Theory of electrothermal behavior of bipolar transistors: part III-impact ionization

A detailed theoretical and numerical analysis of single-finger and two-finger bipolar transistors is proposed, which includes both self-heating and impact-ionization effects. Although related to completely different physical phenomena, self-heating and impact ionization share a common feature in that they introduce a positive feedback mechanism that causes the same singularities in the current-voltage characteristics, namely, a snapback (or flyback) behavior and current bifurcation. These singularities are triggered if either one or both effects are activated. Based on a rigorous mathematical method, referred to as the "Jacobian method," generalized conditions are derived for determining the onset of flyback and bifurcation, which ultimately limit the safe operating region, as a result of the combined action of impact ionization and self-heating. The proposed formulation also includes several important effects not considered in previous contributions. Finally, a detailed analysis of the limiting boundaries for safe device operation is presented, and simple criteria for the optimal choice of the ballasting network are suggested