Chapter 3 Theoretical analysis and structure
3.3 Inductor design
3.3.1 Simulation results
In order to quantify the improvement in area reduction, two inductor patterns, the crossed and the shifted miniature inductor, (with nominal inductance 1nH) have been designed and implemented in UMC 0.18um CMOS technology. The total length of these inductors is expected to be shorter than 200 um (folded). Furthermore, the maximal quality factor is designed near 10 G-Hz to manifest the facility in Q tuning, as mentioned in section 3.1
From (3-4), the propagation constant β and the real part characteristic impedance R of the miniature inductor are derived as 1.8 (rad/mm) and 75 Ω for the required inductance (1nH) and βl product. The HS-CPS line consists of 8um-wide traces separated by 75um gap. Five MIM capacitors, each of 16 fF, are needed to be distributed in the CPS to meet the sufficient β. The total length of the miniature inductors is 172 um and the spacing between MIM capacitors, 64 um, can be decided by the quotient (2*172 /5). The design flow of the proposed miniature inductor is shown in Fig. 3.4.
Fig. 3.5 shows the layout of one spiral and two proposed miniature inductor. The
Fig. 3.4 The design flowchart of the proposed miniature inductor Start
Decide a configuration width
Choose a strip width
Zo= 75 Ω Add MIM capacitors
between CPS
Proper quality factor Q
Zo > 75 Remove a few
MIM capacitors
Zo < 75
END
Derive the required length for 1nH
Acceptable overall length
No
Yes
Q < needed
(a)
(b) Shifted miniature inductor 100 um
172 um
Spiral symmetric inductor 115um
172 um
(c)
Fig. 3.5 Layout of (a) the spiral symmetric inductor, (b) the crossed and (c) the shifted miniature inductor
sizes of the spiral inductor and miniature inductors are 172µm by 115µm and, 172µm by 100µm respectively. In the case for the conventional spiral inductor, the spacing(s) between conductors is 2 um, and the strip width is similarly chosen as 8 um for comparison. In this example, the miniature inductors uses only 87 % of the area to achieve the same inductance as the spiral inductor and the peak Q of the miniature inductor occurs approximately near 10GHz, as shown in Fig. 3.6. However, the miniature inductor decreases self-resonance frequency to 25.5 GHz with 18.6 % degradation of the quality factor, from 22.8 to 17.2.
Moreover, Fig. 3.7 displays the effective inductance and quality factor of the crossed and the shifted miniature inductors with the same area. The shifted miniature inductor increases the quality factor by 6 %, from 16.2 to 17.4, without any degradation of self-resonance frequency. Note that the improvement in Q benefits
100 um
Crossed miniature inductor
172 um
Fig. 3.6 Effective inductance (Leff) and quality factors (Q) of the spiral and the shifted miniature inductors
Fig. 3.7 Effective inductances (Leff) and quality factors of the crossed and shifted miniature inductors.
5 10 15 20 25
Table 3.1 Inductor Comparison
from the removed underpass of the shifted miniature inductor, as demonstrated previously. The performances of the symmetric spiral inductor and the miniature inductors are summarized and compared in Table 3.1.The reduction in Q is for the reason that the energy is saved in the MIM capacitors in the form of electric energy as the phase constant β is enlarged by the increased capacitance per unit length along the transmission line. The quality factor of an inductor is defined as [2]:
Namely, it will be counterproductive that any energy is stored in the inductor’s electric field.
Frequency >30GHz 25.5 GHz 26GHz Area (um2)
3.3.2 The effect of the metal layer shunting
As shown in equation (2.1) of section 2.2, the DC series resistance can be reduced by increasing the effective thickness of the metal strip. Shunting several metal layers is a simple solution in the commercial multilevel interconnects technology without any process modifications. However, shunting of metal layers will also reduce the oxide thickness between inductor and silicon substrate and the Cox, as shown in Fig.2.6, becomes larger. It degrades the quality factor at low frequency compared to a single-layer inductor built by using only the top metal. Therefore, the tradeoff between reducing the series resistance and minimizing the Cox should be concerned. In this thesis, the inductors of a single metal layer (M6), shunted M6/M5 layers, and shunted M6/M5/M4 layers are investigated (with nominal inductance 1nH).
