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We describe our design and fabrication of a low-loss and compact 1.5%-Delta silica-based athermal arrayed waveguide grating (AWG) using a resin-filled groove. We present the theory of athermal AWG design and clarify the relationship between the AWG design parameters and the groove design required for realizing an athermal condition. We also describe approaches for reducing excess loss in the groove, which are used to optimize the groove and arrayed waveguide designs. We examine the performance of a 40-channel 100 GHz spacing athermal AWG module that employs all of the approaches. We successfully reduce the excess loss in the groove to 0.2 dB and achieve a compact chip size of 31times23 mm2 as well as sufficient optical performance and temperature insensitivity for practical use. In addition, we confirm by calculation that our approaches for excess loss reduction are also effective for an athermal AWG with a channel spacing of less than 100 GHz.