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Yield stress and rheological characterization of the low shear zone of an epoxy molding compound for encapsulation of semiconductor devices.


An epoxy molding compound (EMC) for the encapsulation of semiconductor devices is a composite material filled with a large amount of silica filler. Therefore, its melt flow shows the behavior of a pseudo-plastic fluid having yield stress [1]. Furthermore, the flow shear rate inside the cavity in encapsulation molding is generally low. Thus, the evaluation of rheological properties in a low shear zone is even more important [2].

Currently, with increasing integration of semiconductor devices, the trend towards further smaller and thinner sizes and higher pin counts of the package has been rapidly advancing. Accordingly, higher-density bonding using fine gold wire has become necessary. In this high-density bonding using a fine wire, wire sweep during encapsulation has become one of the challenges. Recently, as one countermeasure for this issue, a compression molding method has been developed. In this molding, the shear rate of the melt flow is much lower than that in the transfer molding. Therefore, the evaluation of rheological properties in the low shear zone, including the yield stress, has become critical.

For rheological characterization of EMCs, the Power-law or Cross's viscosity model has been widely adopted for their simplicity [3-5]. However, in the above models, the yield stress is not considered, therefore it is difficult to accurately characterize the rheological properties of EMCs in the low shear zone.

In 1997, Han et al. [1] characterized the rheological properties of EMCs using the Herschel-Bulkley viscosity model [6, 7], which introduced the yield stress. However, it is generally difficult to directly measure the yield stress of a fast curing resin such as an EMC at the actual molding temperature. Therefore, Han et al., measured the low-shear viscosity at a temperature lower than the molding temperature using a parallel-plate dynamic rheometer, and determined the yield stress by applying temperature correction.

Existing evaluation methods currently used for determining rheological properties of EMCs are mapped in Fig. 1. The Spiral-flow and the Capillary-flow method (the so-called Koka-shiki flow tester method) are used to evaluate flowability in a high shear zone. Slit-type viscometers [1, 2] have been developed for evaluation of rheological properties from a low to high shear zone. However, considering the measurement accuracy, the practicable limit for the low shear is thought to be around 50 [s.sup.-1]. On the other hand, Parallel-plate dynamic rheometer and Parallel-plate plastometer methods are used for evaluation of rheological properties in low shear. However, as aforementioned, the Parallel-plate dynamic rheometer has a problem that it is difficult to directly measure the yield of a fast curing resin at the actual molding temperature.

In this study, in order to evaluate the yield stress and rheological property in the low shear, the author has turned his attention to the Parallel-plate plastometer [8-15]. Concerning the analysis methods using a plastometer, it has been established for the pseudo-plastic fluid having the yield stress by Scott [8], and others [10, 11, 15]. On the other hand, concerning the plastometer equipment, various types of plastomers have been developed for different materials [13-15]. Recently, the plastometer called the "Kalyon Rheometer" equipped with LVDT and also controlled the compression speed has been developed [16, 17].


In this study, the specialized plastometer for EMCs was built up. It was simplified as much as possible, and equipped with a noncontact laser displacement meter for precious measuring of melt thickness. Using this plastometer, the yield stress was measured and rheological properties in the low shear zone were evaluated at the actual molding temperature. Finally, the rheological characterization in the low shear zone for an EMC was carried out using Herschel-Bulkley's equation as a viscosity model, Castro-Macosko's equation [18] as a cure dependence model, and the well-known WLF equation [19] as a temperature dependence model.


Epoxy Molding Compound

The encapsulant resin used is a multi-aromatic type EMC (Hitachi Chemical, CEL-9240ZHF10), which is used for encapsulation of MAP (Multi-array package) and BGA (Ball-grid Array) packages. It was filled with 86 mass% (76.5 vol%) spherical silica filler, and has a long spiral-flow length and a long gel time as shown in Table 1.

Evaluation of Curing Properties

As a curing kinetic model for EMC, Kamal's equation [20] is widely used. The curing properties were characterized by this equation in this study as well. The nonisothermal curing properties of EMC were obtained using DSC (Differential Scanning Calorimeter).

Evaluation of Rheological Properties

The newly specialized Parallel-plate plastometer was used for the yield stress measurement and rheological properties evaluation in the low shear zone. Furthermore, the rheological properties in the high shear zone were evaluated by a Slit-type viscometer. These data were used to characterize the degree-of-cure dependence of the viscosity.

