3.3.1 Rigorous Analysis of the Complete Characteristics Charge-Pumping Current versus Gate Top Level



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3.3.1 Rigorous Analysis of the Complete Characteristics Charge-Pumping Current versus Gate Top Level

 

We consider the trapezoidal gate pulse shown in Figure 3.2. The gate top level is variable, whereas the gate bottom level can be either fixed or variable. Let us assume that the bottom level is low sufficiently to fill all interface traps by holes during . The traps are assumed to be located without the junctions to escape the effect of the spatial variations of the charge-pumping threshold and flat-band voltages; the problem is considered in one dimension, perpendicular to the interface. We adopted that the electron surface concentration (in -channel MOSFET) follows instantaneously the surface potential variations during rising edges and falling edges of the gate pulses. Three processes occur at the top level of duration : electron emission with the time constant , electron capture with and hole emission with . The hole capture during the top level may be neglected if the top level lies sufficiently high so that the hole surface concentration is very small (if holds for the hole quasi-Fermi level at the top level). Let us assume rectangular pulses for the moment; and are very short so that the processes occurring during the pulse edges can be neglected. All traps filled by electrons on the top level are recombined by holes at the bottom level. Only those traps which are filled by capturing electrons from the conduction band are active in producing the charge-pumping current. The initial conditions at the beginning of the rising edge are given by the steady-state occupancy function corresponding to the bottom level . At the beginning of the top level the electron capture into traps occurs, obeying equation 3.34

 

with the total time constant , for each individual level with density . Since all time constants , and are constant during (if the charge-potential feedback effect is neglected) the general solution of 3.47 is

 

is the steady-state occupancy function connected with the electron Fermi level at the gate top level . Defining the change in the trap occupancy at the end of the top level by the charge-pumping current is given by

 

if the hole emission is negligible during . is the active charge-pumping area and is the gate pulse frequency. The charge-pumping current given by 3.49 may be considered as the theoretically maximal current . It follows

 

The actual is smaller than due to the hole emission at the top level and the electron and hole emission at the pulse edges. These processes are considered in more detail in the following.

Rather that developing a general theory like this in [49], which yields a complex system of implicit equations, we shall present a phenomenological description, yet accurate sufficiently in most of practical applications. In our approach the band gap is divided into characteristic regions for each time interval of the gate pulse. Individual regions are associated with only one dominant generation-recombination process.





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Martin Stiftinger
Sat Oct 15 22:05:10 MET 1994