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International Journal of Antennas and Propagation
Volume 2015, Article ID 470952, 14 pages
http://dx.doi.org/10.1155/2015/470952
Research Article

Modeling and Electromagnetic Analysis of Multilayer Through Silicon Via Interconnect for 3D Integration

School of Electronic and Information Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100191, China

Received 24 July 2015; Revised 3 November 2015; Accepted 4 November 2015

Academic Editor: Felipe Cátedra

Copyright © 2015 Zhaowen Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Convergence of multiple functions in a single device is the main thought behind the development of the current electronic trends. So, the requirement for higher integration in electronic devices has become more important in present days than in the past. Through silicon via (TSV) is the latest interconnect technology proposed mainly for higher integration and higher frequency. Therefore, cross talk will be an essential issue that needs to be taken into consideration. In this paper, we study the electrical property of a GSSG (S-Signal, G-Ground) TSV structure and propose the accurate lumped model which can be used to predict the TSV performance. Since more dies are used within one chip, the single layer TSV cannot satisfy the requirement. Hence, we propose the multilayer TSV structure and study how the bump radius, bump height, and underfill material affect the TSV transmission performance and coupling issue, so that we can conduct a good TSV design. Furthermore, three multilayer 4 × 4 TSV array models are proposed with different GS distribution to analyze the detailed coupling results.

1. Introduction

The inheritance of planar scaling which has been fulfilling the forecast in Moore’s Law is at the edge of saturation. One of the main reasons of the saturation is the physical size involved in semiconductor lithography that puts a limit to the dimension of transistors. The other important issue related to scaling is interconnect technology. Since the end of last decade, a leading trend in electronics industry is to increase the integration density in electronic devices using three-dimensional (3D) integration. This three-dimensional chip integration can be an alternative solution to planar scaling to achieve higher integration.

At present scientists are realizing 3D integration by stacking integrated circuit (IC) dies, where vertical interconnection is the main path to communicate with other submodules. Thus, to achieve the desired performance in 3D system, TSV interconnection is the key technology.

For the effective use of through silicon via in 3D integration and to ensure the high yield chip design, the most important work to be done for more accurate TSV modeling is to consider the multilayer silicon substrate. Therefore, electromagnetic modeling and analysis of TSVs in multilayer substrate are crucial before it goes for production. Reference [1] discussed simple analytical methods that are available for characterizing one or two TSVs, but they cannot address general multilayer TSV problems.

Hundreds of TSVs are required as interconnects in 3D integration system, so coupling will be one of the most important problems in TSV design. Researchers in both the academic and industrial fields are putting their highest effort to solve different problems that hinder the flourishing of this technology. In the literature there are some works that have been done on the modeling and analysis of coupling issues of through silicon via technology, but all of them are considering single layer substrate. Reference [2] presented a modeling method of TSV, based on lumped element. Lumped element modeling method can provide good results for the insertion loss, though it has some limitations. In [3] an analytical model for fast estimation of coupling capacitance of square shaped TSVs has been proposed for 3D integration. Coupling effect between through silicon via (TSV) in large array structure has been investigated in [4]. A full chip TSV to TSV coupling has been analyzed in [5] where a full chip SI analysis flow has been proposed based on the proposed coupling. Analytical formulas to extract an equivalent circuit model for coupled TSVs have been proposed in [6] where the authors used multiconductor transmission line approach to model the structures. References [7, 8] presented new analytical methods to derive the , , , and parameters in multiport TSV networks.

There are two main innovations of this paper. One is the research on how the bump size and dielectric material influence the transmission and coupling issue of GSSG multilayer TSV structure. The other one is the establishment of three two-layer 4 × 4 TSV array models with different GS TSV distribution and the explanation on how the ground distribution affects TSV transmission and coupling property.

The rest of the paper is arranged as follows. Section 2 explores the electrical property of the proposed TSV structure and gives the equivalent lumped model. The lumped model is verified by comparison with the simulating result. Section 3 studies the multilayer TSV property and how the chosen factors affect the TSV transmission and cross talk performance. Section 4 discusses three multilayer TSV array structures with different GS distribution and emphasizes the coupling issue of the TSV array. Section 5 concludes this paper.

2. Electrical Property of Two TSV Pairs with Bump

Figure 1 shows a typical TSV structure. It is embedded in a silicon substrate which is lossy. Therefore, an insulation layer must be formed between the TSV and the silicon substrate to avoid the leakage of the signal.

Figure 1: TSV structure.

It is of great importance to obtain the accurate electrical model of the TSV, for it can not only indicate its behavior, but also reduce the simulation time. Meanwhile, it is the basis of the multilayer TSV modeling.

