Yield Enhancement Techniques for 3D Memories by Redundancy Sharing among All Layers

Transcription

1 Yield Enhanceent Techniques for 3D Meories by Redundancy Sharing aong All Layers Joohwan Lee, Kihyun Park, and Sungho Kang Three-diensional (3D) eories using through-silicon vias (TSVs) will likely be the first coercial applications of 3D integrated circuit technology. A 3D eory yield can be enhanced by vertical redundancy sharing strategies. The ethods used to select eory dies to for 3D eories have a great effect on the 3D eory yield. Since previous die-selection ethods share redundancies only between neighboring eory dies, the opportunity to achieve significant yield enhanceent is liited. In this paper, a novel die-selection ethod is proposed for ultilayer 3D eories that shares redundancies aong all of the eory dies by using additional TSVs. The proposed ethod uses three selection conditions to for a good ulti-layer 3D eory. Furtherore, the proposed ethod considers eory fault characteristics, newly detected faults after bonding, and ultiple eory blocks in each eory die. Siulation results show that the proposed ethod can significantly iprove the ultilayer 3D eory yield in a variety of situations. The TSV overhead for the proposed ethod is alost the sae as that for the previous ethods. Keywords: Yield enhanceent, ulti-layer 3D eory, redundancy sharing, inter-die redundancy, die-selection ethod. Manuscript received Oct. 1, 11; revised Nov. 9, 11; accepted Dec. 1, 11. This work was supported by the National Research Foundation of Korea (N) grant funded by the Korean governent (MEST) (No. 1-68). Joohwan Lee (phone: , eldsich@yonsei.ac.kr), Kihyun Park (ciabear@yonsei.ac.kr), and Sungho Kang (corresponding author, shkang@yonsei.ac.kr) are with the Departent of Electrical and Electronic Engineering, Yonsei University, Seoul, Rep. of Korea. I. Introduction Three-diensional (3D) integrated circuits (ICs) with through-silicon vias (TSVs) were introduced to overcoe the well-known wall probles of two-diensional (D) ICs, such as interconnect probles [1], []. Meory plays an iportant role in high perforance systes and will likely be the first coercial application of 3D IC technology [3], []. A 3D eory is ipleented with TSVs as vertical buses across eory layers. Thus, the 3D eory can reduce eory access latency and increase eory access bandwidth [3]. Since a 3D eory has an extreely high capacity and density, defects are easily introduced during the anufacturing of ulti-layer 3D eories. Furtherore, additional defects can arise during bonding, which results in a yield drop and quality degradation [5], [6]. Meory repair is used for iproving the yield of 3D eories as well as that of D eories [7]-[17]. To effectively repair eories, a nuber of redundancy analysis (RA) algoriths have been presented [11]-[17]. A eory die typically contains any eory blocks and spare rows and coluns are eployed for each eory block. After the eory repair process is copleted, a eory block can be categorized into one of two basic types: a repairable eory block or an irreparable eory block. If a eory block is repairable, unused redundancies ay reain. However, if a eory block is irreparable, the nuber of redundancies is insufficient to repair the block. Unfortunately, the entire eory die ust be discarded if just one of its eory blocks is irreparable. Intuitively, a eory yield can be increased by letting eory blocks share the precious spare rows and coluns. In [11], the unused redundancies are shared to increase the eory yield in traditional D eories, but 388 Joohwan Lee et al. 1 ETRI Journal, Volue 3, Nuber 3, June 1

2 high routing overhead akes this strategy unpopular for D eories. However, in 3D eories, redundancy sharing aong vertical eory layers is a practicable and effective strategy because the short electrical path length of TSVs can ake routing easy. When inter-die redundancies are used, a eory block that is not self-repairable can borrow redundant resources fro its vertical eory blocks and ay be repairable after bonding. Thus, the 3D eory yield can be significantly enhanced with the use of inter-die redundancies, when copared with no use of inter-die redundancies. With the vertical redundancy sharing strategy, die-selection ethods are increasingly iportant. For exaple, when a 3D eory is coposed of two eory dies, if a self-repairable eory die is bonded with a eory die that is not selfrepairable but they cannot for a good 3D eory, the 3D eory yield ight even be sacrificed. Therefore, to enhance the 3D eory yield, the selection of adequate eory dies is both iportant and relevant. Recently, three die-selection ethods -[1] have eerged for yield enhanceent in twolayer 3D eories. Chou and others exactly atched one die to another with inter-die redundancies. Specifically, the nuber of unused redundancies in a self-repairable eory die was the sae as the nuber of insufficient redundancies in a eory die that was not self-repairable. Jiang and others selectively atched eory dies together using irrespective sub-bipartite graphs. Lee and others [1] selected eory dies to anufacture 3D eories using three search-space conditions (and this ethod is the die-selection ethod that we previously used). The die-atching algoriths in,, and [1] enhanced the 3D eory yield. However, although these die-selection ethods enhance the 3D eory yield, they can only share redundancies between neighboring vertical eory dies. Sharing vertical redundancies aong ultiple eory dies would enable significant yield