Three‐phonon scattering relaxation rate and phonon conductivity. Application to Mg₂Ge

Abstract

The new expression T& = g ( o ) ( B N + BU e-e/aT) T" is proposed for the three-phonon scattering relaxation rate taking into consideration normal and umklapp processes. Incorporating the above expression, the phonon conductivity of Mg,Ge is calculated in the entire temperature range 4 to 1000 K and good agreement is found between calculated and experimental values of phonon conductivity of the sample in the entire temperature range of investigation. Analytical expressions are reported to calculate an approximate value of lattice thermal conductivity. The role of four-phonon processes is also included in the present study. Using the expression for TX,; proposed by Joshi and Verma and Sharma et al. the phonon conductivity of InSb and Mg2Ge is calculated to compare the results obtained using the proposed expression for the three-phonon scattering relaxation rate. Ein neuer Ausdruck TT& = g ( w ) (BN + BU e-e/aT) T*' wird fur die Relaxationsrate der Drei-Phononen-Streuung vorgeschlagen, wobei Kormal-und Umklappprozesse berucksichtigt werden. Mit dieser Formel wird die Phononenleitfahigkeit von Mg,Ge im gesamten Temperaturbereich von 4 bis 1000 K berechnet und gute Ubereinstimmung zwischen den berechneten und den experimentellen Werten der Phononenleitfahigkeit der Probe im gesamten untersuchten Temperaturbereich gefunden. Analytische Ausdrucke werden angegeben, um einen Kaherungswert der Warmeleitung des Gitters zu berechnen. Die Rolle der Vierphononenprozesse wird ebenfalls in die Untersuchung einbezogen. Mit dem von Joshi und Verma und Sharma et al. vorgeschlagenen Ausdruck ~y:~ wird die Phononenleitfahigkeit von InSb und Mg,Ge berechnet, um die Ergebnisse, die mit dem vorgeschlagenen Ausdruck fur die Relaxationsrate der Drei-Phononen-Streuung erhalten werden, zu vergleichen.

Phonon conductivity of InSb and GaAs

“…But none of them has included the contributions of both processes K-and U-processes in the expression of the combined scattering relaxation rate ( Table 2 k, is the Boltzniann constant, h the Planck constant divided by 2z, T and L are suffixes refer to transverse and longitudinal phonons, respectively. The complete expression for z& used in the present study has been reported in Table 1 [15]. Thus in the present study also only one adjustable parameter has been used for the three-phonon scattering strength similar to previous workers.…”

“…From Table 1 of [15], it is clear that the expression for z& used by Callaway [5] is valid for longitudinal phonons only. Truly speaking, Callaway did not make any distinction between transverse and longitudinal phonons.…”

“…As stated in Section 1, it is difficult to express z& by a simple relation due to the strong temperature dependence of the phonon distribution function and the complex structure of the Brillouin zone. Phonon conductivity of the different samples has been calculated by several workers [ 19 to 281 by expressing z& (both N-as well as U-processes) by simple relations as function of phonon frequency w and temperature T (Table 1 of [15]). But none of them has included the contributions of both processes K-and U-processes in the expression of the combined scattering relaxation rate ( Table 2 k, is the Boltzniann constant, h the Planck constant divided by 2z, T and L are suffixes refer to transverse and longitudinal phonons, respectively.…”

“…A good number of workers [4 to 141 have calculated phonon conductivity of different samples by expressing the three phonon scattering processes (both N-as well as U-processes) by simple relations ( to calculate phonon conductivity of insulators (terms are defined in Section 2 ) . I n the present work, our aim is to study phonon conductivity of InSb and GaAs in the temperature ranges 2 to 300 K and 2 to 800 K, respectively, in the frame of the expression for z& proposed by Dubey and Misho [15]. The reduced contributions due to transverse and longitudinal phonons are studied in the entire temperature range of study and it is found that the transverse phonons are major heat carriers.…”

Role of point-defect scattering in the lattice thermal conductivity of an insulator: Application to GaAs

“…GaAs is taken as ma example mad its lattice thermal eonduc-4* .Acta Physir A~miae Sr II~~'ir 46 1979 tivity has been calculated in the entire temperature range 4--100 K for the different values of "p". Following D(mEY and MIsmo [7,8] the phonon conductivity of ma insulator can be expressed as…”