The parents' lawyer, Joseph Williams, could not immediately be reached for comment.
Zhu, from Concord, California, had expressed a desire to have a family of his own, his parents said.
The 21-year-old senior at the US Military Academy at West Point in New York had discussed his dreams with his parents, telling them he wanted to be a father - to five children - and raise them on a ranch, despite their teasing him that such a brood would be expensive, his parents wrote in their March 1 petition.
For a senior class assignment, Zhu recently wrote that he wanted to get married "before 30," have kids and "become a career officer in the military," according to court records.
"Our son's dying wish was to become a father and to bring children into this world," his parents said.
But Art Caplan, a professor of bioethics and head of the division of medical ethics at New York University's school of medicine, said the case is "an ethical quagmire," explaining that there's no set system for asking people what they want for their genetic material after their death and no set system for making that determination in court when they haven't legally made their wishes known.
That, Caplan said, leaves many ethical considerations, particularly about what's in the best interest of the child.
Would the deceased parent have wanted the child to be created using a surrogate? Would that parent have wanted the child to be raised by his or her grandparents or someone other than the actual parent? When and how would that parent have wanted the child to be told the circumstances?
Regarding the Zhu case, Caplan said he disagrees with the judge's decision because he does not believe parents should have control over their children's reproduction. "It doesn't exist in nature," he said. He added that he thinks such allowances should be made only for partners or spouses.
In February, Zhu was gravely injured in a skiing accident on the West Point ski slope, fracturing his spinal cord, according to court documents.
Days later, on February 27, the 21-year-old was declared brain dead.