6.4 Parameter Extraction

To find the best set of parameters for the Gummel-Poon model the SIESTA optimizer[41] was used. From the simulation results provided by MINIMOS-NT initial values of the optimization parameters were extracted manually. Starting from these values the optimizer calls SPICE and compares the results to those obtained by device simulation. For each optimization parameter the gradient has to be calculated to determine how to change the parameter set for the next optimization step. Using the set of calculated gradients the values of the parameters are determined for the next optimization step. This loop is continued until the difference of the device and the circuit simulation falls below a user defined threshold.

Fig. 6.8 shows schematically the control flow of the optimization of the compact model parameters.

The values of the parameters found by optimization are listed in Table 6.3. For parameters not listed in Table 6.3 default values were used in subsequent circuit simulations.

Figure 6.8: Control flow of the optimization of the extracted model parameters.

Table 6.3: Parameters of the Gummel-Poon compact model found by optimization.

parameter	value
Is	4.1 . 10- 17 A
$\beta_{\mathrm{f}}^{}$	397.6
$\beta_{\mathrm{r}}^{}$	98
rc	0.82 $\Omega$
re	0.21 $\Omega$
Ikf	0.0125 A
Ikr	0.025 A
nel	1.6
ncl	2.2
VA	500 V
C2	6 . 10- 18 A
C4	2 . 10- 16 A
Cjc	1 . 10- 13 F
Cje	8 . 10- 14 F
$\phi_{\mathrm{c}}^{}$	0.7 V
$\phi_{\mathrm{e}}^{}$	0.7 V
mc	0.5
me	0.5

Fig. 6.9 shows a comparison of the collector and base currents simulated by MINIMOS-NT and SPICE using the extracted parameters. For base-emitter voltages higher than 0.3 V the agreement between the two simulations is very good. Below 0.3 V the currents simulated by SPICE are too high.

Figure 6.9: Comparison of log(I_c) and log(I_b) vs. V_be simulated by MINIMOS-NT and SPICE.

A comparison of the emitter and base currents for reverse bias conditions simulated by MINIMOS-NT and SPICE is shown in Fig. 6.10. For base-collector voltages between 0.3 V and 0.9 V the agreement between the two simulations is quite good (see Fig. 6.11). For base-collector voltages between 0.6 V and 0.9 V the currents simulated by MINIMOS-NT are slightly lower than those simulated by SPICE. At voltages below 0.3 V the currents simulated by SPICE again are too high. Above 0.95 V the results obtained from SPICE differ considerably from the currents simulated by MINIMOS-NT (see Fig. 6.12). For base-collector voltages higher than 0.95 V the collector current simulated by MINIMOS-NT is higher than in simulations performed with spice. The disagreement is even larger for the base current. The simulations performed with MINIMOS-NT show an increase of the base current which leads to a decrease of the current gain below a value of 1 for base-collector voltages higher than 1.3 V. This behavior is not reproduced by SPICE where the current gain is larger than 1 for all base-collector voltages below 1.4 V.

Figure 6.10: Comparison of log(I_e) and log(I_b) vs. V_bc simulated by MINIMOS-NT and SPICE.

Figure 6.11: Comparison of log(I_e) and log(I_b) vs. V_bc simulated by MINIMOS-NT and SPICE for V_bc = 0.3 - 0.9 V.

Figure 6.12: Comparison of log(I_e) and log(I_b) vs. V_bc simulated by MINIMOS-NT and SPICE for V_bc = 0.9 - 1.4 V.

The output characteristics simulated by MINIMOS-NT and SPICE are plotted in Fig. 6.13. In the device simulated by MINIMOS-NT the quasi-saturation region is very large. This cannot be modeled by the Gummel-Poon model as it is implemented in SPICE and therefore the collector currents differ considerable in this operating region. The Gummel-Poon model can be modified to take the so-called base pushout effect into account which models the variation of the base width in dependence of the collector current. However, in the standard version of SPICE which was used for the circuit simulations these modifications are not implemented.

Figure 6.13: Comparison of the output characteristic simulated by MINIMOS-NT and SPICE.