1 Introduction
2 Oxide degradation processes
2.1 Wearout currents
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Fowler-Nordheim tunneling (FN): the band diagram deforms such that the electron crosses a triangular potential barrier. Such FN current is due to electrons reaching the anode passing through the oxide conduction band, as in Fig. 1(left), and is:where \(q\) is the elementary charge, and \(A\), \(B\) parameters are:$$ J_{FN}= A \cdot {E_{ox}}^{2} \cdot \exp \big( - \frac{B}{E_{ox}} \big) $$(1)with \(m^{*}_{Si}\) the electron rest mass, \(m^{*}_{ox}\) the electron effective mass within the dielectric and \(\phi _{e}\) the injecting electrode barrier height. FN mechanism dominates for high electric fields;$$ A= \frac{q^{3}}{8\pi h \phi _{e} } \cdot \frac{m^{*}_{Si}}{m^{*}_{ox}}\quad \text{and}\quad B= \frac{8 \pi \sqrt{2m^{*}_{ox}} \; {\phi _{e}}^{3/2}}{3hq} $$(2)×
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Direct Tunneling (DT): the current is due to cathode injected electrons crossing a trapezoidal potential barrier (between metal/oxide/Si in CMOS) reaching the anode without flowing into the oxide conduction band as shown in Fig. 1(right). The approximated DT current is:This mechanism dominates for low electric fields;$$ J_{DT}= A \cdot {E_{ox}}^{2} \cdot \exp \Big(- \frac{B}{E_{ox}} \cdot \Big[ 1- {\Big( 1- \frac{V_{ox}}{\phi _{e}} \Big) }^{3/2} \Big] \Big) $$(3)
2.2 Defect generation mechanisms
3 Breakdown physical models
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E Model (also Thermo-Chemical model): the Breakdown results from the covalent \(SiO_{2}\) bonds rupture due to the electric field [7]. In this case:where \(G\) is the electric field acceleration factor and \(E_{a}\) is the activation energy for the oxide Breakdown;$$ T_{BD,E}= (C \cdot e^{\frac{E_{a}}{K_{b} T}}) \cdot e^{- G \cdot E_{ox} } $$(4)
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1/E Model (also AHI model): the Breakdown is due to the hot holes injected from the anode. The hole tunneling current can be expressed as the product between the electron FN tunneling current and a term expressing the probability of the hole generation and tunneling through the anode barrier [3], [4]. The amount of injected holes determines the \(T_{BD}\), expressed as:$$ T_{BD,1/E}= (D \cdot e^{\frac{E_{a}}{K_{b} T}}) \cdot e^{ \frac{F}{E_{ox}} } $$(5)
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Power Law: linked to the hydrogen release phenomena. Hot tunneling electrons may break the Si-H bonds, leading to releasing of hydrogen atoms at the cathode interface. These can subsequently diffuse through the oxide and combine with oxygen vacancies [5]. In such a way, defects are generated till the Breakdown happens and \(T_{BD}\) is given by:where \(\beta \) is the voltage acceleration factor [6], related to the disruption energy of Si-H bonds.$$ T_{BD,\mathrm{Power}} = K\cdot {V_{G}}^{-\beta } $$(6)