Elastodynamic response of photothermoelastic plate with moisture due to various sources

This current study examines how carrier density and moisture sources cause deformation in an isotropic photothermoelastic moisture plate. We develop simplified two-dimensional equations describing the interaction of heat, moisture, and charge carriers within the material. These equations are expressed in a dimensionless form and solved analytically using Laplace and Fourier transformations to obtain the main field quantities—displacement, stress, temperature, carrier density, and moisture distribution. The theoretical results are validated for silicon material and illustrated graphically. The analysis demonstrates that both carrier density and moisture significantly affect the stress, temperature, and carrier concentration within the plate. Moisture tends to stabilize stress variations and reduce temperature fluctuations, while relaxation times strongly influence oscillation patterns in all field quantities. These results underscore the integrated role of thermal, moisture, and photoelastic effects in shaping the mechanical behavior of semiconducting materials. The proposed model aids in analyzing coupled thermoelastic, moisture, and carrier effects in semiconductors, offering improved prediction of transient responses essential for enhancing thermal stability and reliability in electronic and photonic devices.