1. Multi-Objective Optimization of Solar Cells Thermal Uniformity Using Combined Power of ANSYS Multi-Physics, modeFrontier and eArtius Vladimir Kudriavtsev, Terry Bluck (Intevac) Vladimir Sevastyanov (eArtius, Irvine, CA) ANSYS Regional Users Conference, “Engineering the System”, Santa Clara, CA Aug.23, 2011 Draft, Rev 05

4. Morning after Effect 10 hours overnight job or 1 hour overnight job Makes no difference at 8 AM in the morning 10 times CPU speed improvement

6. Facebook Analogy: Cost of “Human Delay” to Engineering Computing How to bring exponential growth to engineering computing? Eliminate weak link, eliminate “Human Delay”.

7. Why Optimization by Computer? Human can not match computer in repetitive tasks and consistency. Assuming computational problem takes 30 minutes of CPU time, then in one day (between 8AM to 8 AM) computer is capable of producing 48 design evaluations, with 144 designs completed in just 3 work days. Coupled with multi-processing capability of i7 workstation this number can easily be multiplied by factors ranging from two to six. Computer will work during the weekend; it will work when user is on vacation, on sick leave or on business trip. Personal “super computer” cost is now inconsequential for the bottom line. Software cost sky-rocketed, and its ROI and utilization efficiency is now most important. Computer needs algorithmic analogy of “human brain” to self-guide solution steps.

8. New Paradigm New paradigm of multi-objective computational design is now being born. No longer designer needs to approach it through “trial-and-error” simulations, but can rather use “artificial intelligence” of optimization method to automatically seek and to find best combination of input parameters (design). Depending on problem size (CPU time) this process can take from minutes to weeks. However, now engineer can view tens and hundreds of possible solutions, automatically singling first truly best designs and then evaluate design trade-offs between conflicting objectives (Pareto Frontier).

9. Benefits Computational software companies: - new demand for products for optimization software modules and schedulers -number of required computations per user increase 100 to 5000 times - new demand for computer speed-up via parallelization, number of CPUs (simultaneous processing), number of PCs(clusters) Engineering users: -detailed computational characterization of designs and new level of understanding -finding truly optimal and innovative engineering solutions -computer does “dirty work”, user spends more time analyzing data and tuning optimization engine

10. INTEVAC’S CASE STUDY

11. Intevac c-Si Technology Si Substrates move on conveyer and heated http://www.intevac.com

12. Heating Challenge to Address Great number of companies and technologists in Silicon Valley are now focused on developing lower-cost processing methods and capital equipment to manufacture solar cells . It is typically done through a variety of high temperature thermal processes, where temperature uniformity is the most critical factor. Using ANSYS Workbench we developed lamp heating surface-to-surface thermal conduction-radiation model for simultaneous transient multi-step heat-up of silicon substrates. Lamp locations, lamp to substrate distances, lamp dimensions, lamp power and its distribution are being optimized to achieve industry standard ±5 degrees thermal uniformity requirement. http://www.intevac.com/solar-process-sources

13. Problem Formulation Minimize thermal variation across single substrate and across a group of substrates during radiant heating stage (TempDiff) Operate in required process temperature window, T- dev1 <Top<T+ dev2 Optimization Formulation Top=400 deg.C min (TempDiff) min abs(Tmax-Top) & min abs(Tmin-Top) Constraints to determine design feasibility: T<Tmax.constr & T>Tmin.constr , where Tmin.constr = Top- dev1 , Tmax.constr = Top+ dev2 If dev1 and dev2 are small, then optimization problem is very restrictive. ANSYS WB Formulation:

14. Problem Parameters – Geometry and Temperature <Tempdiff> =Tmax-Tmin between 3 substrates T1 height T2 plus minus Lamp Bank 1 Lamp Bank 2 gap T1-radiation temperature of first lamp array; T2-radiation temperature of second lamp array; Si subst rate T1,T2 control heat flux from lamps. substrates lamps

