Gravitational wave detectors are observing an increasing number of binary black hole (BBH) mergers, revealing a bimodal mass distribution of BBHs, which hints at diverse formation histories for these systems. Using the rapid binary population synthesis code mobse, we simulate a series of population synthesis models that include chemically homogeneous evolution (CHE). By considering metallicity-specific star formation and selection effects, we compare the intrinsic merger rates and detection rates of each model with observations. We find that the observed peaks in the mass distribution of merging BBHs at the low-mass end ($10M_{\odot }$) and the high-mass end ($35M_{\odot }$) are contributed by the common envelope channel or stable mass transfer channel (depending on the stability criteria for mass transfer) and the CHE channel, respectively, in our model. The merger rates and detection rates predicted by our model exhibit significant sensitivity to the choice of physical parameters. Different models predict merger rates ranging from 15.4 to $96.7{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$ at redshift $z=0.2$, and detection rates ranging from 22.2 to $148.3{\mathrm{yr}}^{-1}$ under the assumption of a detectable redshift range of $z\le 1.0$.

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• Gravitational wave sources