Best Practice Guide for Planar S-Parameter Measurements using Vector Network Analysers : EMPIR - 14IND02 PlanarCal

EMPIR – 14IND02 PlanarCal Best Practice Guide for Planar S-Parameter Measurements using Vector Network Analysers Uwe Arz, Thorsten Probst, Karsten Kuhlmann, PTB Nick Ridler, Xiaobang Shang, NPL Faisal Mubarak, VSL Johannes Hoffmann, Michael Wollensack, Markus Zeier, METAS Gia Ngoc Phung, Wolfgang Heinrich, FVB Konstantin Lomakin, Gerald Gold, Klaus Helmreich, FAU Roger Lozar, FhG Gilles Dambrine, Kamel Haddadi, Univ-Lille1 Marco Spirito, TUD Roland Clarke, ULE https://planarcal.ptb.de September 2018 This Guide has been produced within the EURAMET project entitled Microwave measurements for planar circuits and components. More information about this collaborative research project can be found on the project’s website https://planarcal.ptb.de . Disclaimer Any mention of commercial products within this Guide is for information only; it does not imply recommendation or endorsement by the partners in this project. The views expressed in this Guide are those of the authors and of the EMPIR 14IND02 project team. Acknowledgement of funding The production of this Guide was funded by the European Metrology Programme for Innovation and Research (EMPIR). The EMPIR initiative is co-funded by the European Union’s Horizon 2020 Research and Innovation Programme and the EMPIR Participating States. Authorship Preparation of this Guide was led by Uwe Arz of the Physikalisch-Technische Bundesanstalt (PTB), Braunschweig (Germany) with extensive input from all members of the EMPIR 14IND02 project team. The discussion and input of all the partners in the project and their colleagues are greatly appreciated. Suggestion for the quotation of the references Arz, Uwe ; Probst, Thorsten ; Kuhlmann, Karsten ; Ridler, Nick ; Shang, Xiaobang ; Mubarak, Faisal ; Hoffmann, Johannes ; Wollensack, Michael ; Zeier, Markus ; Phung, Gia Ngoc ; Heinrich, Wolfgang ; Lomakin, Konstantin ; Gold, Gerald ; Helmreich, Klaus ; Lozar, Roger ; Dambrine, Gilles ; Haddadi, Kamel ; Spirito, Marco ; Clarke, Roland. Best Practice Guide for Planar S-Parameter Measurements using Vector Network Analysers : EMPIR — 14IND02 PlanarCal, 2018. Physikalisch-Technische Bundesanstalt (PTB). DOI: https://doi.org/10.7795/530.20190424B This document and all parts contained therein are protected by copyright and are subject to the Creative Commons user license CC by 4.0 (https://creativecommons.org/licenses/ by/4.0/). Best Practice Guide for Planar S-Parameter Measurements using Vector Network Analysers Contents Preface 4 1 Introduction 6 1.1 Probe and Calibration Substrate Selection . . . . . . . . . . . . . . . . . . . 6 1.2 Selection of Calibration Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Selection Between Basic Calibration Algorithms . . . . . . . . . . . . 8 1.2.2 Calibration algorithm involving eigenvalue problems . . . . . . . . . . 8 1.3 Selection of Measurement Boundary Conditions . . . . . . . . . . . . . . . . 9 1.4 VNACharacterization .............................. 9 1.4.1 Noise Floor/Trace Noise . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.2 Linearity.................................. 10 1.4.3 ErrorTermDrift ............................. 10 1.5 CableMovement ................................. 11 1.6 Connection Repeatability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.7 DUT Uncertainty/Crosstalk . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 On-wafer measurements up to 110 GHz 13 2.1 Results from a three-party on-wafer measurement intercomparison . . . . . . 13 2.1.1 Influence of probe pitch . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.2 Importance of measurement speed/instrument drift . . . . . . . . . . 14 2.2 Limits of established techniques for transferring uncertainties . . . . . . . . . 15 2.2.1 Substrate permittivity compensation . . . . . . . . . . . . . . . . . . 15 2.2.2 Residual error correction . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Transfer of uncertainties with the aid of ISS . . . . . . . . . . . . . . . . . . 24 3 On-wafer measurements above 110 GHz 30 3.1 Recommended good practice for making on-wafer measurements at higher frequencies..................................... 30 3.2 Summary of high-frequency parasitic effects . . . . . . . . . . . . . . . . . . 31 3.3 Surface roughness effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.4 Importance of positioning accuracy . . . . . . . . . . . . . . . . . . . . . . . 39 4 Nanodevice measurements 40 4.1 Solving the impedance mismatch problem . . . . . . . . . . . . . . . . . . . 40 4.2 Addressing the scale mismatch challenge . . . . . . . . . . . . . . . . . . . . 41 4.3 Interferometric methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.3.1 Passivemethods ............................. 42 4.3.2 ActiveMethods.............................. 44 2 5 Uncertainties in on-wafer measurements 48 5.1 Introduction.................................... 48 5.2 VNA Tools II on-wafer example . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2.1 Introduction................................ 49 5.2.2 New project and basic definitions . . . . . . . . . . . . . . . . . . . . 49 5.2.3 Measurements............................... 50 5.2.4 Calibration configuration . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2.5 Errorcorrection.............................. 53 5.2.6 DataExplorer............................... 53 5.3 Uncertainty budget examples . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.3.1 Expanded uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.3.2 Uncertainty budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6 Conclusions and Outlook 58 7 Acknowledgements 58 References 59 3 Preface In the European project PlanarCal [1] a major effort has been undertaken to characterise components and devices for eventual use in high-speed and microwave applications (e.g. wireless communications, automotive radar and medical sensing) with known measurement uncertainties. It is the purpose of this Best Practice Guide to give an overview of the major outcomes of this project together with useful information on recommended measurement practice, different sources of uncertainty and the determination of uncertainties. This Best Practice Guide is not intended to replace available literature such as [2], [3], or [4] – just to name a few. All these textbooks offer comprehensive introductions to the subject of on-wafer measurements and deembedding, which are suitable for beginners as well as advanced users in industry and academia. Such information will not be replicated in this Guide. Instead, this Guide aims to present useful best practice recommendations together with key takeaways developed from the research performed in PlanarCal during the project’s lifetime from 2015 until 2018. The research in PlanarCal has been focussed on passive oneand two-port on-wafer measurements on typical microwave substrates such as GaAs, Al2O3(alumina) and fused silica for frequencies up to 325 GHz, including nanodevice measurements. To this end, parasitic modes as well as effects occurring at higher frequencies such as radiation, dispersion and surface roughness have been investigated together with the impact of the probe itself and its neighborhood. The influence of the neighborhood on coplanar waveguides (CPWs) used as standards for multiline Thru-Reflect-Line (TRL) calibrations [5] was demonstrated for CPWs on GaAs and alumina substrates in [6] and [7], respectively. The latter investigation included different probe geometries and suggested measures to suppress the occurrence of substrate modes. In [8], a similar investigation was performed for thin-film microstrip lines. The impact of radiation losses due to multimode propagations on TRL calibrations in the WR10 band was described in [9]. All the investigations confirmed that the measurement result depends on the environment as well as on the specific combination of substrate material, planar waveguide type, and probes. Only for such fully specified combinations, and only when single-mode propagation is ensured, reliable uncertainties for on-wafer S-parameters can be stated. This Best Practice Guide is organized as follows. In the Introduction we give an overview of commonly used terminology and recommendations for the choice of measurement equipment. As Vector Network Analyzers (VNAs) are an indispensable part of each on-wafer measurement setup, we