Free Path Of Energy Carriers Research Articles

Calculation of heat transfer in nanoscale heterostructures

Abstract. The article discusses the calculation of the temperature regime in nanoscale AlAs/GaAs binary heterostructures. When modeling heat transfer in nanocomposites, it is important to take into account that heat dissipation in multilayer structures with layer sizes of the order of the mean free path of energy carriers (phonons and electrons) occurs not at the lattice, but at the layer boundaries (interfaces). In this regard, the use of classical numerical models based on the Fourier law is limited, because it gives significant errors. To obtain more accurate results, we used a model in which the heat distribution was assumed to be constant inside the layer, while the temperature was stepwise changed at the interfaces of the layers. A hybrid approach was used for the calculation: a finite−difference method with an implicit scheme for time approximation and a mesh−free model based on a set of radial basis functions for spatial approximation. The calculation of the parameters of the bases was carried out through the solution of the systems of linear algebraic equations. In this case, only weights of neuroelements were selected, and the centers and «widths» were fixed. As an approximator, a set of frequently used basic functions was considered. To increase the speed of calculations, the algorithm was parallelized. Calculation times were measured to estimate the performance gains using the parallel implementation of the method.

Instrumentation of broadband frequency domain thermoreflectance for measuring thermal conductivity accumulation functions

This paper describes the instrumentation for broadband frequency domain thermoreflectance (BB-FDTR), a novel, continuous wave laser technique for measuring the thermal conductivity accumulation function. The thermal conductivity accumulation function describes cumulative contributions to the bulk thermal conductivity of a material from energy carriers with different mean free paths. It can be used to map reductions in thermal conductivity in nano-devices, which arise when the dimensions of the device are commensurate to the mean free path of energy carriers. BB-FDTR uses high frequency surface temperature modulation to generate non-diffusive phonon transport realized through a reduction in the perceived thermal conductivity. By controlling the modulation frequency it is possible to reconstruct the thermal conductivity accumulation function. A unique heterodyning technique is used to down-convert the signal, therein improving our signal to noise ratio and enabling results over a broader range of modulation frequencies (200 kHz-200 MHz) and hence mean free paths.

On hyperbolic heat conduction in solids: minimum mean free path of energy carriers and a method of estimating thermal diffusivity and heat propagation characteristics

The paper gives the analytical solution to the one dimensional hyperbolic heat conduction equation in an insulated slab-shaped sample that is heated uniformly on the front face with δ or laser impulse. The solution results in a formula that enables to estimate the minimum mean free path of energy carriers in the sample to detect the second sound (i.e. the thermal wave) at the sample rear face. A method of experimental data evaluation at the second sound effect is proposed, which gives the thermal diffusivity of the sample and the parameters of heat propagation.

Simulation of ballistic and non-Fourier thermal transport in ultra-fast laser heating

In this work, the lattice Boltzmann method (LBM) is developed to simulate pico- and femtosecond laser heating of silicon. The temperature fields calculated by the LBM are compared with those obtained from the parabolic heat conduction equation (PHCE) and the hyperbolic heat conduction equation (HHCE). Although the HHCE overcomes the dilemma of infinite thermal propagation speed of the PHCE, it cannot be applied to length scales comparable to the mean free path of energy carriers because of the breakdown of continuum approaches under severe nonequilibrium conditions. The LBM, considering both effects, can be used in both short temporal and spatial scales. From the results of the LBM, it is found that the speed of thermal wave at the ballistic limit is equal to the speed of sound, instead of the value predicted by the HHCE, which is valid only in the diffuse limit. It is also demonstrated that the traditional way of calculating heat flux using the temperature gradient gives rise to physically unreasonable results at the thermal wave front, while the LBM has no such drawback.