結論 - 玻璃基板之螺旋電感物理模型萃取技術

本論文前半段討論薄膜被動元件的基本理論與整理提高薄膜電感Q 值的一些

方法，後半部分利用日月光半導體公司IPD 製程實現兩種不同結構的薄膜電感於玻璃基板上，經量測後得到螺旋電感器品質因素最大值介於20～45 之間，螺線管電感器則介於10～20 之間，且反覆利用電磁模擬軟體抓出材料電性參數，以供設計者可以得到pre-simulation 與成品相同的結果。第四章對螺旋電感器等效電路做

探討，從最簡化之π 模型，一步步加上集總元件，成功符合量測曲線，達到更寬

頻的效果，以利電感資料庫(library)的建立。但未能完成電感的伸縮化模型，建立出此製程完整的薄膜螺旋電感器之資料庫，給設計者方便在ADS 上設計使用，是

本文後續努力之目標。最後討論兩種電感器的結構參數對電感值及Q 值的影響，

以供後續的設計者做參考。

參考文獻

[1] J. Rector, "Economic and technical viability of integral passives," in Electronic

Components & Technology Conference, 1998. 48th IEEE, 1998, pp.

218-224.

[2] R. K. Ulrich, W. D. Brown, S. S. Ang, F. D. Barlow, A. Elshabini, T. G. Lenihan, H. A. Naseem, D. M. Nelms, J. Parkerson, L. W. Schaper, and G. Morcan,

"Getting aggressive with passive devices," Circuits and Devices Magazine,

IEEE, vol. 16, pp. 16-25, 2000.

[3] W. R. Bottoms, W. Chen, K. Pressel, and J. Wolf, "The next STep in Assembly and Packaging: System Level Integration in the package (SiP)," ITRS 2007.

[4] R. K. Ulrich and L. W. Schaper, Integrated Passive Component Technology.

New Jersey: Wiley, 2003.

[5] 翁敏航, 射頻被動元件設計: 東華書局, 民國九十五年.

[6] C. A. Harper and J. E. Sergent, Hybrid Microelectronics Handbook, 2 ed. New York: McGraw-Hill, 1995.

[7] T. Lenihan, L. Schaper, Y. Shi, G. Morcan, and J. Parkerson, "Embedded thin film resistors, capacitors and inductors in flexible polyimide films," in

Electronic Components and Technology Conference, 1996. Proceedings., 46th,

1996, pp. 119-124.

[8] R. Groves, J. Malinowski, R. Volant, and D. Jadus, "High Q inductors in a SiGe BiMOS process utilizing a thick metal process add-on module," in

Bipolar/BiCMOS Circuits and Technology Meeting, 1999. Proceedings of the 1999, 1999, pp. 149-152.

[9] L. Seogoo, C. Jongseong, G. S. May, and A. I. Y. Ilgu Yun, "Modeling and analysis of 3-D solenoid embedded inductors," Electronics Packaging

Manufacturing, IEEE Transactions on, vol. 25, pp. 34-41, 2002.

[10] P. Pieters, K. Vaesen, S. Brebels, S. F. Mahmoud, W. De Raedt, E. Beyne, and R.

P. Mertens, "Accurate modeling of high-Q spiral inductors in thin-film

multilayer technology for wireless telecommunication applications," Microwave

Theory and Techniques, IEEE Transactions on, vol. 49, pp. 589-599, 2001.

[11] M. Tang, H. Y. Li, Q. X. Zhang, E. B. Liao, A. B. Yu, G. Q. Lo, N.

Balasubramanian, and D. L. Kwong, "High-Q on-chip inductors using extremely thick silicon dioxide and copper-damascene technology," Electronics Letters, vol.

44, pp. 241-242, 2008.

[12] T. Huan-Shang, L. Jenshan, R. C. Frye, K. L. Tai, M. Y. Lau, D. Kossives, F.

Hrycenko, and C. Young-Kai, "Investigation of current crowding effect on spiral inductors," in Wireless Applications Digest, 1997., IEEE MTT-S Symposium on

Technologies for, 1997, pp. 139-142.