also give recommendations on how to characterize the performance of such instruments and give typical numbers for one specific setup. In Section 2 we summarize key findings for on-wafer measurements performed in the frequency range up to 110 GHz. In this frequency range, traceability was recently demonstrated for devices fabricated in membrane technology [10]. At the end of the project, the methodology of [10] could also be extended to fused silica [11], paving the way to traceability for most commonly used microwave materials. The biggest challenge remains the transfer of the (supposedly low) uncertainties obtained on a reference substrate to a different substrate incorporating the devices under test (DUTs) to be measured. Some results from techniques developed to this end will also be given in this Section. Finally, the Section concludes with a recommendation for transferring uncertainties from a reference custom calibration to industrial DUT environments making use of commercially available impedance standard substrates (ISS). In Section 3 we address the difficulties associated with measurements above 110 GHz. This includes the consideration of surface roughness, a short summary of high-frequency parasitic effects and an excursion on the importance of probe positioning accuracy. More details on high-frequency parasitic effects can be found in a different document developed in PlanarCal, named “Guidelines for the design of calibration substrates, including the sup4 pression of parasitic modes for frequencies up to and including 325 GHz”, which is also publically available from the PlanarCal website [1]. Section 4 contains useful advice for characterizing nanodevices over a wide frequency range, looking both into the difficulties of size and impedance mismatch compared to ordinary on-wafer measurements. Also, an overview of interferometric methods is given. Section 5 finally covers the subject of uncertainties in on-wafer measurements. Without dedicated software, it is virtually impossible to take into account all the relevant sources of uncertainty. To this end, the VNATools software package [12] developed by METAS has been extended to include uncertainties in on-wafer measurements. In this Section, also an introduction to the main features and use of VNATools is given. To achieve traceability, PTB has developed an uncertainy budget for multiline TRL calibrations in Matlab based on the same measurement model and uncertainty propagation engine [13] as the one used in VNATools. Typical examples from the uncertainty budget calculations are given in Section 5, illustrating the relative importance of the different sources of uncertainty in on-wafer measurements. 5 1 Introduction Design and characterization of high frequency electronics relies upon accurately defining the reference plane of the calibration process, and in general placing it as close as possible to the DUT to remove all unwanted parasitic. In order to define such reference planes and remove all the systematic errors of the measurement setup (i.e., cable and receiver conversion losses, amplitude and phase tracking errors, and other errors), a calibration procedure [14] needs to be carried out prior to the measurement. Calibration techniques for on-wafer measurements typically consist of a probe-level calibration (first-tier) performed on a low-loss substrate (i.e., alumina or fused silica) [15, 16, 17, 5]. This probe-level calibration is then transferred to the environment where the DUT is embedded in and often, to increase the measurement accuracy, this calibration is augmented with a second-tier on-wafer calibration or de-embedding step. This allows moving the reference plane as close as possible to the DUT, by de-embedding the parasitics associated to the contact pads and the device-access vias [18]. The process of transferring the first-tier calibration to another structure assumes that the delta capacitance introduced by changing the substrate under the probes (i.e., boundary conditions) is negligible. As it was shown in [19] this capacitance is dependent on the probe topology and substrate characteristic, creating a coupling which increases with frequencies. To remove the errors arising from neglecting or improperly removing this delta capacitance, the calibration kit should be implemented in the same environment of the DUT. 1.1 Probe and Calibration Substrate Selection Calibration substrates are provided by different vendors to perform probe-level calibration (first-tier). The substrates are realized as a slab of a single material providing low dispersion (i.e., permittivity change versus frequency) and low dielectric losses. The models of the standards provided in most of the available calibration substrates are based on simple (i.e., frequency invariant) C, L and R, as shown in Fig. 1. Figure 1 Equivalent circuits of the planar open, short and load standards. When calibration techniques using full knowledge of the standards are employed (i.e., SOL based) the accuracy of the calibration can be improved by using more accurate (frequency dependent) standard models. This can be achieved using an experimental approach as shown in [20, 21, 22], or a simulation based (EM) one as shown in [23]. The choice for the optimum pitch of the probe to be employed in a given frequency range is dependent on the probe technology implementation and follows the same requirements of low dispersion used in CPW lines. For this reason, assuming that the final part of the probe transition is implemented as a CPW line design, as is the case for the Dominion probe shown in Fig. 2, the choice of the max tip to tip spacing is bounded by the λ/4 at the maximum desirable frequency of operation and the effective permittivity of the line section. When selecting micro-machined probes (i.e., using silicon as carrier) it is important to consider the high permittivity of the material (i.e., 11.9) when computing the effective permittivity of the CPW section. 6 Figure 2 SEM images of the micro-machined probe tips after 3000 contacts (from [24]). When some material properties of the probe tip are known the dispersion characteristics of a CPW versus gap width can be used as a tool to define the maximum probe pitch to be employed. When selecting probes for a given test circuits few things should be kept in mind: 1. The skating area width and length extension are dependent on the probe make, and should be analysed and found compatible with the pad sizes available, or optimized when full custom designs are made (see Fig. 3). Figure 3 Landing area of probe model from company #1 for the WR10 a), WR5 b) and WR3 c) frequency band, probe model from company #2 for the WR3 d) and probe model from company #3 for the WR3 e). 2. When probing on aluminium pads special probe tip alloy should be used, i.e., nickel alloy probe tips, to reduce the contact resistance and improve the probe lifetime. 3. When using commercial technologies, the reduction of the effective pad opening due the scratch protection, as shown in the sketch given in Fig. 4, is reduced from the drawn pad dimension of 1-3um, depending on the technology. Figure 4 Cross sectional sketch view of pad opening and scratch protection. 7 1.2 Selection of Calibration Algorithm Any on-wafer measurement requires the application of a calibration procedure to correct for unwanted but unavoidable perturbation of the data due to the environment, the probes, and the instrumentation itself. This calibration process is supposed to reveal the “true” performance of the DUT. In the following, basic and advanced calibration algortihms will be reviewed. 