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THE increasing demand for powerful electronic devices resulted in a growing need for large scale mixed-signal system-on-chips (SoCs), requiring the integration of digital circuits and analog/RF circuits on the same chip [1]. Analog/RF circuits in mixed-signal SoCs, however, often suffer from performance deterioration because of the substrate noise generated by digital circuits. This is especially the case when CMOS processes with lightly doped substrates are used for the implementation to reduce the cost [2]. Formula${\rm P}^{+}$ guard ring is a layout design approach and one of the most widely used noise suppression methods in modern SoCs as it features low cost and easy implementation [2], [3]. Fig. 1 shows a generic Formula${\rm P}^{+}$ guard ring implemented on a typical lightly doped CMOS substrate. The aggressor contact represents the noise coupling node in digital circuits and the victim contact represents the coupling node of any analog/RF circuits on the same chip. The noise suppression performance of the guard ring is dependent on layout and substrate parameters [2], such as the aggressor-to-guard ring distance Formula$(d_{\rm ag})$, guard ring-to-victim distance Formula$(d_{\rm gv})$, guard ring width Formula$(w_{g})$, resistivity/permittivity of the substrate Formula$(\rho_{1,2}/\epsilon_{{\rm ox},1,2})$, and substrate thicknesses Formula$(t_{{\rm ox},1,2})$.

Figure 1
Fig. 1. (a) Top view and (b) cross-sectional view of a generic Formula${\rm P}^{+}$ guard ring implemented on a lightly doped CMOS substrate.

Currently, the guard ring parameters are mainly investigated by measurements and designed based on empirical rules-of-thumb [2], [3]. However, the noise suppression level of these designs is usually unpredictable and the chip area could easily be wasted as the dependency of the noise suppression performance on guard ring parameters has not been accurately characterized. Recently, efforts have been made to find compact Formula${\rm P}^{+}$ guard ring models, which provide more insights into the dependency [4], [5], [6], [7]. Some of these models require fitting-factors [4], which needs calibration fixtures and therefore are unfeasible for prelayout predictions. Some of the models characterize the guard ring by dividing the guard ring into numerous small contacts/cells [5], [6], which increases the model complexity significantly. Other models failed to address the constriction resistances as well as capacitive coupling, which makes them valid only for low frequency designs on uniform or epitaxial substrates [7]. Unlike uniform or epitaxial substrates, the lightly doped substrates of standard CMOS processes have a thin P-well layer [Fig. 1(b)]. The P-well layer introduces significant current constriction effects at near fields close to the contacts [8]. Such effects cannot be effectively characterized by existing guard ring models. To obtain accurate noise suppression predictions and to help SoC designers to manage the noise issues, new guard ring models feasible for lightly doped substrates are desired.

This paper proposes a Formula${\rm P}^{+}$ guard ring model where constriction resistances and capacitive coupling are included. Equations are derived based on a conformal mapping approach to fully characterize the effects of the layout/substrate parameters, eliminating any fitting factors. Electromagnetic (EM) simulation and experimental verifications on DC resistances and S-parameters have been conducted as well. This paper is arranged as follows. Section II presents the proposed model. EM-simulation validation is presented in Section III, and the experimental verification as well as design guidelines are discussed in Section IV. Conclusions are drawn in Section V.



The proposed three port circuit network model for the guard ring in Fig. 1 is shown in Fig. 2. The proposed model includes both the resistive and capacitive couplings between the aggressor, guard ring, and victim, as represented by ports Formula$a$, Formula$g$ and Formula$v$, respectively. Please note that the model does not include the interconnection of the guard ring to on-chip ground (GND). In the proposed model, Formula$C_{\rm ag}$, Formula$C_{\rm gv}$ denote the capacitances between the aggressor, guard ring, and victim in the oxide layer, respectively. For typical CMOS processes, where the P-well layer is significantly more conductive and two to three orders thinner than the P-substrate, the majority of the noise current flows horizontally from the aggressor to the victim in the P-well. This means, there is no current flowing into the P-substrate except at the near fields of the aggressor, guard ring, and victim. Therefore, the impedances between the aggressor/victim and guard ring are divided into two parallel parts in the P-well layer and P-substrate, e.g., Formula$Z_{\rm aw}/Z_{\rm vw}$ and Formula$Z_{\rm as}$, Formula$Z_{\rm gs}/Z_{\rm vs}$, respectively. It should be noted that Formula$Z_{\rm aw}/Z_{\rm vw}$ and Formula$Z_{\rm as}$, Formula$Z_{\rm gs}/Z_{\rm vs}$ represent the impedances between the dashed surfaces [Fig. 1(b)], which do not include the constriction resistances in the near field of the contacts [8]. In this paper, this error is corrected by adding Formula$Z_{a}$, Formula$Z_{g1-3}$, and Formula$Z_{v}$ to characterize the current constriction effects for the aggressor, guard ring, and victim, respectively.

