In order to study the characteristics of bipolar cascade lasers, we have developed a fully consistent transport model compatible with Esaki tunnel junctions (TJs). First, we compare the calculated electrical characteristics of TJs made of different InGaAsP lattice-matched to InP materials with different doping concentrations. Then, a complex (p-n)-(n++p++)-(p-n)-(n++p++)-p-n) structure is implemented. The Esaki junctions are cladded by doped InP current confining layers, the width of which is optimized to prevent electron leakage. We find that a 25-nm-wide InP barrier confines more than 98% of the electron current for a total injection current of 10 kA.cm-2 at room temperature. The predicted differential quantum efficiency is then 230%.