  Advancements in modern semiconductor devices increasingly depend on the
utilization of amorphous materials and the reduction of material thickness,
pushing the boundaries of their physical capabilities. The mechanical
properties of these thin layers are critical in determining both the
operational efficacy and mechanical integrity of these devices. Unlike bulk
crystalline materials, whose calculation techniques are well-established,
amorphous materials present a challenge due to the significant variation in
atomic topology and their non-affine transformations under external strain.
This study introduces a novel method for computing the elastic tensor of
amorphous materials, applicable to both bulk and ultra-thin films in the linear
elastic regime using Density Functional Theory. We exemplify this method with
a-SiO2, a commonly used dielectric. Our approach accounts for the structural
disorder inherent in amorphous systems, which, while contributing to remarkable
material properties, complicates traditional elastic tensor computation. We
propose a solution involving the inability of atomic positions to relax under
internal relaxation, near the boundaries of the computational unit cell,
ensuring the affine transformations necessary for linear elasticity. This
method's efficacy is demonstrated through its alignment with classical Young's
modulus measurements, and has potential for broad application in fields such as
Technology Computer Aided Design and stress analysis via Raman spectra. The
revised technique for assessing the mechanical properties of amorphous
materials opens new avenues for exploring their impact on device reliability
and functionality.
