Primelite Insights

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Etendue Matching and Performance Limits

Primelite Insights: Etendue
Etendue: Matching LEDs to an Optical System

Current illuminators in UV lithography systems use either mercury discharge lamps, light-emitting diodes (LEDs), or laser sources. Excimer lasers are the only available light source for deep UV (DUV, CWL around 193 and 248 nm) lithography Wafer Steppers. At the same time, conventional mercury discharge lamps and high-power LEDs are ubiquitous in near UV (NUV, spectral range between 350 and 450 nm) exposure tools.

Any light source has a fundamental property called etendue, the product of its emitting area (A) and solid emission angle (Ω). You can calculate a source’s brightness (radiance L) by dividing its emitting power (Φ) and etendue.

L = \frac{Φ}{A Ω}\quad[\frac{W}{m^2 sr}]

If you want to increase the intensity on the exposure plane (i.e., to improve the throughput in an existing lithography system), the only way is to use a source with higher brightness. You can accomplish this by increasing the light source’s power or decreasing its etendue (reducing the source size and aperture). Because conventional mercury lamps and LEDs are extended light sources, more output power usually comes at the cost of increasing the source size. Doubling the output power requires a source of roughly double the size. Hence, the effective brightness of the source remains approximately constant, as well as the intensity at the exposure plane. Throughput (wafers per hour) does generally not improve with larger lamps or LEDs, as the output power cannot be relayed to the wafer. Decreasing the etendue while maintaining the emitted power is equally difficult to achieve: The total usable output of a source will inevitably go down by reducing size and aperture.

It is essential to understand that an optical system conserves the etendue in a best-case scenario (in a real-world optical system, it always gets a bit worse). One cannot reduce the etendue of a given source by optical means to increase the exposure intensity on the wafer plane. For maximum efficiency of the entire lithography setup, the emission from a conventional mercury discharge lamp or high-power LED exposure system must match the etendue of the tool’s optics. Here is a simple equation to help you pick the right illumination source for your lithography application:

A_{emitter} NA^2 = A_{receiver}NA’^2;\\[6pt] NA=sin(θ);\quad NA’=sin(θ’)

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