Measurement and Simulation Results

In the following, selected measurement results are presented. The parameter values (except for the stackup) of all presented structures are given in Table H.2 which refers to the definitions in Fig. 7.10a. All considered combinations of structures and wafer types are listed in Table H.3. In some cases two or three measurements of the same structure are available. As some of the repeated measurements differ in the corresponding setup, the confidence in the measurements is increased if the results show a good agreement.

0 10 20 30 40 50 60 70 80 0

10 20 30 40 50

(a)

10

5

0 10

0 5

(b)

Port 1

Port 2

(c)

Figure 7.12:(a) Photograph of a coupon from one of the fabricated wafers (b) detailed view of the part with the DUTs of the following measurements (c) The two port measurements have port 1 at the respective higher coordinate as illustrated here. All scales/coordinates are inmm. Refer also to the drawing given in Figs. H.2 and H.3.

7.3 Correlation of Measurements and Full-Wave Simulations

Ejector

Compressed air +p

Personal Computer with MMSNT-Software [125]

Negative pressure (vacuum)

-p

XYZ-table Micro-positioner:

GPIB-488 to USB

(a)

Personal Computer

Plastic chuck Probe Probe

Wafer

(b)

Figure 7.13: Measurement setup 1b (→ Table H.4): illustration of (a) the complete me-chanical and electrical setup with all connections and (b) details of the setup 1b used for the electrical characterizations presented in this chapter.

LAN connection

Personal computer with measurement

software Frequency

extender

VNA

Plastic card between coupon and metal chuck

Figure 7.14: Illustration of measurement setup 2b (→ Table H.4).

7.3 Correlation of Measurements and Full-Wave Simulations

(a) (b)

(c)

conductor

(d)

Figure 7.15:Comparison of the excitations in the real measurement and the approximations in the simulations. The illustrations show the field lines of the estimated electric field with red arrows. (a) Probing in the measurement in the case of plane metallizations and (b) cor-responding signal launch of the simulation using a modified pad and a lumped port (marked with purple color). (c) Probing in the measurement in the case without plane metallizations and (d) corresponding excitation of the simulation using a wave port (marked with purple color and with checkerboard pattern) and de-embedding. Measurement drawings refer to the micro-probes used in measurement setups 1a/b and 2a but the probes used in setup 2b should show very similar behavior. Simulation drawings refer to the simulations for correlation carried out with [66]

Differentiation of the Used Parameter Values

For all measurements of this section, at least one simulation result set based on FEM full-wave simulations is given. As there is some uncertainty regarding the exact values of the layer thicknesses, some of these values have been varied in order to achieve a better agreement with the measurement results. A comparison of the nominal values that have been designed for, the estimated values that are based on the cross-sectional values, and the range of simulated values that has been used in order to fit simulation results to the measurement results are given in Table H.3. The focus of the fitting to the measurement results is to obtain both a similar general frequency behavior and the same orders of magnitude as the measurement results. The iterative fitting is based on educated guess rather than a complete investigation of the parameter space. The presented fit might therefore not be the optimal one within the realistic parameter ranges.

Modeling of the Signal Launch

An additional uncertainty is in effect due to the difficulty in appropriately modeling the signal launch. Firstly, the calibration for the (physical) measurement is expected to be slightly more inaccurate than for measurements on many other substrates, such a PCB laminates. This is mainly because the silicon substrate properties differ significantly from the properties of the calibration substrates which are typically ceramic materials. For the FEM simulations with [66], the optimal signal launch (exciting port with auxiliary structures) that corresponds to the micro-probe launch is also not obvious. A model for the micro-probe tip with a de-embedding to the probe tips might lead to a higher accuracy.

Here, simpler excitations are used and explained in the following.

For structures of the type that is illustrated in Fig. 7.10a (with plane metallizations), a lumped port is placed between the outermost edge of the pad and the metallization.

