Albert Barnes Commentary 2 Chronicles 36:20

"And them that had escaped from the sword carried he away to Babylon; and they were servants to him and his sons until the reign of the kingdom of Persia:" — 2 Chronicles 36:20 (ASV)

Servants - Or, “slaves.” They were probably employed by Nebuchadnezzar in the forced labor which his great works necessitated.

His sons - The word probably includes all of Nebuchadnezzar's successors in the independent sovereignty of Babylon.