[13] C. P. Yue and S. S. Wong, "Physical modeling of spiral inductors on silicon,"

Electron Devices, IEEE Transactions on, vol. 47, pp. 560-568, 2000.

[14] O. H. Murphy, K. G. McCarthy, C. J. P. Delabie, A. C. Murphy, and P. J. Murphy,

"Design of multiple-metal stacked inductors incorporating an extended physical model," Microwave Theory and Techniques, IEEE Transactions on, vol. 53, pp.

2063-2072, 2005.

[15] S. Jenei, S. Decoutere, G. Winderickx, H. Struyf, Z. Tokei, I. Vervoort, I. Vos, P.

Jaenen, L. Carbonell, B. De Jaeger, R. A. Donaton, S. Vanhaelemeersch, K.

Maex, and B. Nauwelaers, "High Q inductor add-on module in thick Cu/SiLK single damascene," in Interconnect Technology Conference, 2001. Proceedings

of the IEEE 2001 International, 2001, pp. 107-109.

[16] T. Chih-Ming and L. Chien-Neng, "Multilevel Suspended Thin-Film Inductors on Silicon Wafers," Electron Devices, IEEE Transactions on, vol. 54, pp.

1510-1514, 2007.

[17] J. M. Lopez-Villegas, J. Samitier, C. Cane, and P. Losantos, "Improvement of the quality factor of RF integrated inductors by layout optimization," in Radio

Frequency Integrated Circuits (RFIC) Symposium, 1998 IEEE, 1998, pp.

169-172.

[18] R. P. Ribas, J. Lescot, J. L. Leclercq, J. M. Karam, and F. Ndagijimana,

"Micromachined microwave planar spiral inductors and transformers,"

Microwave Theory and Techniques, IEEE Transactions on, vol. 48, pp.

1326-1335, 2000.

[19] 楊立群, "低溫共燒陶瓷嵌入式電感與電容元件之設計與模型化," 國立中山大學電機工程學系碩士論文, 民國九十一年.

[20] C. A. note, "On-Wafer Vector Network Analyzer Calibration and Measurements," Cascade.

[21] D. M. Pozar, Microwave Engineering, 3 ed. New Jersey: Wiley, 2005.

[22] P. Carazzetti, M. A. Dubois, and N. F. de Rooij, "High-performance

micromachined RF planar inductors," in Solid-State Sensors, Actuators and

Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS '05. The 13th

International Conference on, 2005, pp. 1084-1087 Vol. 1.

[23] T. Kamgaing, T. Myers, M. Petras, and M. A. M. M. Miller, "Modeling of frequency dependent losses in two-port and three-port inductors on silicon," in

Radio Frequency Integrated Circuits (RFIC) Symposium, 2002 IEEE, 2002, pp.

307-310.

[24] C. Yu, R. A. Groves, H. Xuejue, N. D. A. Z. N. D. Zamdmer, J. O. A. P. J. O.

Plouchart, R. A. A. W. R. A. Wachnik, A. T.-J. K. Tsu-Jae King, and A. C. H.

Chenming Hu, "Frequency-independent equivalent-circuit model for on-chip spiral inductors," Solid-State Circuits, IEEE Journal of, vol. 38, pp. 419-426, 2003.

[25] 鄭宏祥, "有機機板上的貫穿孔之電性特性分析與模型化," 國立中山大學電機工程學系IC 封裝產業研發碩士專班碩士論文, 民國九十六年.

[26] Ansoft, "User's guide - High Frequency Structure Simulator V9.2," Ansoft Corporation.

[27] I. J. Bahl, "Improved quality factor spiral inductors on GaAs substrates,"

Microwave and Guided Wave Letters, IEEE, vol. 9, pp. 398-400, 1999.

