  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.
