Moisture Ingress , Behavior , and Prediction Inside Semiconductor Packaging : A Review

Reliability issues associated with moisture have become increasingly important as advanced electronic devices are nowhere more evident than in portable electronic products. The transition to the Pb-free solders, which require higher reflow temperature, makes the problem further exacerbated. Moisture absorbed into semiconductor packages can initiate many failure mechanisms, in particular interfacial delamination, degradation of adhesion strength, etc. The absorbed moisture can also result in catastrophic crack propagation during reflow process, the well-known phenomenon called popcorning. High vapor pressure inside pre-existing voids at material interfaces is known to be a dominant driving force of this phenomenon. This paper reviews various existing mechanisms of water accumulation inside voids. The procedures to obtain the critical hygroscopic properties are described. Advanced numerical modeling schemes to analyze the moisture diffusion phenomenon are followed with selected examples. [DOI: 10.1115/1.4035598]


Introduction
Due to its amorphous nature and topographical imperfection, polymeric materials always contain a large number of molecular scale voids inside them.This "free volume" is classically known to take 2.5% of the whole volume.Water and gas transport through those tiny free volume units present across polymer chain networks.
Nonpolar gases, such as O 2 , N 2 , CO 2 , etc., penetrate through polymers by "jumping" from one void to another without causing considerable change of polymer structures.Polar water molecules, however, tend to form hydrogen bonding with polar groups in polymer chains (hydroxyl, amide, etc.) during diffusion through polymers.It results in structural, physical, and sometimes chemical changes in polymer structures such, as hydrolysis and hygroscopic swelling.
Semiconductor and micro-electromechanical systems (MEMS) packages have unique engineering structures.Various polymeric and inorganic materials are densely packed in millimeter to micrometer-scale configurations.Polymers such as molding compound, die attach, underfill, solder resist, etc., absorb moisture.
Water can reside inside polymer in three different states [1].The first state is nonfreezing water; i.e., bound water that does not exhibit detectable phase transition that bulk water does.Absorbed water through hydrogen bonding in a diffusive way belongs to this state.The second state is free water, which has characteristics similar to bulk water.This state of water flows viscously inside polymer.The last state is freezable bound water; i.e., bound water whose phase transition temperatures are shifted due to interactions with polymer chains and/or capillary effects.Adsorbed water on void surfaces belongs to this state.
As shown in Ref. [1], a portion of water that initially migrates into a polymer becomes nonfreezing water (hydrogen bonding).
After saturation, freezable bound water increases (adsorbed water portion).Then, free water starts to increase, if any.Most polymeric materials used in electronic packaging, however, are nonporous, and thus, this increase seldom occurs.The dominant water in electronic packaging materials is hydrogen-bonded water (nonfreezing bound) absorbed through bulk diffusion.
The absorbed moisture affects reliability in various ways.Accumulated moisture at bonded interfaces degrades the adhesion strength due to aging [2,3].The absorbed moisture, unless properly removed by a baking process, generates internal high vapor pressure during solder reflow [4,5].
Polymers swell with the absorbed moisture [6,7].Inorganic materials, such as silicon, copper, aluminum, etc., are impervious to moisture, and thus the volume does not change under the presence of moisture.This mismatch in hygroscopic swelling between the two material groups produces deformations, which are similar to the deformations induced by the mismatch of thermal expansion [7,8].Various interconnect failures through popcorning and delamination are attributed to the combined effects; e.g., popcorn cracking in a plastic ball grid array (PBGA) package [9] and interconnection failure caused by hygroscopic swelling and adhesion degradation [10].Many articles that address moisture-related failures are available in the literature [11][12][13] (numerous other articles are omitted due to space limitation).
Moisture diffusion in polymers had been a classical research topic [14].The demand for modeling moisture-related phenomena in complex structures was more recently realized as moisturerelated issues became critical to electronic package development [15].This paper reviews various existing mechanisms of water accumulation inside voids.The procedures to obtain critical hygroscopic properties are described.Advanced numerical modeling schemes to analyze the moisture diffusion phenomenon are followed with selected examples.laws.Mass flux in polymers is governed by Fick's first law, which is expressed as where J is the moisture mass flux (kg/m 2 s), D is the diffusivity (m 2 /s), r is the gradient operator, and C is the moisture concentration (kg/m 3 ).The conservation of mass within an infinitesimal volume yields Fick's second law as The equilibrium between saturated moisture concentration and ambient vapor pressure can be expressed as where C sat is the saturated moisture concentration, S is the solubility (s 2 /m 2 ), and p v is the ambient vapor pressure (Pa).Equation ( 3) is based on the well-known Henry's law.For this reason, the solubility is often called as "Henry's coefficient" [16][17][18].Henry's law described the partial pressure of a source solute in a gaseous state [19,20], and thus, the Henry's coefficient is valid only for solute-absorbent systems [19,20].Equation ( 3) is an extended form of Henry's law to moisture-polymer systems, which has been known to be valid.In order to avoid any theoretical confusion, only "solubility" will be used in this paper.
Both the diffusivity and solubility are known to follow the Arrhenius relationship as where D 0 (m 2 /s 2 ) and E D (J/mol) are the constant and the activation energy of diffusivity, R 0 is the universal gas constant, S 0 and E S are the constant (s 2 /m 2 ) and the activation energy (J/mol) of solubility, and T is the temperature (K).

