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We present simulations of the dissociation of perfect dislocations into extended partial dislocations in aluminum, palladium, and nickel using a phase field dislocation dynamics (PFDD) theory that incorporates the surface. As expected from dislocation theory, the simulations show that increasing the intrinsic stacking fault energy, normalized by the product of the shear modulus and Burgers vector, decreases the equilibrium stacking fault width. Significantly, it is also found that increasing the unstable stacking fault energy has the same effect when the intrinsic stacking fault energy is held constant. Furthermore, our results show that the equilibrium configurations cannot be described only by the ratio between the intrinsic and unstable stacking fault energies as previously suggested but rather by their product.