micro-bump assignment for 3d ics using order relation ta-yu kuan, yi-chun chang, tai-chen chen...

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MICRO-BUMP ASSIGNMENT FOR 3D ICS USING ORDER RELATION

TA-YU KUAN, YI-CHUN CHANG,

TAI-CHEN CHEN

DEPARTMENT OF ELECTRICAL ENGINEERING, NATIONAL CENTRAL UNIVERSITY, TAOYUAN, TAIWAN

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OUTLINE• Introduction

• Problem formulation

• Algorithm

• Experimental Results

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INTRODUCTION

3D ICs need to consider inter-die connection problems. Therefore, 3D ICs have connection issues between silicon-base layers and routing layers .

Two popular technologies, through-silicon vias (TSVs) and micro bumps, are adopted widely.

The redistributed layer (RDL) is used to solve the alignment problem. By attaching RDLs on the junction between dies, signals can be distributed to appropriate positions on RDLs.

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INTRODUCTION

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A suitable micro-bump location reduces the wirelength on both upper and lower RDLs.

This paper propose a micro-bump assignment algorithm

based on the order relation, which is generated by adopting a

45-degree coordinate mapping and considering the relative

location of terminals in the upper and lower RDLs simultaneously.

INTRODUCTION

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PROBLEM FORMULATION

The micro-bump location significantly affects the routabilities of the adjacent upper- and lower-RDL.

In order to achieve higher routabilities and shorter wirelength in both upper and lower RDLs, it is necessary to avoid detour paths in both RDLs simultaneously.

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PROBLEM FORMULATION

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ALGORITHM

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ALGORITHM

Since the RDL routing allows 135-degree routing angle, shortest paths of two terminals are inside the X bounding box.

We define the X bounding box as the smallest bounding box formed by the 0°/45°/90°/135° line segments thatenclose two terminals.

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ALGORITHM45-Degree Coordinate mapping

N- and P-axis are the clockwise 45-degree coordinate rotation on X- and Y-axis, respectively.

The terminal orders of a, b, c, and d on N- and P-axis are (c, b, a, d) and (a, d, c, b), respectively.

The relative location of terminals on the plane could be verified by the orders on N- and P-axis.

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ALGORITHM

As shown in Fig. 5(a), since the relative location of ma and mb is different from that of ua and lb or la and ub, two nets have edge crossing problem in the lower RDL.

As shown in Fig. 5(b), since the relative location of ma and mb is the same as that of ua and lb, two nets have no edge crossing problem in both upper and lower RDLs.

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ALGORITHM

Flow of order determination

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ALGORITHM

3Net Picking• Nets are in the unselected group initially.

• Nets with shorter Manhattan distances have smaller bounding boxes and less routing resources for their shortest non-crossing paths, these nets require higher priority to avoid crossing problems.

• As a result, the net with the shortest Manhattan distance in the unselected group is picked as Master.

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ALGORITHM

3Net Picking• Nets which have the higher detour level are picked as

Servants.

• At each iteration, one Master and two Servants (two highest detour-level nets for Servant-1 and Servant-2) are picked from the unselected group to form a 3-net.

• The detour level is graded into the Inner Bounding Box (IBB) and the Outer Bounding Box (OBB).

• Since OBB always incurs detour paths, we define that OBB has higher detour level than IBB does.

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ALGORITHM

Fig. 7. Net-Xi detours round the X bounding box of Master. (a)IBB. Non-crossing paths for net-Xi inside its Manhattan bounding box are existed. (b) OBB. Non-crossing paths for net-Xi inside its Manhattan bounding box are not existed.

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ALGORITHM

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ALGORITHM

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ALGORITHM

Order duplication

• The order duplication can be applied on determining the micro-bump orders to avoid crossing problems.

• Obtain two candidates of micro-bump orders by duplicating the specific terminal orders.

The candidate table consists of two kinds of information: (1) micro-bump orders on N- and P-axis and (2) assignable region. A micro-bump order is a duplication of a terminal order. Assignable region defines an ideal region for assigning micro bump.

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ALGORITHM

Order duplication

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ALGORITHM

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ALGORITHM

Cyclic path checking

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ALGORITHM

The 45-degree coordinate has two axes, so we need to generate two final micro-bump orders for N- and P-axis, respectively.

visit / finish time

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ALGORITHM

MICRO BUMP SHIFTING

There are two kinds of motion affecting on m4.

• The first motion is that m4 is attracted by its signal straight path.

• The other motion is that m4 is repelled by adjacent micro bumps such as m2 on N-axis, m1 and m3 on P-axis.

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ALGORITHMThe shifting rules are defined as follows:

• Start the shifting on the N-direction before P-direction.

• Shift micro bumps which have the positive motion earlier than negative motion.

• Start the shifting from the first micro bump.

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EXPERIMENTAL RESULTS

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EXPERIMENTAL RESULTS

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THANKS