Wepropose an integratedcontact mechanics and density-step-heightmodel of pattern dependencies for the chemical-mechanical polishing (CMP) of multi-level copper interconnects, and show preliminary comparisons with experimental data for the overburden copper removal stage. The model uses contact mechanics to correctly apportion polishing pressure on all sections of an envelop function that reflects the long-range thickness differences on the chip, or region of interest. With the pressure over the entire envelop known, the density-step-height part of the model is then used to compute the amount of material removed in the local “up-areas” and “down-areas”. ThismodelshowspromiseinaccuratelyandefficientlypredictingpostCMPcopperanddielectric thicknesses across an entire chip.

Background Increasing patient numbers, complexity of patient management, and healthcare resource limitations have resulted in prolonged patient wait times, decreased quality of service, and decreased patient satisfaction in many outpatient services worldwide. This study investigated the impact of Lean Six Sigma, a service improvement methodology originally from manufacturing, in reducing patient wait times and increasing service capacity in a publicly-funded, tertiary referral outpatient ophthalmology clinic. Methods This quality improvement study compared results from two five-months audits of operational data pre- and post-implementation of Lean Six Sigma. A baseline audit was conducted to determine duration and variability of patient in-clinic time and number of patients seen per clinic session. Staff interviews and a time-in-motion study were conducted to identify issues reducing clinic service efficiency. Solutions were developed to address these root causes including: clinic schedule amendments, creation of dedicated postoperative clinics, and clear documentation templates. A post-implementation audit was conducted, and the results compared with baseline audit data. Significant differences in patient in-clinic time pre- and post-solution implementation were assessed using Mann-Whitney test. Differences in variability of patient in-clinic times were assessed using Brown-Forsythe test. Differences in numbers of patients seen per clinic session were assessed using Student’s t-test. Results During the baseline audit period, 19.4 patients were seen per 240-minute clinic session. Median patient in-clinic time was 131 minutes with an interquartile range of 133 minutes (84–217 minutes, quartile 1- quartile 3). Targeted low/negligible cost solutions were implemented to reduce in-clinic times. During the post-implementation audit period, the number of patients seen per session increased 9% to 21.1 (p = 0.016). There was significant reduction in duration (p < 0.001) and variability (p < 0.001) of patient in-clinic time (median 107 minutes, interquartile range 91 minutes [71–162 minutes]). Conclusions Lean Six Sigma techniques may be used to reduce duration and variability of patient in-clinic time and increase service capacity in outpatient ophthalmology clinics without additional resource input.

Chemical mechanical polishing (CMP) has become the enabling planarization method for shallow trench isolation (STI) of sub 0.25μm technology. CMP is able to reduce topography over longer lateral distances than earlier techniques; however, CMP still suffers from pattern dependencies that result in large variation in the post-polish profile across a chip. In the STI process, insufficient polish will leave residue nitride and cause device failure, while excess dishing and erosion degrade device performance.Our group has proposed several chip-scale CMP pattern density models [1], and a methodology using designed dielectric CMP test mask to characterize CMP processes [2]. The methodology has proven helpful in understanding STI CMP; however, it has several limitations as the existing test mask primarily consists of arrays of lines and spaces of large feature size varying from 10 to 100 μm. In this paper, we present a new STI characterization mask, which consists of various rectangular, L-shape, and X-shape structures of feature sizes down to submicron. The mask is designed to study advanced STI CMP processes better, as it is more representative of real STI structures. The small feature size amplifies the effects of edge acceleration and oxide deposition bias, and thus enables us to study their impact better. Experimental data from an STI CMP process is shown to verify the methodology, and these secondary effects are explored. The new mask and data guide ongoing development of improved pattern dependent STI CMP models.

Our group has proposed several chip-scale CMP models, with key assumptions including the notion of planarization length in the pattern density model [1], and step height dependent polishing rate in the density step height model [2]. In the effective density model, planarization length is the characteristic length of an elliptic weighting function based on the long-range pad deformation and pressure distribution during CMP. This semi-physical model is often adequate and usually gives a fitting error of a few hundred angstroms. As ever-shrinking device size pushes for tighter control of post CMP uniformity, however, we need a chip-scale CMP model with better accuracy.In this work, we re-examine the physical basis for averaging weighting functions and step height dependence, particularly in the context of contact mechanics based model formulations. The comparison of the two models confirms that the analytical density and step height models can be viewed as approximations to the contact wear model. The study also suggests a new dependence of contact height on line space and pattern density.