Phonon Temperature Distributions Research Articles

Nano Thermal Simulation of Graphene Field Effect Transistor Based on Ballistic Diffusive Model

This paper investigates temperature evolution in graphene field-effect transistors. We present a refined Ballistic-diffusive equation model (BDE) tailored for scrutinizing the phonon transport within GNRFET transistors. Furthermore, we examine the influence of the channel length on thermal characteristics. COMSOL Multiphysics is employed to compute the phonon transport and temperature distribution in nano-GNRFET. Our results reveal that the phonon transport anticipated by the suggested BDE model closely corresponds to that derived from the Boltzmann transport equation. The proposed model proficiently gauges the thermal performance of GNRFET, with the outcomes suggesting that the characteristic length of the GNR has a negligible impact on the temperature increase.

Heating of inhomogeneous electron flow in the hydrodynamic regime

We study the electron temperature profiles for an inhomogeneous electron flow in the hydrodynamic regime. We assume that the inhomogeneity is due to a weakly nonuniform distribution of the momentum relaxation time within a spherically constricted area. We show that the temperature profile dramatically depends on the drive strength and the viscosity of the electron liquid. In the absence of viscosity, a Landauer-dipole-like temperature distribution, asymmetrically deformed along the current by the inelastic electron-phonon scattering, emerges around the inhomogeneity. We find that both the Landauer-dipole temperature profile and its asymmetry in the direction of the driving electric field exist in all dimensionalities and are, therefore, universal features of inhomogeneous hydrodynamic electron flow. We further demonstrate that the electron viscosity suppresses the thermal Landauer dipole and leads to the appearance of a ``hot spot'' exactly at the center of the constriction. We also calculate the phonon temperature distribution, which can be directly measured in experiments on thermal nanoimaging.

Modeling Thermal Performance of Nano-GNRFET Transistors Using Ballistic-Diffusive Equation

This paper inquires the phonon transport and temperature distribution in graphene nanoribbon field-effect transistor (GNRFET). We propose a modified Ballistic-diffusive equation model (BDE) to explore the phonon transport in GNRFET transistors. In addition, we have studied the effect of the channel length on thermal characteristics. Finite-element approximation used to study the temperature distribution in nano-GNRFET. The proposed model has been validated on the basis of available results from the literature. Our results shows that phonon transport predicted by the proposed BDE model is close to that obtained by Boltzmann transport equation. We found that the proposed model is able to estimate the thermal performance of GNRFET. The results prove also that the characteristic length of the GNR has no important role in the increasing of the temperature.

Modeling heat generation in high power density nanometer scale GaAs/InGaAs/AlGaAs PHEMT

A model of heat generation rate for two-dimensional semiconductor devices is established. Electron motion and electron–phonon scattering in nanometer scale GaAs/AlGaAs pseudomorphic high electron mobility transistor (PHEMT) under high power density are simulated by Monte Carlo method. Parameters such as electric field, phonon temperature, and heat generation rate distribution are obtained by solving Boltzmann equation and phonon conservation equations. The heat generation rate distribution and the number of net optical-phonon emission in the presence of different applied voltages are presented. The electric field, electron density, phonon emission and absorption, and lattice temperature are investigated to elucidate the mechanism of heat generation in the devices.

Carrier heating and electron-phonon energy exchange effects on nonlinear transport phenomena in semiconductor films

Theory of nonlinear size effects is developed in semiconductor films in the presence of an external dc electric field. The electron and phonon temperatures are calculated self-consistently with the electron-phonon energy interaction taken into account and its influence on the electron current density is considered. The temperature distributions are calculated using appropriate boundary conditions at the surfaces of the semiconductor film. It is shown that the electron and phonon temperatures depend on the electron-phonon coupling factor and the film thickness. Because the electrical conductivity is a function of the electron and phonon temperature distributions, the electron current density in the semiconductor film becomes nonlinear as a function of the heating electric field. We discuss the nonlinear effects for different special cases.

Phonon transport in silicon–silicon and silicon–diamond thin films: Consideration of thermal boundary resistance at interface

Phonon transport across the silicon–silicon and silicon–diamond dielectric films is examined. To simulate the phonon transport in the films EPRT is accounted and numerical solutions are obtained with the consideration of 1 K difference across the films prior to the initiation of the phonon transport. The diffuse mismatch model is introduced to account for the thermal boundary resistance at the interface of the films. To validate the code developed, the steady and transient cases for phonon transport in silicon film are carried out. It is found that the equilibrium temperature of phonons attains higher value at the interface of silicon films in silicon–silicon films than that corresponding to silicon–diamond films. The predictions of phonon temperature distribution in the silicon film agree well with its counterpart reported in the previous studies.

The effect of electron–phonon energy exchange on thermal pulse propagation in semiconductors

In this work, the nonequilibrium electron and phonon temperature distributions in semiconductors, initially heated on the surface with a short laser pulse, are calculated as a function of position and time. The transient temperatures of both quasiparticle systems are calculated self-consistently with the electron–phonon energy interaction taken into account. The electron and phonon temperature distributions are calculated using the Fourier integral and the coupled time-dependent one-dimensional heat diffusion equations for electron and phonon systems with special boundary conditions according to the experimental set-up.

