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 would impact numerous technologies, including nano-/micro-electronics, optoelectronics, nanosensor arrays, and high-density patterned media for data storage. In this talk, 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. 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 hydrostatic pressure. Compositional analysis of the substrates demonstrates that this approach leads to a transfer of the indenter array pattern into the near-surface compositional distribution, which in turn induces a patterned surface stress.
We then present a multiscale computer simulation approach of the “stress transfer” process. The model is based on a combination of lattice kinetic Monte Carlo (LKMC) and static energy minimization. The LKMC simulation is propagated using rates for atomic diffusion that depend explicitly on local values of stress, composition, and temperature. The dependence of atomic diffusion on composition is regressed to experimental data while the stress dependence is described using the theory of activation volumes . The stress field is updated quasi-statically using a separate energy minimization routine with forces computed based on a Tersoff interatomic potential for the Si-Ge system . The atomic stresses and identities are then smoothed to generate continuous fields that are used as input into the LKMC simulation. Using our model we show that the residual surface stresses induced by compositional patterning should be large enough to break symmetry during subsequent molecular beam deposition of Ge, and thus may provide an efficient approach for producing highly ordered Ge quantum dot structures via the well-known Stranski-Krastanov heteroepitaxial growth mechanism. We also compare our results to recent experimental measurements.
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 J. Tersoff, Physical Review B 39, 5566 (1989).