Our customer, a leading manufacturer of lithography systems for the semiconductor industry from the Netherlands, is constantly striving to introduce equipment that enables chipmakers to produce even finer features on chips. Producing smaller features means that chipmakers can in turn shrink the size of their chips, thereby reducing the cost of production, decreasing the amount of energy needed to operate them and increasing their power.

This project’s goal was to develop a model that predicts chuck deformation owing to water cooling. We developed a full model that describes the evaporation process of the water layer, the thermal (cooling) process of the wafer and the resulting deformation (warping) of the wafer.

Abto specialists successfully built a mathematical model to predict the deformations of the wafer online during the exposition process. Knowing the deformations, the position of the wafer can be adjusted to remain in focus.

We formulated a first-order feed-forward model for the warping of the wafer after exposure in immersion lithography. Our experts managed to show that this warping happens due to local cooling of the upper surface of the wafer, caused by evaporation of small water layer left on the surface after the exposure.

Experiments’ results:

• The local cooling of the wafer due to evaporation is in the order of 1±C.
• The dimensions of the cooled region on top of the wafer plate, below the evaporate water layer, are of the order of 10-3m, or 1 mm.
• The warping of the wafer is due to thermal shrinking in the cooled region on top of the wafer. This warping can very well be modelled as the bending of a thin plate under inhomogeneous thermal loading.
• The order of the calculated deflections of the plate is 107m, or a few hundreds of nanometer.
• The shape of the warped wafer is an upside cup.

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