3.3.1.1 Continuous Quasi-Fermi Level

The Continuous Quasi-Fermi level (CQFL) model assumes a constant Fermi level over the interface during current flow. The relations for the current density $J_\nu$, the carrier concentration $\nu$, the energy fluxes $S_\nu$, and the carrier temperatures ${\it T}_\mathrm{\nu}$ read as follows:

$$J_{\nu2} = J_{\nu1}$$ (3.83)

$$\nu_2 = \nu_1 \cdot \bigg(\frac{m_{\nu2}}{m_{\nu1}} \bigg)^{3/2} \cdot \exp \bigg(-\frac{\Delta E_C}{{\it k}_{\mathrm{B}}\cdot T_ {\nu1}}\bigg)$$ (3.84)

$$S_{\nu2} = S_{\nu1}- \frac{1}{q} \cdot \Delta E_C \cdot J_{\nu2}$$ (3.85)

$$T_{\nu1} = T_{\nu2}$$ (3.86)

The four equations constitute a Dirichlet boundary condition at the interface. The model is mostly used to separate segments with no (homojunction) or little band gap discontinuity relative to ${\it k}_{\mathrm{B}}\cdot{\it T}_\mathrm{L}$ and the band gap. The higher the band gap discontinuity $\Delta E_C$, the less appropriate the model. For heterojunctions the two models of the next section are to be used.