1Scaling pFET Hot-Electron Injection

This paper1 elaborates on a previously introduced [1] analytical model for hot-electron injection in p-channel MOSFET’s. Hot-electron injection is frequently exploited to remove stored charge in floating-gate circuits. As illustrated in Figure 1, hole-induced impact ionization provides an otherwise empty conduction band with electrons (1). Although most of the electrons migrate to the bulk (2), under the proper conditions some inject through the gate oxide (3). It has been shown that impact ionization and hot-electron injection can be analytically solved using a self-consistent model derived from a spatially-varying Boltzmann transport equation [2],[3]. The primary mechanisms for altering the distribution function (and hence the collision operators for the BTE) are the aforementioned impact ionization and optical phonon absorption and emission. We present data from devices fabricated on processes with minimum channel lengths of 2µm, 1µm, 0.5µm, 0.35µm, 0.25µm, 0.18µm, and 0.13µm, modeling these devices analytically in each process. While we can derive the mean free length between phonon collisions, λ, using the well known energy of optical phonons in silicon [4], we must provide a theoretical model and experimental verification of the energy dependence of the mean free lengths between impact-ionization events in the conduction and valence bands, Le−(E) and Lh+(E). Figure 2 verifies that the empirical results may be extrapolate