Analysis of lattice thermal conductivity of GaAs at high temperatures

Abstract

The lattice thermal conductivity of GaAs has been analysed in the entire temperature range 100--800 K in the frame of the Sharma--Dubey--Verma (SDV) model of phonon conductivity, and very good agreement has been found between the calculated and experimental values of the lattice thermal conductivity in the entire temperature range of study. The temperature exponent m(T) for the three-phonon scattering relaxation rate for GaAs has also been calculated in the above temperature range. The separate percentage contributions due to transverse and longitudinal phonons have also been studied.It is now well established that in several semiconductors there occurs a change in the slope of the K (lattice thermal conductivity) vs. T (temperature) curve in the high-temperature region, and the experimental data of phonon conductivity can not be explained by one conductivity integral as given by Callaway [1 ]. The well-known samples are Si [2] and Ge [2]. It was Holland [2] who first introduced the two-mode conduction of phonons to explain the high-temperature data of the lattice thermal conductivities of Si and Ge. Later, the author and his co-workers [3][4][5] proposed a modification of the Holland model, using the Guthrie [6,7] ideas, and this is known as the Sharma-Dubey-Verma (SDV) model [3][4][5] in which the phonon-phonon scattering events are classified into two groups: the class I events, in which a carrier phonon is annihilated by combination, and class II, in which the annihilation takes place by splitting.The phonon conductivity of GaAs has been studied experimentally as well as theoretically by several workers [4,[8][9][10]. However, their studies are limited up to room temperature, i.e. up to 300 K only. Recently, Hunt [11 ] measured the thermal conductivity of GaAs in the temperature range 305-735 K. In the present work, our aim was to analyse the measurements of Hunt by calculating the lattice thermal conductivity of GaAs in the temperature range 100-800 K in the frame of the SDV model. To do so, the temperature exponent re(T) for the three-phonon scattering relaxation rate was calculated in the entire temperature range 100-800 K. To Study the relative contributions of each mode of the phonons, the separate percentage contributions due to transverse and to longitudinal phonons were also calculated in the entire temperature range of study and it was found that in the entire temperature range 100-800 K the percentage contribution 3". Thermal Anal. 14, 1978

Analysis of lattice thermal conductivity and phonon-phonon scattering relaxation rate: Application to Ge

“…Following Guthrie, the three-phonon scattering relaxation rate t~lh can be expressed as t:~h = %~h(ClaSS I) + z3~(class II) (1) He also pointed out that the three-phonon scattering relaxation rate due to each class of events could be expressed as z~ h oc g(w)f(T) (2) wheref(T) = T re(T) and m(T) is a continuous function of temperature T. Verma et al [9,10,[23][24][25] were the first who attempted to incorporate the Guthrie expression to calculate the phonon conductivity of some insulators, by expressing the three-phonon scattering relaxation rate as…”

“…Callaway [5 ] Holland [6] Joshi and Verma [11 ] SDV model [9,10,23] Dubey and Misho [12] Present work …”

“…[23], where r is a constant and depends on the dispersion curve of the sample under study. The constant r can be calculated with the help of the dispersion curve.…”

Analysis of lattice thermal conductivities of rare-earth sulphides at high temperatures

“…Following the earlier work of the author [8,9] and using the analytical expressions reported in the earlier section, the three-phonon scattering strengths BT, I, BE, t, and BL, H have been determined at 500 K, while the four-phonon scattering strengths BHr and BHL are estimated at 700 K. The point-defect scattering strength A has been taken from the earlier report of Edani and Dubey [32]. The constants and parameters used in the present analysis of the lattice thermal conductivity of GdS are listed in Table 1.…”

“…Following the earlier work of the author [8], the lattice thermal conductivity of GdS has been separated by subtracting the electronic part of the thermal conductivity from the total thermal conductivity measured by Khusnutdinova et al [19].…”