Method for planning interlocking micro-bump matrix of overlapped type three-dimensional integrated chips

An integrated chip and three-dimensional integration technology, which is applied in special data processing applications, instruments, electrical digital data processing, etc., can solve the problems that are difficult to meet Moore's Law, and achieve the effects of strong intuition, short running time, and high accuracy

Inactive Publication Date: 2015-07-29

TSINGHUA UNIV

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Problems solved by technology

With the improvement of component integration scale, in the current VLSI circuit, the problem of signal propagation del...

Method used

[0070] Wire winding is one of the methods for eliminating intersections. It can successfully avoid crossings by increasing the length of the wir...

Abstract

The invention relates to a method for planning an interlocking micro-bump matrix of overlapped type three-dimensional integrated chips, and belongs to the technical field of computer aided design of optimum design of three-dimensional wiring of integrated circuit chips. The method mainly comprises the following steps of when the corresponding positions and numbers of fins and micro-bumps of an upper layer and a lower layer are given, establishing an enclosing frame for each group of fins; establishing a matrix A and a matrix B for representing the position relationship of the micro-bumps and the enclosing frame, wherein elements in the matrix A are used for representing whether the micro-bumps exist in the enclosing frame or not, and elements in the matrix B are used for representing the sum of Manhattan distances between the micro-bumps and the enclosing frame; utilizing a Hungary algorithm to realize unique corresponding between the micro-bumps and the surrounding frame and enable the sum of the Manhattan distances to be minimum; according to the results of the Hungary algorithm, pre-connecting the micro-bumps and the fins; comprehensively utilizing an interchange and winding method, and eliminating the crossing of the distributed micro-bumps. The method has the advantages that the running time is short, the accuracy is high, and the intuition is strong.

Application Domain

Special data processing applications

Technology Topic

Optimal designIntegrated circuit +4

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Examples

Experimental program(1)

Example Embodiment

[0042] In three-dimensional design, micro bump technology plays an auxiliary role in the connection of the upper and lower pins. The present invention can connect the micro bumps and pins in the middle layer according to different initial chip states. The connection between the micro bumps and the pins must be in the horizontal or vertical direction, and make the connection the shortest and not Cross each other.

[0043] In order to make the problem concise, we transformed the three-dimensional problem into a two-dimensional problem for solution.

[0044] The method for planning the interconnected micro-bump matrix between stacked three-dimensional integrated chips is characterized in that it is implemented in a computer according to the following steps in sequence:

[0045] Step (1), initialization, given a n, n represents the number of pin pairs, the total number of pins is 2n. Use random number simulation to generate the coordinates of these 2n points. Each coordinate is an integer in the interval [0,100]. The chip is regarded as a standard square with a side length of 100.

[0046] Let m be the number of micro bumps, m is the smallest perfect square number not less than n; micro bumps are standard The matrix array structure is located in the center of the chip at equal intervals (for example, as shown in Figure 2, n=9, m=9, the left side is the upper chip, and the right side is the lower chip).

[0047] The square grid in Figure 2 can be regarded as the upper and lower chips. From the above description, it can be seen that the sizes of the two chips are the same. The set of yellow circles is the micro bump matrix, and the micro bumps with the same position in the left and right figures are the same. The blue and red squares represent two different layers of pins, the blue is the upper pin, and the red is the lower pin. The numbers near the pins represent the pin numbers. The red and blue pins with the same number need to be connected, and the pins must be connected to the micro bumps first. Such as image 3.

[0048] Step (2), allocation of micro bumps:

[0049] The upper chip pins and the corresponding lower chip pins are regarded as the relative vertices of a rectangle, and the sides of the rectangle are parallel to the edges of the chip, that is, the sides of the rectangle are horizontal or vertical. This rectangle is called the "bounding box", such as Figure 4.

[0050] In physical design, it is stipulated that the connection must be horizontal or vertical. If the upper pin 1 is connected to the lower pin 1 via a micro bump, the length of the connection shall be at least half the circumference of the frame Δx+Δy, When the minimum line length is reached, the micro bump must fall within the bounding box.

