Transmission line structures with floating shields

Each distinct conventional transmission line suffers from its own unique type

of loss as a result of structural limitations. Since there are no shields between the CPW and the highly conductive substrate, the dominant loss is the energy coupled to the substrate. In contrast, substrate-induced losses are not critical to the MS lines as a result of the ground plane that exists under the signal line. As the scaling of backend processes continues to trend downward, the height between the signal line and the ground plane becomes significantly reduced, which results in the need for a narrower signal line to achieve the desired characteristic impedance. Therefore, ohmic losses in MS lines are increased significantly. Following investigations, a CPW transmission line using periodical floating shields combining the advantages of both CPW transmission lines and MS lines is proposed, as shown in Fig. 2-5, where the SL is the strip length and the SS is the strip spacing. The concept of floating shields is adopted in order to shield the silicon substrate and achieve a compact transmission line structure. Passive devices with substrate shields that can be isolated from other circuit sub-blocks are required for the high-frequency circuit design.

To observe and estimate the substrate loss of a transmission line, the EM simulator is first adopted to evaluate electric field distribution in the substrate. The energy loss to the substrate from CPW transmission lines and slow-wave transmission lines is estimated by integrating the electric energy density ( )

2

1 _*

E Er⋅ r

ε within the substrate volume as

∫

1ε r r_* , and the result is

summarized in Table 2-1, where ε is the absolute permittivity, and Er is the electric field intensity. As expected, the energy loss to the substrate is increased as

the width of the signal line or the space between the signal line and the ground lines increases. Moreover, the substrate loss of a CPW without floating shields is higher than that of a CPW with floating shields. In summary, a CPW with substrate shields illustrates that the presence of the shield can minimize the energy being coupled to the substrate, thereby reducing the attenuation loss. As can easily be observed from the Table 2-1, the substrate loss is higher if the SS is wider in floating shield design.

2.2 The Optimization of Slot-Type Floating Shields

A schematic view of a slow-wave CPW transmission line structure with slot-type floating shields is shown in Fig. 2-6(a), where the SL is strip length and the SS is strip spacing. The advantage of using slot-type floating shields is that slow-wave transmission lines have a lower electric field leakage to the substrate and a lower conductor eddy-current loss, especially at high frequencies. Fig. 2-6(b) shows the electric field distributions from a 3D EM simulation of slot-type floating shields. The electric field starts from the signal line, couples to the floating shields, and finally terminates on the coplanar ground conductors. Therefore, the effective dielectric thickness of devices with floating shields is larger than that of devices with grounded shields. Thus both capacitance and electric field intensity of devices with floating shields are smaller than those of devices with grounded shields, which leads to lower conductor eddy-current loss. Generally, lower attenuation loss and higher effective relative permittivity are required to achieve a high

performance transmission line and a compact size is desired. Consequently, the incorporation of floating shields into transmission lines as an alternative approach for better performance at high frequencies can be considered.

If the length of the periodical structure is short compared to the wavelength, each segment of the signal line can be modeled by an inductance and capacitance lumped-element equivalent circuit, as shown in Fig. 2-7(a), where inductance (L) and capacitance (C) are the series inductance and the shunt capacitance per unit length, respectively. The density, R, of the slot-type floating shields is defined as:

SS SL R SL

= + (5) Segment I, on top of the open slot, can be modeled by a series inductance L(1-R)(Δz) and a shunt capacitance C(1-R)(Δz). While Segment II, on top of the shield metal line, can be modeled by a series inductance L(RΔz) and an increased shunt capacitance (nC)(RΔz) where n represents the increased ratio in the capacitance as a result of coupling to the slot-type shields, and Δz denotes the differential unit length. When two segments are cascaded together, the combined equivalent circuit can be condensed as shown in Fig. 2-7(b). It should be noted that the equivalent circuit shown in Fig. 2-7(b) is valid only when n is >> 1.

Consequently, the phase velocity Vp with the slow-wave effect can be expressed as:

) (

*

0 1

nR LC Vp c

r r

⋅ =

= μ ε (6)

The slow-wave phenomenon can be explained by equation (6), which shows the

phase velocity is decelerated by a factor of nR .

An optimization of the slot-type floating shields was performed in order to reduce the attenuation loss and also increase the slow-wave features. Both wavelength and attenuation loss can be adjusted by changing both the SL and the SS of the slot-type floating shields while retaining the same area. Optimization analysis of the SL and SS was conducted by evaluating the EM simulation results for structures with a variety of SL and SS dimensions while retaining the same area.

