Raman measurements of Stress and strain in Silicon

Introduction
MEMS technologies are evolving at a rapid rate with applications in a wide variety of sensors and actuators. There is currently great interest in extending these technologies to fabricate micromachines for power generation, propulsion, cooling, and fluid pumping. The resulting structures are often subjected to high mechanical stresses, which if too high, will cause failure. Hence knowing the local stress is an important design consideration.
Here we are using Raman scattering to locally measure the stress in a bent silicon cantilever and comparing with calculations.

Test structure 

We are using Raman spectroscopy to measure the stress and strain in a silicon flexure to compare
the result with simple analytical expressions as well as numerical models. This image shows a SEM image of
the root of the flexure structure we have been using. At the end of the long flexure (dimensions: ~3mm
long, 150 um across and 480um deep), a silicon ball is weged beween two flexures. The resulting deflection
(69um) causes different amount of stress/strain along the leg of flexure.

Measurements 

The strong Raman signal at ~520 ^{1} from silicon can be used to measure stress or strain applied to the silicon structure. We are using a Renishaw Ramascope 1000B for our measurements. A shift of the Raman peak to higher energies indicate compressive stress. Likewise, a shift to lower energies indicate tension. The spectral resolution is 0.02 cm^{1} which corresponds to 10 MPa stress or strain. The spatial resolution is 1um. Hence, the stress is measured locally in a 1um area. The flexure will have the strongest strain and stress field at the root of the flexure. 
Models 

Two approaches were used. In the first, the flexure is considered to be an EulerBernoulli cantilevered beam of uniform rectangular crosssection of length L, width b, thickness h, and tip deflection delta. The analytical EulerBernoulli (EB) model is expected to be valid for small deformations as is the
case here. However, the EB beam model is expected to be invalid in a region approximately 0 < x < h due to the finite compliance of the supporting silicon structure. In order to take these effects into consideration, numerical analyses were performed using the method of finite elements (FEM). The image shows the calculated stresses taking support compliance into account from the FEM. 
Results 

All the models match measurements to 25  35 MPa at locations 600  1000 um from the support, but significantly overestimate the stresses at distances <100 um. Including the support compliance in the numerical model leads to a better match with measurements, as is shown in this figure, comparing the
measurements and calculations at 100 um distance from the root. 
Publications 

V. T. Srikar, A. K. Swan, M. S. Ünlü, B. B. Goldberg, and S. M. Spearing, "MicroRaman measurement of bending stresses in micromachined silicon flexures," IEEE Journal of Microelectromechanical systems, Vol. 12, No. 6, December 2003, pp. 779787
V. T. Srikar, A. K. Swan, B. B. Goldberg, M. S. Ünlü, and S. M. Spearing, "Microscale measurement of stresses in a silicon flexure using Raman spectroscopy," Materials Research Society Symposium  Proceedings, Vol. 741, 24 December 2002, pp. 219224

Collaborators 
V. T. Srikar and
S. M. Spearing , Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

Support 
Micro machines at Sandia national laboratory
MEMS Clearinghouse

