, 92%, and 96% corresponding to 24, 12, and 6 anode rods, respectively. I-V characteristic curves indicate that the electric discharge is in the abnormal glow discharge region. The discharge voltage has the highest values for the low anode transparency for the same value of the discharge current. A double electric probe has been used to measure electron temperature and ion density. The low anode transparency (24 anode rods) enhances field uniformity and aligns the motion of electrons into a chord so that better electrostatic confinement is achieved. This will raise the ion density and lead to thermalization of the plasma, which reduces the electron temperature. The behavior of the electron temperature and the ion density was studied as a function of the gas pressure at the center and near the edge. The variation of the density and temperature in both positions can confirm the plasma confinement. In the low-pressure regime, the confinement process is reinforced. Because of the longer mean free path, electrons cause ionization at the center, which raises the ion density to about 1.44 × 1015 m−3 and the electron temperature to about 2.9 eV.

Phonon-boundary scattering and thermal transport in AlxGa1−xN: Effect of layer thickness

Thermal conductivity of AlxGa1−xN layers with 0≤x≤0.96 and variable thicknesses is systematically studied by combined thermoreflectance measurements and a modified Callaway model. We find a reduction in the thermal conductivity of AlxGa1−xN by more than one order of magnitude compared to that of GaN, which indicates a strong effect of phonon-alloy scattering. It is shown that the short-mean free path phonons are strongly scattered, which leads to a major contribution of the long-mean free path phonons to the thermal conductivity. In thin layers, the long-mean free path phonons become efficiently scattered by the boundaries, resulting in a further decrease in the thermal conductivity. Also, an asymmetry of thermal conductivity as a function of Al content is experimentally observed and attributed to the mass difference between Ga and Al host atoms.

Resonance peak shift in the photocurrent of ultrahigh-mobility two-dimensional electron systems

We report on a theoretical study on the rise of strong peaks at the harmonics of the cyclotron resonance in the irradiated magnetoresistance in ultraclean two-dimensional electron systems. The motivation is the experimental observation of a totally unexpected strong resistance peak showing up at the second harmonic. We extend the radiation-driven electron orbit model (previously developed to study photocurrent oscillations and zero resistance states) to a ultraclean scenario that implies longer scattering time and longer mean free path. Thus, when the mean free path is equivalent, in terms of energy, to twice the cyclotron energy ($2\hbar w_{c}$), the electron behaves as under an effective magnetic field twice the one really applied. Then, at high radiation power and/or low temperature, a resistance spike can be observed {\it at the second harmonic}. For even cleaner samples the energy distance could increase to three or four times the cyclotron energy giving rise to resistance peaks at higher harmonics (third, fourth, etc.), i.e., a resonance peak shift to lower magnetic fields as the quality of the sample increases. Thus, by selecting the sample mobility one automatically would select the radiation resonance response without altering the radiation frequency.

Nano-microstructural control of phonon engineering for thermoelectric energy harvesting

Abstract

Thermal Transport in Nanoporous Yttria-Stabilized Zirconia by Molecular Dynamics Simulation

Yttria-stabilized zirconia (YSZ) is widely used as thermal barrier coatings (TBCs) to reduce heat transfer between hot gases and metallic components in gas-turbine engines. Porous structure can generally reduce the lattice thermal conductivity of bulk material, so porous YSZ can be potentially used as TBCs with better thermal performance. In this work, we investigate the thermal conductivity of nanoporous YSZ using the nonequilibrium molecular dynamics (NEMD) simulation, and comprehensively discuss the effects of cross-sectional area, pore size, structure length, porosity, Y2O3 concentration and temperature on the thermal conductivity. To compare with the results of the NEMD simulation, we solve the heat diffusion equation and the gray Boltzmann transport equation (BTE) to calculate the thermal conductivity of the same porous structure. From the results, we find that the thermal conductivity of YSZ has a weak dependence on the structure length at the length range from 10 to 26 nm, which indicates that the majority of heat carriers have very short mean free path (MFP) but there exists small percentage (about 3%) of phonons with longer MFP (larger than 10 nm) contributing to the thermal conductivity. The thermal conductivity predicted by NEMD simulation is smaller than that of solving heat diffusion equation (diffusive limit) with the same porous structure. It shows that the presence of pores affects phonon scattering and further affects the thermal conductivity of nanoporous YSZ. The results agree well with the solution of gray BTE with a average MFP of 0.6 nm. The thermal conductivity of nanoporous YSZ weakly depends on the Y2O3 concentration and temperature, which shows the phonons with very short MFP play the major contribution to the thermal conductivity. The results help to better understand the heat transfer in porous YSZ structure and develop better TBCs.

