Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper l-filter of a poset is contained in a proper semiprime filter, then it is 0-distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is shown that a 0-distributive poset P is semiatomic if and only if the intersection of all non dense prime ideals of P equals (0]. Some counterexamples are also given.