An semi-empirical equation is derived to relate the effective relative permittivity

ε

582 . 0 ) (

52⋅ ^0.47 ⋅ ^0.167 +

= R SL⁻

εr (7) The correlation coefficient of the semi-empirical equation in (7) is around 0.91, as shown in Fig. 2-8, which is valuable for predicting the optimized relative permittivity. The calculated values approximate well to the simulation results at 50 GHz, as illustrated in Fig. 2-9(a), which exemplifies the slow-wave equation (6) that predicts that a higher density of slot-type floating shields results in a higher effective relative permittivity. Furthermore, Fig. 2-9(a) indicates that a higher effective relative permittivity is obtained when the SL is smaller. The parameter SL has been explicitly introduced into equation (7). When the attenuation loss performance is taken into consideration, it becomes even more obvious that a minimized SL is the best choice for slot-type floating shield design, as illustrated in Fig. 2-9(a). Though the high-density shields minimize the exposure of the signal line to the substrate, field leakage to the substrate can be reduced. However, the

consequence of using high-density shields is that the conductor eddy-current loss is high, and this in turn increases the attenuation loss. In contrast, the opposite is true when the density of the slot-type floating shields is low. There is a trade-off between the slow-wave effect and the attenuation loss in slow-wave CPW transmission lines; namely, that while the wavelength is reduced to facilitate the implementation of smaller devices, greater attenuation loss may be induced by the eddy-current loss on the slot-type floating shields. The optimization index of the slot-type floating shields is defined as ε_r．α^-1 in mm/dB, and Fig. 2-9(b) shows that the optimized performance is achieved when the density R is equal to 0.2 where the SL=1.2 um and the SS=4.8 um. If the specification requirement for the attenuation loss is first determined, then the density of the slot-type floating shields can be calculated. Consequently, the effective relative permittivity can be predicated from the minimum SL and the density of the slot-type floating shields.

2.3 Experiment Results

Five types of transmission lines were fabricated by using CMOS technology, as listed in Tables 2-2 and 2-3, including (1) a CPW transmission line without shields (CPW), (2) five slow-wave CPW transmission lines with slot-type floating shields (FSCPW1, FSCPW2, FSCPW3, FSCPW4, and FSCPW5), (3) a slow-wave CPW transmission line with slot-type grounded shields (GSCPW1), (4) an MS transmission line with plane grounded shields (MS), and (5) four slow-wave MS transmission lines with slot-type grounded shields (SMS1, SMS2, SMS3, and

SMS4). A slow-wave CPW transmission line with slot-type floating shields was designed with slot-type floating shields located periodically beneath the CPW structure, and the slot-type floating shields are oriented transversely to the CPW structure. For all transmission lines listed in Table 2-1, the signal line is formed on the tenth (M10) metal layer and the slot-type shields are created on either the ninth (M9) or eighth (M8) metal layer. The CPW part of the structure has a signal/ground line width of 30 um/10 um, with a 30 um space between the signal and the ground lines. In the slot-type floating shields, the SL is at the minimum length allowed by the design rules to achieve a high performance with a minimized eddy-current loss. The minimum length on M8 is 0.07 um and on M9 is 0.4 um for 45 nm CMOS technology. The slot-type floating shields are designed with the following dimension splits: (1) the SL on M8 is 0.07 um and the accompanying SS is 0.07 um, and (2) the SL on M9 and M8 is 0.4 um and the accompanying SS varies between 0.4 um, 1.6 um, and 3.2 um. For the grounded slow-wave CPW transmission line, it is designed with a similar structure to the slow-wave CPW transmission line with floating shields as described above, but with the slot-type shields connected to the ground. This grounded slow-wave CPW is included for the comparison purpose. A CPW with the same signal/ground line structure but without shields is also included for comparison. The slow-wave MS transmission lines with slot-type grounded shields have a similar structure to the conventional MS lines, but the slot design is used on the ground plane. Similarly, an MS line with the same signal structure but plane shields is also included for comparison.

The backend metal scheme is a dual-damascene copper process with dielectric SiO₂ material that has an effective relative dielectric constant of around 5.4 used as insulator layers. All test structures have the same length of 400 um and width of 120 um to ensure a fair comparison between the different designs. The S-parameters of the transmission line test structures were measured up to 50 GHz using an Agilent 8510C network analyzer.

