In this paper, we discuss the diffusion motion of carriers in the transistor channel in a terahertz frequency range, and propose an resistance-capacitance-inductance (RCL) model based on Boltzmann transport theory, and then put forward the rules to determine whether the diffusion part in the RCL model can be neglected for terahertz field-effect-transistor (FET) detectors. The traditional RCL model for FET detectors is based on classic kinetic theory. In this model only the drift and the scattering motion of the carrier density in transistor channel are considered, and the diffusion part is neglected without giving any explanation. To solve this problem, in this paper we adopt three steps: first, instead of classic kinetic theory, the equations of RCL transistor model including diffusion part are derived from Boltzmann transport equation, and by comparing the two models, the specific expression for the diffusion part is given. Second, the differences between the two models are calculated and simulated, including the conductivity in quasi-static mode and the current response in high frequency mode, with different gate voltages, temperatures and working frequencies. Third, combined with the 3 rules, the conditions to neglect the diffusion motion in the model are put forward. The results show that the diffusion motion of the carriers is caused by the inhomogeneity of the carrier density, affected by the gate voltage, the temperature and the changing speed of the carriers with respect to the local voltage. In quasi-static mode, the role of diffusion part will change with the gate voltage, and when the gate voltage equals threshold voltage (which is the best working point for transistor detector), the diffusion part cannot be neglected, for which the reason is that a larger gate voltage will lead to a smaller inhomogeneity of channel carrier density and then a weaker diffusion effect, thus the effect of diffusion conductance on the whole transistor conductance becomes smaller. For the terahertz-frequency working mode, the diffusion part will depend on temperature and frequency. With temperature increasing, the current responsivity difference caused by the diffusion part in the model slightly decreases; when the working frequency increases but below 1 THz, the diffusion part can be neglected; however, when the working frequency is above 1 THz, the transistor model should contain drift, scattering and diffusion part at the same time, for which the explanation is that when the temperature increases, the random thermal motion of the carrier becomes larger, thus the diffusion effect will be stronger; and if the frequency increases, the number of the carriers in one terminal of the channel will change faster, but due to the channel damping, the number of the carriers in another terminal will always be zero, thus the changing speed of the carrier density between the two terminals will be faster, then a larger inhomogeneity of carrier density and a stronger diffusion effect will appear. In conclusion, normally the transisitor works at the threshold gate voltage, and at this point, the diffusion effect in the channel will increase with working temperature and frequency increasing, thus the diffusion part in the model cannot be neglected. The results in this paper make a significant contribution to a more accurate terahertz transistor detector model.