1.2.1 Selection Between Basic Calibration Algorithms The term basic calibration algorithm refers to calibration algorithms which are simple to execute. The requirements in terms of standards are different for all considered methods and thus it is interesting to compare the field of application of each algorithm, the achievable accuracy and results. Another factor which has to be considered when choosing a calibration algorithm is the amount of real estate on the wafer required by each method. The first calibration routine investigated in PlanarCal was the short open load thru (SOLT) routine. It requires, as the name insinuates, short, open, load and thru as standards. It can be quite easily applied for low frequencies (≈15 GHz) down to DC. A crucial point is often the definition of the load standard. The SOLT technique is more robust against bad definitions of standards. The second calibration algorithm investigated was the line reflect match (LRM) algorithm which requires a transmission line, a reflect (either open or short) and a load. In terms of frequency it has a similar range of application as the SOLT algorithm. Again a crucial point is the definition of the load standard. The LRM technique requires the least connections and standards compared to SOLT and LRRM techniques. The third calibration algorithm was line reflect reflect match (LRRM). It requires a transmission line, a first reflect (e.g. an open), a second reflect (e.g. a short) and a load. The applicable range of frequencies is from medium frequencies (≈40 GHz) down to DC. In this method an inductive component of the load is determined during calibration. This inductive component has its origin in the design of the load itself but as well in the length of the line leading to the load. This length is not easy to control because of probe skating when contacting the load. Thus for loads which are not well defined the LRRM technique can yield good results. Note that the implementation of the LRRM algorithm can differ between different software packages, e.g. VNA Tools II [25, 12] has a different implementation than WinCal [26]. The previous remarks are only applicable to situations where the definition of standards for the respective calibration comes from the manufacturer or from geometry and material properties. All three types of calibrations yield similar results in situations where the definition of standards is derived from another previous calibration. 1.2.2 Calibration algorithm involving eigenvalue problems Calibration algorithms for VNAs which require only partially known standards pose problems for uncertainty calculation. Examples are LRM and TRL calibrations where the reflectivity of the line can not be specified because in the algorithm it is assumed that the line has a characteristic impedance of 50 Ω. In reality the line in use will not have exactly the required characteristic impedance and thus this needs to be taken into account for uncertainty computation. The algorithm presented in [27] is a generalization of calibration schemes with partly unknown standards, including [5]. The generalization consists of constructing an eigenvalue problem for each calibration scheme. One obvious advantage is that the same algorithm can be used for different schemes as TRM, LRM, TRL and LRL. Another advantage is that partly unknown lines can now be described with non-zero reflection and uncertainty, which is a clear improvement over the traditional TRL algorithm. Over-determined calibration with 8 2.2 Limits of established techniques for transferring uncertainties In this section we report on methods to transfer uncertainties from reference calibration substrates to working calibration substrates. The aim is to preserve the low uncertainties in S-parameter measurements achieved on custom-made reference calibration substrates even when using low-cost working calibration substrates, such as e.g. impedance standard substrates, which can be purchased from several on-wafer vendors. Recommendations for the transfer of uncertainties will be given at the end of the section. 2.2.1 Substrate permittivity compensation In [33], a simple capacitance model was developed to account for the effect of a change in substrate permittivity on coplanar waveguide TRL calibrations performed on different substrate materials. For all calibrations, the reference plane was moved to the probe tip and the reference impedance was set to 50 Ω. Whereas in [33] all cross-sectional dimensions of the CPWs on the different substrates were assumed identical, the investigation in [34] demonstrated that also the measurement error caused by differences in the conductor geometry can be accounted for. As the measurements in [33] and in [34] were limited to the 40 GHz frequency range, we investigated the performance of this compensation technique using custom-made fused silica and Al2O3substrates up to 110 GHz. 0 10 20 30 40 50 60 70 80 90 100 110 Frequency (GHz) 0 0.05 0.1 0.15 0.2 0.25 Upper bound on |Sij-Sij)| Silica MTRL 50 Ohm vs. Al2O3 MTRL 50 Ohm Silica MTRL 50 Ohm vs. Al2O3 MTRL 50 Ohm /w permittivity compensation Figure 8 Worst-case error bounds calculated by calibration comparison method [32]. Figure 8 shows the worst-case error bounds calculated for multiline TRL calibrations using [32] on the two different wafers before (blue) and after (red) applying the substrate permittivity compensation technique of [33]. The red curve shows a significant reduction of the error bound after applying the permittivity compensation. As the calibration comparison technique [32] tends to overestimate the actual errors in the measurements, we decided to investigate the actual deviations from the reference measurement result before and after applying the substrate permittivity compensation. 15 To this end, we investigated measurements of different devices fabricated on the Al2O3 wafer in the frequency range from 1 to 110 GHz (see Figs. 9-13). The multiline TRL calibration on the Al2O3wafer gives the most accurate result (black curves), while the multiline TRL calibration on the fused silica wafer (brown curves) will introduce a systematic error due to the differences in substrate permittivity and conductor geometries. The red curves show the result for the multiline TRL calibration on the fused silica wafer after applying the substrate permittivity compensation technique of [33]. In the following figures, the errorcorrected reflection and transmission measurement are shown on the left-hand side, while the differences with regard to the reference calibration are shown on the right-hand side. In the case of one-port devices only the results for reflection are shown. In Fig. 9, the results for an attenuator device are displayed. While the permittivity compensation only slightly improves the error in magnitude of S11 and S21, there is a tangible improvement in the phase over the entire frequency range. For frequencies above 60 GHz, the errors in the magnitude of S21 cannot be compensated by the simple capacitance model of [33]. Figure 10 shows the results for a 11.4 mm long CPW line on Al2O3substrate. For S11, the permittivity compensation does not offer any notable improvement over the fused silica calibration. In the phase of S21, there is a tangible improvement over the entire frequency range. Figure 11 shows the results for a mismatched CPW line on Al2O3substrate. Here, the permittivity compensation leads to an improvement in both S11 and S21. As is evident from the left-hand side, the resonance frequencies of the black and red curve line up after 0 20 40 60 80 100 Frequency /GHz -20 -15 -10 |S11|/dB 0 20 40 60 80 100 Frequency /GHz -2 0 2 |S11|/dB-|S11|ref/dB 0 20 40 60 80 100 Frequency /GHz -100 -50 0 S11/° 0 20 40 60 80 100 Frequency /GHz -20 -10 0 S11/° - S11/° ref 0 20 40 60 80 100 Frequency /GHz -16 -15 -14 |S21|/dB 0 20 40 60 80 100 Frequency /GHz -0.5 0 0.5 |S21|/dB-|S21|ref/dB 0 20 40 60 80 100 Frequency /GHz -200 -100 0 S21/° 0 20 40 60 80 100 Frequency /GHz -10 -5 0 5 S21/° - S21/° ref Figure 9 left: reflection and transmission measurement of attenuator device on Al2O3substrate right: measurement normalized to MTRL result on Al2O3 colors: MTRL on Al2O3(black), on fused silica, on fused silica after perm. comp. 16 0 20 40 60 80 100 Frequency /GHz -60 -40 -20 0 |S11|/dB 0 20 40 60 80 100 Frequency /GHz -20 0 20 40 |S11|/dB-|S11|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° - S11/° ref 0 20 40 60 80 100 Frequency /GHz -4 -2 0 |S21|/dB 0 20 40 60 80 100 Frequency /GHz -0.4 -0.2 0 0.2 |S21|/dB-|S21|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S21/° 0 20 40 60 80 100 Frequency /GHz -5 0 5 S21/° - S21/° ref Figure 10 left: reflection and transmission measurement of 11.4 mm long CPW line on Al2O3 right: measurement normalized to MTRL result on Al2O3 colors: MTRL on Al2O3(black), on fused silica, on fused silica after perm. comp. applying the compensation. Again, the corrective effect of the permittivity compensation is more noteable in the phase, and for frequencies above 60 GHz, the errors in the magnitude of S21 cannot be compensated by the technique of [33]. Figure 12 shows the results for a one-port device, an offset open. The permittivity compensation only improves the phase of S11. The compensation does not work for the magnitude of S11, and again, for frequencies above 60 GHz, the systematic errors in the magnitude of S11 start to increase with frequency. Figure 13 shows the results for a 0.4 mm long thru line on Al2O3substrate. For S11, the permittivity compensation hardly offers any improvement over the fused silica calibration. There is a tangible improvement in the phase of S21 over the entire frequency range. For frequencies above 60 GHz, the systematic errors in the magnitude of S21 cannot be compensated by the technique of [33]. In summary, one can state the permittivity compensation technique of [33] mostly improves on the phase error introduced by the off-wafer calibration on fused silica. The effect is generally more noteable in S21 compared to S11. With regard to the magnitude error, which drastically increases for frequencies above 60 GHz in S21, almost no improvement can be found. 