Adaptive Optics to Counteract Thermal Aberrations: System Design for EUV-Lithography with Sub-nm Precision

In highly precise systems the thermal expansion of system-parts is of increasing concern, since it can severely compromise its performance at sub-nanometre level. An example of such a system is an Extreme UltraViolet (EUV)-lithography machine that is used in the semi-conductor industry to project the pattern of the chip onto a silicon wafer. In order to increase the functionality of the chips, the resolution of lithography machines improved by decreasing the wavelength to EUV of 13.5 nm. Because of the high absorption of EUV-light the projection optics consists of mirrors that have a special coating. Unfortunately it significantly absorbs the EUV-light, causing the mirrors to heat up and therefore deform, resulting in a WaveFront Error (WFE) that evolves over time. To estimate this effect a model of the EUV-projection optical system is obtained that describes the opto-thermo-elastic behaviour. It showed a deformation of 2 nm Root Mean Square (RMS) with spatial frequencies with 2 periods over the pupil, while the allowable residual WaveFront Error is 0.33 nm RMS. In order to counteract these WFEs an Adaptive Optics system is proposed, consisting of a sensor that measures the wavefront, control algorithms that determine the control action based on the sensor signal and an Active Mirror that thermally compensates and corrects for the WFEs by modifying the thermal profile and shape of the reflective surface. The system modelling results form a set of requirements which needs to be fulfilled by this Adaptive Optics (AO)-system. The key differences with conventional Adaptive Optics systems are the precision of the correction, being 2 to 3 orders of magnitude better than conventional systems, the time constants that are significant longer, the restriction of sparsely available sensor information and the aberrations that are generated inside the optical system, instead of outside. The proposed Adaptive Optics-strategy is mainly based on the on-line model based prediction of the thermal aberrations. This prediction is updated with sensor information that is acquired every 30 s, which is the time between two wafer exchange procedures. Based on the prediction, one or more Active Mirrors are being controlled to correct for these WFEs. The principle of the Active Mirror is as following. When a mirror has a uniform temperature, there is no thermal deformation. Therefore, the Active Mirror is exposed to a (thermal) irradiance-profile opposing the predicted heat-load. This principle is referred to as compensation aspect. For correcting the thermal aberrations of the other mirrors in the system, the thermal expansion of the mirror substrate is used, which is referred to as correction aspect. The thermal profile to cause this expansion is provided by the exposure of the correcting irradiance-profile. These two irradiance-profiles are superimposed and exposed from the back of the mirror, so this irradiance travels through the mirror substrate. This irradiance is absorbed by using a special coating, which is deposited on the mirror substrate underneath the reflective coating, and the exposure profile is provided by a video projector. The big advantage of this actuation principle is that the only addition to an EUV-mirror is the absorptive coating, which can be easily implemented in the current production process. Although a projection device needs to be added to the EUV-lithography machine, which needs the sparsely available space, this addition is less critical in terms of precision. In order to verify the Active Mirror on the requirements, six aspects are experimentally validated using an experimental set-up, which realisation and validation became a part of the PhD project. This experimental set-up consists of a Michelson interferometer that has 0.1 nm resolution, which is sufficiently accurate to validate the Active Mirror (AM). The AM consists of a 50×50×4mmBK7 substrate and is prepared as described above. First it is proven that the Active Mirror behaves linearly, by using the formal definition of linearity. Second, the Instrument Transfer Function is obtained, that shows that the amplitude and the time constant are both inversely quadratic proportional to the number of exposed periods on the mirror. Third, the absorptive coating is applied to a sample substrate in combination with the EUV-Multi-Layer-coating. It turns out that the reflectivity of EUV-light of this sample is only 44% instead of the maximum attainable 70%, indicating that the deposition process of the absorptive coating must be optimised. Fourth, irradiance profiles are obtained for creating basic shapes, known as Zernike polynomials, that can be superimposed to obtain a desired surface shape, which is better known as the modal approach. Fifth, to prove the viability of closed loop control, the zonal approach is used, realised by partitioning the mirror surface in sectors and provide feed-forward and feedback control on these sectors. Sixth, the precision of the Active Mirror is fulfilling the requirements: while being actively deformed, the Root Mean Square-deviation did not exceed the 0.33 nm during 17 s; the amplitude of the difference between a modelled deformation and a measured deformation was less than 10% of the amplitude of the deformation; by repeating the experiment the RMS difference did not exceed 0.17 nm. Five of these six aspects are validated for a BK7 mirror substrate, but these results can be extrapolated for other materials. For the Active Mirror in EUV-lithography, the substrate is proposed to be fused silica, which has a 16 times less thermal expansion. Because the requirements are fulfilled by the BK7 substrate, they certainly will be fulfilled by fused silica, while keeping a certain safety margin. Therefore, the over-all conclusion of the thesis is that the thermal induced WaveFront Errors can be counteracted using the counteracting strategy and the AM that are presented in this thesis.