E¤ective density with dummy pattern insertion by Min-Var algorithm

Figure 4.5 demonstrates the metal 1 layer e¤ective density without inserting dummy features. Table 4.4 shows the information of e¤ective density.

Figure 4.5: Metal 1 layer e¤ective pattern density with inesrting dummy features by min-var method

1. Layout uniformity

FMDI algorithm reaches the nearly optimal solution with excellent precision. Low standard deviation and peak to peak value mean the high reliability and manufacturability. Further-more, less dummy features inserted is achieved by better precision.

2. Algorithm speed

As the description in Section 3.2, parameter basic accelerates the speed of algorithm. Algo-rithms proposed before will insert more amount of dummy patterns but less at the termina-tion. By inserting steady number of dummy features, basic can eliminate the drawback of algorithms proposed before and accomplish the insertion jobs more fast.

3. Side e¤ect

RC consideration is now the major and signi…cant a¤ection of dummy feature insertion.

Although the improvement is not purpose in this research, but it is really a good side e¤ect.

Table 4.1: Metal 1 layer e¤ective pattern density data without inserting dummy pattern include maximal value, minimal value, standard deviation, and peak to peak value.

Max( ) Min( ) Sta_Dev( ) peak to peak( ) 0.151912 0.101997 0.00826395 0.049915

Table 4.2: Metal 1 layer local pattern density data with inserting dummy features include maximal value, minimal value, standard deviation, and peak to peak value.

Max(d) Min(d) Sta_Dev(d) peak to peak(d) 0.388521 0.147992 0.0284971 0.240529

Table 4.3: Metal 1 layer e¤ective pattern density data with inesrting dummy features by FMDI algorithm contain maximal value, minimal value, standard deviation, and peak to peak value, and number of inserted dummy features.

Max( ) Min( ) Sta_Dev( ) peak to peak( ) # of dummy 0.160358 0.160137 1.58499e-05 2.21e-04 125670

Table 4.4: Metal 1 layer e¤ective pattern density data with inesrting dummy features by min-var method contain maximal value, minimal value, standard deviation, and peak to peak value, and number of inserted dummy features.

Max( ) Min( ) Sta_Dev( ) peak to peak( ) # of dummy 0.160291 0.159892 3.913e-05 3.99e-04 144457

Table 4.5: Compare the performance between FMDI algorithm and min-var method.

Algorithm Max( ) Min( ) Sta_Dev( ) peak to peak( ) # of dummy iteration

FMDI 0.160358 0.160137 1.58499e-05 2.21e-04 125670 15388

Min-var 0.160291 0.159892 3.913e-05 3.99e-04 144457 29915

Table 4.6: Compare the number of inserted dummy pattern and maximal local pattern density.

Algorithm # of dummy Max(d)

FMDI 125670 0.388521

Min-var 144457 0.450274

It means that the layout uniformity of lower level will a¤ect the layout uniformity in high level, and ILD thickness variation accumulates through …rst one layer to last one. Then we simulate the actual layout uniformity in manufacturing by single-layer consideration data.

Figure 4.7 shows the real status of metal 4 layer in manufacturing. Obviously multi-layer consideration is unavoidable.

Figure 4.6: Metal 4 layer e¤ective density with single layer dummy pattern insertion by FMDI algorithm

Table 4.7: The table contains the analysis data of metal 4 layer e¤ective density include maximal value,minimal value, standard deviation, peak to peak value, and number of dummy pattern inserted.

Max( ) Min( ) Sta_Dev( ) peak to peak( ) # of dummy 0.0614075 0.0612909 1.15803e-05 1.166e-04 199994

Figure 4.7: Simulate metal 4 layer actual(multi-layer) e¤ective density with single layer data

Chapter 5

Conclusion and future works

Chemical mechanical polishing(CMP) has became an improtant process for layout uniformity in chip manufacturing. Through the development of CMP technology, layout global planarization can be accomplished more conveniently and e¤ectively. But there are still some problems in CMP process like dishing and erosion. Since ILD thickness is pro-portional to local pattern density. Therefore dummy feature insertion is a useful method to avoid the defects in CMP process with control local pattern density.

From the large amount of researches[2][3][4][5][6][7][8] before which studied inten-sively in dummy feature insertion algorithm, we remain the best part like density model and concept of problem formulation. The 2-D low pass …lter for improving the detection of low density part is preserved. According to the drawbacks of algorithm processes we improve the algorithm speed and precision by correcting …lling amount calculation and reform the RC problems by deceasing the number of dummy features and keeping away from critical path. Therefore we have proposed fast model-based dummy insertion(FMDI) algorithm to resolve the problem.In experiment, FMDI algorithm performs e¢ cient and high speed CMP dummy pattern insertion and new method has an O(nlogn) time complexity. The experi-mental results shows that the layout uniformity is very smooth. Additionally the precision of FMDI algorithm can decrease the number of inserted dummy features.

We will study the problem for consequent problems in capacitance increase and time issues as future works.

Acknowledgement

We thank Dr. R. Tian for helpful suggestion and discussion, and the design from the design team of Prof. Chen-Yi Lee in NCTU EE for our experiment.

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隋志暉,出生於民國71年1月1日,民國93年7月畢業於中興大學物理學系,並 於民國93年9月進入交通大學電信工程研究所.在研究所中,從事Electronics Design Automation(EDA)的相關研究.於民國95年8月取得碩士資格.碩士論文題 目為[高速模型演算法擺放無意義金屬用以改善化學機械研磨的平整度].