Abstract
General relations are provided for the work rate and complementary work rate on a body containing evolving boundaries, residual stresses, and stresses due to boundary tractions. Closed-form solutions are provided for three simple examples with no residual stresses. Residual stresses are investigated as a means of self-assembling MEMS and NEMS during material deposition and etching. The assembly of two components is considered: one component is subjected to deposition or etching and is modeled as an Euler-Bernoulli beam, and the other component is neither deposited nor etched and is modeled as a linear spring. A linear ordinary differential equation is derived for the beam deflection as a function of the thickness of the deposited layer. Closed-form solutions are not possible, but numerical solutions are plotted for various dimensionless ratios of the beam stiffness, the spring stiffness, the intrinsic strain, and the elastic moduli of the substrate and deposited layer. During deposition, the work performed by the beam on the spring is monotonic. During etching, however, the work is nonmonotonic and the spring eventually performs work on the beam.
Mani, Sathyanarayanan (2002). Residual stress and self-assembly during deposition and etching of MEMS. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -2002 -THESIS -M362.