This excites the coplanar mode with good efficiency. In order to take into account the average probe position which is near the center of the pad, the pad is made slightly shorter (by about one third), such that the port coplanar mode field should be present at this position. The comparison of these signal launch setups of measurement and simulation is also illustrated in Figs. 7.15a and 7.15b, respectively.

For structures of the type illustrated in Fig. 7.10b (without plane metallizations), a wave-guide port is used at the outermost ends of the pads. The wavewave-guide port is assigned to an area above the bottom side metallization of the structure and shaped in a way that the port contour touches the outermost edges of the outer ground conductors. This way the coplanar mode of this structure is excited. Because the ground vias are at some

dis-7.3 Correlation of Measurements and Full-Wave Simulations tance plane from the probing position, the bottom metallization should have no significant influence on the mode field. A de-embedding is used to shift the reference plane half the length to the center of the probing pads. The comparison for this case is illustrated for measurement and simulation in Figs. 7.15c and 7.15d, respectively.

Modeling of the Electromagnetic Environment in the Simulation

The electromagnetic environment can in general not be ignored when carrying out mea-surements and corresponding simulations. For the measured structures this environment consists mainly of the neighboring structures on the silicon wafer coupon, the probe tips above the wafer coupon, and the plastic chuck or card (for the mounting) below the wafer coupon. The neighboring structures are ignored in the following simulations. The simulated area is equal to that of the plane metallizations if present and perfect magnetic conduc-tor boundary conditions are used for the faces of the stackup between these planes. If no metallizations are present, a wave port is used. Therefore, the length of the simulated area is equal to the length of the structure and the width is chosen to be about 5 times the pitch.

The presence of the probe tips is also neglected and signal launches are used as described before. The area above the wafer is extended with an air-box with absorbing boundary conditions except at the wave port areas. For the plastic mounting, a lossless dielectric with a relative permittivity of 4.3 is used with absorbing boundaries. From comparison with simulations where this is replaced by vacuum, it can be seen that the influence is small compared to the variation of uncertain parameter values.

Discussion of Correlation Between Measurement and Simulation Results Figures 7.18–7.20 shows several measurement and simulation results. Due to the mentioned uncertainties, i.e. because the simulated structures could deviate in the relevant dimensions and material properties from the measured structures, some adaptations of dimensions and material properties have been tested by variation of several parameters within a plausi-ble range. The electromagnetic environment has been taken into account in the manner discussed in the previous section.

The measurement results show several spikes that cannot be explained at this point and can most likely be attributed to the measurement devices. The measurements up to50 GHz show spikes near20 GHzin Fig. 7.20a (S_1,1) and in Fig. 7.18c (S_2,1). The measurements up to65 GHzshow spikes near61 GHzin Fig. 7.16. While the overall behavior with frequency is the same for different measurements of the same structure, some larger deviations can also be observed.

It must be mentioned that no effort has been made during these measurements to inves-tigate the effects due to depletion layers. As seen in section 2.5, this effect is relatively small and therefore out of the scope of the investigations presented here. For more rigor-ous investigations the power of the measurements could be calibrated and varied or the full-depletion case could be enforced by substrate biasing [126,127]. The latter requires an ohmic contact attached to the silicon layer.

Discussion of Test Structure Properties

Figures 7.16, 7.17, and 7.18 show structures on the same wafer, W23B. Due to the high resistivity, a good transmission is obtained, e.g., below 30 GHz the transmission is above

−2 dB for all three structures. As seen for structures V10 and V13 with the low-loss silicon wafer W23B in Figs. 7.16 and 7.17, respectively, the planes introduce significant resonances which deteriorate the transmission at higher frequencies. Figures 7.19 and 7.20 show results for structure V13 on wafers with silicon of lower electrical resistivity. Except at the resonance frequencies of structure V13 on the high resistivity wafer W23B, the transmission is about one order of magnitude lower for these wafers of lower resistivity compared to the high resistivity wafer.