EXPERIMENTAL CHARACTERIZATION AND MULTI-PHYSIC MODELLING OF
DIRECT BONDING MECHANICAL BEHAVIOUR : APPLICATION TO SPATIAL
OPTICAL SYSTEM

N. Cocheteau(1), A. Maurel-Pantel(1), F. Lebon(1), I. Rosu(1), S. Ait-Zaid(2), I. Savin De Larclause(2), Y. Salaun(3)

(1) LMA, Mechanics and Acoustics Laboratory, CNRS, UPR 7051, Aix-Marseille Univ, Centrale Marseille, 31, Chemin Joseph Aiguier, F-13402 Marseille Cedex 20, France,
Email:maurel@lma.cnrs-mrs.fr

(2) CNES, National Center for Spatial Studies, 18 Avenue Édouard Belin 31400 Toulouse, France,
Email: sonia.aitzaid@cnes.fr

(3) WINLIGHT OPTICS, 135 rue Benjamin Franklin, ZA Saint Martin, 84120 Pertuis, France,
Email: yves.salaun@winlight-optics.com

ABSTRACT

Direct bonding is a well-known process. However in
order to use this process in spatial instrument fabrication
the mechanical resistance needs to be quantified
precisely. In order to improve bonded strength, optimal
parameters of the process are found by studying the
influence of annealing time, temperature and roughness
which are studied using three experimental methods:
double shear, cleavage and wedge tests. Those
parameters are chosen thanks to the appearance of
time/temperature equivalence. All results brought out
the implementation of a multi-physic model to predict
the mechanical behavior of direct bonding interface.

1. INTRODUCTION

Direct bonding or molecular bonding consists in joining
two surfaces without the use of any adhesives or
additional material [1, 2]. Usually, by bringing two flats,
well-polished surfaces into contact at room temperature,
they locally attracted to each other by Van der Waals or
hydrogen bonds and adhere or bond [3]. This
technology is already used in optical system
manufacturing due to the very high precision of the
process and complex geometries which are able to be
bonded. More recently, this process was used in the
manufacturing of high performance optical systems for
terrestrial application such as Fabry-Perot
interferometers, prism assemblies, etc. For instance, this
bonding process has been used in the manufacture of the
largest slicer ever used in the Multi Unit Spectroscopic
Explorer (MUSE) for the Very Large Telescope (VLT)
as related in Fig. 1.

Now direct bonding is of particular interest for optical
system manufacturing for spatial application. However,
even if a first spatial prototype already passed with
success space environment test, quantification and
improvement of the mechanical strength of assemblies
are essential to validate the assembly's life expectancy
and to validate the European Space Agency standards
[4]. So, this work proposes to study the influence of
process parameters, such as roughness, relative air
humidity during room temperature bonding, annealing
time and temperature, on mechanical strength of an
elementary mechanical structure using a wedge test
procedure. For the Winlight Optics process considered

in this study, a parallel is made between chemical
phenomena, surface roughness and mechanical strength.
In the same time a summary of some previous results
confirm the choice of the optimal process parameters
and highlight a damaging phenomenon of bonded
interfaces with successive re-adhesion. Then an usual
wedge test is developed to measure the bonding energy
versus process parameters in order to identify law of the
direct bonding model. An interface mechanical model of
the direct bonding is developed. The implemented law
links the bonding energy, the mechanical critical strain
energy, the process parameters and the chemical kinetic
with a multi-physic and multi-scale formalism. Then the
direct bonding interface model is implemented in a
finite elements code, in the end a confrontation is led
between numerical and experimental results.

<figure><img src="image_1.png" /><figcaption>Figure 1. Slicer made with direct bonding method
developed for the Multi Unit Spectroscopic Explorer
(MUSE) in the Very Large Telescope (VLT).</figcaption></figure>

2. DIRECT BONDING

2.1. Materials

In optical applications, three materials are mainly used: fused silica glasses, Zerodur®, and Zinc Selenide (ZnSe). In this work, we chose to study two of them the fused silica glasses and Zerodur® glasses which are the most commonly used in spatial optical applications with a reasonable cost.
Silica is the main constituent of glass. However, glass is an amorphous material, therefore, it shows major structural disorder. Fused silica glass can be seen as an anarchistic stacking of SiO₂ tetrahedra, in which, only short range order is maintained.