enhanceent. Naely, when a eory die that is not self-repairable is not repaired by sharing redundancies with a self-repairable eory die, it ay be repaired by sharing redundancies with ultiple self-repairable eory dies. Furtherore, the previous ethods, do not consider the eory fault characteristics, and the ethods -[1] do not consider additionally detected faults after bonding or ultiple blocks in a eory die. If redundancies are shared aong all of the eory dies, additional TSVs are required when copared with the previous ethods -[1]. However, TSV overhead is less of a concern because of the continuing iproveent of TSV anufacturing technology. The nuber of TSVs can also be reduced without a severe 3D eory yield loss by decreasing the redundancy sharing ratio of global spares to local spares. In this paper, we propose an efficient die-selection ethod for yield enhanceent in ulti-layer 3D eories. Unlike the previous ethods -[1], the proposed die-selection ethod shares redundancies aong all of the eory dies within a ulti-layer 3D eory. Furtherore, since the proposed ethod considers both eory fault characteristics and additionally detected faults, its 3D eory yield can be higher than those of previous ethods. The proposed ethod also takes ultiple blocks into account, which is practical because a eory die contains a nuber of eory blocks. The rest of this paper is structured as follows. Section II introduces background inforation related to the proposed dieselection ethod. Section III illustrates the proposed dieselection ethod with a siple exaple to provide a ore detailed explanation of the ethod. The fault distributions used in siulations, the yield of 3D eories in various situations, and the TSV overhead are shown and analyzed in section IV. Finally, section V concludes the paper. II. Background 1. 3D Meory Stacking There are three basic ways to stack 3D eories -[1], [18]: wafer-to-wafer (WW), die-to-wafer (DW), and die-todie (DD). Each integration ethod has advantages and disadvantages. WW integration technology has a siple anufacturing process and creates hundreds or thousands of eories at once. However, its yield of 3D eories can be quite low because WW integration technology cannot use known-good-die inforation. On the other hand, DW and DD integration technologies require ore coplex anufacturing processes. However, the 3D eory yield fro the DW and DD ethods can be uch higher than that of the WW ethod because of the use of known-good-die inforation. In this paper, we assue 3D eory stacking with DD integration technology. However, DW integration technology can also be used to build 3D eories by adding the position constraint of a die in a wafer. In 3D eories, eory dies are stacked vertically upon each other and TSVs are utilized as buses to link the stacked dies together, as shown in Fig. 1. This organization enables redundancy sharing across eory dies using short TSVs while causing very little overhead routing.. Meory Die Classification After the pre-bond test and repair, eory dies with interdie redundancies are classified into the following four types: fault-free, self-repairable, inter-repairable, and irreparable. A fault-free die has no faults and uses no redundancies. A selfrepairable die can be repaired with its self-contained ETRI Journal, Volue 3, Nuber 3, June 1 Joohwan Lee et al. 389

3 Meory array Redundant eory Peripheral logic Meory die TSV bundle according to their states after the pre-bond test and repair. Secondly, the classified dies are carefully selected for stacking as 3D eories since a die-selection can significantly affect the 3D eory yield. After bonding, the post-bond test and repair is carried out to ensure the reliability of the 3D eory. Good 3D eories, which do not have any faults after the test and repair, are then shipped while faulty 3D eories are scrapped. 3. Meory Fault Characteristics Repairable dies (w/o sharing) Fault-free dies Peripheral layer Fig. 1. Overview of 3D eory. Self-repairable dies Pre-bond test & repair Die-selection to stack 3D eories Post-bond test & repair Inter-repairable dies Meory controller Irreparable dies (w/o sharing) Irreparable dies Before bonding After bonding The ajority of eories popularly use spare row lines and spare colun lines [1]-[17]. A eory with spare row lines and spare colun lines obeys the line replaceent policy [1], [17], which dictates that any fault in a eory has to be replaced with a spare line. To for an operational 3D eory, all of the faults should be allocated to spare row lines or spare colun lines. Aong the faults assigned to spare lines, there are single cell faults, which do not share row and colun addresses with other faults. A single cell fault can be repaired by either a spare row line or a spare colun line. Therefore, as in D eory repair [1], [17], the repair decision for single cell faults can be postponed until the dies have been properly selected to asseble a 3D eory. This characteristic of single cell faults is used to enhance the 3D eory yield in the proposed die-selection ethod. III. Yield Enhanceent Techniques Good 3D eories Faulty 3D eories Fig.. Procedure to anufacture 3D eories with inter-die redundancies. redundancies and ay leave unused redundancies. An interrepairable die cannot be repaired with the self-contained redundancies, but can be repaired by the inter-die redundancies. An irreparable die cannot be repaired by either the selfcontained redundancies or the inter-die redundancies. Without the use of inter-die redundancies, a 3D eory can only be coposed of repairable dies, that is to say fault-free dies and self-repairable dies. However, 3D eories using inter-die redundancies are stacked with fault-free dies, selfrepairable dies, and inter-repairable dies. Therefore, the redundancy sharing strategy can significantly enhance the 3D eory yield. The procedure to anufacture 3D eories with inter-die redundancies based on DD integration technology is shown in Fig.. The procedure in Fig. is siilar to the stacking flow in. However, four die types are used in Fig. instead of three die types in. In Fig., first of all, eory dies are classified 1. 