An in-depth analysis of valley physics in 2D materials like transition metal dichalcogenides requires the measurement of many material properties as a function of Fermi level position within the electronic band structure. This is normally done by changing the charge carrier density of the 2D material via the gate electric field effect. Here, we show that a comparison of gate-dependent measurements, which were acquired under different measurement conditions can encounter significant problems due to the temporal evolution of the charging of trap states inside the dielectric layer or at its interfaces. The impact of, e.g., the gate sweep direction and the sweep rate on the overall gate dependence gets especially prominent in optical measurements due to photo-excitation of donor and acceptor states. Under such conditions the same nominal gate-voltage may lead to different gate-induced charge carrier densities and, hence, Fermi level positions. We demonstrate that a current flow from or even through the dielectric layer via leakage currents can significantly diminish the gate tunability in optical measurements of 2D materials.
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