Zerodur® is a glass-ceramic type invented in 1968 by the optical materials producer Schott AG™ and it is specifically designed for astronomy observations in terrestrial and spatial fields. The special feature of this material comes from its thermal expansion coefficient almost null and homogeneous in all directions. So, Zerodur® offers a very high thermal stability [7]. Small changes can occur in coefficient of thermal expansion (CTE) with the annealing treatment and can affect the geometric accuracy and stability of the high precision optical assemblies. So, it is interesting to note that for Zerodur®, there are three temperature ranges where different behaviours of CTE are observed:

- When $T > 700°C$ (ceramising range)

- Between $320°C < T < 700°C$ (steady state)

- Between $130°C < T < 320°C$ (superior relaxation range)

- Between $40°C < T < 130°C$ steady state

- Between $-70°C < T < 40°C$ (inferior relaxation range)

For temperature above $700°C$, the material ceramising continues in an irreversible way, changes in material properties appear and the CTE is irreversibly changed. Fig. 2 relates limits and temperature influence on dimensional stability for samples initially annealed at different temperatures and cooled at room temperature. Up to annealing temperature about $130°C$, there is no modification in CTE. Above this temperature, CTE increases to a specific constant value, in order to not degrade the thermal expansion parameter (CTE), the cooling speed has to be choosen between $1°C/h$ and $6°C/h$ (cooling procedure during Zerodur manufacturing) [7].

Direct bonding is possible as long as the two surfaces have similar geometries and requires clean surfaces free of contaminants [5, 6]. Therefore, first steps of the Winlight Optics Company process consist in physical and chemical preparation of surfaces.

<figure><img src="image_2.png" /><figcaption>Figure 2. Variation of the coefficient of thermal expansion CTE (0°C; 50°C) – first cooling at 0.1 K/min- as a function of the initial temperature of a secondary cooling in open air to room temperature [28].</figcaption></figure>

## 2.1. Surface preparation

Several polishing of both surfaces to adhere were manually performed in order to obtain the exact surface roughness (here, roughness is always less than 1 nm RMS), flatness and deflection required. Indeed, a high level of roughness results in a weak contact zone and thus in the occurrence of defects during the bonding process. When the roughness is too great, bonding becomes impossible [8-11]. Then, surfaces undergo a chemical treatment in order to eliminate any contaminating particles [12].

With ambient water, free silicon surfaces are recovered by silanol (Si-OH) groups which are the precursor of the bonding [13,14]:

$$ Si-O + H_2O \rightarrow Si-OH \quad (1) $$

Then, silanol groups react with ambient humid air to form clusters of water [15, 16] on surfaces. Indeed, formation of clusters is energetically favorable compared to the formation of one silanol bond.

The adsorption of water can be written as:

$$ -OH_{I} + H_{2}O \rightleftharpoons -OH_{II} + H_{2}O_{I} \quad (2) \\ \Delta_{R}H = 6 \text{kcal.mol}^{-1} $$

<figure><img src="image_3.png" /><figcaption>Figure 3. Behaviour of surfaces during room temperature bonding according to their hydroxylated rate (from [15]).</figcaption></figure>
And the adsorption of an additional molecule of water can be written as:

$$ \begin{gathered} H_2O_I + H_2O \rightleftharpoons H_2O_I + H_2O_{II} \\ \Delta_R H = 10,5 \text{ kcal.mol}^{-1} \end{gathered} \quad (3) $$

Thus, the water forms clusters on the surface before all the Si-OH groups have adsorbed water molecules. With this chemical treatment, the more silanol groups possible on both surfaces is seek. On Fig. 3, one component of the roughness is represented, each line represents a bonding site, and obviously a lack of bonding sites causes incomplete bonding.

## 2.2. Room temperature bonding

Once physical preparation and surface treatment has been completed, surfaces are brought into contact and bonding occurs between clusters of the two surfaces. A process of capillarity occurs due to the humid air trapped between the surfaces [17]. By applying a slight local pressure, the surfaces are brought closer together, and hydrogen bonds developed between molecules of water present at the interface and the two surfaces. A bonding wave propagates from the contact point through the whole sample, resulting in the bonding of the surfaces. Molecules of water migrate from the bonding interface and/or diffuse at the interface, bringing the surfaces even closer together and initiating silanol-silanol covalent bonds [16, 18, 19].

