Integrated circuit capacitors have composite dielectric layers therein. These composite dielectric layers include crystallization inhibiting regions that operate to increase the overall crystallization temperature of the composite dielectric layer. An integrated circuit capacitor includes first and second capacitor electrodes and a capacitor dielectric layer extending between the first and second capacitor electrodes. The capacitor dielectric layer includes a composite of a first dielectric layer extending adjacent the first capacitor electrode, a second dielectric layer extending adjacent the second capacitor electrode and an electrically insulating crystallization inhibiting layer extending between the first and second dielectric layers. The electrically insulating crystallization inhibiting layer is formed of a material having a higher crystallization temperature characteristic relative to the first and second dielectric layers.