There is no
prohibition against giving Zakah money to your half brothers and sisters, if they are poor and do not have any wealth that makes them not in need of Zakah. It is also permissible for you to give Zakah to your elder brother if he is poor and does not have any wealth or income that makes him not in need of Zakah. This is due to the general meaning of the Ayah (Qur'anic verse) about Zakah:
As-Sadaqât (here it means Zakât) are only for the Fuqarâ’ (poor), and the Masâkin (needy) and those employed to collect (the funds), and to attract the hearts of those who have been inclined (towards Islâm), and to free the captives, and for those in debt, and for Allâh’s Cause, and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allâh. And Allâh is All-Knower, All-Wise.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.