Warpage Estimation of a Multilayer Package Including ... - IEEE Xplore

IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 3, NO. 3, MARCH 2013

459

Warpage Estimation of a Multilayer Package Including Cure Shrinkage Effects Kaspar M. B. Jansen and Berkan Öztürk

Abstract— Warpage and residual stresses in plastic electronics packages are partly due to the shrinkage of the epoxy molding compound during the cure stage and partly due to the mismatch in thermal expansions during the cooling stage. Here, we present a simple but robust way of estimating the warpage part due to the curing effects. The main assumption of our analytical model is that the molding compound remains in the rubbery phase during cure. Using this model, we derive expressions for the effective cure shrinkage and the stress-free temperature. The effective cure shrinkage is a single parameter that can be used as an intrinsic strain value in numerical simulations, which then allows accounting for the curing effects. The solutions are benchmarked with both experimental warpage curves from the literature and with full numerical simulations on a fourlayer package consisting of lead frame, die attach, die, and the molding compound. Both comparisons show that our analytical predictions are well capable of accurately predicting cure-induced warpage in multilayer systems.

z

y

L1

L2

L3

L4

L5

L6

L7

x

Fig. 1. Schematic overview of multichip assembly (molding compound top layer and die attach layer not shown).

Index Terms— Analytical model, cure effect, intrinsic strain, warpage. Fig. 2.

I. I NTRODUCTION

W

ARPAGE of flat IC packages is a major problem for memory packages [1] and QFNs [2]. There are two major sources for this warpage: the shrinkage of the glue and molding compound layers during their curing stage, and the difference in thermal shrinkages of the individual layers during cooling. The nonflatness at room temperature causes problems in subsequent processing steps, such as singulation (sawing) and mounting. A typical example of a structure where warpage can be critical is the multichip assembly as shown schematically in Fig. 1. It consists of a substrate (a copper lead frame or wafer) onto which several chips (dies) are attached with a thin glue layer (die attach). This structure is then covered with a molding compound layer which cures (reacts) and shrinks with respect to the other layers. As a result, the structure will warp. The warpage will be larger in the areas Manuscript received August 27, 2012; revised January 9, 2013; accepted January 23, 2013. Date of publication February 12, 2013; date of current version February 21, 2013. Recommended for publication by Associate Editor I. C. Ume upon evaluation of reviewers’ comments. K. M. B. Jansen is with the Design Engineering Department, Delft University of Technology, Delft 2628 CE, The Netherlands (e-mail: [email protected]). B. Öztürk is with the Engineering, Validation, and Reliability Department, Automotive Electronics Division Robert Bosch GmbH, Reutlingen 72762, Germany, and also with the the Mechanical, Maritime and Materials Engineering Department, Delft University of Technology, Delft 2628 CE, The Netherlands (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCPMT.2013.2243497

Layered stacks as appearing in a multichip assembly.

without the die (areas L1 , L3 , L5 , and L7 in Fig. 1) and less in those containing a rigid die (L2 , L4 , and L6 ); therefore the warpage analysis should comprise both two-layered and four-layered structures (Fig. 2). The total deflection (bow) of the assembly can then be obtained by summing up the deformations of the individual segments. In this paper, we will derive expressions for the warpage of the individual layers in multilayered structures. The theory proposed here is general and can also be used to calculate warpage for wafer packaging assemblies, warpage and residual stresses in two rigid layers bonded by an adhesive layer, stresses during solvent evaporation as occurring after a solution-spinning process, or warpage of a metal strip due to the curing of an applied coating layer. The problem of warpage predictions for assemblies of isotropic elastic plates is well known in the literature. It started with Stoney [3], who derived a simple analytical expression for relating the stress in a thin elastic coating on a substrate to the observed curvature. This analysis was later modified to allow for constructions with arbitrary thickness ratios as well as arbitrary ratios between coating and substrate moduli. A good overview of this literature is given by Klein [4]. The analysis was later extended to cover constructions consisting of more than two layers (e.g. [5]–[11]). Some of these papers come up with analytical expressions for the in-plane thermal stresses [7], [8], [12], while others include shear and peeling stresses [9], [10], but most of the studies focus on warpage predictions [5]–[8], [11]. Warpage and thermal stresses in

