# 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-SiO 2-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-βE OX1/2 -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.