3D Meory Architecture with Multi-layer Redundancy Sharing Two types of redundancies have been considered when repairing defective eories with inter-die redundancies. The shift reconfiguration echanis is used to exchange a defective eleent with an inter-die redundancy, as described in. In and [1], both a prograable decoder and ultiplexers are used for redundancy sharing. However, these existing 3D eory architectures for inter-die redundancies are only used when redundancies are shared between neighboring vertical eory dies. Thus, a new 3D eory architecture is required for sharing redundancies aong ultiple eory dies. The inter-die redundancy schees used in the previous dieselection ethods, [1] and the proposed die-selection ethod are depicted in Fig. 3. Redundancies are shared between two layers in the previous ethods (Fig. 3(a)), and aong ulti-layers in the proposed ethod (Fig. 3(b)). In Fig. 3(a), a spare row and two spare coluns in each eory block are connected to the prograable decoder of a neighboring layer using TSVs as well as the decoder in its own layer. 39 Joohwan Lee et al. ETRI Journal, Volue 3, Nuber 3, June 1

4 A spare row TSVs A spare row TSVs Meory array Meory array Decoder Decoder (b) Redundancy sharing aong ulti-layers L1 L L3 L (a) Redundancy sharing between two layers L1 L L3 L Fig. 3. Inter-die redundancy schee. Spare coluns Meory block Spare coluns Meory block However, in Fig. 3(b), the redundancies are not only connected to the decoder in their own layer but also linked to the decoders of all the other layers. In both cases, the ultiplexers deterine which eory blocks use the redundancies. The routing overhead to support inter-die redundancies is quite low due to the use of short TSVs. In the previous ethods, [1], two global redundancies can be used in the two dies with a coon TSV because redundancies are shared between neighboring dies, as shown in Fig. 3(a). However, in the proposed ethod, nine coon TSVs are required for sharing four global redundancies because all the relevant redundancies can siultaneously be used in a die, as shown in Fig. 3(b). Generally, when a eory die contains B eory blocks and when R S global spare rows and C S global spare coluns are added to each eory block, sharing redundancies between two neighboring dies requires B (R S + C S ) [L/] TSVs to for an L-layer 3D eory. However, the proposed ethod, which shares redundancies aong all the dies, requires B (R S + C S ) (L 1) TSVs to stack an L-layer 3D eory. For exaple, in each of the ethods illustrated in Figs. 3(a) and 3(b), there is a four-layer 3D eory (L=) that has a eory block (B=1) with a global spare row (R S =1) and a global spare colun (C S =1) in each eory die. Thus, the 3D eory that shares redundancies between neighboring dies requires four TSVs, as shown in Fig. 3(a). On the other hand, the 3D eory that shares redundancies aong all the dies uses eighteen TSVs, as shown in Fig. 3(b). The nuber of TSVs used in the proposed schee is the sae as that used in the previous schee when the nuber of layers in a 3D eory is two. But, when the nuber of layers is greater than or equal to three, the proposed ethod requires ore TSVs to share redundancies aong all the dies than the previous ethod requires. However, with the continuing iproveent of TSV anufacturing technology, TSV overhead is less of a concern. Furtherore, since soe redundancies can only be used to repair their own blocks without sharing, the nuber of TSVs can be reduced. In other words, they can be locally used. For instance, in Fig. 3, a spare row and a spare colun (global R S = 1 and global C S = 1) in each eory block are used for redundancy sharing but a spare colun (local C S = 1) is not shared. Multi-layer redundancy sharing, in the proposed 3D eory architecture, iproves the efficiency of redundancy utilization because global redundancies can be used in all layers. When the proposed schee is applied, ore redundancies are used in each eory block, yet the overall nuber of redundant resources is unchanged. Using the previous schee, a eory block can only utilize two spare rows and three spare coluns, as shown in Fig. 3(a). Yet that increases to four spare rows and five spare coluns with the proposed schee, as shown in Fig. 3(b). In other words, when the proposed schee is used, it is possible to share fewer redundancies while aintaining the 3D eory yield. Therefore, the nuber of TSVs needed for the proposed ethod can be reduced. Moreover, when there are any eory layers, it is also possible to reduce the nuber of redundancies. For exaple, each eory block in Fig. 3(a) can use five redundancies. However, even if a local spare colun is not used in Fig. 3(b), each eory block can use eight redundancies, which is still three ore than that in Fig. 3(a). Although the nuber of TSVs used in the 3D eory can be reduced by sharing fewer redundancies, it is possible that one of the additional TSVs added for the proposed schee is defective. Since a defective TSV does not transit a proper signal, the 3D eory yield can possibly be dropped. However, the proposed schee can tolerate soe TSV defects. For exaple, if one of the three TSVs connecting the global spare coluns fro the L1 layer to the L layer in Fig. 3(b) is defective, the corresponding spare coluns can be used as partially global redundancies. As long as a eory block does not require borrowing all the three global spare coluns to ETRI Journal, Volue 3, Nuber 3, June 1 Joohwan Lee et al. 391

