Fluence is a term that represents energy density or the amount of energy per unit of area. Since the pulse duration in most excimer lasers is approximately the same, fluence is analogous to power density. Fluence is frequently used in place of power density in optical computations because its units (J/cm2) are easier to work with.
Specific materials require minimum levels of fluence to support the micromachining process. Often, the required fluence is determined by experimentation. The amount of fluence that ends up on-target is affected by the spatial compression of the beam. This is shown by the following equation:
Where r is the fluence (mJ/cm2), E is the energy contained in the laser pulse, and A is the area of the beam. If the beam area changes, the relationship of power densities is given by the following equation:
Shape and size changes to the beam are achieved through the use of optics. Commonly used optics for excimer beam delivery include dielectric-coated mirrors and refractive lenses, often with anti-reflective coatings.
If a cylindrical optic is used to compress the beam, the dimension of the beam changes only in one direction. Therefore, the power density after compression, r1, is given as:
Where r0 is the initial fluence, d is the demagnification factor, and Lf is the percent loss through the optic.
If a spherical optic is used to compress the beam, the dimension of the beam changes in both directions. Therefore, the power density after compression, r1, is given as:
Where r0 is the initial fluence, d is the demagnification factor, and Lf is the percent loss through the optic.