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Modeling the dynamics of Si wafer bonding during annealing. Weihua Han,a) .... surface energy of the SiO2 /SiO2 bonding interface is only about 400 mJ/m2, ...
JOURNAL OF APPLIED PHYSICS

VOLUME 88, NUMBER 7

1 OCTOBER 2000

Modeling the dynamics of Si wafer bonding during annealing Weihua Han,a) Jinzhong Yu, and Qiming Wang State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, P. O. Box 912, Beijing 100083, People’s Republic of China

共Received 17 December 1999; accepted for publication 10 July 2000兲 The bonding behavior of silicon wafers depends on activation energy for the formation of siloxane bonds. In this article we developed a quantitative model on the dynamics of silicon wafer bonding during annealing. Based on this model, a significant difference in the bonding behaviors is compared quantitatively between the native oxide bonding interface and the thermal oxide bonding interface. The results indicate that the bonding strength of the native oxide interface increases with temperature much more rapidly than that of the thermal oxide interface. © 2000 American Institute of Physics. 关S0021-8979共00兲05520-1兴

I. INTRODUCTION

face atoms. Assuming that n 0 is the saturated density of Si dangling bonds on the wafer surface, the bonding reaction rate3 is

Silicon direct bonding is a technology which allows two silicon wafers to stick together by covalent bonds. The technology has the following advantages: First, a silicon wafer pair can be welded together without any adhesives; Second, the source of misfit dislocations is located at the bonding interface; And third, the resistivity and doping type can be chosen freely. Therefore silicon wafer bonding has emerged as an important technique for the formation of structures such as silicon-on-insulator materials, microelectromechanical system, and power devices. Several authors1–4 have proposed and studied the Si wafer bonding mechanism as follows: At low temperatures, a hydrophilic Si wafer pair can be adhered together via hydrogen bonds of the silanol groups on both surfaces. With the increase of temperatures, siloxane bonds can be formed between the two surfaces by dehydration condensation of the silanol groups. Although significant progress has been made in explaining the Si wafer bonding mechanism, a quantitative understanding of the bonding mechanism is still lacking. Stengl3 developed a quantitative model of the bonding process, which explained why the surface energy increases in two distinct steps during annealing. Tong4 proposed a model to quantitatively compare saturated surface energies during four stages. Based on those models, we developed a quantitative model on the dynamics of silicon wafer bonding during annealing. The main goal of our work is to quantitatively study and compare the bonding behaviors for the native oxide interface and for the thermal oxide interface during annealing.

d 关 SiOSi兴共 t 兲 ⫽k 关 n 0 ⫺ 关 SiOSi兴共 t 兲兴 , dt and the reaction rate constant is 1 k⫽ exp共 ⫺E a /k B T 兲 , ␶

共2兲

where E a is the activation energy, k B stant, T is the absolute temperature, parameter ␶ is 0.7 ms, which may stretching frequency of surface atom siloxane bonds can be obtained from

is the Boltzmann conthe phenomenological depend on the native bonds. The density of

关 SiOSi兴共 t 兲 ⫽n 0 关 1⫺exp共 ⫺kt 兲兴 .

共3兲

It has been proven that the surface energy of the Si bonded wafer pair increases in two steps with annealing temperature. This phenomenon is relevant to activation energies. The higher the activation energy at a given temperature, the less the reactive molecules and the slower the reaction rate. The activation energy in the high temperature range should be larger than that in the low temperature range. Therefore, in the total temperature range, the gain in the surface energy can be expressed by using two reaction rate constants k 1 and k 2 as

␥ 共 t,T 兲 ⫺ ␥ B 共 t,T 兲 ⫽ 关 ␥ 3 ⫺ ␥ B 共 t,T 兲兴关 1⫺exp共 ⫺k 2 t 兲兴 , 共4兲 ␥ B 共 t,T 兲 ⫺ ␥ 1 ⫽ 共 ␥ 2 ⫺ ␥ 1 兲关 1⫺exp共 ⫺k 1 t 兲兴 ,

共5兲

where ␥ 1, ␥ 2 , and ␥ 3 are saturated surface energies at low, moderate, and high temperatures, respectively.

