Optimal Thermal Actuation for Mitigation of Heat-Induced Wafer Deformation

An important step in the production of integrated circuits is the projection of the pattern of electronic connections on a silicon wafer. The light used to project the pattern moves over the wafer and induces a local temperature increase. The resulting thermal expansion of the wafer leads to a significant reduction in the imaging quality of next-generation wafer scanners. Thermal actuators that move together with the projection light can be used to improve the imaging quality. Because the placement of these actuators largely determines the performance of the resulting control system, a method to support the design of an effective thermal actuator layout is presented. The proposed method computes the smallest actuation heat load that consists of a single spatial shape and respects certain constraints on wafer deformations. A gradient-based optimization algorithm is presented to compute the optimal actuation heat load. The proposed method is applied to a wafer heating problem for which the resulting shapes of the actuation heat load have a clear physical interpretation

The method of images in thermoelasticity with an application to wafer heating

The well-known method of images relates the solution of the heat equation on (Formula presented.) (typically n = 2 or n = 3) to the solution of the heat equation on certain spatial subdomains Ω of (Formula presented.) By reformulating the method of images in terms of a convolution kernel, two novel extensions are obtained in this paper. First, the method of images is extended from thermal problems to thermoelastic problems, that is, it is demonstrated how the heat-induced deformations on (Formula presented.) can be related to the heat-induced deformations on certain subdomains Ω of (Formula presented.) Secondly, an explicit expression for the convolution kernel for the disk is obtained. This enables the application of the method of images to circular domains to which it could not be applied before. The two obtained extensions lead to a computationally efficient simulation method for repetitive heat loads on a disk. In a representative simulation example of wafer heating, the proposed method is more than ten times faster than a conventional Finite Element approach

Accelerometry based assessment of gait parameters in children

The objective of this study was to examine if spatio-temporal gait parameters in healthy children can be determined from accelerations measured at the lower trunk as has been demonstrated in adults, previously. Twenty children aged 3-16 years, participated in a protocol that involved repeated walks of different distances in an indoor environment. During walking, accelerations were measured by three orthogonally mounted acceleration sensors in a small wireless device (DynaPort MiniMod) that was attached to the lower back. Based on an inverted pendulum approach, spatio-temporal gait parameters and walking distances were computed from the acceleration signals. Results were compared to video observations and known walking distances and durations. Steps were successfully detected in 99.6+/-0.6% of all observed steps (n=5554). On average, walking distance was accurately estimated (100.6+/-3.3%, range 93-106.7%). No correlation was found between the number of miscounted steps and the total number of steps or the age of the subject. It can be concluded that the use of an inverted pendulum model provides the possibility to estimate spatio-temporal gait parameters in children as well as in adults. The method allows an inexpensive and comfortable assessment of gait parameters in children, is applicable in controlled, indoor environments and could be tested for applicability under free living conditions