**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 deembedding technique.

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 Ohm.

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

> 0 10 20 30 40 50 60 70 **Frequency (GHz)**

> > (b) Phase

3-D FEM (HFSS) 2-D FEM (HFSS) TRL TL OS

**Figure 25.** Extracted transmission coefficient *S*21 of the 600 μm-length G-MSL (*l*=420 μm in Figure 24).


**Phase (deg)**

0 10 20 30 40 50 60 70 **Frequency (GHz)**

(a) Amplitude

3-D FEM (HFSS) 2-D FEM (HFSS) TRL TL OS

**Figure 26.** Extracted transmission coefficient *S*21 of the 600 μm-length G-MSL for several length of

To investigate the accuracy of the open-short de-embedding technique, numerical simulation was performed to extract *S*21 of a G-MSL with 600 μm-length. Figure 26 shows extracted *S*21 for the 600 μm-length G-MSL using calibration patterns with *l*=20 μm, 120 μm, 220 μm, 420 μm, respectively. A line of "3-D FEM (HFSS)" is the result obtained by *S*21 of the 3-D FEM analysis for the 600 μm-length G-MSL. The result indicated by "2-D FEM (HFSS)" is port analysis solution. Results indicated by "TRL", "TL" and "OS" are obtained after

open/short patterns.


**Amplitude (dB)**

**Figure 23.** Extracted Characteristic impedance of the G-MSL.

### **5.2. Accuracy investigation of open/short de-embedding technique**

The accuracy of de-embedding methods using thru-line patterns, thru-reflect-line patterns and open/short patterns will be discussed numerically in this section. Open and short patterns used in the simulation are shown Figure 24. The lengths from left and right pads to the open or short ends are *l* / 2 . Figure 25 shows the transmission coefficient *S*21 for the G-MSL with the length of 600 μm extracted by each method. The line with "3-D FEM (HFSS)" is the result directly obtained by the *S*21 of the 3-D FEM analysis using wave port excitation in HFSS. The line with "2-D FEM (HFSS)" is the result obtained using the propagation constant analyzed by the port solution by the 2-D FEM analysis in HFSS. These must be identical, and the differences are negligible. The results with "TRL", "TL", and "OS" are obtained after de-embedding the influence of the pads and using the TRL, TL, and open/short de-embedding techniques, respectively. Except for the "OS" they agreed very well with the results of the "3-D FEM (HFSS)," and the effectiveness of the TL and TRL de-embedding methods is verified. The accuracy of the open/short de-embedding method becomes poorer as the frequency increases. This is because the pads cannot be approximated well by an equivalent circuit in the high frequency band [12]. The accuracy of the ''OS'' can be improved if patterns with shorter lengths are used [17]. The accuracy of the TL deembedding method is as good as that of TRL de-embedding method, allowing the conclusion that the accuracy of the TL de-embedding method is validated.

**Figure 24.** Extracted Characteristic impedance of the G-MSL.

**Figure 23.** Extracted Characteristic impedance of the G-MSL.

**Characteristic impedance (Ohm)**

that the accuracy of the TL de-embedding method is validated.

*l*/2 *l*/2

**Figure 24.** Extracted Characteristic impedance of the G-MSL.

S

G

G

**5.2. Accuracy investigation of open/short de-embedding technique** 

Imaginary part

The accuracy of de-embedding methods using thru-line patterns, thru-reflect-line patterns and open/short patterns will be discussed numerically in this section. Open and short patterns used in the simulation are shown Figure 24. The lengths from left and right pads to the open or short ends are *l* / 2 . Figure 25 shows the transmission coefficient *S*21 for the G-MSL with the length of 600 μm extracted by each method. The line with "3-D FEM (HFSS)" is the result directly obtained by the *S*21 of the 3-D FEM analysis using wave port excitation in HFSS. The line with "2-D FEM (HFSS)" is the result obtained using the propagation constant analyzed by the port solution by the 2-D FEM analysis in HFSS. These must be identical, and the differences are negligible. The results with "TRL", "TL", and "OS" are obtained after de-embedding the influence of the pads and using the TRL, TL, and open/short de-embedding techniques, respectively. Except for the "OS" they agreed very well with the results of the "3-D FEM (HFSS)," and the effectiveness of the TL and TRL de-embedding methods is verified. The accuracy of the open/short de-embedding method becomes poorer as the frequency increases. This is because the pads cannot be approximated well by an equivalent circuit in the high frequency band [12]. The accuracy of the ''OS'' can be improved if patterns with shorter lengths are used [17]. The accuracy of the TL deembedding method is as good as that of TRL de-embedding method, allowing the conclusion