II. THE BONDING DYNAMICS OF SILICON WAFERS

The surface energy of the Si wafer is proportional to the density of siloxane bonds, which is a function of annealing temperature and of bonding time. The formation of siloxane bonds is determined by dehydrated condensation of doublelinked silanol groups or by the rearrangement of oxide sur-

III. DISCUSSION

During room-temperature bonding, hydrophilic Si wafers bond to each other via hydrogen bonding between adsorbed water molecules on the two surfaces. The surface coverage by water molecules depends on relative humidity. The linkage of water cluster and silanol groups consists of a three-dimensional network of hydrogen bonding. Because

a兲

Author to whom correspondence should be addressed; electronic mail: [email protected]

0021-8979/2000/88(7)/4404/3/$17.00

共1兲

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© 2000 American Institute of Physics

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J. Appl. Phys., Vol. 88, No. 7, 1 October 2000

Han, Yu, and Wang

FIG. 1. Bonding energy as a function of annealing temperature for Si/Si and SiO2 /SiO2 bonding interface.

there are two different stretching frequencies for water in infrared spectra,3 the network may include isolated and associated hydroxyl groups. One isolated silanol group can form two hydrogen bonds, while one pair of associated silanol groups need to form two hydrogen bonds.4 The surface energies for the native oxide interface and for the thermal oxide interface are different because of the different surface density of the bonding species. The surface energy of the native oxide interface can be estimated as 1 2 ␥ Si 1 ⫽ 2 共 2n OHiE hi⫹n OHHE hH 兲 ⫽165 mJ/m ,

共6兲

where n OHi⫽1.4⫻1014 cm⫺2 and n OHH⫽3.2⫻1014 cm⫺2 are saturated density of isolated and associated silanol groups; E hi⫽7⫻10⫺17mJ, and E hH⫽4.2⫻10⫺17mJ are the hydrogen bond energy of the isolated silanol groups and the associated silanol groups, respectively. On the thermal oxide surface, these species are not so prevalent that the surface SiO energy ␥ 1 2 of thermal oxide is about 100 mJ/m2 at room temperature. Above 110 °C, most of the water molecules migrate out of the interface. Some of the water clusters form tetramers around the developing double-linked silanol groups. At temperatures up to 120 °C, strong siloxane bonds can be generated from dehydrated condensation of silanol groups as follows: k

SiOH: OHSi → SiOSi ⫹ H2O.

共7兲

The reaction is reversible below 400 °C when water is present. If the water migrated out of the bonding interface, the double-linked silanol bonds will be more easily transformed into strong siloxane bonds. For the bonding interface of the native oxide, the water tetramers can diffuse through the surrounding native oxide layer into silicon crystal. Below 300 °C, the activation energy for dehydrated condensation of silanol groups should correlate with the diffusivity of water through the oxide layer5 D⫽10⫺6 exp共 ⫺0.794 eV/kT兲 cm2/s.

共8兲

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FIG. 2. Si/Si bonding energy vs annealing time for temperatures from room temperature to 800 °C.

Thus the activation energy is estimated as 0.7⫾0.2 eV. Then water reacts with silicon according to 2H2 O ⫹ Si→SiO2 ⫹ H2 ↑.

共9兲

A hydrogen-induced pressure develops in the microgap of the bonding interface. Above 300 °C, hydrogen bubbles can enlarge in size due to gas volume expansion. Several bubbles then have a chance to merge to a larger bubble. In this temperature range, the total activation energy is water diffusion energy of 0.7 eV plus hydrogen diffusion energy of 0.48 eV. With temperature increasing, two conflicting effects occur. On one hand, volume expansion of hydrogen with temperature enhances the lateral gap diffusion. On the other hand, the pumping caused by hydrogen results in a partial vacuum. The wafer pair contacts more intimately. The lateral diffusion of hydrogen is hampered. In the range of 300– 400 °C, the two conflicting effects tend to an equalibrium. The surface energy will become independent of annealing time. The saturated surface energy of the Si/Si bonding interface is about 1000 mJ/m2 by using the crack-opening method.6 Assuming that there are 60%–70% silanol groups to condense, then the surface energy can be estimated as 1 2 ␥ Si 2 ⫽ 2 共 0.65n OHE Si–O 兲 ⫽1078 mJ/m ,

共10兲

where the density of hydrogen groups n OH is 4.6 ⫻1014 cm⫺2 , and the siloxane bond energy E Si–O is 7.2 ⫻10⫺16 mJ. Above 400 °C, the desorption rate of hydroxyl group improve rapidly. By 600 °C, dehydrated condensation of silanol groups finish completely.7 Furthermore, the density and number of bubbles are a maximum.8 The surface energy is enhanced to a saturation, which can be estimated as 1 2 ␥ Si 3 ⫽ 2 共 n OHE Si–O 兲 ⫽1658 mJ/m .