5 becoe reparable, it is still sufficient.. Basic Die-Selection Method A eory die typically consists of ultiple eory blocks. However, to siplify the proble, we assue that a eory die is coposed of only one eory block. First, the basic dieselection ethod, which uses the siplified eory dies, is proposed in this subsection. Then in section III., we discuss the advanced die-selection ethod for ultiple eory blocks. The redundancy sharing ratio of global spares to local spares greatly affects the 3D eory yield. With different redundancy sharing ratios, 3D eory yields are evaluated and copared in section IV. However, for the sake of siplicity, in the rest of this paper, only shared redundancies are considered, unless otherwise specifically stated. In other words, unless otherwise noted, all of the spare rows and coluns are used globally. During the pre-bond test and repair, eory repair inforation for the proposed die-selection ethod is collected. Like our previous ethod [1], the proposed ethod requires inforation about the nuber of faulty row lines, the nuber of faulty colun lines, and the nuber of single cell faults in each eory block because both ethods use the eory fault characteristics. However, the previous ethod [1] does not consider redundancy sharing aong ultiple eory dies, additionally detected faults after bonding, or ultiple blocks in a eory die. Therefore, the proposed ethod is different fro the previous ethod [1]. Unlike the previous ethod, the proposed ethod does not require fault bitaps. Therefore, the proposed ethod is cost-effective. Using the collected inforation, the proposed basic die-selection ethod selects a target eory die to be stacked and then instantly identifies counterpart eory dies that eet three basic selection conditions. The eory fault characteristics stated in subsection II.3 are reified as the basic selection conditions. These three conditions are as follows: Basic selection condition 1: Rk L RS, Basic selection condition : Ck L CS, Basic selection condition 3: ( Rk + Ck + Sk) L ( RS+ CS), where is the present nuber of stacked eory dies and L is the total nuber of layers in a 3D eory. R k, C k, and S k represent the nubers of faulty row lines, faulty colun lines, Fault-free dies Self-repairable dies Inter-repairable dies Irreparable dies Fig.. A eory die classification ap (L =, R S = 1, and C S = ). Input: the sorted list of N eory dies Output: sets of eory dies to for a good 3D eory 3 1 SELECT_DIES (the sorted list) { while (there is die data to be checked in the sorted list) { 3 t_die = SELECT_T_DIE (); for all k, 1 < k L { 5 the k-th selected die = SELECT_C_DIE (t_die, the already selected dies); } 6 if (the selected dies are suitable for a good 3D eory) { 7 OUTPUT_GOOD_DIES (t_die, the selected dies); 8 DELETE_GOOD_DIES (t_die, the selected dies); } 9 else { 1 DELETE_IRREPARABLE_DIE (t_die); } 11 RESET_EXCLUDED_DIES (); } } Fig. 5. Pseudo-code for proposed die-selection ethod. and single cell faults for the k-th stacked eory die, respectively. If the first basic selection condition is satisfied, then the total nuber of faulty row lines in the stacked eory dies is fewer than or equal to the total nuber of spare rows in a 3D eory. Therefore, all the row faulty lines in the stacked eory dies can be repaired. Siilarly, if the second basic selection condition is satisfied, all of the colun faulty lines in the stacked eory dies can be repaired. When considering single cell faults, the third basic selection condition should also be satisfied to repair the 3D eory. Unlike the previous ethod, the proposed ethod uses the eory fault characteristics, thus enabling a higher 3D eory yield. A eory die classification ap is used to detect the counterpart eory dies as quickly as possible. Meory repair inforation for the proposed die-selection ethod is iediately recorded in the eory die classification ap after the eory die is classified. The eory die classification ap for a two-layer 3D eory is shown in Fig. ; each eory die has one spare row and two spare coluns. In Fig., () denotes the nuber of faulty row (colun) lines in a eory die after the pre-bond test and repair. Since there are two layers in the 3D eory, the total nuber of spare rows (coluns) is two (four). Thus, if () exceeds two (four), the eory die is irreparable. There 5 39 Joohwan Lee et al. ETRI Journal, Volue 3, Nuber 3, June 1