2.1. Electrical Modeling of the TSV Structure

Some models were proposed in the literature, among which the GS and GSG models (S-Signal, G-Ground) were the most popular ones [9, 10]. Most of the works were emphasized on the transmission quality of a single TSV and the interference from the active circuits. A differential GSSG TSV model was established and analyzed in [11]. Here, we researched on the GSSG model in Figure 2, and the signals were two single-ended signals with the same phase.

Figure 2: Proposed TSV model.

In Figure 2, TSVs are formed in the silicon substrate, with the silicon dioxide (insulation layer) surrounding them. The central two TSVs serve as the signal TSV and the peripheral ones are the ground TSV. Bumps have a direct contact with the TSV. And the underfill material is CYCLOTENE 4000 series BCB with high strength, good thermal stability, and good microwave performance. The electrical property of the TSV is decided by its parameters and the electrical property of the surrounding materials. The parameters of the proposed model are shown in Table 1, while the material property is showed in Table 2.

Table 1: Parameters of proposed model.
Table 2: Material property of proposed model.

Since TSV is filled with copper, it can be modeled as a series of and . The DC resistance is shown in (1). As the frequency increases, the skin effect must be considered. Meanwhile, since TSVs are in close proximity, the proximity effect will lead to an increase in resistance. Equation (2) gives the resistance considering both the skin effect and the proximity effect [13]. And can be described in (3). When the bump parameters are used in (1), (2), and (3), the resistance of the bump can be gained and we call it :

Referring to the calculation of the inductive parasitic parameters, self-inductance and mutual-inductance must be taken into account. Their quasistatic inductances are calculated usingwhere is the variable presenting the radius in the self-inductance calculation and the pitch in the mutual-inductance calculation and indicates the height of the TSV or bump. Therefore, the inductance of the signal and ground TSV can be described in (5). When the is replaced by and is replaced by , the inductance of the signal bump and the ground bump can be gained, respectively:

Since the silicon is conductive, there exists a capacitance between the silicon substrate and the TSV, which can be modeled as a coaxial cable. Table 3 gives RLC analytical formula of different transmission lines. According to Table 3, can be expressed in

Table 3: RLC analytical formula of different transmission lines [12] see Figure 3.
Figure 3

There is also a capacitance between a bump and the silicon substrate. And it can be modeled as two parallel plates. Thus, is proportional to the facing area and reciprocal proportional to the height, , as shown in

As TSV and bump are both in cylindrical shape, capacitance between adjoining bumps or adjoining TSVs can be modeled as two parallel wires. That means the capacitance is correlated with the height, pitch, and the radius of the research objects. Therefore, the capacitance between two TSVs in the substrate, , can be calculated in (8). Meanwhile, the capacitance between two bumps in the underfill layer, , can be derived in (9) and the capacitance between TSV and silicon substrate, , can be calculated in (10):

The silicon substrate is lossy, and the conductance can be derived in

2.2. Verification of the Proposed Electrical Model

To verify the proposed lumped model, we established a model in EM simulator HFSS. The parameters are the same in Table 1. And the entire simulating frequency is from 100 MHz to 20 GHz. Then a model in Figure 4 has been set up in ADS, and the RLCG is obtained according to formulas (1)–(11). The simulation result is shown in Figure 5. and indicate the transmission property of the TSV. It shows a good correlation between the EM simulation and the lumped model result. The maximum difference of the is about 0.02 dB in 20 GHz, while also gains the maximum difference, 0.6 dB, in 20 GHz. represents the near cross talk between two signal TSVs. The difference between two simulating methods decreases as the frequency goes up. The maximum difference is 18.2 dB in 0.1 GHz and keeps within 3 dB from 1.2 GHz to 20 GHz. Therefore, the near cross talk accuracy is better with higher frequency. reflects the far cross talk between two signal TSVs. The tendency is the same in the entire frequency, but the difference value decreases first and then increases as the frequency goes up. The maximum difference is 20.3 dB in 0.1 GHz and keeps within 8 dB from 0.6 GHz to 20 GHz.

Figure 4: Electrical model of the proposed TSV structure. (, , , , and ).
Figure 5: Simulation results in HFSS and ADS.

In this way, the lumped model is verified and can be used to predict the TSV performance well.

3. Research on the Multilayer TSVs

Nowadays, TSV has already been used in the new 3D-integration products. And the TSV structure may flourish in the chip field during the next few years. As the requirement for higher bandwidth, more I/O interface, smaller size, more layers will be stacked in the same chip and multilayer TSVs will be a unique technique to build the structure. Therefore, research on the electrical property of the multilayer TSVs and the coupling issues are urged to be conducted.