Low-Frequency Acoustic Phonon Temperature Distribution in Electrically Biased Graphene

On the basis of scanning thermal microscopy (SThM) measurements in contact and lift modes, the low-frequency acoustic phonon temperature in electrically biased, 6.7-9.7 μm long graphene channels is found to be in equilibrium with the anharmonic scattering temperature determined from the Raman 2D peak position. With ∼100 nm scale spatial resolution, the SThM reveals the shifting of local hot spots corresponding to low-carrier concentration regions with the bias and gate voltages in these much shorter samples than those exhibiting similar behaviors in the infrared emission maps.

Improved Two-Temperature Model and Its Application in Ultrashort Laser Heating of Metal Films

The two-temperature model has been widely used to predict the electron and phonon temperature distributions in ultrashort laser processing of metals. However, estimations of some important thermal and optical properties in the existing two-temperature model are limited to low laser fluences in which the electron temperatures are much lower than the Fermi temperature. This paper extends the existing two-temperature model to high electron temperatures by using full-run quantum treatments to calculate the significantly varying properties, including the electron heat capacity, electron relaxation time, electron conductivity, reflectivity, and absorption coefficient. The proposed model predicts the damage thresholds more accurately than the existing model for gold films when compared with published experimental results.

NONEQUILIBRIUM ELECTRONS AND PHONONS IN THIN FILM THERMIONIC COOLERS

The effect of hot carriers on the cooling performance of single barrier heterostructure thermionic coolers is studied theoretically. By studying nonequilibrium characteristics of electrons and phonons in the device, fundamental limitation in the cooler performance is analyzed. In particular, we investigated the effect of various boundary conditions at heterojunctions on the electron and phonon temperature distributions. These boundary conditions have a strong impact on the device operation. Thin film devices under high voltage or in high current density are examples of situations where electrons and phonons are not in equilibrium and a coupled transport equation should be solved for an accurate analysis. In a thermoelectric/thermionic device one measures the lattice temperature while cooling occurs in the electron gas. Although at low currents electrons and phonons have the same equilibrium temperature, by increasing the current they may have different temperatures, which can lead to a reduction in cooling power density. We will show that in materials with faster electron energy relaxation, that is, higher electron-phonon coupling, thermionic cooling performance is less affected by high current injection and that recently demonstrated SiGe thin film coolers are not limited by hot carrier effects.

Electron and phonon thermal waves in semiconductors: the effect of carrier diffusion and recombination on the photoacoustic signal

The electron and phonon temperature distributions are calculated in bipolar semiconductors by taking into account generation and heating of carriers on the surface due to the incident modulated laser beam as well as the finite carrier diffusion and recombination in the solid. We solve the coupled one-dimensional heat and carrier diffusion equations in the linear approximation using appropriate boundary conditions according to the photoacoustic experimental conditions. In addition, special emphasis is laid on the dependence of the electron system heat flux on the electron and phonon temperature. We also consider the influence of both temperatures on the recombination of the electron–hole pairs. The dependence of the amplitude of the electron and phonon temperatures on the modulation frequency are analyzed for different values of characteristic parameters of the problem: electron–phonon energy exchange and carrier thermal generation rate.

Simulation of nonequilibrium thermal effects in power LDMOS transistors

The present work considers electrothermal simulation of LDMOS devices and associated nonequilibrium effects. Simulations have been performed on three kinds of LDMOS: bulk Si, partial SOI and full SOI. Differences between equilibrium and nonequilibrium modeling approaches are examined. The extent and significance of thermal nonequilibrium is determined from phonon temperature distributions obtained using a common electronic solution and three different heating models (Joule heating, electron/lattice scattering, phonon scattering). The results indicate that, under similar operating conditions, nonequilibrium behavior is more significant in the case of full SOI devices, where the extent of nonequilibrium is estimated to be twice that of the partial SOI device and four times that of the bulk device. Time development of acoustic phonon and lattice temperatures in the electrically active region indicates that nonequilibrium effects are significant for times less than 10 ns.

Electron and phonon temperature relaxation in semiconductors excited by thermal pulse

Electron and phonon transient temperatures are analyzed in the case of nondegenerate semiconductors. An analytical solution is obtained for rectangular laser pulse absorption. It is shown that thermal diffusion is the main energy relaxation mechanism in the phonon subsystem. The mechanism depends on the correlation between the sample length l and the electron cooling length lε in an electron subsystem. Energy relaxation occurs by means of the electron thermal diffusion in thin samples (l≪lε), and by means of the electron–phonon energy interaction in thick samples (l≫lε). Characteristic relaxation times are obtained for all the cases, and analysis of these times is made. Electron and phonon temperature distributions in short and long samples are qualitatively and quantitatively analyzed for different correlations between the laser pulse duration and characteristic times.