17 0 20 40 60 80 100 Frequency /GHz -60 -40 -20 0 |S11|/dB 0 20 40 60 80 100 Frequency /GHz -20 -10 0 10 |S11|/dB-|S11|ref/dB 0 20 40 60 80 100 Frequency /GHz -100 0 100 S11/° 0 20 40 60 80 100 Frequency /GHz -200 -100 0 100 S11/° - S11/° ref 0 20 40 60 80 100 Frequency /GHz -2 -1 0 |S21|/dB 0 20 40 60 80 100 Frequency /GHz -0.4 -0.2 0 0.2 |S21|/dB-|S21|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S21/° 0 20 40 60 80 100 Frequency /GHz -10 -5 0 5 S21/° - S21/° ref Figure 11 left: reflection and transmission measurement of mismatched line on Al2O3 right: measurement normalized to MTRL result on Al2O3 colors: MTRL on Al2O3(black), on fused silica, on fused silica after perm. comp. 0 20 40 60 80 100 Frequency /GHz -1 -0.5 0 0.5 |S11|/dB 0 20 40 60 80 100 Frequency /GHz -0.5 0 0.5 |S11|/dB-|S11|ref/dB 0 20 40 60 80 100 Frequency /GHz -150 -100 -50 0 S11/° 0 20 40 60 80 100 Frequency /GHz -10 -5 0 S11/° - S11/° ref 0 20 40 60 80 100 Frequency /GHz -80 -60 -40 -20 |S21|/dB 0 20 40 60 80 100 Frequency /GHz -2 -1 0 1 |S21|/dB-|S21|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S21/° 0 20 40 60 80 100 Frequency /GHz -6 -4 -2 0 S21/° - S21/° ref Figure 12 left: reflection and transmission measurement of open device on Al2O3 right: measurement normalized to MTRL result on Al2O3 colors: MTRL on Al2O3(black), on fused silica, on fused silica after perm. comp. 18 0 20 40 60 80 100 Frequency /GHz -80 -60 -40 -20 |S11|/dB 0 20 40 60 80 100 Frequency /GHz -20 0 20 40 |S11|/dB-|S11|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° - S11/° ref 0 20 40 60 80 100 Frequency /GHz -0.4 -0.2 0 0.2 |S21|/dB 0 20 40 60 80 100 Frequency /GHz -0.4 -0.2 0 0.2 |S21|/dB-|S21|ref/dB 0 20 40 60 80 100 Frequency /GHz -150 -100 -50 0 S21/° 0 20 40 60 80 100 Frequency /GHz -5 0 5 S21/° - S21/° ref Figure 13 left: reflection and transmission measurement of thru line on Al2O3 right: measurement normalized to MTRL result on Al2O3 colors: MTRL on Al2O3(black), on fused silica, on fused silica after perm. comp. 19 2.2.2 Residual error correction A more general approach for compensating systematic errors introduced by the VNA calibration is the determination of residual errors and the application of a second-order error correction afterwards. In [35], a method for determining complex residual errors of two-port VNA calibrations was presented which makes use of a time-domain approach. The residual errors are extracted from a distance-frequency system model using a special estimation algorithm based on the quasi-optimal unscented Kalman filter. Since the method requires only three measurement conditions, it is particularly suited for on-wafer applications, as these conditions can be obtained from using only one verification line. In [36], the same measurement conditions are exploited, but since the residual error terms are now estimated by applying a least-mean-squares method the calculation time is significantly reduced. Here, we determined the residual errors of calibrated two-port on-wafer measurements up to 110 GHz with the method of [36], utilizing the commercial calibration substrate GGB CS5 and GGB100 microwave probes. As verification line, line 10 with a length of 6600 µm was used. As DUTs lines of different lengths were used. By analyzing the error-corrected measurements of the DUTs, we compared the accuracy of SOLT calibrations with characterized standards to SOLT calibrations with manufacturer definitions and to second-order-corrected SOLT calibrations with manufacturer definitions. In the following figures, the error-corrected reflection and transmission measurement are shown on the left-hand side, while the differences with regard to the reference calibration (SOLT with characterized standards) are shown on the right-hand side. Figures 14-16 show the results for lines with lengths in the range 550 . . . 1500 µm. One obvious disadvantage of the second-order error correction becomes apparent for frequencies below 10 GHz: additional errors are introduced leading to unphysical behavior in both reflection and transmission. For higher frequencies, however, the second-order correction is mostly working as expected. In the measured reflections, the second-order error correction is beneficial in both magnitude and phase, as can be seen from the red S11 curves approaching the black S11 curves in a range of approximately 20 . . . 110 GHz. In the measured transmission, there is almost no improvement for the magnitude of S21, while the phase of S21 even deteriorates slightly by means of the second-order error correction. In summary one can state that the second-order error correction of [36] shows some promise but is currently limited by the accuracy with which the residual errors can be determined. At the edges of the frequency range (ca. 5% of the frequency band), the error of the filtering algorithm increases. This applies to measurements of both transmission and reflection coefficients. In principle, the effect can be reduced by applying a verification line with a longer length. The current study was limited by the number of DUTs and the verification line available on the commercial calibration substrate. Future investigations should try to extend the study to better understand and overcome the current limitations of the method of [36]. 20 0 20 40 60 80 100 Frequency /GHz -80 -60 -40 -20 |S11|/dB 0 20 40 60 80 100 Frequency /GHz -20 0 20 40 |S11|/dB-|S11|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° 0 20 40 60 80 100 Frequency /GHz -200 -100 0 100 S11/° - S11/° ref 0 20 40 60 80 100 Frequency /GHz -0.4 -0.2 0 0.2 |S21|/dB 0 20 40 60 80 100 Frequency /GHz -0.2 0 0.2 |S21|/dB-|S21|ref/dB 0 20 40 60 80 100 Frequency /GHz -200 -100 0 S21/° 0 20 40 60 80 100 Frequency /GHz -10 -5 0 S21/° - S21/° ref Figure 14 left: SOLT-corrected reflection and transmission of 550 µm long line on GGB CS5 right: measurement normalized to SOLT with characterized standards colors: characterized standards (black), manufacturer definitions, manufacturer definitions after residual error correction 21 0 20 40 60 80 100 Frequency /GHz -60 -40 -20 |S11|/dB 0 20 40 60 80 100 Frequency /GHz -20 0 20 |S11|/dB-|S11|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° - S11/° ref 0 20 40 60 80 100 Frequency /GHz -0.5 0 0.5 |S21|/dB 0 20 40 60 80 100 Frequency /GHz -0.2 0 0.2 |S21|/dB-|S21|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S21/° 0 20 40 60 80 100 Frequency /GHz -10 -5 0 S21/° - S21/° ref Figure 15 left: SOLT-corrected reflection and transmission of 1000 µm long line on GGB CS5 right: measurement normalized to SOLT with characterized standards colors: characterized standards (black), manufacturer definitions, manufacturer definitions after residual error correction 22 0 20 40 60 80 100 Frequency /GHz -60 -40 -20 |S11|/dB 0 20 40 60 80 100 Frequency /GHz -20 0 20 |S11|/dB-|S11|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S11/° - S11/° ref 0 20 40 60 80 100 Frequency /GHz -1 -0.5 0 0.5 |S21|/dB 0 20 40 60 80 100 Frequency /GHz -0.2 0 0.2 |S21|/dB-|S21|ref/dB 0 20 40 60 80 100 Frequency /GHz -400 -200 0 200 S21/° 0 20 40 60 80 100 Frequency /GHz -10 -5 0 S21/° - S21/° ref Figure 16 left: SOLT-corrected reflection and transmission of 1500 µm long line on GGB CS5 right: measurement normalized to SOLT with characterized standards colors: characterized standards (black), manufacturer definitions, manufacturer definitions after residual error correction 23 2.3 Transfer of uncertainties with the aid of ISS In [22] it was demonstrated that properly characterized standards can be used to account for differences between the commercial ISS and the target DUT measurement situation. The results