Current-Voltage Characteristics of MOS Gate Oxides
An ideal gate insulator does not conduct any current, but for real insulators there can be some leakage current which varies with the voltage or electric field across the gate oxide.
Current - Voltage Characterstics:
- By looking at the band diagram of the MOS system perpendicular to the oxide-silicon interface, we see that for electrons in the conduction band, there is a barrier, ΔEC (= 3.1 eV).
- Although electrons with energy less than this barrier cannot go through the oxide classically, electrons can tunnel through a barrier, especially if the barrier thickness is sufficiently small.
The detailed calculation of the Fowler-Nordheim tunneling current for electrons going from the Si conduction band to the conduction band of Si02, and then having the electrons "hop" along in the oxide to the gate electrode, involves solving the Schrodinger equation for the electron wave function.
The Fowler-Nordheim tunneling current IFN can be expressed as a function of the electric field in the gate oxide:
where B is a constant depending on m* and the barrier height.
- As gate oxides are made thinner in successive generations of MOSFETs, the tunneling barrier in the gate oxide becomes so thin that the electrons in the conduction band of Si can tunnel through the gate oxide and emerge in the gate, without having to go via the conduction band of the gate oxide. This is known as direct tunneling rather than Fowler-Nordheim tunneling.
- The overall physics is similar, but some of the details are different. For instance, Fowler-Nordheim tunneling involves a triangular barrier, while direct tunneling is through a trapezoidal barrier that is shown in figure. Such tunneling currents are becoming a major problem in modern devices because the useful feature of high input impedance for MOS devices is degraded.