Short gamma-ray bursts (SGRBs) with extended emission (EE) are composed of initial main emission (ME) with a short hard spike, followed by a long-lasting EE. Whether the ME and EE originated from the same origin or not, as well as the jet composition, remains an open question. In this paper, we present a systematic analysis of 36 gamma-ray bursts (GRBs) in our sample, which are identified as the category of SGRBs with EE as observed by Fermi/Gamma-ray Burst Monitor. By extracting time-integrated spectra of ME and EE with cutoff power-law or Band models for our sample, we find that 20 out of 36 SGRBs have α values that exceed the death line (e.g., −2/3) of synchrotron emission within either ME or EE phases, and we suggest that the quasi-thermal component should exist in the prompt emission. Then, we extract the time-resolved spectra of our samples, but only four GRBs are bright enough to extract the time-resolved spectra. We find that both thermal and nonthermal emissions do exist in the prompt emission of those four bright GRBs, which suggests that a hybrid jet (e.g., matter and Poynting-flux outflow) in GRBs should exist. Moreover, strong positive correlations (e.g., F tot–Γ and F tot–kT) in the time-resolved spectra of ME and EE for those four GRBs have been discovered. This indicates that the spectral evolution of both ME and EE seem to share similar behavior, possibly from the same physical origin.
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