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#using the Poisson and continuity equations as defined above for DevPsi, Elec, and
Hole device init
For the DC solution, no recombination/generation terms are included in the continuity equations.
16.3.4 Results and Modeling Capabilities
Simulation can be very useful when it is not possible to decouple physical effects experimentally. Understanding the individual contributions of proposed mechanisms, and how results change due to their coupling, can lead to insights into the cause of experimentally observed effects such as oxide degradation.
For example, Fig. 16.11 shows how the two different proton production mechanisms discussed above contribute to interface trap creation in test devices
Fig. 16.11 FLOORS simulations showing each mechanism simulated separately to show the individual contributions of the two mechanisms (The data are from [22]. Reprinted, with permission, from [29], Figure 3)
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Fig. 16.12 FLOORS results showing the two mechanisms simulated together (Results quantitatively match the data of [22] very well. Reprinted, with permission, from [29], Figure 1)
exposed to a wide range of ambient H2 concentrations. When simulated alone, the direct release mechanism can account for interface trap buildup at low H2 concentrations. The cracking reaction can account for the increased interface trap buildup at high H2 concentrations but is not significant at low H2 concentrations. Simulated together, these mechanisms account for the buildup of interface traps over a comprehensive range of hydrogen environments (Fig. 16.12). The concentration of preexisting hydrogenated oxygen vacancies controls the concentration of interface traps generated at low H2 concentrations. The concentration of preexisting nonhydrogenated oxygen vacancies accounts for the concentration of interface traps generated at the high-H2 plateau [29]. Both the barrier for proton release and the depth of each hole trap play a role in the concentration of interface traps generated [32].
First principles calculations, such as those used to obtain the forward and reverse reaction energies discussed above, contain inherent statistical error and also depend on assumptions made about the physical system. FLOORS can be used to narrow down this error and to test certain physical assumptions made. A sensitivity analysis can be performed, in which each parameter supplied by density functional theory is varied slightly, within the statistical error bars of the first principles calculation. The effect of this variation on the FLOORS simulation results, in this case, buildup of
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Fig. 16.13 FLOORS results showing how the energy barrier to the cracking reaction controls the H2 concentration at which the shift from the direct release to the cracking mechanism occurs (The data are from [22]. Reprinted, with permission, from [29], Figure 9)
interface trap density, can be observed. In this way, it can be determined which parameters affect the results very strongly and which do not have any effect on the results, i.e., which parameters are sensitive and which are not.
For example, the energy barrier to H2 cracking that was originally obtained from first principles calculations was 0.4 eV. This value produces the simulation results that make up the leftmost curve in Fig. 16.13, which does not match the data. The sensitivity analysis showed that raising this barrier to 0.5 eV, which is within the statistical error bounds of the first principles calculations, shifts the results to the right to match the data [32].
The model presented here for radiation-induced interface trap buildup, and the more complicated one investigated in [32], contain many parameters to vary, and a separate simulation is required for each point on the curves in Figs. 16.11 through 16.13. But this can be scripted in a tool such as FLOORS, allowing for systematic investigation of each parameter and mechanism and for efficient organization of results. Most parameters will be known within a range of uncertainty, either from first principles calculations or from experiment. Then, most of these parameters will not be sensitive within this range. For example, varying the energy in Fig. 16.13, only 0.1 eV affects the H2 concentration at which the cracking mechanism takes