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460


the field of electronic devices is discussed by Rzepka [1], Yang [2], Suhir [10], [11], and many others [13]–[17], [19]. However, all of these (analytical) models consider reversible thermal stresses and the corresponding warpage. What they cannot do, however, is predict the residual stress and warpage related to the cure shrinkage of the molding compound layer itself, i.e., predicting the irreversible processing-induced warpage. Consider, for example, a metal strip on which a layer of molding compound is applied at a certain elevated temperature. At this temperature, the compound starts to cure, during which it transforms from a liquid to a viscoelastic solid. This curing process is always accompanied with shrinkage. For unfilled epoxies, this cure shrinkage is about 3–4 vol%, whereas for the highly filled molding compounds it is always close to 0.6 vol%. Due to the combination of this cure shrinkage and the increasing modulus, residual stresses build up during the curing stage. The usual assumption of a stress-free state at the end of cure does not apply, and the cure-induced stresses have to be added to the thermal stresses that develop during cooling. The existence of the cure-induced stresses can be simply demonstrated by heating a warped structure and observing at what temperature the curvature disappears. If this “stressfree temperature” is different from the temperature at which curing occurred, it means that the curing process must have resulted in extra stresses. Another example of the existence of cure-induced stresses are the fractures that sometimes occur if fragile (optical) components are glued to rigid substrates with a room-temperature-curable adhesive. In that case, the coolingrelated stresses are absent, and the observed fracture can only be attributed to cure induced stresses. For thermosets cured at temperatures above room temperature, both cure and thermal contributions are of the same order of magnitude and should therefore in principle be considered in any stress analysis. In practice, however, the cure-induced stress part is often neglected [12], or at best taken into account with an adjustable stress-free temperature [13]–[16] or initial strain contribution [1], [17]. In all these papers, the stress-free temperature and initial strain are used as empirical fit parameters to match simulation results to experimental warpage. In that way, reasonable estimates of residual stress distributions in series of similar products can be obtained. However, a priori prediction of warpage of new packaging designs or packages with a different molding compound material was not possible with that approach. In this paper, we develop analytical equations for the cure-induced warpage of multilayer structures as well as closed-form expressions for the stress-free temperature and stress-free strain (initial strain). With the latter quantity, curing stress effects can be accounted for in a simple way in numerical simulations, which is therefore of considerable practical importance. II. T HEORY Including the effect of cure on warpage is complicated by the fact that, during cure, not only the intrinsic strain in the molding compound layerbut also its modulus changes. Initially, the molding compound is liquid-like and the cure

shrinkage after each incremental time step does not result in a stress increase. However, if the molding compound polymerizes beyond what is called the gel point, the polymer has started to form a 3-D network structure in which mechanical stress can persist. An increase in cure shrinkage now causes a small stress, which partially relaxes due to the viscoelastic nature of the incomplete polymer network. During the next time step, the same amount of chemical shrinkage results in a larger stress buildup, followed by a smaller stress relaxation. This process of stress buildup and relaxation continues until the polymer layer is fully cured. It is clear that the above process is difficult to evaluate further without making simplifications. Therefore, we restrict ourselves to thermosets that cure above their final glass transition temperature. Note that all molding compounds used in the electronics industry fall into this class of materials. In this way, we assume that the dominating effect will be from the combination of progressing cure shrinkage and modulus increase and that viscoelastic effects (stress relaxation) are of less importance. Above the glass transition, the material can be considered to be in its rubber elastic state and only depends on the chemical conversion. Such a situation is quite common for molding compounds that cure at about 180 °C, which is usually far above their glass transition (120–150 °C). Because we neglect viscoelastic effects, we always evaluate the molding compound layer in its lowest (equilibrium) stress state; this approximation will underestimate the stress buildup in the coating layer and thus also underestimate the warpage of the bilayer assembly. It is, however, expected that the effect of this underestimation is small. The analysis of the residual stresses and warpage generated during the curing stage can be done for two types of boundary conditions: free-standing cure, and constrained cure. In the first case, the package is free to shrink and warp during the curing stage. This applies, for example, to the curing of a glob top type package. The constrained cure case corresponds to what occurs during the encapsulation of electronic packages in a closed mold [1], [16], [17]. During this process, a metal lead frame with chip is placed in a heated mold, after which the mold is filled with the molding compound by a moving plunger. During the filling and cure, the lead frame is fixed and warpage is prevented. After mold opening, the assembly is free to warp. We do expect differences between the two cases since in the case of unconstrained cure each new gelled layer adheres on a curved structure and then starts with its shrinkage and stress generation, whereas in the constrained case each new layer adheres on the flattened structure. We thus expect the free cured structure to show most warpage. A. Free Cure Analysis We start the analysis by considering a structure consisting of N elastic layers with thickness h i , modulus E i , and Poisson’s ratio ν i (Fig. 3). The first layer is the substrate, and all subsequent layers are numbered consecutively. The thickness up to (and including) layer i is denoted as Hi . We assume that the layers are elastic and that the strains are isotropic and uniform through the thickness. During each time