S

S

G

G

(a) Open (b) Short

S

G

*l*/2 *l*/2

G

G

G

0 10 20 30 40 50 60 70

w/o dummy w/ dummy

Real part

Exp Cal

**Frequency (GHz)**

**Figure 25.** Extracted transmission coefficient *S*21 of the 600 μm-length G-MSL (*l*=420 μm in Figure 24).

**Figure 26.** Extracted transmission coefficient *S*21 of the 600 μm-length G-MSL for several length of open/short patterns.

To investigate the accuracy of the open-short de-embedding technique, numerical simulation was performed to extract *S*21 of a G-MSL with 600 μm-length. Figure 26 shows extracted *S*21 for the 600 μm-length G-MSL using calibration patterns with *l*=20 μm, 120 μm, 220 μm, 420 μm, respectively. A line of "3-D FEM (HFSS)" is the result obtained by *S*21 of the 3-D FEM analysis for the 600 μm-length G-MSL. The result indicated by "2-D FEM (HFSS)" is port analysis solution. Results indicated by "TRL", "TL" and "OS" are obtained after

applying TRL, TL, and open-short de-embedding techniques, respectively. Results are obtained by simulation using HFSS. The accuracy of the TRL and TL de-embedding techniques is very good while that of open-short de-embedding technique differs in high frequency. The accuracy becomes higher as the length *l* of the open and short patterns becomes shorter. Figure 27 shows the error of the extracted *S*21 defined by

$$error \equiv \left| \frac{S\_{21}^{\text{true}} - S\_{21}^{\text{extracted}}}{S\_{21}^{\text{true}}} \right|. \tag{14}$$

Accuracy Investigation of De-Embedding Techniques Based on Electromagnetic Simulation for On-Wafer RF Measurements 255

**Author details** 

**Acknowledgement** 

**Appendix** 

*Tokyo Institute of Technology, Japan* 

STARC /TOSHIBA for their fruitful discussion.

Example Mathematica [13] code is shown here.

Takuichi Hirano, Kenichi Okada, Jiro Hirokawa and Makoto Ando

This work was supported in part by Semiconductor Technology Academic Research Center (STARC). The chip in this study has been fabricated in the chip fabrication program of the VLSI Design and Education Center (VDEC), the University of Tokyo in collaboration with Rohm Corporation and Toppan Printing Corporation. The authors would like to express their deepest gratitude to Toshihiko Mori of FUJITSU, Osamu Kobayashi of STARC, Naoko Ono of TOSHIBA, Toshiakira Ando of STARC/PANASONIC, and Ryuichi Fujimoto of

The result indicated by "3-D FEM (HFSS)" is used for true <sup>21</sup> *S* . The error becomes larger when the length of the open and short pattern becomes longer.

**Figure 27.** Error of the extracted transmission coefficient *S*21 of the 600 μm-length G-MSL with openshort de-embedding technique.

## **6. Conclusion**

In this paper, EM simulation modeling for on-wafer measurement using a GSG probe was presented. The gap between ground (G) and signal (S) pads is excited by a lumped source. Transformation formula from 4-port to 2-port S-matrix expression was derived. The accuracy of EM simulation was verified by comparing with measurements. Results of EM simulation by changing excitation model suggest that the probe positioning error is not serious in measurement.

TL de-embedding technique was applied for on-wafer measurement using a GSG probe. The accuracy of de-embedding techniques (open-short, TRL, and TL) were compared and discussed. It was found that the accuracy of TRL and TL de-embedding technique is approximately the same. Degradation of accuracy in open-short de-embedding technique was quantitatively investigated via numerical simulation. In the open-short de-embedding technique, the accuracy becomes higher as the lengths of the open and short patterns become shorter.