附錄 A

各電感器電感值(2.4GHz)、品質因素最大值及諧振點頻率

51.28 46.48

41.92 38.55

30.51

SRF(GHz) Qmax

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

50 40

30 20

>20

18.27 43.82

41.87 38.3

30.84

1.05 1.07

1.08 1.1

1.15 50

>20

46.13 48.47

42 37.98

30.72

1.02 1.04

1.05 1.07

1.12 40

>20

44.97 46.37

42.43 37.48

31.83

1.01 0.98

1.04 1.01

1.1 30

>20

0.96 0.98

0.99 1

1.06 20

>20

45.6 48.2

42.96 37.93

30.26

0.94 0.94

0.95 0.97

1.03 10

Spiral Inductor t=1.5 r=25μm

51.28 46.48

41.92 38.55

30.51

SRF(GHz) Qmax

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

50 40

30 20

>20

18.27 43.82

41.87 38.3

30.84

1.05 1.07

1.08 1.1

1.15 50

>20

46.13 48.47

42 37.98

30.72

1.02 1.04

1.05 1.07

1.12 40

>20

44.97 46.37

42.43 37.48

31.83

1.01 0.98

1.04 1.01

1.1 30

>20

0.96 0.98

0.99 1

1.06 20

>20

45.6 48.2

42.96 37.93

30.26

0.94 0.94

0.95 0.97

1.03 10

Spiral Inductor t=1.5 r=25μm w(μm)

s(μm)

34.15 31.47

29.59 27.72

23.82

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

50 13.7

15.3 16.4

18.3

39.31 35.62

33.38 29.04

25.05

2.86 2.22

2.19 2.01

2.02 50

13.1 14.6

15.7 17.8

19.5

37.38 36.1

32.38 30.22

25.01

2.18 2.11

1.93 1.89

1.88 40

14 15.6

17.1 19.1

>20

34.65 34.93

32.82 29.39

24.58

2.08 1.99

1.83 1.76

1.75 30

15 16.2

18.2

>20

1.94 1.73

1.68 1.64

1.6 20

15.5 17.4

19.7

>20

28.8 29.11

28.65 25.26

32.3

1.66 1.59

1.57 1.5

1.48 10

Spiral Inductor t=2.5 r=25μm

34.15 31.47

29.59 27.72

23.82

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

50 13.7

15.3 16.4

18.3

39.31 35.62

33.38 29.04

25.05

2.86 2.22

2.19 2.01

2.02 50

13.1 14.6

15.7 17.8

19.5

37.38 36.1

32.38 30.22

25.01

2.18 2.11

1.93 1.89

1.88 40

14 15.6

17.1 19.1

>20

34.65 34.93

32.82 29.39

24.58

2.08 1.99

1.83 1.76

1.75 30

15 16.2

18.2

>20

1.94 1.73

1.68 1.64

1.6 20

15.5 17.4

19.7

>20

28.8 29.11

28.65 25.26

32.3

1.66 1.59

1.57 1.5

1.48 10

Spiral Inductor t=2.5 r=25μm w(μm)

s(μm)

28.97 29.41

27.63 23.93

20.59

SRF(GHz) Qmax

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

50 10.3

11.9

30.84 30.23

29.99 26.68

24.01

5.5 5.16

4.85 4.01

3.88 50

7.5 8.4

9.5 11.1

12.7

31.27 32.52

30.24 24.8

23.17

5.09 4.77

4.52 3.57

3.33 40

8 8.9

10.8 12.5

14.2

31.04 30.03

28.27 27.14

21.72

4.76 4.35

3.57 3.33

2.95 30

8.5 10.2

11.9 13.6

4.24 3.43

3.2 2.83

2.61 20

9.6 11.2

12.8 14.9

17.9

22.91 23.79

21.99 21.17

19.5

3.24 3.07

2.67 2.47

2.28 10

Spiral Inductor t=3.5 r=25μm

28.97 29.41

27.63 23.93

20.59

SRF(GHz) Qmax

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

50 10.3

11.9

30.84 30.23

29.99 26.68

24.01

5.5 5.16

4.85 4.01

3.88 50

7.5 8.4

9.5 11.1

12.7

31.27 32.52

30.24 24.8

23.17

5.09 4.77

4.52 3.57

3.33 40

8 8.9

10.8 12.5

14.2

31.04 30.03

28.27 27.14

21.72

4.76 4.35

3.57 3.33

2.95 30

8.5 10.2

11.9 13.6

4.24 3.43

3.2 2.83

2.61 20

9.6 11.2

12.8 14.9

17.9

22.91 23.79

21.99 21.17

19.5

3.24 3.07

2.67 2.47

2.28 10

Spiral Inductor t=3.5 r=25μm w(μm)

s(μm)