Analytical Solutions of Isothermal Diffusion Equation.
Analytical solutions of Fick's second law are available for several single (homogeneous) material with simple geometry.For the isothermal one-dimensional (1D) problems illustrated in Fig. 1, the diffusion equation is reduced to In Fig. 1, the one side of a polymer specimen is exposed to an ambient with an upstream vapor pressure (p u ), while the other side is impervious to moisture.It is also equivalent to a polymer specimen with a thickness of 2L, both sides of which are exposed to a humid ambient.The boundary and initial conditions are where C u is the concentration at the top surface (kg/m 3 ), L is the thickness of the substrate (m), and C i and p i are the initial concentration and pressure, respectively.The closed-form analytical solution is expressed as [21] C The moisture content inside the specimen is obtained by integrating the above solution as where m is the moisture content (kg) and m sat is the saturated moisture content.The above solution can be easily extended to a three-dimensional (3D) block specimen subjected to moisture weight gain test, where all exterior surfaces of the block are exposed to a humid ambient.The solution of a 3D block specimen is given as [9] where L y , and L z are the length of the block in each direction.Note that L x in the 1D case is equal to 2L.Equation ( 9) has been widely used to determine the diffusivity of block-shape polymer specimens inversely from experimentally measured moisture weight gain data.

Consideration for Multimaterial Systems.
The moisture concentration is discontinuous at the interface between different polymeric materials.The maximum amount of moisture that each polymer can absorb is a material property, and thus, the concentration at a bimaterial interface becomes discontinuous.
A physical illustration of interfacial conditions is provided in Fig. 2, where x is any vector, that is, perpendicular to the interface where v is Nernst partition coefficient at a specific temperature and C int,1 and C int,2 are concentrations of two materials at the interface.The corresponding mass continuity is given by A new term, /, in Fig. 2 is called "normalized concentration," which is defined to be C/S [16,17].The normalized concentration will be discussed in Sec. 4.
The units of the moisture-related properties are not intuitive.Table 1 summarizes the constants and the corresponding SI units.It is worth noting that the normalized concentration has the unit of pressure.Although the unit is the same, the normalized concentration should not be confused with pressure.
3 Characterization of Hygroscopic Behavior 3.1 Diffusion Coefficient and Solubility.Two hygroscopic properties-diffusivity and solubility-are required in order to analyze moisture diffusion behavior quantitatively.They can be measured using the moisture weight gain/loss tests [23].Property data for various packaging polymers are available in the literature [6,7,9,10,[24][25][26][27][28][29][30][31][32] (numerous other articles are omitted due to space limitation).The majority of them were measured at low temperatures below 100 C. A handful of property data at above 100 C can be found in the literature [31,33].More recently, an extensive experimental study on high-temperature measurements was conducted for more accurate modeling of moisture diffusion during reflow process [34,35].
Figure 3 shows moisture weight gain data obtained from two epoxy molding compounds (EMCs) at three different temperatures [34].After the specimens were dried at 160 C, they were subjected to a humid environment of 75%RH at three temperatures.An environmental chamber (ESPEC SH-241) was used to attain controlled humid environments.Moisture weight gain was measured periodically by a high precision balance (PI-225D, Denver Instrument, Bohemia, NY) until the measured weight of each sample remained unchanged for an extended period of time.
The moisture weight gain and the saturated weight gain in % wt. is defined as where w is the specimen weight gain (kg).The saturated weight gain, w sat , is the maximum weight gain at the end of measurement.
The corresponding (average) moisture concentration and saturated concentration are given by where w dry@160 o C and V p are the polymer specimen mass and volume.Then, the solubility is determined from Eq. ( 3).
A nonlinear regression analysis was conducted to determine the diffusion coefficient at each temperature.The results from the regression are also shown in Fig. 3.
Equation ( 4) can be rewritten as Fickian diffusion coefficients obtained from three temperature data of Fig. 3 are plotted using Eq. ( 14).The results are shown in Fig. 4, where the slope represents the activation energy, E D /R 0 , of each material.The Fickian diffusivities followed the Arrhenius relationship well over the entire temperature range used in the study (45-85 C).The constant and the activation energy of diffusivity were determined from the plots and they are summarized in Table 2.
The constant and the activation energy of solubility can be determined in a similar way.The solubility can be determined  from the saturated concentrations marked in Fig. 3.The values are plotted in Fig. 5 using Eq. ( 14).The solubility also followed the Arrhenius relationship well over the entire temperature range.The constant and the activation energy of solubility were determined from the plots and they are summarized in Table 3.
