Temporal variation in stress and temperature during a thermal anneal comprises another section of the parametric space that governs the patterning process. While full consideration of this area is left to future work, we ran an example variable stress anneal to demonstrate the viability of this concept: We subjected a Si0.8Ge0.2 film to a cylindrical indenter with its axis the y-direction during an anneal for 3 hours at 1000 °C. We then
this Chapter, we did not re-compute a stress field, as our previous analysis showed that the impact of the indenter is far greater than the contribution from internal mismatch stresses or the change in moduli [100] (see Chapter 4)), and then continued the anneal. Figure 5.14 and Figure 5.15 show the results of this study. There is a period (at approximately one minute) that there was greater than 60% Ge in the near surface region of the film, but it was very short. The precision in timing required will make annealing experimentally very difficult. In addition, although not shown on the color scale which was chosen to enhance patterning features in every image, the maximum composition in the near surface region of the film is roughly 75% Ge in the brief moment of extreme compositional enhancement after the rotation of the indenter array, a result which shows promise for the viability of the variable stress approach. A detailed parametric scan will be difficult to conduct, however, as the annealing schedule can vary over a wide range of times before and after the stress field is changed.
Figure 5.14. (a) Stress before (left) and after (right) rotation of cylindrical indenter after 3 hours of thermal annealing of a Si0.8Ge0.2 substrate annealed at 1000 °C (b) compositional profile at time of rotation.
Figure 5.15. Compositional profiles after rotating indenter field and continuing the thermal anneal at 1000 °C for (a) 1 minute (b) 10 minutes (c) 1 hour (d) 3 hours.
5.6 Conclusions
In this chapter, we performed a targeted parametric scan of the high-dimensional space of indenter pitches, geometries, and film compositions for patterning QCSs in Si1- xGex thin films via nanoindentation. By choosing the appropriate indenter pitch and geometry, even in a film as low as 20% Ge, we were able to generate periodic, three- dimensional, Ge-rich regions in the near-surface region of an initially uniform film. These Ge-rich regions meet the requirements set out in the literature for potential use as addressable QDs in future technologies.
We recognize that we just considered a small subspace of the vast parametric space describing the compositional redistribution process. A full systematic optimization of all of the parameters involved in the patterning process could potentially discover alternative combinations of parameters that are capable of producing Ge QDs, perhaps using even lower composition Ge films than the standard 20% Ge considered here.
In addition, we demonstrated the feasibility of temporally varying the stress field during a thermal anneal, as we were able to generate significantly different patterns after changing the stress field orientation. This fact, along with the possibility of altering the temperature during an anneal, provides an additional large segment of the parametric space to explore. We leave a full parametric analysis of the entire parameter space to future work.
Analysis of Point Defect Diffusion In Stressed Si and Ge
Chapter 6.
6.1 Introduction
As clearly evident in the previous Chapters, atomic diffusion is at the heart of the stress transfer process, as well as much of the processing that takes place in the fabrication of microelectronic and optoelectronic devices. For example, short-range atomic diffusion is critical in the electrical activation of implanted dopants (e.g., B or P), but must be controlled carefully to ensure that it does not lead to undesirable long-range spreading of the dopant profile [101, 102].
In crystalline semiconductors, such as Si, Ge, and the various III-V materials (e.g., GaAs and InAs), this diffusion is mediated principally by point defects, namely interstitials and vacancies, that exist in one or more electrical charge states. The role of point defects in the evolution of microstructure in crystalline semiconductors is multifaceted. In addition to being the mediators of atomic mobility as described in the previous Chapters, they are also directly responsible for the formation of various types of crystallographic defects that can play important roles in device performance. In the well- established case of Si bulk crystal growth, for example, the aggregation of large numbers of vacancies leads to the formation of nanoscopic voids [103], while an excess of self- interstitials generates a multitude of defect structures ranging from small, three- dimensional clusters [104] to large, tangled networks of dislocations [105]. However, such aggregation processes require significant supersaturations of point defects and are generally not relevant for the situations considered in this thesis and here we focus on their role as atomic diffusion mediators.
The capacity for point defects to move atoms across the bulk of a material depends on their intrinsic diffusivity as well as their concentrations. In Chapters 4 and 5, it was assumed that point defects always exist in their (spatially and temporally varying) locally equilibrium concentrations. It is well established that both the diffusivity and equilibrium concentration, and hence the total transport capacity (see Chapter 4), of each point defect species depends approximately exponentially on temperature. This is particularly true for Si, where numerous experimental [106-108] and theoretical [109, 110] studies have focused on estimating the temperature dependence of self-interstitial and vacancy diffusivities and equilibrium concentrations.
On the other hand, the impact of lattice stress on point defect transport and thermodynamics is much less well established. The importance of stress in the types of processes relevant to this thesis is of course obvious—stress is intentionally applied to diffusionally drive a system towards some desired configuration. But the role of stress in modulating point defect properties is also increasingly appreciated in other settings. For example, stress arising from temperature gradients is always present during crystal growth of Si from the melt, e.g., by the Czochralski or floating-zone methods [111]. Ion- implantation of dopants into semiconductor wafers also potentially produces large amounts lattice stress that evolves as the wafer is annealed [112]. In the case of Si crystal growth, thermal stresses are now known to influence the subtle balance between self- interstitial and vacancy populations and can alter the dominant point defect species, and therefore the type of defect aggregate, remaining in the crystal after it is grown and cooled. Some recent theoretical studies based on electronic structure calculations have
therefore equilibrium concentrations) on various types of stress states [78, 113]. Much less attention has been given to the impact of stress on point defect diffusivities and even less is known about the impact of stress on point defect properties in pure Ge and SiGe alloys.
In Chapters 4 and 5, we adopted the parameter values suggested in ref. [38] to describe the impact of stress on point defect properties in the SiGe alloy system. In some sense, these parameter values may be considered as being ‘internally consistent’ with the other model parameters in ref. [38] in that the interdiffusion model results were validated against experimental data. However, there remains much ambiguity regarding the robustness of the assumed values, their relationship to other literature estimates, and sensitivity of the model to them. In this Chapter, we employ a series of well-known empirical potentials for Si and Ge to study the impact of stress on point defect transport and equilibrium properties. The calculations are based on a theoretical formalism put forward by Aziz [32, 73], which is described in detail in Section 6.2. The predictions obtained with the various empirical potentials first are compared to each other and then to existing literature values in Section 6.4. Finally, conclusions and outlook are presented in Section 6.5.