Document Type



Doctor of Philosophy


Mechanical Engineering

First Adviser

Webb, Edmund B.

Other advisers/committee members

Nied, Herman F.; Delph, Terry; Vinci, Richard P.; Misiolek, Wojciech Z.


Evolution of deformation and stress in growing thin films has been studied in this work using computational simulations that resolve matter at atomic length and time scales. Thin films are ubiquitous in technology; further, deformation in structures with at least one very small dimension (e.g. thin films) manifests correspondingly large strain and stress, with concomitant effects on device performance. Knowledge is lacking about the spatial and temporal stress distribution in growing thin films and how this relates to specific mechanisms of stress evolution. Thus, developing highly detailed, fundamental atomic scale understanding of stress evolution during thin film growth is important to optimizing humankind’s ability to engineer useful devices based on thin film technology. It is well known for bulk systems and analytically has been shown that stress localization occurs around defects, edges, vacancies or impurity regions. However, in thin films, particularly for dissimilar material interfaces, analytical solutions are not available. For the surface layers of films laying on the substrate of a dissimilar material, the stress distribution analysis around defects becomes more challenging. Herein, spatial and temporal distribution of deformation and stress are presented for different thin film formation events including 1) sub-monolayer growth during an early film nucleation stage, 2) coalescence of adjacent monolayer ‘islands’, and 3) post-coalescence equilibration during subsequent film growth. Stress behavior during these events was evaluated spatially and temporally to reveal direct connections between atomic scale film growth behavior and the associated stress evolution. Validity of the stress computed via local computations of the virial expression for stress in a system of interacting particles was checked by comparing to results obtained from considerations of local atomic deformation in conjunction with existing expressions for epitaxial thin film growth stress. For the geometries studied here, where a monolayer of film with a highly characterized linear defect, a stacking fault, was simulated for coalescence, fairly good agreement was found. This result demonstrates that, for similar defects at the surface layer, with sufficient sub-ensemble averaging of the standard virial expression for stress, semi-quantitative spatial stress distribution information can be obtained from atomic scale simulations. Using our validated stress computation method, we reveal significant stress localization during thin film growth processes, leading to pronounced differences in maximum and minimum stress observed over very small spatial extent (of order multiple GPa over 3-6 nm distances). One prominent mechanism of stress localization revealed here is coalescence between adjacent growing islands. Coalescence eliminates surface energy but it typically occurs at the expense of generating elastic energy. For geometries explored here, stress manifesting during coalescence is highly localized. Atomic structure in stress localized regions is presented and shown to agree well qualitatively with a locally deformed structure (i.e. corresponding gradients in deformation). Though MD simulations are constrained temporally, relatively long simulations (hundreds of ns) were employed to reveal any evidence of temporal evolution. No such evolution was observed, lending confidence that localized stress states are thermodynamically meta-stable to stable. Furthermore, a size dependence study was employed to verify that results obtained herein extrapolate to film dimensions typically employed in practice. While stress relatively far from coalesced regions was shown to go to zero with increasing system size, neither the extent of stress manifestation spatially nor the peak magnitude in stress/strain showed notable dependence on system size. Stress relaxation during subsequent film growth is also presented and shown to preferentially eliminate localized deformation in the coalesced region. However, significant lattice mismatch for the system explored here is predicted by epitaxial thin film stress theory to lead to misfit dislocation generation for of order one to two monolayers of film material. In direct agreement with theoretical predictions, simulations here showed dislocation generation occurred, relieving misfit stress, after roughly a second monolayer was deposited. Again, deformation and stress due to defect generation are explored and shown to exhibit significant localization. In concluding, the implications of results presented are discussed, including the effects that stress localization can have on film properties. We note that success here in computing local stress on such small spatial scales bodes well that future investigations at the atomic scale can contribute quantitative stress knowledge to thin film growth theory development. We also highlight how results such as those herein can guide future development of continuum constitutive relations in the form of improved cohesive zone models. We finally point out simulation challenges that must be confronted for future similar work to extend success here to more general material systems as well as thin film growth geometries.