25.04 25.34

24.29 23.96

20.2

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

26.33 28.04

26.29 24.36

22.2

9.87*

11.38 9.13

8.61 7.71

26.15 28.03

27.93 25.96

21.95

9.02*

9.17 8.28

7.45 6.02

5.3 6

6.9 8.4

10.1

27.67 26.86

26.15 24.29

21.68

9.12 8.06

7.28 5.78

5.24 30

5.7 6.6

7.9 9.6

11.4

8.01 7.2

5.6 5.04

4.32 20

6.2 7.4

9 10.8

13.3

19.75 19.63

20.18 18.56

17.13

6.89 5.34

4.8 4.1

3.6 10

Spiral Inductor t=4.5 r=25μm

25.04 25.34

24.29 23.96

20.2

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

26.33 28.04

26.29 24.36

22.2

9.87*

11.38 9.13

8.61 7.71

26.15 28.03

27.93 25.96

21.95

9.02*

9.17 8.28

7.45 6.02

5.3 6

6.9 8.4

10.1

27.67 26.86

26.15 24.29

21.68

9.12 8.06

7.28 5.78

5.24 30

5.7 6.6

7.9 9.6

11.4

8.01 7.2

5.6 5.04

4.32 20

6.2 7.4

9 10.8

13.3

19.75 19.63

20.18 18.56

17.13

6.89 5.34

4.8 4.1

3.6 10

Spiral Inductor t=4.5 r=25μm w(μm)

s(μm)

*:在 1GHz 的電感值

21.21 19.94

22.67 22.22

20.85

SRF(GHz) Qmax

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

27.32 25.87

25.21 23.49

20.96

16.76*

15.46*

14.04*

13.22*

13.27 50

26.21 23.98

23.92 23.5

22.58

15.17*

13.84*

12.93 12.93

11.45 40

25.54 24.05

21.69 23.96

21.36

13.65*

12.38*

10.46 11.3

8.55 30

10.09*

10.97 8.3

7.03 20

4.5 5.3

6.4 8.1

10.3

11.79 17.11

17.86 18.22

16.81

9.28*

10.01 7.98

6.71 5.44

Spiral Inductor t=5.5 r=25μm

21.21 19.94

22.67 22.22

20.85

SRF(GHz) Qmax

L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

27.32 25.87

25.21 23.49

20.96

16.76*

15.46*

14.04*

13.22*

13.27 50

26.21 23.98

23.92 23.5

22.58

15.17*

13.84*

12.93 12.93

11.45 40

25.54 24.05

21.69 23.96

21.36

13.65*

12.38*

10.46 11.3

8.55 30

10.09*

10.97 8.3

7.03 20

4.5 5.3

6.4 8.1

10.3

11.79 17.11

17.86 18.22

16.81

9.28*

10.01 7.98

6.71 5.44

Spiral Inductor t=5.5 r=25μm w(μm)

s(μm)

*:在 1GHz 的電感值

42.89 39.12

33.36

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

>20

46.52 37.96

33.13

1.47 1.46

1.55 30

>20

1.42 1.43

1.53 20

>20

46.8 41.2

32.5

1.41 1.45

1.51 10

Spiral Inductor t=1.5 r=50μm

42.89 39.12

33.36

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

>20

46.52 37.96

33.13

1.47 1.46

1.55 30

>20

1.42 1.43

1.53 20

>20

46.8 41.2

32.5

1.41 1.45

1.51 10

Spiral Inductor t=1.5 r=50μm w(μm)

s(μm)

