## 6 High Frequency Characterization and Modelling
### High Frequency Characterization of InP DHBTs
#### 6.1.2 Measurement Results and HiCuM Compact Model Validation Up to 330 GHz  
The HiCuM model parameter extraction was performed with S-parameter measurements up to 40 GHz and validated against the measurements up to 330 GHz. Among these two separate measurement campaigns, the former was dedicated to parameter extraction while the latter targets high-frequency characterization and model validation. The HiCuM compact model scalability was first verified with RF measurements up to 40 GHz. Five different geometries of transistors were measured and the transit frequency, \(f_{T}\), was extracted at 15 GHz for different bias points. The complexity of the HiCuM model requires a systematic extraction of device parameters, especially when different parameters are strongly correlated at high-current conditions. Hence, the interlinked parameter extraction flow described in Section 3 has been used to extract the parameters related to transit time along with the capacitance and current parameters. Moreover, the temperature-related parameters are also extracted for each quantity at all steps. The comparison between the measurement and simulation results is depicted in Figure 13a. A good agreement is observed between the measurements and the geometry-scalable compact model simulation  
Figure 12: (**a**) InP DHBT test structures for measurements beyond 110 GHz; (**b**) Layout view of the Pad-Open. with HiCuM, where the 0.7 \(\times\) 5 \(\upmu\)m\({}^{2}\) InP DHBT presented the maximum RF performance. The corresponding Gummel plot and static gain are shown in Figure 13b. Then, the S-parameter measurements were carried out up to 330 GHz using three measurement benches: (i) up to 110 GHz using an Agilent(r) E8361 PNA, with frequency extenders for the 67-110 GHz frequency range; (ii) in the G-band (140-220 GHz) and J-band (220-330 GHz) using a Rohde & Schwarz(r) ZVA24, coupled with Rohde & Schwarz(r) frequency extenders. Hence, Picoprobe(r) probes were used in the 1-110 GHz and J-band, and Cascade Infinity(r) probes in the G-band. As mentioned earlier, the transistor under test has an emitter length of 5 \(\upmu\)m and an emitter width of 0.7 \(\upmu\)m, since it showed the maximum current gain among all the geometries measured. The measurements were made up to 330 GHz using on-wafer TRL calibration. The transistor was biased under a fixed 1.6 V collector-to-emitter voltage and a sweep of the base-to-emitter voltage from 830 to 910 mV with a 10 mV-step. The maximum gain is obtained for \(V_{BE}\) = 910 mV. The gain curves, cut-off frequencies and S-parameters are depicted in Figure 14, where a comparison is drawn between the measured quantities and the ones obtained after simulation of the HiCuM compact model up to 330 GHz. A pretty good agreement can be observed between measurement and simulation up to 330 GHz for the different bias points. Interestingly, a slight discrepancy can be observed between the measurement and the HiCuM simulation for the Mason's gain (Figure 14b). This is due to the limitation of the TRL calibration below 35 GHz. The design of the on-wafer TRL calibration kit focuses on the very high-frequency measurements beyond 110 GHz, and due to the constraints of wafer area, a compromise was made in selecting the line dimensions to be fabricated. Hence, a maximum length of 180 \(\upmu\)m (equivalent to a minimum frequency of 35 GHz) was chosen for the lines. In addition, due to the high sensitivity of the measurements of the Mason's gain, even the slightest variation in the measurement environment may lead to deviation from what is predicted by the model. Despite the use of three different on-wafer probing setups, an excellent band continuity could be achieved among the measurement frequency bands. Figure 13: (**a**) Measured and simulated \(f_{T}\) versus \(I_{C}\) for several transistor geometries; (**b**) Gummel plots and static current gain curve superimposition between measurement and HiCuM simulation.