Figure 2
Fig. 2. Proposed circuit model for the Formula${\rm P}^{+}$ guard ring in Fig. 1.

In consistence with in [7], the model proposed here approximates the layout of the square contacts and guard rings using circular shapes. The approximation is based on the condition that circular contacts or guard rings have the same area as the corresponding rectangular contacts and guard rings. As has been discussed in [7], the approximation error is acceptable for practical use. Thus Formula$r_{a,v}={L_{a,v}}/{\sqrt{\pi}}$, where Formula$r_{a}$ and Formula$r_{v}$ are the radii of the circular contacts approximating the square aggressor and victim contact (with side length Formula$L_{a,v}$), respectively. For a square guard ring with an outer side length of Formula$L_{g}$ and a width of Formula$w_{g}$, it is approximated as a circular guard ring with the outer and inner radius of Formula$r_{g}={L_{g}}/{\sqrt{\pi}}$ and Formula$r_{\rm gin}=({L_{g}-w_{g}})/{\sqrt{\pi}}$, respectively.

A. Model Components Without Constriction Effects

For a homogeneous medium with resistivity of Formula$\rho$ and permittivity of Formula$\epsilon$, there exists the relationship [9] Formula TeX Source $$R=\rho{\epsilon}/C\eqno{\hbox{(1)}}$$ where Formula$R$ and Formula$C$ are the resistance and capacitance of the medium. Therefore, this paper only discusses either Formula$R$ or Formula$C$ in Formula$Z_{\rm ij}$. The corresponding Formula$C$ or Formula$R$ can be obtained using (1). Based on the square-to-circular layout approximations the capacitance Formula$C_{\rm ag}$ is derived as Formula TeX Source $$C_{\rm ag}={2\pi{\epsilon_{\rm ox}t_{\rm ox}}}/{{\rm acosh}\,\left[{{1}\over{2}}\left({{D^{2}}\over{r_{a}r_{g}}}-{{r_{a}}\over{r_{g}}}-{{r_{g}}\over{r_{a}}}\right)\right]}\eqno{\hbox{(2)}}$$ where Formula$D=d_{\rm ag}+r_{a}+r_{g}$ and Formula$C_{\rm gv}$ is the capacitance between the lateral surfaces of a cylindric ring with inner radius Formula$r_{v}$, outer radius Formula$r_{\rm gin}$, and height Formula$t_{\rm ox}$ Formula TeX Source $$C_{\rm gv}={2\pi{\epsilon_{\rm ox}t_{\rm ox}}}/{\ln{{r_{\rm gin}}\over{r_{v}}}}\eqno{\hbox{(3)}}$$ and similarly Formula$C_{\rm aw}$ can be derived as Formula TeX Source $$C_{\rm aw}={2\pi{\epsilon_{1}t_{1}}}/{{\rm acosh}\,\left[{{1}\over{2}}\left({{D^{2}}\over{r_{a}r_{g}}}-{{r_{a}}\over{r_{g}}}-{{r_{g}}\over{r_{a}}}\right)\right]}.\eqno{\hbox{(4)}}$$

In practical cases, the conductivity in a P-well layer is a function of the distance to the top of the layer (Fig. 3). In this paper, the thickness of the P-well layer is defined as the conductivity drops to 10% of Formula$\sigma_{p}-\sigma_{\rm sub}$, where Formula$\sigma_{p}$ and Formula$\sigma_{\rm sub}$ are the conductivities of the P-well and P-substrate, respectively. Through dividing the P-well into infinitely thin layers, uniform doping can be assumed for each layer and hence it has Formula TeX Source $$R_{\rm aw}={{1}\over{2\pi{G}}}{{\rm acosh}\,\left[{{1}\over{2}}\left({{D^{2}}\over{r_{a}r_{g}}}-{{r_{a}}\over{r_{g}}}-{{r_{g}}\over{r_{a}}}\right)\right]}\eqno{\hbox{(5)}}$$ where Formula TeX Source $$G=\int_{t_{\rm ox}}^{t_{1}}\sigma{(t)}dt.\eqno{\hbox{(6)}}$$ Similarly, Formula$R_{\rm vw}$ is derived as Formula TeX Source $$R_{\rm vw}={{1}\over{2\pi{G}}}{\ln{{r_{\rm gin}}\over{r_{v}}}}.\eqno{\hbox{(7)}}$$

Figure 3
Fig. 3. Typical conductivity profile by ion implantation in P-well layer. The bottom of the oxide layer is set as the origin in the coordinate.

