Fracture of notched silicon microstructures

Mechanical properties such as elastic constants, ultimate strength, fracture strength, and fatigue properties are fundamental quantities that are needed for the design of reliable microelectromechanical systems (MEMS). These properties acquired from test structures at the length scales of MEMS are currently lacking. In response to this situation, the ultimate tensile strength and Young's moduli in the {dollar}langle{dollar}100{dollar}rangle{dollar} and {dollar}langle{dollar}110{dollar}rangle{dollar} directions were measured for single crystal silicon. The test structures were 15 {dollar}mu{dollar}m thick, 28-100 {dollar}mu{dollar}m wide, and 630-1000 {dollar}mu{dollar}m long. The resulting measured properties were {dollar}sigmasb{lcub}u{rcub}{dollar} = 1.21 GPa, {dollar}Esb{lcub}langle 100rangle{rcub}{dollar} = 123 GPa, and {dollar}Esb{lcub}langle 110rangle{rcub}{dollar} = 166 GPa.; Furthermore, MEMS structures fabricated by anisotropic etching often contain sharp corners. Stress and failure analyses were performed with the intent of providing a rational mechanics framework for the design of such structures. A fracture initiation criterion in the spirit of linear elastic fracture mechanics was proposed. The criterion was verified experimentally using single crystal silicon T-structures and notched beams. The T-structures are representative of typical details in MEMS structures where cross-sections change abruptly forming 90{dollar}spcirc{dollar} corners. The T-structures were fabricated from 15 {dollar}mu{dollar}m thick epitaxially grown single crystal silicon and were tested in tension. The notched beams were fabricated from 1.08 mm thick (100) silicon wafers and were tested in three-point flexure. Notch angles of 70.53{dollar}spcirc{dollar} and 125.26{dollar}spcirc{dollar} were studied. The results show that the critical notch stress intensity factor {dollar}(Ksp{lcub}n{rcub}sb{lcub}Ic{rcub}){dollar} can accurately correlate fracture initiation for each notch angle tested. The critical notch stress intensity factors are 0.76 MPa{dollar}cdot{dollar}m{dollar}sp{lcub}0.4814{rcub}{dollar} and 6.48 Mpa{dollar}cdot{dollar}m{dollar}sp{lcub}0.3743{rcub}{dollar} for 70.53{dollar}spcirc{dollar} and 125.26{dollar}spcirc{dollar} notch angles, respectively, in bulk silicon, and 2.1 MPa{dollar}cdot{dollar}m{dollar}sp{lcub}0.4518{rcub}{dollar} for the 90{dollar}spcirc{dollar} notch angle in epitaxial silicon films. Furthermore, excellent failure correlation with a critical notch stress intensity factor is also obtained for macroscopic acrylic for notch angles of 60{dollar}spcirc{dollar}, 90{dollar}spcirc{dollar} and 120{dollar}spcirc{dollar} in mode I, mode II, and mixed-mode I and II loading.