JANSEN AND ÖZTÜRK: WARPAGE ESTIMATION OF A MULTILAYER PACKAGE

461

N

z=HN=

layer N

∑h

such that we get for the curvature due to unconstrained curing, κ c, f ree

i'

i '=1

i

z=Hi=

hi

layer i

∑h i '=1

i'

HN Hi

z=H2=h1+h2

t κ c, f ree = 6

z=H1=h1

layer 1

z=H0=0

N

Yi

i=1

dεi0 dt

N(t)

dt

0

Fig. 3.

Yi = Z 2 Z 1i − Z 1 Z 2i N = 4Z 1 Z 3 − 3Z 22

Schematic view of system consisting of N layers.

increment dt, these strains generate biaxial in-plane stresses dσi = E i [dεi − dεi0 ]

(1)

where E i = E ı /(1 − νi ) is the biaxial modulus and dε0i is the initial strain which is usually the thermal strain dε0,T i = α i dT but can, in principle, be of any origin (i.e., strains due to the deposition of additional layers or, as is the case here, chemical shrinkage during cure). The strain increment dεi in each layer consists of a planar strain increment d ε¯ , which is identical for all layers, and a bending contribution (z–z b )dκ dεi = d ε¯ + (z − z b )dκ

(2)

where κ is the curvature and z b is the neutral plane. Due to the change ininitial strains, the structure with width W will expand and warp, and this can be calculated by simply assuming equilibrium of forces and moments during the time increment dt d Ft ot =

N

d Fi = W

i=1

d Mt ot =

N

Hi

N

(3)

zdσi dz = 0.

(4)

i=1 H

i−1

d Mi = W

i=1

N Hi i=1 H

i−1

Combining the first three equations results in N N 2 2 d Ft ot = (5) E i [d ε¯ − dεi0 ]h i + 12 E i Hi − Hi−1 i=1

i=1

where we used h i = Hi –Hi−1 (see Fig. 3). This must be true for any value of dκ, thus both the first term and the term between curly brackets must vanish. Solving for the mid-plane strain increment d ε¯ and the neutral plane z b then gives N i=1

Zp =

N

Z pi ,

1 2 Z2

p

(6)

p

Z pi = E i (Hi − Hi−1 )

(7)

Z 1 , for example, equals Z 1 = E 1 h 1 + E 2 h 2 + · · · and Z 22 = E 2 (2h 1 h 2 + h 22 ). Integrating the moment balance, (4) then results in N i=1

Z 2i [d ε¯ −

dεi0 ] +

1

3 Z3

−

1 2 zb Z 2

t

= 6Y N 0

E N (t) dε0N dt N(t) dt

Y N = Y N /E N = h N [Z 2 − Z 1 (2H N − h N )].

(8b)

It is easy to show that the term Y N is independent of the (changing) modulus of the top layer and thus can be placed outside the integral. For a two-layer system in which only layer 2 changes during cure we get, using a = h 2 / h 1 and b = E 2 /E 1 [24] κ

c, f ree

6a(a + 1) = h1

1 0

b(ζ ) dε20 dζ N (ζ ) dζ (9)

Note that we replaced cure time with conversion ζ , since both the modulus E 2 and the cure shrinkage ε02 are direct functions of conversion and only indirectly depend on time. Further simplifications are possible for thin top layers (a 1) and in cases where the modulus of the curing polymer is much lower than that of the substrate (b 1). For cases where the modulus does not change with time and only the intrinsic strain changes, the equations reduce to those of Klein [4]. In that way, we can obtain the equations for warpage due to thermal strains, κ T κ

