Design of random doping fluctuation resistant structures of semiconductor devices

2017

ECS Trans.

In this paper the sensitivity of proton exchange membrane fuel cells (PEMFCs) parameters to catalyst variations is analyzed using the adjoint method. The adjoint method is used to compute the catalyst sensitivity functions, which show how much a given parameter of the cell increases by adding one unit mass of Pt at a given location in the catalyst layers. Numerical results are presented for the sensitivity of polarization voltage at different values of the operating current for a 25 µm membrane PEMFC. The results show that the catalyst sensitivity functions depend on the operating current and voltage, as well as the catalyst distribution.

Section: Catalyst Sensitivity Functionsmentioning

confidence: 99%

Analysis of Sensitivity of PEMFC Parameters to Non-Uniform Platinum Deposition

2017

ECS Trans.

“…Then, the section continues with the presentation of the numerical algorithm and the efficient computation of catalyst sensitivity functions. It should be noted that an optimization method similar to the one presented in this section has been introduced by our group in (10)(11)(12) for the optimization of doping profiles in semiconductor devices, in which case the catalyst density functions were replaced by doping sensitivity functions.…”

Section: Optimization Algorithmmentioning

confidence: 99%

“…This problem can be solved by defining Lagrangean [9] where λ is a Lagrange multiplier and calculating the extreme points of [9]. Indeed, by introducing [5] into [9] we obtain [10] Writing the first-order necessary conditions (Kuhn-Tucker conditions) we get the following system of equations…”

Section: Numerical Algorithm To Solve Problemmentioning

confidence: 99%

Mathematical Optimization of the Spatial Distribution of Platinum Particles in the Catalyst Layer of PEMFCs

Mixon²,

2017

ECS Trans.

An adjoint-space technique is presented for the large-scale optimization (i.e. optimization with over 10 2 design variables) of the catalyst distribution in fuel cells. The algorithm is based on evaluating the catalyst sensitivity functions of the discharge voltage under specified current conditions. The catalyst sensitivity functions are computed efficiently using a gradient maximization algorithm, which requires solving a small number of sparse linear systems of equations to find the Gâtaux derivatives of the discharge current of the cell with respect to the design variables. It is shown that the optimum distribution of the catalyst varies with the discharge conditions, with the positions of landings and openings, as well as with the geometry and dimensions of the layers. It should be noted that our numerical algorithm can be used to describe the complete profile of the optimal catalyst by providing the full (mathematically exact) distribution of platinum particles in the catalyst layer.

“…[34][35][36][37][38] In the area of electrochemical energy storage, Carraro et al 39 and Kapadia et al 40 were the first to use adjoint method to study the sensitivity of cell voltage with respect to cell parameters for solid oxide fuel cells, however, they limited their analysis to only a few parameters such as average porosity, reaction rate, tortuosity, and mean pore radius, and have not performed a large-scale sensitivity analysis of the cells. It was only recently that a widely spread commercial simulation software, COMSOL, 41 has introduced the adjoint method for the calculation of sensitivities of platinum distribution in PEMFCs and the adjoint method become more popular for optimization purposes.…”

mentioning

confidence: 99%

“…It should be noted that adjoint methods have been used before independently by the applied mathematics community to solve 1-D problems in fluid dynamics, climate, and heat transfer, 28,29 by the aerodynamic community to perform sensitivity analysis studies, [30][31][32][33] and by our group to estimate parameter variability and optimize the doping profiles in 2-D and 3-D semiconductor devices. [34][35][36][37][38] In the area of electrochemical energy storage, Carraro et al 39 and Kapadia et al 40 were the first to use adjoint method to study the sensitivity of cell voltage with respect to cell parameters for solid oxide fuel cells, however, they limited their analysis to only a few parameters such as average porosity, reaction rate, tortuosity, and mean pore radius, and have not performed a large-scale sensitivity analysis of the cells. It was only recently that a widely spread commercial simulation software, COMSOL, 41 has introduced the adjoint method for the calculation of sensitivities of platinum distribution in PEMFCs and the adjoint method become more popular for optimization purposes.…”

mentioning

confidence: 99%

Adjoint Method for the Optimization of the Catalyst Distribution in Proton Exchange Membrane Fuel Cells

Mixon

2017

J. Electrochem. Soc.

Self Cite

In this article we present an adjoint method for the optimization of the catalyst distribution in proton exchange membrane fuel cells (PEMFCs). By using the theory of functional analysis we derive analytical equations for the sensitivity functions of the cell voltage with respect to the catalyst distribution in a very general framework, independent on the transport model used to simulate the PEMFC. Then we present an efficient numerical algorithm to calculate the sensitivity functions using the adjoint method. The adjoint method has the advantage that it can be applied to the optimization of systems with a large (>10 4 ) number of optimization variables that are computed simultaneously and independently to maximize the objective function. Finally, we apply the method to the optimization of 2-D platinum distribution in PEMFCs. We show that the optimum platinum distribution varies with the operating conditions, position of landings and openings, cell geometry, and dimensions of the catalyst layers. The method presented in this work can be naturally extended to the optimization of other 2-D and 3-D field variables such as the porosity of catalyst and gas diffusion layers, particle size distribution, or microstructure of the cell. Proton exchange membrane fuel cells (PEMFCs) have attracted the attention of the research community because of their high power density, energy efficiency, and environmentally friendly characteristics. Operating at low temperatures, PEMFCs are suitable for a variety of applications ranging from automotive applications to stationary and portable applications. In the area of automotive applications, PEMFCs have already been introduced commercially or for demonstration purposes by all the major car manufacturing companies; in addition, they are increasingly being used in busses, motorcycles, boats, submarines, and airplanes.1,2 In the area of stationary and portable applications, PEMFCs are employed as emergency power systems, such as uninterrupted power supplies, and have the potential to be used for energy storage in electric grid systems.3 Since the technical feasibility of PEMFCs has already been established, a significant amount of current research focuses on increasing the durability and decreasing the total manufacturing cost, which, at large manufacturing volumes, is mainly given by the cost of the catalyst layers (CLs), bipolar plates, and membrane.4-8 (For instance, the US Department of Energy estimates that 45% of the cost of fuel cell stack fabricated at a volume of 500,000 systems/year is due to the cost of platinum, 27% to bipolar plates, 10% to the cost of membrane 9 ). In this article, we address the problem of decreasing the manufacturing cost of the CLs by presenting a large-scale optimization technique to optimize the platinum deposition in the CLs of PEMFCs. The technique can also be applied to the optimization of other two-dimensional (2-D) and three-dimensional (3-D) field variables, such as porosity distribution and ionomer content, in which the number of optimization p...