共11兲

The bonding behaviors are different between the native oxide interface and the thermal oxide interface. Below 800 °C, the activation energy of bonding the thermal oxide surfaces is similar to that of bonding the native oxide surfaces. The slow diffusion of water through the thick thermal oxide layer hampers the formation of covalent bonds.9 In addition, the thermal oxide surface is rougher than the native oxide one. At temperatures up to 600–800 °C, the saturated

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J. Appl. Phys., Vol. 88, No. 7, 1 October 2000

Han, Yu, and Wang

been explained by the diffusion behavior of water. The bonding strength of the Si/Si interface above 400 °C is as high as that of the SiO2 /SiO2 interface above 1100 °C. In Figs. 2 and 3, the surface energy steadily increases to a saturation with annealing time both for the Si/Si interface and for the SiO2 /SiO2 interface. The surface energy will be time dependent when the surface energy at a given annealing temperature is saturated after a certain bonding time. IV. CONCLUSION

FIG. 3. SiO2 /SiO2 bonding energy vs annealing time for temperatures from 200 to 1400 °C.

surface energy of the SiO2 /SiO2 bonding interface is only about 400 mJ/m2 , which was measured by using crackopening method.10 Assuming that there are 20%–30% silanol groups to condense on the contact area, the saturated surface energy of thermal oxide interface can be estimated as SiO ␥ 2 2 ⫽ 21 共 0.25n OHE Si–O兲 ⫽414

2

mJ/m .

共12兲

In the temperature range of 800–1200 °C, the bonding strength of the thermal oxide interface is enhanced by the rearrangement of oxide surface atoms. The saturated surface energy can be estimated as SiO2

␥3

⫽ 21 共 n SiE Si–O兲 ⫽2439 mJ/m2 ,

共13兲

where the density of Si dangling bonds on the oxide surface n Si⫽6.755⫻1014/cm2 . In this temperature range, the activation energy relates to viscous flow of the oxide. It can be estimated as 2.2⫾0.2 eV according to the diffusivity of oxygen interstitial into the silicon wafers11 D i ⫽0.07 exp共 ⫺2.44eV/k B T 兲 cm2 /s.

共14兲

In order to compare theoretical curves with experimental results measured by Cha6 and Maszara,10 the surface energy of the Si/Si bonding interface and that of the SiO2 /SiO2 bonding interface are shown in Fig. 1. The theoretical curves are in agreement with experimental results, which demonstrate the two-step tendency of the surface energy during annealing. At a certain specific temperature, the surface energy increases remarkably. The bonding strength of the native oxide interface increases with temperature much more rapidly than that of the thermal oxide interface. This has

The dynamics model of the Si wafer bonding quantitatively explains the two-step increase of the surface energy, which is determined by activation energies. Based on this model, the bonding behaviors are studied, respectively, for the native oxide interface and for the thermal oxide interface. First, water at the bonding interface diffuses more easily through the native oxide layer. Second, the surface of the thermal oxide layer is rougher than that of the native oxide layer. Therefore the bonding strength of the native oxide interface increases with temperature much more rapidly than that of the thermal oxide interface. ACKNOWLEDGMENTS

The authors wish to thank Dr. Cheng Li and Chuang Shen for their assistance during this work, and Daniel Coutts for his critical reading of this manuscript. This work is financially supported by National Natural Science Foundation of China under Grant Nos. 69990540, 69896260-06, and by Ministry of Sciences and Technologies of China, Project 973 under Grant No. G20000366. Q.-Y. Tong and X.-L. Xu, J. Appl. Sci. 8, 303 共1990兲 共in Chinese兲. M. Shimbo, K. Furukawa, K. Fukuda, and K. Tanzawa, J. Appl. Phys. 60, 2987 共1986兲. 3 R. Stengl, T. Tan, and U. Go¨sele, Jpn. J. Appl. Phys., Part 1 28, 1735 共1989兲. 4 Q.-Y. Tong and U. Go¨sele, J. Electrochem. Soc. 143, 1773 共1996兲. 5 Q.-Y. Tong, X.-L. Xu, H. Shen, and H.-Z. Zhang, Acta Electron. Sinica 19, 27 共1991兲. 6 G. Cha, W.-S. Yang, D. Feijoo, W. J. Talor, R. Stengl, and U. Go¨sele, Proceedings of the First International Symposium on Semiconductor Wafer Bonding: Science, Technology and Applications, edited by U. Go¨sele, T. Abe, J. Haisma, and M. Schmidt 共The Electrochemical Society, Pennington, NJ, 1992兲, p. 249. 7 M. K. Weldon, Y. J. Chabal, D. R. Hamann, S. B. Christman, E. E. Chaban, and L. C. Feldman, J. Vac. Sci. Technol. B 14, 3095 共1996兲. 8 T. Abe, T. Takei, A. Uchiyama, K. Yoshizawa, and Y. Nakazato, Jpn. J. Appl. Phys., Part 2 29, L2311 共1990兲. 9 G. Kra¨uter, A. Schumacher, and U. Go¨sele, Sens. Actuators A 70, 271 共1998兲. 10 W. P. Maszara, G. Goetz, A. Caviglia, and J. B. McKitterick, J. Appl. Phys. 64, 4943 共1989兲. 11 K.-Y. Ahn, R. Stengl, T. Y. Tan, and U. Go¨sele, J. Appl. Phys. 65, 561 共1989兲. 1 2

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