<figure><img src="image_4.png" /><figcaption>Figure 4. Evolution of the nature of bonds at the interface during thermal treatment.</figcaption></figure>

## 2.3. Direct bonded interfaces with temperature

In order to obtain a stronger or irreversible sealing by increasing the number of covalent bonds, it is necessary to change the nature of bonds at the interface by applying for instance a thermal treatment (figure 4). Indeed, between 25°C and 200°C, surfaces are contacted via clusters of waters [15, 16]. When temperature is lower than 110°C, chemical reactions at the bonded interface are the same than during room temperature bonding i.e. formation of hydrogen bonds between molecules of water and surfaces.

- Between 110°C and 150°C, molecules of water start to release (Phase I) as shown in Fig. 4a.

- When temperature is between 200°C and 700°C, there is formation of cyclic tetramers of water; surfaces are directly contacted via double hydrogen bond (Phase II) as shown in Fig. 4b [20].

- Up to 700°C the polymerization reaction is triggered, resulting in the formation of covalent siloxane bonds (Phase III, Fig. 4c) [13, 14]:

$$ Si-OH + HO-Si \rightarrow Si-O-Si + H_2 \quad (4) $$

Previous experimental works have investigated links between mechanical strength, annealing treatment and material choice. Some tests have been performed to characterize surface chemical properties, and mechanical strength in mode I & II with double shear and cleavage tests [19]. At the end, Zerodur® samples seem to be a better candidate for direct bonding. Despite the dispersion of the experiments, optimal parameters of the process have been found, annealing treatment at 200°C during 120h for fused silica glass samples with a 0,4 nm RMS roughness and 55% of humidity, and, 200°C during 120h with a 0,4 nm RMS roughness and 32% of humidity for Zerodur® samples. Moreover, a kind of equivalence between a long thermal treatment at low temperature and a short thermal treatment at high temperature appears. Cleavage tests performed confirm the choice of the optimal parameters and highlight a damaging phenomenon of bonded interfaces with successive re-adhesion. With these optimal parameters, the mechanical strength is twice as much as the strength obtained with the initial parameters. We found a way to increase the mechanical strength of direct bonded interfaces for the Winlight Optics procedure.

# 3. BONDING ENERGY MEASUREMENTS

Then to characterize interfaces assemblies, we proposed to develop a test to measure interface bonding energy of an elementary mechanical structure using a wedge test procedure. With these mechanical tests, the influence of the process treatment parameters on failure mode I is observed.

## 3.1. Wedge Tests

One of the main parameters classically used to characterize adhesion is the bonding energy [21], which can be connected to the critical strain energy release rate [17]. The most popular method to measure the bonding energy is the crack propagation method or wedge test. A razor blade is inserted at the interface between two blades bonded together.

A crack will appear along the bonded interface until the establishment of equilibrium between the elasticity of blades and the bonds responsible for the adhesions which are hydrogen bonds in our case. The length of the crack 1 is measured with a camera using interference fringe due to the small thickness of air trapped at the open interface. At the equilibrium, the critical strain energy release rate is equal to the work of adhesion [20] and related to the crack length using linear elastic fracture mechanics. When both surfaces are identical:

$$ G_{1C} = W_{adhesion} = 2\gamma \quad (5) $$

With $\gamma$ the surface energy of surfaces.
<figure><img src="image_5.png" /><figcaption>Figure 5. Experimental device of wedge test developed</figcaption></figure>

The critical strain energy release rate can be approximately related to the length l using the following equation [26]:

$$G_{1C} = \frac{3Et^3 y^2}{8l^4} \quad (6)$$

Where E is the Young modulus of blades, t the blade thickness, y the razor blade thickness and l the length of the crack. Samples are constituted with two blades of silica with 500 µm of thickness (t), 10 mm of width and 80 mm of length bonded together. The razor blade (100 µm (y) of thickness) is always inserted by the same length using a mobile plate and the insertion is controlled with a camera above the blades as related in Fig. 5.

<table><caption>Table 1. Summary of wedge tests performed on fused silica samples</caption><thead><tr><th>Annealing temperature (°C)</th><th>Annealing time (h)</th><th>Roughness (nm RMS)</th></tr></thead><tbody><tr><td>x</td><td>x</td><td>0.4, 0.8</td></tr><tr><td>100</td><td>5, 35, 120</td><td>0.4, 0.8</td></tr><tr><td>200</td><td>5, 35, 120</td><td>0.4, 0.8</td></tr></tbody></table>

Wedge test has been performed to study the evolution of the bonding energy with annealing parameters and roughness. Tab. 1 relates the experiments performed, two samples have been tested for each parameter twice. Between each tests, surfaces have been cleaned and re-adhered without being polished anew. Thermal treatments were limited to 200°C due to the results of the first study [19] and due to the optical and coating industrial constraints.