Calculating Formula$Z_{\rm as}$, Formula$Z_{\rm gs}$, and Formula$Z_{\rm vs}$ is different from that of Formula$Z_{\rm aw}$ and Formula$Z_{\rm vw}$. This is because the current in the P-substrate is spreading over a much thicker substrate and cannot be assumed to be horizontal. The spreading resistance of a circular contact on a semi-infinite substrate has been discussed in [10] and it is given as Formula TeX Source $$R_{\rm as}={{\rho_{2}}\over{4r_{a}}}\left[1-{{2}\over{\pi}}\arcsin\left({{r_{a}}\over{r_{a}+d_{\rm ag}}}\right)\right].\eqno{\hbox{(8)}}$$ For a Formula${\rm P}^{+}$ guard ring on a thick substrate, the current spreads in the way similar to a circular contact at far field [11] (Fig. 4), whereas the constriction effects at the near field are different. In this paper, the far field resistance of the guard ring is calculated by treating the ring as a circular contact with a radius of Formula$r_{g}$ Formula TeX Source $$R_{\rm gs}={{\rho_{2}}\over{4r_{g}}}\left[1-{{2}\over{\pi}}\arcsin\left({{r_{g}}\over{r_{g}+d_{\rm ag}}}\right)\right]\eqno{\hbox{(9)}}$$ where Formula$r_{g}=r_{\rm gin}+w_{g}$. The near field constriction effects are described by Formula$R_{g1-3}$ (discussed in Section III) in Fig. 2. Different from the aggressor, the victim is inside the guard ring. Thus, Formula$R_{\rm vs}$ is the resistance between the victim and the equipotential surface at distance of Formula$d_{\rm gv}$ Formula TeX Source $$R_{\rm vs}={{\rho_{2}}\over{4r_{g}}}\left[1-{{2}\over{\pi}}\arcsin\left({{r_{v}}\over{r_{v}+d_{\rm gv}}}\right)\right].\eqno{\hbox{(10)}}$$

Figure 4
Fig. 4. Simulated electric potential field of a circular ring contact on a thick substrate when a current Formula$I$ is fed into the contact.

B. Model Components With Constriction Effects

Formula$Z_{a}$, Formula$Z_{v}$, and Formula$Z_{g1-3}$ that denote the constriction effects are calculated based a conformal mapping approach. The conformal mapping approach was used for 2-D thin film patterns in [12] and [13], whereas recent research has shown its potential in 3-D substrate resistances [14]. Fig. 5(a) shows the cross-sectional view of two back-to-back connected contacts (C–D and Formula${\rm C}^{\prime}{-}{\rm D}^{\prime}$) in complex plane Formula$z$. The resistance between the two contacts cannot be easily derived because simple closed-form expressions for the current flow lines (dashed lines with arrows) or the equipotential surfaces (dot lines) at the near field are usually unavailable (such as the case in Fig. 1). Using conformal mapping, the contacts in the Formula$z$-plane can be mapped to a Formula$z1$-plane, where the structure is, however, simple and the resistance can be derived. Because the mapping is conformal, the current flow and equipotential surface are kept perpendicular at any places. This guarantees that the resistance between the contacts in the Formula$z1$-plane is the same as that in the Formula$z$-plane. In the Formula$z1$-plane, half of the resistance between the contacts is Formula TeX Source $$R={{\rho}\over{t}}L_{1}/W_{1}\eqno{\hbox{(11)}}$$ where Formula$\rho$ is the resistivity of the medium and Formula$t$ is the thickness (perpendicular to this paper). Formula$R$ can also be represented using the available parameters (layout/substrate parameters) in Formula$z$-plane with a correction term Formula TeX Source $$R={{\rho}\over{t}}[(1-Y)/X+L_{e}/XL]\eqno{\hbox{(12)}}$$ where Formula$L_{e}$ is the equivalent length for correction of the neglected constriction resistance. It is clear that Formula TeX Source $$L_{e}=XLL_{1}/W_{1}-(1-Y)L.\eqno{\hbox{(13)}}$$

Figure 5
Fig. 5. (a) Conformal mapping for the calculation of the constriction resistance of a contact on a P-well layer. (b) Formula$\Pi$ to Y network transform for the constriction resistances at the near field of a contact.