Scanning thermal microscopy of carbon nanotubes using batch-fabricated probes

We have designed and batch-fabricated thin-film thermocouple cantilever probes for scanning thermal microscopy (SThM). Here, we report the use of these probes for imaging the phonon temperature distribution of electrically heated carbon-nanotube (CN) circuits. The SThM images reveal possible heat dissipation mechanisms in CN circuits. The experiments also demonstrate that heat flow through the tip-sample nanoscale junction under ambient conditions is dominated by conduction through a liquid film bridging the two surfaces. With the spatial resolution limited by tip radius to about 50 nm, SThM now offers the promising prospects of studying electron-phonon interactions and phonon transport in low dimensional nanostructures.

Transient heat transport by carriers and phonons in semiconductors

The electron and phonon temperature distribution in semiconductors initially heated on the surface with a short laser pulse is calculated as a function of position and time. We solved the coupled one-dimensional heat diffusion equations for electron and phonon systems in the linear approximation in which the physical parameters of the sample are temperature independent. We also consider the heat pulse at the surface of the semiconductor as a boundary condition for each electron and phonon system. We believe that the transient heat transport experiments are a very suitable way of measuring the electron and phonon temperatures ${T}_{e,p}(x,t)$ in the sample, and they also yield the relaxation time associated with the different relaxation processes, e.g., electron-electron, phonon-phonon, and electron-phonon relaxation times, respectively. We provide a detailed quantitative theory for heat transient transport and find that the mechanism for electron energy relaxation time is strongly dependent on the size of the sample. For thin-film semiconductors the main relaxation process is due to heat diffusion by carriers, however the energy relaxation in larger samples is due to electron-phonon energy interaction. On the other hand, for nondegenerate semiconductors the typical ratio of the heat conductivities of electrons and phonons satisfies ${\ensuremath{\kappa}}_{e}/{\ensuremath{\kappa}}_{p}\ensuremath{\sim}{10}^{\ensuremath{-}3};$ under these circumstances the phonon energy relaxation time is due to heat diffusion by phonons and it is sample size independent. It is exciting that the electron temperature distribution function can be measured experimentally by means of the thermoelectric effect in semiconductors as a function of time.

Time-dependent heat diffusion in semiconductors by electrons and phonons

In this work the electron and phonon temperature distribution functions in semiconductors are calculated. We consider the time-dependent heat flux at the surface of the sample as a boundary condition for the electron and phonon systems, and a fixed temperature at the opposite surface. Those boundary conditions reflect the usual experimental setup in some photothermal experiments where the most common mechanism for producing interacting ``thermal waves'' is the absorption of an intensity-modulated light beam by the semiconductor. The electron and phonon temperature distributions in the sample are given as a function of both, time and position valid for a wide range of the modulation frequency \ensuremath{\omega} of the incident light. The response of the system in the limit of high- and low-frequency \ensuremath{\omega} with respect to the characteristic time ${\ensuremath{\tau}}_{e}({\ensuremath{\tau}}_{p})$ of the electron (phonon) system is analyzed.

Electron and phonon thermal waves in semiconductors: An application to photothermal effects

The electron and phonon temperature distribution functions are calculated in semiconductors. We solved the coupled one-dimensional heat-diffusion equations in the linear approximation in which the physical parameters of the sample are independent of temperature. We also consider the heat flux at the surface of the semiconductor as a boundary condition for each electron and phonon system instead of using a fixed temperature. From this we obtain an expression for electron and phonon temperature, respectively. The characterization of the thermal wave properties is discussed and some practical procedures for this purpose provide us with information about the electron and phonon thermal parameters.

Concurrent thermal and electrical modeling of sub-micrometer silicon devices

High electric fields, that are characteristic of sub-micron devices, produce highly energetic electrons, lack of equilibrium between electrons, optical phonons, and acoustic phonons, and high rates of heat generation. A simple coupled thermal and electrical model is developed for sub-micron silicon semiconductor devices consisting of the hydrodynamic equations for electron transport and energy conservation equations for different phonon modes. An electron Reynolds number is proposed and used to simplify the electron momentum equation. On a case study of the metal-oxide-semiconductor field-effect transistor with 0.24 μm gate length, the calculated transconductance of 0.175 1/Ω m agreed well with measured value of 0.180 1/Ω m at 2 V drain voltage. The maximum electron temperature is found to occur under the drain side of the gate where the electric field is the highest. Comparison with experimental data shows the predictions of optical and acoustic phonon temperature distributions to have the correct trend and the observed asymmetric behavior. Increase in substrate boundary temperature by 100 °C reduces the drain current by 17% and decreases the maximum electron temperature by 8%. The first effect increases device delay and the second effect decreases the possibility of device degradation by charge trapping in the gate oxide.

Electron and phonon temperature fields in bounded semiconductors in a magnetic field

The electron and phonon temperature distributions in a semiconductor sample with finite dimensions, placed in a thermostat with an arbitrary, fixed temperature profile, were studied. Heat transfer between the thermostat and the electrons and phonons through the wall is assumed to be arbitrary, while the magnetic field is assumed to be weak.