Implementation in SmartSpice


The MEXTRAM bipolar transistor model was developed by Philips Electronics N.V. and released into the public domain in 1994.[1,2] A subsequent release of the model equations (Version 503.2) has been recently incorporated into SmartSpice and can be accessed by setting the LEVEL parameter on the BJT model card to 503. This new version has an improved description of the Early voltage and cut-off frequency (ft) characteristics compared to the previous version[3]. This was obtained by adding an extra collector charge to account for the collector transit time when the transistor enters quasi-saturation. These enhancements have been achieved without adding to the number of model parameters. This allows parameter sets developed for use with the previous version of MEXTRAM to be used without modification.[4]


The MEXTRAM model is a strongly physics based model, which has been developed to address many of the shortcomings of the Gummel-Poon model (also available in SmartSpice). These shortcomings include :

  • Constant bias independent Early voltages
  • Poor modeling of substrate effects
  • No modeling of avalanche effects
  • Poor geometry and temperature scaling
  • Inadequate modeling of high frequency effects
  • Weak quasi-saturation modeling

The MEXTRAM model has been developed to be a more physical model than the Gummel-Poon model. The model equations are more complex and as a result the model will execute typically 2-3 slower than the Gummel-Poon model. The model uses 39 current and charge modeling parameters and 13 temperature model parameters. A schematic representation of the model is shown in Figure 1.

The effects modeled by MEXTRAM include :

  • Variation in base resistance due to emitter current crowding and conductivity modulation
  • Monotonic bias-dependent forward and reverse Early effects
  • Built-in electric field in the base region


Figure 1. Equivalent circuit diagram for the MEXTRAM model.

  • Monotonic Early voltages and ft behavior for lightly doped epilayer devices
  • First order approximation of high frequency effects in the intrinsic base (high frequency current crowding and excess phase shift)
  • Physical formulation of collector epilayer resistance including hot carrier behavior and current spreading
  • High injection effects in the base
  • Substrate effects including parasitic PNP
  • Weak avalanche effects
  • Hard and quasi-saturation

In order to simplify the model and reduce compute time, some effects are optional and can be switched off if the appropriate flags are specified in the .MODEL card. These effects and the corresponding flags are

  • Extended modeling of the reverse behavior (EXMOD)
  • Increase in avalanche current when the current density in the epilayer exceeds the
    doping level (EXAVL)
  • Distributed high frequency effects (EXPHI)


To validate the implementation of the MEXTRAM model within SmartSpice, simulation results were compared with results obtained from the PSTAR simulator. PSTAR is Philips own in-house simulator and it contains the latest version of the model. DC, AC and transient tests were performed and the differences between both sets of results were negligible and can be attributes to differences between simulation approaches and numerical methods used within the simulators.


Avalanche Multiplication

Due to the high electric field in the space-charge region, avalanche currents are generated. At low current levels, (Ic1c2 < Ihc) the generation of avalanche current is a function of the electric field at the internal base-collector junction. As an optional feature, activated using the EXAVL model parameter, the model is extended for current levels exceeding Ihc. The plots shown in Figures 2 and 3 illustrate the effect that the extended model has upon the collector current. This is known as snap-back behavior.


[1] `Nat. lab Unclassified Report No. 006/94, the Mextram bipolar Transistor Model (Level S03.2).' H.C. de Graff, W.J. Kloosterman.

[2] `Compact Transistor Modeling for Circuit Design. ' H.C. de Graff, F.M. Klaassen.

[3] `HF Silicon ICs for Wide-Band communications Systems,' PhD Thesis, L. de Vreede, Tu Delft, June 1996.

[4] `Modeling Bipolar Devices Using the Mextram Model,' Simulation Standard Vol 6, No 7, July 1995.

Figure 2. PSTAR output illustrating compatibility between SmartSpice and PSTAR implementation.

Figure 3. SmartSpice plot of collector current vs Vce illustrating the effect of the EXAUL model parameters.