Subsections

• 4.2.2.1 Forward and Reverse Gummel Plots
• 4.2.2.2 Simulation with Self-Heating
• 4.2.2.3 Simulation of Output Characteristics

4.2.2 Simulation Results

One concise set of model parameters is used in all simulations. The extrinsic parasitics, e.g. the emitter interconnect resistance, are accounted for in the simulation by adding lumped resistances of 1 $\Omega$ to all electric contacts.

4.2.2.1 Forward and Reverse Gummel Plots

In Fig. 4.15 the simulated forward Gummel plot for Dev. 1 at 293 K is shown and compared to experimental data. Note the good agreement at moderate and high voltages, typical for operation of this kind of devices. The measured leakage currents at V $_{\mathrm {BE}}$ $\leq$ 1 V cannot be reproduced by simulation, despite of the fact that several generation/recombination mechanisms, such as SRH recombination, surface recombination, and BB are taken into account.

Figure 4.15: Forward Gummel plots at V $_{\mathrm {CB}}$ = 0 V for Dev. 1: Comparison with measurement data at 296 K

Figure 4.16: Forward Gummel plots at V $_\mathrm {CB}$ = 0 V for Dev. 2: Comparison with measurement data at 296 K and 376 K

Figure 4.17: Forward Gummel plots at V $_{\mathrm {CB}}$ = 0 V for Dev. 4: Comparison with measurement data

Figure 4.18: Reverse Gummel plots at V $_{\mathrm {CB}}$ = 0 V for Dev. 4: Comparison with measurement data at 293 K and 373 K

4.2.2.2 Simulation with Self-Heating

In order to account for self-heating effects the lattice heat flow equation (3.14) is solved self-consistently with the energy transport equations (3.6) and (3.7), which results in a system of six partial differential equations. An additional, substrate thermal contact is introduced. The thermal heat flow density is calculated by (3.28) using a thermal contact resistance $R_{\mathrm{T}}$ with a measured value of about 400 K/W [27,199]. The thermal dissipation through the emitter and base contacts is neglected, therefore a Neumann boundary condition is assumed.

4.2.2.3 Simulation of Output Characteristics

It is a severe problem to achieve realistic results in simulation of output HBT characteristics. This is especially true for power devices which are considered in this work. As stated in [71] the power dissipation increases with collector-to-emitter voltage V $_{\mathrm {CE}}$, gradually elevating the junction temperature above the ambient temperature. This leads to gradually decreasing collector currents I$_\mathrm {C}$ at constant applied base current I$_\mathrm {B}$ or, respectively, gradually increasing I$_\mathrm {C}$ at constant base-to-emitter voltage V $_{\mathrm {BE}}$. The simulated output device characteristics compared to measurements for constant V $_{\mathrm {BE}}$ = 1.4 V to 1.45 V using a 0.01 V step are shown in Fig. 4.19. A good agreement is achieved by simulation including self-heating effects. In Fig. 4.20 the intrinsic temperature $T_j$ in the device depending on the V $_{\mathrm {CE}}$ is presented. For Dev. 3 the temperature reaches as much as 400 K for the specified thermal resistance. As already stated in [63] such lattice temperatures significantly change the material properties of the device and, consequently, its electrical characteristics. This confirms the necessity of exact DC-simulations at several high ambient temperatures before including self-heating effects.

Hydrodynamic simulation is needed to account for non-local effects. For example, the electron temperature (see Fig. 4.21) is used as an input to the hydrodynamic mobility model and therefore allows to simulate the electron velocity overshoot in the collector space charge region. The carrier temperature also influences the current flux across the heterointerfaces - the higher it is the more carriers are able to surmount the energy barrier. This effect is referred to as real-space transfer [70]. Considering the nature of the simulated devices (including graded and abrupt heterojunctions) and the high electron temperatures observed at maximum bias (above 2500 K - see Fig. 4.21) a thermionic-field emission interface model (3.48) is used in conjunction with the hydrodynamic transport model.

The resulting lattice temperature distribution in the device at V$_\mathrm {CE}$ = 6.0 V and V$_\mathrm {BE}$ = 1.45 V is shown in Fig. 4.22. The heat generated at the heterojunctions flows out of the device in the direction of the substrate heat sink. In the opposite direction the heat cannot leave the device and therefore the emitter finger is heated up significantly up to 400 K. The simulation shown is of practical interest and demonstrates the necessity of a thermal shunt at the emitter contact rather than reducing the substrate thickness.

Figure 4.19: Output characteristics for Dev. 3: Simulation with and without self-heating compared to measurement data

Figure 4.20: Intrinsic device temperature vs. V $_{\mathrm {CE}}$ for Dev. 3

Figure 4.21: Electron temperature distribution [K] at V$_\mathrm {CE}$ = V$_\mathrm {BE}$ = 1.6 V

Figure 4.22: Lattice temperature distribution [K] at V$_\mathrm {CE}$ = 6.0 V and V$_\mathrm {BE}$ = 1.45 V: A substrate thermal contact with $R_{\mathrm{T}}$=400 K/W is added.