======================================================  
Wide Temperature Range Compact Modeling (93-393K)
======================================================


Background
===========

One of the remarkable characteristics of SiGe HBT is
the ability to operate over a wide temperature range,
from as low as sub 1K, to as high as over 400 K.
This, together with excellent total dose radiation tolerance,
makes it very attractive for
implementing space electronics
that can operate over a wide temperature range in presence of
radiation as found in space missions. 

Recently, a research team led by Prof. John Cressler at
Georgia Tech took on the challenge of developing
SiGe electronics that can operate in
extreme environments as found in many space missions as is, 
without warms boxes and radiation shields. 

To enable such extreme electronics designs, and in 
collaboration with Prof. Cressler's team at Tech and
Prof. Mantooth's team at Arkansas,
my team developed new SiGe HBT compact model
that can function from 43 to 393K.
Existing design kit simply fails to run 
or give erroneous results
outside its intended temperature range, typically from
-50 C and +120 C (223 to 393K), making
necessary development of 
wide-temperature range compact models.


Approach and Challenges
=========================

The effort turned out to be much more involved and harder
than I had originally expected. 

Our starting point
was to take an existing
SiGe HBT compact model, 
and modify the temperature scaling 
of model parameters to "fit"
measurement data over a wider temperature range.
However, 
we often find that a model parameter extracted
at various temperatures does not show any physically
meaningful temperature dependence. 
The parameters extracted for
a given temperature are not unique, 
and several
different parameters sets 
could all yield acceptable fitting. This is primarily the case
at higher temperatures.

At lower temperature, 
we found that no matter what parameters we use at
a given temperature, the model cannot possibly 
fit certain characteristics.
This means that new model equations 
must be developed. Existing
transistor theories may not be able to explain measured low-temperature
characteristics, making empirical or semi-empirical equations necessary.


In modern SiGe HBTs, 
operating current density is on the order 
of mA per square micron, causing
severe self-heating.
The degree of self-heating is 
biasing current and voltage dependent.
For extraction of high current 
model parameters, we had to deal with
self-heating by
accounting for known t-dependence
functional form of all model parameters,
which is how it is done 
in commercial compact modeling 
around room temperature.
The situation is much worse in bipolar transistors compared to field-effect transistors,
because bipolar transistors operate on the principles of
minority carrier injection and diffusion, both are
strongly temperature dependent.
For extremely
wide temperature range, 
we do not know what functional form
a high current parameter t-dependence will take.
We will need to assume a functional form, extract parameters over
temperature, and then update the functional form iteratively.

As a result, extending T-scaling capability of a compact model
is not as straightforward as simply extracting model
parameters at different temperatures and construct
new T-scaling equations for these model parameters.

We chose Mextram as basis of our
model development, and made extensive new developments to 
enable wide temperature range modeling. 
All of the important cryo physics such as 
freeze-out and trap-assisted tunneling are accounted
for. 

Modeling Results
===================

Below are the DC and AC modeling results from 393K down to
43K, from DC to 5GHz, over a wide range of biases of
interest to circuit design, all with a single T-scalable 
model.

Gummel Plots
-----------------

:num:`Figure #fig-gummel` shows comparison of 
measured and modeled Gummel plots. A reasonable
accuracy across temperature is achieved for all levels of
injection. Trap-assisted tunneling is obvious below 93K and 
clearly needs to be accounted for. A high injection kink 
is clearly visible at nearly all temperatures and becomes more
important with cooling. Modeling of the kink is closely related to 
the epi-layer quasi saturation model parameters (e.g. VDC) as well as
the emitter resistance.


.. _fig-gummel:   
.. figure:: figure/gummel.png
    :scale: 100 %
    :alt: gummel plots
    :align: center

    Gummel plots.

fT-IC 
------------

:num:`Figure #fig-gummel` shows
:math:`f_{T}-I_{C}` characteristics at .
:math:`V_{CB}=0`, 1 and 2V.


.. _fig-ft:   
.. figure:: figure/ft.png
    :scale: 100 %
    :alt: ft-Ic plots
    :align: center

    fT-IC plots.

Y-parameters vs IC
--------------------

.. _fig-ypara:   
.. figure:: figure/ypara.png
    :scale: 100 %
    :alt: Y-Ic plots
    :align: center

    Y-IC plots.

    
Circuit Applications
===========================    

Bandgap Reference
---------------------


Precision bandgap references (BGRs) are extensively used in a wide variety
of circuits required for wide temperature range operation.
SiGe BGRs have shown excellent over temperature stability. 
The circuit is also an excellent candidate for 
validating a compact model in the low to medium injection region.
Simulated and measured BGR output versus temperature 
is shown in
:num:`Figure #fig-vref`. 
The same transistors used in the measured BGR are used for 
model parameter extraction.
The excellent agreement indicates the accuracy of the compact
model. 

.. _fig-vref:   
.. figure:: figure/vref.png
    :scale: 100 %
    :alt: Vref vs T plots
    :align: center

    Bandgap reference circuit output voltage vs T plots.
   
    
Single-Event Upset Threshold LET
---------------------------------------------

One important advantage of SiGe HBTs is the "free" total dose 
tolerance which holds at low temperatures as well.
The bigger concern is single-event upset (SEU).
Energetic particles passing through the junctions can deposit
electron-hole pairs, which are then collected by transistor terminals.
Such transient currents can cause problems to digital, analog and RF circuits.
Of particular importance is the drift charge collection in
the collector-base (CB) and collector-substrate (CS) junction.
Even though the CB junction charge is not large in amount, it is not negligible and can be important
for circuit SEU, simply because the charge collection current appears
between the collector and base, a feedback position.


For a given Linear Energy Transfer (LET), which measures the number of electron-hole pairs deposited per linear
distance of particle travel, CB and CS junction charge collection currents $I_{CB}$ and $I_{CS}$
are simulated using 3-D device simulation, and then fed into
Cadence to determine circuit response.
The LET at which an upset occurs is called threshold LET, 
and is used as an SEU figure-of-merit.
 

Simulated threshold LET vs temperature is given below for 
a master-slave D flip flop when the tail current is kept constant
over temperature. Simulations were done with different combinations of the CS and CB 
transient SEU currents.  

The results are shown in :num:`Figure #fig-let`. Threshold LET 
increases overall with cooling, which is certainly
good news, as no additional SEU hardening is necessary
for circuit operation at cryogenic temperatures.


.. _fig-let:   
.. figure:: figure/let.png
    :scale: 100 %
    :alt: LETth vs T plots
    :align: center

    Threshold LET vs T plots.