Phonon transport governed by intrinsic scattering in short-period AlN/GaN superlattices

We employ density functional theory based phonon transport methods to provide a rigorous understanding of the nature of thermal transport in coherent short-period AlN/GaN superlattices (SLs), with period lengths up to three unit cells of each, and compare these with properties of their bulk constituents. Increasing the period length leads to phonon band folding with frequency gaps and thus smaller phonon velocities and more phonon scattering than in bulk, both of which reduce lattice thermal conductivity ($\kappa$). Contrary to expectations, we find that velocity variations among larger-period AlN/GaN SLs play only a minor role in cross-plane $\kappa$ reductions, while variations in intrinsic phonon scattering are strongly correlated with their transport behaviors. This work provides insights into the microscopic behaviors of technologically relevant nanostructured materials, which are likely applicable to a wider range of SL systems and other nanostructures.

Figure 1

1+1 SL structure. A single unit cell is outlined and labeled within. Image produced using vesta [21].

Figure 2

Temperature-dependent cross-plane thermal conductivities of AlN (blue), GaN (black), $\frac{1}{2}+\frac{1}{2}$ SL (red), 1+1 SL (green), 2+2 SL (orange), and 3+3 SL (purple)—curves for calculations; symbols for measurements: black circles [32], black squares [33], and blue triangles [34]. The inset gives the temperature-dependent in-plane thermal conductivities of the SL systems.

Figure 3

Cross-plane phonon dispersions for AlN (left), GaN (middle), and the $\frac{1}{2}+\frac{1}{2}$ SL (right). Note that each system has band folding in this direction. For bulk, this arises due to the internal symmetry of the formula units within the wurtzite unit cell. Black squares [43] (GaN) and blue squares [44] (AlN) are measured data from inelastic x-ray scattering.

Figure 4

Room-temperature thermal conductivity accumulations with frequency for the 1+1 SL (green curves), the 2+2 SL (orange curves), and the 3+3 SL (purple curves). Dashed curves correspond to in-plane ${\kappa }_{\mathrm{acc}}$, while solid curves correspond to cross-plane ${\kappa }_{\mathrm{acc}}$.

Figure 5

(Top) Absolute values of cross-plane group velocities of TA phonons (solid curves) and associated folded bands (dashed curves) as a function of frequency for bulk GaN (black) and the $\frac{1}{2}+\frac{1}{2}$ SL (red). (Bottom) Corresponding room-temperature cross-plane thermal conductivity accumulations with frequency for the TA phonons (and associated folded bands). Arrows highlight the correspondence between features in the velocities and the ${\kappa }_{\mathrm{acc}}$.

Figure 6

(Top) Absolute values of group velocities of TA phonons (and associated folded bands) as a function of frequency for bulk GaN (black dotted curve), the 1+1 SL (green dashed curves), and the 3+3 SL (purple solid curves). (Bottom) Corresponding room-temperature cross-plane thermal conductivity accumulations with frequency for the TA phonons (and associated folded bands). Arrows highlight the correspondence between disappearing velocities and reduced thermal conductivity contributions.

Figure 7

(Top) Room-temperature phonon lifetimes for AlN (blue squares), GaN (black circles), and the $\frac{1}{2}+\frac{1}{2}$ SL (red triangles). (Bottom) Corresponding cross-plane thermal conductivity accumulations.

Figure 8

(Top) Calculated room-temperature scattering rates for GaN (black circles) and AlN (blue squares). (Bottom) Corresponding calculated mode-dependent phase spaces for each material. Note that these calculations used harmonic and anharmonic IFCs as in Refs. [9] and [47].

Figure 9

Room-temperature scattering rates (top) and mode-dependent phase spaces (bottom) for a toy model built from the harmonic and anharmonic IFCs of GaN with one Ga mass varied: 69.72 amu (Ga mass; black circles), 48.35 amu (average of Ga and Al masses; orange diamonds), and 26.98 amu (Al mass; red triangles). The inset gives the low-frequency $c$-axis phonon dispersion for each system. For the scattering rates (top), hollow symbols correspond to rates that involve at least one folded LA mode (7–15 THz range) and filled symbols correspond to the total rates. Note that these calculations used harmonic and anharmonic IFCs as in Ref. [9].

Figure 10

Room-temperature phonon lifetimes for the 1+1 SL (green circles), the 2+2 SL (orange triangles), and the 3+3 SL (purple squares).

Figure 11

(Left) Mode contributions to room-temperature $\kappa$ versus magnitude of cross-plane velocity component ($v_{\mathrm{cross}}$) for the 1+1 SL (green circles) and the 3+3 SL (purple squares). Only modes with frequencies less than $\sim 10$ THz with $v_{\mathrm{cross}}>1$ km/s are shown; these sum up to $\sim 95\%$ of the total $\kappa$. Numbers label the lifetimes in picoseconds for select modes that give relatively large $\kappa$ contributions. The black line highlights the square dependence of the mode $\kappa$ on velocity. (Right) Room-temperature cross-plane thermal conductivity accumulation versus frequency for the 1+1 SL (green circles and curve) and the 3+3 SL (purple squares and curve). Numbers give the lifetimes for select modes corresponding to the left figure.