T

=6

Tend N Yi αi (T ) i=1 T

N

cure

N 6 Yi αi (Tend − Tcure ). N

(10)

i=1

i=1

1 2

κ

c, f ree

dT =

Z 1i dεi0

, zb = Z1 Z1 where we introduced the following notations: d ε¯ =

where it should be noted that all Z p terms change with time due to the fact that the modulus of one or more layers changes during cure. If the cure shrinkage is only in the top layer (layer N), then this simplifies to

N = 1 + b(4a 3 + 6a 2 + 4a) + b2 a 4 .

dσi dz = 0

(8a)

dκ = 0

In the last part of (10), it was assumed that the coefficients of thermal expansions (CTEs) are constant. Equations (10) and (8b) are in fact rather straightforward and lend themselves to be put in a spreadsheet such that for arbitrary geometries a quick estimate for warpage due to cure or due to thermal effects can be obtained. B. Constrained Cure Analysis Here we assume that the structure is constrained during the curing process such that both mid-plane strain and curvature are suppressed. We thus can use (5) with d ε¯ = dκ = 0 and

462


obtain for the incremental increase in total force and moment per unit width

d Ft ot = 0 −

d Mt ot = 0 −

N

Z 1i dεi0 + 0,

i=1 N 1 2 i=1

Z 2i dεi0 + 0.

C. Relation Between Warpage and Curvature

At the end of cure, we thus have N

tend

Ftend ot

=−

Mtend ot =

Z 1i ε˙ i0 dt,

i=1 0 N t end − 12 i=1 0

Z 2i ε˙ i0 dt

(11)

where the dot on the initial strain denotes differentiation with respect to time. Note that the changes in shrinkage strain, dεi0 , are negative such that Fend is of tensile in nature. This force is balanced by forces in the mold walls. When the mold opens and the structure is released, it will shrink and warp with the force and moment given by (11) as driving forces. Denoting ¯ε and κ as the changes in in-plane shrinkage and curvature, respectively, and using (5) we obtain N

Z 1i [¯ε − 0] +

1

2 Z2

− z b Z 1 κ + Ftend ot = 0

such that N t end

¯ε =

i=1 t

Z 1i ε˙ i0 dt , zb =

Z 1 (tend )

1 2 Z2

Z1

.

(12)

Similarly for the moment equation N

In practice, warpage is often expressed as the vertical deflection (bow) of a curved plate placed on a flat surface. This measure of warpage depends on the length of the package. The relation between the curvature κ and mid deflection dmid follows from geometrical considerations. Consider a circle segment of length L and radius R. The enclosed angle φ is found from the arc length: 1/2 L =Rφ, or φ=R/2L. Furthermore, cosφ = (R–dmid )/R. Solving and using κ= 1/R then gives ∼ 1 L 2 κ. dmid = R[1 − cos(2L/R)] = (15) 8

This means that the deflection increases quadratically with the length of the structure under consideration. Further, note that we defined expansion as positive and shrinkage as negative. Therefore, contraction of the top layer due to cure shrinkage corresponds to a negative curvature (“smiling” warpage). The warpage is defined as positive (usually referred to as “crying” warpage) if the top layer expands more than the lower layers. III. VALIDATION OF T HEORY BY C OMPARISON W ITH N UMERICAL S IMULATIONS

i=1

1 2

only differ in the part which is integrated with respect to time (or conversion). In the free curing case, both the numerator and denominator are evaluated together in the integral, whereas for the constrained cure analysis only parts of the numerator are integrated.

Z 2i [¯ε − 0] +

1

i=1

3 Z3

− 12 z b Z 2 κ + Mtend ot = 0

giving for the curvature after mold opening N t end

κ

c,constr

=6

i=1 0

Yi ε˙ i0 dt

N(tend )

.

