Application of Paris’s law to thermal cycling-induced failure in semiconductor device patterns

• Published in: Metals and materials international 2008, 14(6), , pp.799-802
• Main Author: Lee, Seong-Min
• Format: Article
• Language: English
• Subjects: Alloys; Characterization and Evaluation of Materials; Chemistry and Materials Science; Communication; Crack propagation; Cracks; Direct current; Displacement; Engineering Thermodynamics; Growth rate; Heat and Mass Transfer; Law; Machines; Magnetic Materials; Magnetism; Manufacturing; Materials Science; Mathematical models; Metallic Materials; Processes; Semiconductor devices; Solid Mechanics; Stress intensity factor; Thermal cycling; 재료공학
• ISSN: 1598-9623; 2005-4149
• DOI: 10.3365/met.mat.2008.12.799

The present work provides a semi-empirical model to show that the growth rate of thermal displacement-induced cracks in semiconductor devices depends on pattern thickness. Paris’s law is adopted to characterize the growth rate of cracks during thermal-cycling. The crack propagation rate is estimated from the semi-empirical relation (dc/dN) v =C(ΔK) n , where ΔK indicates the range of an applied stress intensity factor, and C is a scaling constant. The applied stress intensity factor is related to the initial crack length as ΔK=YΔσ(πc) 1/2 , where σ represents the thermal displacement-induced normal stress, c describes the pre-existing crack length, and Y is a geometrical factor. The resulting crack growth rate can be expressed as a function of device pattern thickness: dc/dN∞(1/t) m , where t describes the pattern thickness, and m is another constant. The present semi-empirical results showing the relationship between the crack growth rate and pattern thickness indicate that if a semiconductor device pattern becomes thinner by 68%, its susceptibility to thermal cycling-induced damage will be enhanced by 76%.