15. Thermal Problem – Setup <Tdiff>= Tmax-Tmin between 3 substrates Mesh Elements Parameters set inside ANSYS Workbench: Geometry in Design Modeler and temperature in Workbench Model Optimization Parameters:

16. Thermal Heating (Radiation) Solution Lamp Bank 2 Multi-Step Transient History Substrate Motion Direction Interplay between two lamp arrays Lamp Bank 1 Transient Heating Scenario: Row1 of substrates is first heated by Lamp Bank1, then these Substrates moved to Lamp Bank2 and get heated again till desired Top=400 deg.C is reached. Simultaneously, new substrates with T=Tambient populate Row1 and get heated. Thus, Row1 heats from 22 to 250 deg.c and Row 2 from 250 to 400 deg.C. at time t=3.5 sec Row1 T is reset at 22 deg.C; Row2 T is reset at 250 deg.C. at time t=0 sec Row1 T is set at 22 deg.C; Row2 T is set at 250 deg.C.

17. Design Explorer with ANSYS Workbench Seeking desired (Target) Top (operational temperature T=400 deg.C) Minimize temperature variation, TempDiff T1 T2 Height Excellent tool for Design of Experiment Studies with extension to Response Surface based optimization. DOE data analyzed after the fact , Response surfaces created and theoretically optimal values are predicted. Accuracy of this prediction is limited by number of design points available for approximation and nonlinearity inherent to physics. Theoretical estimates need to be re-run again to verify their accuracy. TempDiff

18. Mode Frontier and eArtius Roles In our study we used modeFrontier as optimization enabling (Scheduler) and statistical data post-processing tool and eArtius multi-objective optimization methods plug-in tool to guide continuous process of selecting better input variables to satisfy multiple design objectives. This process follows “fire and forget ” principle and relies on combination of self-guiding gradient methods with genetic selection (crossover and mutation). Algorithm automatically use current results to best select inputs for the next design decision step. Gradient based computer thinking combines advantages of precise analytics with human like decision making (selecting roads that lead to improvement, avoiding weak links, pursuing best options, connecting dots). Genetic component guides selection and allows to jump out if local improvements can not be found.

19. Detail of modeFrontier GUI & Functions Design of Experiments DOE Methods: Rich selection of optimization methods Design Table ANSYS Interface Can automatically email results SolidWorks Interface Excel,Matlab,Labview,etc Interfaces Work flow Optimization Problem Definition

20. Problem Analogy – Hidden Valley in the Mountains Sub-Optimal range Optimal range Gradient method requires path, to enter narrow optimal range (due to nonlinearity) it requires guidance or coincidence. Guidance comes from the previous history (steps taken before, gradients) and coincidence from DOE or random mutations. Narrow process window Narrow optimum xT^4 nonlinear steep change

21. eArtius – new word in multi-objective optimization capabilities Used in this study

22. Hybrid Multi-Gradient Explorer-1 New Hybrid Multi-Gradient Explorer (HMGE) algorithm for global multi-criteria optimization of objective functions considered in a multi-dimensional domain is utilized in this study. This hybrid algorithm relies on genetic variation operators for creating new solutions, but in addition to a standard random mutation operator, HMGE uses a gradient mutation operator, which improves convergence. Thus, random mutation helps find global Pareto frontier, and gradient mutation improves convergence to the Pareto frontier. In such a way HMGE algorithm combines advantages of both gradient-based and Genetics-based optimization techniques: it is as fast as a pure gradient-based algorithm, and is able to find the global Pareto frontier with robustness similar to genetic algorithms (GA).

23. Hybrid Multi-Gradient Explorer-2 Method also dynamically recognizes the most significant design variables , and builds local approximations based only on these variables. This allows high efficiency in gradients estimation and can be achieved within 4-5 model evaluations without significant loss of accuracy. On test problems HMGE efficiency is 2-10 times higher when compared to the most advanced commercial genetic algorithms. As a result, HMGE is a natural choice to be coupled with ANSYS Workbench for fully automatic computational engineering optimization.