Largely reduced cross-plane thermal conductivity of nanoporous In0.1Ga0.9N thin films directly grown by metal organic chemical vapor deposition

In recent year, nanoporous Si thin films have been widely studied for their potential applications in thermoelectrics, in which high thermoelectric performance can be obtained by combining both the dramatically reduced lattice thermal conductivity and bulk-like electrical properties. Along this line, a high thermoelectric figure of merit (ZT) is also anticipated for other nanoporous thin films, whose bulk counterparts possess superior electrical properties but also high lattice thermal conductivities. Numerous thermoelectric studies have been carried out on Si-based nanoporous thin films, whereas cost-effective nitrides and oxides are not systematically studied for similar thermoelectric benefits. In this work, the cross-plane thermal conductivities of nanoporous In0.1Ga0.9N thin films with varied porous patterns were measured with the time-domain thermoreflectance technique. These alloys are suggested to have better electrical properties than conventional Si x Ge1–x alloys; however, a high ZT is hindered by their intrinsically high lattice thermal conductivity, which can be addressed by introducing nanopores to scatter phonons. In contrast to previous studies using dry-etched nanopores with amorphous pore edges, the measured nanoporous thin films of this work are directly grown on a patterned sapphire substrate to minimize the structural damage by dry etching. This removes the uncertainty in the phonon transport analysis due to amorphous pore edges. Based on the measurement results, remarkable phonon size effects can be found for a thin film with periodic 300-nm-diameter pores of different patterns. This indicates that a significant amount of heat inside these alloys is still carried by phonons with ~300 nm or longer mean free paths. Our studies provide important guidance for ZT enhancement in alloys of nitrides and similar oxides.

Performance Analysis of Single-Wall Carbon Nanotubes and Copper as VLSI Interconnect

The work in this paper analyses the performance of Single Wall Carbon Nanotube (SWCNT) bundles as VLSI interconnect. Using equivalent RLC circuit models described in this paper, comprehensive analysis of delay and power is done at 22nm technology node for both SWCNT bundle and copper. Results show that SWCNT bundle has smaller value of resistance due to longer mean free path and lesser delay than copper. Therefore, SWCNT bundle is a promising alternative to copper as VLSI interconnect for advanced technology nodes.

Molecular simulations and lattice dynamics determination of Stillinger-Weber GaN thermal conductivity

The bulk thermal conductivity of Stillinger-Weber (SW) wurtzite GaN in the [0001] direction at a temperature of 300 K is calculated using equilibrium molecular dynamics (EMD), non-equilibrium MD (NEMD), and lattice dynamics (LD) methods. While the NEMD method predicts a thermal conductivity of 166 ± 11 W/m·K, both the EMD and LD methods predict thermal conductivities that are an order of magnitude greater. We attribute the discrepancy to significant contributions to thermal conductivity from long-mean free path phonons. We propose that the Grüneisen parameter for low-frequency phonons is a good predictor of the severity of the size effects in NEMD thermal conductivity prediction. For weakly anharmonic crystals characterized by small Grüneisen parameters, accurate determination of thermal conductivity by NEMD is computationally impractical. The simulation results also indicate the GaN SW potential, which was originally developed for studying the atomic-level structure of dislocations, is not suitable for prediction of its thermal conductivity.