As a viscosity model, Herschel-Bulkely's equation was adopted, which can characterize flow behavior of a pseudo-plastic fluid having yield stress. Castro-Macosko's equation was adopted as the degree-of-cure dependency model, and the WLF equation was adopted as a temperature dependence model.


Curing Kinetic Equation

As a curing kinetic equation for EMC, Kamal's equation shown below, was adopted to characterize its curing properties.

d[alpha]/dt = ([K.sub.1] + [K.sub.2][[alpha].sup.m]) (1 - [alpha])[.sup.n] (1)

[K.sub.1] = [A.sub.1] exp (-[E.sub.1]/T) (2)

[K.sub.2] = [A.sub.2] exp (-[E.sub.2]/T) (3)

where, [alpha]: Degree of cure, T: Temperature (K), m, n, [A.sub.1], [E.sub.1], [A.sub.2], [E.sub.2]: Coefficients.

Nonisothermal Curing Properties and Curing Kinetics Coefficients

Nonisothermal curing properties were obtained for temperature ramps of 10, 20, and 40[degrees]C/min using DSC. The results are shown in Fig. 2. Six coefficients in Kamal's equation were determined by data-fitting. In this case, [K.sub.1] was negligible small from the obtained coefficients, [A.sub.1] and [E.sub.1]. Therefore, the four obtained coefficients are listed in Table 2.

Using coefficients listed in Table 2, the relationship between the cure time and the degree-of-cure at the designated temperature can be estimated. Figure 3 shows the curing behavior of EMC used in this study at 165, 175, and 185[degrees]C.



Theory of Rheology

Herschel-Bulkley's Viscosity Equation. An EMC for encapsulation is filled with a large amount of silica filler, and its melt shows flow behavior of a pseudo-plastic fluid having yield stress. That is, its viscosity is expressed using Herschel-Bulkely equation as shown below.

[eta] = [[[[tau].sub.y](T)]/[dot.[gamma]]] + K(T)[dot.[gamma].sup.n-1] (4)

where, [eta]: viscosity, [dot.[gamma]]: shear rate, [[tau].sub.y](T): yield stress, n: flow index, K(T): Consistency (Pseudo-plastic viscosity).

Accordingly, if [[tau].sub.y](T), n, and K(T) are determined, the rheological properties can be characterized by Eq. 4.

Yield Stress, Flow Index, and Consistency. In measurements using the Parallel-plate plastometer, in the case in which the melt does not flow out from between the parallel plates shown in Fig. 4, the relation curve between the melt thickness, log(h) and the compression rate, log(-dh/dt) has two asymptotes [8, 9]. One is "Asymptote A" which relates to the yield stress and the other is "Asymptote B" which relates to the flow index. Therefore, from this curve of the melt thickness versus the compression rate, the yield stress, flow index, and consistency can be obtained.


a. Yield stress: The melt flow stops due to yielding. Therefore, the yield stress [[tau].sub.y] can be obtained using the following equation [8, 11, 12, 15].

[[tau].sub.y] = [3[[pi].sup.0.5]W[h.sub.L.sup.2.5]]/[2[V.sup.1.5]] (5)

where, [h.sub.L]: Melt thickness at stop of flow, V: Melt volume, W: Compression force applied to melt.

b. Flow index: In the measurement using the Parallel-plate plastometer for a non-Newtonian fluid, the relationship between the melt thickness, h and the compression rate, (-dh/dt) can be expressed by the following equation [8].

log(-[dh/dt]) = ([5v + 5]/2) log h + v log W - v log K - ([3v + 1]/2) log V + log [[(3v + 1)[.sup.v][[pi].sup.(v+1)/2]]/[[2.sup.v][v.sup.v](v + 2)]] (6)

where, v: reciprocal of the flow index, n.


Equation 6 indicates that log(h) and log(-dh/dt) have a linear relationship with the gradient of (5v + 5)/2. Therefore, from the gradient [k.sub.B] of "Asymptote B," the flow index, n, can be calculated by the following equation.


n = 5/[2[k.sub.B] - 5] (7)

c. Consistency: The consistency, K can be obtained by substituting the reciprocal of the flow index, v, the compression force, W, the melt thickness, h, the volume, V, and the compression rate, (-dh/dt) into Eq. 6.

Apparatus and Measurement Conditions

A schematic view of the newly specialized Parallel-plate plastometer is shown in Fig. 5. A resin sample is set between the upper and lower heated plates. The resin is melted by the heated plates and the melt flows in a disc-shape under the compression force.