of a reference MTRL calibration using custom standards were in essence duplicated with the aid of characterized ISS standards and a much simpler calibration, in this case SOLT. This constitutes a big improvement over any of the approaches discussed in the two previous subsections, where a systematic error with regard to the reference result remained. Therefore, in order to transfer uncertainties to industrial applications where commercial ISS substrates and simple calibration algorithms have to be used, one has to first characterize the standards in a manner which is adequate for the target application. This requires building custom calibration standards on the target DUT wafer, which serve for characterizing the ISS calibration standards appropriately. In the following, we demonstrate this approach with the custom-made Al2O3wafer as the target DUT wafer and the GGB CS5 calibration substrate as commercially available ISS substrate. Recently, PTB developed a traceability path for on-wafer S-parameter measurements based on the MTRL calibration algorithm [10]. The methodology of [10] for establishing a comprehensive uncertainty budget can also be applied to other substrates, as long as the wideband material properties are known and single-mode propagation can be assumed. For the custom-made Al2O3wafer used in our studies, the latter condition is strictly fulfilled only for frequencies below ca. 70 GHz. For higher frequencies, the effects of dispersion and interaction with higher-order and other parasitic modes are currently not fully captured in the uncertainty budget. Nonetheless we used this preliminary uncertainty budget and treated the Al2O3wafer as reference calibration wafer for characterizing the standards on the GGB CS5 substrate. Figures 17 and 18 show the result of characterizing the Open/Short/Load/Thru standards by means of a reference multiline TRL calibration on the custom-made Al2O3wafer. The figures also show the expanded uncertainty intervals comprising the influences of MTRL calibration standard uncertainties, uncertainties from the instrumentation used, cabling influences and repeatability effects. It may appear surprising that some of the characterized standards show gain even though they are passive devices. This can easily be explained by the fact that the distance between the probe tips on the CS5 standards was smaller than the distance between the calibration reference planes on the Al2O3wafer. Nonetheless the characterized CS5 standards can be used as transfer standards for accurately measuring DUTs on the Al2O3wafer. Fig. 19 compares the measurement results for an attenuator DUT and a mismatched line DUT fabricated on the Al2O3wafer. The black curves show the reflection and transmission when using the reference MTRL calibration on the Al2O3substrate, the red curves show the corresponding results for the SOLT calibration with the characterized CS5 standards. The shaded areas indicate the expanded uncertainty intervals. It can be clearly seen that the nominal values coincide for both calibrations, proving the consistency of the approach. The only differences appear in the expanded uncertainties, which are usually slightly increased for the calibration with the characterized standards. Exemplary uncertainty budget values for the DUTs corrected via the SOLT calibration with characterized CS5 standards are given in the Tables 5-8. These tables show the uncertainty budget composition for the magnitude of S11 and the phase of S21 of the DUTs at a frequency of 65 GHz. The calibration standard uncertainties are designated with PTB ML in the beginning, pointing to the fact that the characterization was performed with the PTB multiline calibration. The tables clearly show that the budgets are mostly dominated by the calibration standard uncertainties. For the phase of S21, also cable effects and DUT uncertainty provide significant contributions to the total uncertainty at 65 GHz. 24 exhibit higher-order modes above 50 GHz, depending on the boundary conditions above and below the substrate. It is good practice to use an absorbing material (with similar dielectric constant as the substrate) between the metallic wafer chuck and the DUT, which will suppress unwanted modes. The DUT is effectively a different structure (electromagnetically) with and without this absorber, and measurement results can differ widely depending on whether or not it is used. Sometimes the presence of systematic errors in the measurements can be detected especially when non-physical behaviour is observed – e.g. when the observed linear magnitude of the reflection coefficient is greater than unity. This is indicative of an inappropriate reference standard used during calibration. Additionally, the presence of significant ripple on some measurement traces suggest perhaps the use of an inferior calibration technique. Generally, the choice of reference calibration substrate can have a major impact on the achieved measurements. This is because the different calibration substrates provide different calibration reference values (e.g. due to the use of different substrate materials for the calibration substrate). This means that even the same uncorrected measurement data for a given device under test (DUT) will give rise to different corrected S-parameter values due to different reference values being used during the calibration process. This occurs when a VNA is calibrated using standards found on one wafer (e.g. a commercial impedance standard substrate), and then measurements are made subsequently of DUTs on another wafer (e.g. the wafer containing the devices that need testing). For this reason, when making on-wafer S-parameter measurements that are not SI traceable, it is very important to state what references were used during calibration. In fact, as a general rule, it is good practise to state everything about the measurement setup that might have an impact on the obtained measurement results – e.g. VNA, probes (including probe pitch) and associated calibration hardware and software (i.e. the calibration substrate, the calibration method and the calibration standards used). Whenever possible, it is preferable to fabricate some appropriate reference standards on the same wafer as the DUT. As a minimum, some lengths of CPW line and some highreflecting standards (usually short-circuits) are needed. These enable the use of one of the calibration techniques derived from the TRL approach [44, 5] which make use of the CPW lines to acquire a reference value which is determined by the properties of the DUT substrate material. These techniques are generally superior to the more conventional ShortOpen-Load-Thru (SOLT) technique, and are less dependent on accurate and repeatable probe-placement. For manual probe stations, this can be a significant source of error at higher frequencies if the calibration method requires known values for the phase of the calibration standards. 3.2 Summary of high-frequency parasitic effects When operating in the mm-wave frequency range (i.e., in the context of this section above 110 GHz), the calibration errors arising from the inaccuracy of standard models and multimode propagation start to severely impact the calibration accuracy that can be achieved. For this reason a guideline to inform the reader on these potential problems and the means to minimize them was compiled in the EMPIR PlanarCal project, namely, “Guidelines for the design of calibration substrates, including the suppression of parasitic modes for frequencies up to and including 325 GHz ”. The interested reader is invited to familiarize himself with these effects using the above mentioned document. In the following a selection of the suggestions provided in the document is given: Choice of substrate thickness (Guideline #1) Compute the critical frequency (fc) of parasitic modes (e.g. higher order modes and substrate modes) [45] of the calibration substrate employed in the given configuration (i.e., metallic 31 or dielectric chuck) and select those in which fcis outside the calibration frequency or only occurs in the upper calibration range, to avoid excessive coupling of power to unwanted modes. Impact of ground-to-ground spacing in CPWs (Guideline #4) The influences of CPW ground width and of ground-to-ground spacing, are contributing to parasitic effects in the calibrated results, in this case a dip in S-parameters at a certain frequency. Total CPW width determines the frequency where this dip