Wong et al. [31,33] first reported that the activation energy for the solubility of the packaging materials ranges from À44,000 to À46,000 J/mol.The results imply that there is no strong correlation between the saturated concentration and the temperatures below 100 C [18,31,33].A similar trend was observed for both specimens.
More evidence is shown in Fig. 6, where the solubility versus temperature values obtained from four different materials are plotted [18].As mentioned earlier, the slope represents the activation energy, E s /R 0 , of each material.The slopes are nearly identical, which indicates a nearly constant value of the activation energy.
A typical non-Fickian behavior with normalized weight gain (w % nwg ) is shown in Fig. 7, which was obtained from an EMC at 180 C [34].A modified approach to obtain a diffusivity equation as a function of both temperature and concentration was proposed, where the Arrhenius equation was combined with the concentration dependency [34].It is expressed as where D 0C is a dimensionless adjustment coefficient for concentration dependence and a is the exponent constant relevant to concentration dependence.Accordingly, the diffusion equation can be modified as The constant, a, represents the degree of concentration dependency of the diffusivity.It governs the magnitude of discrepancies between Fickian curves and experimental data.Since the diffusivity monotonically changes with the concentration from unity at C ¼ 0 to e aCsat at C ¼ C sat , weight gain can be accelerated or retarded depending on the sign of a.Such a biased change is adjusted by another constant D 0C .
Using the Fickian constants (D 0 and E D ), nonlinear regression analyses were repeated to determine the values of a and D 0C .Since an analytical solution of Eq. ( 16) was not available, a finiteelement model based on a thermal-moisture analogy was implemented to solve the non-Fickian diffusion problem using ANSYS [17,34].The constants determined through this procedure are listed in Table 2.The weight curve using the four constants is also plotted in Fig. 7 along with the Fickian curve.A better fit over the entire history was resulted.
3.2 Hygroscopic Swelling Coefficient.The polar water molecules form hydrogen bonds with the hydroxyl groups in the polymer chains and disrupt interchain hydrogen bonding.These water molecules increase the intersegmental hydrogen bond length and collectively cause the polymeric material to swell.This dimensional increase due to the absorption of moisture is called hygroscopic swelling.The hygroscopic strain is known to have a linear relationship with moisture concentration as [7] where e h is the hygroscopic strain and b is the coefficient of hygroscopic swelling (CHS).DC is the moisture concentration difference.
The CHS can be measured by various tools and techniques including a bending cantilever method [38], a micrometer [39], Michelson interferometry [40], and thermomechanical analyzer (TMA) combined with thermogravimetric analyzer (TGA) [6].A full-field deformation analysis can be used to cope with the limitation of point-measurement methods.Moir e interferometry [41] and digital image correlation (DIC) [42] have been utilized for hygroscopic swelling strains in bulk polymers [43] and thin film polymers [44], respectively.The CHS measurement using moir e interferometry is reviewed here.
The overview of the experimental procedure is illustrated in Fig. 8 [7].Two samples of a material of interest were first baked to remove any initial moisture content (a).After the bake is completed, cross-line diffraction gratings were replicated onto the samples at an elevated temperature of 85 C using a hightemperature curing epoxy (Tra-Con Tra-Bond F230) (b).One of the two samples (reference sample) was left in the baking oven to ensure no extra moisture gain (c).The second sample (test sample) was subjected to an 85 C/85%RH environment and its weight was periodically monitored until a saturation state was reached (d).Once the saturation state was achieved, the hygroscopic swelling measurement was performed by moir e interferometry during desorption process (e).
It was vital to eliminate thermal expansion during moir e measurements so that only hygroscopic swelling was documented.This was accomplished by using the reference sample.The reference and test samples are positioned side by side during measurements.
The interferometer was first tuned to produce a null field (devoid of fringes) on the reference sample and the test sample was viewed subsequently.This procedure canceled any thermally induced deformations in the test sample since the deformed state of the reference sample was used as a reference datum for zero hygroscopic deformation of the test sample.
The null field fringe pattern obtained from the reference sample is shown in Fig. 9(a).The representative fringe patterns of the test sample obtained right after saturation (t ¼ 0) and after 40 h are shown in Figs.9(b) and 9(c), respectively.The hygroscopic strain, e h , can be determined directly from moir e fringe patterns by where f s is the frequency of the specimen grating (1200 lines/ mm), DN is the change of fringe orders in the moir e pattern, and DL is any gage length across which DN is determined.The hygroscopic strains are plotted against moisture content (%) in Fig. 10.
It is evident that a linear relationship exists between hygroscopic swelling and moisture content.The slope is the CHS value of the material (b ¼ 0.27).

Modeling of Moisture Diffusion
Commercially available software packages are preferred choices to solve the diffusion problems of semiconductor/MEMS packages as they typically have complex geometries, material configurations, and loading conditions.Not all commercial finiteelement analysis (FEA) software packages offer the moisture (or mass) diffusion function [17].Furthermore, when moisture transport into/out of a cavity is involved, the modeling task becomes Fig. 8 Overview of CHS measurement procedure using moir e interferometry even more complicated.This section presents numerical schemes to handle the two issues effectively.
4.1 Thermal-Moisture Analogy.Heat conduction is a diffusive process and thus has a governing equation similar to that of mass diffusion.Fourier's law of heat conduction is expressed as where q is the heat flux (W/m 2 ), T is the temperature (K), and k is the conductivity (W/m K).Assuming no internal heat generation, the energy balance yields the governing equation of heat conduction as where a is the thermal diffusivity (m 2 /s) and q and c p are the density (kg/m 3 ) and the specific heat (J/kg K), respectively.Due to the similarity in governing equations (Eqs.( 2) and ( 20)), heat conduction and mass diffusion have been often treated in a "unified" way [45].The resulting "thermal-moisture" analogy is very attractive, since moisture diffusion can be solved using the heat transfer function of any FEA software.As a consequence, the thermal-moisture analogy has been utilized extensively to address water diffusion inside semiconductor packages [9,10,46], food [47], and gas barrier films [48,49].
4.1.1Direct Analogy.For a homogenous and isotropic material, a thermal-moisture analogy can be established from direct comparison between Eqs. ( 2) and ( 20) [17].This direct analogy can be expressed as The direct analogy scheme is simple, but this analogy is applicable to only single-material or homogeneous problems; it cannot handle the interface discontinuity that occurs in multimaterial problems [17].

Multimaterial
Problems.The moisture concentration is discontinuous at a bimaterial interface as mentioned earlier.In order to make this problem numerically possible, normalized field variables are introduced, which are continuous across the material interfaces.

Normalized Analogy. A normalized concentration is defined as [17]
where / is normalized concentration (Pa).Substituting Eq. ( 22) into Eq.( 2), Fick's equation yields The corresponding boundary condition at the exterior surface is given from Eq. ( 3) as When rS ¼ _ S ¼ 0, the solubility is constant and Eq. ( 23) becomes Then, the normalized analogy can be established by comparing Eqs. ( 25) to (20) as It is important to note that S should be included in the normalized analogy; if the analogy is set as qc p 1 and K D, the mass continuity (Eq.( 11)) will not be satisfied.
The above analogy should properly handle the interface condition as the field variable is the concentration normalized by Transactions of the ASME solubility which is continuous at the material interface.It is important to remember, however, that the normalized analogy was established for the condition of constant solubility; the temperature distribution must be uniform ðrS ¼ 0Þ and independent of time ð _ S ¼ 0Þ, since solubility is a temperature-dependent property.This condition is met only when the loading is isothermal, and thus, the normalized analogy should be applied only to isothermal problems.
The normalized concentration, /, is often referred to as the "activity" of the diffusing material [16], which provides the physical meaning of the normalized concentration using the dissociation of a diatomic gas during diffusion.Equilibrium requires the partial pressure to be continuous across an interface, and thus, the normalized concentration will be continuous as well.Galloway and Miles [9] used a similar argument and called the normalized concentration moisture partial pressure, P, and used the following expression, which is basically identical to Eq. ( 22): It is important to note that the moisture partial pressure, P, is just a symbol for solution variable and should not be confused with either the ambient vapor pressure, p v , or the chemical potential inside a polymer, which usually defined in terms of Gibbs free energy [50].
An alternate normalized variable, W, called relative concentration or wetness, was introduced by Puig et al. [51] and later Wong et al. [52][53][54][55][56].It is defined as Under the assumption that solubility remains constant regardless of the level of concentration, the wetness can be expressed as It is clear from the above equation that the two normalized variables are basically the same since the ambient vapor pressure, p v , is constant at a given temperature.The term moisture partial pressure implies the vapor phase of water, while the concept of wetness does the liquid phase of water.In fact, water diffused into a solid exists as water molecules and its phase can change by numerous conditions.Regardless of the phase, however, the physical meaning of the normalized variables is nothing more than normalized concentration for the case of moisture diffusion.Consequently, the normalized concentration or wetness yields identical result when the analogy is implemented to determine the moisture concentration.

Advanced
Analogy.The advanced analogy scheme was proposed to cope with the limitations of the normalized analogy [18].It was established based on the unique behavior of the most commonly used packaging polymers that the saturated concentration is linearly proportional to the ambient relative humidity but not dependent on the temperature.
The experimental evidence of the behavior is shown in Fig. 11, where the saturated moisture concentrations obtained at 25 C, 55 C, and 85 C are plotted as a function of relative humidity.It clearly shows that there exists a linear relationship between the saturated concentration and the relative humidity over the temperature range used in the measurements (below the glass transition temperature of the polymer).This behavior has been observed in numerous other studies [31,42,50,52,[57][58][59][60].
The linear relationship between the saturated concentration and the relative humidity can be expressed as where p sat is the saturated vapor pressure (Pa), RH% is the relative humidity, and M is the "modified solubility," which is a temperature-independent material property.The advanced analogy uses the modified solubility.An advanced normalized concentration, u, is defined using the modified solubility as Substituting Eq. ( 31) into Eq.( 2) yields Thus, the advance analogy is established by comparing Eq. (32) with Eq. (20) as The modified solubility automatically satisfies the mass continuity at the interface.The boundary condition of the new normalized concentration becomes ambient relative humidity (RH%), i.e., The above derivation clearly indicates that the advanced analogy is valid for multimaterial systems subjected to anisothermal loading conditions (nonuniform temperature fields that change with time).
It is important to note that temperature-independent linear relationship between the saturated moisture concentration and the relative humidity may not exist above the glass transition temperature as well as for polymer composites [61][62][63][64].The temperature-independent linearity must be confirmed experimentally to utilize the proposed scheme accurately.

Validation of Analogies.
The three analogy schemes are summarized in Table 4.They were validated by numerically solving the original diffusion equation, Eq. ( 2) [17,18,57].
The validity of the normalized concentration was verified first [17,57].As illustrated in Fig. 12(a), the simulation considered moisture diffusion in a 0.2 mm-thick double-layered wall.For an The distribution of moisture concentration obtained from the direct and normalized analogy schemes are shown in Fig. 12(b) [17,57], where the results are compared with the results of the diffusion analysis.The normalized analogy handles the bimaterial problem effectively and produces a correct distribution of moisture, where the discontinuity of moisture concentration at the interface is evident.
The validity of the advanced analogy was also verified using a bimaterial structure subjected to anisothermal loading [18]; the loading incorporated not only temperature change with time ð _ T 6 ¼ 0; and thus _ S 6 ¼ 0Þ but also spatially nonuniform temperature distribution ðrT 6 ¼ 0; and thus rS 6 ¼ 0Þ.
The configuration of the structure and loading conditions are illustrated in Fig. 13(a).The problem was solved by the normalized and advanced analogies.The results at t ¼ 3600 s are plotted in Fig. 13(b) together with the solution of the diffusion equation.The advanced analogy scheme predicted the moisture concentration accurately, while the normalized analogy significantly deviated from the solution.The results confirmed that the advanced analogy is applicable to all anisothermal cases.4.3 Moisture Transport for MEMS Cavity.MEMS devices have an internal cavity for moving parts and proper packaging should be provided to maintain the internal condition of the cavity.The cavity is formed by sealing a gap between cap and substrate wafers.Hermeticity of MEMS packages is a measure of the ability to maintain an acceptable level of stable and sometimes inert ambient in the cavity.Good hermeticity is essential for compliance with performance and reliability standards [65].
The most commonly used sealing materials to provide hermeticity are low-melting point eutectics, such as AuSn, AuSi, and other tin-based alloys.More recently, polymers have gained widespread acceptance due to many advantages that they offer [66,67].Examples of polymeric seals include benzocyclobutene (BCB), parylene, polyimide, and negative photoresists [68,69].Modeling of moisture transport into and out of a cavity through a polymeric seal is crucial in assessment of hermeticity performance of polymer-sealed MEMS packages.
Assuming that water vapor obeys the ideal gas law, the cavity vapor pressure by moisture transport through polymeric seals can be determined by  A 3D package (Fig. 14(a)) can be modeled as a twodimensional (2D) structure (Fig. 14(b)) since a cavity and a seal are sandwiched by a silicon chip through which gas cannot penetrate.The 2D diffusion model can be solved numerically by commercially available FEA software packages.It is important to recall that the boundary condition at the polymer seal and cavity interface is transient; the cavity pressure increment at each time step should be calculated and subsequently used to update the boundary condition at the inner surface after each time step.This updating process requires a user-defined algorithm (this scheme is referred to as "the original" scheme).An effective modeling scheme was proposed to cope with the problem (this scheme is referred to as "effective volume") [65].
A schematic illustration of the effective volume scheme is shown in Fig. 14(c).It modeled the package cavity as a fictitious polymer with an extremely large diffusivity and an "equivalent solubility."The large diffusivity ensured the uniform vapor pressure inside the cavity.It is important to note, however, that the solubility of the fictitious polymer cannot be chosen arbitrary.Instead, the effective solubility should be derived from the gas law and Henry's law as where q, V, and n are the water vapor density (kg/m 3 ), the volume (m 3 ) of the cavity, and the number of moles (mol).Note that the water vapor density has the same dimension as the moisture concentration and it can be interpreted as moisture concentration inside the imaginary polymer.
The effective volume scheme transforms the original single material diffusion problem with transient boundary conditions into a bimaterial gas diffusion problem with fixed boundary conditions.Consequently, the Nernst distribution law should be considered for mass continuity at the cavity-polymer seal interface (the inner surface of the polymer seal, x ¼ L in Fig. 14(b), which can be expressed as [22] / where C c and C p is the moisture concentration of the cavity and the polymer seal, respectively.In the effective volume scheme, the mass continuity is automatically satisfied at the interface, and thus, the interface condition does not have to be updated manually.As a results, the commercial FEA software packages can be employed to implement the effective volume scheme with either normalized or advanced analogy.It is important to note, however, that only isothermal cases should be solved even when the advanced analogy is employed, because Eq. ( 36) is not valid for general anisothermal cases.
The effective-volume scheme was validated with the original scheme.In the validation, a simple 1D axisymmetric geometry was considered, which simulated an MEMS device with a cavity at the center [70].Since no closed-form solution was available for the original schemes, it was solved by a numerical scheme based on the finite-difference method (FDM) [71].
Figure 15 shows cavity pressure evolution as a function of time for the case, where the seal width and the inner cavity radius are the same [70].The two schemes produce identical curves, confirming the validity of the effective volume scheme.Validation with experimental data can be also found in Refs.[65,72].