Fig. 2-10(a) shows that the attenuation loss of a CPW with slot-type floating shields is lower than the CPW without shields. It also shows that at frequencies above 50 GHz, slot-type floating shields on M8 is needed as it has the least amount of eddy-current loss on the floating shields. Among the CPW designs with slot-type floating shields, in the 30-50 GHz frequency range, the attenuation loss of an SL of 0.4 um and an SS of 0.4 um on M8 is less than that on M9, because the dielectric thickness between the signal line on M10 and the floating shields on M8 is 3.2 um, which is thicker than the dielectric thickness between the signal line on M10 and the floating shields on M9 (0.74 um). By now, it can be concluded that the smaller the SL, the wider the SS, and the greater the thickness between the signal line and the floating shields, the lower the attenuation loss will be induced.

Fig. 2-10(b) compares the effective relative permittivity constants of different CPW designs, both with and without floating shields. In slow-wave CPW transmission lines with slot-type floating shields, a reduction in wavelength results in a corresponding increase in both the phase constant and the effective relative permittivity, pursuant to the relationship

λ

β = ²π and ε_r =52⋅(R^0.47⋅SL^−0.167)+0.582.

The effective relative permittivity increases to 51 at 50 GHz, for the CPW with shields on M9 where SL = 0.4 um and SS = 0.4 um. This is an improvement by a factor of more than 9 compared to a conventional CPW transmission line. As expected, the wider the SS and the greater the dielectric thickness between the signal line and the floating shields, the lower the effective relative permittivity will be obtained. Conventional passive devices in RF circuit design do not gain as much benefit from CMOS scaling as active devices. Passive devices play the role of a bottleneck in area reduction and performance improvement. Since the SL and the SS can be adjusted along technology scaling, a scaled slow-wave CPW can continue to offer lower attenuation loss and higher effective relative permittivity, a significant advantage for future technology scaling, which is a great breakthrough for RF circuit design.

An optimized design requires a good quality factor,

α β

= 2

Q whereβ is the phase constant and α is the attenuation loss. Therefore, the quality factor should be used to judge an overall trade-off between attenuation loss and effective relative permittivity. Guidelines for designing a transmission line with a high quality factor are illustrated in Fig. 2-10(c). The crossover of the quality factor is around frequencies of 30 GHz, so the appropriate choice for designs operating at frequencies below 30 GHz is to create floating shields on M9 with an SL of 0.4 um and an SS of 0.4 um. At frequencies in the range of 30 to 50 GHz, floating shields on M9 with an SL of 0.4 um and a variety of SS values is preferred. As a result, a quality factor of 18 can be achieved at 40 GHz, which is more than 6 times that of

a conventional CPW transmission line, whose value is around 2.8. At significantly higher frequencies above 50 GHz, floating shields on M8 are strongly recommended. The wider the SS, the lower the attenuation loss will be obtained, but the corresponding effective relative permittivity will also be lower. As discussed above and as demonstrated in the experiments, the designers must weigh among SL and SS dimensions, as well as metal layer positions, to design a proper slow-wave CPW with slot-type floating shields with a good quality factor to achieve a functional circuit at the operating frequency.

Fig. 2-10(d) shows that the characteristic impedance can be tuned by changing the SL, the SS, and the metal layer position of the slot-type floating shields. A low characteristic impedance can be achieved by increasing slot-type floating shield density or higher metal layer position. Characteristic impedance tuning by changing the metal density and metal layer position in the slot-type floating shields is also a new design approach.

Furthermore, the wavelength of a transmission line indicates if the transmission line design is compact in size. The wavelengths of transmission lines with a variety of slot-type floating shield design are compared in Fig. 2-10(e), which indicates that the best choice is FSCPW1 with floating shields on M9, SL = 0.4 um and SS = 0.4 um. The wavelength of FSCPW1 is reduced to 0.85 mm, i.e., is by a factor of more than 3 as compared to a conventional CPW transmission line, whose wavelength is 2.63 mm. The reduction in chip area and wavelength for FSCPW1, FSCPW2, FSCPW3, FSCPW4, FSCPW5, and GSCPW1 in terms of

percentage and wavelength are illustrated in Fig. 2-11. A saving in silicon area of more than 67% can be achieved for FSCPW1, which demonstrates that this approach could have extremely high potential for MMIC applications.