In the case of Formula$X\ll 1$, and Formula$Y<0.5$, Formula$L_{e}$ can be approximated as [12], [13] Formula TeX Source $$L_{e}={{Y}\over{X}}-{{2}\over{\pi}}\ln{\left[\sinh\left({{Y\pi}\over{2X}}\right)\right]}\eqno{\hbox{(14)}}$$ and for the case of Formula$X\ll 1$ and Formula$Y>0.5$, Formula$L_{e}$ can be approximated as [13] Formula TeX Source $$L_{e}=K(p)/K^{\prime}(p)-(1-Y)K(k)/K^{\prime}(k)\eqno{\hbox{(15)}}$$ where Formula$p=\tanh [{\pi (1-Y)}/{2X}]$. Formula$K$ is the complete elliptic integral of first kind and Formula$K^{\prime}(k)=K(\sqrt{1-k^{2}})$.

Given that Formula$R_{p2}$ and Formula$R_{p3}$ are the lateral constriction resistances of the contact [Fig. 5(b)], they can be easily calculated by extending the lateral length by Formula$L_{e}$. Formula$R_{p1}$ represents the resistance between the inner two dashed lines beneath the contact. For circular aggressor and victim, the inner dashed lines represent the same equipotential surface around the contact and thus Formula$R_{p1}=0$. Thus, the value for Formula$R_{a}$ in Fig. 2 can be found by Formula TeX Source $$\eqalignno{R_{a}=&\,{{1}\over{2\pi{G}}}{{\rm acosh}\,\left[{{1}\over{2}}\left({{(D+L_{\rm ea})^{2}}\over{r_{a}r_{g}}}-{{r_{a}}\over{r_{g}}}-{{r_{g}}\over{r_{a}}}\right)\right]}\cr &-{{1}\over{2\pi{G}}}{{\rm acosh}\,\left[{{1}\over{2}}\left({{D^{2}}\over{r_{a}r_{g}}}-{{r_{a}}\over{r_{g}}}-{{r_{g}}\over{r_{a}}}\right)\right]}&{\hbox{(16)}}}$$ where Formula$L_{\rm ea}$ is the equivalent length for calculating the constriction resistances of the aggressor. Similarly Formula TeX Source $$R_{v}={{1}\over{2\pi{G}}}{\ln{{r_{v}+L_{\rm ev}}\over{r_{v}}}}\eqno{\hbox{(17)}}$$ where Formula$L_{\rm ev}$ is the equivalent length for calculating the constriction resistances of the victim. For guard rings, the inner dashed lines are not necessarily on the same equipotential surface as they are at the side facing the aggressor and victim, respectively. Hence Formula$R_{p1}$ is not necessarily zero and it can be calculated by Formula TeX Source $$R_{p1}={{1}\over{2\pi{G}}}\ln{{r_{g}}\over{r_{\rm gin}}}.\eqno{\hbox{(18)}}$$

Assuming Formula$R_{p2}$ of the guard ring is at the aggressor side, then it can be calculated by Formula TeX Source $$R_{p2}={{1}\over{2\pi{G}}}\ln{{r_{g}+L_{\rm eag}}\over{r_{g}}}\eqno{\hbox{(19)}}$$ where Formula$L_{\rm eag}$ is the equivalent length of the constriction resistance. Formula$R_{p3}$ is the lateral resistance of a ring with inner radius of Formula$r_{\rm gin}-L_{\rm egv}$ and outer radius of Formula$r_{\rm gin}$ Formula TeX Source $$R_{p3}={{1}\over{2\pi{G}}}\ln{{r_{\rm gin}}\over{r_{\rm gin}-L_{\rm egv}}}\eqno{\hbox{(20)}}$$ where Formula$L_{\rm egv}$ is the equivalent length of the constriction resistance at the victim side. The Formula$\Pi$ network in Fig. 5(b) is transferred to a Y-network to obtain Formula$R_{g1-g3}$: Formula$R_{g1}={R_{p2}R_{p3}}/{(R_{p1}+R_{p2}+R_{p3})}$, Formula$R_{g2}={R_{p2}R_{p1}}/ {(R_{p1}\!+\! R_{p2}\!+\! R_{p3})}$, Formula$R_{g3}\!=\!{R_{p3}R_{p1}}/{(R_{p1}\!+\!R_{p2}\!+\!R_{p3})}$.



