Ion acceleration is of interest for applications in fast ignition, compact particle sources, medical science, and others. The formation of plasma is of fundamental importance for understanding ion acceleration driven by intense laser. In order to further understand the solid dense material ionization dynamics under ultra-strong field, we use two-dimensional particle-in-cell code to study the ionization process of ultra-thin carbon film, driven by ultra-short intense laser pulse, particularly to see the plasma generation and distribution during the interaction. When an ultra-intense short pulse laser irradiates a solid dense nm-thick film target, the collisional ionization can be ignored for such a thin film target. If the target thickness is larger than laser pulse skin depth, the formation of plasma is contributed from laser field direct ionization and the ionization of electrostatic field inside the target, both of which are discussed and compared by the simulation results in this work. The ionization directly stimulated by laser field happens only near the laser-target interaction surface. After the generation of plasma on the target surface, electrons are accelerated into the target because of laser ponderomotive force. A huge electrostatic field is formed inside the target as a result of hot electron transport in it, and ionizes the target far from the interaction surface. It is found that a bigger fraction of ionization is contributed from electrostatic field ionization inside the target. The effect of laser pulse intensity on ionization is studied in detail, in which the laser pulse intensity is changed from 11018 W/cm2 to 11020 W/cm2. Comparing the results obtained under different intensities, we can see that higher intensity results in higher ionization speed, and much higher-order ions can be generated. At an intensity of 11020 W/cm2, although the intensity much higher than the threshold can generate C+6, only a small part of ions can be ionized into C+6. The reason is that the C+6 ions can be generated directly only by laser field, and the total number of C+6 ions is determined by laser pulse skin depth and spot size. We also consider the effect of laser pulse duration from 30 fs to 120 fs at an intensity of 11020 W/cm2. It is found that higher ionization speed can be obtained, while much less higher-order ions can be generated under shorter laser pulse duration. This description of the generation of solid density plasma driven by intense laser interacting with nm-thick target helps us to further understand the material characteristic under ultra-strong field. This work also benefits the numerical model of plasma in application, namely laser driven ultra-thin film ion acceleration.