When the junction between a metal and a behaves the same whichever metal is used. The choice of metal ought to set the height of the energy step electrons must climb to get into the semiconductor, but stray electron states at the interface take up charge and hold the step at much the same height every time. It makes low-resistance contacts hard to engineer.
Going deeper
In an ideal contact the barrier height would follow the metal’s work function. In practice, interface states fix the Fermi level near one position, so swapping the metal changes the barrier very little – the measured slope for monolayer MoS2 is about 0.1 instead of 1.
What should happen, and what does
The Schottky–Mott rule predicts that the barrier between a metal and an semiconductor equals the metal work function minus the semiconductor’s electron affinity. Plotting measured barriers against work function should then give a line of slope one.
Real contacts give much less. The slope, called the pinning factor S, is a measure of how much freedom is left: S = 1 is the ideal, S near 0 means the barrier is fixed whatever metal is used. Measurements on MoS2 and MoTe2 gave S of about 0.11 and −0.07 – strong pinning, and barriers lower than simple theory predicts.
Where the pinning comes from
Two sources dominate. The first is intrinsic: the wavefunctions of the metal decay into the semiconductor’s gap, creating that can absorb charge and hold the near a characteristic energy. The second is extrinsic: the energetic metal atoms that arrive during evaporation damage a monolayer, creating , chemical reactions and right at the interface, which add their own states.
Atomically thin semiconductors are especially vulnerable, because there is no bulk underneath to buffer the damage: the damaged region is the whole channel. This is one reason the same material gives spread over orders of magnitude between laboratories.
Getting around it
The cleanest demonstration is to avoid depositing the metal at all. Metal films peeled from a growth and onto a monolayer make a contact with no and no damage – and with those, the Schottky–Mott behaviour is largely restored, with barriers that follow the metal’s work function.
Other routes soften the problem rather than remove it: that do not induce strong gap states, insulating buffer layers a few ångström thick that decouple the metal, phase-engineered or heavily doped contact regions, and edge contacts. Each has costs in resistance, scalability or complexity, and none is yet a manufacturable answer – which is why contacts remain the acknowledged bottleneck for 2D .
For specialists
The fixing of the Fermi level at a metal–semiconductor interface by interface states, so the Schottky barrier barely depends on the metal work function.