Chapter 15
Die and Package Level Thermal
and Thermal/Moisture Stresses in 3-D
Packaging: Modeling
and Characterization
Liangbiao Chen, Tengfei Jiang, and Xuejun Fan
List of symbols
A
Geometry factor for calculating thermal stress in multi-layered
structure
¯
ε T
Average thermal strain
a
Via radius
σ θ
Circumferential stress
T y
Critical thermal load for plastic yielding
C sat
Saturated moisture concentration
α Cu
CTE of copper
α si
CTE of silicon
D
Moisture diffusivity
d
Via diameter
E
Total volumetric strain
E
Young’s Modulus
k P
Factor for hydrostatic pressure gradient-driven diffusion
k T
FACTOR for thermal gradient-driven diffusion
L. Chen (B)
ON Semiconductor, 82 Running Hill Rd, South Portland, ME 04106, USA
e-mail: bill.chen@onsemi.com
T. Jiang
Department of Material Science and Engineering, University of Central Florida, Orlando, FL
32816, USA
e-mail: Tengfei.Jiang@ucf.edu
X. Fan
Department of Mechanical Engineering, Lamar University, Beaumont, TX 77710, USA
e-mail: xuejun.fan@lamar.edu
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2021
Y. Li and D. Goyal (eds.), 3D Microelectronic Packaging,
Springer Series in Advanced Microelectronics 64,
https://doi.org/10.1007/978-981-15-7090-2_15
431
Die and Package Level Thermal
and Thermal/Moisture Stresses in 3-D
Packaging: Modeling
and Characterization
Liangbiao Chen, Tengfei Jiang, and Xuejun Fan
List of symbols
A
Geometry factor for calculating thermal stress in multi-layered
structure
¯
ε T
Average thermal strain
a
Via radius
σ θ
Circumferential stress
T y
Critical thermal load for plastic yielding
C sat
Saturated moisture concentration
α Cu
CTE of copper
α si
CTE of silicon
D
Moisture diffusivity
d
Via diameter
E
Total volumetric strain
E
Young’s Modulus
k P
Factor for hydrostatic pressure gradient-driven diffusion
k T
FACTOR for thermal gradient-driven diffusion
L. Chen (B)
ON Semiconductor, 82 Running Hill Rd, South Portland, ME 04106, USA
e-mail: bill.chen@onsemi.com
T. Jiang
Department of Material Science and Engineering, University of Central Florida, Orlando, FL
32816, USA
e-mail: Tengfei.Jiang@ucf.edu
X. Fan
Department of Mechanical Engineering, Lamar University, Beaumont, TX 77710, USA
e-mail: xuejun.fan@lamar.edu
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2021
Y. Li and D. Goyal (eds.), 3D Microelectronic Packaging,
Springer Series in Advanced Microelectronics 64,
https://doi.org/10.1007/978-981-15-7090-2_15
431