Analysis of Charge Conservation in Isolated Silicon Regions

A simple formalism for charge conservation is presented, which allows the physically correct prediction of the electrical behavior of isolated silicon regions in two or three dimensions. It is shown that an integral boundary condition can be applied to the semiconductor equations to obtain a physical solution. The charge conservation formalism has been used to study the physics of isolated silicon regions. The influence of charge conservation on the electrical coupling of multi-layered structures is seen in the C-V curve of a two-terminal SOI capacitor. This formalism does not only allow the correct modeling of the electrical characteristic of a trench isolation with polysilicon as trench filling and a capping oxide, it does also allow the prediction of the electrical behavior influenced by a mobile charge confined in the trench filling.