In this plastometer, a noncontact laser-displacement meter was adopted in order to avoid an additional applied force by measuring the melt thickness during flowing. Since its displacement resolution is 2 [micro]m, and the time interval of the displacement signal output is 60 ms, it enables to evaluate a fast-flowing resin such as an EMC. The melt thickness data. h, were downloaded into a PC and the compression rates, (-dh/dt), were obtained by time-differentiation of the thickness data.

The Plastometer measurement conditions are listed in Table 3. Three values of the plate temperature i.e., melt temperature, of 165. 175, and 185[degrees]C were used, and five applied compression forces from 1.27 to 5.19 N were used.


Measurement Results

Melt Thickness and Compression Rate. a. Melt thickness change with elapsed time: As an example of the measurement data, the thickness change in the case of T = 175[degrees]C and W = 1.27 N is shown in Fig. 6. This figure shows that the flow stops within about 4 s after it starts. Considering that the gel time of this EMC is 41 s and the rise in viscosity by curing occurs in 12-13 s as shown later, this flow stop is not caused by curing but by the yield stress.

b. Relationship between melt thickness and compression rate: From the melt thickness change with elapsed time shown in Fig. 6, the relationship between the logarithm of the resin thickness, log(h), and the logarithm of the thickness change rate, log(-dh/dt) is shown in Fig. 7, where the presence of "Asymptote A" relating to the yield stress and "Asymptote B" relating to the flow index can be recognized.


Yield Stress, Flow Index, and Consistency

a. Yield Stress. Yield stresses in the case of T = 175[degrees]C and W = 1.27 - 5.19 N are determined by Eq. 5 and the results are shown in Fig. 8. From Fig. 8, it is considered that there is almost no influence of the applied force below 4.21 N and no of wall slip [14, 15, 21]. Therefore, in this study, the yield stress for W = 1.27 N was adopted as the yield stress of the EMC used.


Similarly, yield stresses at 165 and 185[degrees]C were obtained, and the results are shown as a function of the reciprocal of the temperature (K) in Fig. 9 and are listed in Table 4. As shown in Fig. 9, the yield stress decreases with increasing temperature.

The temperature-dependency of yield stress is expressed as:

[[tau].sub.y](T) = [[tau].sub.y.sub.0] exp ([T.sub.y]/T) (8)

By data-fitting the measured data shown in Fig. 9, [[tau].sub.y0] and [T.sub.y] were determined as 0.8732(Pa) and 2493(K), respectively.

b. Flow Index. The flow index, n, at each temperature was obtained using the gradients of "Asymptote B," [k.sub.B] and Eq. 7. The results are shown in Table 4. With higher temperature and easier flow, the flow index appears to shift toward 1.


c. Consistency. The consistency, K(T), at each temperature was obtained by Eq. 6, and the results are shown in Fig. 10 as well as Table 4. As shown in Fig. 10, the consistency decreases with increasing temperature.

The temperature dependency can be expressed by the WLF equation shown below,

K(T) = [K.sub.0] exp{[-[C.sub.A](T - [T.sub.g])]/[[C.sub.B] + (T - [T.sub.g])]} (9)

where, [T.sub.g]: glass transition temperature (K), 291.25 K, [K.sub.0], [C.sub.A], [C.sub.B]: Coefficients, where, assuming [C.sub.A] is 51.6(K) based on WLF paper [19] and data-fitting (see Fig. 10), [K.sub.0] and [C.sub.A], were determined as 2.968 x [10.sup.8] (Pa [s.sup.n]), and 18.88, respectively. Coefficients in Eqs. 8 and 9 are listed in Table 5.

Viscosity in the Low Shear Zone

The maximum shear in the Parallel-plate plastometer measurement occurs at the wall of the rim. The maximum shear rate can be obtained by the following equation.

([dot.[gamma].sub.a])[.sub.max] = [[(v + 2)[V.sup.0.5]]/[[[pi].sup.0.5][h.sup.2.5]]] (-dh/dt) (10)

The maximum shear rate in this study was evaluated using the above equation and the measurement data. As a result of that, shear rates were less than 10 [s.sup.-1]. Accordingly, the apparent viscosities in the shear rate range from 0.1 to 10 [s.sup.-1] were calculated by Herschel-Bulkley's Eq. 4 using the coefficients listed in Table 4. The results are shown in Fig. 11.



