**4. Electromagnetic modeling**

This section verifies the modeling and accuracy of the electromagnetic (EM) simulator. The FEM-based EM simulator, Ansoft HFSS Ver.11 [14], was used for EM analysis in the chapter.

## **4.1. Symmetric pattern**

Figure 7 shows the model for the analysis of the thru-pattern in HFSS. Due to the symmetry of the structure and excitation, the model for the analysis of the Figure 3 thru-pattern can be reduced to half of the whole structure, as suggested in Figure 7. A magnetic wall, or perfect magnetic conductor (PMC), is assumed at the center of symmetry. The absorbing boundary, or radiation boundary in HFSS, conditions are applied to the other outer boundary walls. The gap between ground (G) and signal (S) pads is excited by a lumped source. Lumped ports with 100 Ohm intrinsic impedances, which is double of probe impedance because of image theory, were used for the excitations.

240 Numerical Simulation – From Theory to Industry

(i) Measure the S-matrix of the SUT (SUT) *S* .

elements obtained in (6) (See also Figure 6).

A sample Mathematica source code is given in Appendix.

Line pattern

G

S

G

*L*

Left pad Right pad

Thru pattern

*L L L*

*L*

*L* / 2 *L* / 2

can be performed.

**Figure 5.** Thru and line patterns.

**4.1. Symmetric pattern** 

**4. Electromagnetic modeling** 

G

S

G

(ii) Transform (SUT) *S* into a cascade matrix (T-matrix) (SUT) *T* . Now (SUT) *T* is implied to be (SUT) (PAD-L) (D ) (PAD-R) *UT T T TT* , where (PAD-L) *T* , (PAD-R) *T* and (D ) *UT T* are the T-matrixes of the left pad, right pad, and device under test (DUT) embedded in the pads, respectively. The (PAD-L) *T* and (PAD-R) *T* values can be calculated from (PAD-L) *S* and (PAD-R) *S* , with the

(iii) (D ) *UT <sup>T</sup>* can be obtained by matrix operations: 1 1 (D ) (PAD-L) (SUT) (PAD-R) *UT T T TT*

Finally, (DUT) *S* is obtained by transformation from (D ) *UT T* , and de-embedding of the pads

G

S

G

This section verifies the modeling and accuracy of the electromagnetic (EM) simulator. The FEM-based EM simulator, Ansoft HFSS Ver.11 [14], was used for EM analysis in the chapter.

Figure 7 shows the model for the analysis of the thru-pattern in HFSS. Due to the symmetry of the structure and excitation, the model for the analysis of the Figure 3 thru-pattern can be reduced to half of the whole structure, as suggested in Figure 7. A magnetic wall, or perfect magnetic conductor (PMC), is assumed at the center of symmetry. The absorbing boundary, or radiation boundary in HFSS, conditions are applied to the other outer boundary walls. The gap between ground (G) and signal (S) pads is excited by a lumped source. Lumped

.

 

 

*l l l l*

*t t t t*

 

 

*t S*

*l S*

G

S

G

To verify the accuracy of the EM simulation, the calculated value is compared with the measured one. A micrograph of a fabricated chip is shown in Figure 8. The chip is 2.5 mm square and an 0.18 μm CMOS process is used. In the measurements, 100 μm-pitch GSG probes were used, and the system was calibrated using the impedance standard substrate (ISS). Smith charts of the S-parameters for the thru, line, and reflect patterns are shown in Figures 9, 10, and 11, respectively. The calculated and measured results agreed very well for all three patterns.

Then, sensitivity of lumped port position and size is investigated. Figure 12 shows position and size of lumped port in the GSG pad. Reflection coefficient *S*11 and transmission coefficient *S*12 (=*S*21) are shown in Figure 13 and Figure 14, respectively, with various sets of width (*w*), left pad offset (*dl*) and right pad offset (*dr*) (both offsets are prescribed in a similar manner). *w* is varied from 10 μm to 30 μm. *dl* and *dr* are varied from -15 μm to 15 μm. It is found that there are no significant differences in results. These results suggest that the probe positioning error is not serious in measurement. Results indicated by "edge1" and "edge2" are obtained with the excitation model in which lumped port is arranged at the edge of the GSG pad as shown in Figure 15. *wa* in Figure 15 is 20 μm for "edge1" while it is 50 μm for "edge2". The phase of *S*11 begins to show different value in high frequency region. The result indicated by "vertical" is obtained with the excitation model in Figure 16. The phase of *S*<sup>12</sup> begins to show different value in high frequency region. However, the results of these excitation models show good agreement.