46.01 38.14

30.87

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

18.8 19.5

19.7

45.46 39.52

30.1

1.82 1.87

1.88 30

19 19.6

>20

1.8 1.84

1.95 20

19.1 19.7

>20

45.55 39.68

30.11

1.81 1.83

1.93 10

Spiral Inductor t=1.5 r=100μm

46.01 38.14

30.87

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

18.8 19.5

19.7

45.46 39.52

30.1

1.82 1.87

1.88 30

19 19.6

>20

1.8 1.84

1.95 20

19.1 19.7

>20

45.55 39.68

30.11

1.81 1.83

1.93 10

Spiral Inductor t=1.5 r=100μm w(μm)

s(μm)

42.32 37.62

31.12

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

13.6 14

14.4

43.3 37.77

29.49

2.69 2.76

2.94 30

13.5 14

14.4

2.64 2.77

2.95 20

13.3 13.7

42.02 37.39

28.44

2.68 2.79

2.97 10

Spiral Inductor t=1.5 r=200μm

42.32 37.62

31.12

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

13.6 14

14.4

43.3 37.77

29.49

2.69 2.76

2.94 30

13.5 14

14.4

2.64 2.77

2.95 20

13.3 13.7

42.02 37.39

28.44

2.68 2.79

2.97 10

Spiral Inductor t=1.5 r=200μm w(μm)

s(μm)

37.7 32.77

27.47

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

14.1 15.3

16.2

38.34 32.39

26.13

2.76 2.69

2.62 30

14.8 16

17.2

2.62 2.54

2.56 20

15.3 16.6

17.9

33.44 30.52

25.91

2.46 2.41

2.39 10

Spiral Inductor t=2.5 r=50μm

37.7 32.77

27.47

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

14.1 15.3

16.2

38.34 32.39

26.13

2.76 2.69

2.62 30

14.8 16

17.2

2.62 2.54

2.56 20

15.3 16.6

17.9

33.44 30.52

25.91

2.46 2.41

2.39 10

Spiral Inductor t=2.5 r=50μm w(μm)

s(μm)

40.38 34.15

27.94

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

10.9 11.8

12.5

38.8 34.36

27.41

3.78 3.83

3.82 30

11.2 12.1

12.9

3.68 3.69

3.73 20

11.4 12.2

37.86 32.56

27.63

3.57 3.6

3.74 10

Spiral Inductor t=2.5 r=100μm

40.38 34.15

27.94

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

10.9 11.8

12.5

38.8 34.36

27.41

3.78 3.83

3.82 30

11.2 12.1

12.9

3.68 3.69

3.73 20

11.4 12.2

37.86 32.56

27.63

3.57 3.6

3.74 10

Spiral Inductor t=2.5 r=100μm w(μm)

s(μm)

37.77 35.9

27.85

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

36.09 34.95

26.25

6.28 6.4

6.71 30

7.6 8.135

8.5

6.31 6.44

6.76 20

7.4 7.8

8.2

36.39 33.27

26.8

6.29 6.48

6.93 10

Spiral Inductor t=2.5 r=200μm

37.77 35.9

27.85

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

36.09 34.95

26.25

6.28 6.4

6.71 30

7.6 8.135

8.5

6.31 6.44

6.76 20

7.4 7.8

8.2

36.39 33.27

26.8

6.29 6.48

6.93 10

Spiral Inductor t=2.5 r=200μm w(μm)

s(μm)

31.48 29.73

25.77

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

9 10.1

11.4

32.44 30.23

25.69

5.07 4.78

4.6 30

9.7 10.9

12.2

4.71 4.44

4.23 20

10.2 11.7

27.31 26.69

22.92

4.29 4.06

3.86 10

Spiral Inductor t=3.5 r=50μm

31.48 29.73

25.77

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30 20

9 10.1

11.4

32.44 30.23

25.69

5.07 4.78

4.6 30

9.7 10.9

12.2

4.71 4.44

4.23 20

10.2 11.7

27.31 26.69

22.92

4.29 4.06

3.86 10

Spiral Inductor t=3.5 r=50μm w(μm)

s(μm)