6 is no need to store irreparable dies in the eory die classification ap because irreparable dies are not used for 3D eory stacking. Classified eory dies that are not irreparable are recorded in the eory die classification ap. Pseudo-code for the proposed die-selection ethod is shown in Fig. 5. SELECT_DIES represents the process of selecting eory dies to for 3D eories (line 1). This function does not terinate until all dies are checked (line ). It uses the sorted list of N eory dies as input, where N is the total nuber of eory dies to be checked. SELECT_DIES outputs sets of eory dies to for a good 3D eory. In the sorted list, the eory dies are arranged using the sus of,, and SF, where SF represents the nuber of single cell faults in a eory die after the pre-bond test and repair, and they are organized in descending order. If the total of,, and SF is large, the eory die is generally hard to repair. On the other hand, it can be easily repaired when the su is sall. In Fig. 5, if there is die data to be checked in the sorted list, the target eory die (t_die) is deterined by SELECT_T_DIE (line 3). The target die is located at the very front of the sorted list. Once the target eory die is chosen, candidates for its counterpart are analyzed with SELECT_C_DIE (lines and 5), which uses the three basic selection conditions and the die classification aps. If there is at least one candidate, the first available eory die in the sorted list is selected as the counterpart. This process using SELECT_C_DIE is repeated L 1 ties (line ) because L 1 counterpart eory dies are required to stack. If the selected eory dies can stack into a good 3D eory (line 6), they are outputted at OUTPUT_ GOOD_DIES (line 7) and deleted fro the sorted list at DELETE_GOOD_DIES (line 8). Otherwise, the target eory die is deleted at DELETE_IRREPARABLE_DIE (line 1) because it cannot be repaired by redundancy sharing. Finally, the eory die status is reset by RESET_ EXCLUDED_DIES (line 11). For a worst-case evaluation, the outer loop (line ) is executed N+1 ties and the function (line 5) in the inner loop (line ) is carried out approxiately (L 1) N ties, where N is the nuber of eory dies in the sorted list, as shown in Fig. 5. Hence, the coputational coplexity of the proposed ethod is O(N ). An exaple for the proposed die-selection ethod is shown in Fig. 6. The proposed ethod finds the counterpart dies to for two-layer 3D eories using four eory dies with one spare row and two spare coluns, as shown in Fig. 6. Meory repair inforation for four eory dies is displayed in Fig. 6(a). Meory dies are sorted in descending order (dies B-A-D- C), and then they are recorded in the sorted list. With the sorted list, proper eory dies are selected to stack good 3D eories with the proposed die-selection, as shown in Fig. 6(b). In the eory die classification ap, SF is written as the Die A = = SF=1 Die classification ap 1 3 A 1 1 C B 1 D Die B =1 =3 SF=1 Die C =1 = SF= Die D = =1 SF= (a) Meory repair inforation of eory dies Sorted list B target A excluded D excluded C selected Die classification ap (b) Die-selection procedures 1 3 Sorted list A target D selected Fig. 6. An exaple for proposed die-selection ethod (L =, R S = 1, and C S = ). nuber positioned at the right botto of the die. When die A in Fig. 6(a) has a single cell fault, this is written in Fig. 6(b) as die A 1. Siilarly, dies B, C, and D can be expressed as dies B 1, C, and D. In the left side of Fig. 6(b), the inter-repairable die B 1 is selected as the first target eory die since it is located on the first line of the sorted list. Since the three basic selection conditions instantly deterine the search space for finding counterpart dies, the self-repairable die C is atched with the first target die B. In the right-hand side of Fig. 6(b), the data of dies B and C is deleted fro the sorted list and the die classification ap because these dies can ake a good 3D eory. The self-repairable die A is atched with the interrepairable die D to create a good 3D eory stack, in the sae way. 3. 3D Meory Repair for Additionally Detected Faults after Bonding After eory dies are selected to stack good 3D eories, eory dies are bonded to each other. Additional faults can arise during bonding, and they should be repaired during the post-bond test and repair. To repair newly detected faults, unused redundancies are required. However, since the three basic selection conditions do not consider additionally detected faults after bonding, the proposed basic die-selection ethod cannot guarantee the existence of unused redundancies and the repair of newly detected faults. To prevent the unexpected yield drop, the three basic selection conditions are odified as follows: Modified selection condition 1: Rk L RS RM, 1 Modified selection condition : Ck L CS CM, Modified selection condition 3: ( Rk + Ck + Sk) L ( RS+ CS) SM, D A 1 ETRI Journal, Volue 3, Nuber 3, June 1 Joohwan Lee et al. 393

7 where R M, C M, and S M denote the spare row argin, the spare colun argin, and the single cell fault argin, respectively. The argin range can be deterined based on the characteristics of the anufacturing process. With the odified selection conditions, the proposed die-selection ethod can guarantee the 3D eory yield, in spite of additional faults detected after bonding.. Advanced Die-Selection Method Considering Multiple Meory Blocks A eory die is usually coposed of ultiple eory blocks. If a single eory block is irreparable after bonding, the entire 3D eory is scrapped. Therefore, all the eory blocks in a 3D eory should be repairable. Unlike the previous die-selection ethods -[1], our proposed dieselection ethod specifically considers how to for 3D eories with ultiple eory blocks. Thus, the 3D eory yield with the proposed ethod is higher than that fro previous ethods, especially when there are any eory blocks. To stack good 3D eories, ultiple eory die classification aps are used. Each eory die classification ap records eory repair inforation for a given eory block position, so the nuber of ultiple eory die classification aps is deterined by how any eory blocks are in a eory die. A