Based on previously reported studies, yttria stabilized zirconia [Y 0.15 Zr 0.85 O 1.93 (YSZ)] has been used as an epitaxial buffer layer on Si(001) substrates. However, a considerable lattice mismatch exists between the YSZ and Si (¹5.4 %). This work elucidates the reported relationship between the lattice parameter and composition of neodymia stabilized zirconia [(Nd X Zr 1¹X O 2¹X/2) (NdSZ)]. According to the relation, the lattice parameter of NdSZ is the same as that of Si at x = 0.75. Therefore, if the epitaxial growth of NdSZ thin film with x = 0.75 is realized on a Si(001) substrate, then zero lattice mismatch can be expected. The deposition of NdSZ thin film on Si(001) substrate was done by dynamic aurora pulsed laser deposition (PLD). Results show that cube-on-cube epitaxial growth (NdSZ(001)[100]//Si(001)[100]) is realized between x = 0.16 and x = 0.52. The best composition of epitaxial NdSZ thin film is regarded as x = 0.47 from the point of crystallinity, orientation and lattice mismatch (¹1.1 %). When composition x is larger than x = 0.57, the NdSZ thin film orientation becomes (111). Results also show that the lattice parameter of the NdSZ thin film is larger than that of NdSZ bulk. For x = 0.47 thin film, the coexistence of the epitaxial (221) domains is detected in addition to the (001) cube-on-cube domain. The (221) domain is formed due to lattice matching of the oxygen sub-lattice, which has an isosceles triangle shape. We produced cube-on-cube epitaxial NdSZ thin film on Si(001) substrate with a very small lattice mismatch. However, such a small lattice mismatch brings about additional (221) domains that have been reported in the epitaxial growth of CoSi 2 thin film on Si(001) substrate. The lattice mismatch between CoSi 2 and Si is ¹1.2 %, which is approximately equal to that between NdSZ (x = 0.47) and Si.