Briefly, a high-power (~50 to 100 mW) laser pulse impinged on a metal optothermal transducer layer coated on the sample. This laser pulse excited surface electrons that quickly thermalized, sending a heat pulse propagating through the metal and then through the sample, away from the surface. A time-delayed probe pulse measured the changing surface reflectivity caused by changing temperature. A multidimensional, multilayer heat equation was fit to the resulting cooling curve, yielding the thermal conductivity of the SL layers (13). The system used here is described in further detail in a previous publication (44). We deposited a 100-nm-thick Al optothermal transducer layer on the SLs and a calibration sapphire substrate. We confirmed the thickness of the Al transducer layer by matching the TDTR-measured thermal conductivity value of the sapphire substrate with the known literature value. Low-temperature measurements were conducted by mounting the samples in a high-vacuum (~10−3 Pa) cryostat. The transient reflectance of the sample surface was measured with a Si photodiode.

Each sample was probed at around three to five different locations. At each location, the samples were measured under four different pump modulation frequencies—3, 6, 9, and 12 MHz—with three individual data traces collected for each modulation frequency. The three runs at each frequency were averaged, and the Fourier fitting analysis was performed on the resultant average curve at each modulation frequency for each location. Sample sets of fitting curves for the reference samples and the 25% ErAs coverage samples for different SL thicknesses and at different temperatures are shown in figs. S4 and S5.

The data were fit to a four-layer model comprising the metal optothermal transducer, the interface between the metal and the SL, the SL, and a semi-infinite substrate. The data were fit for the interface conductance between the metal and the SL, and the SL thermal conductivity. The other required parameters for the fitting were taken from the literature. Since the volumetric fraction of ErAs was small compared with GaAs and AlAs (0.32 and 1 ML of ErAs per 10 MLs of GaAs or AlAs for the 8 and 25% nanodot areal coverage samples, respectively), the heat capacity was taken to be the average of GaAs and AlAs. An initial guess for the interface conductance between the SL, capped by a 3-nm GaAs layer, and the Al optothermal transducer layer were taken from previous measurements of the interface conductance between a bulk GaAs substrate and an Al layer deposited with an identical procedure. Due to its size dependence, the effective thermal conductivity of GaAs at low temperatures was also taken from previous measurements.

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