6.1 McWhorter Model

In the middle of the last century, McWhorter [182] dealt with the spectrum of 1∕f  -noise observed at germanium-oxide interfaces. This kind of noise is attributed to fluctuations in the trap occupancy ft  due to charge carriers tunneling forth and back between the bulk and the defects. McWhorter described these fluctuations using a simple SRH-based model, which can be considered as a prototype for other charge trapping models. His model extends the conventional SRH theory by the effect of charge carrier tunneling, which is accounted for by the factor exp(xt∕xp,0)  . Thus, the simplified time constants read as

                 (    )
τ      = τSRH exp  xt--  Nv-,                        (6.1)
 cap,h     p,0       xp,0   p
          SRH    ( xt )
 τem,h  = τp,0  exp  xp,0- exp(βΔEt ) exp(- βq0Foxxt) . (6.2)
The model presumes that all traps are energetically located within the substrate bandgap so that none of them will be found below E
 v  . Furthermore, they are assumed to be spatially distributed over the entire dielectric.

In the following, the McWhorter model will be evaluated against the findings of the TDDS experiments (see Section 1.3.4).

The term exp(xt∕xp,0)  in τcap,h  and τem,h  accounts for the trap depth dependence of tunneling and leads to an upwards shift of the entire τcap,h  and τem,h  curves with an increasing trap depth xt  . Due to the wide distribution of xt  , the McWhorter model allows a wide range of capture and emission times in thick oxides. In modern device technologies, however, the time constant of the devices with an oxide thickness of 2nm  would be limited to 1ms  after the model. As such, this model cannot explain time constants larger than 1ms  for devices with an oxide thickness of 2nm  . This is in contrast to the experimental results (cf. Fig. 1.2), in which τem,h  extends well into the kilosecond regime. In conclusion, this model cannot be reconciled with the findings of the TDDS and is thus inadequate to describe the traps involved in NBTI.