| Autor: |
Darlington TP; Department of Physics, University of California, Berkeley, California 94720, USA., Krayev A; Horiba Scientific, Novato, California 94949, USA., Venkatesh V; Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA., Saxena R; Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA., Kysar JW; Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA., Borys NJ; Department of Physics, Montana State University, Bozeman, Montana 59717, USA., Jariwala D; Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA., Schuck PJ; Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA. |
| Abstrakt: |
When layers of van der Waals materials are deposited via exfoliation or viscoelastic stamping, nanobubbles are sometimes created from aggregated trapped fluids. Though they can be considered a nuisance, nanobubbles have attracted scientific interest in their own right owing to their ability to generate large in-plane strain gradients that lead to rich optoelectronic phenomena, especially in the semiconducting transition metal dichalcogenides. Determination of the strain within the nanobubbles, which is crucial to understanding these effects, can be approximated using elasticity theory. However, the Föppl-von Kármán equations that describe strain in a distorted thin plate are highly nonlinear and often necessitate assuming circular symmetry to achieve an analytical solution. Here, we present an easily implemented numerical method to solve for strain tensors of nanobubbles with arbitrary symmetry in 2D crystals. The method only requires topographic information from atomic force microscopy and the Poisson ratio of the 2D material. We verify that this method reproduces the strain for circularly symmetric nanobubbles that have known analytical solutions. Finally, we use the method to reproduce the Grüneisen parameter of the E' mode for 1L-WS 2 nanobubbles on template-stripped Au by comparing the derived strain with measured Raman shifts from tip-enhanced Raman spectroscopy, demonstrating the utility of our method for estimating localized strain in 2D crystals. |