## 3.2. Results and discussion

Fig. 6 presents the evolution of the bonding energy with

roughness; full line represents results for the first adhesion and the dotted line for the second adhesion. Results show the same trends observed in previous results [19], a higher bonding energy with an optimal roughness, which is not the lower one. Results also show a decrease of the bonding energy for the second adhesion highlighting a phenomenon of surface damaging with successive adhesion - wedge tests - re-adhesion. Those results suggest that for our physical and chemical preparation, a quite higher roughness is preferable.

<figure><img src="image_6.png" /><figcaption>Figure 6. results of the wedge test, influence of annealing time, temperature and roughness (solid line: adhesion 1, dashed line: adhesion 2)</figcaption></figure>

Too low roughness leads to the appearance of residual stresses on surfaces during polishing process. Moreover we have seen before that between 150°C and 450°C the bonding energy is limited by the contacted area which is higher for surfaces with higher roughness explaining better results for high roughness. This phenomenon increases with thermal treatment; indeed, thermal treatment promotes the formation of siloxane covalent bonds [13] and thus increases the mechanical resistance and the bonding energy. In wafer bonding field, it is commonly accepted that the roughness minimal value gives the best bonding energy. But the experimental
investigations performed and related results confirm the existence of a roughness optimal value in direct bonding strength improvement of fused silica glasses or Zerodur® assemblies.

# 4. MULTI-PHYSIC MODELING

The final aim of this work consists in the development of an interface mechanical model of the direct bonding. The developed law relates the bonding energy, the mechanical critical strain energy, the process parameters and the chemical kinetic in a multi-physic and multi-scale formalism.

## 4.1. phenomenological modeling

A predictive phenomenological model is proposed to give an evolution law of the bonding energy in function of mechanical preparation and annealing treatment process parameters (annealing time, temperature, roughness). The phenomenological model is validated with the results obtained on the wedge test related in previous section as related in Fig. 6.

$$ 
\begin{aligned}
W_{\text{adhesion}} &= W^n(T, t, R_a) \\
&= z(R_a, n) (W_{\text{max}}(T, R_a) - W_0(R_a)) \left[ (1 - e^{-k_1 t}) + W_0(R_a) \right]
\end{aligned}
\quad (7) $$

With T the annealing temperature, t the annealing time, and R_a the roughness, the maximal bonding energy for an infinite annealing time W_max(T,R_a)=W_max(t=120h), the initial bonding energy W_0(R_a)=W(initial), n number of successive adhesions. The bonding energy equation proposed is based on the chemical kinetic evolution law and its constant characteristic k_1 written as :

$$ k_1 = \frac{1}{\tau} \exp \left( - \frac{E a_1}{K_B T} \right) \quad (8) $$

With Ea=65,5 meV the activation energy, K_B the Boltzmann constant and τ the characteristic time constant. The parameters of the phenomenological law is identified with the confrontation of the bonding energy prediction and the results of the wedge test. The comparison is related in Fig. 7.

<figure><img src="image_7.png" /><figcaption>Figure 7. Comparison between experiments and the predictive model</figcaption></figure>

## 4.2. Interface modeling

The interface model is developed to model the mechanical behavior described in Fig. 8. As seen before the critical energy release rate is equal to the bonding energy calculated with the phenomenological law. This model allow to link the direct bonding interface normal behavior to the forming and treatment process parameters. The model is implemented in a finite element code Abaqus in order to simulate the wedge test and to validate our modeling.

<figure><img src="image_8.png" /><figcaption>Figure 8. Description of the direct bonding normal interface behavior modeled with the interface law coupled to the phenomenological modeling.</figcaption></figure>

# 5. FINITE ELEMENT SIMULATION

The finite element model proposes to simulate the wedge test presented above. The specifications of silica material are provided by the supplier and correspond to a Young modulus E=72700 MPa, and a Poisson ratio v=0,16. The simulation consist to impose a displacement corresponding to the razor blade thickness and to measure the numerical crack length as related in Fig. 8. Confrontation between experimental and numerical results is summarized in Tab.2.

