Transient Phenomena in Sub-Bandgap Impact Ionization in Si n-i-p-i-n Diode

Sub-bandgap (SBG) impact ionization (II) enables steep subthreshold slope that enable devices to overcome the thermal limit of 60 mV/decade. This phenomenon at low voltage enables various applications in logic, memory, and neuromorphic engineering. Recently, we have demonstrated sub-0.2-V II in n-i-p-i-n diode experimentally primarily based on steady-state analysis. In this paper, we present the detailed experimental transient behavior of SBG-II in n-i-p-i-n. The SBG-II generated holes are stored in the p-well. First, we extract the leakage mechanism from the p-well to show two mechanisms: 1) recombination–generation and 2) over the barrier (OTB), where OTB dominates when barrier height <inline-formula> <tex-math notation="LaTeX">${\phi }_{b}<\textsf {0.59}~\textsf {eV}$ </tex-math></inline-formula>. Second, we analytically extract the SBG-II current (<inline-formula> <tex-math notation="LaTeX">${I}_{\textsf {II}}$ </tex-math></inline-formula>) at 300 K from the experimental results. The drain current (<inline-formula> <tex-math notation="LaTeX">${I}_{D}$ </tex-math></inline-formula>), electric field (<inline-formula> <tex-math notation="LaTeX">${E}{-}\textsf {field}$ </tex-math></inline-formula>), and <inline-formula> <tex-math notation="LaTeX">${I}_{\textsf {II}}$ </tex-math></inline-formula> are plotted in time. We observe that <inline-formula> <tex-math notation="LaTeX">${I}_{\textsf {II}}$ </tex-math></inline-formula> increase as <inline-formula> <tex-math notation="LaTeX">${E}{-}\textsf {field}$ </tex-math></inline-formula> reduces which indicates that <inline-formula> <tex-math notation="LaTeX">${E}$ </tex-math></inline-formula>-field does not primarily contribute to <inline-formula> <tex-math notation="LaTeX">${I}_{\textsf {II}}$ </tex-math></inline-formula>. Furthermore, <inline-formula> <tex-math notation="LaTeX">${I}_{D}$ </tex-math></inline-formula> shows two distinct behaviors: 1) <inline-formula> <tex-math notation="LaTeX">${I}_{\textit {II}} ({I}_{D}$ </tex-math></inline-formula>) is constant at the beginning and 2) eventually “universal” <inline-formula> <tex-math notation="LaTeX">${I}_{\textsf {II}} ({I}_{D}$ </tex-math></inline-formula>) is linear, i.e., <inline-formula> <tex-math notation="LaTeX">${I}_{\textsf {II}}={k}\times {I}_{D}$ </tex-math></inline-formula> where <inline-formula> <tex-math notation="LaTeX">${k} = \textsf {1}\textsf {0}^{-\textsf {3}}$ </tex-math></inline-formula>; we also show that the electrons primarily contributing to <inline-formula> <tex-math notation="LaTeX">${I}_{D}$ </tex-math></inline-formula> are directly incapable of II due to insufficient energy (<inline-formula> <tex-math notation="LaTeX">$< {E}_{g}$ </tex-math></inline-formula>). Fischetti’s model showed that SBG-II is primarily caused by “hot” electrons that accept energy in an Auger-like process from “cold” drain electrons to enable SBG-II. We speculate that if <inline-formula> <tex-math notation="LaTeX">${I}_{D}$ </tex-math></inline-formula> electrons “heat-up” the cold drain electrons, which would further energize the hot electrons to produce the observed <inline-formula> <tex-math notation="LaTeX">${I}_{\textsf {II}}{(}{I}_{D}$ </tex-math></inline-formula>) universal dependence.