Phonon Dynamics at an Oxide Layer in Silicon: Heat Flow and Kapitza Resistance

Abstract

The interactions between heat flow and an oxide layer in Si are studied within two temperature windows using non‐equilibrium ab initio molecular‐dynamics (MD). The model system is a H‐saturated Si nanowire containing an amorphous SiOx layer. The nanowire is in a large 1‐D periodic box which prevents thermal contamination between image nanowires. The results show that the oxide acts as barrier to heat flow and substantially increases the time required for the system to reach thermal equilibrium. This effect is caused by the higher‐frequency vibrational modes in the oxide relative to Si, and is unrelated to the low thermal conductivity of SiOx. A new first‐principles method to calculate the Kapitza resistance of the interface directly from the MD data is proposed.

Thermal Characterization and Modelling of AlGaN-GaN Multilayer Structures for HEMT Applications

“…Above the Debye temperature of Pt (240 K [36]), this increase indicates a dominating inelastic scattering of phonons at the interface [37]. The temperature dependence of the thermal boundary conductance is also in line with results obtained from ab-initio molecular dynamics simulations [38], which showed an increase of the thermal conductivity with temperature due to the increase of available spatially localized modes at the interface. In the range of temperatures between 300 K and 523 K, the value increased from (269 ± 54) MWm −2 K −1 to (380 ± 76) MWm −2 K −1 .…”

The Role of Interface Vibrational Modes in Thermal Boundary Resistance

“…Looking at previous work on this exact interface, the Kapitza resistance was found to be 0.696 × 10 −9 K m 2 W −1 . [ 21 ] The basic equation for thermal boundary resistance is , where is the temperature gradient across the interface, is the time of the simulation, is the cross sectional area of the interface, and Q is the heat transported across the interface. Using this equation, we can subtract off the energy transported by these modes and find what the thermal boundary resistance would be if they did not exist, or at least did not transport any energy.…”

“…This was done using a technique that modeled the nanowire as a series of resistors, along with the interface, as described previously. [ 21 ] This is a method in which a running average of the temperature gradient and heat flux are used, and the researcher runs the simulation until the values are sufficiently converged. The advantage is that the researcher does not use unnecessary CPU time.…”

“…In fact, this lower temperature nanowire was designed specifically so that it would have the same relative phonon population in each mode as its high-temperature cousin. That is, to lower the temperature of the nanowire all we did was reduce the magnitude of each vibrational mode amplitude by an appropriate scaling factor (see the studies by Stanley and coworkers [14,21] ). Therefore, we can be sure that these different phonon interactions are caused by an increase in amplitude (temperature), and not just by chance from a different statistical mix of phonon population.…”

Perspectives on the Theory of Defects

“…Thus, the Kapitza resistance depends on the temperature window and the direction of heat flow. Stanley and Estreicher (2018) This explanation for the atomistic origin of the Kapitza resistance differs from the models (Swartz and Pohl, 1989) that include only the mismatch between the phonon densities of states of the two materials but do not include the localized vibrational modes associated with the interface. Note that the first-principles calculations performed so far involved systems too small to include the low-frequency (long-wavelength) phonons.…”