**Figure 6.** Cascading expression of the line pattern.

Accuracy Investigation of De-Embedding Techniques Based on Electromagnetic Simulation for On-Wafer RF Measurements 243

**Figure 8.** Chip photo (process: CMOS 0.18μm, chip size: 2.5 mm x 2.5 mm)

DC 67GHz

*S*11, *S*<sup>22</sup>

*S*12, *S*21

**Figure 9.** Smith chart of thru-pattern. (Solid line: measurements, broken line: simulation)

(c) Cross-sectional view

**Figure 8.** Chip photo (process: CMOS 0.18μm, chip size: 2.5 mm x 2.5 mm)

242 Numerical Simulation – From Theory to Industry

**Figure 7.** Analysis model of thru-pattern in HFSS.

(a) Bird's eye view

(b) Top view

(c) Cross-sectional view

**Figure 9.** Smith chart of thru-pattern. (Solid line: measurements, broken line: simulation)

**Figure 12.** Position and size of lumped port in the GSG pad.

**Figure 13.** Position sensitivity of lumped port for *S*11 of thru-pattern.

0 10 20 30 40 50 60 70

(10,-15,-15) (10,-15,15) (10,-15,0) (10,-10,0) (10,-5,0) (10,0,0) (10,5,0) (10,10,0) (10,15,0) (10,15,15) (20,-10,0) (20,-5,0) (20,0,0) (20,5,0) (20,10,0) (30,-10,0) (30,-5,0) (30,0,0) (30,5,0) (30,10,0) edge1 edge2 vertical

(*w*, *dl*, *dr*) unit: m

**Frequency (GHz)**


*S***11 (dB)**

(a) Amplitude (b) Phase


*S***11 (deg)**

0 10 20 30 40 50 60 70

(10,-15,-15) (10,-15,15) (10,-15,0) (10,-10,0) (10,-5,0) (10,0,0) (10,5,0) (10,10,0) (10,15,0) (10,15,15) (20,-10,0) (20,-5,0) (20,0,0) (20,5,0) (20,10,0) (30,-10,0) (30,-5,0) (30,0,0) (30,5,0) (30,10,0) edge1 edge2 vertical

(*w*, *dl*, *dr*) unit: m

**Frequency (GHz)**

**Figure 10.** Smith chart of line-pattern in HFSS.

**Figure 11.** Smith chart of reflect-pattern in HFSS.

**Figure 12.** Position and size of lumped port in the GSG pad.

**Figure 10.** Smith chart of line-pattern in HFSS.

*S*11, *S*<sup>22</sup>

*S*12, *S*<sup>21</sup>

DC 67GHz

DC 67GHz

**Figure 11.** Smith chart of reflect-pattern in HFSS.

*S*12, *S*<sup>21</sup>

*S*11, *S*<sup>22</sup>

**Figure 13.** Position sensitivity of lumped port for *S*11 of thru-pattern.

**Figure 16.** Lumped port arranged vertically in the GSG pad.

In this section, excitation modeling is extended in order to treat more general problem. Figure 17 shows EM excitation-modeling for GSG pad include asymmetric pattern while symmetric pattern is considered in the previous section. Port 1, 2, 3 and 4 have 100 Ohm intrinsic impedance when the impedance of the GSG probe is 50 Ohm. The objective of the following discussion is to convert 4 4 S-matrix obtained by simulation into 2 2 S-matrix

> 1 1 11 12 13 14 2 2 21 22 23 24 3 3 31 32 33 34 4 4 41 42 43 44

Port 1 and Port 2 are identically excited ( <sup>121</sup> *aaa* ), and Port 3 and Port 4 are also identically excited ( <sup>342</sup> *aaa* ). The GSG pad is symmetric and coming waves to Port 1 and Port 2 are identical ( <sup>121</sup> *bbb* ) because they are guided by the G-MSL. This is same for

> 1 1 11 12 13 14 1 1 21 22 23 24 2 2 31 32 33 34 2 2 41 42 43 44

*b a SSSS b a SSSS b a SSSS b a SSSS*

*b a SSSS b a SSSS b a SSSS b a SSSS*

.

