Frequency and bias dependent modeling of induced gate noise and cross-correlation noise in 40 nm metal-oxide-semiconductor field-effect transistors

With the development of down-scaling of CMOS technology for low power, mixed-signal, and high frequency applications, the optimal high frequency performance is shown to be shifted from lower moderate inversion toward weak inversion regimes. High-frequency noise model is a prerequisite for designing the radio frequency and millimeter-wave circuits, and is essential for the noise analysis of nanoscale metal-oxide-semiconductor field-effect transistors (MOSFETs). In this paper, based on the physical structure of 40 nm MOSFET and by considering the drift-diffusion equation and charge conservation law, accurate physics-based unified high-frequency noise model is developed for induced gatecurrent noise and its cross-correlation with drain-current noise under different bias conditions, which is used to describe the frequency and bias dependence of 40 nm MOSFET from weak inversion to strong inversion regime. Especially, the effective gate overdrive is explicitly included in unified noise model to offer excellent accuracy, continuity and smoothness, and this makes the proposed analytical models convenient to directly reflect the relationship between the noise model and bias condition. Besides, new analytical model is derived for the induced-gate current noise and its cross-correlation term of weakly inverted MOSFET. These simple expressions not only serve as the asymptotic limit for the validation of the proposed physics-based unified model, but also provide a clearer insight into and better understanding of the gate noise behavior and their cross-correlation in the weak-inversion region. Moreover, in terms of the proposed subthreshold noise model, the charge of weak inversion rather than the normal effective channel thickness approximation is involved. In this way, the model accuracy can be improved. Furthermore, a detailed derivation and discussion are presented by analyzing the physics-based noise generation mechanism of transistor including the channel thermal noise and the shot noise based on the small-signal equivalent circuit of the 40 nm MOSFET device. Using these expressions it is possible to extract the values of all the noise model parameters directly from measurement. The proposed model is demonstrated by using noise data from both measurement and the noise simulation. Excellent agreement between simulated and measured noise data shows that the proposed model can be used for predicting the noise behavior of 40 nm MOSFET under different dimensions and operating conditions. The applicability of reported model for drain-current noise is also verified. As far as small-signal (i.e., linear) bias-dependent operation is concerned, it is shown how most of the findings of this work can also be used to predict the data of long channel devices in the strong-inversion regimes.