Q-factor definition and evaluation for spiral inductors fabricated using wafer-level CSP technology

• Published in: IEEE transactions on microwave theory and techniques 2005-10, Vol.53 (10), p.3178-3184
• Main Authors: Aoki, Y., Honjo, K.
• Format: Article
• Language: English
• Subjects: Applied sciences; Chip scale packaging; Copper; Copper interconnect; Design. Technologies. Operation analysis. Testing; Devices; Electronic equipment and fabrication. Passive components, printed wiring boards, connectics; Electronics; Exact sciences and technology; high; Inductors; Integrated circuits; Isolation technology; low-loss; Magnetic devices; Polyimides; Ports; Power gain; Q factor; Q factors; Q values; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Silicon; silicon substrate; spiral inductor; Spirals; Wafer scale integration; wafer-level chip-scale package (WLP); Wiring
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2005.855147

A novel Q-factor definition and evaluation method are proposed for low-loss high-Q spiral inductors fabricated by using the wafer-level chip-size package (WLP) on silicon substrates, where the copper wiring technology with a polyimide isolation layer is used. In conventional Q-factor evaluation for inductors, a short-circuited load condition is used, where the Q factor is represented by using Y-parameters as Q=Im{1/Y/sub 11/}/Re{1/Y/sub 11/}. This conventional method provides a Q factor of 20 with 2-5-nH inductance around 3.9 GHz. However, since structures for the spiral inductors are asymmetrical, the short-circuited load condition and short-circuited source condition give different Q values, respectively. The Q-value differences of approximately 100% have often been observed in the WLP. The differences mainly come from differences in loss estimation. In a novel method, a complex conjugate impedance-matching condition is retained both at an input port and an output port of the inductor. The maximum available power gain (G/sub AMAX/) is introduced to evaluate the energy loss in one cycle. This condition provides a unique insertion loss of passive devices. Thus, the difference of the Q factor depends only on the difference of magnetic and electric energy. The difference of the Q value is reduced.