**DFM Dictionary - Public View/DFMC User Edit**

# Numerical Aperture

## Numerical Aperture

NA

Numerical Aperture = NA = n · sine Θ

Where: n = index of refraction at the interface (Air has an index of refraction of 1.0, water has a index of fraction of 1.4) Θ = half-angle of light projected onto the resist

Numerical Aperture (NA) is a measure of the total light power of the stepper projection system. It is equal to the sine of the maximum half-angle of light that can make it through the projection system multiplied by the real index of refraction (n) of the medium between the final lens and the resist interface. The half-angle Θ is half of the angle from the focal point on the wafer to the stepper lens. A moderate Θ of 450 produces a NA = 0.70 (= 1.0 · sine 45 degrees) with an air interface. A very aggressive Θ of 72 degrees produces a NA = 0.95 (= 1.0 · sine 72) for an air interface and a NA = 1.36 (= 1.4 · sine 72) for a water interface since water has a real index of refraction of 1.4 and air is only 1.0.