Abstract
Exact closed-form expressions have been derived for the stresses and the electric fields induced in piezoelectric multilayers deposited on a substrate with lattice misfit and thermal expansion coefficient mismatch. The derived formulations can model any number of layers using recursive relations that minimize the computation time. A proper rotation matrix has been utilized to generalize the expressions so that they can be used for various growth orientations with each layer having hexagonal crystal symmetry. As an example, the influence of lattice misfit and thermal expansion coefficient mismatch on the state of electroelastic fields in different layers of GaN multi quantum wells has been examined. A comparison with the finite element analysis results showed very close agreement. The analytical expressions developed herein will be useful in designing optoelectronic devices as well as in predicting defect density in multi quantum wells.
Highlights
Piezoelectric multilayers are widely used in high performance sensors, actuators and electronic devices
The closed-form expressions derived is capable of evaluating the electroelastic fields in each layer having various growth orientations
To validate the analytical results, multi quantum well layers with c, a- and m-growth orientations were modeled by the commercial finite element analysis code ABAQUS 6.14
Summary
Piezoelectric multilayers are widely used in high performance sensors, actuators and electronic devices. There are some other works available in the literature on multilayer thin films deposited on a substrate which are subjected to non-uniform misfit strains and non-uniform temperatures derived by modifying the original Stoney formula to evaluate stresses and curvature in each layer.[7,8] Hsueh et al provided analytical formulations for thermal stresses in joining two layers with multi and graded interlayers.[9] Recently, Gao et al developed an elastic multilayer model in evaluating the thermal stress distribution in a multilayer coating by defining the reference plane at the neutral axis when the multilayer system is subjected to bending only.[10] This model avoids solving simultaneous equations as it calculates the total curvature and the inplane reference strains in place of calculating these parameters for individual layer This can greatly reduce the computation time and complications in the calculations. The influence of thermal expansion coefficient and lattice mismatches on the electroelastic fields are examined along with the effects of piezoelectricity in different growth orientations
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