On-Wafer 16-Term Calibration for Characterization of InP HBTs Featuring Sub-THz fmax

On-Wafer 16-Term Calibration for Characterization of InP HBTs Featuring Sub-THz fmax Abhijeet Kanitkar#1, Ralf Doerner#, Tom K. Johansen$, Wolfgang Heinrich#, Thomas Flisgen#* #Ferdinand-Braun-Institut (FBH), Germany $Technical University of Denmark, Denmark *Brandenburg University of Technology (BTU), Germany 1[email protected] Abstract — In this paper, InP HBTs featuring maximum oscillation frequencies fmax in the sub-THz range are characterized by conducting on-wafer 16-term calibration. A direct comparison between 8-term calibration and 16-term calibration demonstrates that the 16-term calibration improves the way transistor Mason’s gain is derived. The on-wafer measurements of transistors with emitter widths of 0.5µmand 0.85 µmyield extracted fmax values of 0.44 THz and 0.33 THz, respectively. The study shows that choosing proper on-wafer calibration techniques is highly important for reliable transistor characterization. Keywords — InP HBTs, On-wafer measurements, Transistor characterization, 8-term calibration, 16-term calibration. I. INTRODUCTION Future wireless systems will operate in the upper millimeter wave and sub-THz frequency range and will enable a variety of applications such as wireless cognition, sensing, imaging, high-capacity communication and high-accuracy positioning, as discussed, in e.g. [1], [2]. Since these systems require circuits with sufficiently fast transistors, a lot of effort is currently being invested to further increase their speeds. Indium phosphide (InP) transistors are promising technologies for such high-speed applications as they provide a transit frequency fTand a maximum oscillation frequency fmax in the sub-THz range [3]. The fmax is often determined by extrapolating the Mason gain or unilateral gain Uof the transistor to 0 dB assuming a simple −20 dB per decade dependency at higher frequencies. The frequency-dependent Mason’s gain is usually deduced from on-wafer scattering parameter measurements far below fmax. This requires accurate and reliable on-wafer calibration. However, the calibrated data arising from on-wafer measurements is notorious for artifacts and inaccuracies resulting from a multitude of origins, such as radiation of energy into the substrate, excitation of surface waves, influence of neighboring structures, influence of chuck material, incorrect horizontal probe positioning, and probe-to-probe coupling. Therefore, fmax determination of downscaled sub-THz transistors is a critical task. While the majority of articles, see e.g. [4], [5], discusses the influences of parasitic effects in on-wafer measurements on calibrated scattering parameters, publications in the context of these effects with regard to Mason’s gain are scarce. In [6] and [7], unexpected trends in Mason’s gain are explained by parasitic probe-to-probe coupling. As a possible solution [8], [9], [10] reported and explained the application of 16-term on-wafer calibration for transistor characterization. However, for the successful implementation of a 16-term error model, an accurate description of the scattering parameters of the standards is necessary [11], [12]. In [8] and [9], lumped element models of the calibration standards are used to characterize 0.13 µmMOSFET, whereas [10] uses a combination of TRL-calibrated data and EM simulations to characterize the silicon-germanium transistor. This paper focuses on the most promising InP technology, which opens up applications with much higher frequencies. The devices used in this study are InP heterojunction bipolar transistors (HBTs) having a 0.5µmand 0.85 µm technology node. We propose the direct use of 8-term corrected scattering parameters of standards to perform 16-term calibration. For this purpose, first, the raw measured scattering parameters are corrected by applying an 8-term error model (multiline Thru-Reflect-Line, aka mTRL), and thereby scattering parameters of actual standards are obtained. A 16-term calibration is then performed to correct the raw transistor scattering parameters. Subsequently, fTand fmax are determined using 8-term and 16-term corrected scattering parameters, and a direct comparison is made. II. TEST STRUCTURE LAYOUT