A simple formula for calculating the carrier relaxation time

An empirical formula to calculate the carrier relaxation time as a function of temperature (τT) has been presented. The method mainly depends on the Seebeck coefficient and the temperature. The formula was tested on metals and several types of semiconductors (Clathrate, Half Heusler Alloy, Zintl phases…). The obtained values are in good agreement with the available experimental results, especially in poor metals and heavily doped semiconductors at low temperatures especially room temperature. On the other hand, the calculated values of electrical conductivity σ(T) and electronic thermal conductivity ke(T) under the constant relaxation time approximation (CRTA) are given as fractions (σ/τorke/τ). Treating τ as an empirical parameter (τ=cte) by fitting to one value at a specific carrier concentration is a common method utilized by researchers. However, it cannot explain the behaviour of conductivity as temperature rises. Whereas, in this case, using our formula is useful to investigate σ(T) and the obtained curves show a similar behaviour to the experimental ones when the temperature increases.