The proposed model is based on the approximation of horizontal current flow in the P-well layer, which is valid for thin P-wells but less so for thicker P-wells. EM simulation has been done to validate the model and to illustrate the applicable range of the model in processes with different P-well resistivity and thickness. The schematic in Fig. 1 and EM simulation software CST STUDIO SUITE were used for the simulation. To simplify the simulation uniform conductivity is used for the P-well layer because nonuniform conductivity profile cannot be defined in the EM simulator. Fig. 6(a) and (b)show the calculated and simulated Formula$R_{\rm gv}$ and Formula$R_{\rm ag}$, respectively. Here, Formula$R_{\rm ag}=R_{a}+R_{g1}+(R_{\rm aw}+R_{g2})//(R_{\rm as}+R_{\rm gs})$, and Formula$R_{\rm gv}=R_{v}+R_{g1}+(R_{\rm vw}+R_{g3})//R_{\rm vs}$. It can be seen that the calculated resistances match the simulated results well, especially for small thicknesses (error Formula${<}{5\%}$ for Formula$t_{1}<5 \mu{\rm m}$). As most CMOS processes fall within this range the proposed model is widely applicable.

Figure 6
Fig. 6. Modeled and simulated (a) guard ring-victim resistance and (b) aggressor-guard ring resistance versus P-well thickness. The used parameters are: Formula$L_{a}\>=\>L_{v}\>=\>20 \mu{\rm m}$, Formula$L_{g}\>=\>40 \mu{\rm m}$, Formula$w_{g}\>=\>5 \mu{\rm m}$, Formula$d_{\rm ag}=20 \mu{\rm m}$, Formula$t_{2}=200 \mu{\rm m}$, and Formula$\rho_{2}=20 \Omega\hbox{-}{\rm cm}$.


Fig. 7(a) shows the guard ring testing fixtures (denoted by A-L) that have been fabricated using a standard 0.18 Formula$\mu{\rm m}$ 6-metal CMOS process to verify the proposed model. The process is aluminum and silicon dioxide-based and the process parameters are given in Fig. 7. The value for Formula$G$ is calculated using (6) based on the ion implantation profile of the process.

Figure 7
Fig. 7. (a) Microphotograph of the fabricated guard ring testing fixtures. (b) Example fixture with equivalent circuit. (c) Formula${\rm P}^{+}$ diffusion to top metal connection using a large number of vias.

The reference fixture M has no guard ring and the circuit model for it is a two-port network (port Formula$g$ is removed and so the components related to guard ring.). The calculation of remaining impedance components are the same as the calculation in fixtures A-L except that Formula$R_{\rm vw}$ is calculated using the same (5) as Formula$R_{\rm aw}$ instead of (7) [14]. Fixtures O and P are the open and short fixtures for deembedding. Fixture O has the same layout as fixtures A-L except that the guard ring, the aggressor contact, the victim contact, and their connections to the top metal are removed (Metal-6 straps are kept). Fixture P has the same layout as O but with signal pads connected to the GND pads on the top metal layer. The side length of all the aggressor and victim contacts was chosen to 20 Formula$\mu{\rm m}$.

Ground-Signal-Ground (G-S-G) pads are used for on-wafer resistance and S-parameter measurements. An example fixture and the simplified three-port model of Fig. 2 are shown in Fig. 7(b). The aggressor and victim contacts are connected to the signal pads using vias and metal1–6 [Fig. 7(c)]. The Formula${\rm P}^{+}$ guard ring is connected to metal-1, and then connected to the top metal layer, metal-6 using vias at point Formula$C$. A strap on metal-6 is connecting point Formula$C$ to the reference GND (point GND). Due to the nonzero resistivity the metal straps add on more impedance in the path from the guard ring to GND, which cannot be deembedded. As shown in Fig. 7(b), an impedance Formula$Z_{\rm gg}$ is used to include this effect into the equivalent circuit of the guard ring as Formula$Z_{\rm gg}=R_{\rm gg}+j\omega{L_{\rm gg}}=R_{\rm ring}+R_{\rm st}+j\omega{L_{l1}}+j\omega{L_{l2}}$, where Formula$R_{\rm ring}$ is the resistance between points Formula$A$ and Formula$C$. Two metal-1 straps A-C, and A-B-C are connected in parallel. Formula$R_{\rm ring}$ can be calculated based on the resistance of each strap using their lengths and sheet resistivity of metal-1. Formula$R_{\rm st}$ is the resistance of the strap connecting the guard ring and the GND. Formula$L_{l1}$ and Formula$L_{l2}$ are the inductance of the straps C-D and D-GND, respectively. Formula$R_{\rm st}$ is calculated in the similar way as Formula$R_{\rm ring}$ but using the sheet resistivity of metal-6. Formula$L_{l1,2}$ (in nH) are given by the equation of the self inductance for a Formula$l$-meter long strap [15] as follows: Formula TeX Source $$L_{l}={{l}\over{5}}\left[\ln{\left({{2\cdot l}\over{(w+t)}}\right)+{{0.223(w+t)}\over{l}}}+0.5\right]\eqno{\hbox{(21)}}$$ where Formula$w$ and Formula$t$ are the width and thickness of the metal strap C-D and D-GND, respectively.

