4.5.3 Device Simulation Results and Comparison with Measurements

As shown in previous example (see Section 4.1.3) proper modeling of bandgap narrowing (BGN) and recombination have particular importance. In addition, the polysilicon contact model (see Section 3.1.6) is used. The contribution of BGN to the conduction band $\Delta E_{C}/\Delta E_{\mathrm{g}}$, the trap charge density $N_{\mathrm{T}}$ from the SRH model, and the velocity recombination for holes at the emitter contact $S_p$ are the only fitting parameters used.

The result for the electron current density at V$_\mathrm {BE}$ = 1.5 V (V$_\mathrm {CE}$) is shown in Fig. 4.42. Note, the comparatively high electron current portion of the base current. The simulation gives an explanation of the experimentally observed decrease in the current gain at high bias. Comparisons between the measured and simulated forward Gummel plot (Fig. 4.43) and current gain (Fig. 4.44) show good agreement.

Figure 4.43: Measured and simulated forward Gummel plot at V$_\mathrm {BC}$ = 0 V at 300 K

Figure 4.44: Current gain vs. collector current

In the case of simulation of the output characteristics one meets severe problems to achieve realistic results, especially in the case of power devices. Therefore, self-heating (SH) effects have to be accounted for by solving the lattice heat flow equation self-consistently with the energy transport equations. An alternative Global SH model (GSH) has been offered in [211]. The model calculates a spatially constant (global) lattice temperature $T_{{\mathrm{L}}}$ in the device from the dissipated power as

$$T_{{\mathrm{L}}}= T_{\mathrm{C}}+ R_g \cdot \sum_C I_C \cdot V_C$$ (4.5)

with $I_C$ and $V_C$ being the contact currents and voltages, $T_{\mathrm{C}}$ being contact temperature, and $R_g$ being the global thermal resistance.

In Fig. 4.45 the simulated output device characteristics compared to measurements for base currents of 2, 4, 6, and 8 $\mu$A are shown. The GSH model with $R_g$ = 800 K/W delivers the same results (within 2%) as the SH model, but for 40% less CPU time. Both models deliver results in very good agreement with the measured output device characteristics. In contrast to that, simulation without including of SH effects cannot reproduce the experimental data, especially at high power levels. Similar and even stronger observation were already done in the case of GaAs power HBTs (see Section 4.2.2).

Figure 4.45: Simulation with SH (solid lines) and without SH (dashed lines) compared to measurement data (symbols)