Semiconductor & Computer Engineering
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{{title|Equivalent Oxide Thickness (EOT)}}{{confuse|oxide thickness|l1=Oxide Thickness (t<sub>OX</sub>)}} | {{title|Equivalent Oxide Thickness (EOT)}}{{confuse|oxide thickness|l1=Oxide Thickness (t<sub>OX</sub>)}} | ||
| − | '''Equivalent Oxide Thickness''' ('''EOT'''), represented by <code>t<sub>eq</sub></code> or <code>t<sub> | + | '''Equivalent Oxide Thickness''' ('''EOT'''), represented by <code>t<sub>eq</sub></code> or <code>t<sub>OX</sub></code>, is the [[gate oxide thickness]] of the SiO<sub>2</sub> layer of a [[transistor]] that would be required to achieve similar capacitance density as the [[high-κ]] material used. |
| − | A [[gate dielectric]] with a [[dielectric constant]] that is substantially higher than that of SiO<sub>2</sub> will initially have a much smaller equivalent electrical thickness. As the semiconductor industry began to experiment with transitioning from a SiO<sub>2</sub> gate oxide to a [[high-κ]] material, EOT can be used to quickly compare those materials using existing SiO<sub>2</sub>-based models. | + | A [[gate dielectric]] with a [[dielectric constant]] that is substantially higher than that of SiO<sub>2</sub> will initially have a much smaller equivalent electrical thickness. This key feature allowed for the industry to continue on with [[Moore's Law]]. As the semiconductor industry began to experiment with transitioning from a SiO<sub>2</sub> gate oxide to a [[high-κ]] material, EOT can be used to quickly compare those materials using existing SiO<sub>2</sub>-based models. |
== Equation == | == Equation == | ||
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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- | + | :: <math>\frac{A\epsilon_{SiO2}\epsilon_0}{t_{ox}} = \frac{A\epsilon_{high-\kappa}\epsilon_0}{t_{ox-high-\kappa}}</math> |
| − | :: <math> | + | :: <math>t_{ox-high-\kappa} = \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_{ox-high-\kappa} = \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 6.15 nm in thickness [[Hafnium Dioxide]] (HfO<sub>2</sub>) would result in an equivalent SiO<sub>2</sub> oxide thickness of around <math>t_{ox} = \frac{24}{3.9}6.15\text{ nm} = 38\text{ nm}</math>. This is indeed the material used by [[Intel]] following their transition to [[high-κ]] at the [[45 nm process]] node. |
Latest revision as of 07:30, 29 April 2024
- Not to be confused with Oxide Thickness (tOX).
Equivalent Oxide Thickness (EOT), represented by teq or tOX, is the gate oxide thickness of the SiO2 layer of a transistor that would be required to achieve similar capacitance density as the high-κ material used.
A gate dielectric with a dielectric constant that is substantially higher than that of SiO2 will initially have a much smaller equivalent electrical thickness. This key feature allowed for the industry to continue on with Moore's Law. As the semiconductor industry began to experiment with transitioning from a SiO2 gate oxide to a high-κ material, EOT can be used to quickly compare those materials using existing SiO2-based models.
Equation[edit]
One can treat MOSFET behavior like two parallel plate capacitors,
Where is the relative dielectric constant of SiO2 in our case. Therefore one calculate the equivalent oxide thickness as,
Note that the dielectric constant SiO2 is 3.9
Where toxe is the equivalent oxide thickness, εhigh-κ is the dielectric constant of the high-κ material used, and tox is the physical oxide layer thickness.
Example[edit]
For example, consider Hafnium Dioxide (HfO2) which has an (subject to variations in temperature). A layer of just 6.15 nm in thickness Hafnium Dioxide (HfO2) would result in an equivalent SiO2 oxide thickness of around . This is indeed the material used by Intel following their transition to high-κ at the 45 nm process node.