25. HMGE Algorithm Generate Initial Designs Sort Designs by Crowding Distance (descent) Apply Crossover Operator Apply Gradient Mutation Operator Apply Random Mutation Operator Add New Designs to Archive Check Exit Condition Exit No The crowding distance value of a solution provides an estimate of the density of designs surrounding that design The crowding distance mechanism together with a mutation operator maintains the diversity of non-dominated designs in the archive Crossover is a genetic operator used to vary the programming of chromosomes from one generation to the next— to find new designs inheriting best features of previously found designs Random Mutation : take any random individual and take a random design. Change the gene on that design with another random value— to find global optimum Gradient Mutation : take any non-dominated individual and perform a gradient-based step towards simultaneous improvement of all objective functions— to increase convergence towards local Pareto frontier

28. Optimization Flow Chart in ModeFrontier Inputs: Objectives- to minimize Constraints Constraints Estimations Optimizer Design of Experiment Setup ANSYS WB Interface Optimization (HMGE) Setup

29. Thermal System Optimization Task Formulation Minimize+ – preferable objectives Minimize – regular objective 278 feasible designs of 317 evaluations 18 Pareto+ designs of 35 Pareto optimal designs Need to carefully consider

30. “ Fire And Forget” Solution Process - HMGE deg.C Temperature Uniformity 9 5 13 17 46 21 92 138 184 230 276 300 DOE Second Wave First Wave Touchdown Design ID (#)

31. HMGE Optimization of Temperature Difference deg.C Temperature Uniformity 34 DOE 184 data accumulation Design ID (#) 104 DOE Builds approximations around best designs 9.2 15.2 25.2

32. Optimization Solution: Pareto Front deg.C Temperature Uniformity Maximum Temperature, (T-Tmax) Zoom-In Detail Two conflicting Objectives Best Designs

33. Example of Extremely Long Run DOE, preselected Best points, Design table reloaded 9.83 4.9 7.5 5.56/ 8.93 Temperature Uniformity deg. C Design ID (#) 1056 2336

34. Multi-Design Decision Making in mFrontier MDDM—initially very cluttered and confusing Tempdiff is narrowed to Less than 6 deg.C and suddenly way more clarity

35. Best Designs Selected -MDDM Tempdiff is narrowed to less than 6 deg.C and allowable deviation from maximum temperatuire reduced to 10 deg.C. Only several acceptable designs are left to consider.

36. Scatter Optimization Summary Matrix

37. Student t-Test for our System -1 Increase in Height+ has direct effect on uniformity and proximity to desired operating T; Increase in T1 (lamp bank1 flux) has direct positive effect on TempDiff and proximity to desired T; an increase in T2 achieves opposite effect.

38. Student t-Test for our System - 2 Increase in the gap between Row1 and Row2 provides inverse effect on temperature difference.

39. Pareto Optimal Solution Pareto+ and Pareto optimal designs belong to different brunches of Pareto frontier in criteria space Pareto optimal points in design space have two disjoint areas. It is noticeable that majority of Pareto+ and Pareto optimal designs belong to different disjoint areas We hypothesized that there are two zones of optimality in this problem.

40. Going Head-to-Head with Human In head-to-head competitions best “human guided” (case-by-case) studies resulted in system design with ±10-20 deg.C thermal uniformity and took several weeks to accomplish, while computer optimization based approach allowed to quickly yield multiple solutions capable of reaching ± 3 deg. C. It took only two 24 hour cycles for CPU to “independently” accomplish this task. But most importantly, multi-objective optimization analysis provided unique insights into system behavior and lead to innovative enabling design solutions. Statistical analysis of designs provided confidence that we found solutions that are truly best. Thus, we can conclude that “Optimization Equals Innovation”

41. ANSYS WorkBench eArtius modeFrontier Conclusion: Optimization = Innovation