(9)

(10)

to compare with VNA measurement. S-matrix for the Figure 17 is written as

**4.2. Asymmetric pattern** 

Port 3 and Port 4 ( <sup>342</sup> *bbb* ).

**Figure 14.** Position sensitivity of lumped port for *S*12 of thru-pattern.

**Figure 15.** Lumped port arranged at the edge of the GSG pad.

**Figure 16.** Lumped port arranged vertically in the GSG pad.

#### **4.2. Asymmetric pattern**

246 Numerical Simulation – From Theory to Industry


*S***12 (dB)**

**Figure 14.** Position sensitivity of lumped port for *S*12 of thru-pattern.

0 10 20 30 40 50 60 70

(10,-15,-15) (10,-15,15) (10,-15,0) (10,-10,0) (10,-5,0) (10,0,0) (10,5,0) (10,10,0) (10,15,0) (10,15,15) (20,-10,0) (20,-5,0) (20,0,0) (20,5,0) (20,10,0) (30,-10,0) (30,-5,0) (30,0,0) (30,5,0) (30,10,0) edge1 edge2 vertical

(*w*, *dl*, *dr*) unit: m

**Frequency (GHz)**

(a) Amplitude (b) Phase


*S***12 (deg)**

0 10 20 30 40 50 60 70

(10,-15,-15) (10,-15,15) (10,-15,0) (10,-10,0) (10,-5,0) (10,0,0) (10,5,0) (10,10,0) (10,15,0) (10,15,15) (20,-10,0) (20,-5,0) (20,0,0) (20,5,0) (20,10,0) (30,-10,0) (30,-5,0) (30,0,0) (30,5,0) (30,10,0) edge1 edge2 vertical

(*w*, *dl*, *dr*) unit: m

**Frequency (GHz)**

**Figure 15.** Lumped port arranged at the edge of the GSG pad.

In this section, excitation modeling is extended in order to treat more general problem. Figure 17 shows EM excitation-modeling for GSG pad include asymmetric pattern while symmetric pattern is considered in the previous section. Port 1, 2, 3 and 4 have 100 Ohm intrinsic impedance when the impedance of the GSG probe is 50 Ohm. The objective of the following discussion is to convert 4 4 S-matrix obtained by simulation into 2 2 S-matrix to compare with VNA measurement. S-matrix for the Figure 17 is written as

$$
\begin{bmatrix} b\_1 \\ b\_2 \\ b\_3 \\ b\_4 \end{bmatrix} = \begin{bmatrix} S\_{11} & S\_{12} & \stackrel{\circ}{1}S\_{13} & S\_{14} \\ S\_{21} & S\_{22} & \stackrel{\circ}{1}S\_{23} & S\_{24} \\ S\_{31} & S\_{32} & \stackrel{\circ}{1}S\_{33} & S\_{34} \\ S\_{41} & S\_{42} & \stackrel{\circ}{1}S\_{43} & S\_{44} \end{bmatrix} \begin{bmatrix} a\_1 \\ a\_2 \\ a\_3 \\ a\_4 \end{bmatrix}. \tag{9}
$$

Port 1 and Port 2 are identically excited ( <sup>121</sup> *aaa* ), and Port 3 and Port 4 are also identically excited ( <sup>342</sup> *aaa* ). The GSG pad is symmetric and coming waves to Port 1 and Port 2 are identical ( <sup>121</sup> *bbb* ) because they are guided by the G-MSL. This is same for Port 3 and Port 4 ( <sup>342</sup> *bbb* ).