(13a)

If only layer N shrinks due to cure this becomes κ

c,constr

YN =6 R N

tend

E N (t)

dε0N dt. dt

(13b)

0

For two-layer systems this reduces to [19] 6a(1 + a[a + 2]b) κ = − h1 N

1 b(ζ )

c

dε2c (ζ ) dζ dζ

(14)

0

where, again, we took the conversion as the integration variable. Also note that this may further simplify since the cure shrinkage is usually a linear function of conversion: ε2c = εc,max ζ , where εc,max then denotes the cure shrinkage after full conversion. By comparing (8b) and (13b), we see that they

The main assumption in the present cure-dependent warpage model is that viscoelastic effects are negligibleduring cure. That means that the stresses in the top layer are always evaluated using the lowest modulus limit (i.e., in the rubbery state). The stresses as well as the curvature are therefore under estimated. In order to check the validity of the assumption, warpage predictions using (8) were compared with numerical simulations involving a fully cure-dependent viscoelastic material model. As an example, we consider the warpage of a structure consisting of a molding compound used for chip encapsulation, asilicon die, die attach, and a copper lead frame. Accurate predictions of warpage and cure-induced stresses are important in the microelectronics industry since they are seen as one of the main causes for product failure. We therefore take the material data of an actual well-characterized molding compound [18]. The molding compound is a commercial epoxy resin with a high amount of silica filler (about 90 wt%). All relevant properties and dimensions of the four materials are listed in Table I. Note that the molding compound shear modulus is evaluated in its rubbery state and found to be 590 f MPa at the end of cure (G R ). The final rubbery elongation modulus therefore equals 1700 MPa. In addition, a linear cure shrinkage until a final value of εc,max =–0.207% was adopted [18]. Measurements of the increase of the rubber modulus during cure were fitted to the Martin and Adolf model [23] 2

8/3 2 ζ − ζgel f G R (ζ ) = G R , ζ > ζgel . (16) 2 1 − ζgel


463

TABLE I P ROPERTIES AND T HICKNESS OF M ATERIAL L AYERS U SED FOR M ODEL P REDICTIONS . T HE T WO CTE VALUES FOR M ATERIAL 2 AND 4 A RE THE G LASSY AND THE RUBBERY S TATE , R ESPECTIVELY. T HE G LASS T RANSITION T EMPERATURES A RE 38 °C (D IE ATTACH ) AND 92 °C (M OLDING C OMPOUND )

1, Copper lead frame 2, Die attach 3, Silicon die 4, Mold compound

Fig. 4.

h α [mm] [10−6 /K ]

E R [GPa]

N [-]

120

0.33

0.5

17

–

0.17 170

0.5 0.26

0.06 0.3

80/180 3

– –

0–1.7

0.47

2.0

11/31

–0.00207

ε c,max


Here, ζ gel denotes the conversion at gelation, which is 0.40 for the material under consideration. Details about the viscoelastic behavior during and after cure can be found in [18]. The die attach is in the rubbery phase during and after the EMC curing and therefore has a low modulus and a poisson’s ratio of 0.5. Since we wanted to separate the curing from the cooling, we assumed a fictive temperature profile of 160 °C for 1000 s and then linear cooling to room temperature with a rate of 5.6 °C/min. The finite element simulations were performed with Ansys for which special Fortran subroutines were implemented to deal with the cure-dependent viscoelasticity (for details see [19]). Fig. 4 shows a detail of the mesh and applied boundary conditions. The development of the warpage during cure is shown in Fig. 5 during both the curing part (first 1000 s) and the cooling part. We will first discuss the curing part since that is the part in which our theory applies and where the derived equations can be validated. The full warpage lines correspond to predictions according to (8b), whereas the symbols result from Ansys calculations assuming a full cure-dependent viscoelastic material model for the molding compound material. The four different lines correspond to die thicknesses varying from 0.1 to 0.4 mm. The thinnest die resulted in the largest curvature (–0.22 m−1 , “smiling warpage”). In all curves, the warpage builds up in the first 100–300 s. After about 350 s, the reaction is completed and the warpage does not change anymore. It is clear that during the full cure trajectory our

Fig. 5.


