6.2 The Compact Model

To simulate the BJT with the circuit simulator SPICE the Gummel-Poon model is used. Table 6.1 and Table 6.2 show the parameters of the static and the large-signal model, respectively. The values of these parameters are extracted from the results of appropriate device simulations performed with MINIMOS-NT. A common problem of compact models is that the extracted parameters are only valid for a small range of bias points. When generating the data from which the values of the parameters are extracted this has to be taken into account.

Table 6.1: Parameters of the static Gummel-Poon model.

symbol	description	default value
Is	saturation current	10- 16 A
$\beta_{\mathrm{f}}^{}$	maximum forward current gain	100
$\beta_{\mathrm{r}}^{}$	maximum reverse current gain	1
rb	zero-bias base resistance	0 $\Omega$
rc	collector resistance	0 $\Omega$
re	emitter resistance	0 $\Omega$
VA	forward Early voltage	$\infty$ V
VB	reverse Early voltage	$\infty$ V
Eg	band gap energy	1.11 eV
C2	base-emitter leakage saturation current coefficient	0 A
C4	base-collector leakage saturation current coefficient	0 A
Ikf	corner for $\beta_{\mathrm{f}}^{}$ high-current roll-off	$\infty$ A
Ikr	corner for $\beta_{\mathrm{r}}^{}$ high-current roll-off	$\infty$ A
nel	base-emitter leakage emission coefficient	1.5
ncl	base-collector leakage emission coefficient	2
rbm	minimum base resistance at high currents	$\Omega$
Irb	current where base resistance falls halfway to its minimum value	$\infty$ A
nf	forward current emission coefficient	1
nr	reverse current emission coefficient	1

Table 6.2: Parameters of the large-signal Gummel-Poon model.

symbol	description	default value
Cjc	zero-bias base-collector junction capacity	0 F
Cje	zero-bias base-emitter junction capacity	0 F
Cjs	zero-bias collector-substrate junction capacity	0 F
$\phi_{\mathrm{c}}^{}$	base-collector built-in potential	0.75 V
$\phi_{\mathrm{e}}^{}$	base-emitter built-in potential	0.75 V
$\phi_{\mathrm{s}}^{}$	substrate-junction built-in potential	0.75 V
$\tau_{\mathrm{f}}^{}$	ideal forward transit time	0 s
$\tau_{\mathrm{r}}^{}$	ideal reverse transit time	0 s
mc	base-collector junction grading coefficient	0.33
me	base-emitter junction grading coefficient	0.33
ms	substrate junction exponential factor	0
Xcjc	fraction of base-collector junction capacity connected to internal base node	1
FC	coefficient for forward-bias junction capacitance formula	0.5
X$\tau_{\mathrm{f}}$	coefficient for bias dependence of $\tau_{\mathrm{f}}^{}$	0
V$\tau_{\mathrm{f}}$	voltage describing Vbc dependence of $\tau_{\mathrm{f}}^{}$	$\infty$ V
I$\tau_{\mathrm{f}}$	high-current parameter for effect on $\tau_{\mathrm{f}}^{}$	0 A
P$\tau_{\mathrm{f}}$	excess phase at f = ${\frac{1}{2\cdot\pi\cdot\ensuremath{\tau_{\mathrm{f}}}}}$	0o
XT$\beta$	forward and reverse $\beta$ temperature coefficient	0
XTI	saturation current temperature exponent	3

The Gummel-Poon model is based on a one-dimensional device geometry and therefore cannot account for effects caused by the two-dimensional nature of the simulated device. The model equations for the base and collector currents are listed in Appendix C.