counterpart eory die is deterined when the three odified selection conditions are siultaneously satisfied in all the eory die classification aps. The eory die classification aps share the sorted list. The standard su for ordering is calculated using the hard to repair eory block. An exaple of the proposed die-selection ethod for ultiple blocks is shown in Fig. 7; four-layer 3D eories are stacked using six eory dies. The eory dies consist of two eory blocks with one spare row and two spare coluns added to each eory block. All-zero argins are used. Meory dies are arranged in descending order (dies A- B-C-D-E-F) and recorded in the sorted list. With the sorted list, proper eory dies are selected to stack good 3D eories with the proposed die-selection, as shown in Fig. 7. In Fig. 7(a), the inter-repairable die A is first selected as the target eory die. Four eory dies (B, C, E, and F) can be used as the counterpart for die A in the eory die classification ap of the first eory block; however, only two eory dies (D and F) can be used in the second one. Therefore, die F is selected as the counterpart eory die for die A because it can siultaneously satisfy all three selection conditions. However, since there are no ore unchecked eory dies in the sorted list, dies A and F cannot for a 3D eory. After die A is deleted fro the sorted list and the die classification aps, the E 1 F D 3 1 F C 1 B 1 B E C A 1 3 D 3 A 1 (a) Die-selection for die A E 1 1 F C 1 B 3 D E 1 1 F C 1 B 3 D E 1 1 F C 1 B 3 D Block 1 Block Sorted list F D 3 1 B E C 3 (b) Die-selection for die B F D 3 1 B E C 3 (c) Die-selection for dies B and C F D 3 1 B E C 3 (d) Die-selection for dies B, C, and E A target B excluded C excluded D excluded E excluded F selected B target C selected D - E - F - B target C selected D excluded E selected F - B target C selected D excluded E selected F selected Fig. 7. An exaple of proposed die-selection ethod for ultiple blocks (L =, R S = 1, C S =, R M =, C M =, S M =, and B = ). inter-repairable die B is selected as the target eory die. According to the eory die classification aps, all the reaining eory dies can be a counterpart eory die for die B, as shown in Fig. 7(b). However, die C is adopted as the counterpart eory die for die B because it is the ost difficult eory die to repair aong the reaining eory dies. In other words, using a hard-to-repair eory die first provides ore opportunities for stacking 3D eories. Siilarly, die E is chosen as the counterpart eory die for dies B and C, as shown in Fig. 7(c). Finally, die F is selected to for a good 3D eory in Fig. 7(d). IV. Siulation Results and Analysis To evaluate the perforance of the proposed die-selection ethod, we upgraded our yield enhanceent siulator, naed YES, which had been developed in C language to easure the 39 Joohwan Lee et al. ETRI Journal, Volue 3, Nuber 3, June 1

8 General info. # of dies per wafer, # of layers, fault distribution Yield enhanceent siulator (YES) Meory die info. Die size, argins, # of blocks, # of redundancies Fault generation Meory die classification Die-selection for stacking Yield evaluation Algorith info.,, the proposed Relative probability λ = 8, α =.38 λ = 8, α = Faults per eory block Fault statistics 3D eory yields TSV overhead Analysis speed Fig. 9. Polya-Eggenberger distributions with λ = 8, α =.38 and λ = 8, α =.63. Fig. 8. Overview of a yield enhanceent siulator (YES). 1 1 perforance of various die-selection ethods during our previous research, as in [1]. The overall diagra of YES is shown in Fig. 8. In reference to the inforation associated with several inputs, YES generates faulty addresses. Then, eory dies are classified with their states after the pre-bond test and repair. The classified eory dies are selected for 3D eory stacking. After evaluating 3D eory yields, YES generates output data as follows: fault statistics, 3D eory yields, TSV overhead, and analysis speed. For the coparison of yields, various eory dies are considered for foring 3D eories with,, or 8 layers. We use 1, eory dies to obtain each siulation result. Each eory die contains, 8, or 16 eory blocks, and each eory block has 1, 1, bit-cells. Different cobinations of spares are used, and the redundancies are vertically shared with different ratios. To handle additional faults detected after bonding, argins are also considered. In our siulation, a different nuber of faults is injected into each eory block at rando locations using Polya- Eggenberger distribution, [19]-[], as shown in Fig. 9. Polya-Eggenberger distribution is suitable for odeling integrated circuit yields [19]-[]. The two distributions share the paraeter λ and have different paraeters for α: (a) Polya- Eggenberger distribution with λ = 8 and α =.38; (b) Polya- Eggenberger distribution with λ = 8 and α =.63. The two distributions represent the cases with clustered faults (λ = 8 and α =.38) and evenly distributed faults (λ = 8 and α =.63), respectively. Thus, siulation results are obtained in both cases. The proposed die-selection ethod is copared with the two previous die-selection ethods,. However, since the proposed ethod is based on the previous ethod [1], it is not copared with the previous ethod [1]. Without the Layers (a) λ=8, α=.38 8 Layers Fig. 1. Coparison of yields with different layers (R S = 3, C S =, R M =, C M =, S M =, and B = 16). 