$$
\begin{bmatrix} b\_1' \\ b\_1' \\ b\_2' \\ b\_2' \end{bmatrix} = \begin{bmatrix} \mathbf{S}\_{11} & \mathbf{S}\_{12} & \mathbf{S}\_{13} & \mathbf{S}\_{14} \\ \mathbf{S}\_{21} & \mathbf{S}\_{22} & \mathbf{S}\_{23} & \mathbf{S}\_{24} \\ \mathbf{S}\_{31} & \mathbf{S}\_{32} & \mathbf{S}\_{33} & \mathbf{S}\_{34} \\ \mathbf{S}\_{41} & \mathbf{S}\_{42} & \mathbf{S}\_{43} & \mathbf{S}\_{44} \end{bmatrix} \begin{bmatrix} a\_1' \\ a\_1' \\ a\_2' \\ a\_2' \\ a\_2' \end{bmatrix} \tag{10}
$$

$$\begin{cases} b\_1' = (\mathcal{S}\_{11} + \mathcal{S}\_{12})a\_1' + (\mathcal{S}\_{13} + \mathcal{S}\_{14})a\_2' \\ b\_1' = (\mathcal{S}\_{21} + \mathcal{S}\_{22})a\_1' + (\mathcal{S}\_{23} + \mathcal{S}\_{24})a\_2' \\ b\_2' = (\mathcal{S}\_{31} + \mathcal{S}\_{32})a\_1' + (\mathcal{S}\_{33} + \mathcal{S}\_{34})a\_2' \\ b\_2' = (\mathcal{S}\_{41} + \mathcal{S}\_{42})a\_1' + (\mathcal{S}\_{43} + \mathcal{S}\_{44})a\_2' \end{cases} \tag{11}$$

0 10 20 30 40 50 60 70

Cal

Cal (4-ports to 2-ports)

**S11** Exp

**Frequency (GHz)**

Cal

Cal (4-ports to 2-ports)

**S21** Exp

0 10 20 30 40 50 60 70

**Frequency (GHz)**

**Figure 18.** Four port excitation model for thru-pattern.

0 10 20 30 40 50 60 70

Exp Cal

Cal (4-ports to 2-ports)


**Phase (deg)**

(a) Reflection coefficient *S*<sup>11</sup>

**S21**

**Frequency (GHz)**

0 10 20 30 40 50 60 70

Exp Cal

Cal (4-ports to 2-ports)

**Frequency (GHz)**





**Amplitude (dB)**


0




**Amplitude (dB)**


0

**S11**

**Figure 19.** Comparison between two-port and four-port excitation model for thru-pattern.

(b) Transmission coefficient *S*<sup>21</sup>




0

**Phase (deg)**

60

120

180

Because of the symmetry of the GSG pad, 11 22 *S S* , 12 21 *S S* , 13 14 23 24 *SSSS* , 31 32 41 42 *SSSS* , 33 44 *S S* , 34 43 *S S* holds. The first and second equations in (11) are identical. Also, the third and fourth equations in (11) are identical. As a result, the following 2 2 S-matrix is obtained.

$$
\begin{bmatrix} S\_{11}' & S\_{12}' \\ S\_{21}' & S\_{22}' \end{bmatrix} = \begin{bmatrix} \mathbf{S}\_{11} + \mathbf{S}\_{12} & \mathbf{S}\_{13} + \mathbf{S}\_{14} \\ \mathbf{S}\_{31} + \mathbf{S}\_{32} & \mathbf{S}\_{33} + \mathbf{S}\_{34} \end{bmatrix} \tag{12}
$$

If only one GSG probe is used to measure reflection, the reflection coefficient can be obtained by

$$
\Gamma = \frac{b}{a} = \mathbf{S}\_{11} + \mathbf{S}\_{12} = \mathbf{S}\_{21} + \mathbf{S}\_{22}.\tag{13}
$$

To verify the formulation of (12), the EM excitation-modeling for thru-pattern shown in Figure 18 is compared with the modeling shown in Figure 7. Figure 19 shows the frequency characteristic of reflection and transmission coefficient for the thru-pattern. The result indicated by "Cal" is obtained by the model in Figure 7, and the result indicated by "Cal (4 ports to 2-ports)" is obtained by the model in Figure 18. They agreed very well each other. Figure 19 shows two short-circuited lines, which have asymmetric structure as an example. Figure 20 shows the frequency characteristic of S-parameters for the structure shown in Figure 19. Calculated results agreed very well with measured results, and (12) is validated.