A slow-wave CPW transmission line with slot-type grounded shields is shown in Fig. 2-12(a). The slot-type shields are connected to ground by two parallel conductors added at the two ends of the slot-type shields. When the shields are grounded, the electric field starts from the signal line and terminates directly on the grounded shields, as illustrated in Fig. 2-12(b). In Fig. 2-13(a), the measured capacitance of the devices with grounded shields is higher than that of the devices with floating shields, which implies that the effective dielectric thickness of the devices with grounded shields is smaller than that of the devices with floating shields. Consequently, the electric field intensity of the devices with grounded shields is larger than that of the devices with floating shields, resulting in the eddy-current loss induced by increased voltage variation at extreme high frequency.

As the signal frequencies increase, the number of voltage variations between the positive and the negative potential in unit time increases, resulting in an increase in eddy-current loss on the grounded shields and the eddy-current loss on the conductors is proportional to the square of the frequency. Since the presence of the grounded shields increases the slow-wave feature as compared to floating shields, the wavelength of the grounded slow-wave transmission line is shorter than that of the floating slow-wave transmission line, as illustrated in Fig. 2-13(b). Although the increase in the slow-wave feature facilitates the fabrication of relatively smaller

devices, higher electric field intensity will enhance the eddy-current loss on the grounded shields.

The optimization index of the slot-type floating shields is defined as ε_r．α^-1 in mm/dB, and Fig. 2-14 shows that the optimized performance is achieved when the density R is equal to 0.2 where the SL=0.4 um and the SS=1.6 um. If the specification requirement for the attenuation loss is first determined, then the density of the slot-type floating shields can be calculated. Consequently, the effective relative permittivity can be predicated from the semi-empirical equation in (7) related to minimum SL and the density of the slot-type floating shields. Then, the transmission line length can be calculated, which is useful information for circuit designers.

A slow-wave MS transmission line with slot-type grounded shields is shown in Fig. 2-15. The slot-type technique is designed on the plane ground and two parallel conductors are added to the two ends of the slot-type shields. The flexible characteristic impedance range can be obtained by adjusting the distance between the two substantially identical parallel conductors. The characteristic value varies with the different inductance return paths. The measured results show that a 218%

improvement in characteristic impedance at 50 GHz (from 34.91^Ω to 76.37^Ω) is achieved through an adjustment of the strip width to 66 um, as illustrated in Fig.

2-16(a). Flexible characteristic impedance can be easily obtained by adjusting the strip shield width or SS. If the strip shield width between the parallel conductors is increased, a larger inductance return loop will be created, resulting in higher

characteristic impedance. In contrast, the opposite is true when the strip shield width is decreased. Also, a smaller capacitance can be obtained if the SS is increased, resulting in higher characteristic impedance. Similarly, the opposite is true if the SS is decreased. Accordingly, the desired characteristic impedance can be obtained by adjusting either the position of the two parallel conductors or the SS value. Another significant improvement is a 42.5% saving in silicon area with the wavelength reduced from 2.03 mm to 1.16 mm) at 50 GHz when the strip width is increased to 66 um, as indicated in Fig. 2-16(b). Thus, the wavelength can be reduced to facilitate implementation in smaller devices.

2.4 Conclusion

High performance slow-wave transmission lines with optimized slot-type floating shields have been analyzed. It has been shown that the wavelength, attenuation loss, and characteristic impedance can be adjusted by the SL, the SS, and the metal layer position of the slot-type floating shields while retaining the same area. A semi-empirical equation that can predict a rough value for the effective relative permittivity has been presented. An optimization index of the floating slow-wave CPW transmission lines has been developed to enable circuit designers to expediently determine the most appropriate slot-type floating shields to meet design specifications. The designers must weigh among SL and SS

High performance slow-wave transmission lines with optimized slot-type floating shields have been analyzed. It has been shown that the wavelength, attenuation loss, and characteristic impedance can be adjusted by the SL, the SS, and the metal layer position of the slot-type floating shields while retaining the same area. A semi-empirical equation that can predict a rough value for the effective relative permittivity has been presented. An optimization index of the floating slow-wave CPW transmission lines has been developed to enable circuit designers to expediently determine the most appropriate slot-type floating shields to meet design specifications. The designers must weigh among SL and SS