A new model for thermally induced redistributions of free carriers in centrosymmetric flexoelectric semiconductor beams

A new model is developed for thermally induced redistributions of free carriers in flexoelectric semiconductor beams using a thermoflexotronic theory. This theory, which accounts for flexotronic, strain gradient and temperature effects, is first proposed using the theory of flexoelectric semiconductors, thermoelasticity and strain gradient elasticity. The new beam model is then formulated by applying the thermoflexotronic theory and Bernoulli-Euler kinematic relations, which simultaneously incorporates the flexoelectric, temperature and semiconducting effects and provides all the governing equations and boundary conditions, unlike existing models. To illustrate the new model, the concentration perturbation in a simply supported beam induced by temperature changes in the transverse and axial directions respectively is analytically determined. For the former, the deformed shape and redistribution of free carriers in the beam are analytically obtained and graphically displayed, and the charge accumulation formula capturing the thermoflexotronic effect is analytically derived. For the latter, the axial displacement, electric potential and concentration perturbation of free carriers are analytically determined and graphically illustrated. It reveals that the distribution of the electric potential and redistribution of free carriers can be tailored by controlling the mode and amplitude of the prescribed temperature change.