  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.
