In photonic crystals, electromagnetic waves can be confined in all three dimensions leading to very small mode volumes, a computational search has been made for the smallest electromagnetic mode volume which occurs in two-dimensional. dielectric photonic crystals slabs. The smallest mode volume found was V approximate to 2(lambda/2n)(3), where n is the refractive index. This small mode volume can lead to significant enhancement of spontaneous emission rates in semiconductor nano-cavities due to the Purcell effect.