occurs, and groundto-ground spacing influences the strength of the dip behavior. Thus, the best way to mitigate the impact of this dip is to keep the total CPW width smaller than the formula given in [45], which requires a tradeoff between the CPW total width, the used material and the upper frequency limit fmax. Chuck topology (Guideline #5) Using for the chuck a material which has a permittivity value similar to the calibration substrate reduces the effects which contribute to the degradation of the accuracy of CPW mTRL calibrations. Further investigations have shown that this is true also for a chuck material with a permittivity larger than that of the wafer, because such a layered structure does not support surface waves either. Influence of in-line and side-way neighbouring structures (Guideline #6) One should keep sensitive regions of the probe shadow free of structures to avoid probe coupling to neighboring structures, as shown in the figure below (investigations performed up to 70 GHz). Custom designed TRL kit (Guideline #8) When designing custom kits for LRM/TRL calibration the reflect should be realized as an offset one, keeping the minimum distance between the effective reflect and the center of the thru line (intrinsic calibration plane) to avoid requiring sign changes in the solution of the calibration equations. 3.3 Surface roughness effects Surface roughness is one among different parasitic effects that affect signal integrity of propagating signals on transmission lines. While radiation mainly increases the attenuation α, dispersion effects have a direct influence on the phase velocity vph and only indirectly affect attenuation by increasing the line capacitance and thus, dielectric loss. In contrast thereto, surface roughness has shown to directly impacting on both, attenuation and phase velocity. The impact magnitude depends on the actual roughness on the one hand and the operation frequency on the other. Although it is a an inevitable property of real surfaces and can be appropriately taken into account by modeling and simulation, for many practical applications an impact of only little surface roughness causing deviations between rough and 32 smooth responses within <5 % in attenuation αand <0.5 % in phase coefficient βmay be considered as negligible. Table 9 Frequency Bands and Waveguide Definitions. Band Waveguide Frequency Limits W WR10 75 −110 GHz F WR08 90 −140 GHz D WR06 110 −170 GHz G WR05 140 −220 GHz Y WR04 170 −260 GHz Y WR03 220 −325 GHz Y WR02 325 −500 GHz Y WR01.5 500 −750 GHz For this purpose, this section provides margins for the root-mean-square (RMS) roughness Rqwhich meet these requirements over the frequency bands from Wto Y-Band as shown in Table 9 in terms of both, a general consideration and specific application to certain transmission lines. −0.4−0.3−0.2−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 depth x( µ m) Normalized σand H σ(x)/σDC ˆ=CDF |B0,ideal| |B0,rough| Figure 20 Conductivity profile and skin effect on smooth and rough surface at 50 GHz with Rq= 1 µ m By making use of the Gradient Model [46], the penetrating magnetic field can be calculated for a given surface which is represented either by a measured bearing area curve (BAC) or Rqas shown in Fig. 20. As explained in [46], these responses may be used to derive effective material parameters which in turn account for the impact of surface roughness in transmission line models such as e.g. [45] for a CPW or [47] for rectangular waveguides (RWG). While the magnitude and ratio of surface roughness impact on αand vph depend on the type, specific cross section geometry and materials of the transmission line, the surface impedance as described in [46] provides an independent approach for illustration and comparison: Z=1 σeffδ(σeff)+j1 σDCδ(µr,eff)=rπµ0µrf σeff +jrπµ0µr,efff σDC =R+jωLi,(1) where σDC is the bulk conductivity as a material property of the conductor (e.g. 58 MS/m in case of bulk copper) and σeff and µr,eff denote effective, frequency dependent material 33 parameter values derived from the Gradient Model approach which represent the impact of surface roughness. While the real part of Zaffects the attenuation and is therefore related to R, its imaginary part influences vph and is related to Li,, which is the inner inductance. 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 0 5 10 15 20 25 Rq(nm) ∆< {Z}(%) 110 GHz 140 GHz 170 GHz 220 GHz 260 GHz 325 GHz 500 GHz 750 GHz Figure 21 Relative deviation ∆< {Z}between rough and smooth case in % 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 0 100 200 300 400 Rq(nm) ∆= {Z}(%) 110 GHz 140 GHz 170 GHz 220 GHz 260 GHz 325 GHz 500 GHz 750 GHz Figure 22 Relative deviation ∆= {Z}between rough and smooth case in % Figs. 21 and 22 show the relative deviation between the rough and smooth Zdepending on Rqfor the considered frequency band limits. From the real part, a 5 % margin can therefore be derived for each band, indicating the need for lower Rqwith increasing operation frequencies. Although the deviation within the imaginary part of Zin Fig. 22 exceeds 100 % for relatively small Rqalready, it is worth to mention, that it only contributes to the inner inductance term Liwhich is much smaller than the outer inductance Lo(LiLo) and is therefore only a fraction of the total inductance for most practical transmission lines. Furthermore, the 5 % limit in < {Z}is not directly related to the attenuation of a specific transmission line, since the conductor circumference must be considered according to the cross section geometry [48]. While the layout of a CPW allows for various implementations depending on the substrate material, manufacturing aspects and others, rectangular waveguides are typically produced 34 in standardized dimensions according to their identifier WR-XX in Table 9. This allows for precise predictions of the surface roughness impact which is shown in Figs. 23 and 24. 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 Rq(nm) ∆α(%) WR10 WR08 WR06 WR05 WR04 WR03 WR02 WR01.5 Figure 23 Relative deviation ∆αbetween rough and smooth RWG in %. 0 5 10 15 20 25 30 35 40 45 50 0 2 4 6 8 10 Rq(nm) ∆β(o / oo) WR10 WR08 WR06 WR05 WR04 WR03 WR02 WR01.5 Figure 24 Relative deviation ∆βbetween rough and smooth RWG in o / oo. Note, that the deviation in βis provided in o / oo as it is rather small as compared to the impact on α. However, it comes along with a small shift of the cutoff frequency fctowards lower values. The Rq-margins for CPWs can be provided for certain cases only, since CPW lines can be fabricated in a much greater variety compared to standardized RWG. Exemplarily, a CPW implemented on Al2O3substrate (εr= 9.7) is considered with the cross section geometry as provided in Fig. 25. In addition to the phase coefficient β, in this case, also the effective relative permittivity is considered according to: εr,eff =c0 vph 2 (2) The corresponding Rqmargins are provided in Figs. 26 to 31 for attenuation and phase coefficient for different substrate thicknesses of h= 100 µ m and h= 10 mm, respectively. 35 wc= 50 µ m wg= 270 µ mwg= 270 µ m s= 25 µ ms= 25 µ mt= 5 µ m h Figure 25 Cross section geometry of a CPW structure as considered in this comparison. 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 0 5 10 15 Rq(nm) ∆α(%) 110 GHz 140 GHz 170 GHz 220 GHz 260 GHz 325 GHz Figure 26 Relative deviation ∆αbetween rough and smooth CPW in % for h= 100 µ m. 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 0.2 0.4 0.6 0.8 1 Rq(nm) ∆β(%) 110 GHz 140 GHz 170 GHz 220 GHz 260 GHz 325 GHz Figure 27 Relative deviation ∆βbetween rough and smooth CPW in % for h= 100 µ m. 36 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 0.5 1 1.5 2 Rq(nm) ∆εr,eff (%) 110 GHz 140 GHz 170 GHz 220 GHz 260 GHz 325 GHz Figure 28 Relative deviation ∆εr,eff between rough and smooth CPW in % for h= 100 µ m. 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 0 2 4 6 Rq(nm) ∆α(%) 110 GHz 140 GHz Figure 29 Relative deviation ∆αbetween rough and smooth CPW in % for h= 10 mm. 