A. DC Resistance Verification

In the verification. Formula$R_{\rm ag}$ and Formula$R_{\rm gv}$ and Formula$R_{\rm av}$ are used to represent the resistance between point Formula${\rm S}_{1}$-GND, Formula${\rm S}_{2}$-GND, and Formula${\rm S}_{1}-{\rm S}_{2}$, respectively. Hence, Formula$R_{\rm ag}=R_{a}+R_{g1}+(R_{\rm aw}+R_{g2})// (R_{\rm as}+R_{\rm gs})+R_{\rm gg}$, Formula$R_{\rm gv}=R_{v}+R_{g1}+(R_{\rm vw}+R_{g3})//R_{\rm vs}+R_{\rm gg}$, and Formula$R_{\rm av}\!=\!R_{a}\!+\!R_{v}\!+\!(R_{\rm vw}\!+\!R_{g3})//R_{\rm vs}\!+\!(R_{\rm aw}\!+\!R_{g2})//(R_{\rm as}+R_{\rm gs})$. Further, the sum Formula$R_{g1}+R_{\rm gg}$, has been extracted from the measured results using Formula$R_{g1}+R_{\rm gg}={(R_{\rm ag}+R_{\rm gv}-R_{\rm av})}/{2}$.

The measured and calculated Formula$R_{\rm ag}$ and Formula$R_{\rm gv}$ of guard ring fixtures with varying Formula$d_{\rm gv}$ are shown in Fig. 8(a). It can be seen that the calculated results match the measured results very well. It should be noted that Formula$R_{\rm gv}$ is still about 20 Formula$\Omega$ even when the guard ring is very close to the victim contact Formula$(d_{\rm gv}\>=\>0.28 {\mu}{\rm m})$. In this case, the constriction resistances at the near field of the victim and guard ring Formula$(R_{g1},R_{v})$ dominate the value of Formula$R_{\rm gv}$.

Figure 8
Fig. 8. Measured and calculated aggressor-to-guard ring and guard ring-to-victim resistances versus (a) guard ring-to-victim distance (Formula$d=40 \mu{\rm m}$ and Formula$w_{g}=5 \mu{\rm m}$), (b) aggressor-to-guard ring distance (Formula$d_{\rm gv}=0.28 \mu{\rm m}$ and Formula$w_{g}=5 \mu{\rm m}$), (c) guard ring width with fixed Formula$d$ (Formula$d_{\rm gv}=0.28 \mu{\rm m}$ and Formula$d=40 \mu{\rm m}$), and (d) guard ring width with fixed Formula$d_{\rm ag}$ and Formula$d_{\rm gv} (d_{\rm gv}=d_{\rm ag}=0.28 \mu{\rm m})$. Formula$L=20 \mu{\rm m}$ for all cases.

The measured and calculated Formula$R_{\rm ag}$ and Formula$R_{\rm gv}$ of guard ring fixtures with varying Formula$d_{\rm ag}$ are shown in Fig. 8(b). It can be seen that the measured and calculated Formula$R_{\rm gv}$ is almost constant. This is because only Formula$d_{\rm ag}$ is varying but not the guard ring layout in this test. It can also be seen that Formula$R_{\rm ag}$ increases as Formula$d_{\rm ag}$ is increasing. In addition, a saturation effect can be observed for longer distances.

Guard ring fixtures with varying Formula$w_{g}$ and fixed aggressor-to-victim distance are also investigated. The measured and calculated Formula$R_{\rm ag}$ and Formula$R_{\rm gv}$ are shown in Fig. 8(c). It can be seen that Formula$R_{\rm ag}$ decreases as the guard ring widens and approaches the aggressor. Formula$R_{\rm gv}$ is almost constant for most of the width values. This is because the charge distribution is mainly at the edge of the contact. Thus, the guard ring spreading resistance is close to the resistance of a circular contact with the same radius [11]. When Formula$w_{g}$ is close to zero, both Formula$R_{\rm ag}$ and Formula$R_{\rm gv}$ increase drastically because of the significantly increased constriction resistance of the guard ring Formula$(R_{g1})$. When Formula$w_{g}=0$, which is the case of no guard ring (fixture M), Formula$R_{g1}=\infty$, and Formula$R_{g2}=R_{g3}=0$. In this scenario, there is no resistive coupling between port Formula$a$ and port Formula$g$.

