Investigating and modeling impact ionization current in MOSFETs

• An efficient method of evaluating substrate current is introduced.
• T-dependent substrate current’s behaviors are analyzed, summarized, and explained.
• At sub-bandgap bias, new substrate current formula is derived.

Substrate current caused by impact ionization in Si-metal-oxide-field-effect transistors is investigated and modeled with the aids of Monte Carlo simulations. At high biases, the substrate current’s temperature-coefficient is systematically summarized with respect to the device’s characteristic length. Physical factors affecting the substrate current’s temperature-dependent behaviors are discussed. As the supply bias is scaled down to near or below the bandgap energy, impact ionization is mainly caused by the mobile charge carriers in the tails of the distribution functions. Those tail carriers are negligible in high-bias applications such as the experiments measuring the impact ionization coefficients. Consequently, conventional models that use the macroscopic coefficients fail to describe the impact ionization current’s behaviors in this low-bias regime. Based on the specific characteristics of the distribution functions’ tails, a new analytical model for the substrate current, for the first time, is derived in the low-bias regime accounting for different important physical factors.