8 6 (b) λ=8, α=.63 additional considerations (redundancy sharing aong ultiple eory dies, additionally detected faults after bonding, and ultiple blocks in a eory die) in the proposed ethod, siulation results of the proposed ethod are identical with those of the previous ethod [1]. When different nubers of layers are used, the yield of the proposed die-selection ethod is greater than that of the previous die-selection ethods, as shown in Fig. 1. The previous ethods, share redundancies only between neighboring eory dies. However, the proposed ethod shares the redundancies aong all the eory dies. Therefore, the gaps between the 3D eory yield with the proposed ethod and the 3D eory yields with the previous ethods are great, especially when the nuber of layers is large. Furtherore, since the proposed redundancy sharing strategy is used, the 3D eory yield using the proposed ethod increases as the nuber of layers grows. Next we copare the 3D eory yield of the proposed ethod with that of the previous ethods, when there are different nubers of eory blocks, as shown in Fig. 11. The yield using the proposed ethod is higher in all cases. As the nuber of eory blocks increases, the difference between ETRI Journal, Volue 3, Nuber 3, June 1 Joohwan Lee et al. 395

9 Blocks (a) λ=8, α= Blocks (b) λ=8, α=.63 Fig. 11. Coparison of yields with different blocks (L = 8, R S = 3, C S =, R M =, C M =, and S M = ) Redundancies (Global R S - local R S - global C S - local C S ) (a) λ=8, α=.38 Fig. 1. Coparison of yields with different redundancy sharing ratios (L = 8, R M =, C M =, S M =, and B = 8) Redundancies (Global R S - local R S - global C S - local C S ) (b) λ=8, α= layers layers layers layers 8 layers 8 layers 1 1 Margins (S M ) Margins (S M ) (a) λ=8, α=.38 (b) λ=8, α=.63 Fig. 1. Coparison of yields with different argins (R S = 3, C S =, R M =, C M =, and B = 8). 8 6 TSVs per block with --- with with --- with and with Layers Redundancies (R S C S ) (a) λ=8, α=.38 Fig. 13. Coparison of yields with different redundancies (L = 8, R M =, C M =, S M =, and B = 8) Redundancies (R S C S ) (b) λ=8, α=.63 the 3D eory yield with the proposed ethod and that with the previous ethods grows. Therefore, the proposed dieselection ethod is very practical. The 3D eory yield using the proposed ethod with different argins is shown in Fig. 1. In Fig. 1, the spare row argin (R M ) and spare colun argin (C M ) are fixed at zero but the single cell fault argin (S M ) varies fro to. It is natural that the 3D eory yield is low when the single cell fault argin is large. However, when the nuber of layers increases, the effect of the argin decreases because the proposed ethod shares inter-die redundancies aong all the eory dies. Thus, the proposed die-selection ethod has the Fig. 15. Coparison of nubers of TSVs in each block with different redundancy sharing ratios. advantage of repairing additionally detected faults after bonding. As the nuber of redundancies increases, the 3D eory yield drastically increases in all cases, as shown in Fig. 13. The average nuber of faults in each eory die is 8 because the paraeter λ of the Polya-Eggenberger distribution is 8. When the sae nuber of redundancies is used, the 3D eory yield with the proposed ethod is higher than the yields with the previous ethods. Therefore, the proposed die-selection ethod is superior to previous ethods. Different redundancy sharing ratios are used in Fig. 1. When all of the redundancies are shared, the difference of the 3D eory yield is not large. However, as global spares decrease and local spares increase, the gap in the 3D eory yield grows. Furtherore, the 3D eory yield with the proposed ethod does not drop until all the redundancies becoe local. Therefore, since there is no need to share all the redundancies in the proposed die-selection ethod, the TSV overhead can be significantly reduced. The nuber of TSVs in each block is shown in Fig. 15 according to three die-selection ethods (,, and the 396 Joohwan Lee et al. ETRI Journal, Volue 3, Nuber 3, June 1

10 proposed ethod) and different redundancy sharing ratios. When all of the redundancies are shared, there is a great gap between the nuber of TSVs for the previous ethods ( and with ---, L=8) and that for the proposed ethod (the proposed with ---, L=8), as shown in Fig. 15. This is because the nuber of TSVs for ipleenting L-layer 3D eories with the previous ethods, is proportional to L but with the proposed ethod is proportional to (L 1). With the continuing iproveent of TSV anufacturing technology, this overhead is likely to be less of a concern. However, as the redundancy sharing ratio is decreasing, the difference between the previous ethods and the proposed ethod can be reduced. Nevertheless, if the nuber of TSVs is critical, a lesser nuber of layers can be used for redundancy sharing. For exaple, when four layers are used for sharing and the redundancy sharing ratio is low, the nuber of TSVs for the proposed ethod is alost the sae as that for the previous ethods, as shown in Fig. 15. In this case, the yield of the proposed ethod is also greater than the yields of the previous ethods. V. Conclusion A die-selection ethod using three selection conditions was proposed for yield enhanceent in ulti-layer 3D eories. Previous die-selection ethods share redundancies only between neighboring eory dies. However, the proposed die-selection ethod shares redundancies aong all the eory dies within a ulti-layer 3D eory. Furtherore, the 3D eory yield with the proposed ethod is higher than the yields with previous die-selection ethods since the proposed die-selection ethod considers both eory fault characteristics and additionally detected faults. The