Incentivize earning of advanced degrees for those who will work within the U.S.

PhD degrees within the U.S. are primarily earned by foreign nationals, many of whom return to their home country after graduation. PhD degrees teach innovation, research and advancement. While I support education for all, I believe there to be a large gap between the U.S and other technologically advanced countries due to lack of higher degrees earned by those who remain within the U.S, especially STEM degrees. I believe there should be federal encouragement for this (not just "in-state tuition"), to incentivize both a) U.S. citizens to earn PhD degrees and b) foreign nationals who come here for education to remain within the U.S. to use their degree. This can be monetary and/or a faster way to allow citizenship to be earned.