Recent observations of Type Ia supernovae (SNe Ia) have shown diversified properties of the explosion strength, light curves and chemical composition. To investigate possible origins of such diversities in SNe Ia, we have presented multi-dimensional hydrodynamical study of explosions and associated nucleosynthesis in the near Chandrasekhar mass carbon-oxygen (CO) white dwarfs (WDs) for a wide range of parameters (Leung and Nomoto 2018 ApJ). In the present paper, we extend our wide parameter survey of models to the explosions of sub-Chandrasekhar mass CO WDs. We take the double detonation model for the explosion mechanism. The model parameters of the survey include the metallicity of $Z = 0 - 5~Z_odot$, the CO WD mass of $M = 0.90 - 1.20~M_odot$, and the He envelope mass of $M_{rm He} = 0.05 - 0.20~M_odot$. We also study how the initial He detonation configuration, such as spherical, bubble, and ring shapes, triggers the C detonation. For these parameters, we derive the minimum He envelope mass necessary to trigger the C detonation. We then examine how the explosion dynamics and associated nucleosynthesis depend on these parameters, and compare our results with the previous representative models. We compare our nucleosynthesis yields with the unusual abundance patterns of Fe-peak elements and isotopes observed in SNe Ia 2011fe, 2012cg and 2014J, as well as SN Ia remnant 3C 397 to provide constraints on their progenitors and environments. We provide the nucleosynthesis yields table of the sub-Chandrasekhar mass explosions, to discuss their roles in the galactic chemical evolution and archaeology.
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