A filamentary dielectric barrier discharge (DBD) is ignited on a silicon wafer under atmospheric pressure conditions in a mixture of argon and air (0.5/0.5) in two different modes, namely a stochastically ignited filamentary discharge and a self‐organized filamentary discharge by the application of high voltage (HV) pulses at two repetition frequencies, 0.5 and 5 kHz. The discharge conditions are characterized by optical emission spectroscopy and current–voltage measurements. The silicon wafer surface treated with the DBD is studied with an electron microscope. The formation of a homogeneous silicon oxide layer is observed after treatment under a stochastically filamentary DBD. Whereas, in the self‐organized filamentary DBD, etching tracks (thin channels) and blisters are produced on the silicon wafer surface, which are interpreted as tracks of plasmoids, namely plasma objects without any direct contact to a power supply. The transition between the different filamentary modes of the DBD plasma occurs in the presented study through an increase of the repetition frequency of HV pulses, but it can also be caused by small silicon splinters on the wafer surface. The splinters cause ignitions in stable positions, and therefore induce a combination of discharge modes, namely stochastically and self‐organized DBD mode. In close proximity to the splinters, tracks of plasmoids are observed, even in the DBD at low frequency.