Theory of Rheology

When non-Newtonian fluid flows in the rectangular channel (slit), whose height (gap) is 2h, width is 2c, and length is L, the apparent wall shear rate. [dot.[gamma].sub.a], and the apparent viscosity, [[eta].sub.a], can be expressed respectively by the following equations [1, 22].

[dot.[gamma]] = 4Q/[(1 + h/c)c[h.sup.2]f(c/h)] (11)

[[eta].sub.a] = [Pc[h.sup.3]f(c/h)]/4QL (12)

where, Q: flow rate, P: pressure loss, f(c/h) is the shape factor, that is.

f(c/h) = [16/3] [1 - [192h/[[[pi].sup.5]c]] [[infinity].summation over (n=1,3 ...)] tan h (n[pi]c/2h)] (13)

Consequently, by controlling the flow rate and detecting the pressure loss at the slit, the apparent shear rate and viscosity can be determined using Eqs. 11-13.


Apparatus and Measurement Conditions

A schematic view of the Slit-type Viscometer used in this study is shown in Fig. 12 [2]. After filling the reservoir at a fast speed, the melt is pushed out from the slit under the controlled speed. The flow rate, in other words the shear rate, is determined by the plunger speed controlled by the servomotor, and the pressure loss is detected using the pressure transducer installed at the slit entrance. The detected pressure loss is downloaded into a PC and the apparent shear rate and viscosity are calculated using Eqs. 11-13.


The measurement was conducted using a slit of height 0.4 mm, a width of 4 mm and a length of 12.6 mm under conditions of mold temperature of 165, 175, and 185[degrees]C, with the shear rates from 50 to 1,000 [s.sup.-1].

Measurement Results

Figure 13 shows the shear rate dependency, and Fig. 14 shows the viscosity with elapsed time at the shear rate of 500 [s.sup.-1]. As shown in Fig. 14, the viscosity increases with the elapsed time, that is, curing. The relationship between the degree-of-cure and the viscosity can be calculated by Kamal's equation and Castro-Macosko's degree-of-cure dependency equation. The details will be mentioned in the next section.



The Degree-of-Cure Dependency

The degree-of-cure dependency of viscosity was characterized by Castro-Macosko's equation shown below.

([[eta].sub.[alpha]]/[[eta].sub.0]) = ([[alpha].sub.gel]/[[[alpha].sub.gel] - [alpha]])[.sup.[C.sub.1]+[C.sub.2][alpha]] (14)

where, [[eta].sub.0]: viscosity at degree-of-cure, 0

[[eta].sub.[alpha]]: viscosity at degree-of-cure, [alpha]

[[alpha].sub.gel]: degree of cure at gel point,

[C.sub.1], [C.sub.2]: Coefficients.

The relationship between the cure time and the degree-of-cure at each temperature (165, 175, and 185[degrees]C) was obtained using Kamal's equation. Then, the relative viscosity ([[eta].sub.[alpha]]/[[eta].sub.0]) with the degree-of-cure was determined using the viscosity data shown in Fig. 14. The results are shown in Fig. 15 with the fitting curve using Eq. 14. The fitting coefficients [C.sub.1], [C.sub.2], and [[alpha].sub.gel] are listed in Table 6.


The comparison of the experimental results in Fig. 14 with the calculated results of the relative viscosity using the coefficients in Table 5 is shown in Fig. 16. The approximation is observed to be fairly accurate.


The characterization of rheological properties from low shear to high shear was attempted. The procedure is showed as following.

The viscosity data (see Fig. 11) measured by the plastometer were used as the low-shear viscosity. On the other hand, the viscosity data (see Fig. 13) using the slit-type viscometer were used as the high-shear viscosity. Concerning the Rabinowitsch correction, for the Herschel-Bulkley fluid having the yield stress, its correction is greatly a complicated issue [23]. However, in the case of the Power law fluid, as the flow index, n, decreases, the flow behavior approaches plug flow over a substantial part of the flow channel like the Herschel-Bulkley fluid. In this study case, the apparent flow index between 0.1 and 10 [s.sup.-1] is very low, that is, about 0.2. Therefore, in this article, the Rabinowitsch correction was done using the following equations



[dot.[gamma]] = ([3n + 1]/4n)[dot.[gamma].sub.a] (15)

[eta] = (4n/[3n + 1])[[eta].sub.a] (16)

After the above correction, the characterization was conducted for the viscosities at 165, 175, and 185[degrees]C using Eq. 17.

