# MEXTRAM Bipolar

Implementation in SmartSpice

Introduction

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]

Description

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)**

Validation

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.

Example

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.

References

* [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.