direct bonding, intermediate layer bonding and anodic bonding. Anodic bonding is firstly introduced by Wallis and Pomerantz [2] as a technique for joining metal ...
STR/03/021/JT
Modelling of Electrostatic Force for Glass-to-Glass Anodic Bonding S. M. L. Nai, J. Wei, and C. K. Wong subjecting the substrates to a temperature range that is compatible with microelectronic processing. During anodic bonding, the electrostatic force generated by the bonding voltage is the driving force to bring two wafers into intimate contact, which is also the prerequisite for the bonding reaction to occur.
Abstract – In this paper, a model for evaluating the electrostatic force for glass-to-glass wafer anodic bonding will be presented. 4-inch glass wafers (Pyrex 7740), with one wafer surface sputtered with a layer of amorphous Si, were successfully bonded together using anodic bonding technique at different process parameters such as: (i) bonding temperature, (ii) voltage applied, (iii) bonding duration and (iv) vacuum o o level, ranging from 200 C to 400 C, 400 V to 1200 V, 10 min to 30 min and 0.1 mbar to 0.001 mbar, respectively. Based on the model established, the experimental results were evaluated theoretically. It was found that both the bonding temperature and voltage applied had significant effects on the magnitude of the electrostatic force. At a high bonding temperature, a larger electrostatic force was generated due to higher ion mobility. More sodium and potassium ions drifted to the cathode, which resulted in a larger depletion region. Furthermore, a higher voltage applied could generate more free sodium ions, and thus contributed to a higher electrostatic force.
Several models on electrostatic force for siliconto-glass bonding have been established by other researchers, however, to our best understanding, no literature has been reported on the modelling of electrostatic force for glassto-glass bonding. Thus, in this paper, a model on electrostatic force for glass-to-glass bonding has been developed. Relationships between the electrostatic force and process parameters such as bonding temperature and bonding voltage will also be established, so as to provide a more thorough understanding from the theoretical approach, for further in-depth analysis and for further improvements on the bonding quality.
Keywords: Glass-to-glass, Anodic bonding, Modelling, Electrostatic force 1
2
EXPERIMENTAL
2.1
Wafer preparation and pre-cleaning
The glass wafers used in this study are the 4-in commonly used Pyrex 7740 borosilicate glass wafers. The surface roughness of the glass wafers, Ra is less than 15 Å and the flatness is better than 5 µm. The thickness of the glass wafer is about 500 µm. On one glass wafer, an amorphous and hydrogen-free silicon thin film was deposited onto one of its surface using a DC magnetron sputtering system (Unaxis LLSEVO). To achieve a hydrogen-free film, the base pressure of the chamber was pumped down to 5x10 5 Pa. A high purity 99.99% silicon planar target was mounted at a distance of 10 cm from the substrate and Ar was used as the sputtering gas. The gas flow rate was typically 100 sccm (standard cubic centimeter per minute) and the pressure was about 0.2 Pa. The target power 2 density was set in the range of 1.1 to 1.5 W/cm . By controlling the deposition time, a film thickness of about 100 nm was obtained. The surfaces of the film coated glass wafer and bare glass wafer were then cleaned in RCA solutions o at a temperature range of 60-80 C. RCA is made up of the following chemicals; RCA-1 (NH4OH:H2O2:H2O = 0.25:1:5) and RCA-2 (HCl:H2O2:H2O = 1:1:6). After cleaning, the wa-
BACKGROUND
Wafer bonding has increasingly become a key technology for materials integration in various areas of microelectromechanical systems (MEMS), microelectronics, microfluidic devices, bio-MEMS and optoelectronics [1]. It is also widely used for vacuum packaging, hermetic sealing and encapsulation. To-date, several techniques have been developed to bond the wafers together and they can be grouped into: direct bonding, intermediate layer bonding and anodic bonding. Anodic bonding is firstly introduced by Wallis and Pomerantz [2] as a technique for joining metal to sodium-containing glass. This technique has been widely used since then, for bonding glass wafer to other conductive materials due to the good bonding quality. It is capable of establishing a hermetic and mechanically solid connection between glass- and metal-wafers or between glass- and semiconductor-wafers [2-7]. In anodic bonding, glass, metal or semiconductor is bonded to another glass substrate, by applying an external voltage and
1
Modelling of Electrostatic Force for Glass-to-Glass Anodic Bonding
fers were rinsed with deionized (DI) water and then dried with pure N2. 2.2
2.3
After wafer cleaning process, the two glass wafers were aligned and bonded using the EV501 Bonding System (EVGroup, Austria). A schematic diagram of the anodic bonding setup is shown in Fig. 1. In order to avoid wafer contact during vacuumizing, the two wafers were separated by spacers, which were introduced at the wafer’s edges. During vacuumizing, both wafers were heated to the predetermined temperature. Upon reaching the temperature, the two wafers were first brought into point contact under pressure in the central area. The spacers were then pulled out to allow the rest of the top glass wafer surface to be in contact with the bottom glass wafer. Lastly, anodic bonding of both wafers was conducted by applying a voltage on the two wafers such that the voltage applied on the Si coated glass wafer was positive with respect to that of the other bare glass wafer.
