Computational Challenges for Reliability Assessment of Next-Generation Micro & Nano Systems

The computational engineering community is facing new modeling challenges because the advent of nanotechnology is clearly demonstrating the limitations of classical continuum mechanics. The discrete nature of matter leads to nonlinear and scale-dependent phenomena at the nanoscale, which cannot be captured in simple homogenization schemes such as those used in classical continuum mechanics. Discrete molecular or atomistic modeling clearly indicates the reasons for the inadequacies of classical continuum mechanics. However, discrete modeling still requires intense computational investment that limits its use to problems of very small length scales (sub-microns) and very short time scales (nanoseconds). Thus, although discrete modeling is a valuable technique to gain fundamental scientific insights into nanoscale phenomena, it is not a feasible strategy over length scales and time scales that are important in nanoscale problems of engineering significance. For example, it is still computationally infeasible to construct a discrete atomistic model of a complete nano-electronic device for design optimization purposes. It is equally difficult to develop a discrete molecular description of the construction of a nano-bio sensor that is based on the self-assembly of hundreds of protein molecules onto a functionalized gold substrate. As a final example, consider the difficulty of developing a discrete molecular model of a composite nanodielectric consisting of hundreds of nanoparticles embedded in a continuous matrix material. Clearly, a formal framework is needed to bridge between discrete molecular modeling and classical continuum modeling, for nano-engineering problems