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**1 - 2**of**2**### Model derivation of Mextram 504: The Physics behind the Model

, 2002

"... Mextram 504 is the new version of the Philips compact model for bipolar transistors. This document contains the derivation of all the equations that are part of the model. This includes the description of the equivalent circuit of Mextram, the equations for the currents and the charges, the temperat ..."

Abstract
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Mextram 504 is the new version of the Philips compact model for bipolar transistors. This document contains the derivation of all the equations that are part of the model. This includes the description of the equivalent circuit of Mextram, the equations for the currents and the charges, the temperature-scaling model, the way self-heating is handled, and the noise model. We then discuss some small-signal approximations and the basis of geometric scaling.

### The Mextram Bipolar Transistor Model

- Unclassified Report NL-UR 2000/811, Philips Nat.Lab., 2000. See Ref. [1
, 2002

"... A new version of the Philips model for vertical bipolar transistors has been developed, Mextram level 504. This model gives better results for the description of first and higher-order derivatives of the characteristics than Mextram level 503. This can be especially seen in the output-cunductance, t ..."

Abstract
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A new version of the Philips model for vertical bipolar transistors has been developed, Mextram level 504. This model gives better results for the description of first and higher-order derivatives of the characteristics than Mextram level 503. This can be especially seen in the output-cunductance, the cut-off frequency and the low-frequency third order distortion. Special attention was paid to the modelling of SiGe transistors. Furthermore we included self-heating in the description. It has also become easier to do parameter extraction. The goal of this report is to present the full definition of the model, including the parameter set, the equivalent circuit and all the equations for currents, charges and noise sources. Apart from the definition also an introduction into the physical background is given. We have given also a very basic parameter extraction procedure. Both the background and the parameter extraction will be documented separately in forthcoming reports. The transition from Mextram 503 to Mextram 504 is described, to enable the translation of a 503 parameter-set to a 504 parameterset. At last we have given some numerical examples that can act as a test of implementation.