A new method is proposed to distinguish the contributions of the low-frequency noise (LFN) from the channel and the source/drain Schottky contacts in MOS devices. The method is applied to back-gated nMOSFETs with MoS2 channel and Al2O3 gate dielectric. To avoid a possible noise signal contamination from the top MoS2 surface by oxygen or water molecules absorption, the nMOSFETs with multilayer MoS2 are fabricated, and the measurements are carried out in the vacuum. The trap density Not at the MoS2/Al2O3 interface is derived for the first time using the proposed method. It is found that the Not responsible to LFN depends strongly on the surface potential, ranging from $4\times 10^{10}$ cm $^{\mathrm {-2}}$ in the weak over-drive region to $5\times 10^{11}$ cm $^{\mathrm {-2}}$ in the strong over-drive region.