The turn ON field would be something analogous to work function. At a certain field strength, the electron emission begins. For any nano-structure of a material, the field strength would be lower for the field emission as compare to the filed strength required to start the field emission in its bulk form due to but obvious size effect. As it happens in thermionic emission, the energy required to just pull out an electron from the metal and into the immediate vacuum. We can on the similar lines can generalized this definition for the field emission from the graphene samples.
Turn-on field is defined as the applied field strength at which field emission from the material begins. Most popularly, the applied field at which the emission current density reaches to 10 µA/cm2 is termed as Turn-on field.