Simulation of TSV Protrusion in 3DIC Integration by Directly Loading on Coarse-Grained Phase-Field Crystal Model

As thermal management in 3DIC integration becomes increasingly important in advanced semiconductor node processes, novel experimental and modeling approaches are in great demand to reveal the critical material issues involving multiscale microstructures that govern the behavior of through-silicon-via (TSV) protrusion. Here, a coarse-grained phase-field crystal model properly coupled with mechanics through the atomic density field is used to simulate the formation of polycrystalline structures and protrusion of nano-TSVs from the atomic scale. TSVs with different grain structures are directly loaded, and protrusion/intrusion profiles are obtained along with displacement, stress, and strain fields. Thermodynamic driving forces from external loadings and the mismatch of Young’s modulus between adjoining grains as well as detailed displacement and strain distributions are ascribed to control the complex deformation in TSVs. TSVs with sizes up to around 30 nm and an aspect ratio of 4 are successfully investigated, and a further increase in the size and aspect ratio to cover the micrometer range is feasible, which lays down a solid basis toward a multiscale material database for simulation inputs to the design of TSV-based 3DIC integration and relevant electronic design automation (EDA) tools.

Efficient Fully Discrete Finite-Element Numerical Scheme with Second-Order Temporal Accuracy for the Phase-Field Crystal Model

In this paper, we consider numerical approximations of the Cahn–Hilliard type phase-field crystal model and construct a fully discrete finite element scheme for it. The scheme is the combination of the finite element method for spatial discretization and an invariant energy quadratization method for time marching. It is not only linear and second-order time-accurate, but also unconditionally energy-stable. We prove the unconditional energy stability rigorously and further carry out various numerical examples to demonstrate the stability and the accuracy of the developed scheme numerically.

Structure diagram and dynamics of formation of hexagonal boron nitride in phase-field crystal model

The phase-field crystal (PFC-model) is a powerful tool for modelling of the crystallization in colloidal and metallic systems. In the present work, the modified hyperbolic phase-field crystal model for binary systems is presented. This model takes into account slow and fast dynamics of moving interfaces for both concentration and relative atomic number density (which were taken as order parameters). The model also includes specific mobilities for each dynamical field and correlated noise terms. The dynamics of chemical segregation with origination of mixed pseudo-hexagonal binary phase (the so-called ‘triangle phase’) is used as a benchmark in two spatial dimensions for the developing model. Using the free energy functional and specific lattice vectors for hexagonal crystal, the structure diagram of co-existence of liquid and three-dimensional hexagonal phase for the binary PFC-model was carried out. Parameters of the crystal lattice correspond to the hexagonal boron nitride (BN) crystal, the values of which have been taken from the literature. The paper shows the qualitative agreement between the developed structure diagram of the PFC model and the previously known equilibrium diagram for BN constructed using thermodynamic functions. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

A phase field crystal model for materials crystallization in the presence of of nanoscale pores

The present work focuses on the development of a relatively simple phase field crystal model for materials with nanoscale porous inclusions. We found that the pore's main effect is to act as a nucleation agent, promoting crystallization of material at the pore’s interface, followed by micro-structural evolution of the solid in the supercooled liquid. Details of the crystal around the pore are investigated in terms of the pore radius and density of material outside the pore. Moreover, details of the pore-material interface is investigated through the interfacial tension and pressure. Finally, the model is extended to investigate the effect of multiple pores on the kinetics of crystallization.

Breaking stress of Coulomb crystals in the neutron star crust

It is generally accepted that the Coulomb crystal model can be used to describe matter in the neutron star crust. In [1] we study the properties of deformed Coulomb crystals and how their stability depends on the polarization of the electron background. The breaking stress in the crust σmax at zero temperature was calculated based on the analysis of the electrostatic energy and the phonon spectrum of the Coulomb crystal. In this paper, I briefly discuss the influence of zero-point, thermal contributions and the internal magnetic field on σmax.