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Equivalent Oxide Thickness (EOT)

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

One can treat MOSFET behavior like two parallel plate capacitors,

Equation upper C Subscript o x Baseline equals StartFraction upper A epsilon Subscript r Baseline epsilon 0 Over t Subscript o x Baseline EndFraction

Where Equation upper A epsilon Subscript r is the relative dielectric constant of SiO2 in our case. Therefore one calculate the equivalent oxide thickness as,

Equation StartFraction upper A epsilon Subscript upper S i upper O Baseline 2 Baseline epsilon 0 Over t Subscript o x Baseline EndFraction equals StartFraction upper A epsilon Subscript h i g h minus kappa Baseline epsilon 0 Over t Subscript o x minus h i g h minus kappa Baseline EndFraction
Equation t Subscript o x minus h i g h minus kappa Baseline equals StartFraction CrossOut upper A EndCrossOut epsilon Subscript h i g h minus kappa Baseline CrossOut epsilon 0 EndCrossOut Over CrossOut upper A EndCrossOut epsilon Subscript upper S i upper O Baseline 2 Baseline CrossOut epsilon 0 EndCrossOut EndFraction t Subscript o x Baseline equals StartFraction epsilon Subscript h i g h minus kappa Baseline Over epsilon Subscript upper S i upper O Baseline 2 Baseline EndFraction t Subscript o x

Note that the dielectric constant SiO2 is 3.9

Equation t Subscript o x minus h i g h minus kappa Baseline equals StartFraction epsilon Subscript h i g h minus kappa Baseline Over 3.9 EndFraction t Subscript o x

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

For example, consider Hafnium Dioxide (HfO2) which has an Equation epsilon Subscript r Baseline equals 24 (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.

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