The quality factor of the three cases is illustrated in Fig. 3.8. It is found that the maximal quality factor can be achieved for the M6/M5 coil compared to the M6 and M6/M5/M4 inductors, especially at our design frequency (10GHz), without any degradation of self-resonant frequency. Since the M6/M5 inductor has the lowest real part of the input impedance, as depicted in Fig.3.9, the shunting of M6/M5 is the optimal choice for our design. Besides, according to the maximal quality factor of three cases, layer shunting is beneficial at lower frequencies (i.e. lower than 10 GHz in this case) where coil losses dominate but are less advantageous at higher frequencies where substrate losses are significant. The observation is also consistent with the published early work [3].
5 10 15 20
Quality factor (Q) M6M5
M6M5M4
Quality factor (Q) M6M5
M6M5M4 M6 M6M5 M6M5M4 M6
Fig. 3.8 Quality factor comparison of shunting of three (M6/M5/M4), two (M6/M5), and the top metal layer (M6)
5 10 15 20
Fig. 3.9 Quality factor comparison of shunting of three (M6/M5/M4), two (M6/M5), and the top metal layer (M6)
3.3.3 The effect of the arrangement of MIM capacitors
In order to find out the effect of the arrangement of MIM capacitors, the performance of two miniature inductors containing eight 3.16x3.16um2 and two 6.32x6.32 um2 MIM capacitors respectively, as shown in Fig.3.10, are compared with the aforementioned miniature inductor including five 16x16um2 MIM capacitors. That is, the total inserted capacitance remains the same but the number of MIM capacitors is different. Fig.3.11 and Fig.3.12 show the simulation results of the effective inductance and quality factor of three miniature inductors individually. It is found that there is no significant difference between three miniature inductors. In other words, the arrangement of MIM capacitors does not matter.
172 um
100 um
8 um 6.32 um
(a)
172 um
100 um
8 um 3.16 um
(b)
Fig. 3.10 The miniature inductors of (a) two 6.32x6.32 um2
5 10 15 20
Leff (nH) 5 cell8 cell
2 cell
Leff (nH) 5 cell8 cell
2 cell
Quality factor 5 cell
8 cell
Quality factor 5 cell
8 cell
3.3.4 The performance of the inductor consists of different phase constant (β) HS-CPS
In order to evaluate the relationship between phase constant (β) and inductor parameters, two analyses are conducted.
First, this analysis is under the constraint that the inductor is made of constant characteristic impedance transmission line. The strip width of the HS-CPS can be reduced and the capacitance of MIM capacitors can be inserted for higher inductance and capacitance per unit length along the HS-CPS. Therefore, the higher phase constant (β) and shorter required length can be obtained. However, as the strip width shrinks, the series resistance of the HS-CPS would rise up leading to the degraded quality factor. That is, the trade-off between phase constant and series resistance should be made. Three HS-CPS structures of different strip width, 3μm, 8μm, and 13μm, as depicted in Fig.3.13, are investigated. Through the simulator, ADS momentum, MIM capacitors of different capacitance, 21.6fF, 16fF, and 13.1 fF are used in the three HS-CPS structures respectively to maintain the same characteristic impedance, 70 Ω at 10 GHz. Phase constant (β), quality factor of the inductors, and imaginary part of characteristic impedance, overall attenuation, i.e. the product of attenuation constant and inductor length, are given in Fig.3.14 and Fig. 3.15 (a), (b), (c). The corresponding phase constant at 10 GHz of HS-CPS of three strip width is 1.63, 1.38, and 1.14, respectively. According to equation (3.4), the inductors with effective inductance 1nH are designed and overall length of three configurations, 0.449 mm, 0.558 mm, and 0.643 mm, is required.