For a 3D-stacked DRAM module, some of the signals can be shared with other different chips (supposing the chips have the same layout), including address bus, data bus, read control, write control, and power [14]. And some structure has already been made for the experimental test. Though the fabrication process seems to attract more attention, the simulation research still needs to be emphasized.

The multilayer structure was established in Figure 6. It can be stacked layers. And the insertion loss of different layer TSV has been shown in Figure 7. Since the one-layer TSV has already been studied in part II, we focus on the electrical property of the intermetallic dielectric layer, which consists of the bump, the adhesive material, and the underfill material. And parameter is used to indicate the TSV channel performance.

Figure 6: Multilayer TSV structure (parameters of the structure: thickness of the SnAg is 2 μm, bump height is defined as , μm, and bump radius is defined as , μm, μm, μm, μm, μm, and μm).
Figure 7: Insertion loss of multilayer TSV.

SnAg was chosen to be the adhesive material. It is a good flux material with high conductivity. The electromigration phenomenon may happen between the Cu and the SnAg, which will cause the mechanical instability, but it does not account much for the electrical property of the TSV.

Here we study how the bump size and the underfill material affect the insertion loss and the coupling result of the proposed TSV structure. The model used in the HFSS was the same as in Figure 6.

Firstly, BCB and silicon dioxide are used as underfill material, respectively, in the simulation; the result is shown in Figure 8. It shows that parameters are almost the same in the different underfill material and the difference in 20 GHz is shown in Table 4. It indicates that the TSV transmission property is a little better when the BCB is used. Since the is bigger than , it results in a bigger value. The signal will be transmitted from one TSV to another through this capacitor in the intermetallic dielectric layer. Since the bigger capacitor can offer lower impedance path, more loss of the TSV may happen. When μm, the value of the capacitor is 0.46 fF with the BCB underfill and 0.70 fF with the silicon dioxide underfill.

Table 4: parameter comparison at 20 GHz.
Figure 8: parameters of the TSV model with different underfill material.

Secondly, the bump radius is studied with the BCB as the underfill material. The result is shown in Figure 9. It shows that decreases over the entire frequency when the radius changes from 12 μm to 18 μm. When the bump radius increases, the value becomes larger and the impedance discontinuity becomes more obvious, both of which add transmission loss of the TSV channel. The results also indicate that the change of the radius has more influence on the far coupling than the near coupling.

Figure 9: parameters of the TSV model with different bump radius.

Thirdly, the bump height is taken into consideration. As shown in Figure 10, the parameters do not change much as changes. Maybe the bump height is too small compared to the TSV height, it can only affect the TSV performance slightly. The results also indicate that the change of the radius does more influence on the far coupling than the near coupling.

Figure 10: parameters of the TSV model with different bump height.

4. Research on the Multilayer TSVs Array

TSVs are mainly intended to be used for 3D integration technology for heterogeneous integration. In reality, there are always amounts of TSVs in one design, so the coupling between TSVs in the multilayer substrate is crucial to be analyzed before it goes for production.

Figure 11 shows a 4 × 4 multilayer TSV array and all TSVs were signal TSVs. The parameters of the 4 × 4 array model are different from that in part II. This change target is to guarantee the TSV performance as more TSVs are added to the structure. The insertion loss of TSV1 is calculated and shown in Figure 12. We see that, in this condition, the insertion loss is large. In order to improve the TSV transmission property, three 4 × 4 array models with different GS distribution have been proposed in Figure 13. Ground TSV offers the low impedance return path for the signal and can reduce the coupling issues effectively. Some researches have been done to explore the GS distribution effect on the systematic coupling issue [15]. However, their studies were limited to the single TSV layer. Here, we analyzed the three models, respectively. The simulation is conducted in HFSS from 1 GHz to 20 GHz.

Figure 11: 4 × 4 multilayer TSV array, all TSVs are signal TSVs. There exist two copper layers on both sides serving as ground plane (parameters of the structure: thickness of the SnAg is 2 μm, μm, μm, μm, μm, μm, μm, and μm).
Figure 12: Insertion loss of TSV1.
Figure 13: Three different GS distribution models of multilayer TSV array: blue indicates the ground TSV and yellow indicates the signal TSV.
4.1. Model 1

Figure 14 shows the simulation results of model 1. Because of the symmetrical TSV array structure, the central four TSVs have almost the same insertion loss, so are the four TSVs in the corner. In this condition, there is no need to study every TSV to obtain the coupling results. TSV1 and TSV6 can reflect the coupling information of all the corner TSV and central TSV, respectively. Since the cross talk gets worse with the higher frequency, we only give the coupling results in 20 GHz. Figure 14(b) gives the near and far coupling results at 20 GHz from the aggressive TSV to TSV1. Figure 14(c) also reflects the cross talk at 20 GHz from the aggressive TSV to TSV6. In the following, coupling refers to the near coupling. Meanwhile, the cross talk could be ignored if the coupling coefficient was below −40 dB. For TSV1, TSV5 is the nearest one and thus results in the largest cross talk, −39.9 dB. The coupling from the other aggressive ones is below −40 dB, which could be ignored. For TSV6, cross talk value is −31.6 dB from TSV5 and TSV7 and −39 dB from TSV7. It is clear that cross talk decreases as the distance increases. And in Model 1, the cross talk can be ignored when the distance is beyond pitch.