33.52 30.15

26.73

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

32.86 29.12

25.56

7.32 7

6.92 30

7.3 8.2

6.9 6.71

6.66 20

7.6 8.4

9.2

31.23 28.24

25.16

6.54 6.42

6.41 10

Spiral Inductor t=3.5 r=100μm

33.52 30.15

26.73

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

32.86 29.12

25.56

7.32 7

6.92 30

7.3 8.2

6.9 6.71

6.66 20

7.6 8.4

9.2

31.23 28.24

25.16

6.54 6.42

6.41 10

Spiral Inductor t=3.5 r=100μm w(μm)

s(μm)

29.07 30.02

26.22

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30.75 28.66

24.49

10.66 12.92

13.16 30

4.9 5.3

5.8

10.48 12.88

13.02 20

5 5.3

5.7

30.76 27.11

26.54

10.62 12.88

13.37 10

Spiral Inductor t=3.5 r=200μm

29.07 30.02

26.22

SRF(GHz) Qmax

L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

30.75 28.66

24.49

10.66 12.92

13.16 30

4.9 5.3

5.8

10.48 12.88

13.02 20

5 5.3

5.7

30.76 27.11

26.54

10.62 12.88

13.37 10

Spiral Inductor t=3.5 r=200μm w(μm)

s(μm)

SRF(GHz) Qmax

SRF(GHz) Q_max SRF(GHz)

Qmax

L(nH) L(nH) L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

50 40

30 20

>20

17.556 14.4

15.339 14.015

17.81

0.829 0.91

1.038 1.229

2.225 90

>20

17.694 16.766

17.6 16.5

16.8

0.808 0.895

1.014 1.193

1.481 70

>20

18.5 18.46

17.7 15.4

16.1

0.792 0.862

0.972 1.157

1.428 50

>20

16.5 15.2

14.9 16.3

15.5

0.787 0.854

0.963 1.12

1.392 40

>20

17.6 18.05

16.7 14.2

14.7

0.782 0.855

0.943 1.102

1.377 30

>20

19.2 18.3

15.6 13.6

0.859 0.849

0.932 1.074

1.339 20

>20

18.5 23.77

17.2 15.47

0.805 0.776

0.929 1.048

1.282 10

Solenoid Inductor t=3

SRF(GHz) Qmax

SRF(GHz) Q_max SRF(GHz)

Qmax

L(nH) L(nH) L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Qmax

L(nH)

50 40

30 20

>20

17.556 14.4

15.339 14.015

17.81

0.829 0.91

1.038 1.229

2.225 90

>20

17.694 16.766

17.6 16.5

16.8

0.808 0.895

1.014 1.193

1.481 70

>20

18.5 18.46

17.7 15.4

16.1

0.792 0.862

0.972 1.157

1.428 50

>20

16.5 15.2

14.9 16.3

15.5

0.787 0.854

0.963 1.12

1.392 40

>20

17.6 18.05

16.7 14.2

14.7

0.782 0.855

0.943 1.102

1.377 30

>20

19.2 18.3

15.6 13.6

0.859 0.849

0.932 1.074

1.339 20

>20

18.5 23.77

17.2 15.47

0.805 0.776

0.929 1.048

1.282 10

Solenoid Inductor t=3 w(μm)

s(μm)

11.976 12.59

12.8 13.3

19.77

SRF(GHz) Qmax

SRF(GHz) Q_max SRF(GHz)

