<p>Beyond graphene, two-dimensional (2D) atomic layered materials have drawn considerable attention as promising semiconductors for future ultrathin layered nano-electronic device applications, transparent/flexible devices and chemical sensors. But, they exhibit high levels of low-frequency due to interfacial scattering (small thickness) and interlayer coupling (large thickness). The sources and mechanisms of low frequency noise should be comprehensive and controlled to fulfill practical applications of two-dimensional transistors. This work seeks to understand the fundamental noise mechanisms of 2D transistors to find ways to reduce the noise level. It also verifies how noise can provide a spectroscopy for analysis of device quality.</p> <p>Most noise analysis tend to apply classical MOSFET models to the noise and electrical transport of 2D transistors, which put together all possible independent noise sources in 2D transistors, ignoring the contact effects. So this could lead to wrong estimation of the noise analysis in 2D transistors. This work demonstrates how the noise components can come from the channel and contact/access regions, all independently adding to the total noise. Each noise source can contribute and may dominate the total noise behavior under the specific gate voltage bias. Herein, the measured noise amplitude in our MoS₂ and MoSe₂ FETs shows a direct crossover from channel- to contact-dominated noise as the gate voltage is increased. The results can be interpreted in terms of a Hooge relationship associated with the channel noise, a transition region, and a saturated high-gate voltage regime whose characteristics are determined by a voltage-independent conductance and noise source associated with the metallurgical contact and the interlayer resistance. The approach for separating channel contributions from those contact/access region allows clear evaluation of the channel noise mechanism and also can be used to explain the qualitative differences in the transition regions between contact- and channel-dominated regimes for various devices.</p>