Mextram is an advanced compact model for the description of bipolar transistors. It contains many features that the widely-used Spice-Gummel-Poon model lacks. Mextram can be used for advanced processes like double-poly or even SiGe transistors, for high-voltage power devices, and even for uncommon situations like lateral NPN-transistors in LDMOS technology. It provides an excellent description of the forward and reverse modes of operation for both digital and analogue circuits.
Mextram has proved itself during intensive use within the Philips design community, because of its combination of good effects description and parameter set with good convergence. Mextram models a great number of effects enabling realistic transistor predictions to be made. The full documentation and source code of the Mextram Bipolar Transistor Model is available on this web site.
Good IC design is, of course, dependent on good simulation, which in turn is dependent on the availability of good physical device models. The development and continuous refinement of Mextram by Philips Research, using feedback from practical design tasks, make it an excellent and robust model that has proved its accuracy, good convergence and wide applicability. Mextram is suitable for use in both circuit design and process technology, as well as CAD tool development.
Mextram has been developed by Philips Research. It was first released for use within Philips in 1985. Mextram level 503 was released into the public domain by Koninklijke Philips Electronics N.V. in 1994, has had a small model update in 1995, and has been unchanged ever since. Mextram level 504 has been developed as an update to level 503 for several reasons, the main ones being the need for even better description of transistor characteristics and the need for an easier parameter extraction. A more detailed history is available here.
The improved description of transistor characteristics of Mextram 504 compared to Mextram 503 is achieved by changing some of the formulations of the model. For instance, Mextram 504 contains the Early voltages as separate parameters, whereas in Mextram 503 they were calculated from other parameters. This is needed for the description of SiGe processes and improves the parameter extraction (and hence the description), in the case of pure Si transistors. An even more important improvement is the description of the epilayer. Although the physical description has not changed, the order in which some of the equations are used to get compact model formulations has been modified. The result is much smoother behaviour of the model characteristics, i.e. the model formulations are now such that the first and higher-order derivatives are better. This is important for the output-characteristics and cut-off frequency, but also for (low-frequency) third order harmonic distortion. To achieve the same smoothness, some other formulations, like that of the depletion capacitances, have been changed.
In Mextram almost all of the parameters have a physical meaning. This has been used in Mextram 503 to relate different parts of the model to each other, using a limited number of parameters. Although this is the most physical way to go, it makes it difficult to do parameter extraction, since some parameters have an influence on more than one physical effect. In Mextram 504 as much of this interdependence as possible has been removed, without losing the physical basis of the model. To do this some extra parameters have been added. At the same time some parameters of Mextram 503, that were introduced long ago but which had a limited influence on the characteristics and were therefore difficult to extract, have been removed. The complete Mextram model has been thoroughly revised. The documentation of the model has also been extended.
The sophisticated modelling of the avalanche multiplication, the epitaxial collector layer resistance and charge storage of advanced high frequency transistors, is unsurpassed. When compared to existing Spice models, this results in improved modelling, of all relevant transistor characteristics, such as: current gain, output conductance/conductivity, cut-off frequency, distributed high-frequency effects, noise figures and temperature behaviour.
Mextram does not contain extensive geometrical or process scaling rules (only a multiplication factor to put transistors in parallel). The model is well scalable, however, especially since it contains descriptions of the various intrinsic and extrinsic regions of the transistor. By exploiting the solid physics at the basis of the Mextram model, the statistical analysis of the spread in the processing and geometrical layout of the transistor is brought to a very high level of accuracy and reliability. This also enables the calculation of predictive parameter sets, derived from the process and layout data of the transistor.
Some parts of the model are optional and can be switched on or off by setting flags. These are
- the extended modelling of reverse behaviour,
- the distributed high-frequency effects in the base, and
- the increase of the avalanche current when the electron density in the epilayer exceeds the doping level (including snap-back).
Besides the NPN transistor, a PNP model description is available also. Both three-terminal devices (discrete transistors) and four-terminal devices (IC-processes which also have a substrate), can be described. An extra terminal is present when including self-heating. This makes it possible to embed the transistor in a heating network and perform combined electro-thermal simulations.
Effects modelled by Mextram
As the following table shows, Mextram enables a number of effects to be modelled that older models do not address, including Early voltage bias dependency, explicit modelling of inactive regions, current crowding and conductivity modulation for base resistance and quasi-saturation.
Effects modelled by Ebers-Moll, Spice-Gummel-Poon, and Mextram
|X||Explicit modelling of inactive regions|
|X||Substrate effects and parasitic PNP|
|X||Current crowding (both DC and AC)|
|X||Quasi-saturation and Kirk effect|
|X||Velocity saturation in the collector epilayer|
|X||Weak avalanche, including optional snap-back effect|
|X||Early effect in case of a graded Ge-profile|
|X||X||High-injection effects in the base|
|X||X||Low-level non-ideal base currents|
|X||X||Split base-collector depletion capacitance|
|X||X||Excess phase shift|
|X||X||X||Thermal noise, shot noise and flicker noise|
Initial reactions from the first (non-Philips) designers to receive the documentation are enthusiastic. "I have gone through the Mextram model documentation and I am impressed. It is obvious that the model is very complete and that the documentation presents it in a very clear and readable way. The model parameters are largely physically based, which is very important to most of us users. Including the examples in the Modelkit is a nice touch."