## 6 High Frequency Characterization and Modelling
### TCAD and Monte Carlo Simulations
It can be attributed to the energy level of the \(X\) valley, \(E_{X}\), which, on one hand, is not exactly known, and whose behavior, on the other hand, is not accurately reproduced by our tight-binding model. Figure 20: (**a**) Simulated bulk bandstructure of In\({}_{0.53}\)Ga\({}_{0.47}\)As; (**b**) energy level of the different valleys of In\({}_{\text{x}}\)Ga\({}_{1\text{-x}}\)As as a function of \(x\)[30]. Extrapolation of Figures of Merits to State-of-the-Art (0.13 \(\times\) 2 \(\mu\)m\({}^{2}\)) DHBTs Using Compact Model  
Another important aspect of a co-simulation framework is the predictive capabilities of the compact models. In order to achieve the desired functionality of an integrated circuit, it is imperative that the mathematical model formulation ensures a strong correlation between geometry scaling and model parameters to be able to correctly predict performances for an extrapolated dimension. In order to continually enhance figures of merits along the technology scaling roadmap, various scaling approaches have been adopted or envisioned including process optimization to reduce the capacitances and transit delays [31], or even a hybrid approach for silicon-germanium (SiGe) HBTs consisting doping profile optimization through TCAD simulations and predictive compact modeling through HiCuM/L2 model simulation [32]. With the same fundamental approach for III-V DHBTs, we used geometry scaling laws for HiCuM model parameters to extrapolate the major figures of merit (\(f_{T}\), \(f_{MAX}\), \(\beta\) and R\({}_{\rm TH}\)), without modifying the epitaxial structure or any other process features, to obtain reasonable prediction results. This requires an accurate scalable model card extracted for the geometries under test, which was further used to extrapolate the figures of merit of the current technology generation to DHBTs with the emitter dimensions of 0.13 \(\times\) 2 \(\mu\)m\({}^{2}\), in order to compare them with those of the state-of-the-art InP HBT [1; 33]. Figure 22 shows the scaling prediction results for these figures of merit using our scalable HiCuM model card for the current technology generation (G1). The extrapolated  
Figure 21: (a) Simulated conduction band diagrams of the considered DHBT with increasing \(V_{CE}\) (1, 1.4, 1.6, 1.8 and 2 V) at \(V_{BE}\) = 0.9 V; (b) spatially resolved electron concentration inside the active E–B–C domain at \(V_{CE}\) = 1, 1.6, 1.8 and 2 V for \(V_{BE}\) = 0.9 V; (c) energy and spatially resolved electron concentration \(n\) (\(x\), \(E  
\(f_{T}\) and \(f_{MAX}\) are compared with that of the 0.13 \(\times\) 2 \(\upmu\)m\({}^{2}\) state-of-the-art for a \(V_{CE}\) of 1 V. The predicted peak\(f_{T}\) [Figure 22a] shows that a higher value can be expected compared to the reported value for the experimental devices [33]. The new technology generation shows a similar \(f_{T}\) compared to the previous generation [34]. The reduction in the transit time with emitter width scaling has been observed at high current densities, which can be attributed to a pronounced collector current spreading in smaller emitter dimensions [34], leading to larger critical current and smaller transit time values. Small emitter dimension particularly poses a challenge to maintain an acceptable current gain (\(\beta\)), of which rather low (15-20) values have been reported for the 0.13 \(\upmu\)m InP HBT process [1; 33]. On the other hand, the prediction for the current generation shows an extrapolated current gain of 25-30 for the 0.13 \(\times\) 2 \(\upmu\)m\({}^{2}\) DHBT (Figure 22b). The predicted current gain is comparatively lower than the prediction of the previous generation [33], owing to the higher effective base doping in the new technology generation, which in turn lowers the base sheet resistance and results in a lower static current gain as well as a higher \(f_{MAX}\).