Researchers from the University of Illinois at Urbana-Champaign (UIUC) and Max Planck Institut für Eisenforschung have developed a model to predict the deformation of silicon microbeams under bending. By using a combination of scanning and transmission electron microscopies along with atomic force microscopy, the research team determined that the nucleation of dislocations mediates the unexpected plastic deformation with time at 400°C, whereas bulk Si becomes ductile at ~540°C and shows creep at high temperatures (800°C). This research may have implications for small electronics that operate at high temperatures.

“At a fundamental level, what mechanisms are involved when silicon is subjected to high stresses and temperatures, still sparks debates,” say UIUC professor Taher Saif and research assistant Mohamed Elhebeary. “In particular, in micro- and nanomechanical devices, silicon structures are often subjected to bending when high stresses are limited to small volumes. The mode of failure of such structures at elevated temperatures remains [unknown].”

“Silicon-based devices must be dislocation-free,” says William Nix, professor emeritus at Stanford University, “Transistors are compromised by the presence of dislocations. Until now we have thought that if dislocations are not present in the silicon wafer used to create the devices, they would not be formed during processing, provided the temperature is kept below the so-called brittle-to-ductile-transition (BDT) temperature.” Nix was not involved in the current study. 

Saif, Elhebeary, and their colleagues now report, in a recent issue of the Proceedings of the National Academy of Sciences, that as the threshold stress is approached at ~400°C, multiple dislocation nucleation sites appear simultaneously from the high-stressed surface of the beam with a uniform spacing of about 200 nm between them. Dislocations then emanate from these sites with time, lowering the stress while bending the beam plastically.

“Surface dislocation nucleation has been recently observed in Si nanowires with feature size less than 100 nm or so. This work unequivocally shows that the dislocation mechanism works for microscale Si as well, which leads to interesting time-dependent plasticity,” says Yong Zhu of North Carolina State University, who was not involved in the study.

“The rate of dislocation generation determines the deformation rate of silicon,” Saif and Elhebeary tell MRS Bulletin.

In order to apply bending on silicon microbeams, the research team designed a microelectromechanical system (MEMS) platform with a micro-spring that can apply and measure micro-Newton loads on the sample. A set of springs enabled the research team to maximize the bending to a normal stress ratio at the most stressed volume of the beam sample. They then measured the sample and spring deformations through image analysis. “We micro-fabricated the MEMS stage with a co-fabricated standalone silicon micro-beam that can operate at high temperature inside [the scanning electron microscope] chamber,” Saif and Elhebeary say.

The researchers’ model predicting the deformation history of Si microbeams subjected to bending agrees with experimental results. “The key discovery here is that at high enough stress with highest stress near the surface, multiple dislocation nucleation sites appear at the surface simultaneously with uniform spacing. Dislocations nucleate from these sites with time and move into the bulk against Peierls barrier,” Saif and Elhebeary tell MRS Bulletin. 

“Although we know that dislocations are often nucleated at free surfaces, we are rarely able to link the kinetics of dislocation nucleation to the kinetics of plastic deformation. Through their modeling of their exquisite experiments, Elhebeary et al. appear to have done just that for silicon,” Nix says.

“How Si behaves mechanically at high temperature is of critical relevance to the reliability of microelectronics,” says Zhu, regarding one of the impacts of the study on electronics. “Second, the brittle nature of Si presents a challenge for some unconventional forms of electronics such as flexible and stretchable electronics. Ductility in micro/nano-scale Si can be conducive to these applications.” 

Read the abstract in Proceedings of the National Academy of Sciences.