As shown in Fig.3.14 and 3.15(a), the highest phase constant is obtained by the HS-CPS of 3µm strip width with value about 1.63 but the quality factor is the lowest
13µm strip width has the least phase constant but the most superior quality factor.
According to (3.5), the imaginary part of characteristic impedance of the HS-CPS of 13µm strip width reaches the highest value with 0.858 and compensates the significant overall attenuation, as given in Fig. 3.15(b), (c), Although the HS-CPS of 8µm strip width shows the least overall attenuation, the imaginary part of characteristic impedance is not large enough to maximize the quality factor.
Second, the inductors are formed by the HS-CPS with different characteristic impedance and phase constant. Three HS-CPS structures of different MIM capacitors spacing, 32 μm, 64 μm, and 128 μm, depicted in Fig.3.16, are investigated. The strip width and spacing between strips is fixed at 8μm and 84 μm. The MIM capacitors are inserted for higher capacitance per unit length along the HS-CPS.
Therefore, the higher phase constant (β) and shorter required lengthcan be obtained.
Through the simulator, ADS momentum, the phase constant (β), real part of characteristic impedance, quality factor is given in Fig.3.17 and Fig. 3.18(a), (b). As shown in Fig.3.17 and Fig. 3.18(a), the corresponding phase constant of three HS-CPS configurations is 1.78, 1.31, and 1.14, respectively. According to equation (3.4), the inductors with effective inductance 1nH are designed and the required length is 0.497 mm, 0.558 mm, and 0.6 mm, separately. The highest phase constant is obtained by the HS-CPS of 32 µm MIM capacitors spacing with value about 1.78 but the real part of characteristic impedance is the lowest one due to the increased distributed capacitance. The quality factor of the HS-CPS of 1.14 phase constant reaches the highest value about 16.9, as shown in Fig. 3.18(b).
Above all, the trade-off between phase constant and quality factor (Q) should be made. By shrinking the strip width and inserting the MIM capacitors, the higher phase constant and size reduction will be available but the quality factor is degraded
simultaneously.
3.3.5 The influence of folded HS-CPS
In this section, the effect of the folded HS-CPS is studied. Two folded structures, crossed and shifted patterns, are proposed in this thesis and the crossed configuration is taken as an instance. Two HS-CPS structures, unfolded and folded, depicted in Fig.3.19 (a), (b), are analyzed. Both configurations have the same strip width, 8um, and MIM capacitors distribution (16 fF per 64μm).
By 2.5D simulator, ADS momentum, distributed inductance (L), capacitance (C), resistance (R), and conductance (G) per mm of the two HS-CPS structures are given in Fig. 3.20(a), (b), (c), (d). According to Fig 3.20(a), (b), the folded structure has higher inductance per mm than unfolded one since magnetic flux of the folded structure is enhanced due to positive mutual inductive coupling. However, the folded structure would also show higher distributed capacitance due to the decreased spacing between strips from 84μm to 64μm and the capacitive effect of two adjacent HS-CPS. Besides, as depicted in Fig 3.20(c), (d), since the current distribution is disturbed and the induced eddy current in the inner HS-CPS, the series resistance per mm in the folded formation is increased. In addition, the folded structure shows better immunity to substrate due to the lower distributed conductance.
From viewpoints of wave characteristics, the behavior of transmission line can be sketched with propagation constant (γ) and characteristic impedance (Zo). Real and imaginary part of propagation constant and characteristic impedance of the two HS-CPS structures is illustrated in Fig. 3-21(a),(b), and Fig. 3-22(a),(b). According to [6], the two HS-CPS structures satisfy the low-loss conditions and the propagation constant and characteristics impedance can be expressed as:
LC
where R, L, C, G are the distributed transmission line parameters. According to (3.6) and (3.7) and the observation on transmission line parameters as aforementioned, the trend and variation of propagation constant and characteristic impedance of unfolded and folded patterns can be explained sufficiently.