Another investigation focuses on guard rings with varied Formula$w_{g}$ and fixed Formula$d_{\rm ag}$ and Formula$d_{\rm gv}$. Results show that both Formula$R_{\rm ag}$ and Formula$R_{\rm gv}$ are almost constant when the width of the guard ring is increasing [Fig. 8(d)]. This is because the near field constriction resistance is dominating the total values of Formula$R_{\rm ag}$ and Formula$R_{\rm gv}$ for the fixtures in this test. Similar to the case in Fig. 8(c), Formula$R_{\rm ag}$ and Formula$R_{\rm gv}$ increase remarkably when the width of the guard ring is close to zero.

B. S-Parameter Verification

The proposed model has been verified by S-parameter measurements. Fig. 9(a) shows the measured and calculated Formula$\vert{\rm S}_{21}\vert{\rm s}$ of the reference fixture and guard rings with varying guard ring width. Good match between the modeled and the measured results is shown. In addition, stronger coupling in the guard ring fixtures is observed at higher frequencies. This is mainly because of Formula$L_{\rm gg}$ [Fig. 7(b)] and parasitical capacitances between the aggressor, guard ring, and victims. A decreased coupling in the reference fixture is observed at higher frequencies. This is mainly because of the aggressor-to-GND and victim-to-GND capacitances [16]. It can be seen that the noise suppression level decreases drastically when the guard ring is wide and close to the aggressor. This indicates that a wide guard ring may lead to deteriorations of the noise suppression performance.

Figure 9
Fig. 9. Measured and calculated Formula${\rm S}_{21}$-magnitudes versus frequency with varying (a) guard ring width (Formula$d_{\rm gv}=0.28 \mu{\rm m}$ and Formula$d=40 \mu{\rm m}$), (b) guard ring-to-victim distances (Formula$w_{g}=5 \mu{\rm m}$ and Formula$d=40 \mu{\rm m}$), (c) aggressor-to-guard ring distances (Formula$w_{g}=5 \mu{\rm m}$ and Formula$d_{\rm gv}=0.28 \mu{\rm m}$), and (d) aggressor-to-victim distances and guard ring width (Formula$d_{\rm ag}=0.28 \mu{\rm m}$ and Formula$d_{\rm gv}=0.28 \mu{\rm m}$). Formula$L=20 \mu{\rm m}$ in all cases.

Fig. 9(b) shows the measured and calculated Formula$\vert{\rm S}_{21}\vert{\rm s}$ of guard rings with varying guard ring-to-victim distances. Apart from the good agreement between the measured and calculated results, it can also be seen that the coupling strength increases when the distance between the guard ring and victim increases. This indicates that the guard ring should be placed close to the victim to achieve a better suppression of the substrate noise when the distance between aggressor and victim is fixed.

Fig. 9(c) shows the measured and calculated Formula$\vert{\rm S}_{21}\vert{\rm s}$ of guard ring fixtures with varying aggressor-to-guard ring distances. A clear enhancement of the noise suppression level can be obtained as Formula$d_{\rm ag}$ is increasing. But, the enhancement is saturated for longer distances, which is consistent with the results in Fig. 8(b).

The measured and calculated S-parameters of guard rings with varying Formula$W_{g}$ and fixed Formula$d_{\rm ag}$ and Formula$d_{\rm gv}$ are shown in Fig. 9(d). It can be seen that the suppression levels of the fixtures are close to each other even though the guard ring widths are drastically different. This feature is accurately predicted by the calculated results based on the proposed model. This indicates that increasing the guard ring width cannot guarantee an improved noise suppression performance.

C. Discussion and Design Guidelines

As shown in Fig. 9, the predicted S-parameters well match the experimental results in a broad frequency band ranging from 45 MHz to 10 GHz. Therefore, the proposed model is of interest not only for narrow-band mixed-signal ICs, in which the interested noise frequency band is usually at a few hundred MHz [17], but also for broad band systems such as UWB ICs [18]. In addition, the proposed model reveals the area effectivenesses of different guard ring designs. Here, an area effectiveness factor is defined by Area/Iso, where Area is calculated by multiplying the length and width of the guard ring fixture and Iso is the measured Formula$\vert{\rm S}_{21}\vert$ at 100 MHz of each guard ring fixture. A small area effectiveness value indicates a chip area-saving design. As shown in Table I, the guard ring with small Formula$w_{g}$ and small Formula$d_{\rm gv}$ (fixture C and D) provides the best area effectiveness among all the fixtures. When Formula$d_{\rm ag}$ increases (fixture I), the area effectiveness drops, but is still better than other fixtures. Based on the proposed model design guidelines for area-efficient Formula${\rm P}^{+}$ guard rings can be concluded as follows.

