In this thesis, advanced characterization tools, i.e., low-frequency noise (LFN) and AC-transconductance (AC-gm) technique were applied to FETs composed of 2D materials (2DM) to provide optimization points for future practical usage of 2D materials for channel of the FETs. Therefore, the LFN and AC-gm measurement systems were established in this works and they were used for characterizing the 2DM FETs, e.g., $MoS_2$ FETs. However, there were several obstacles to investigate the interface and bulk oxide traps of $MoS_2$ FETs. First of all, absorbed water vapors on top of $MoS_2$ channel without passivation layer were served as traps which induce large hysteresis in transfer curves. The clockwise hysteresis provoked a current drop as measurement time goes. Thus, the accurate measurement of LFN and $AC-g_m$ were not possible without proper passivation method. Specially, the oxide trap density ($N_T$) near the interface significantly increased up to 75 % after 2 days from passivation and high vacuum annealing (HVA). The increased interface trap densities $(N_{it})$ extracted from SS, hysteresis voltage, and $AC-g_m$ have similar values $(an order of 10^{12} cm^{-2})$. Furthermore, the injected water molecule density was theoretically extracted as $10^{14} cm{-2}$. Therefore, the probability that the transmitted molecules act as electrical traps is approximately 1/100. In order to prevent the deterioration of DC characteristics and increase of $N_{it}$, an appro-priate passivation method should be developed and be applied to the $MoS_2$ FETs. The passivation layer that has the lowest water vapor transmission ratio (WVTR) value of under $10^{-5} g/m^2/day$ was formed by multi-dyad (3.5 dyads) sequential stacking of inorganic film $(Al_2O_3)$ and polymer film. With the passivation layer on surface of the $MoS_2$ channel, the highly stable electrical characteristics of $MoS_2$ were demonstrated for 1 month with negli-gible hysteresis. In fact, the hysteresis-free $MoS_2$ FETs composed of bilayer $MoS_2$ (BMFET) shows an accurate LFN characteristic according to the drain current $(I_D)$ with low drain voltage condition (0.5 V). The power spectral density (PSD) of BMFET followed the $g_m^2/I_D^2$ trends according to ID modulated by gate voltage $(V_G)$. From the LFN characteristic, it can be concluded that the series resistance $(R_S)$ and dirty interface between $MoS_2$ and $SiO_2$ were origins for inferior electrical characteristics of the $MoS_2$ FETs. Meanwhile, the FETs composed of thick $MoS_2$ layers (> 7 layers) showed abnormal LFN characteristics according to $I_D$ due to the bulk traps which were not removed even by passivation process and HVA. Due to the abnormality of LFN characteristics, further inter-pretation of $MoS_2$ FETs with LFN could not possible and it is limitation of carrier number fluctuation (CNF) model of LFN. Therefore, $AC-g_m$ characterization tool was introduced and developed for further accurate and reliable characterization of $MoS_2$ FETs. Meanwhile, the hexagonal boron nitride (hBN) has been well known as a material that reduce surface roughness and lattice mismatch with 2D materials (e.g., graphene and MoS2) when it is used as an interlayer between 2D materials and SiO2 (gate insulator). In this work, the buffer layer of hBN promoted carrier mobility of MoS2 FETs attributed formerly listed reasons (reduced surface roughness and mis-match). However, it has a critical drawback as a gate insulator or interlayer of MoS2 FETs. The carrier (electron) trap/de-trap behaviors are highly generated at a Van der Waals gaps (VDWGs) that exists between single hBN layers with low frequency (~ order of 10 Hz). Therefore, it induced a virtual capacitor between gate electrode and the $MoS_2$ channel. $AC-g_m$ signal obtained from drain node shows specific signal delay due to the capacitor com-pared to input of gate voltage at gate node. Therefore, hBN layer should be re-considered as a gate insulator when $MoS_2$ FETs are pursued as electronics operated at low frequency or low-noise application.