Bonding condition design for Taguchi analysis
Here, four process parameters which were identified to influence the bonding quality, are used in the design of experiment: (1) bonding temperature, (2) voltage, (3) bonding time, and (4) vacuum level. The bonding parameters are designed to determine the factor levels that produce the best performance of the process. Three levels for each parameter are designed as shown in Table 1. Table 1. Anodic bonding conditions and process parameters.
Process Parameters o Temperature ( C) Voltage (volt) Bonding Time (minute) Vacuum Level (mbar)
Bonding Condition a b c 200 300 400 400 800 1200 10
20
30
0.1
0.01
0.001
Experiment setup
Top Heater Top electrode Glass Si film Glass
The full factorial experiment for the designed factors requires 81 sets of bonding conditions. However, an efficient design utilizing nine experiments can be realized using the Taguchi method [8]. A common orthogonal array of 4 factors for 3 levels is shown in Table 2. The array has 9 rows and 4 columns. Each row represents a trial condition with factor levels indicated by the alphabets in the row. The vertical columns correspond to the process parameters specified in the study.
Bottom Electrode Bottom Heater
Fig. 1. A schematic diagram of the anodic bonding setup.
2.4
A one dimensional model for analyzing the electrostatic force generated for glass-to-glass wafer bonding is set-up as shown in Fig. 2. The one dimensional cross-sectional model is adopted here, since the dimension of the surface area of the wafer is much larger than that of the wafer thickness. The uniform distribution of the electrostatic field is assumed across the entire area of the wafer surface. The nomenclatures of various symbols used throughout this paper are defined as follows:
Table 2. The nine experimental conditions designed by Taguchi method.
Sample Number
Temp.
Tag-1 Tag-2 Tag-3 Tag-4 Tag-5 Tag-6 Tag-7 Tag-8 Tag-9
a a a b b b c c c
Bonding condition Bonding Volt. Time a a b b c c a b b c c a a c b a c b
Model development
Vac. a b c c a b b c a
2-
ρ: volume charge density (based on O ) + σ: surface charge density (based on Na ) E: the magnitude of the electrical field -3 2 S: surface area of wafer (=7.85 × 10 m ) -3 d: the thickness of glass wafer (=0.5 × 10 m) -9 t: the thickness of the Si film (=100 × 10 m )
2
Modelling of Electrostatic Force for Glass-to-Glass Anodic Bonding
Vo: the magnitude of DC voltage applied on wafers -12 εo: the dielectric constant (= 8.854 × 10 F/m) εg: the dielectric coefficient of glass wafer, which equals εoεr,gl εf: the dielectric coefficient of intermediate film, which equals εoεr,si εr,gl: the relative dielectric constant of the glass wafer (=4.6) εr,si: the relative dielectric constant of the silicon wafer (= 11.9)
positive charge (image charge) on the Si side of the Si/glass interface, resulting in a high electrostatic force at the interface between the Si film and the glass wafer in region III. When the anodic bonding process achieves the electrostatic equilibrium condition, the electric potential in each region is governed by the Poisson’s equation, which can be expressed as: ∇ 2V = −
V
Glass I
d
+ + + + + + + t
ρ εg
∇ 2V = 0 -
d 2V dx
Glass III
2
d 2V dx 2
Si Film II
=−
ρ εg
=0
(Regions I & III)
(1)
(Region II)
(2)
(Regions I & III)
(3)
(Region II)
(4)
Since the electric potential is continuous across the three regions, the boundary conditions can be established as:
d
Fig. 2. The schematic of glass-to-glass bonding for developing the model.
