3.1.6.3 Polysilicon Contact

The dielectric flux $\mathrm{D}$ through the oxide reads

$${\mathbf{n}}\cdot{\mathbf{D}} = - \frac{\varepsilon_{\mathrm{ox}}}{d_\mathrm{ox}}\cdot V_\mathrm{ox}$$ (3.54)

where $V_\mathrm{ox}$ is the voltage drop over the thin oxide layer which is introduced between polysilicon and silicon, and $\varepsilon_{\mathrm{ox}}$ and $d_\mathrm{ox}$ denote the permittivity and thickness of this layer. The electron and hole current densities across the contact interface read [107]

$${\mathbf{n}}\cdot{\mathbf{J}}_n = \sigma_\mathrm{ox} \cdot V_{ox},$$ (3.55)

$${\mathbf{n}}\cdot{\mathbf{J}}_p = {\mathrm{q}}\cdot p \cdot S_p,$$ (3.56)

where $\sigma_\mathrm{ox}$ is the oxide conductivity, $p$ is the hole concentration in the semiconductor, and $S_p$ is the hole surface recombination velocity. $V_\mathrm{ox}$ depends on the quasi-FERMI level in the metal (which is specified by the contact voltage $\phi_{\mathrm{m}}$), the potential in the semiconductor $\phi_{\mathrm{s}}$, and the built-in potential $\psi_{\mathrm{bi}}$.

$$V_\mathrm{ox} = \phi_{\mathrm{s}}- \phi_{\mathrm{m}}- \psi_{\mathrm{bi}}.$$ (3.57)

The polysilicon contact boundary conditions for the carrier temperatures $T_n$ and $T_p$ and the lattice temperature $T_\mathrm{L}$ are similar to the ones which apply for the Ohmic contact, i.e. (3.36) and (3.37), or (3.38), respectively.

T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation