15 Die and Package Level Thermal and Thermal/Moisture Stresses …
455
encapsulated moisture in packaging material may evaporate to generate high internal
vapor pressure, causing interface delamination and even pop-corning [14, 27, 77–
79]. During the highly accelerated temperature and humidity stress test (HAST),
moisture-induced stress also becomes very critical to cause package failures as high
temperature, high humidity, and high atmospheric pressure are applied.
Due to the deleterious effects caused by moisture, extensive efforts have been
made to investigate the moisture diffusion, desorption, and the ensuing mechanical
stresses in encapsulated microelectronics devices [16, 26, 80–84]. More importantly,
since moisture-induced stress is often accompanied with thermal stress (e.g., during
reflow or HAST condition), it is necessary to perform integrated stress analysis to
combine all these effects including thermal expansion, hygroscopic swelling, and
internal vapor pressure development [17, 63, 77, 85].
To investigate the combined effects of thermal stress and moisture-induced stress,
this section starts with the examination of moisture diffusion equation with varying
temperature and relative humidity (RH) conditions in Sect. 15.4.2. Then the theory
for incorporating moisture-induced stress is given in Sect. 15.4.3, where the concept
of effective stress is introduced. The model for calculation of vapor pressure is
described in Sect. 15.4.4, in which the void volume fraction and vapor pressure
are introduced as two internal field variables. Section 15.4.5 then summarizes the
complete set of governing equations including temperature, moisture, displacement,
void volume fraction, and vapor pressure based on the literature [17]. Commercial finite element analysis software ANSYS is used to solve the equations. With a
representative bi-material configuration, the solutions for moisture diffusion, vapor
pressure, and integrated stress effects are presented in Sect. 15.4.6.
15.4.2 Moisture Diffusion
The transient moisture diffusion equation based on the Fick’s law [86] is the most
widely used in semiconductor engineering, which has a form as:
∂ C
∂ t
= −∇ · (−D∇C)
(15.6)
where C is the local moisture concentration and D is the diffusivity (the rate of diffusion), and t is time. However due to dissimilar materials are used in 3D packaging,
the moisture concentration C is discontinuous at the interface of different materials,
creating numerical difficulty. As a result, a normalized concentration, or the activity
of the diffusing material (denoted as φ here), is introduced [87]
φ = C/S(T )
(15.7)
455
encapsulated moisture in packaging material may evaporate to generate high internal
vapor pressure, causing interface delamination and even pop-corning [14, 27, 77–
79]. During the highly accelerated temperature and humidity stress test (HAST),
moisture-induced stress also becomes very critical to cause package failures as high
temperature, high humidity, and high atmospheric pressure are applied.
Due to the deleterious effects caused by moisture, extensive efforts have been
made to investigate the moisture diffusion, desorption, and the ensuing mechanical
stresses in encapsulated microelectronics devices [16, 26, 80–84]. More importantly,
since moisture-induced stress is often accompanied with thermal stress (e.g., during
reflow or HAST condition), it is necessary to perform integrated stress analysis to
combine all these effects including thermal expansion, hygroscopic swelling, and
internal vapor pressure development [17, 63, 77, 85].
To investigate the combined effects of thermal stress and moisture-induced stress,
this section starts with the examination of moisture diffusion equation with varying
temperature and relative humidity (RH) conditions in Sect. 15.4.2. Then the theory
for incorporating moisture-induced stress is given in Sect. 15.4.3, where the concept
of effective stress is introduced. The model for calculation of vapor pressure is
described in Sect. 15.4.4, in which the void volume fraction and vapor pressure
are introduced as two internal field variables. Section 15.4.5 then summarizes the
complete set of governing equations including temperature, moisture, displacement,
void volume fraction, and vapor pressure based on the literature [17]. Commercial finite element analysis software ANSYS is used to solve the equations. With a
representative bi-material configuration, the solutions for moisture diffusion, vapor
pressure, and integrated stress effects are presented in Sect. 15.4.6.
15.4.2 Moisture Diffusion
The transient moisture diffusion equation based on the Fick’s law [86] is the most
widely used in semiconductor engineering, which has a form as:
∂ C
∂ t
= −∇ · (−D∇C)
(15.6)
where C is the local moisture concentration and D is the diffusivity (the rate of diffusion), and t is time. However due to dissimilar materials are used in 3D packaging,
the moisture concentration C is discontinuous at the interface of different materials,
creating numerical difficulty. As a result, a normalized concentration, or the activity
of the diffusing material (denoted as φ here), is introduced [87]
φ = C/S(T )
(15.7)