  Thicknesses-dependent performance of metal-two-dimensional (2D) semiconductor
junctions (MSJ) in electronics/optoelectronics have attracted increasing
attention, but till present, people have little knowledge about the
micro-mechanism of the thicknesses (or layer-number) dependence. Here, by
first-principles calculations based on density functional theory, we show that
the Fermi-level pinning (FLP) factor of MSJ depends sensitively on the
layer-number of few-layer 2D semiconductors, and, an extended FLP theory is
proposed for metal-2D multilayered semiconductor junctions (MmSJ). Taking
multilayered MoS2 as a typical example for van der Waals (vdW) semiconductor in
MmSJ, the extended FLP theory has the following character: strong pinning right
at the metal-1st-layer semiconductor interface while depinning occurs between
MoS2 layers. This depinning effect between vdW layers has several important
consequences: 1) the overall pinning in MmSJ is greatly weakened; 2) p-type
contact, rarely obtained in metal-monolayer MoS2 junctions, becomes favored in
MmSJ, which is important for CMOS logical devices; 3) depinning between MoS2
layers result in type II band alignment in MoS2 'homojunction' supported on
metals, which is useful for optoelectronics. Moreover, our extended FLP theory
sheds light on the recent controversial experimental observation and paves a
new and universal route to type II band alignment in vdW 'homojunctions'.