(a)
(b)
(c) 3 um
0.449 mm
4.65 um 100 um
3 um
0.449 mm
4.65 um 100 um
100 um 0.558 mm
8 um
4.0 um 100 um
0.558 mm 8 um
4.0 um
100 um 13 um
0.643 mm
3.62 um 100 um
13 um
0.643 mm
3.62 um
Fig. 3.13 Three HS-CPS structures of (a) 3 μm strip width (b) 8 μm strip width (a) 13 μm strip width
0 5 10 15 20
0 5 10 15 20 25
Frequency (GHz)
Q ua lity fa ct or
β=1.14 β=1.31 β=1.63
(a)
0
1 2 3 4
0 5 10 15 20 25
Frequency (GHz)
B et a (r ad/ m m )
width=13 um width=8 um width=3 um
Fig. 3.14 phase constant of the HS-CPS structures with different strip width
0.000 0.015 0.030 0.045 0.060
0 5 10 15 20 25
Frequency (GHz)
al pha* l (N eper )
β=1.14 β=1.31 β=1.63
(c)
Fig. 3.15 (a) quality factor, (b) imaginary part of characteristic impedance (c) overall attenuation (Neper) of the HS-CPS structures with different phase constant.
-10 -5 0 5
0 5 10 15 20 25
Frequency (GHz)
Im ag(Zo) (ohm s)
β=1.14 β=1.31 β=1.63
(b)
Fig. 3.16 Three HS-CPS structures of different spacing between MIM capacitors (a) per 32μm (b) per 64 μm (a) per 128 μm
0 1 2 3 4 5
0 5 10 15 20 25
Frequency (GHz)
B eta(rad/m m )
spacing=128 um spacing=64 um spacing=32 um
Fig. 3.17 phase constant of the HS-CPS structures with different spacing between MIM capacitors
0 5 10 15 20
0 5 10 15 20 25
Frequency (GHz)
Quality factor
β=1.14 β=1.31 β=1.78
(b)
Fig. 3.18 (a) real part of characteristic impedance (b) quality factor for the 1nH inductor of the HS-CPS structures with different phase constant
0 20 40 60 80 100
0 5 10 15 20 25
Frequency (GHz)
re al( zo ) ( oh ms )
β=1.14 β=1.31 β=1.78
(a)
100 um 8 um
4 um
344 um
100 um 8 um
4 um
344 um
(a)
8 um
4 um
172 um
100 um 8 um
4 um
172 um
100 um
(b)
Fig. 3.19 (a) unfolded (b) folded HS-CPS structures
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0 5 10 15 20
Frequency (GHz)
L (nH/m m )
unfolded folded
(a)
0 100 200 300 400 500
0 5 10 15 20
Frequency (GHz)
C ( fF /mm )
unfolded folded
(b)
0 2 4 6 8 10
0 5 10 15 20
Frequency (GHz)
R (ohms/ mm)
unfolded folded
(c)
0 300 600 900 1200 1500
0 5 10 15 20
Frequency (GHz)
G ( uS / mm )
unfolded folded
(d)
Fig. 3.20 (a) Inductance (b) capacitance (c) resistance (d) conductance per mm of the unfolded and folded HS-CPS
0.00 0.03 0.06 0.09
0 5 10 15 20
Frequency (GHz)
al pha( N eper /m m )
unfolded folded
(a)
0 1 2 3 4 5
0 5 10 15 20
Frequency (GHz)
B et a(ra d/ m m )
unfolded folded
(b)
Fig. 3.21 (a) real part (attenuation constant) (b) imaginary part (phase constant) of propagation constant of two HS-CPS structures
40 50 60 70 80
0 5 10 15 20
Frequency (GHz)
real( zo) ( ohm s)
unfolded folded
(a)
-12 -9 -6 -3 0 3
0 5 10 15 20
Frequency (GHz)
Im ag( Zo) ( ohm s)
unfolded folded
(b)
Fig. 3.22 (a) real part (b) imaginary part of characteristic impedance of two HS-CPS structures
CHAPTER 4
Experimental results and application of the miniature inductor
In this chapter, the experimental results of the proposed miniature inductors which are fabricated in UMC 0.18 technology are presented. The measurement test structure and the de-embedding procedures used to extract the experimental results are described as well. Besides, the 5-GHz CMOS LC-VCO has also been fabricated in TSMC 0.18 technology to verify the functions of the miniature inductors.
