3.6 Conclusion

A transient two-dimensional numerical model of MOSFETs including selfconsistently the dynamics of interface and bulk traps has been developed. The model has been applied to study the charge-pumping effect in silicon bulk MOSFETs and SOI devices on a rigorous footing.

The charge-pumping effect has been considered in detail by means of analytical methods. The analytical models proposed in the literature have been critically examined. A tight interplay between the analytical and the numerical approaches has provided a better inside in the charge-pumping effect in MOS devices.

In particular, we have studied the following problems:

• The time discretization error in solving the trap-dynamics equations by the numerical approach has been studied. The numerical results have been compared with the analytical results for the cases where the analytical models provide exact solutions. This study is covered by Appendix B.
• A phenomenological analytical model of the complete characteristics charge-pumping current versus gate-bottom level has been developed in Section 3.3. The accuracy of the analytical approach has been investigated by comparison with the numerical simulation.
• We have studied the errors in the calculation of the trap density distribution in the energy space from the experimental charge-pumping data in Section 3.3. A systematic error has been detected in some of the present methods. In this study, the numerical results have been used instead of the measurements.
• The extraction of the spatial distribution of the trap density along the oxide/silicon interface has been carefully analyzed in Section 3.5.2 and Appendix G. Both cases, a slowly varying trap distribution in virgin devices and a strongly localized damaged region in stressed devices have been considered. A systematic error in the extracted trap distributions has been observed for some of the present techniques. Several approaches to suppress the error have been proposed. A method for the extraction of the spatial distribution of fixed oxide charge has been proposed in Appendix G. In these studies, the numerically calculated charge-pumping characteristics which represent the exact solution to the problem, have been used instead of the measured data.
• By employing the transient simulation of the charge-pumping experiment the geometric current and other anomalous effects can be directly investigated. Such a study is interesting not only to suppress the geometric current, but also to model it, since this effect can be used for device operation in some specific applications. The geometric current components are studied in Section 3.4. In addition to a large geometric currents, some parasitic effects can also be latently presented in the charge-pumping measurements (Section 3.4).
• The charge-pumping characteristics of LDD MOSFETs differ from the characteristics of conventional MOSFETs. These differences have been studied in detail and fully explained by using the analytical and the numerical methods in Section 3.5.3 and Appendix E.
• The numerical model of the charge-pumping experiment has been used to confirm the accuracy of the spatial trap distributions extracted from the experimental data for -channel LDD MOSFETs in Section 3.5.4. The obtained distributions clearly show that most of the damage occurs under the spacer-oxide due to the injection from the LDD field-peak, but not in the gate/LDD overlap region due to the injection from the conventional field peak in our -channel LDD devices stressed at maximal substrate-current conditions.
• In some cases, it is difficult to interpret the changes in the charge-pumping characteristics after hot-carrier stress, particularly when both, a localized interface trap creation and a charge trapping in the oxide occur simultaneously. The numerical simulation enables us to calculate the charge-pumping characteristics for arbitrarily distributed interface traps and fixed oxide charge. This peculiarity has been exploited in modeling of several standard electrical stress-experiments in Section 3.5.1. The present interpretations of these experiments and the quantitative information they are able to provide have been critically evaluated.
• The coupling between the front and the back interface and the geometric (dimensional) parasitic current components make a quantitative interpretation of the charge-pumping measurements on thin-film SOI devices quite difficult [445][357]. The two-dimensional transient model enables us to study these effects in order to improve the present understanding of them. Some of our analyses have been presented in [192].

The transient model of MOS devices including the trap-dynamics can be additionally applied to study several problems:

• Modeling of the DLTS signals in silicon bulk MOSFETs, SOI MOSFETs made on the recrystallized silicon and polysilicon films and GaAS MESFETs where a large amount of deep bulk traps can influence the transient and the AC characteristics.
• The charge-pumping characteristics of SOI MOSFETs and the thin-film MOSFETs realized on the polysilicon films can be studied in order to propose the quantitative methods for the measurement of the physical properties of traps at the grain boundaries. A convenient approach to measure, but also to simulate the charge-pumping characteristics of those devices is to characterize the SOI gated-diodes.
• To analyze the dynamic characteristics of SOI MOS devices.
• The cases not yet experimentally studied can be simulated, as the charge-pumping characteristics of small MOSFETs which contain only a few interface or bulk traps.