With the development of the integrated circuit manufacturing process, the device dimensions have been on a nanoscale, while the device performance, such as the mobility and thermal noise, is significantly affected by the hot-carrier effect, which further affects the channel thermal noise of the device. However, the thermal noise model based on the existing electron temperature expression does not take into account the influence of the temperature gradient on the electron temperature when it deals with the influence of the hot carrier effect. As the size of the device decreases, the thermal noise model based on the existing electron temperature expression underestimates the influence of the hot carrier effect and the channel thermal noise cannot be accurately predicted with this expression.

In this paper, the expression of the channel transverse electric field is derived based on the channel potential equation and the boundary condition of the channel electric field. By combining the distribution of the temperature gradient and the expression of the transverse electric field, the energy balance equation is solved with considering the influence of the temperature gradient, and then the electron temperature expression is obtained. The electron temperature expression shows the distribution of the electron temperature along the channel. By utilizing the derived electron temperature expression and combining with the drain current expression, a channel thermal noise model is established. The hot carrier effect is taken into account in the thermal noise model by utilizing the proposed electron temperature expression. Meanwhile in calculating the thermal noise, the influence of the electron temperature on mobility degradation and the temperature gradient on thermal noise are also involved.

The results show that the temperature gradient has a significant influence on the electron temperature with the reduction of the device size, which further increases the influence of the hot carrier effect, resulting in the increase of the thermal noise caused by the hot carrier effect exceeding the decrease of the thermal noise caused by the mobility degradation, thus leading the thermal noise to increase. The influence of the hot carrier effect on the channel thermal noise also increases significantly with the bias increasing. The channel thermal noise model proposed in this paper can be applied to analyzing the noise performance and modeling the nano-sized MOSFET devices.