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 3σ 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.%针对基于经典动力学理论传统模型中忽略扩散效应的问题,通过对基于玻尔兹曼理论的场效应管传输线模型的理论分析,建立了包含扩散效应的太赫兹互补金属氧化物半导体(CMOS)场效应管探测器理论模型,研究扩散效应对场效应管电导及响应度的影响.同时,将此模型与忽略了扩散效应的传统模型进行了对比仿真模拟,给出了两种模型下的电流响应度随温度及频率变化的差别.依据仿真结果,并结合3σ 原则明确了场效应管传输线模型中扩散部分省略的依据和条件.研究结果表明:扩散部分引起的响应度差异大小主要由场效应管的工作温度及工作频率决定.其中工作频率起主要作用,温度变化对差异大小影响较为微弱;而对于工作频率而言,当场效应管工作频率小于1 THz时,模型中的扩散部分可以忽略不计;而当工作频率大于1 THz时,扩散部分不可省略,此时场效应管模型需同时包含漂移、散射及扩散三个物理过程.本文的研究结果为太赫兹CMOS场效应管理论模型的精确建立及模拟提供了理论支持.
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