Since the atomistic Green’s function method models harmonic systems, scattering comes from the breaking of translational symmetry. In this particular case, the suppression of phonon transport is due to the presence of interfacial roughness and ErAs nanoparticles. Within one unit cell on each side of the interface, coordinates corresponding to the Ga/Al sublattice were chosen at random. In the case of interface roughness, the Ga or Al atom was replaced with Al or Ga, respectively. In the case of randomly placed ErAs nanodots, the coordinate corresponds to the center of the dot; consequently, all Ga and Al atoms within 0.5 nm of this point were replaced with Er atoms. In all these replacements, only mass was changed, while force constants were maintained the same. ErAs grows in the rock salt structure instead of the zinc-blende structure of GaAs. Our approximation assumes that the mass difference is the major mechanism of phonon scattering, which is reasonable considering that Er is 6.29 and 2.40 times heavier than Al and Ga, respectively. Since the randomness introduces variance in the calculated thermal conductivity, a configurational average is necessary. The number of configurations, for a given sample thickness, is inversely proportional to its sample thickness to ensure constant computational cost for each data point in Fig. 3 (E and F). For our data, one configuration was used for the 100-period device regions, four configurations were used for the 25-period device region, and 100 configurations were used for the 1-period device region, etc.

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