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

The three-phonon scattering relaxation rates and their temperature exponents have been analysed in the frame of Guthrie's classification of the phonon-phonon scattering events as class I and class II events and as a result of this, a new expressionτ _3ph ^-1 =(B _N,I+B _U,Ie^-θ/αT) g(w)T ^m I ^(T)+(B _N,II+B _U,IIe^-θ/αT)g(w)T ^mII^(T) for the three phonon scattering relaxation rates has been proposed for the first time to calculate the lattice thermal conductivity of a sample. Using the expression proposed above, the lattice thermal conductivity of Ge has been analysed in the temperature range 2–1000K and result obtained shows a very good agreement with the experimental data. The percentage contributions due to three-phonon normal and umklapp processes are also reported. The role of four phonon processes is also included at high temperatures. To estimate an approximate value of the scattering strength and the phonon conductivity, the analytical expression is also obtained in the frame of the expression proposed above forτ _3ph ^-1 .