15 Die and Package Level Thermal and Thermal/Moisture Stresses …
459
force equilibrium equation with the above strain definitions and the governing equations of heat conduction and moisture diffusion. Since they are virtually independent
of the stress state (if stress gradient-driven diffusion mechanism can be neglected),
the temperature and moisture concentration fields can be determined, respectively,
prior to a stress analysis, and then they can be incorporated into a subsequent stress
analysis.
15.4.4 Vapor Pressure Modeling
To evaluate the total strain, vapor pressure must be determined first. Generally, vapor
pressure is related to the local moisture concentration and free volume fraction as
well (according to the porous media assumption). Although moisture diffusion is
analyzed at a macroscopic level, the vapor pressure model should be considered at a
microscopic level. Based on this principle, a micromechanics-based vapor pressure
model has been proposed [89] and is well accepted in semiconductor packaging.
Other vapor pressure models, such as those based on Henry’s law [19, 20, 78, 79],
do not consider the microscopic effect. Therefore, the micromechanics-based model
is adopted and described in this chapter.
The micromechanics-based model considers a representative elementary volume
(REV) as shown in Fig. 15.20. The RVE exists at any considered point in porous
medium. All moisture absorbed is either in liquid water or vapor form. Moisture collects at the micro-/nano-pores, in free volumes, at the interfaces, and/or in
micro/macro-voids. Unbound moisture will evaporate during the reflow process. The
total moisture content in a REV is obtained from the local moisture concentration C
at a macroscopic level. If the void volume fraction φ (or interstitial space fraction)
is known, then the ‘apparent’ moisture density (ρ a ) in pores can be defined as [89]
ρ a = C/φ
(15.23)
Fig. 15.20 Representative
elementary volume (REV)
describing two distinct states
of moisture in pores in
polymer materials [89]
459
force equilibrium equation with the above strain definitions and the governing equations of heat conduction and moisture diffusion. Since they are virtually independent
of the stress state (if stress gradient-driven diffusion mechanism can be neglected),
the temperature and moisture concentration fields can be determined, respectively,
prior to a stress analysis, and then they can be incorporated into a subsequent stress
analysis.
15.4.4 Vapor Pressure Modeling
To evaluate the total strain, vapor pressure must be determined first. Generally, vapor
pressure is related to the local moisture concentration and free volume fraction as
well (according to the porous media assumption). Although moisture diffusion is
analyzed at a macroscopic level, the vapor pressure model should be considered at a
microscopic level. Based on this principle, a micromechanics-based vapor pressure
model has been proposed [89] and is well accepted in semiconductor packaging.
Other vapor pressure models, such as those based on Henry’s law [19, 20, 78, 79],
do not consider the microscopic effect. Therefore, the micromechanics-based model
is adopted and described in this chapter.
The micromechanics-based model considers a representative elementary volume
(REV) as shown in Fig. 15.20. The RVE exists at any considered point in porous
medium. All moisture absorbed is either in liquid water or vapor form. Moisture collects at the micro-/nano-pores, in free volumes, at the interfaces, and/or in
micro/macro-voids. Unbound moisture will evaporate during the reflow process. The
total moisture content in a REV is obtained from the local moisture concentration C
at a macroscopic level. If the void volume fraction φ (or interstitial space fraction)
is known, then the ‘apparent’ moisture density (ρ a ) in pores can be defined as [89]
ρ a = C/φ
(15.23)
Fig. 15.20 Representative
elementary volume (REV)
describing two distinct states
of moisture in pores in
polymer materials [89]