Spectral phonon mean free path and thermal conductivity accumulation in defected graphene: The effects of defect type and concentration

The spectral phonon properties in defected graphene have been unclear due to the lack of advanced techniques for predicting the phonon-defect scattering rate without fitting parameters. Taking advantage of the extended phonon normal mode analysis, we obtained the spectral phonon relaxation time and mean free path (MFP) in defected graphene and studied the impacts of three common types of defects: Stone-Thrower-Wales (STW) defect, double vacancy (DV), and monovacancy (MV). The phonon-STW defect scattering rate is found to have no significant frequency dependence, and as a result, the relative contribution of long-wavelength phonons sharply decreases. In contrast, the phonon scattering by DVs or MVs exhibits a frequency dependence of ${\ensuremath{\tau}}_{p\ensuremath{-}d}^{\ensuremath{-}1}\ensuremath{\sim}{\ensuremath{\omega}}^{1.1\ensuremath{-}1.3}$ except for a few long-wavelength phonons, revisiting the traditionally used $\ensuremath{\sim}{\ensuremath{\omega}}^{4}$ dependence. We note that although MV-defected graphene has the lowest thermal conductivity as compared to the other two defected graphene samples at the same defect concentration, it has a portion of phonons with the longest MFP. The contribution from the long-MFP and long-wavelength phonons does not decrease much as the vacancy concentration increases. STW defect and MV block more out-of-plane modes than in-plane modes, while DV has less bias for which mode to block. As the MV concentration increases from 0 to 1.1%, the relative contribution from out-of-plane modes decreases from 30% to 18%, while that of the transverse acoustic mode remains at around 30%. These findings of spectral phonon properties can provide more insight than the effective properties and benefit the prospective phononic engineering.

Neutron radiation measurements on several international flights.

The earth is continually exposed to cosmic radiation of both solar and galactic origin. High-energy particles interact with the constituents in the atmosphere producing secondary particles that create radiation fields at aircraft altitudes. These secondary particles consist mainly of photons, protons, neutrons, charged and uncharged pions, and muons. The neutron component dominates the hadron cascade at lower altitudes as a result of its longer mean free path. Since air transportation has become more available to a greater number of people, this has led to an increase in the number of persons exposed to ionizing radiation of cosmic origin. This concerns pilots and cabin crews as well as frequent flyers. A neutron component of cosmic radiation was measured using an LR 115/CR-39 track detector associated with a 10B converter foil. The measurement of the neutron dose is a good approximation of the total dose since neutrons carry about 50% of the total ambient dose equivalent at aircraft altitudes. Also, the results of the measurements were compared with the data obtained by EPCARD software simulation. The measured neutron dose rate had a span from 0.36 to 8.83 μSv h(-1) (dose enhancement due to high solar activity in the flight period).

Anomalous diameter dependence of thermal transport in ultra-narrow Si nanowires

We present atomistic valence force field calculations of thermal transport in Si nanowires of diameters from 12 nm down to 1 nm. We show that as the diameter is reduced, the phonon density-of-states and transmission function acquire a finite value at low frequency, in contrast to approaching zero as in the bulk material. It turns out that this effect results in what Ziman described as the “problem of long longitudinal waves” [J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids (Clarendon, Oxford, 1962)], which states that the thermal conductivity of a material increases as its length is increased due to the vanishing scattering for long-wavelength phonons. We show that this thermal transport improvement also appears in nanowires as their diameter is decreased below D = 5 nm (not only as the length increases), originating from the increase in the density of the long wavevector modes. The observation is present under ballistic transport conditions, and further enhanced with the introduction of phonon-phonon scattering. Because of this, in such ultra-narrow nanowires, as the diameter is reduced, phonon transport is dominated more and more by lower energy phonons with longer mean-free paths. We show that ∼80% of the heat is carried by phonons with energies less than 5 meV, most with mean-free paths of several hundreds of nanometers.