The structures required for on-wafer calibration are realized in thin-film microstrip configuration with signal conductor width of 12.8µmand 4µmthick gold metalization. A ground layer is buried in 7.5µmbenzocyclobutene (BCB) layer with εr= 2.65. Facilitating on-wafer probing, coplanar pads in ground-signal-ground (GSG) configuration are realized on the top of the BCB. The calibration standards comprise a THRU, an OPEN, a 50 Ω LOAD, and asymmetric standards in terms of SHORT-OPEN and OPEN-SHORT. They are shown in Fig. 1 from the top without depicting the InP substrate and the BCB, so that the metalizations are visible. In addition, LINE standards with multiple lengths for, e.g., 420 µm,1250 µm,1950 µm,2850 µm, and 8500 µmare also manufactured to implement the preferred 8-term mTRL algorithm. © 2025. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to use any copyrighted component of this work in other works must be obtained from the European Microwave Association, EuMA. Link to publisher version with DOI: 10.23919/EuMC65286.2025.11235132 (a) (b) (c) (d) (e) (f) Fig. 1. Top view of on-wafer calibration standards showing (a) THRU, (b) OPEN, (c) 50 Ω LOAD, (d) asymmetric standards in terms of OPEN-SHORT, and (e) SHORT-OPEN and (f) transistor test structure layout. InP substrate and BCB layer are not shown. The dotted lines depict the calibration reference planes. III. INP HBT DEVICE MEASUREMENTS Two HBT devices in single-finger configuration are manufactured with an emitter area of 0.5×6µm2(referred to as S500) and 0.85 ×6µm2(referred to as S850). The transistors are embedded in the thin-film microstrip line configuration and coplanar pads for GSG probing, as shown in Fig. 1(f). Measurements up to 67 GHz are conducted on a setup consisting of a Keysight PNA-X vector network analyzer and a pair of GSG probes with 100 µmpitch. The bias point VCE = 1.5 V and IB= 0.6 mA is chosen for both devices. IV. COMPUTATION OF CORRECTED SCATTERING PARAMETERS A. 8-Term Calibration The topology in Fig. 2 is assumed for the 8-term calibration. The properties of the error networks SEBL ∈C2×2 and SEBR ∈C2×2are determined by the scikit-rf [13] implementation of mTRL algorithm. The scattering parameters of the standards, THRU in Fig. 1(a), OPEN in Fig. 1(b) and multiple lines of length 420 µm,1250 µm,1950 µm,2850 µm, and 8500 µmare measured up to 67 GHz using the same setup as explained in Section III. For the 50 Ω normalization of the corrected scattering parameters, the characteristic impedance Z0is determined by calculating the capacitance per unit length, C′[14]. The LOAD standard, Fig. 1(c), is used to estimate C′ by measuring the dc-resistance at port 1 and port 2. The error networks are then applied on the raw scattering parameters of the devices measured in Section III. Fig. 2. Schematic representation of 8-term error model. Two-port networks SEBL and SEBR constitute eight error terms. The dotted lines depict the calibration reference planes. Fig. 3. Schematic representation of 16-term error model. SEB constitutes sixteen error terms. The dotted lines depict the calibration reference plane. B. 16-Term Calibration The topology in Fig. 3 is assumed for the 16-term calibration. The properties of the error network SEB ∈ C4×4are determined by the scikit-rf [13] implementation of 16-term algorithm [11], [12] based on the measured scattering parameters of the calibration standards, i.e. THRU in Fig. 1(a), the OPEN in Fig. 1(b), the LOAD in Fig. 1(c), the OPEN-SHORT in Fig. 1(d) and SHORT-OPEN in Fig. 1(e). For an accurate 16-term calibration, it is crucial that the pad-to-pad distance of all calibration structures is equal, so that the coupling remains constant throughout the measurements. This is ensured by keeping the pad-to-pad distance of 390 µm when designing the calibration standards and the transistor layout. In addition, the 16-term algorithm [11], [12] requires the scattering parameters of the actual calibration standards. We used the 8-term error model to obtain the scattering parameters of the actual standards. For this purpose, the error networks SEBL and SEBR arising from the mTRL approach described in Section IV-A are used to calibrate THRU, LOAD, OPEN, OPEN-SHORT and SHORT-OPEN. The error network SEB arising