On the Shockley Diode Equation and Analytic Models for Modern Bipolar Transistors

Shockley stated in his 1949 paper that, “The p–n–p transistor has the interesting feature of being calculable to a high degree.…” The features of bipolar transistors are calculable to a high degree because the minority‐carrier current in the base flows in a single direction, from emitter to collector, enabling the formulation of analytic but mathematically simple models for the various device parameters. Shockley derived the boundary condition, the Shockley diode equation, for solving the diffusion equation governing the transport of minority carriers in the base region of a bipolar transistor. For an n–p–n transistor, this gives the local electron density, n _p (x) in the p‐type base region, which is then used to derive the equations for collector current, Early voltage, and base transit time. The ${\mathit{n}}_{\mathit{i}}^{\mathbf{2}}$ factor in the Shockley diode equation is adapted in a natural manner to account for the new physics, i.e. heavy‐doping effect and base‐bandgap engineering, responsible for the enhanced performance of the modern bipolar transistors.