4.3.2 Simulation Results

The combined Smith/polar charts in Fig. 4.24 and Fig. 4.25 show comparisons of the simulated and measured S-parameters of a 90 $\mu$m$^2$ AlGaAs/GaAs HBT with InGaP ledge at V$_\mathrm {CE}$ = 3 V and I$_\mathrm {C}$ = 22 mA in frequency range between 0 and 20 GHz. Due to the large emitter area, the limitations of the eight-element intrinsic circuit, and the fact that the physical extraction procedure includes no fitting perfect agreement cannot be expected. As shown in Fig. 4.24 the deviations of measured and simulated S-parameters are more pronounced than for unipolar devices given the bias point is in a typical operation regime of a high power device. However, the small-signal extraction supplies valuable information about the modeling and the device itself.

Figure 4.24: S-parameters in a combined Smith chart (S$_{11}$ and S$_{22}$) and a polar graph (S$_{21}$ and S$_{12}$) from 0 to 20 GHz at V$_\mathrm {CE}$ = 3 V, I$_\mathrm {C}$ = 22 mA: Simulation (solid lines) vs. experiment (dashed lines)

Using the extraction above it is found that the physical background of some crucial elements can be improved. These are the small-signal elements base resistance R$_\mathrm {b}$ and the emitter junction capacity C$_\mathrm {je}$, which show significant deviations on first approach. It is found that neglecting the difference between majority and minority electron mobilities results in underestimation of the electron mobility in the GaAs base of the HBT (see Section 3.4). This results in a significant overestimation of the extracted base resistance, as can be seen in Fig. 4.24. Including the respective mobility model much better agreement is achieved (see Fig. 4.25).

Figure 4.25: S-parameters in a combined Smith chart (S$_{11}$ and S$_{22}$) and a polar graph (S$_{21}$ and S$_{12}$) from 0 to 20 GHz at V$_\mathrm {CE}$ = 3 V, I$_\mathrm {C}$ = 22 mA: Simulation (solid lines) vs. experiment (dashed lines)

For S$_{11}$ and S$_{22}$ good agreement with the measurements is obtained. The remaining underestimation of the magnitude of S$_{21}$ is partly due to the fact that no HD simulation is performed. Further, R$_\mathrm {b}$ and C$_\mathrm {je}$ are still overestimated including the improved mobility model. For S$_{12}$ very good agreement is achieved, given the the uncertainties of the measurement process of the feedback.

The simulated S-parameter are converted to h-parameters at 5 GHz. The current gain cutoff frequency $f_{\mathrm{T}}$ is obtained by extrapolation of the element $\Vert$h21$\Vert$ by 20 dB/decade frequency dependence. In addition, the dependence of $f_{\mathrm{T}}$ on important parameters, such as base width and ambient temperature, is investigated by simulation. The results are shown in Fig. 4.26 and Fig. 4.27, respectively. The contribution of the base delay time to the total delay can be estimated from the decrease of $f_{\mathrm{T}}$ with the base width, shown in Fig. 4.26. The degradation of $f_{\mathrm{T}}$ at high temperatures, shown in Fig. 4.27, is experimentally observed. The simulated $f_{\mathrm{T}}$ is in good agreement with the measured value at ambient temperature of 293 K.

This section shows, that given the constraints mentioned due to the compact modeling of HBT S-parameters, the RF extraction is available and suitable for predictive simulations, especially for quantitative estimations of dependence on not experimentally available degrees of freedom during device design.

Figure 4.26: Cutoff frequencies vs. base width

Figure 4.27: Cutoff frequencies vs. ambient temperature