Kolomgeneratie wafer-to-wafer

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Kolomgeneratie wafer-to-wafer

Berichtdoor ellenbmoder » 13 Aug 2013, 09:30

We moesten voor onze case (wafer-to-wafer stacking probleem) bepalen of kolomgeneratie hierop toepasbaar is of niet. Nu weet ik al dat dit mogelijk is, maar weet nie hoe ik dit zou kunnen toepassen.
Ik zal eerst even de case zelf geven, zodat de situatie wat duidelijker wordt (de case is in het Engels).


In this case, we look at the production process of so-called three-dimensional integrated circuits (3D-ICs). We will not wonder what such a 3D-IC exactly is, or where we use them, instead, we simply accept the fact that 3D-IC’s are necessary components in many electronic devices. Compared to the traditional production technique – which is essentially 2-dimensional - 3D-ICs offer many advantages. One way of producing 3D-ICs is called wafer-to-wafer integration (WtW), and although other production techniques exist, we will focus on this technique. It consists of squares called dies. A die can either be good (0), or bad (1). Of course, ideally all dies are good, and in practice most dies are, however, we assume that inspection tells us precisely which die is good and which die is bad. Thus, a wafer can be represented by a string of 0’s and 1’s indicating the quality of each die, and hence, the quality of a wafer can be represented by the number of ones in this string.

We are given m sets of different wafers, called wafer lots, say V1, V2, … Vm, with each lot Vi containing n wafers.. The new production technique WtW now means that we are going to construct n stacks, where a stack is nothing else but a collection of m wafers, one from each lot Vi. How to measure the quality of a stack? The m wafers making up a stack can be seen as being superimposed on top of each other. Thus, m corresponding dies (those that lie on top of each other) in the individual wafers correspond to a single position in the stack. A position in this stack can be either good or bad, depending upon whether all dies corresponding to that position are good, or when at least one of these dies is bad. This means that bad dies of different wafers that are in the same position contribute only once (negatively) to the quality of a stack. In other words, the number of positions in the stack that have a bad die (coming from one of the wafers in the stack) is in fact the quality of a stack.

Summarizing, it is your task to find m stacks such that total quality is optimized by minimizing the number of bad positions.

Example: You are given 3 lots, each consisting of 3 items, each item has 10 dies. The data are represented in Table 1. A 1 represents a bad die, a 0 a good die. (De verschillende stijlen (onderlijn/cursief en vetgedrukt dienen enkel om de items en lots te onderscheiden)

lot Item 1 Item 2 Item 3
1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0
2 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1
3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0

A feasible solution would be, e.g., putting all item 1’s in stack 1, all item 2’s in stack 2, and all item 3’s in stack 3. Stacks 1, 2, and 3 then each have 5 bad positions, yielding an objective value of 15. (Is this optimal? Check!)

A dataset is given in data_wafer.txt. This dataset consists of 21 lines, each line represents a lot. Each lot contains 16 wafers; each wafer contains 16 dies. A 0 represents a good die, a 1 refers to a bad die.


Iemand die mij hiermee kan helpen? Dus iemand die weet hoe op deze case kolomgeneratie toe te passen?
ellenbmoder
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