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 0.2 0.4 0.6 0.8 1 Rq(nm) ∆β(%) 110 GHz 140 GHz Figure 30 Relative deviation ∆βbetween rough and smooth CPW in % for h= 10 mm. 37 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 0.5 1 1.5 2 Rq(nm) ∆εr,eff (%) 110 GHz 140 GHz Figure 31 Relative deviation ∆εr,eff between rough and smooth CPW in % for h= 10 mm. 38 3.4 Importance of positioning accuracy Conventional RF test structures require probing pads whose dimensions are around 50×50 µm2 to accommodate the probe tip geometry (example: pitch of 100 µm, contact area of 30×30 µm2). The manual positioning of the probe onto the CPW test structure generates misalignment measurement errors that impact notably on the measured impedance. In particular, these measurement errors increase in the millimeter-wave and sub-millimeter-wave regimes. The positioning accuracy is also crucial when measurement of high impedance devices such as nanoscale structures are considered. Indeed, phase-shift and magnitude errors inherent to the positioning accuracy offset the impedance to be measured. Consequently, piezo-based nano-positioning (X-Y-Z controls) and strain-sensing (Z control) strategies are used to provide automated and accurate control of the probe landing onto the test structure [49, 50]. 39 4 Nanodevice measurements 4.1 Solving the impedance mismatch problem Vector network analyzers have been introduced in the seventies to measure the electrical properties of materials and circuits. Since then, there has been considerable work to extend their measurement capabilities such as frequency coverage from low RF to hundreds of GHz, multi-port devices characterization, balanced, differential, harmonic, modulation and pulsed measurements. Nowadays, there is an urgent need to further extend the network analyzer capabilities to meet the specific needs of characterization tools for impedances clearly higher than the 50 Ω reference impedance of the VNA. In particular, the electrical characterization of high impedance nanodevices is a well-known scientific challenge. The main measurement limitation in these applications is the impedance mismatch between the reference impedance of the network analyzer close to 50 Ω that is too different compared to the impedance of nanodevices that is in the range of tens or hundreds of kΩ. Indeed, when high impedances are considered, the VNA is insensitive to the variations of the reflection coefficient. The issue of dealing with extreme impedance measurement has yielded a variety of measurement techniques. In 2005, the first measurements of the high frequency conductance of a metallic single walled nanotube (SWNT) with resistance below 200 kΩ inserted in a coplanar waveguide (CPW) transmission line were performed up to 10 GHz [51]. In 2010, to improve the VNA sensitivity, an individual SWNT iwas inserted in a specific high impedance Wheatstone bridge that helps to reduce the impedance mismatch between the VNA and the high-impedance nanodevice [52]. Among the alternatives to these studies, the interferometric principle commonly used in optics through Michelson or Mach Zender configurations has gained the interest from the microwave research community to measure small complex impedance contrasts. Basically, a monochromatic signal is split with one part traveling a fixed path and the other a variable one. The two resulting signals are reunited, amplified if necessary, and produce the wellknown interference. In 1949, a Michelson-type microwave interferometer was introduced for the first time at the free-space wavelength of 3.2 cm for free-space dielectric characterization [53]. In 2007, microwave interferometry was applied for the first time to the measurement of high impedance devices around 1.8 GHz [54, 55]. In particular, the setup included a vector network analyzer interfaced with an interferometric setup built up with a hybrid coupler associated to low noise amplifiers. In 2011, a mechanically tunable interferometric matching network in the range 1-18 GHz built up with a power divider, a variable attenuator and a sliding-short was applied to high impedance measurements [56]. To further enhance the sensitivity in a broadband frequency range, an interferometer built up with a high-resolution programmable delay line and a motor-driven variable attenuator has been developed [57]. In 2015, an I/Q-mixer-based interferometric technique is developed for speed operation [58]. These studies have proven that RF interferometric techniques are candidates to tackle the problem of impedance mismatch. The recommendation for high impedance measurements is to insert a tuning matching network between the measurement port of the vector network analyzer and the measurement of the port of the device under test. The tuning matching network based on microwave interferometry remains the most efficient method. This latter can be built up easily with coaxial or guided commercial equipment (couplers, power dividers, variable attenuators and phase-shifters). In addition, the method offers broadband frequency measurements. 40 port-4. Subsequently, the stability between a1and aint signals in single-source interferometer is evaluated using port-1 of the VNA to provide the a1signal source and to serve as input for the single-source interferometer as shown in Fig. 32(b). Again, both signals are subsequently measured by the receivers of port-2 and port-4. In both experiments, the power level of each signal source is set to -10 dBm, and subsequently 20 ·103measurement values are extracted at 3 GHz from both receivers (port-2 and port-4). From these values, the ratio aint/a1is calculated and normalized to demonstrate the stability between the two signals. Figure 36 Measurement results from [68] showing the cancellation sensitivity for the phasecomponent realized with two active interferometer topologies at 3 GHz (dual-source: blue circles; single-source: red squares, and inset). The black line depicts phasecomponent stability of b-wave measured using method outlined in (9). The linear magnitude stability of aint/a1for both methods is found to be comparable and smaller than 1 ·10−4. The result of the relative phase stability between a1and aint signals is shown in Fig. . As expected, these results demonstrate the much higher phase stability of the single-source configuration compared to the dual-source method [64]. Moreover, as shown in Fig. 36, the model predictions, plotted as black dashed line, accurately correlate with the experimentally found phase fluctuations for the dual-source method. 47 5 Uncertainties in on-wafer measurements 5.1 Introduction The evaluation of uncertainties in VNA measurements is a challenging task because of 1. the multivariate nature of the measurand. S-parameters are two-dimensional quantities, expressed either in magnitude and phase or complex-valued with real and imaginary components. 2. the multistep measurement process with calibration and error correction. This leads to an elaborate measurement model. 3. The relatively large number of data points. It is not unusual to collect data at several hundred frequency points and the uncertainty might show a pronounced frequency dependence. There has been significant progress in the last years to improve uncertainty evaluation in VNA measurements. A supplement [69] of the GUM [70] has been published, specifically dealing with multivariate and complex-valued quantities. This document serves as the basic guideline to determine uncertainties associated with estimates of S-parameters. Just recently a revised version of the EURAMET VNA Guide [28] has been published embracing the principles of the GUM supplement and promoting an uncertainty evaluation based on a measurement model, which represents the entire measurement process and takes quantities influencing the measurement into account. The EURAMET VNA Guide has been primarily written for coaxial measurements, but its basic principles are applicable for on-wafer measurements as well. An essential part of uncertainty evaluation is the characterisation of influence quantities. This is discussed in some detail in [28] and the same influences need to be considered in on-wafer measurements too. The characterisation procedures given in [28] can generally be applied with little and straightforward modifications. Under connector repeatability different contributions specific to on-wafer positioning and alignment can be summarized, by performing the following characterizations 1. Repeated connections by keeping probes at same position and moving sample in z. 2. Repeated positioning of probe station for each measurement of same standard at same position. 