At the positive electrode: x = 0, V1 = Vo At the interface of the glass wafer at positive electrode and Si film:
The following are some assumptions and mechanisms adopted when setting up the model:
x = x1, V1 = V2 ∂V2 ∂V εf − ε g 1 = −σ = ρd ∂x ∂x
The model does not take into consideration the transition period prior to the establishment of the equilibrium state.
(5)
The leaking current due to the resistivity of the electric circuit once the equilibrium state is established is ignored in this model due to its insignificant value.
where σ is the surface density of sodium ions distributed at the interface, which in fact can be expressed as the product of the thickness of the glass wafer and the volume density of oxygen ions according to charge conservation law.
Sodium ions in region III are neutralized at the surface once they reach the cathode.
At the interface of the glass wafer at the negative electrode and Si film:
It should also be noted that though A. Berthold et al. [7] has reported that some sodium ions accumulated at the boundary in region I are in fact partially diffused into region II (intermediate layer) during the anodic bonding process, no relevant research work can be found, especially on the relationships of the quantity of sodium ions which are diffused into the intermediate layer and the influencing parameters. Thus, for simplicity in this model development, we have assumed that all sodium ions remain at the interface of the glass wafer I.
x = x2, V2 = V3 ∂V ∂V ε g 3 − ε f 2 = −σ '' ∂x ∂x
(6)
where σ′ is the surface density of oxygen ions near the interface. At the negative electrode: + Considering that the Na ions have been neutralized once reach the negative electrode. x = x3, V3 = 0 Solving the differential equations (3) and (4), and by applying the boundary conditions stated earlier, the potential distribution can be expressed as follows:
Positive sodium ions migrate towards the cathode, leaving behind a fixed charge in the glass III region. This in turn creates an equivalent
3
Modelling of Electrostatic Force for Glass-to-Glass Anodic Bonding
In region I (glass wafer attached to anode):
ρ
V1 = −
x 2 + Dx + Vo
2ε g
ρ 2 d − Vo εg ρ F = ρSd ( d− ) εg 2ε g t + 2d εf
(7)
In region II (Si film):
V2 =
εg ρ 2 Dx − d + (d + t ) D + d ε 2 ε f g
εg εf
From equation (14), it can be seen that the electrostatic force is a function of various parameters, namely, the voltage applied (Vo), the charge density (ρ), the thickness of the wafer (d), as well as the thickness (t) of the Si film. Experimentally, the charge density, which possesses significant influences on the determination of the force magnitude, depends on the voltage applied and the bonding temperature during the anodic bonding process. However, it is not possible to derive the charge density from theoretical approach. Hence, experimental work has to be conducted and the charge density can be determined by analyzing the current-time curve, which was recorded during the anodic bonding.
(8)
In region III (glass wafer attached to cathode):
ρ 2 ρ ρt x + D + (d + t ) x − ( D + )(2d + t ) 2ε g 2ε g εg
V3 = −
(9)
D=
where
B A,
A = −( B=−
εg εf
t + 2d )
and
2.5
ρ 2 d + Vo εg
ρ x−D εg εg
E2 = − E3 =
D
εf
ρ ρ x − D + (d + t ) εg εg
(10) (11) (12)
The electrostatic force that brings two wafers into close contact is contributed by the force at the interface of Si film and the glass wafer in region III, as mentioned earlier. As the electrostatic force is the product of the electric field and the charges in the field, the magnitude of electrostatic force can then be calculated as:
F =
∫
2d +t
d +t
= ρSd (
{
ρ 2ε g
3
RESULTS & DISCUSSION
3.1
Taguchi analysis of anodic bonding process
Fig. 3 shows the comparison of the response of each factor on bond strength. The bonding temperature shows the greatest response among all factors and it imposes a positive effect on bond strength. The bond strength obtained in this study is comparable to those reported by other researchers for Si/glass wafers [6, 9-11]. The voltage shows the second greatest response, and the bonding time and vacuum level, however, do not exhibit as much significant influence as temperature and voltage. This finding is similar to an earlier study conducted on Si-to-glass anodic bonding [6]. It is believed that the bonding time of 10 minutes is sufficient for the completion of the bonding reaction and further in-
ρ ρ x − D + (d + t )}dq εg εg d − D)
Bond strength
Following wafer anodic bonding, the bond strength of the bonded pairs is determined using the Instron tensile testing machine. The bonded 2 pairs were firstly diced into 10×10 mm pieces. Prior to tensile test, the top and bottom surfaces of the bonded pairs were roughened with abrasive paper and ultrasonically cleaned in acetone. The bonded pair was then fixed between two aluminum alloy socles and then tested by applying a mechanical force [6]. For each bonding condition, three samples are tested and the bond strength is calculated based on the average fracture force.
