Phonon Spectrum,Group Velocity And Thermal Conductivity Of The Semiconductor Superlattice Thermoelectric Material

More and more, people put their interest into"the thermoelectric material"because of the extrusive environment and energy problems in the 21th century. It is shown that the thermoelectric properties of the materials are closely related to their thermal transport characteristics.In this paper, the heat transport characteristics such as the phonon spectrum ,the group velocity and the thermal conductivity of the semiconductor superlattice thermoelectric materials were studied.Based on the phonon gas dynamic theory, the thermal conductivity is calculated as follows: ( cv :heat capacities for unit volume, v g: the average phonon group velocity, l :the mean free path) .The average group velocity mostly attributes to the thermal conductivity ,so there are many papers about the average group velocity in the current literature,however, the studies about the group velocity according to a certain energy level are rare. The research of the group velocity is helpful to understand the phonon dispersion. We adopted a "semi-analytic approach" to calculated the phonon group velocity for different energy states .In order to calculate the thermal conductivity, we must have some knowledge about the lattice heat capacity from the gas dynamic theory.The lattice dynamices theory is strict for the lattice heat capacity,but it needs to calculate the dispersion relations and the state density function ,what's more , it needs to make clear of the value of the great deal of points.Therefore, the calculation is often complex.We firstly made use of the"special K-space points"method to calculated the heat capacity and thermal conductivity of the superlattice materials as a function of temperature .The result shows that the heat capacity approached to a limit value (about 24.9J.mol^-1.K^-1)as the temperature increased to a relatively large value (about 350K).The conclusion is consistent with the basic thermodynamic theory.We studied the effects of the hydrostatic pressure on the phonon spectrum and the group velocity of the Si/Ge, GaAs/AlAs Superlattices .We studied the effects of the hydrostatic pressure on the phonon spectrum of the superlattices by amending the atomic force .The result suggest that the phonon frequence were systematically increased due to the hydrostatic pressure.The group velocity of the acoustic phonon in the different energy states were calculated by the semi-analytic method.We also considered the hydrostatic pressure effects.The result suggest that the acoustic phonon group velocity square in the vertical(z) were increased because of the hydrostatic pressure.Till now, only a few reports about the effect of hydrostatic pressure on the phonon spectrum of semiconductor materials are presented. To the best of our knowledge, this is the first work for considering the hydrostatic pressure effect on the group velocity.Further considerations should be made in this aspect.