Qmax

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

50 40

30 20

>20

>20 19.7

17.89 16.51

15.086 15.581

15.29 15.608

15.02

1.102 1.226

1.429 1.735

2.153 90

>20

>20 17.69

11.1 13.5

13.795 14.54

15.018

0.875 0.981

1.175 1.439

1.872 70

>20

>20 19.53

14.353 14.141

12.478 16.115

13.816

0.853 0.957

1.119 1.396

1.814 50

>20

11.713 13.905

13.766 16.5

18.837

0.847 0.94

1.102 1.356

1.769 40

>20

10.686 14.4

13.436 11.81

11.4

0.836 0.923

1.075 1.301

1.711 30

>20

0.829 0.929

1.06 1.265

1.636 20

>20

12.975 12.12

12.585 12.124

13.92

0.857 0.912

1.043 1.215

1.573 10

Solenoid Inductor t=5

11.976 12.59

12.8 13.3

19.77

SRF(GHz) Qmax

SRF(GHz) Q_max SRF(GHz)

Qmax

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

50 40

30 20

>20

>20 19.7

17.89 16.51

15.086 15.581

15.29 15.608

15.02

1.102 1.226

1.429 1.735

2.153 90

>20

>20 17.69

11.1 13.5

13.795 14.54

15.018

0.875 0.981

1.175 1.439

1.872 70

>20

>20 19.53

14.353 14.141

12.478 16.115

13.816

0.853 0.957

1.119 1.396

1.814 50

>20

11.713 13.905

13.766 16.5

18.837

0.847 0.94

1.102 1.356

1.769 40

>20

10.686 14.4

13.436 11.81

11.4

0.836 0.923

1.075 1.301

1.711 30

>20

0.829 0.929

1.06 1.265

1.636 20

>20

12.975 12.12

12.585 12.124

13.92

0.857 0.912

1.043 1.215

1.573 10

Solenoid Inductor t=5 w(μm)

s(μm)

10.76 10.51

9.939 10.53

12.782

SRF(GHz) Qmax

SRF(GHz) Q_max SRF(GHz)

Qmax

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

50 40

30 20

15.6 16.87

16.39 14.01

12.91

15.274 12.839

14.75 11.675

12.6

1.777 1.553

1.829 2.26

2.681 90

18.33 18.1

17.89 15.22

13.18

13.182 12.344

11.231 13.024

12.612

1.322 1.281

1.554 1.939

2.569 70

>20 19.45

17.9 15.6

15.22

9.62 11.965

12.05 12.352

13.602

1.084 1.229

1.478 1.842

2.411 50

>20

>20 18.26

16.14 15.75

8.847 8.387

12.394 11.732

13.168

1.074 1.21

1.429 1.791

2.342 40

>20

>20 19.18

17.49

10.286 11.22

10.745 11.56

13.016

1.049 1.005

1.137 1.496

2.063 30

>20

>20 18.58

0.879 0.994

1.161 1.447

1.967 20

>20

>20 19.6

11.21 11.5

12.1 8.51

11.29

0.85 1.032

1.136 1.368

1.867 10

Solenoid Inductor t=7

10.76 10.51

9.939 10.53

12.782

SRF(GHz) Qmax

SRF(GHz) Q_max SRF(GHz)

Qmax

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

50 40

30 20

15.6 16.87

16.39 14.01

12.91

15.274 12.839

14.75 11.675

12.6

1.777 1.553

1.829 2.26

2.681 90

18.33 18.1

17.89 15.22

13.18

13.182 12.344

11.231 13.024

12.612

1.322 1.281

1.554 1.939

2.569 70

>20 19.45

17.9 15.6

15.22

9.62 11.965

12.05 12.352

13.602

1.084 1.229

1.478 1.842

2.411 50

>20

>20 18.26

16.14 15.75

8.847 8.387

12.394 11.732

13.168

1.074 1.21

1.429 1.791

2.342 40

>20

>20 19.18

17.49

10.286 11.22

10.745 11.56

13.016

1.049 1.005

1.137 1.496

2.063 30

>20

>20 18.58

0.879 0.994

1.161 1.447

1.967 20

>20

>20 19.6

11.21 11.5

12.1 8.51

11.29

0.85 1.032

1.136 1.368

1.867 10

Solenoid Inductor t=7 w(μm)

s(μm)

9.78 9.98

9.81 9.596

9.282

SRF(GHz) Qmax

SRF(GHz) Q_max SRF(GHz)