4.1 Measurement results and discussions
4.1.1 Measurement setup
Figure 4.1 shows the measurement setup. The raw S-parameters of the device under test (DUT) were measured by HP 8510 Network analyzer and Cascade Microtech probe station. Measuring with the RF probes, as illustrated in Fig.4.2, GSG-pads consist of three 80μm by 80μm square pads where the DUT is the proposed miniature inductor in this thesis. The spacing between two pads from center to center is 150 μm.
4.1.2 De-embedding method
Since the parasitic effects of the GSG pads should be removed to acquire the intrinsic S-parameters of the DUT, a process called “de-embedding” should be performed for a complete two port calibration. A general procedure of de-embedding consists of open circuit, short circuit, and through circuit de-embedding (OSTD) and is used in this measurement. The equivalent circuit model of the parasitics of the pad
Fig. 4.1 Experimental set up for measurement
G
S
G
G
S
G
RF Probe RF
Probe
Fig. 4.2 Coplanar GSG RF probes and the DUT
HP 8510 Network Analyzer
Coplanar GSG Probe
DUT
port1 port2
and interconnect (Zi ,yp,Zl) and DUT is depicted in Fig. 4.3(a). After the input impedances of the open (Zin, open), short (Zin,short), and through (Zin,through) pads, as depicted in Fig. 4.3 (b) are measured, the three parasitics (Zi ,yp,Zl) can be extracted from the following equations:
short
The ABCD matrix of the DUT,
D DUT
Therefore, the S-parameters of the DUT,[ ]S DUT, can be derived from:
[ ]
(a)
(b)
Fig. 4.3 (a) The equivalent circuit model of the DUT and the parasitics of the pads and
Zi Z
yp
Zi
Z
yp
Zen, through
S
G
S
G Zi
Z
in,shortZi
Z
in,openyp
S
G
S
G
ZiZL DUT
yp
Zi ZL
yp
S
G
S
G
Then, we can derive the differential one port S parameters (Sd) from the single-ended
and the corresponding input impedance for differential excitation
⎟⎟⎠
As mentioned in section 2.3, the effective inductance and quality factor can be written in terms of Zd :
4.1.3 Measurement results and discussions
The micrograph of test chip is shown in Fig.4.4. The upper and lower hand corner
Fig. 4.4 Micrograph of test chip
pattern is crossed and shifted inductor, respectively. The upper and lower right hand corner is de-embedding pattern and conventional spiral inductor. The measurement results of three patterns together with simulation results are shown in Fig. 4.5, 4.6, and 4.7 and are summarized in Table 4.1. The solid line shows the measured data and the curve with square marker presents the simulation data.
For effective inductance, good agreement with the simulation is shown with only minus 0.06 nH that is nearly 6 % deviation, maximally for all three inductor patterns and the effective inductance is about 0.92 nH at 10 GHz. Moreover, the self resonant frequency of the crossed and shifted inductor is 27.5 and 26.2 GHz, respectively. The increment about 1~1.5 GHz is mainly due to the slight deviation of the inductance. The resonant frequency of spiral inductor is more than 40 GHz as expected.
As shown in Fig.4.5 (b) and Fig.4.6 (b), the measured Q of the crossed, shifted and spiral inductor is 13.9, 13.3, and 16.9 at 10 GHz, individually. The measured Qmax
is near 10GHz as we artificially designed. Besides, the measured Q of spiral inductor is 15.3 at 10 GHz. However, there is a discrepancy of measured and simulated Q observed during 5~15 GHz. Since there is no significant difference between measurement and simulation results in inductance, the degradation in quality factor implies the raising of input impedance according to the definition of quality factor. As shown in Table 4.2, the increment of input impedance ranges from 0.33 to 0.8 ohms.