[0051] Each pair of pins can get a bounding box, and a total of n bounding boxes can be obtained.

[0052] The bounding box is a rectangle, and the micro bump matrix can be regarded as a collection of some points. Given a micro bump and a bounding box, the micro bumps either fall inside or outside of the bounding box (in this article, the edge is regarded as falling inside). According to this situation, a matrix can be made to represent the positional relationship between the micro bumps and the bounding box.

[0053] For example, when the number of bounding boxes is 5 and the size of the micro bump matrix is 9, the following table can be obtained.

[0054]

[0055] A ij Representative micro bump m j Is it in the bounding box u i -l i Internal, 1 means inside, 0 means not inside.

[0056]

[0057] B ij Representative micro bump m j With u i And l i The sum of Manhattan distances.

[0058] These two matrices have the following properties:

[0059] ●A matrix is generally a sparse matrix;

[0060] ●If there is only one "1" in a row of A matrix, then in matrix B, the element at the corresponding position is the smallest element of the row;

[0061] ●If a row of A matrix has several "1"s, then in matrix B, the elements at the corresponding positions are equal and the row is the smallest;

[0062] From the definition of the B matrix, it can be seen that to find the allocation scheme of the micro bump and the bounding box, it is to find an element in each row of the B matrix so that the sum of these elements is the smallest.

[0063] Store the matrices A and B in the computer memory and use the Hungarian algorithm to solve the matrix B to find the optimal solution. For the above matrix B, the results are as follows.

[0064]

[0065] C ij =1 means micro bump m j Assigned to bounding box u i -l i. There is one and only one "1" in each row of matrix C, and there is at most one "1" in each column. According to the position of "1" in matrix C, find the corresponding elements in B, and sum these elements to get the initial line length.

[0066] Step (3), judge and eliminate the intersection:

[0067] The method of eliminating crossover is winding and interchange, and the two methods are combined.

[0068] The connection between the micro bump and the pin must be horizontal or vertical. A key definition is given below.

[0069] Definition: Cross-after step 2, on the same layer, if two sets of pins and micro bumps are found to be connected inside the bounding box anyway, one of the lines must intersect with the other, then just say These two pins crossed. At this time, draw the bounding box when the pin and the micro bump are connected, and the two bounding boxes must appear cross-shaped overlap ( Figure 5 ).

[0070] Winding is one of the ways to eliminate the cross. It can successfully avoid the cross by increasing the length of the wire and connecting the wires outside the bounding box. In the entire step of winding, the old crossing is eliminated and no new crossing is generated.

[0071] Winding can avoid crossing, but with it, the bus length must increase.

[0072] Another way is to swap. The swap is to swap the two assigned micro bumps in the cross, so that the cross can sometimes be unlocked.

[0073] Swap may not always avoid crossover, as follows Image 6 , Even if the micro bumps 1 and 2 are interchanged, the upper layer cross is solved, but the lower layer will cross again.

[0074] When operating in the computer, first judge whether it is a cross situation according to the positions of the four points. If you encounter a cross situation, first try to use the interchange to unlock the cross ( Image 6 b). If it can, then successfully eliminate the crossing; if not, cancel the swap operation, and use winding to avoid the crossing ( Figure 7 b).

[0075] 4. Calculate the bus length according to the distribution results currently obtained:

[0076] The bus length is the sum of the wiring length of the micro bump and its corresponding upper and lower pins.

[0077] The invention has the following advantages:

[0078] (1) The Hungarian algorithm is an existing mature algorithm with high accuracy and short running time

[0079] (2) It is intuitive and convenient to judge the intersection

[0080] Table 1 Experimental results

[0081]

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Classification and recommendation of technical efficacy words

short runtime
improve accuracy

Method for planning interlocking micro-bump matrix of overlapped type three-dimensional integrated chips

AI-Extracted Technical Summary

Problems solved by technology

Method used

Abstract

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Example Embodiment

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Description & Claims & Application Information

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