Qmax

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

50 40

30 20

13.61 13.88

12.14 10.75

10.15

11.646 12.68

11.872 10.605

11.811

1.897 2.12

2.535 3.115

3.904 90

14.32 13.86

13.33 11.32

9.95

12.15 12.364

12.3 11.744

10.34

1.52 2.034

2.395 2.94

3.83 70

18.86 17.51

15.75 13.48

12.76

11.475 11.356

10.918 10.44

11.345

1.319 1.459

1.791 2.278

3.01 50

19.33 18.12

17.39 16.12

12.64

10.164 10.51

10.71 11.37

9.461

1.289 1.423

1.55 1.977

2.73 40

19.51 19.02

18.82 17.52

14.31

11.186 10.5

10.03 10.12

9.2

1.3 1.323

1.46 1.81

2.435 30

>20

>20 19.2

18.08 15.15

1.019 1.265

1.35 1.611

2.298 20

>20

>20 19.45

17.41

8.51 8.03

9.5 8.01

9.944

0.912 1.134

1.244 1.57

2.137 10

Solenoid Inductor t=9

9.78 9.98

9.81 9.596

9.282

SRF(GHz) Qmax

SRF(GHz) Q_max SRF(GHz)

Qmax

SRF(GHz) Qmax

SRF(GHz) Q_max

L(nH) L(nH) L(nH) L(nH) L(nH) L(nH) SRF(GHz)

Q_max L(nH)

50 40

30 20

13.61 13.88

12.14 10.75

10.15

11.646 12.68

11.872 10.605

11.811

1.897 2.12

2.535 3.115

3.904 90

14.32 13.86

13.33 11.32

9.95

12.15 12.364

12.3 11.744

10.34

1.52 2.034

2.395 2.94

3.83 70

18.86 17.51

15.75 13.48

12.76

11.475 11.356

10.918 10.44

11.345

1.319 1.459

1.791 2.278

3.01 50

19.33 18.12

17.39 16.12

12.64

10.164 10.51

10.71 11.37

9.461

1.289 1.423

1.55 1.977

2.73 40

19.51 19.02

18.82 17.52

14.31

11.186 10.5

10.03 10.12

9.2

1.3 1.323

1.46 1.81

2.435 30

>20

>20 19.2

18.08 15.15

1.019 1.265

1.35 1.611

2.298 20

>20

>20 19.45

17.41

8.51 8.03

9.5 8.01

9.944

0.912 1.134

1.244 1.57

2.137 10

Solenoid Inductor t=9 w(μm)

s(μm)

在文檔中玻璃基板之螺旋電感物理模型萃取技術 (頁 68-79)

結論

參考文獻

Components &amp; Technology Conference, 1998. 48th IEEE, 1998, pp.

IEEE, vol. 16, pp. 16-25, 2000.

Electronic Components and Technology Conference, 1996. Proceedings., 46th,

Bipolar/BiCMOS Circuits and Technology Meeting, 1999. Proceedings of the 1999, 1999, pp. 149-152.

Manufacturing, IEEE Transactions on, vol. 25, pp. 34-41, 2002.

Theory and Techniques, IEEE Transactions on, vol. 49, pp. 589-599, 2001.

Technologies for, 1997, pp. 139-142.

Electron Devices, IEEE Transactions on, vol. 47, pp. 560-568, 2000.

of the IEEE 2001 International, 2001, pp. 107-109.

Frequency Integrated Circuits (RFIC) Symposium, 1998 IEEE, 1998, pp.

Microwave Theory and Techniques, IEEE Transactions on, vol. 48, pp.

Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS '05. The 13th

International Conference on, 2005, pp. 1084-1087 Vol. 1.

Radio Frequency Integrated Circuits (RFIC) Symposium, 2002 IEEE, 2002, pp.

Microwave and Guided Wave Letters, IEEE, vol. 9, pp. 398-400, 1999.

附錄 A

Components & Technology Conference, 1998. 48th IEEE, 1998, pp.