Advanced Modeling and Simulation
The current trend in advanced modeling has been to go small- down to the molecular level. For developing improved thermal materials, molecular dynamics and ab initio simulations have been used to predict material and fluid properties. As transistor sizes continue to decrease, thermal engineers are investigating ways to decouple the electron and phonon transport physics that are typically combined in the classical Fourier's Law of Conduction.
ACT's MD simulation of a melting process is shown. Heat applied to the left side raises the temperature of the atoms to above their melting point, causing them to diffuse as a liquid. Molecules on the right side remained below the freezing point, causing them to remain in a lattice structure while oscillating.
Molecular Dynamics (MD) is an advanced simulation method where the trajectories of atoms are tracked as they move about due to the attractive and repulsive forces between neighboring atoms. Using interatomic potentials that describe the forces between atoms, Newton's Second Law of Motion, and subjecting the ensemble of atoms to the desired temperature and pressure, the trajectories are computed by numerical integration of the equations of motion. Based on these calculated trajectories, transport properties, structural characteristics and reaction pathways can be predicted for various materials, liquids and gas mixtures. Using modern computing processors and parallel processing techniques, MD simulations can calculate systems with millions of atoms, large enough to model complex material systems and chemically reactions, for time periods up to 10's of nanoseconds, long enough to calculate time averaged transport properties and kinetics.
The movie shows the formation of graphitic precursors during resin pyrolysis.
Ab initio is Latin for "from the beginning". It is generally accepted as the most fundamental level of computational modeling. Compared to MD, ab initio does not make significant approximations to the electrostatic forces between atoms. As such, ab initio simulations are typically limited to systems with 10’s and 100’s of atoms. The ab-initio simulations involve electronic structure calculations to find the ground energy state of the material system (in absence of temperature input). Still, ab initio simulations can reveal useful information such as interfacial energies and restructuring characteristics. More recently, a new technique called ab initio molecular dynamics (AB MD) has been developed where the accuracy of the interatomic force calculation can be maintained while allowing the atoms to move. This new technique essentially eliminates the force potential approximations in traditional MD. Although a powerful simulation technique, AB MD simulations are limited in the system size and time scale.
Boltzmann Transport Equation (BTE) modeling is used to model electrical and thermal transport in semiconductor devices. In semiconductors, the total thermal conductivity can have significant combinations from both electrons and phonons. For most thermal calculations, the total thermal conductivity is all that is required. However, in transistor and thermoelectric materials, the nanometer length scales combined with Joule heating, requires the conduction due to electrons and phonons to be modeled separately. The distributions of phonons and electrons need to be captured as well. Using the BTE framework, transport equations in the form of partial differential equations can be solved numerically to capture these effects. In turn, more accurate predictions of device temperatures can be made.
Electronics cooling is currently one of the largest areas for thermal research and development. The decreasing size and increasing power consumption in transistors have led to many thermal challenges. MD, ab initio and BTE modeling techniques are required to accurately predict the chip level thermal transport process. Accurate modeling of the electron conduction, phonon conduction, and energy transfer between electrons and phonons is required to capture the heating process in a transistor. This technical understanding is important since the relative proportions of electron conduction, phonon conduction and electron to phonon conversion are important.
ACT's BTE simulation of a transistor is shown. Plotted is the voltage distribution for a semiconductor transistor.
At the various semiconductor/metallic interfaces, heat traveling in the phonons in the semiconductor material must first conduct heat to the phonons in the metal. The phonons in the metal must then transfer heat to the electrons in the metal. These extra transport steps add additional resistances that are not present if only contact resistance and Fourier type conduction are included. MD, ab initio and other advanced modeling techniques can be used to estimate the atomic structure at the interface and the "bottlenecks" that occur when conducting between phonons and electrons at the interface between two materials.
Analytical/numerical simulations of new materials can reduce the cost of discovery when compared to experimental investigation. In addition, these simulations can estimate physical properties in environments where experiments are prohibitively expensive. One example is the ablative thermal protection system for re-entry vehicles. As space vehicles reenter the atmosphere the outer surface encounters extremely high temperatures.
ACT's MD simulation of a carbon nanotube embedded in a phenolic resin is shown.
Ablative materials are used to address this issue. Ablative materials are organic polymer based materials that pyrolize at high temperatures, releasing protective gases and creating protective char layers to keep the outer surface cool. Currently ACT is developing carbon fiber and carbon nanotube composite ablative materials with the help of MD simulations.
