A Method of Extracting Metal-Gate High- $k$ Material Parameters Featuring Electron Gate Tunneling Current Transition

For metal-gate high-k dielectrics, there is a transition region in the electron gate tunneling current I_g, as characterized by a plot of dlnI_g/dV_g versus V_g. In this paper, we systematically construct a new fitting over the region, which can accurately determine material parameters, including metal work function, high- k electron affinity, and tunneling effective masses of electrons. First of all, a calculation of gate current due to electron direct tunneling and/or Fowler-Nordheim tunneling from an inversion layer is performed, yielding the guidelines of the fitting. Experimental samples are presented with n-channel metal-oxide-semiconductor field-effect transistors having low effective oxide thickness (1.4 nm) TaC/HfSiON/SiON gate stacks. Underlying material parameters are extracted accordingly and remain valid for higher temperature and gate voltage. We also demonstrate that a conventional method without a dlnI_g/dV_g fitting might lead to erroneous results. Thus, the dlnI_g/dV_g fitting is crucial to metal-gate high-k material parameter assessment.