[eta] = [[[[tau]*.sub.y](T)]/[dot.[gamma]]] + K*(T)[dot.[gamma].sup.n*-1] (17)

where, [[tau]*.sub.y](T), n*, K*(T): Characterized yield stress, flow index, and consistency, respectively.

The results of the characterization were shown in Fig. 17 and Table 7. The viscosities in a low shear zone were generally considered to be characterized, but it was observed there was a considerable difference in high shear zone above 100 [s.sup.-1]. To characterize with sufficient accuracy, it is considered that it is necessary to express the How index as a function of shear rate.


Since the EMC for encapsulation of semiconductor devices is filled with large amount of silica filler, it shows the flow behavior of a pseudo-plastic fluid having the yield stress. Therefore, it is very important to clarify the rheological properties in the low shear zone for the moldability evaluation in the encapsulation processing.

In this study, the newly specialized Parallel-plate plastometer was built up for EMC. This plastometer is equipped with a precision laser-displacement meter therefore, it is suitable to evaluate the rheological properties of the low viscosity resins like EMC for encapsulating of IC.

Using this plastometer, the yield stress of EMC was directly measured at the actual molding temperature and its temperature dependency was clarified and characterized using the Arrhenius equation. And also, the low shear viscosities below 10 [s.sup.-1] were obtained. As the result of that, the rheological properties in the low shear rate zone from 0.1 to 10 [s.sup.-1] was characterized by applying Herschel-Bulkley's viscosity equation. WLF temperature-dependency equation, and Castro-Macosko's degree-of-cure dependency equation.


The author thank Dr. S. Han of Nanoflow Corporation, for his very valuable knowledge and advice, and also thank Mr. R. Kawasaki and Mr. H. Narita of Hitachi Chemical Co., Ltd. for their support of the experiments. The reviewers' comments and advice are also gratefully acknowledged.


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Masaki Yoshii

Semiconductor Materials Division, Hitachi Chemical Co. Ltd., 1772-1 Kanakubo, Yuki-city, Ibaraki 307-0015, Japan

Correspondence to: Masaki Yoshii e-mail:
TABLE 1. Composition and flow Properties of CEL-9240ZHF10 (Hitachi
Chemical) used in this study.

 Epoxy resin Multi-aromatic type, ~7 mass%
 Harder resin Xylene type phenol, ~5 mass%
 Silica filler Spherical silica, 86 mass%
 Others Catalyst, Release agent, Carbon, etc.
Flow properties
 Spiral flow length 165 cm
 Gel time 41 s
 [T.sub.g] at uncured state 291.3 K

TABLE 2. Coefficient in Eqs. 1-3.

M(-) 4.42E-1
N(-) 1.20E0
[A.sub.2] ([s.sup.-1]) 1.23E7
[E.sub.2] (K) 8.76E3

TABLE 3. Plastometer measurement conditions.

Supplied compound [phi]20 (Pellet). 1 gf
Preheating time (s) 7
Temperature ([degrees]C) 165, 175, 185
Compression force (N) 1.27, 2.25, 3.23, 4.21, 5.19

Underlining indicates common condition.

TABLE 4. Yield stress, flow index, and consistency at each temperature.

Temperature ([degrees]C) 165 175 185

Yield stress, [[tau].sub.y] (Pa) 254.1 237.6 195.9
Flow index, n(-) 0.29 0.35 0.43
Consistency, K (Pa s) 251.0 205.5 157.9

TABLE 5. Coefficients in Eqs. 8 and 9.

[[tau].sub.y0] (Pa) 8.73E-1
[T.sub.y] (K) 2.49E3
K (Pa [s.sup.n]) 2.97E8
[C.sub.A] (-) 1.89E1
[C.sub.B] (K) 5.16E1
[T.sub.g] (K) 2.913E2

TABLE 6. Coefficients in Eq. 14.

[C.sub.1] (-) 1.05E-1
[C.sub.2] (-) -1.24EI
[[alpha].sub.gel] (-) 7.00E-1

TABLE 7. Characterized yield stress, flow index, and consistency.

Temperature ([degrees]C) 165 175 185

Yield stress, [[tau].sub.y]* (Pa) 275.4 214.8 181.2
Flow index, n* (-) 0.38 0.39 0.46
Consistency, K* (Pa [s.sup.n*]) 155.4 149.1 118.5
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Author:Yoshii, Masaki
Publication:Polymer Engineering and Science
Article Type:Technical report
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Date:Apr 1, 2008
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