6.1 Simulation of an InGaP/GaAs Heterojunction Bipolar Transistor

By means of the small-signal simulation mode of MINIMOS-NT, various high-frequency data for a one-finger InGaP/GaAs HBT with an emitter area of $3\,\mu$m $\times$ $30\,\mu$m were extracted. This high-power device has been used for power amplifier circuits for mobile communication. Figure 6.1 shows the simulated device structure and the pad parasitics (capacitances and inductances) of the measurement environment used for the S-parameter measurement in the two-port pad parasitic equivalent circuit.

Figure 6.1: Simulated device structure together with pad parasitics used for S-parameter calculation [161].

The pad capacitances of the equivalent circuit are $C_\mathrm{pBE} =$150$\,$fF, $C_\mathrm{pCE} =$75$\,$fF, and $C_\mathrm{pBC} =$24$\,$fF. The parasitic inductance values are $L_\mathrm{pE} =$1$\,$pH, $L_\mathrm{pB} =$75$\,$pH, and finally $L_\mathrm{pC} =$50$\,$pH. The resistive parasitics are neglected, since a rather small device and therefore only low currents are considered.

Figure 6.2 shows a comparison between measured and simulated collector currents $i_\mathrm{C}$ and an almost perfect match of the curves in the small-signal area of the figure. A further increase of the input power causes harmonics in the device, which cannot be obtained by the linear small-signal mode (see Section 2.6).

The combined Smith/polar charts with a radius of one in Figure 6.3 show a comparison of simulated and measured S-parameters at $\ensuremath{V_\mathrm{CE}}=$3$\,$V, with current densities ${\ensuremath{J_\mathrm{C}}} = 2\,$kA/cm$^2$, ${\ensuremath{J_\mathrm{C}}} = 8\,$kA/cm$^2$, and ${\ensuremath{J_\mathrm{C}}} = 15\,$kA/cm$^2$, respectively, for the frequency range between 50$\,$MHz and 10$\,$GHz. For the same device the high-frequency figures of merits current gain $g_\mathrm{m}$ and the squared absolute value of the current ratio parameter $\underline{H_{21}}$ were extracted. The cut-off frequency $f_\textrm {T}$ and maximum oscillation frequency $f_\mathrm{max}$ are found at the intersection of these curves with the 0$\,$dB line. The lower right side of Figure 6.3 shows a comparison of the simulated and measured $g_\mathrm{m}$ and the absolute value of $\underline{H_{21}}$. The measurement data ends at 10$\,$GHz, whereas the simulation could be continued to $20\,$GHz showing another important advantage of simulators to measurement equipments. In addition, a mixed-mode circuit was set up to compare large signal measurement data in the small-signal range.

The AC-simulation takes about 200$\,$s CPU-time on a 2.4$\,$GHz Intel Pentium IV with 1$\,$GB memory running under Suse Linux 8.2 for a S-parameters computation with 20 frequency steps. A number of 20 steps is more than sufficient to produce the graphs. For comparison, the conventional small-signal equivalent-circuit approach takes about 590$\,$s CPU-time at the same machine for 200 time steps at only one given frequency. As stated in the introduction, many time steps have to be performed to ensure appropriate accuracy in the time-domain to obtain sufficient accuracy for one frequency. To avoid this number of time steps for all frequencies required, only one frequency is used to extract an equivalent circuit valid in a specific frequency range. The time for such a post-processing of the transient simulation results to obtain the S-parameters at all frequencies is not included. Thus, the more accurate approach can speed up the frequency-domain simulation by about 98% (taking one frequency into account).

Figure 6.2: Comparison of simulated and measured AC collector current i $_\textrm {C}$ over AC input power $P_\textrm {IN}$ (left). Comparison of simulated and measured AC output power $P_\mathrm{OUT}$ over AC input power $P_\textrm {IN}$ (right).

Figure 6.3: S-parameters in a combined Smith/polar chart with a radius of one from $50\$MHz to $10\$GHz at $\ensuremath{V_\mathrm{CE}}= 3\$V, ${\ensuremath{J_\mathrm{C}}} = 2\,$kA/cm$^2$ (upper left), ${\ensuremath{J_\mathrm{C}}} = 8\,$kA/cm$^2$ (upper right), and ${\ensuremath{J_\mathrm{C}}} = 15\,$kA/cm$^2$ (lower left). In the lower right figure the short-circuit current gain and matched gain versus frequency at ${\ensuremath{J_\mathrm{C}}} = 15\,$kA/cm$^2$ is shown.