G.1 Interface Trap Spatial Distribution



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G.1 Interface Trap Spatial Distribution

The expression will be derived for method II discussed in the main text. In this method the trapezoidal pulses with all parameters fixed are applied on the gate, while the drain-bulk reverse bias is changed. Drain and source are connected together. Let us assume that:

The charge-pumping current is given by

 

The capture cross-sections occurring as and in the expressions for the emission levels are assumed to be spatially constant. Differentiating G.1 with respect to the reverse bias it follows without any simplification

 

The factors can be approximated as follows:

 

From the relationship between the emission times and the emission levels, 3.66 and 3.81, one obtains

 

Differentiating the expressions for the emission times in the trapezoidal wave-form charge-pumping technique (3.77) it follows

 

where and are the charge-pumping threshold and flat-band voltage which determine the start and the end of the non-steady-state electron emission. and are the corresponding levels for the non-steady-state hole emission. It may be adopted that and are nearly equal to each other when and are comparable, finally resulting in

 

Employing G.6, relationship G.2 can be simplified. In the following, special cases are discussed.

Symmetrical case (virgin devices):

We assume that

 

holds. After replacing G.7 in G.2, with benefit of G.6, it follows

 

Several aspects deserve attention here:

For the purpose of model-evaluation, the parasitic term which contains can be calculated in different ways. Since the dominant contribution to this factor comes from the channel region and less from the junctions, we can evaluate this term in the channel region and apply it for the interface in complete. In order to calculate this factor we further assume that the traps are uniformly distributed in the channel (they can vary in the junctions). Approaches we analyzed are listed:

Whether the latter method based on two devices with different channel lengths can be exploited in measurements is quite questionable, because also devices laying close to each other on the same wafer differ in the distributions. Experimental work is necessary here. Nevertheless, using all the methods noted above we have evaluated the parasitic term and have shown that expression G.8 provides correct results. Therefore, no additional undesired effects occur in this kind of charge-pumping experiment.
In fact, it is not important in practice to estimate this parasitic term. A much better approach is the use of charge-pumping techniques in which this term vanishes, as discussed in the main text.

Note that in the investigation in Section 3.5.2 we calculate an average trap density in the energy space instead of the total density actually scanned. The active energy interval has also been obtained by the methods discussed above.

Non-symmetrical case (stressed device):

The interface trap density in the stressed device can be represented by , where is the trap density in the virgin device. The stress-generated traps are localized near the drain junctiongif. We assume that the boundary after the stress at the source side is the same as before stress . If we assume that the stress-generated traps do not influence the capture boundary at the drain side , it follows

 

where is the charge-pumping current in the virgin device. The second parasitic term is small for the strongly localized traps in comparison with the desired factor due to scanning of the interface. This term may be omitted in practice. The main contribution to this factor is from the channel region and it vanishes when processing the differential characteristics instead of . A general expression which accounts for the influence of the stress-generated traps on the capture boundary () can be trivially derived. It is omitted here.

Constant amplitude technique:

In this method all parameters of the trapezoidal gate pulse are constant. The top level is sufficiently high so that the complete interface is inverted during the course of experiment. The reverse bias is kept constant. The interface is scanned by changing the gate bottom level . The emission times do not change with , but only the active interface area changes. Differentiating G.1 with respect to it follows

 

In symmetrical cases may be assumed. With benefit of G.7 it follows

 



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Next: G.2 Filtering and Differentiation Up: Appendix G: Relations for the Previous: Appendix G: Relations for the



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