Even though the order of increment is lower than 1 ohm, that still puts the dramatic influence on quality factor especially near its maximal. This addition might source from the contact resistance during on-wafer probing and insufficient-deembedding of thru parasitics. First, the typical contact resistance of a probe is 0.03~0.15 ohms [7] in case the touchdown is regular and repeatable. As probing is not so perfect, the extra
contact resistance is generated and the decrease of quality factor follows. Compared with the larger inductance measurement, the smaller inductor in our case is more sensitive to the increased contact resistance. Next, as depicted in Fig. 4.8 , the resistance of thru parasitics might be lower than usual during 5 ~ 15 GHz and it results in the insufficient deembeding for the interconnect between pad and inductor.
This also raises the measured resistance of the inductor.
5 10 15 20 25
5 10 15 20 25
10 20 30
5 10 15 20 25
Fig. 4.8 the measured resistance of through parasitics
Table 4.1 Summary of simulated and measured results of proposed miniature
inductor and conventional spiral inductor
Area(um2) 172*100 172*100 172*115
A.R. -13 % -13 %
Table 4.2 The measurement and simulation results of input impedance for three inductor patterns
4.2 Circuit application
Differentially driven symmetric inductor is widely used in balance circuit applications, such as VCO. The 5-GHz LC-VCO utilizing the proposed miniature inductor is implemented in TSMC 0.18μm technology.
4.2.1 Design Flow and Simulation Results
The schematic of oscillator circuit is depicted Fig. 4.9, which uses a complementary structure to omit a connection to the common-mode point of the inductor. It is possible to use only one symmetric inductor in this design. Besides, the crossed coupled pair formed by NMOS and PMOS transistors is used to generate a negative conductance and the output buffer is realized by a common-drain PMOS transistor. Providing the sufficient bias current for VCO, the current mirror comprises an N+ diffusion resistor (R2) and two PMOS transistors, which have larger channel width to suppress the thermal noise.
The tank of LC-VCO consists of the proposed miniature inductor and group 3(G3) varactor available in TSMC process. The tunable capacitances range from 0.4pF to 1.8pF with different applied voltage at 5GHz, as shown in Fig.4.10.
Accordingly, the single-turn inductor with the nominal inductance 0.7nH is needed to form a 5GHz resonator. Just as the design flow illustrated in Fig.3.4, there are several steps to design a miniature inductor. First, since the Q of resonator has significant effects on phase noise in a LC-tank VCO, the wider strip width (25μm) is adopted to improve the quality factor of the miniature inductor. Next, in order to satisfy the βl product (17o)and the expected length (300 μm), the required phase constant β and real part characteristic impedance R is 1.54 (rad/mm) and 27.9 ohms, respectively.
Then, three MIM capacitors, each of 21.5 fF, are uniformly distributed
M1 M2
M3 M4
M5 M6
M7 M8
Vdd
Vcontrol
M3
C1 C2 R1 R2
Bias-T Bias-T
Fig. 4.9 Schematic of 5GHz LC-VCO circuit utilizing the proposed miniature inductor
within the CPS and the distance between two MIM capacitors can be estimated by the quotient of (300/3). Finally, finely tuning the spacing between the CPS is to have the sufficient effective inductance. The dimensions, effective inductance, and quality factor of the single-turn inductor and miniature inductor, for the same inductance, are shown at Fig.4.11(a),(b),and (c) individually and are summarized in Table 4.3. As expected, the proposed miniature inductor uses 90% of the area of the single turn inductor for the same inductance.
Simulation results of phase noise and tuning range of the voltage-controlled
Simulation results of phase noise and tuning range of the voltage-controlled