  1. Determine Formula$w_{g}$. Guard ring widths of a few Formula$\mu{\rm m}$, e.g., 5 Formula$\mu{\rm m}$, should be appropriate for most cases.
  2. Determine Formula$d_{\rm gv}$. The guard ring should be placed close to the victim. The minimum Formula${\rm P}^{+}\hbox{-}{\rm P}^{+}$ distance in layout design constrain could be used.
  3. Determine Formula$d_{\rm ag}$. Formula$d_{\rm ag}$ should be less than the side length of the contacts, as the enhancement in noise suppression saturates for large Formula$d_{\rm ag}$ values.
  4. S-parameter calculation. The components in the model can be calculated using (2) to (20) with the designed parameters. Then the S-parameters can be calculated using SPICE simulations.
Table 1

For designs aiming at optimum noise suppression level instead of layout area efficiency, the design guidelines for Formula$w_{g}$ and Formula$d_{\rm gv}$ are still applicable. But Formula$d_{\rm ag}$ should be as large as possible [Fig. 9(c)]. Besides, the guard ring should always be well connected to the closest GND to minimize Formula$Z_{\rm gg}=R_{\rm gg}+jwL_{\rm gg}$ in practical designs. It can help to maximize the noise suppression performance and improve the performance at higher frequencies. It is, however, difficult to achieve a zero Formula$Z_{\rm gg}$ because of the nonzero resistivity of interconnects. Using the proposed model achievable values of Formula$Z_{\rm gg}$ can be included in the calculation, which is useful to obtain more accurate predictions of the noise suppression performance.



This paper presents a compact Formula${\rm P}^{+}$ guard ring model for substrate noise analysis. Different from existing compact models, the proposed model can handle Formula${\rm P}^{+}$ guard rings implemented using lightly doped CMOS substrates with a P-well layer. The model is scalable to guard ring parameters and requires no fitting factors. Based on the proposed model, the substrate noise suppression performance of Formula${\rm P}^{+}$ guard rings in terms of S-parameters can be efficiently predicted in a broad frequency band up to at least 10 GHz. The model has been validated by EM simulations and experimental measurements using a standard 0.18-Formula$\mu{\rm m}$ CMOS process. In addition, design guidelines of Formula${\rm P}^{+}$ guard rings have been provided to miniaturize the chip area occupied by guard rings, while maintaining a desired noise suppression level. The approach used to obtain the model of Formula${\rm P}^{+}$ guard rings in this paper can also be helpful for other guard ring designs such as Formula${\rm N}^{+}$ guard rings.


This work was supported by the Danish Research Council for Technology and Production Sciences. The review of this paper was arranged by Editor M. Darwish.

M. Shen, J. H. Mikkelsen, O. K. Jensen, and T. Larsen are with the Technology Platforms Section, Department of Electronic Systems, Aalborg University, Aalborg 9220, Denmark (e-mail:;;;

K. Zhang and T. Tian are with the Shanghai Institute of Microsystem and Information Technology, Shanghai 200050, China (e-mail:;


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Ming Shen

Ming Shen

Ming Shen (S'09–M'10) received the Ph.D. degree in electronic engineering from Aalborg University, Aalborg, Denmark, in 2010.

His current research interests include onchip structure modeling, low power circuit design, and UWB systems.

Jan Hvolgaard Mikkelsen

Jan Hvolgaard Mikkelsen

Jan Hvolgaard Mikkelsen (M'12) received the Ph.D. degree in electronic engineering from Aalborg University, Aalborg, Denmark, in 2005.

His current research interests include low-power CMOS circuit design, PA linearization, UWB systems, and wireless sensor networks.

Ke Zhang

Ke Zhang

Ke Zhang received the Ph.D. degree in microelectronics from Fudan University, Shanghai, China, in 2011.

His current research interests include power amplifier and data converter for wireless communication systems.

Ole Kiel Jensen

Ole Kiel Jensen

Ole Kiel Jensen received the M.Sc. degree from Aalborg University, Aalborg, Denmark, in 1979.

His current research interests include microwave electronics, RF integrated circuits and antenna measurements.

Tong Tian

Tong Tian

Tong Tian received the Ph.D. degree in microelectronics from Xi'an Jiaotong University, Xi'an, China, in 1998.

His current research interests include ultralow power CMOS RF/mm-wave integrated circuits and systems, healthcare technologies, and wireless sensor networks.

Torben Larsen

Torben Larsen

Torben Larsen (S'88–M'99–SM'04) received the M.Sc.E.E. and Dr.Techn. degrees from Aalborg University, Aalborg, Denmark, in 1988 and 1998, respectively.

His current research interests include scientific computing, compressive sensing, numerical algorithms, and signals and systems theory.

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