We studied the size distribution and its scaling behavior of self-assembled InAlAs/AlGaAs quantum dots (QDs) grown on GaAs with the Stranski-Krastanov (SK) mode by molecular beam epitaxy (MBE), at both 480{deg}C and 510{deg}C, as a function of InAlAs coverage. A scaling function of the volume was found for the first time in ternary alloy QDs. The function was similar to that of InAs/GaAs QDs, which agreed with the scaling function for the two-dimensional submonolayer homoepitaxy simulation with a critical island size of i = 1. However, a character of i = 0 was also found as a tail in the large volume.
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