<figure><img src="image_9.png" /></figure>
<table><caption>Table 2. Results: Confrontation between crack length measured experimentally and numerically for an annealing at 200°C.</caption><thead><tr><th>Annealing time (h)</th><th>G<sub>1C</sub> (J.m<sup>-2</sup>)</th><th>l<sub>exp</sub> (mm)</th><th>l<sub>num</sub> (mm)</th></tr></thead><tbody><tr><td>5</td><td>0.113</td><td>22.97</td><td>23</td></tr><tr><td>30</td><td>0.208</td><td>19.75</td><td>19.75</td></tr><tr><td>120</td><td>0.234</td><td>19.08</td><td>19.25</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>Figure 7. Comparison of crack length between experiments and the finite element model</figcaption></figure>

## 6. CONCLUSIONS

The final results of this work consists in the development of an interface mechanical model of the direct bonding. The implemented law relates the bonding energy, the mechanical critical strain energy, the process parameters and the chemical kinetic in a multi-physic and multi-scale formalism. A wedge test has been set up to measure the bonding energy versus process parameters in order to identify the law of the direct bonding model and to implement it in a finite elements model. The model exhibit a good correlation between the numerical prediction of the crack length and the experimental measurements.

For the future, new investigations will be lead on to find new original process in order to improve the mechanical strength and to develop simulation of complex real multi part spatial optical assemblies.

## 7. REFERENCES

1. Tong Q.Y., Gösele U. (1994). Semiconductor wafer bonding: recent developments. Mat. Chem. and Phys. 37 101-127.

2. Kendall K. (2001). Molecular adhesion and its applications. Kluwer Academic Publishers.

3. Plobl A., Krauter G. (1999). Wafer direct bonding: tailoring adhesion between brittle materials. Material Science and Engineering. R25 1-88.

4. Pamplona T., Rossin Ch., Martin L., Moreaux G., Prieto E., Laurent P., Grassi E., Boit J.-L., Castinel L., Garcia J., Milliard B. (2008). Three bipods slicer prototype: tests and finite element calculations. Proc. SPIE 7018, Advanced Optical and Mechanical Technologies in Telescopes and Instrumentation. 701828. doi: 10.1117/12.789243

5. U. Gösele (1999). Fundamental issues on wafer bonding, in: American Society of Vacuum.

6. K. Johnson (1995). The adhesion of two elastic bodies with slightly wavy surfaces, International Journal of Solids and Structures. 32, 423-430.

7. H. Hamaker (1937). The London-Van der Waals attraction between spherical particles, Physica IV, 10 1058-1072.

8. B. Galanov (2011). Models of adhesive contact between rough elastic solids, International Journal of Mechanical Science, 53 968-977.

9. G. Liao, X. Lin (2011). Surface roughness modeling for silicon direct bonding, IEEE transaction on components, packaging and manufacturing technology, 1(8) 1171-1177.

10. S. Lai, H. Lin, C. Yu (2004). Effect of surface treatment on wafer direct bonding process, Material Chemistry and Physics, 83 265-272.

11. R. K. Iler (1979). The chemistry of Silica, Wiley.

12. J. D. Bene, J. Pople (1970). Theory of molecular interactions. I. Molecular orbital studies of water polymers using a minimal slater-type basis, The Journal of Chemical Physics, 52 4858-4866.

13. Y. Bertholet, F. Iker, J.P. Raskin, T. Pardoen (2004). Steady-state measurement of wafer bonding cracking resistance, Sensors and Actuators A, 110 157-163

14. G. Liao (2010). Effect of surface characteristic on room-temperature silicon direct bonding, Sensors and Actuators, A: Physical, 158 335-341.

15. R. Stengl, T. Tan, U. Gösele (1989). A model for the silicon wafer bonding process, Japanese Journal of Applied Physics, 28(10) 1735-1741

16. Z. Tang (2008). Modeling the formation of spontaneous wafer direct bonding under low temperature, Microelectronic Engineering, 85 1754-1757.

17. A. Plöbl, G. Kräuter (1999). Wafer direct bonding: tailoring adhesion between brittle materials, Material Science and Engineering, R25 1-88.

18. D. Murphy (2001). Fundamentals of Light Microscopy and Digital Imaging, Wiley-Liss.

19. N. Cocheteau, A. Maurel-Pantel, F. Lebon, I. Rosu, S. Ait Zaid, I. Savin Delarclause (2014). Influence of process parameters on the mechanical resistance of direct bonded silica glasses, Journal of Adhesion Science and Technology, 28(10) 915-934.

20. J. Cognard (1986). The Mechanics of the Wedge Test, The Journal of Adhesion, 20 1-13.

21. W. Maszara, G. Goetz, A. Caviglia (1988). Bonding of silicon wafers for silicon-on insulator, Journal of Applied Physics, 64 4943-4950.