An accurate prediction of the particle charge in plasmas is of fundamental importance for a wide range of problems from the study of dusty or complex plasmas to the controlled synthesis of nanoparticle materials in plasmas. Despite its known deficiencies, the orbital motion limited (OML) theory, which strictly applies only to collisionless plasmas, is the most widely used model to describe particle charging. This paper develops a simple, analytical model to describe the charging of particles in plasmas over a wide range of pressures and particle sizes. In spite of its simplicity, excellent agreement is found with results of a self-consistent molecular dynamics Monte Carlo model and with experimental results found in the literature. In particular, the model presented here provides significant improvements compared to the OML theory.

Low pressure silane plasmas are known for their ability to synthesize silicon nanoparticles via gas phase nucleation. While in the past this particle formation has often been considered from the viewpoint of a contamination problem in semiconductor processing, we here describe a silane low pressure plasma that enables the synthesis of highly oriented, cubic-shaped silicon nanocrystals with a rather monodisperse size distribution. These silicon nanocubes have successfully been used in the manufacture of single nanoparticle vertical transistors. We discuss the advantages of this new paradigm of building nanoelectronic devices. The plasma synthesis process is characterized in more detail than in prior work. The particle nucleation, growth and shape evolution are studied. Results indicate that the process provides two spatially distinct zones: a diffuse plasma for particle growth and a constricted plasma zone for particle annealing. Measurements of the plasma ion density using a capacitive probe suggest that the plasma density in the constricted region of the plasma is about an order of magnitude higher than in the diffuse region, likely aiding the formation of cubic silicon nanocrystals. The process of particle extraction from the plasma reactor is discussed based on the balance of various forces acting on the particles. It is found that the use of a critical orifice for particle extraction enables the detrapping of particles which carry as many as 35 elementary charges.