Since the current relations were introduced by using two separate subsystems it is convenient to also split up the current continuity equation eqn. (2.18) into two equations by introducing a formal separation parameter
By summarizing POISSON's equation (2.38), the current continuity equations (2.39) and (2.40), and the current relations (2.35) and (2.36), the set of basic semiconductor equations is obtained. This set of equations was first presented by VANROOSBROECK in 1950 .
M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF