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Editing equivalent oxide thickness
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Where <math>A\epsilon_r</math> is the relative [[dielectric constant]] of SiO<sub>2</sub> in our case. Therefore one calculate the equivalent oxide thickness as, | Where <math>A\epsilon_r</math> is the relative [[dielectric constant]] of SiO<sub>2</sub> in our case. Therefore one calculate the equivalent oxide thickness as, | ||
− | :: <math>\frac{A\epsilon_{SiO2}\epsilon_0}{t_{ox}} = \frac{A\epsilon_{high-\kappa}\epsilon_0}{t_{ | + | :: <math>\frac{A\epsilon_{SiO2}\epsilon_0}{t_{ox}} = \frac{A\epsilon_{high-\kappa}\epsilon_0}{t_{oxe}}</math> |
− | :: <math>t_{ | + | :: <math>t_{oxe} = \frac{\cancel{A}\epsilon_{high-\kappa}\cancel{\epsilon_0}}{\cancel{A}\epsilon_{SiO2}\cancel{\epsilon_0}}t_{ox} = \frac{\epsilon_{high-\kappa}}{\epsilon_{SiO2}}t_{ox}</math> |
Note that the dielectric constant SiO<sub>2</sub> is 3.9 | Note that the dielectric constant SiO<sub>2</sub> is 3.9 | ||
− | :: <math>t_{ | + | :: <math>t_{oxe} = \frac{\epsilon_{high-\kappa}}{3.9}t_{ox}</math> |
Where <code>t<sub>oxe</sub></code> is the equivalent oxide thickness, <code>ε<sub>high-κ</sub></code> is the [[dielectric constant]] of the [[high-κ]] material used, and <code>t<sub>ox</sub></code> is the physical oxide layer thickness. | Where <code>t<sub>oxe</sub></code> is the equivalent oxide thickness, <code>ε<sub>high-κ</sub></code> is the [[dielectric constant]] of the [[high-κ]] material used, and <code>t<sub>ox</sub></code> is the physical oxide layer thickness. | ||
== Example == | == Example == | ||
− | For example, consider [[Hafnium Dioxide]] (HfO<sub>2</sub>) which has an <math>\epsilon_r = ~24</math> (subject to variations in temperature). A layer of just | + | For example, consider [[Hafnium Dioxide]] (HfO<sub>2</sub>) which has an <math>\epsilon_r = ~24</math> (subject to variations in temperature). A layer of just 1 nm in thickness would result in an equivalent oxide thickness of around <math>t_{oxe} = \frac{24}{3.9}1\text{ nm} = 6.15\text{ nm}</math>. This is indeed the material used by [[Intel]] following their transition to [[high-κ]] at the [[45 nm process]] node. |