from 16-term calibration is then applied on the raw scattering parameters of the measured devices. V. RESULTS COMPARISON A. Scattering Parameters The magnitude and phase of the 8-term and 16-term corrected scattering parameters of S850 are plotted in Fig. 4(a) and Fig. 4(b), respectively. The corrected scattering parameters of both techniques refer to the same reference planes, as shown in Fig. 1(f). It should be noted that the magnitudes of S11 and S22 are the most sensitive parameters, while the difference in phase is negligible, except for S12. Similar trends are observed (a) (b) Fig. 4. (a) Magnitude and (b) phase of 8-term corrected scattering parameters and 16-term corrected scattering parameters of S850. in the 8-term and 16-term corrected scattering parameters of the S500. Fig. 5(a) and Fig 5(b) show its corrected magnitude and phase, respectively. B. Determination of Transistor Properties The accurate determination of fTand fmax is very important from the circuit designers’ perspective. Usually, designers take half of fmax as their upper frequency limit for oscillator and amplifier design. Fig 6(a) and Fig. 6(b) show the Mason’s gain deduced from the 8-term and 16-term corrected scattering parameters of S850 and S500, respectively. It can be observed that Mason’s gain computed from 8-term corrected scattering parameters does not follow the fundamental assumption of −20 dB per decade slope at higher frequencies. To our knowledge, an 8-term error model, as schematically depicted in Fig. 2, is not capable of fully addressing probe-to-probe coupling in its error correction algorithm, leading to an underestimation and/or overestimation of fmax. This is clearly visible in Fig. 7(a) and Fig. 7(b). Plotting the square root of Mason’s gain multiplied with the corresponding frequency √U×fis a common representation of the extrapolated maximum oscillation frequency fmax. On the other hand, Mason’s gain determined using 16-term corrected scattering parameters improves the way fmax is extracted. It is noticeable that, despite the differences in (a) (b) Fig. 5. (a) Magnitude and (b) phase of 8-term corrected scattering parameters and 16-term corrected scattering parameters of S500. Mason’s gain, the scattering parameters used to deduce Mason’s gain are very similar. This highlights the sensitivity of Mason’s gain against inaccuracies in the corrected scattering parameters. It is worth noticing from Fig. 7(b) that the difference in fmax deduced from the 8-term calibration and the 16-term calibration is around 100 GHz for S500, which is critical for circuit design. Lastly, the determination of fTis straightforward. The short circuit current gain h21 of S850, in Fig. 8(a), and of S500, in Fig. 8(b), is obtained by converting the corrected scattering parameters into hybrid parameters using both calibration techniques. The transit frequency fTis then determined by extrapolating h21 to 0 dB assuming −20 dB per decade slope. In particular, fTis robust against inaccuracies in corrected scattering parameters. The results presented in this paper show that the 16-term calibration improves the way transistor properties are extracted. However, the sensitivity of 16-term calibration against different asymmetric structures such as LOAD-OPEN or LOAD-SHORT, at various biasing conditions, and its validity at higher frequencies remain topics for further investigation. VI. CONCLUSION This paper demonstrates the application of 16-term calibration by conducting on-wafer measurements of InP HBTs (a) (b) Fig. 6. Mason’s gain deduced using 8-term corrected scattering parameters and 16-term corrected scattering parameters of (a) S850 and (b) S500. (a) (b) Fig. 7. √U×frepresentation of fmax extracted using 8-term corrected scattering parameters and 16-term corrected scattering parameters for (a) S850 and (b) S500. (a) (b) Fig. 8. Short-circuit current gain h21 deduced using 8-term corrected S21 and 16-term corrected S21 of (a) S850 and (b) S500. up to 67 GHz. The scattering parameters of the actual standards required for the 16-term calibration are defined by performing an on-wafer 8-term calibration. HBTs with emitter widths of 0.5µmand 0.85 µmare characterized by applying 8-term and 16-term calibrations, and a direct comparison is carried out. In summarizing the results, it can be concluded that a 16-term calibration improves the way the maximum oscillation frequency fmax is estimated, while the transit frequency fTis robust against inaccuracies in the corrected scattering parameters. ACKNOWLEDGMENT The authors would like to thank S. Schulz for on-wafer measurements. