3.3.2 Semiconductor-Insulator Interfaces

The condition for the semiconductor-insulator interface equivalently is determined by a continuous potential and by an applied surface charge density $\sigma_{surf}$ according to the Gauß law:

$$\varphi_{semi} = \varphi_{ins}$$ (3.95)

$${\bf n}\cdot \varepsilon_{semi}\cdot {\bf E}_s - {\bf n}\cdot \varepsilon_{ins} \cdot {\bf E}_{ins} = \sigma_{surf}$$ (3.96)

The carrier flux and the carrier energy flux are zero. The lattice temperature ${\it T}_\mathrm{L}$ is continuous. To describe the Fermi level pinning at the surface due to a high density of states for traps, distributed surfaces charges are introduced which describe the surface depletion due to the band bending. The current densities $\mathbf{n}\cdot\mathbf{J}$ and the energy fluxes $\mathbf{n}\cdot\mathbf{S}$ are set to zero.