Follow Up Questions

Some follow-up Q&A to Steve's device benchmarking report

Q: Regridding tool: Are the capabilites of pdMesh that different
from devedit(SILVACO) or from MESH, MDRAW(ISE) or from the

A: The main thing I noticed about pdMesh was its relative ease of
use when you have a good command script.  My work with devedit,
MDRAW, and others has been very time consuming by comparison, and
the grids do not tend to be nearly as efficient or smooth.  For the
benchmarking, the pdMesh was not used in the Atlas structures,
although the currents were not really affected by the different

Michael: pdMesh also has the benefit that when a given grid spacing
is requested in pdMesh, that is the spacing pdMesh generates. Other
programs seem to take user defined grid spacings as merely a
suggestion.  Also, the gate oxide interface can be reproduced
exactly with pdMesh.

Q: Transfer characteristics: Why didn't you also compare Id/Vg

A: The subthreshold behavior was used to set the workfunctions in
the different simulators to make sure the devices were as close to
the same as I could make them.  The reason this information wasn't
included in my report was a space consideration mainly.  My thesis
will contain IdVg comparisons as well (used to show similar
behavior below threshold).

Q: Parameter Consistency (Drift Diffusion): Besides the comparison
of default parameters, were the parameters of all the DD Lombardi
models identically set in the different simulators to check whether
results are comparable?

A: Yes, the default parameters were the same across simulators
(matching the published parameters).  However, only the default
parameters were used across different simulators, the suggested
parameter set was only used in one of the packages.

Q: Model Consitency (Drift Diffusion): Are all the different
Lombardi models comparable in the different simulators?  The
physical way to parameterize the high field saturation within
DD-simulators is to use the gradient of quasi-fermi level: 
mu = mu(grad Phi , ...).  This is not the case in Silvaco's 
simulator Atlas. The field parallel to current flow is used there,
which is believed to be historical ballast from PISCES. The ISE
code has both possibilites, ie  mu(grad Phi)  OR mu(E_parallel). I
don't know the situation in MEDICI. The latter parametrization is
unphysical because it results in a large mobility reduction within
a diode with zero or nearly zero forward bias, because E_parallel
is large, though the driving force (electric + diffusion force) is
small. Though the resulting currents may not be influenced too much
is this case, there might be differences in other cases.

A: Medici also uses the parallel field for its mobility reduction.
I did not see much difference between the two methods in ISE on the
250 nm device (comparing only on-current, so this is a very limited
answer, there is definitely room for more investigation, but my
research is taking me elsewhere).

Follow-up comment from questioner: Maybe results do not change very
much. But we have the suspicion that convergence behavior is
degraded by the E_parallel parametrization, especially for small
currents when the direction of current flow is not well defined in
some device regions. If anyone had the time and all the tools to
compare convergence behavior of the simulators systematically, I
would be very interested in the results.

Q: Mobility model selection: Though I personally do not have
experiences with alternatives, I was told that the conventional
models like Lombardi are insufficient for large channel doping
levels. For this case it seems to be important to not only model
the dependen cy from high field, from E_eff and from doping, but
also from carrier densities.  Especially when the region of the
universial relationship for the channel mobility is left, E_eff and
doping are not sufficient to model the mobility. The screening of
impurities by free carriers and thus the strength of impurity
scattering depend on free carriers. I know of improved results in a
research simulator of an experienced simulation reserch group after
implementing the model after:  S.A. Mujtaba and R.W. Dutton,
Semi-Empirical Local NMOS Mobility Model for 2-D Device Simulation
Incoporating Screened Minority Impurity Scattering, NUPAD Tech.
Dig., vol.5, Honolulu, pp. 3-6, 1994.  Maybe this model is similar
to the one you mention (Darwish). But the main question is: Did you
perform at least test simulations with improved models that also
account for the screening of impurity scattering?  At least
Klaassen's model that can be selected in ISE's Dessis claims to
account for this effect.

A: This is the reason for comparing more than one mobility model on
the two different devices.  We know that all of today's mobility
models breakdown for the high doping densities that will be
required if we stay with the SIA roadmap.  What was found in this
work was that we can't just blindly extrapolate any of these models
to the higher doping densities, since the models extrapolate

[The following is a series of comments from the questioner in
chronological order that pertain to advanced DD mobility models]

C: I wrote that Klaassen's model is in a sense more sophisticated
than Lombardi (eg screening of impurities). But of course the pure
Klaassen it is not sufficient for your simulation since it has no
E_eff-dependency for inversion channels.

Silvaco's Klaassen model cannot be used together with Silvaco's
CVT model, because CVT overrides any other mobility specification.
Maybe Silvaco's C-interpreter for mobility models can be used for a
workaround. From ISE's manual I conclude that a combination of
Klaassen and of an E_eff-dependent model is possible (similar to
eq.(1) and (2) in Darwish).

Of course a combination of Klaassen and an E_eff-dependent model is
required, as proposed in Darwish et al.. ISE's simulator claims to
be capable of modeling the mobility according to Darwish by just
setting some parameters (see manual of DESSIS, release 5, page

In the meantime I was told that although Mujtaba,Dutton is better
than Lombardi for higher doping levels, it is not satisfactory for
highest dopings.  Darwish et al. state something similar, so maybe
Darwish et al. is the best reference for a more advanced mobility

Q: Model Consistency (Drift Diffusion vs Energy Transport or
Hydrodynamic):  In my experience it is useful to check model
consistency (DD vs ET) on a homogeneous level (only field current,
ie small diffusion forces) before comparing device results.
Sometimes even for bulk silicon DD results differ from ET results,
because the high field saturation is not always being "translated"
correctly into a mu(T_carrier)-relationship.  Did you perform some
checks for the ET model? (You mentioned the inconsistency only for
the HD model).

A: The HD comparison is a fairly limited comparison because I was
only able to get UT-Minimos to run its HD with any regularity.
Because UT-Minimos is a fairly closed simulator (in my opinion, it
is very difficult to adjust parameters), I simply ran the test
devices with the default settings.

Q: Usability of ET models and HD models:  You decided not to use
the ET-option of Silvaco (convergence problems).  Did you try the
ET model of another simulator? Do you think a DD-simulation can
still be predictive for such small devices? At least for substrate
currents an examination of the need for ET models could be

A: Yes, I also tried to use the ET models in Medici (similar
problems) and Dessis (didn't have enough time to give it a fair
shake, and decided to not include it since I had troubles with
Medici, figured it would probably be the same story here).  You use
the word "predicitve" which I would call some question to.
Personally, I don't really see a situation where TCAD is able to
get ahead of actual silicon, so I am going to take the word
"predictive" to mean accurate (Do I think a DD-simulation can still
be "accurate" for such small devices?).  In this case, from what I
have seen, the mobility and parameters still have an effect of
these small devices.  So yes, I think it is within the realm of
reason that DD can still function at that level, with a lot of
effort to "calibrate" the models.

Steve Bourland
Nov 2, 1998

Reply from Silvaco:  Nov 4, 1998.

In ATLAS for mobility models combining KLA and an E_perp model you
can use the Shirahata model along with Klaassen's model. These two
are designed to work together.

As seen in our example (mos2ex14) the results from KLA SHI and CVT
are similar.

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