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The Physics of Non–Equilibrium Reliability Phenomena

6.2 Outlook

A fundamental understanding of reliability issues on a microscopic scale provides the basis for new developments and emerging technologies alike in the field of microelectronics. The concepts derived within this thesis enable new insight into the main degradation modes and should serve as a basis for subsequent research activities. In the following some ideas are listed which hopefully inspire subsequent studies.
Atomistic Models

need to be thoroughly analyzed. The utilized Si/SiO\(_2\) interface structures exhibit a cell size of \(16\times 16\times \SI {32}{\angstrom }\) with around 475 atoms. Although their geometrical and electronic properties compare well to experimental perceptions, see Section 3.1 and Appendix A, a rather large residual strain at the interface seems to be present. Test calculations with increasing \(xy\) and \(z\) dimensions, see Appendix A, indeed show pronounced relaxation effects for both variants. Therefore, further insights into the actual oxidation process are required for a better microscopic picture of the Si/SiO\(_2\) transitions regions. Currently, these next steps are part of the EU project "Modeling Unconventional Nanoscaled Device FABrication" (Mundfab) which should help to identify the optimal atomistic model dimensions in terms of accuracy and computational effort.

Defect Configurations

and their properties have been investigated in Sec. 3.1 as well as in Appendix B. Selected \(P_\mathrm {b}\) center configurations within this thesis reflect the prevailing opinion of an \(sp^3\) hybridized dangling bond orbital together with an amphoteric trap level character [84, 88, 91, 93]. However, their detailed microscopical structure can not be fully validated using this information. An ultimate benchmark offers the selectivity of electrically detected magnetic resonance (EDMR), a method frequently used in the literature. Thus, the theoretical values for the defect electronic structure and the (super–) hyperfine interactions can directly be compared to experimental data [314, 315]. The utilized DFT setup, see Chapter 3, however, is not suitable for such calculations, as they require an explicit description of the core electrons, and hence, an all electron basis set2.

Resonance scattering mechanisms

as introduced in Chapter 2 and theoretically described in Chapter 4, are commonly used to explain electron stimulated and current driven desorption phenomena on surfaces [102, 103, 316]. Despite the use of ab initio methods to characterize this process, see Chapter 3, a more rigorous approach utilizing time dependent density functional theory (TDDFT) could complement the findings. TDDFT explicitly takes the wavefunction of the incident charge carriers into account and allows one to study the interaction between a single electron and a molecular resonance [317, 318]. Thereby, the hot electron directly probes the resonance state and its properties. Furthermore, once the electron scattered at the resonance and the Si–H bond has been excited, the actual bond breaking dynamics can be simulated in real time using TDDFT.

The resonance potential energy curves \(V^{-/+}(q)\) presented in Chap. 3 have been calculated assuming the same bond breaking trajectory as for the neutral configuration \(V(q)\). However, the excited state motion of the Si–H bond, or more generally, adsorbates, possibly follows substantially different dynamics3. Hence, a more rigorous description of the negatively and positively charged potential energy surfaces is highly desired. Constrained DFT [238, 319] and \(\delta \) self consistent field [320322] are two methods particularly suited for such calculations, although computationally challenging for the Si/SiO\(_2\) system.

Recovery Dynamics

of interface defects need to be further investigated. Despite the predominant and experimentally validated opinion that H\(_2\) is responsible for the passivation of active \(P_\mathrm {b}\) centers [221, 222, 248, 249], several important question remain open. First, the preferred H\(_2\) cracking site and the reaction pathway of the remaining H atom. Expanding on the results presented in Section 3.6, a much larger statistics of possible reactions within the SiO\(_2\) network is required to identify the dominant dynamics. Second, while the various experimental studies extracted consistent energies of \(P_\mathrm {b}\) center passivation between \(\SI {1.4}{}\) and \(\SI {1.6}{eV}\), the reaction rate constant within the formula proposed by Stesmans is largely treated as an empirical fitting parameter. Values between \(\SI {e-4}{}\) and \(\SI {e-9}{cm^3\per mol\,s}\) have been reported which seems inconsistent with a unique reaction [248, 249]. A possible explanation could be given in terms of the different technologies used for the studies. While the H\(_2\) content as well as the associated reactions in devices having thicker oxides (\(>\SI {10}{nm}\)) are mainly determined by SiO\(_2\) bulk properties, their characteristics in thinner oxides (\(<\SI {4}{nm}\)) can be distorted due to the influence of the interfacial regions, see Section 3.1 and Appendix A. Assuming an interfacial transition region of \(\SI {0.5}{nm}\), a substantial part of the oxide is governed by the SiO\(_2\) properties of the transition region, e.g. distorted bond lengths and angles. However, this idea needs to be thoroughly tested using ab initio methods.

Modeling of Hot Carrier Degradation

can be further extended towards novel material system based on Germanium. Similar to Si–H bonds at the Si/SiO\(_2\) interface being responsible for HCD in Si based devices, Ge–H bonds can be expected as defect precursors in Ge transistors. However, recent DFT studies suggest a more intricate picture in which O vacancy related defects play a major role for degradation [MJC8, 323325]. Likewise, HCD, and in general reliability issues, in transistors employing 2D channel materials is largely unexplored and an emerging research field [MJC11].

Additionally, the harmonic approximation of the full framework introduced in Chapter 4 and Section 4.1.7, can be further simplified by assuming that both potential energy curves, \(V(q)\) and \(V^{-/+}\), have the same frequency. Thus, for displaced harmonic oscillators the formula for the effective cross section can be reduced to an analytic expression [280]. However, only transition rates between neighbouring levels \(\Delta n=1\) are allowed within this approximation, whereas overtone excitations are explicitly neglected. Therefore, its applicability needs to be thoroughly tested and significant deviations of certain parameters compared to ab initio results are to be expected.

Full bias space

degradation characteristics have recently gained attention. The presented approach, the NMP\(_\mathrm {eq.+II}\) model in conjunction with the framework describing HCD, properly captures the trends across {\(V_\mathrm {G},V_\mathrm {D}\)} bias space. Nevertheless, small yet important differences can be noted, such as strong distortion of \(I_\mathrm {D,lin}\) and the position of the drift minimum, see the discussion in Sec. 5. Such peculiar features could possibly be understood using a microscopical description of defect creation and transformation, as provided by the recently developed Hydrogen release model [16, 18, 19, 326]. The redistribution of neutral hydrogen within the oxide is assumed to be responsible for transformation of active precursor sites into positive defects as well as the creation of \(P_\mathrm {b}\) centers at the interface due to the formation of H\(_2\). An extension towards interfacial H release together with its subsequent migration pathways, see Section 3.6, could reveal an interplay between HCD and BTI on an atomistic level, not accessible in current modeling approaches.

2 Note that such a complete basis set dramatically increases the computational efforts.

3 see, Sec. 3.4, the discussion on the positively charged complex V\(^+(q)\).