simplified analytical model perfectly agrees with the numerical predictions. Therefore, it should be concluded that for the geometries considered here our model works well. The second part of the warpage curves (from 1000 s onwards) reflects the warpage generated during cooling. Although it was not the goal of this paper, we still included this part in the present analysis. We included our predictions until the temperature dropped below the glass transition temperature (about 100 °C). The simulated curves show an interesting rise, decrease, and increase in warpage pattern, which can be understood on the basis of the large changes in both the modulus and CTE of the molding compound when going through the glass transition region. For very thin dies, the package can be essentially considered to consist of a copper lead frame and a molding compound top layer. Above the glass transition, the CTE of the molding compound is 31 ppm/K which is larger than that of the copper (17.5 ppm/K). Therefore, in that region cooling results in a stronger contraction of the top layer and thus in an increase of smiling warpage (warpage with a negative sign). For very thick dies, on the other hand, the shrinkage of the top layer is prevented by the stiff die and the warpage is dictated by the shrinkage of the copper layer. This results eventually in “crying warpage” (warpage with a positive sign). At the onset of the glass transition, the molding compound modulus already increases rapidly (until a final value about 28 GPa) such that a small thermal shrinkage immediately results in a much larger thermal stress than before and the warpage therefore will go in the smiling direction. Near the mid-point of the transition (at about 1700 s), the CTE deceases by a factor of three and is now lower than that of the copper. Therefore, the warpage will go towards the crying direction again. Note that, for the dimensions chosen here, the thicker dies resulted in crying warpage and the thinner ones in smiling warpage. The die thickness is therefore an important design parameter for decreasing the overall package warpage. In order to verify whether our model also holds for different geometries, we now take the die thickness as constant (at 0.3 mm) and vary the molding compound thickness, h 4 from 0 to 5 mm. In addition, we consider three different die attach layer thicknesses: 30, 60, and 90 μm. In Fig. 6 we show the warpage at the end of cure (after 1000 s) for these

464


Fig. 6.

Schematic view of system consisting of N layers. Fig. 7.

geometries and also include the constrained cure predictions (14). As expected, the warpage for a free curing system is larger than that for a system which is constrained during cure and deforms instantaneously after the mold opening. This is particularly apparent for molding compound thicknesses above 2 mm. For h 4 values below 1 mm, the difference between free and constrained curing is small. Note that, also in Fig. 6, the agreement between numerical predictions and our analytical model is good. Typically, our model predictions are about 3% lower than the numerical results, which agrees with our expectation of a small underprediction. The effect of the die attach thickness is small. A threefold increase of the die attach layer thickness results in a curvature reduction of only about 7%. IV. S TRESS -F REE T EMPERATURE AND E FFECTIVE C URE S TRAIN A multilayer structure that is curved after processing can always be heated to such a temperature that the curvature just vanishes. This temperature is then called the “stress-free temperature” (SFT) although internally it is, in general, not free of stresses. The SFT is easy to measure and is therefore often used in numerical simulations of cooling stresses as an approximate way to account for the cure-induced stresses discussed above. Related to this is what we will call the “stress-free strain” or “effective cure strain” (ECS), which can be defined as a fictive uniform strain in the curing layer which produces a curvature in the multilayer structure equal to the one caused by the cure processing step. This ECS is of large practical importance as a simple means of incorporating the curing step in numerical calculations. For the derivation of an expression for the effective cure strain, ε2EC S , we assume that we have an assembly of N–1 layers with zero initial strain and a layer N with strain ε2EC S . Combining this, results in an assembly with curvature κ=

6Y N,R EC S ε NR N

(17)

where we used the subscript R to indicate that the top layer modulus E N needs to be evaluated in its rubbery state. Equating this to the cure-induced warpage, κ c, f ree (8) then


results in ε NEC S =

N R c, f ree κ . 6Y N,R

(18)

Note that this effective cure strain is always lower than . This is because, initially, the the maximum cure strain εc,max N curing layer is liquid-like and no shrinkage stresses are built up yet. Only after the gel point, (part of) the stresses will persist is and result in warpage. Typically, the ratio ε NEC S /εc,max N between 0.3 and 0.5. This ratio can be referred to as the cure shrinkage efficiency factor f c . Next we will derive an expression for the SFT. According to its definition, we must balance the thermal and cure-induced warpage terms such that κ T +κ c = 0. Since we want to express it in terms of the effective cure strain, we combine (17) with (10) and obtain N 6 6Y N,R EC S εN + Yi αi (T S F − Tcure ) = 0 NR NR

(19)

i=1

where T S F denotes the SFT. Rearranging then gives Y N,R ε EC S T S F = Tcure − N Yi αi

(20)

S Note that the SFT is above the cure temperature since ε EC N is negative. Typically, the difference is about 20–50 °C.

