Investigation of the Correlation Between Temperature and Enhancement of Electron Tunneling Current Through $\hbox{HfO}_{\bf 2}$ Gate Stacks

A model is established to describe the temperature dependence of the electron tunneling current through HfO
₂
gate stacks based on analyzing the coupling between the longitudinal and transverse components of electron thermal energy caused by the difference of the effective electron mass between the HfO
₂
gate stacks and silicon. By analyzing the three-dimensional Schrodinger equation for a MOS structure with HfO
₂
gate stacks, a reduction in the barrier height is resulted from the large effective electron mass mismatch between the gate oxide and the gate (substrate). The calculated electron tunneling currents agree well with the experimental data over a wide temperature range. This coupling model can explain the temperature dependence of the electron tunneling current through HfO
₂
gate stacks very well. The numerical results also demonstrate that the temperature dependence of the electron tunneling current strongly depends on the effective electron mass of HfO
₂
. This temperature sensitivity of the electron tunneling current can be proposed as a novel method to determine the effective electron mass of the gate oxide.