Toroidal drift precession and wave–particle interaction in shaped tokamaks with finite beta and neoclassical equilibrium effects

The drift kinetic equation is analysed for linear instabilities that are sensitive to the toroidal drift motion of long-mean free path particle populations. The interaction Lagrangian is resolved, and the toroidal drift precession evaluated for realistic tokamak equilibria, including the effects of cross section shaping and finite beta. The drift kinetic equation is expanded around a flux surface in accordance with a neoclassically resolved equilibrium and coincident bootstrap current. Analytical results pertaining to the effect of shaping, magnetic shear and finite beta on the toroidal drift and bounce/transit frequencies of passing and trapped particles are shown.

Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane

The "textbook" phonon mean free path of heat carrying phonons in silicon at room temperature is ∼40 nm. However, a large contribution to the thermal conductivity comes from low-frequency phonons with much longer mean free paths. We present a simple experiment demonstrating that room-temperature thermal transport in Si significantly deviates from the diffusion model already at micron distances. Absorption of crossed laser pulses in a freestanding silicon membrane sets up a sinusoidal temperature profile that is monitored via diffraction of a probe laser beam. By changing the period of the thermal grating we vary the heat transport distance within the range ∼1-10 μm. At small distances, we observe a reduction in the effective thermal conductivity indicating a transition from the diffusive to the ballistic transport regime for the low-frequency part of the phonon spectrum.

ZnO nanowires as effective luminescent sensing materials for nitroaromatic derivatives

We report on the efficient room-temperature photoluminescence (PL) quenching of ZnO in the presence of 2,4-dinitrotoluene (DNT) vapor and for concentration as low as 180 ppb. Compared to ZnO thin films, ZnO nanowires exhibit a strong (95%) and fast (41 s) quenching of the PL intensity in the presence of DNT vapor. Assuming that the PL quenching is due to a trapping of the ZnO excitons by adsorbed DNT molecules, Monte-Carlo calculations show that the nanometric dimensions as well as the better crystallographic quality (longer mean free path) of the ZnO nanowires result in an enhanced trapping process at the origin of the improved sensing properties of the nanowires. The results demonstrate the importance of nanostructures in improving the sensitivity of ZnO. The study also reveals the sensing capability of ZnO nanowires and paves the path towards the potential realization of low-cost sub-ppb nitroaromatic derivative sensors.

The Studies on the Thermophysical Properties of Binary Systems of Neopentylglycol and the Derives

Specific capacity and thermal conductivity are two very important physical quantities that characterize the heat performance of heat storage material. This paper measured the specific capacities and thermal conductivities of binary systems formed by NPG、TRIS and PE in the temperature range from 30oC to 70 oC and analyzed the experimental results from the point of view of crystal vibration. Hydrogen bonds exert great influence on the thermophysical properties of the binary systems. Although the components are only simply blended, substitutional impurity defects are incurred. As a result hydrogen bond will be affected in a complex way. There is no uniform trend between the value of x and specific capacity. Because of the influence of structure defect, specific capacity and phonon speed which all change with the strength of hydrogen bond, the relationship between thermal conductivity and the value of x is non-linear too. Because 40oC is near the phase transition temperature of NPGxTRIS1-x (x=0.618), its specific capacity at 40oC decreases and thermal conductivity increases. Because hydrogen bond changes with temperature, specific capacity of PExTRIS1-x (x=0.618) rises. Since 60oC is near the phase transition temperature, its specific capacity at 60oC falls. PExTRIS1-x (x=0.618) shows smaller thermal conductivities at temperatures higher than 30oC. This is because the hydrogen bonds become weaker with temperature. Blending impurities possessing longer mean free path with polyalcohol can change the thermal conductivity.