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) under grants FL 1201/1-1 and HE 1676/25-1. Also, parts of the work were performed in the framework of the European Partnership on Metrology (EPM) project under grant 23IND10 OnMicro. The 23IND10 OnMicro project was co-financed by the European Union’s Horizon Europe Research and Innovation Program and by the Participating States. With regard to the InP transistor process, funding by the German BMBF through the Research Fab Germany (FMD) under reference FMD02 is gratefully acknowledged. REFERENCES [1] T. S. Rappaport, Y. Xing, O. Kanhere, et al., “Wireless communications and applications above 100 ghz: Opportunities and challenges for 6g and beyond,” IEEE Access, vol. 7, pp. 78 729–78 757, 2019. DOI: 10. 1109/ACCESS.2019.2921522. [2] M. Božani´ c and S. Sinha, “Emerging transistor technologies capable of terahertz amplification: A way to re-engineer terahertz radar sensors,” Sensors, vol. 19, no. 11, p. 2454, 2019. [3] B. Markman and M. Schröter, “Indium-phosphide transistors: A review of current state and suitability for commercial > 100-ghz wireless communication systems,” IEEE Microwave Magazine, vol. 25, no. 10, pp. 38–53, 2024. DOI: 10.1109/MMM.2024.3428191. [4] G. N. Phung, F. J. Schmückle, R. Doerner, T. Fritzsch, and W. Heinrich, “Impact of parasitic coupling on multiline trl calibration,” in 2017 47th European Microwave Conference (EuMC), 2017, pp. 835–838. DOI: 10.23919/EuMC.2017.8230974. [5] G. N. Phung, F. J. Schmückle, R. Doerner, et al., “Influence of microwave probes on calibrated on-wafer measurements,” IEEE Transactions on Microwave Theory and Techniques, vol. 67, no. 5, pp. 1892–1900, 2019. DOI: 10.1109/TMTT.2019.2903400. [6] A. Kanitkar, R. Doerner, T. K. Johansen, W. Heinrich, and T. Flisgen, “Influence of on-wafer parasitic effects on mason’s gain of down-scaled inp hbts,” in 2024 54th European Microwave Conference (EuMC), 2024, pp. 252–255. DOI: 10.23919/EuMC61614.2024.10732142. [7] S. Fregonese, M. De Matos, M. Deng, D. Céli, N. Derrier, and T. Zimmer, “Importance of probe choice for extracting figures of merit of advanced mmw transistors,” IEEE Transactions on Electron Devices, vol. 68, no. 12, pp. 6007–6014, 2021. DOI: 10 . 1109 / TED . 2021 . 3118671. [8] X. Wei, G. Niu, S. L. Sweeney, Q. Liang, X. Wang, and S. S. Taylor, “A general 4-port solution for 110 ghz on-wafer transistor measurements with or without impedance standard substrate (iss) calibration,” IEEE Transactions on Electron Devices, vol. 54, no. 10, pp. 2706–2714, 2007. DOI: 10.1109/TED.2007.904362. [9] X. Wei, G. Niu, S. L. Sweeney, and S. S. Taylor, “Singular-value-decomposition based four port de-embedding and single-step error calibration for on-chip measurement,” in 2007 IEEE/MTT-S International Microwave Symposium, 2007, pp. 1497–1500. DOI: 10.1109/MWSYM.2007.380537. [10] S. Fregonese and T. Zimmer, “Establishing on-wafer calibration standards for the 16-term error model: Application to silicon high-frequency transistor characterization,” IEEE Journal of Microwaves, vol. 4, no. 3, pp. 381–388, 2024. DOI: 10.1109/JMW. 2024.3413865. [11] J. Butler, D. Rytting, M. Iskander, R. Pollard, and M. Vanden Bossche, “16-term error model and calibration procedure for on-wafer network analysis measurements,” IEEE Transactions on Microwave Theory and Techniques, vol. 39, no. 12, pp. 2211–2217, 1991. DOI: 10.1109/22. 106567. [12] K. Silvonen, “Calibration of 16-term error model,” Electronics Letters, vol. 29, no. 17, pp. 1544–1545, 1993. [13] A. Arsenovic, J. Hillairet, J. Anderson, et al., “Scikit-rf: An open source python package for microwave network creation, analysis, and calibration [speaker’s corner],” IEEE Microwave Magazine, vol. 23, no. 1, pp. 98–105, 2021. [14] D. Williams and R. Marks, “Transmission line capacitance measurement,” IEEE Microwave and Guided Wave Letters, vol. 1, no. 9, pp. 243–245, 1991. DOI: 10.1109/75.84601.