Figure 14: parameters result of Model 1. (a) Insertion loss of each TSV, (b) the cross talk from the aggressive TSV to TSV1 at 20 GHz, and (c) the cross talk from the aggressive TSV to TSV6 at 20 GHz.
4.2. Model 2

The simulation results of Model 2 are showed in Figure 15. All the signal TSVs are arranged in the middle and all the ground TSVs are placed at sides. Meanwhile, the signal TSV can be divided into two groups referring to the location. One includes TSV2, TSV3, TSV6, and TSV7 and the other includes TSV1, TSV4, TSV5, and TSV8. The TSV in one group has the same surrounding environment, which results in the same insertion loss as shown in Figure 15(a). Therefore, TSV1 and TSV2 can represent each group to obtain the coupling information, respectively. The near and far coupling results at 20 GHz from the aggressive TSV to TSV1 are shown in Figure 15(b), while the cross talk at 20 GHz from the aggressive TSV to TSV2 is given in Figure 15(c). For TSV1, it gains the coupling mainly from TSV8, TSV2, and TSV7. Although TSV8 and TSV2 have the same distance from TSV1, the coupling results to TSV1 were different. This is due to the different TSV distribution around them. TSV2 has more return path and more signal TSVs around, which could both directly reduce the effect to the TSV1. For TSV2, there are more coupling sources to be considered. TSV1, TSV8, TSV7, TSV6, and TSV3 are all near the TSV2 and the coupling values are all above −40 dB. Only the effect from TSV4 and TSV5 can be ignored. It can be concluded that, in Model 2, the cross talk can also be ignored when the distance is beyond 2 × pitch.

Figure 15: parameters result of Model 2. (a) Insertion loss of each TSV, (b) the cross talk from the aggressive TSV to TSV1 at 20 GHz, and (c) the cross talk from the aggressive TSV to TSV2 at 20 GHz.
4.3. Model 3

Figure 16 shows the simulation results of Model 3. The structures of Model 3 and Model 1 are alike, but the signal and ground TSV exchanged. All the signal TSV has the same surrounding GS distribution, which results in the same insertion loss as shown in Figure 16(a). TSV8 was chosen to be analyzed. The near and far coupling results at 20 GHz from the aggressive TSV to TSV8 are shown in Figure 16(b). The coupling coefficient from TSV7 and TSV1 is −29.2 dB and −39 dB, respectively. Others are below −40 dB. It can be concluded that, in Model 3, the cross talk can also be ignored when the distance is beyond pitch.

Figure 16: parameters result of Model 3. (a) Insertion loss of each TSV and (b) the cross talk from the aggressive TSV to TSV8 at 20 GHz.
4.4. Comparison of the Three Models

From the comparison of the three models, Model 1 results in the least coupling value. This may benefit from the four ground TSVs surrounding each signal TSV. Referring to Model 2 and Model 3, the ground distribution is not the same around each TSV. For Model 1 and Model 3, the coupling can be ignored when the distance between two TSVs is beyond pitch. However, the distance extends to 2 × pitch for Model 2 which means worse coupling. Therefore, GS distribution of Model 1 is a good choice when the amount of ground TSV is limited in real application.

5. Conclusion

In this paper, we give the lumped model of the GSSG TSV structure and it is verified by comparing the parameter result with the EM simulation result. Then, multilayer TSV structure has been proposed and the effect of bump radius, bump height, and dielectric material on the TSV performance has been explored. It concludes that the bump radius weighed most heavily among the three variables. Big bump radius will cause more cross talk issue. For effective use of TSVs in 3D integration, it requires hundreds of TSVs for high density integration. Such large number of TSVs suffer more from the coupling problem. Therefore, we established the 4 × 4 multilayer TSV array to further explore the coupling between each signal TSV. Three models with different GS distribution have been proposed to study the surrounding environment effect on the TSV performance and cross talk level. It concluded that the GS distribution of Model 1 is best in coupling comparison. All the results above can give some guidance in the production design.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

This work is supported by the National Natural Science Foundation of China (NSFC) under Grants 61271044 and 61427803.

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