The electric fields in corresponding regions can be obtained as follows:
E1 =
(14)
(13)
Hence the electrostatic force derived from the model can be expressed as follows,
4
Modelling of Electrostatic Force for Glass-to-Glass Anodic Bonding
crease of the bonding time will not have any apparent advantage.
4.0E+08 Charge Density (mAs/m 3)
3.5E+08
After identifying the two most influencing factors (bonding temperature and bonding voltage) on the bond strength, their effects on the magnitude of electrostatic force are also evaluated using the established model.
2.5E+08 2.0E+08 1.5E+08
25.0
1.0E+08
20.0
5.0E+07 150
400 1200
15.0
300
800 400
30
0.1
0.01
10
200
0.0
Voltage (V)
Bonding Time (min)
Vacuum (mbar)
Fig. 3. Comparison of the response of each factor on bond strength.
3.2
400
450
1.40E+08 1.20E+08 1.00E+08 8.00E+07 6.00E+07 4.00E+07 2.00E+07 150
Effect of bonding temperature
ρ = 8.4 × 10 5 T + 3 × 10 7
300
350
400
450
From Fig. 5, it shows that as the bonding temperature increases, it results in a corresponding increase in the electrostatic pressure. This could be due to more ion mobility occurring at higher bonding temperature. More sodium and potassium ions drift to the cathode, which results in a larger depletion region at the glass wafer in region III (see Fig. 2). Thus, an equivalent increase in image charge is created on the Si side of the Si/glass interface, giving rise to higher electrostatic forces, which pull the two wafers into intimate contact.
(15)
3.3
Effect of bonding voltage o
When the temperature is at 300 C, and the voltage is in the range of 400 to 1200 V, the linear fit equation ρ = 3.8 ×10 5 V + 1×10 6 obtained from Fig. 6, can be used to simplify equation (14), and therefore, the electrostatic force F can be expressed as:
(16)
or the electrostatic pressure P (force magnitude 2 divides the area in m ) :
F S
250
Fig. 5. Relationship between electrostatic pressure and bonding temperature at bonding voltage of 800 V.
When the voltage is kept at 800 V, and the temo perature ranging from 200 to 400 C, the linear fit 7 equation ρ = 839705T + 3 × 10 can be used to simplify equation (14), and thus, the electrostatic force F can be expressed as:
F = 2.6 ×10 6 T + 9.4 × 10 7
200
Temperature (Deg. C)
In order to relate the effects of the bonding temperature and bonding voltage on the electrostatic force, expressions relating these factors have to be firstly established. The charge densities for the different Taguchi experiments can be determined by integrating the area under the current density-time curve and dividing it by the thickness of the glass wafer, d. An equation relating the charge density to the bonding temperature at a bonding voltage of 800 V, is found by plotting the graph as shown in Fig. 4.
P=
250 300 350 Temperature (Deg. C)
1.60E+08
5.0
Temp (°°C)
200
Fig. 4. Relationship between charge density and bonding temperature at bonding voltage of 800 V.
0.001
2
10.0
20
Electrostatic pressure(kN/m )
Response
3.0E+08
F = 1.5 ×10 3 V 2 + 3.9 × 10 3 V
(17)
= 3.4 × 10 8 T + 1.2 × 1010
5
(18)
Modelling of Electrostatic Force for Glass-to-Glass Anodic Bonding
or the electrostatic pressure P (force magnitude 2 in N divides the area in m ):
P=
F = 1.9 × 10 5 V 2 + 5 × 10 5 V S
established. Using the Taguchi analysis, bonding temperature is identified to be the most dominant parameter on the bond strength, followed by the bonding voltage. The effect of temperature and voltage on electrostatic force is also studied and based on the established model, it is found that with an increase in bonding temperature, there is a corresponding increase in electrostatic force. A similar trend is observed for an increase in the applied bonding voltage.
