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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$\scriptstyle \tau_{\mathrm{f}}$ coefficient for bias dependence of $ \tau_{\mathrm{f}}^{}$ 0
V$\scriptstyle \tau_{\mathrm{f}}$ voltage describing Vbc dependence of $ \tau_{\mathrm{f}}^{}$ $ \infty$ V
I$\scriptstyle \tau_{\mathrm{f}}$ high-current parameter for effect on $ \tau_{\mathrm{f}}^{}$ 0 A
P$\scriptstyle \tau_{\mathrm{f}}$ excess phase at f = $ {\frac{1}{2\cdot\pi\cdot\ensuremath{\tau_{\mathrm{f}}}}}$ 0o
XT$\scriptscriptstyle \beta$ 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.

next up previous
Next: 6.3 Simulation of the Up: 6. Extraction of Compact Previous: 6.1 The Simulated Device
Martin Rottinger
1999-05-31