V. C OMPARISON W ITH WARPAGE E XPERIMENTS FROM THE L ITERATURE In order to demonstrate the direct industrial relevance of this paper, we now will compare the analytical predictions with experimentally determined warpage profiles [19]. The simplified mold map package consists of a 220-μm copper lead frame and a 650-μm molding compound layer. The leadframe had a modulus of 115 GPa and a Poisson’s ratio of 0.34. The molding compound is the same as used in Section III. Directly after molding and post-curing at 180 °C, the mold map is cooled down and its deformation is measured contactless using an INSIDIX device [19]. Fig. 7 presents the measured warpage profiles at 50, 180, and 220 °C as well as the predictions based on (8b) and the mid-plane deflection


(15) resulting in a profile which depends quadratically on the length coordinate x

2 x z = dmid 1 − 1 . (21) 2L Our predictions for the mid-plane deflections amount to –304, –960, and 64 μm for the 50, 180, and 220 °C curves, respectively. Fig. 7 shows that the predicted warpage profiles correspond well with the experimental profiles. Note that the 180 °C curve represents the warpage due to cure-induced stresses. Neglecting these stresses would result in severe under prediction of package warpage. The experimentally observed SFT is close to 222 °C, whereas (18) predicts 213 °C. This again shows the practical usefulness of our model. VI. C ONCLUSION In this paper, we derived closed-form expressions for warpage of multilayer structures due to curing effects. We distinguished between free cure (cure of a glob top package) and constrained cure (cure in a mold), and our calculations showed that for relatively thick molding compound layers the free cure warpage is about twice the constrained cure warpage. Comparison with simulations showed that our model exactly traced the numerical warpage predictions during the curing part. Deviations were typically less than 4%. A benchmarking with experimental warpage curves again showed good agreement, which clearly demonstrated the predictive power of our solution. In addition, we derived expressions for SFT and ECS. Note that the maximum cure strain is a material parameter, whereas the ECS is not. It depends on the geometry and the material stiffness. In this paper, we show for the first time exactly how. The practical importance of our closed-form expressions for this ECS becomes clear if one considers the effort needed to use only numerical simulations to calculate both the cure and the cooling parts. In that case, a full cure-dependent viscoelastic material model for the molding compound is needed, which requires extensive material characterization (measure and model the viscoelastic curve of each cure state, [18]) as well as the need of special (Fortran) subroutines to implement these material models in the standard FEM software. This procedure can take months for each new molding compound. In contrast to this, now consider using our effective cure strain method. This requires only the fully cured rubbery modulus (standard), an estimate of the gel conversion (for molding compounds close to 0.40), and the total amount of cure shrinkage (which depends essentially only on the volumetric filler content). For a simulation of a multichip assembly as in Fig. 1, then ECS values must be determined for areas with and without die using (13b) and (17). These two values are then used in the numerical simulation as intrinsic strain values of the molding compound at the end of the curing process. A viscoelastic material model is then required to simulate the cooling and possible subsequent thermal cycling steps. The standard viscoelastic characterization of a fully cured molding component typically takes less than a day. In this way, it will become possible to include cure effects in thermomechanical simulations on a regular basis.

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Kaspar M. B. Jansen received the M.S. degree in chemical engineering from Twente University, Twente, The Netherlands, in 1987, and the Ph.D. degree from the Delft University of Technology, Delft, The Netherlands, in 1993. He was with the Philips Research Laboratories, Eindhoven, The Netherlands. From 1993 to 1995, he was a Post-Doctoral with the University of Salerno, Salerno, Italy, followed by a Post-Doctoral position with the Mechanical Engineering Department, Twente University from 1995 to 1998, and a PostDoctoral position with the Physics Department, Twente University, from 1998 to 2000. From 2001 to 2012, he was an Associate Professor with the Mechanical Engineering Department, Delft University of Technology and since April 2012, he has been an Associate Professor with the Industrial Desing Engineering Department, Delft University of Technology. He is the author of more than 60 articles and 150 conference papers. His current research interests include polymer processing, mechanical behavior of polymers and polymer composites as well as thermosets and microelectronics packaging, nano-reinforced polymers, and health monitoring.

Berkan Öztürk received the B.S. degree in metallurgical and materials engineering from Middle East Technical University, Ankara, Turkey, in 2008, and the M.S. degree in advanced materials and processes from Friedrich-Alexander-University, Erlangen, Germany, in 2010. He is currently pursuing the Ph.D. degree in precision and microsystems engineering with the Delft University of Technology, Delft, The Netherlands, in cooperation with Robert Bosch GmbH. His current research interests include material characterization of electronic materials and finite element modeling of electronic control units.