(19)
5.0E+08
3
Charge Density (mAs/m )
4.5E+08 4.0E+08 3.5E+08 3.0E+08 2.5E+08
5
2.0E+08
The bonding technique can be widely used in following areas:
1.5E+08 1.0E+08 5.0E+07 200
400
600
800
1000
1200
1. Micro electromechanical system (MEMS) packaging 2. Micro optoelectromechanical system (MOEMS) packaging 3. Substrate fabrication 4. Semiconductor-on-insulator 5. Microelectronics 6. Optoelectronics 7. Hermetic and vacuum sealing 8. Encapsulation
1400
Voltage (V)
Fig. 6. Relationship between charge density and o bonding voltage at bonding temperature of 300 C.
From Fig. 7, it shows that the voltage has an important effect on the electrostatic pressure since magnitude of the electrostatic pressure increases when the voltage increases from 400 V to 1200 V. At higher voltage, a higher electric field is generated, which in turn increases the drift velocity of the sodium ions. Moreover, higher voltage will also accelerate the detachment of the sodium ions from the lattice matrix and contribute to the concentration of free sodium ions. Therefore, a higher applied voltage can generate more free sodium ions and thus contribute to a higher electrostatic pressure, as experimentally reflected in Fig. 7.
REFERENCES 1. W.H. Ko, J.T. Suminto and G.J. Yeh, “Bonding techniques for microsensors: Micromachining and Micropackaging for Transducers”, Elsevier, Amsterdam, (1985). 2. G.D. Wallis and D.I. Pomerantz, “Field assisted glass-metal sealing”, J. App. Phys., Vol. 40, pp. 3946-48, (1969). 3. T. Rogers and J. Kowal, “Selection of glass, anodic bonding conditions and material compatibility for silicon-glass capacitive sensors”, Sensors Actuators A, Vol. 46-47, pp. 113-20, (1995). 4. H. Henmi, S. Shoji, Y. Shoji, K. Yoshimi and M. Esashi, “Vacuum packaging for microsensors by glass-silicon anodic bonding”, Sensors Actuators A, Vol. 43, pp. 243-8, (1994). 5. D.J. Lee, Y.H. Lee, J. Jang and B.K. Ju, “Glass-to-glass electrostatic bonding with intermediate amorphous silicon film for vacuum packaging of microelectronics and its application”, Sensors and Actuators A, Vol. 89, pp. 43-48, (2001). 6. J. Wei, H. Xie, M.L. Nai, C.K. Wong and L.C. Lee, “Low temperature wafer anodic bonding”, J. Micromech. Microeng., Vol. 13, pp. 217-222, (2003). 7. A. Berthold, L. Nicola, P.M. Sarro and M.J. Vellekoop, “Glass-to-glass anodic bonding
Electrostatic pressure (kN/m 2)
3.00E+08 2.50E+08 2.00E+08 1.50E+08 1.00E+08 5.00E+07 0.00E+00 200
400
600 800 Voltage(V)
1000
1200
Fig. 7. Relationship between electrostatic pressure and bonding voltage at bonding temperature of o 300 C.
4
INDUSTRIAL SIGNIFICANCE
CONCLUSION
A model for evaluating the electrostatic force for glass-to-glass wafer anodic bonding has been
6
Modelling of Electrostatic Force for Glass-to-Glass Anodic Bonding
with standard IC technology thin films as intermediate layers”, Sensors and Actuators A, Vol. 82, pp. 224–228, (2000). 8. R.K. Roy, A primer on the Taguchi method, New York, Van Nostrand-Rein-hold, (1990). 9. A. Cozma and B. Puers, “Characterization of the electrostatic bonding of silicon and Pyrex glass”, J. Micromech. Microeng., Vol. 5, pp. 98-102, (1995).
10. T.M.H. Lee, I.M. Hsing and C.Y.N. Liaw, “An improved anodic bonding process using pulsed voltage technique”, J. Microelectromech. Syst., Vol. 9, pp. 469-473, (2000). 11. J.S. Go and Y.H. Cho, “Experimental evaluation of anodic bonding process based on the Taguchi analysis of interfacial fracture toughness”, Sensors Actuators A, Vol. 73, pp. 52-7, (1999).
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