Numerical study of the effect of gas temperature on the time for onset of particle nucleation in argon–silane low-pressure plasmas

Abstract

Particle nucleation in silane plasmas has attracted interest for the past decade, both due to the basic problems of plasma chemistry involved and the importance of silane plasmas for many applications. A better understanding of particle nucleation may facilitate the avoidance of undesirable particle contamination as well as enable the controlled production of nanoparticles for novel applications. While understanding of particle nucleation has significantly advanced over the past years, a number of questions have not been resolved. Among these is the delay of particle nucleation with an increasing gas temperature, which has been observed in experiments in argon-silane plasmas. We have developed a quasi-one-dimensional model to simulate particle nucleation and growth in silane containing plasmas. In this paper we present a comparative study of the various effects that have been proposed as explanations for the nucleation delay. Our results suggest that the temperature dependence of the Brownian diffusion coefficient is the most important effect, as diffusion affects both the loss rate and growth rate of particles.

Gas temperature dependence of coagulation onset times for nanoparticles in low pressure hydrocarbon plasmas

“…Finally, Warthesen et al 16 proposed a decreased gas density (at constant pressure) explaining the observed effect. Bhandarkar et al 17 showed in a comparisonal numerical study that-although present-none of these processes could adequately explain the observed delay. Those authors demonstrated that the temperature dependence of the Brownian diffusion coefficient was the most dominant factor in the nucleation delay in silane.…”

“…Those authors demonstrated that the temperature dependence of the Brownian diffusion coefficient was the most dominant factor in the nucleation delay in silane. 17 With respect to the gas temperature dependence of nanoparticles formation in silane based plasmas, some researchers have discussed processes in terms of diffusion times of protoparticles and their critical density necessary of coagulation onset. 18,19 For Ar/CH 4 discharges, the temperature dependence of the coagulation time has been studied experimentally.…”

“…This is indeed demonstrated in the work of Ravi and Girshick, 21 where the density negatively charged particles grows with respect to the density of neutral particles as discharge time evolves. When the gas temperature is elevated, the Brownian diffusion coefficient-scaling with T g 3/2 when the gas pressure is kept constant-increases as well, 17 leading according to Eq. (1) to a shorter diffusion time and, hence, to a shortened particle residence time in the plasma as well.…”

Nanoparticles in SiH4-Ar plasma: Modelling and comparison with experimental data

“…To this end, one such task is the investigation of Si nanoparticles, which are often studied using plasma chemical reactors at low pressure (10 to 100 Pa), and radio frequency (RF) discharge in pure silane or gas mixtures such as Ar-SiH 4 and He-SiH 4 (see, for example, the book 1 ). Detailed experimental investigations of Si particle growth have been performed, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] while theoretical studies of Si nanoparticle growth have also been carried out, developing both complex [19][20][21][22] and relatively simple [23][24][25][26][27][28] models. However, direct comparisons of experimental and theoretical results have not been shown in most cases.…”

“…In fact, this must be the maximal rate of production of cluster-dimers. Detailed chemical analyses 20,21,30 have shown that SiH 3 -SiH 3 collisions do not lead to the formation of Si 2 H m dimer-radicals. These dimers can be obtained due to the SiH 2 radical.…”