(Invited) Multiscale Modeling of Stress-Mediated Compositional Patterning in SiGe Substrates
Authors: Kaiser Daniel , Ghosh Swapnadip , Han Sang , Sinno Talid 
Published: February 2020

The ability to scalably fabricate periodic, large-area assemblies of Ge quantum dots (QDs) on Si or SiGe substrates with high degree of spatial and size uniformity is expected to impact numerous technologies, including nano-/micro-electronics, optoelectronics, nanosensor arrays, and high-density patterned media for data storage. One approach to achieve this goal is to harness the Stranski-Krastonov (SK) growth mechanism [1,2]. Here, a lattice mismatched species is heteroepitaxially deposited on a substrate (e.g., Ge on Si or InAs on GaAs), creating strain that increases with film thickness, leading to the spontaneous formation of a distribution of islands. The size and shape of such islands has attracted much attention in regards to their potential use as arrays of QDs, but island evolution during SK growth is inherently stochastic, leading to broad distributions of island size with random locations. As a result, much effort has been directed towards substrate patterning in order to spatially direct island formation and narrow the size distribution [2-4]. While these approaches have proven successful in principle, they are generally process-intensive and will be difficult to scale to large-area applications.
Here, we describe a process in which SiGe substrates are compositionally patterned over large areas using spatially-modulated elastic fields applied by a nano-indenter array [5]. The indenter array, which is fabricated by interferometric lithography and dry etching, is pressed against a Si0.8Ge0.2 wafer in a custom-made mechanical press. The entire assembly is then annealed at high temperatures, during which the larger Ge atoms are selectively driven away from areas of compressive stress via the process of interdiffusion. Compositional analysis of the substrates demonstrates that this approach leads to a transfer of the indenter array pattern into the near-surface compositional distribution. In particular, the process leads to sharp compositional gradients that separate well-delineated regions in the near-surface region of the SiGe substrate, suggesting the possible use of this approach to simply and robustly create structures with quantum confinement properties.
Employing this approach in practice to create useful configurations, however, requires a systematic assessment of the processing parameter space. For example, the final compositional distribution in the substrate depends on the indenter tip shapes and sizes, the indenter array geometric pattern, the annealing temperature-time history, as well as the initial substrate composition and thickness. In order to fulfill this task, we have developed a multiscale computer model based on the lattice kinetic Monte Carlo (LKMC) method to simulate the ‘stress transfer’ process. The LKMC simulation is propagated using rates for atomic diffusion that depend explicitly on local values of stress, composition, and temperature [6,7]. The dependence of atomic diffusion on composition is regressed to experimental data while the stress dependence is described using the theory of activation volumes [8]. The model is used to investigate the dynamics of the compositional patterning process, as well as the impact of various parameters on the compositional configurations that result. We find that certain indenter configurations produce compositional patterns that may be favorable for engineering lateral arrays quantum-confined structures. Some comparisons also are made to preliminary experimental demonstrations.
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