Thermal lagging in multi-carrier systems

Nonequilibrium heating in multi-carrier systems is captured by the high-order effects in thermal lagging. Following the general formulation for the N-carrier system, a three-carrier system follows, aiming toward extracting the intrinsic behavior of ultrafast thermalization and relaxation among different carriers. For the first time to our knowledge, it shows that energy coupling among three carriers gives rise to the new τT2-effect, which also results in a flux-precedence type of heat flow. Nondimensional analysis is made to extract the dominating parameters, including the ratio between the two phase lags expressed in terms of two heat-capacity and two energy-coupling-factor ratios. In the numerical example, the method of Laplace transform is used to solve the heat equation with nonlinear effects of both τT2 and τq2. Thermal lagging with the additional effect of τT2 further elevates the field temperature as compared to the τq2-effect alone.