Emission probability of hot electrons from silicon into silicon dioxide

Abstract

An experimental method is described for directly measuring the probability of electron emission from the silicon substrate into the SiO2 layer after the electron has fallen through a certain potential drop in traversing the depletion layer and reached the Si-SiO2 interface. The method is based on optically induced hot-electron injection in polysilicon-SiO2-silicon field-effect-transistor structures of reentrant geometry. The emission probability was studied as a function of substrate doping profile, substrate voltage, gate voltage, and lattice temperature. It was found that the hot electrons could be emitted by tunneling as well as by surmounting the Schottky-lowered barrier. Over-the-barrier emission dominates at large substrate voltages, where the emission probability is high, and tunnel emission becomes appreciable and may even dominate at small substrate voltages where the emission probability is low. A simple model was developed based on the assumption that only those hot electrons lucky enough to escape collision with optical phonons were emitted. Using this model, we found that the expression P=A exp(−d/λ) described very well the dependence of the emission probability on doping profile, substrate voltage, and gate voltage. Here A=2.9 is a constant, λ is the optical-phonon-electron collision mean free path, d is the distance from the Si-SiO2 interface where the potential energy is equal to the ’’corrected’’ barrier of (3.1 eV−βEOX1/2 −αEOX2/3ox), βEOX1/2 is the Schottky lowering of the barrier, and αEOX2/3 is a ’’barrier-lowering’’ term introduced to account for the probability of tunneling. The temperature dependence of the collision mean free path was found to follow the theoretical relationship λ=λo tanh(ER/2kbT), with λo=108 Å and ER=0.63 eV. This model is useful for evaluating potential hot-electron-related instability problems in IGFET and similar structures.

Electron injection in MOSFETs with a self-consistent Si and SiO2 BTE solution based on spherical-harmonics expansion

“…The structure suggested in [6] has been simulated, with a 2 µm gate length and 42.8 nm oxide thickness, and with the channel-doping profile defined as "15-12-8" in [6]. A first example of the results given by the solver is reported in figure 1, where the distribution function f 0 at a cross-section in the middle of the channel is shown.…”

Yet Another Hydrodynamic Model with Correlated Parameters for Silicon Devices

“…On the basis of the lucky-electron model, it can be shown that the fraction of the channel carrier supply which is injected into the gate o xide is given by [129] : . As the substrate current is generated due to impact ionization in the lateral electric field close to the drain, it is linearly proportional to the drain current.…”

On the accuracy of current TCAD hot carrier injection models in nanoscale devices

“…This formalism transforms the initial integro-differential Boltzmann Transport equation into a 2nd order differential equation. The model, based on the results in [19], uses a single isotropic non-parabolic band-structure and includes acoustic and optical phonon scatterings, as well as impact ionization scattering, which have been adjusted to reproduce the Ning's experiment [20].…”