proposed die-selection ethod also takes ultiple blocks into account, which is practical because a eory die typically contains a nuber of eory blocks. Siulation results showed that the proposed die-selection ethod can further iprove 3D eory yields. The TSV overhead for the proposed ethod is alost the sae as that for the previous ethods. In conclusion, the proposed die-selection ethod using three selection conditions effectively enhances the yield of ulti-layer 3D eories with inter-die redundancies. References [1] V.F. Pavlidis and E.G. Friedan, Interconnect-Based Design Methodologies for Three-Diensional Integrated Circuits, Proc. IEEE, vol. 97, no. 1, Jan. 9, pp [] W.R. Davis et al., Deystifying 3D ICs: The Pros and Cons of Going Vertical, IEEE Design Test Coput., vol., no. 6, Nov. 5, pp [3] H. Sun et al., 3D DRAM Design and Application to 3D Multicore Systes, IEEE Design Test Coput., vol. 6, no. 5, Sept. 9, pp [] S.S. Iyer et al., Process-Design Considerations for Three Diensional Meory Integration, Proc. Syp. VLSI Tech., Jun. 9, pp [5] E.J. Marinissen and Y. Zorian, Testing 3D Chips Containing Through-Silicon Vias, Proc. Int. Test Conf. (ITC), Nov. 9, pp [6] H.-H.S. Lee and K. Chakrabarty, Test Challenges for 3D Integrated Circuits, IEEE Design Test Coput., vol. 6, no. 5, Sept. 9, pp [7] Y.-F. Chou, D.-M. Kwai, and C.-W. Wu, Meory Repair by Die Stacking with Through Silicon Vias, Proc. Int. Workshop Meory Tech., Design, and Testing (MTDT), Aug. 9, pp C.-W. Chou, Y.-J. Huang, and J.-F. Li, Yield-Enhanceent Techniques for 3D Rando Access Meories, Proc. Int. Syp. VLSI Design Autoat. Test (VLSI-DAT), Apr. 1, pp L. Jiang, R. Ye, and Q. Xu, Yield Enhanceent for 3D-Stacked Meory by Redundancy Sharing Across Dies, Proc. Int. Conf. Coput.-Aided Design (ICCAD), Nov. 1, pp [1] J. Lee, K. Park, and S. Kang, A Die-Selection Method Using Search-Space Conditions for Yield Enhanceent in 3D Meory, ETRI J., vol. 33, no. 6, Dec. 11, pp [11] T. Yaagata et al., A Distributed Globally Replaceable Redundancy Schee for Sub-Half-Micron ULSI Meories and Beyond, IEEE J. Solid-State Circuits, vol. 31, no., Feb. 1996, pp [1] C.-T. Huang et al., Built-in Redundancy Analysis for Meory Yield Iproveent, IEEE Trans. Relia., vol. 5, no., Dec. 3, pp [13] M.-H. Yang et al., A Novel BIRA Method with High Repair Efficiency and Sall Hardware Overhead, ETRI J., vol. 31, no. 3, June 9, pp [1] W. Jeong et al., A Fast Built-in Redundancy Analysis for Meories with Optial Repair Rate Using a Line-Based Search Tree, IEEE Trans. Very Large Scale Integr. Syst., vol. 17, no. 1, Dec. 9, pp [15] H. Cho, W. Kang, and S. Kang, A Built-In Redundancy Analysis with a Miniized Binary Search Tree, ETRI J., vol. 3, no., Aug. 1, pp [16] T. Han et al., High Repair Efficiency BIRA Algorith with a Line Fault Schee, ETRI J., vol. 3, no., Aug. 1, pp [17] W. Jeong et al., An Advanced BIRA for Meories with an Optial Repair Rate and Fast Analysis Speed by Using a Branch Analyzer, IEEE Trans. Coput.-Aided Design Integr. Circuits Syst., vol. 9, no. 1, Dec. 1, pp [18] A. Papanikolaou, D. Soudris, and R. Radojcic, Three Diensional Syste Integration: IC Stacking Process and Design, Springer, 1. ETRI Journal, Volue 3, Nuber 3, June 1 Joohwan Lee et al. 397

11 [19] C.H. Stapper, On a Coposite Model to the IC Yield Proble, IEEE J. Solid-State Circuits, vol. 1, no. 6, Dec. 1975, pp [] C.H. Stapper, A.N. McLaren, and M. Dreckann, Yield Model for Productivity Optiization of VLSI Meory Chips with Redundancy and Partially Good Product, IBM J. Research Developent, vol., no. 3, May 198, pp [1] C.-L. Wey and F. Lobardi, On the Repair of Redundant RAM s, IEEE Trans. Coput.-Aided Design Integr. Circuits Syst., vol. 6, no., Mar. 1987, pp [] R.-F. Huang et al., A Siulator for Evaluating Redundancy Analysis Algoriths of Repairable Ebedded Meories, Proc. Int. Workshop Meory Tech., Design, and Testing (MTDT), Jul., pp Joohwan Lee received his BS, MS, and PhD in electrical and electronic engineering fro Yonsei University, Seoul, Rep. of Korea, in 3, 5, and 1, respectively. He was also a research engineer with the university s ASIC Research Center. Currently, he is working in the S. LSI Division of Sasung Electronics as a senior engineer. His ain research interests include VLSI design, fault siulation, fault diagnosis, BISR, BIST, BIRA, RA algorith, reliability, 3D eory yield enhanceent, and TSV repair. Kihyun Park received his BS in electrical and electronic engineering fro Yonsei University, Seoul, Rep. of Korea in 7, then went on to work as a research engineer with the university s ASIC Research Center. Currently, he is working toward a cobined MS/PhD in electrical and electronic engineering at Yonsei University. His current research interests include BISR, BIST, BIRA, test algoriths, and VLSI design. Sungho Kang received his BS in control and instruentation engineering fro Seoul National University, Seoul, Rep. of Korea, and MS and PhD in electrical and coputer engineering fro the University of Texas at Austin, Austin, USA, in 199. He was a research scientist with the Schluberger Laboratory for Coputer Science, Schluberger Inc., and a senior staff engineer with Seiconductor Systes Design Technology, Motorola Inc. Since 199, he has been a professor in the Departent of Electrical and Electronic Engineering, Yonsei University, Seoul, Rep. of Korea. His ain research interests include VLSI/SOC design and testing, design for testability, and design for anufacturability. 398 Joohwan Lee et al. ETRI Journal, Volue 3, Nuber 3, June 1