Band filling and cross quantum capacitance in ion gated semiconducting transition metal dichalcogenide monolayers

Ionic liquid gated field-effect transistors based on semiconducting transition metal dichalcogenides are attracting significant scientific interest, but important aspects of how charge carriers are accumulated in these systems remain elusive. Here we present a thorough analysis of charge accumulation in MoSe₂ and WSe₂ monolayers. We identify the conditions when the chemical potential enters different valleys in the monolayer band structure (the K and Q valleys in the conduction band and the two spin-split K-valleys in the valence band) and find that an independent electron picture describes the occupation of states well. Unexpectedly, however, the same analysis shows that the total device capacitance cannot be simply described in terms of the series connection of a geometrical capacitance and of a quantum capacitance given by C_Q=e²/(dμ/dn), as commonly assumed. This unexpected behavior is attributed to the presence of a cross quantum capacitance, which originates physically from mutual screening of the electric field generated by charges on one plate from charges sitting on the other plate. Our findings therefore reveal an important contribution to the capacitance of physical systems that had been virtually neglected until now.