Summary
Fundamentals of moisture transport inside semiconductor packaging were reviewed.The procedures to obtain critical hygroscopic properties (diffusivity, solubility or saturated concentration, and hygroscopic swelling coefficient) were established well for the past decades, and abundant data were available in the literature.However, most of the data were obtained below 100 C and under RH less than 85%, and the data above the water boiling temperature were still limited in the literature.More experiments to measure the data above 100 C as well as at RH of 100% are warranted to provide complete understanding about the moisture behavior during solder reflow after preconditioning.
Numerical modeling schemes for diffusion analyses of packaging structures were developed for the last two decades and have been used extensively for various moisture transport problems including MEMS devices containing an internal cavity.The thermal analogy schemes are convenient and effective for the diffusion analysis, but cautions must be given to their applicable domains when implemented for diffusion problems with complex geometries and loading conditions.

Fig. 3
Fig. 3 Weight gain histories of: (a) EMC A and (b) EMC B, obtained at three temperatures and the humidity environment of 75%RH.Bullets and solid lines indicate the measurement data and corresponding Fickian curves, respectively.

Fig. 9
Fig. 9 Moir e fringe patterns: (a) null fields obtained from the reference sample; fringe patterns of the test sample at time intervals of (b) zero and (c) 40 h

Fig. 11
Fig. 11 Saturated concentration of various packaging polymers versus relative humidity

Fig. 12
Fig. 12 Implementation of normalized analogy: (a) bimaterial specimen subjected to an isothermal loading condition and (b) distribution of moisture concentration at t 5 3600 s

Fig. 14
Fig. 14 Schematic illustration of: (a) cross section of MEMS devices; and (b) "original" model and (c) effective volume model in a simplified 1D configuration[65]

Table 1
Constants and SI units

Table 4
Summary of three analogy schemes