**Figure 17.** EM excitation-modeling for GSG pad include asymmetric pattern.

**Figure 18.** Four port excitation model for thru-pattern.

2 2 S-matrix is obtained.

obtained by

S

Port1

Port2

G

1 11 12 1 13 14 2 1 21 22 1 23 24 2 2 31 32 1 33 34 2 2 41 42 1 43 44 2

*b S Sa S Sa b S Sa S Sa b S Sa S Sa b S Sa S Sa*

 

Because of the symmetry of the GSG pad, 11 22 *S S* , 12 21 *S S* , 13 14 23 24 *SSSS* , 31 32 41 42 *SSSS* , 33 44 *S S* , 34 43 *S S* holds. The first and second equations in (11) are identical. Also, the third and fourth equations in (11) are identical. As a result, the following

> 11 12 11 12 13 14 21 22 31 32 33 34 *S S SSSS S S SSSS*

If only one GSG probe is used to measure reflection, the reflection coefficient can be

11 12 21 22. *<sup>b</sup> SSSS*

To verify the formulation of (12), the EM excitation-modeling for thru-pattern shown in Figure 18 is compared with the modeling shown in Figure 7. Figure 19 shows the frequency characteristic of reflection and transmission coefficient for the thru-pattern. The result indicated by "Cal" is obtained by the model in Figure 7, and the result indicated by "Cal (4 ports to 2-ports)" is obtained by the model in Figure 18. They agreed very well each other. Figure 19 shows two short-circuited lines, which have asymmetric structure as an example. Figure 20 shows the frequency characteristic of S-parameters for the structure shown in Figure 19. Calculated results agreed very well with measured results, and (12) is validated.

G Si

(13)

Port3

Port4

*a*

Arbitrary Circuit

**Figure 17.** EM excitation-modeling for GSG pad include asymmetric pattern.

( )( ) ( )( ) ( )( ) ( )( )

(11)

(12)

SiO2 Al

(b) Transmission coefficient *S*<sup>21</sup>

**Figure 19.** Comparison between two-port and four-port excitation model for thru-pattern.

(b) Analysis model in HFSS

Accuracy Investigation of De-Embedding Techniques Based on Electromagnetic Simulation for On-Wafer RF Measurements 251

**5. Results** 

embedding technique.

**Figure 22.** Extracted propagation constant of the G-MSL.

0 10 20 30 40 50 60 70

TL (w/o dummy) TRL (w/o dummy) OS (w/o dummy) Cal. (w/o dummy) TL (w/ dummy) TRL (w/ dummy) OS (w/ dummy) Cal. (w/ dummy)

**Frequency (GHz)**

Ohm.

0 0.5 1 1.5 2 2.5 3

**Attenuation constant (dB/mm)**

**5.1. Comparison of accuracy between de-embedding techniques** 

The frequency characteristic of the propagation constant for the G-MSL is extracted by deembedding techniques, and shown in Figure 22. The solid and broken lines represent results without and with dummy metal fills (5 m square; w=5 m and p=10 m in Figure 3) in the G-MSL, respectively. The loss of the G-MSL with dummy metal fills is slightly larger than that without dummy metal fills. The phase constant of the G-MSL with dummy metal fills is slightly larger than that without dummy metal fills because the dummy metal fills result in an effect like an artificial dielectric compound. The line with "Cal." is the calculated result with the method in [15]. The measured results agreed well with the calculations. Figure 22 shows that the accuracy of TL de-embedding technique is as good as that of the TRL de-

Figure 23 shows the characteristic impedance of the transmission lines. The characteristic impedance was obtained from the ratio of the voltage *V* to the current *I*. The voltage *V* is calculated by the tangential line integral of the electric field from the ground plane to the signal line. One half of the current *I*/2 is calculated by the tangential line integral of the magnetic field around the signal line. The characteristic impedance is obtained using the deembedding technique [16] together with a characterization of the pads using the TL deembedding technique. Very good agreement between the calculated and measured results was obtained. As the frequency increases, the real part of the characteristic impedance approaches 50 Ohm and the imaginary part of the characteristic impedance approaches 0

(a) Attenuation constant (b) Phase constant

**Phase constant (deg/mm)**

0 10 20 30 40 50 60 70

TL (w/o dummy) TRL (w/o dummy) OS (w/o dummy) Cal. (w/o dummy) TL (w/ dummy) TRL (w/ dummy) OS (w/ dummy) Cal. (w/ dummy)

**Frequency (GHz)**

**Figure 20.** Two short-circuited lines.

**Figure 21.** Frequency characteristic of S-parameters for two short-circuited lines shown in Figure 20.
