| Due to certain limitations of silicon for particular device applications, there has been increasing interest in the use of compound semiconductors. However, the growth of compound semiconductors in single crystal form is not always feasible on a large scale or even wanted for particular applications, such as solar cells or thin film transistors. The material for these applications is usually polycrystalline, and the presence of grain boundaries limits the performance of these devices. In our work, we present two models that take into account the effect of grain boundaries in nanocrystalline field-effect transistors.;In our "macroscopic" model, we modify the field-effect mobility to include terms dependent upon the local carrier density and the longitudinal field along the channel. These terms are motivated by the expected carrier density and field dependences of transport across grain boundaries. In general, we find that the addition of each mobility term separately changes the carrier profile along the channel in opposite ways, and the inclusion of these terms increases the magnitude of the current. Furthermore, the addition of the longitudinal field dependent mobility term is only significant for large values of drain bias, i.e. near saturation.;The limitation of the macroscopic model is that it inherently averages over the grains present in the channel. In order to further study the role of grains in the channel, we developed our "mesoscopic" model that incorporates ideas from percolation theory. Here, individual grains are represented as sites in our percolation problem, while the bonds represent the energy barriers between neighboring grains. The relative occupation of sites and bonds is connected to the carrier statistics of the device, whereby the carriers can be either free carriers in the grain or trapped carriers at the grain boundary. The relative occupations are controlled by the applied gate bias. Through the combination of a site-bond percolation problem and the carrier statistics, we describe the behavior of the transistor near threshold and illustrate a method to determine the threshold voltage. |
