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Controlling thermal stress is a promising way to reduce the temperature instability of arrayed waveguide gratings (AWGs). A simple method to apply thermal stress is to attach stress plates on the arrayed waveguides. In this paper, a general analytical method to study the temperature sensitivity of the central wavelength in modified AWGs with stress plates is developed. The complete analysis shows that the temperature sensitivity can be controlled effectively by tuning the material parameters and the thickness of the stress plates. To obtain athermal AWGs, a stress plate with large positive thermal expansion coefficient and small Young's modulus should be attached on the bottom of the arrayed waveguides. The material with large negative thermal expansion coefficient suggests another potential scheme.