Interesting semiconducting material families in current research, such as van der Waals layered solids and conductive oxides, have the potential to play a crucial role in the development of the next generation of electronic devices, from electrodes, through to sensors and up to encryption keys. To deliver this promise, they will need to be industrially up-scaled, which will inevitably be in the form of polycrystalline films.  

Theories developed in the 1970’s [1] and 80’s [2], describing the electrostatics and transport through grain-grain boundaries in polycrystalline semiconductors (PC-S), have facilitated their modern use despite being afflicted with inaccuracies, which often result in significant discrepancies between model predictions and experimental observations. For example, the potential drop over the depletion region surrounding the grain boundary is usually assumed to be symmetric about the peak energy, whereas self-consistent models suggest that this is rarely true. While these discrepancies have been largely mediated in conventional PC-S applications, e.g. by high doping concentration in CMOS gate electrodes, emerging new applications for PC-S will require a more rigorous understanding of the electrostatic structure and the resulting transport behaviour in these material systems.

We propose a new model that combines a detailed, self-consistent description of the non-equilibrium electronic structures surrounding grain boundaries, with a probability-based treatment of material parameters such as grain size distribution and non-uniform doping profiles. Modelling large films is achieved through two separate approaches; i) a finely-tuned Monte Carlo simulation acting in both position and momentum spaces and ii) a ‘coarse-grain’ sparse matrix equivalent circuit model, aimed at facilitating knowledge transfer to industry. The two models, informed by experimental results, deviate from the comfortable deterministic view of PC-S characteristics, and instead offer a realistic probability density-based description of electronic behaviour that will underpin future applications of these materials.

 

[1] J. Y. Seto, J. Appl. Phys. 46, 5247 (1975)

[2] J. Martinez & J. Piqueras, Solid-State Electron. 23, 297 (1980)