Strain Mapping of Two-Dimensional Heterostructures with Subpicometer Precision

Yimo Han, Kayla Nguyen, Michael Cao, Paul Cueva, Saien Xie, Mark W. Tate, Prafull Purohit, Sol M. Gruner, Jiwoong Park, David A. Muller

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


Next-generation, atomically thin devices require in-plane, one-dimensional heterojunctions to electrically connect different two-dimensional (2D) materials. However, the lattice mismatch between most 2D materials leads to unavoidable strain, dislocations, or ripples, which can strongly affect their mechanical, optical, and electronic properties. We have developed an approach to map 2D heterojunction lattice and strain profiles with subpicometer precision and the ability to identify dislocations and out-of-plane ripples. We collected diffraction patterns from a focused electron beam for each real-space scan position with a high-speed, high dynamic range, momentum-resolved detector-the electron microscope pixel array detector (EMPAD). The resulting four-dimensional (4D) phase space data sets contain the full spatially resolved lattice information on the sample. By using this technique on tungsten disulfide (WS2) and tungsten diselenide (WSe2) lateral heterostructures, we have mapped lattice distortions with 0.3 pm precision across multimicron fields of view and simultaneously observed the dislocations and ripples responsible for strain relaxation in 2D laterally epitaxial structures.

Original languageEnglish (US)
Pages (from-to)3746-3751
Number of pages6
JournalNano Letters
Issue number6
StatePublished - Jun 13 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • Condensed Matter Physics
  • Mechanical Engineering
  • Bioengineering
  • General Materials Science


  • 2D lateral heterostructure
  • STEM
  • dislocation
  • ripple
  • strain


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