Low-pressure high density plasma processes are indispensable today for the microelectronic manufacturing industry. Classic plasma global models have been important tools for studying the properties of low pressure plasmas due to their highly computational efficiency and large chemical reaction capacity. However, the lack of detailed description of surface processes rendered these classic plasma global models incapable of predicting the surface-process-dominated phenomena such as the several times [O] (atomic oxygen density) increase in an SF6/O2 plasma compared to a pure O2 plasma when even small amount of SF6 is added to the feedstock gas composition (e.g. 5%). It seemed like global modelling in the field of low pressure plasma material processing had reached a dead end. But things were not so hopeless, to combat the challenge global modelling faces, in 2009 Kokkoris et al published an SF6 plasma global model with heterogeneous surface model. However, the details of their surface model and how it was coupled to a plasma global model was not given. In this work, I start from the detailed descriptions of a plasma global model with heterogeneous surface model and then show that my methods for modelling the surface processes of a plasma are viable. The mechanisms are then extended to the development of an SF6/O2 plasma model. I will model and give explanations on the mechanisms governing the aforementioned [O] increase in an SF6/O2 plasma, which was only reported in experimental works. The work on the fluctuations of a plasma model's outputs due to the statistical variations of the electron-involving reactions' rate coefficients is also discussed in this thesis. The current trend in the microelectronic manufacturing industry is to deploy ECR (electron cyclotron resonance) source plasmas for material processing. To follow this trend, the most crucial step of modelling an ECR discharge, namely the electron heating calculation is also given a detailed discussion in this work.