Nonlocal transient photo-thermoelastic responses of semiconductors based on a mixed spatio-temporal three-phase-lag model with two-parameter Mittag-Leffler kernel function

The extensive applications of ultra-fast heating technology (e.g., laser etching, etc.) in the manufacturing/processing of semiconductor device give rise to the multi-physics coupling mechanisms exploration and transient thermal shock predictions, of which the evident spatial-temporal nonlocal effects and thermal lagging behavior (i.e., heat flux, temperature gradient and thermal displacement gradient) in such spatio-temporal micro/nano-scale. To address the deficiencies, the present work aims to establish a new carrier-photo-thermo-mechanical model of semiconducting solids based on a new mixed space-temporal nonlocal three-phase-lag heat conduction model with Goufo-Caputo two-parameter Mittag-Leffler kernel function via higher-order Taylor expansions. The proposed model is applied to investigate the nonlocal thermal-carrier-elastic dynamic response of 1D semiconducting thin strip subjected to transient thermal shock via the Laplace transformation technique. Dimensionless results reveal that the Goufo-Caputo two-parameter fractional derivative exert opposite effects: the heat-flux-related fractional parameter increases the peak values of temperature, carrier concentration, displacement, and stress, whereas the temperature-gradient-related fractional parameter reduces these peak values and accelerates the relaxation process. In addition, reducing the spatial nonlocal parameter leads to lower peak values of temperature, carrier concentration, displacement, and stress.