This Letter reports a modeling study on the formation of streamer discharges from an isolated ionization column under subbreakdown condition. Numerical simulations show that positive streamers are able to form from the tip of an ionization column in a uniform applied electric field well below the breakdown threshold field. However, even when the applied field approaches the breakdown threshold field, negative streamers fail to originate from the other tip of the ionization column after the positive streamer has propagated a certain distance. The results reported explain some puzzling observations on streamer discharges in nature such as the predominant initiation of sprites by downward propagating positive streamers and help advance the initiation theories of sprites and lightning.

Electric field values measured inside thunderclouds have consistently been reported to be up to an order of magnitude lower than the value required for the conventional electrical breakdown of air. This result has made it difficult to explain how lightning frequently occurs in thunderclouds. A few different theories have been offered to explain the lightning initiation process, one of them being the theory of lightning initiation from hydrometeors. According to this theory, lightning can be initiated from electrical discharges originating around thundercloud water or ice particles in the measured thundercloud electric field. These particles, called hydrometeors, are believed to cause significant enhancement of the thundercloud electric field in their vicinity and then initiate streamers that are the precursor discharges for the hot lightning leader channel. Previously, Liu et al. (2012a) reported streamer formation from a model hydrometeor in an electric field value of half of the conventional breakdown threshold (E k ) for air. In this paper, we present modeling results for streamer formation in electric fields as low as one third of the breakdown threshold. According to our results, initiation of stable streamers from thundercloud hydrometeors in a 0.3E k electric field is possible, only if enhanced ambient ionization levels (e.g., the ionization created by corona discharges around the same or other nearby hydrometeors) are present ahead of the streamer. The magnitude and distribution of this ambient density may be a determining factor on whether the streamer branches, recovers after the prebranching stage, or continues propagating stably. We investigate the streamer branching behavior and characteristics and test a theory that has recently been proposed to explain this phenomenon. We find that the geometry of the streamer head plays an important role in the streamer branching phenomena. The fast radial movement of the maximum streamer head curvature, combined with the slow reduction of the maximum curvature value, eventually leads the streamer head to branching. Finally, we compare our modeling results with laboratory experiments and realistic thundercloud conditions and discuss the implications of this study to lightning initiation and other lightning-related phenomena.

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A coupled plasma-feature scale model is employed to investigate the etching of high aspect ratio (HAR) silicon (Si) structures using a cyclic multi-step pulsed plasma process in an inductively coupled plasma (ICP) reactor. This process sequence includes an oxidation step to help protect the Si sidewalls, a main Si etch step where the ion energy and angular distribution (IEAD) and ion/neutral flux ratio are controlled through power pulsing, and a clean step prior to repeating the multi-step process. Two-dimensional plasma models are used to compute the IEAD as well as the fluxes of relevant ions and neutral radicals at the wafer. These plasma models are coupled to a three-dimensional feature scale model, where multiple cycles of the three-step etch sequence are simulated. The paper focuses on evaluation of several pulsing modes during the main Si etch step including separate pulsing of the ICP source or RF bias power, and their synchronized pulsing (with phase control). Process performance has been quantitatively evaluated by examining etch rates for Si and the SiO 2 -like mask, Si/mask etch selectivity, and CDs within the HAR features. When only the RF bias power is pulsed, Si and mask etch rates scale with pulse duty cycle (DC). As a result, if Si is etched to the same depth, the HAR trenches are wider at higher DCs due to less total oxidation time and less protection of the sidewalls. ICP source power pulsing provides higher Si etch rate because of RF bias power being on continuously, but suffers from poor mask selectivity. Synchronized pulsing of both the ICP source and RF bias powers in conjunction with phase control provides additional flexibility in modulating the IEAD and the ion/neutral flux ratio. RF bias pulsing and in-phase synchronized pulsing yield the best selectivity for the conditions explored.