3. Repeated measurement of same standard at slightly different contact points. On-wafer measurements are affected more by crosstalk compared to coaxial measurements. The effect is strongly dependent on the distance between probes and therefore on the device under test. One way to acknowledge this effect in the uncertainty evaluation is to come up with an additional DUT uncertainty (as shown in the example in the next section), which can be characterized by the transmission coefficient as a function of distance when measuring two one-port standards. Other approaches might be possible. In the multivariate case the propagation of measurement uncertainties is more involved, see [71]. If correlations should be taken into account properly it is unavoidable to use specialized software. Suitable software solutions, which are able to handle the uncertainty propagation of complex-valued quantities, are available nowadays [72, 73]. These tools provide general frameworks to realize custom-built implementations of S-parameter uncertainty evaluation. For software solutions that are specifically targeting S-parameter measurements see [12, 74]. These solutions already contain the VNA measurement models and support different calibration algorithms, i.e. programming is not necessary. 48 Figure 37 Basic setup of new project. One of these solutions is the software VNA Tools II. Originally developed for coaxial VNA measurements it has been recently extended to support on-wafer measurements as well. In the next section the different steps in an on-wafer measurement with VNA Tools II are explained. An overview of the features of VNA Tools II is given in [75]. Further information and user guidance can be found at [12]. Measurement models, calculations and data formats are documented in publicly available documents, which can be downloaded from the website as well. 5.2 VNA Tools II on-wafer example 5.2.1 Introduction This example shows the use of the VNA Tools software to perform an SOLT on-wafer measurement. The following typical steps are covered: 1. Definition of a new project. 2. Collection of measurement data and record of the measurement process in the Measurement Journal. 3. Configuration of VNA calibration and computation of error coefficients. 4. Error correction of the raw measurement data. 5. Use of data explorer for visualization. 5.2.2 New project and basic definitions The first step in VNA Tools II is to define a new project. This defines the location, where the data files of the project are stored and some basic settings. It can be specified in the navigation bar on the top. By selecting New Project the dialog in Fig. 37 opens. The entries under Name and Location will define the global root path. Under VNA Setup a VNA 49 Figure 38 VNA Settings. device, test port cable and probe can be selected. In this example a Test VNA is selected, which usually serves just for test purposes. Clicking OK will store these entries and close the dialog. By selecting VNA Settings VNA device parameters can be set in a separate dialog, see Fig. 38. The dialog allows to set some parameters and specify the sweep mode, which in this case is a segmented sweep. The sweep is defined by the entries in the segment table, e.g. the maximum frequency is set to 50 GHz and the IFBW to 10 Hz. By clicking Set Segment Table the values will be saved to the VNA. By clicking OK the VNA Settings are saved to the measurement journal. Selecting Custom DUT Unc in New DUT Unc opens the dialog in Fig. 39 to account for crosstalk between probes during measurements. The values entered as transmission uncertainties are dependent on distance and probe type. In this example all measurements are done on the same substrate, with the same probes and the same distance between probes. The size of the uncertainty contribution is therefore the same for each measurement, but uncorrelated when changing from one standard to another. When clicking OK the first two entries, VNA Settings and Custom DUT Unc can be seen in the measurement journal. 5.2.3 Measurements For the simultaneous measurement of the opens of both ports an uncertainty contribution due to crosstalk between probes needs to be taken into account. This is generated by clicking on New DUT Unc and selecting from the drop-down menu Custom, see Fig. 40. Increase the number in the Index field when measuring a new standard. Use same index if measuring the same standard again. This keeps track of the correlation. Click OK to generate the uncertainty contribution. It will show up in the measurement journal. To start the measurement the boxes under New Connection need to be checked for both ports, see Fig. 41. Because both probes are kept at a fixed position during the measurements no uncertainty contributions due to cable movement need to be accounted for. The boxes under Cable Movement 50 Figure 39 Setting custom DUT uncertainty. Figure 40 Selecting custom DUT uncertainty to create an uncertainty contribution due to cross talk. 51 Figure 41 Cable movements and new connections before measurements are indicated by checking boxes. Figure 42 Measurement dialog box. therefore remain unchecked. As soon as one of the probes is moved before a measurement the corresponding box needs to be checked. Selecting Open next to the VNA Device field, see Fig. 41, will open the connection to VNA. Selecting Measurement opens the dialog in Fig. 42. In this dialog the setup needs to be specified in the drop-down menu Setup, in this case Sx,x Ports: 1,2. Clicking on Measure will initiate the measurement and the data will be displayed in the graph. The measurement of the open in this example is showing noise contributions for S21 and S12. When satisfied with the measurement the data can be stored with Save Data. The same procedure will be repeated for the measurement of short, load and through. In the final measurement step the DUT, in this case a line, is measured, see Fig. 43. When the measurements are finished the measurement journal can be saved by clicking Save Journal. 52 Figure 43 After final measurement of DUT performed. 5.2.4 Calibration configuration After clicking on the tabs Calibration Config and New Config we select SOLT in the dropdown menu as the calibration type, see Fig. 44 After clicking on OK the template can be filled in by linking measurement data, in column Raw Measurement, and definitions, in column Definition, of the calibration standards, see Fig. 45. In the same dialog the measurement journal needs to be specified, in this case Journal 01.vnalog. With Save Config the calibration configuration can be saved to a file SOLT 01.calcfg. By clicking on Start Computation the error coefficients are computed and stored as SOLT 01.calb. 5.2.5 Error correction After selecting the tab Error Correction the dialog in Fig. 46 opens The fields need to be populated with the location of measurement journal, error coefficients, raw measurements and output folder. With Save Config the configuration will be saved to a file SOLT 01.corcfg. Clicking on Start Computation will initiate the error correction and store error corrected S-parameter files in SOLT 01 out. 5.2.6 Data Explorer By selecting the tab Data Explorer the measurement results can be visualized as shown in Fig. 47. The Data Explorer has a data browser on the left. By clicking on data files they will be displayed on the right. There are different basic display modes, which can be selected with Graph,Table,Point and Covariance. As for setup and format there are various selections as well. Uncertainties can be tuned on or off. Data can as well be exported to other file formats. 53 Figure 44 Selection of calibration type. Figure 45 Calibration Configuration. 54 Figure 46 Error Correction. Figure 47 Data Explorer. 55 5.3 Uncertainty budget examples In the following uncertainty results for three typical devices on a fused silica substrate are shown for the case of a multiline TRL calibration (from [11]), covering a large portion of the impedance range measurable by a VNA: a nominally 15 dB matched attenuator (termed ‘attenuator’), a 7065 µm-long mismatched line (termed ‘mismatch’), and a 2-port open (high-reflect device, termed ‘open’)). 5.3.1 Expanded uncertainties 10 20 30 40 50 60 70 80 90 100 110 Frequency (GHz) -0.04 -0.02 0 0.02 0.04 |S11| (exp. unc.) attenuator mismatched line open 10 20 30 40 50 60 70 80 90 100 110 Frequency (GHz) -15 -10 -5 0 5 10 15 (S11)/°(exp. unc.) attenuator mismatched line open 10 20 30 40 50 60 70 80 90 100 110 Frequency (GHz) -0.05 0 0.05 |S21| (exp. unc.) attenuator mismatched line open Figure 48 Expanded uncertainty intervals at a coverage probability of 95% (k=2). 56 [60] K. Haddadi, A. E. Fellahi, J. Marzouk, S. Arscott, C. 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