OK, maybe these aren't frequently asked questions, but someone did ask me.

Question about interconnect simulation 7/98
Arsenic and Phos interactions 6/98
Why are obtuse triangles bad? 6/98
Subject: Student skills/knowledge
Subject: RE: Opinions about TCAD group organization

Question about interconnect simulation

I was reading some of the material on your Web site concerning
interconnect simulation using a traditional device simulator,
and I was curious about one point.

You were apparently using the ac small signal module in your device
simulator, which requires a two carrier solution, even though there
may be no carriers at all in the device being simulated!

Why don't you just use a Poisson-only (carriers=0) solution and get
the capacitances via putting a small change on one electrode and
resolving, and getting the capacitance from dQ/dV? This should be
accurate for interconnect capacitances, and generally speaking,
faster.  At least one 4 conductor example I ran using ac analysis
vs. dQ/dV ran 2X faster using dQ/dV. Actually, I could shave more
off time because the cap matrix is indefinite, I really only need 3

you're right, of course. i used two carriers because it was easier (for me, at least). Medici has a dqdv option on the SOLVE statement and Atlas does not. Despite using two carriers, the problems I have tried have run pretty quickly, and the results are in a LOG file, so I can plot them directly without any manual dq/dv calculations. Now, AC calculations take twice as much memory as DC calculations, so that could be an issue on computers with low amounts of RAM.

Arsenic and Phos interactions

> have you come across any paper showing SIMS and SRP profiles
> of arsenic (n+) with and without phos. (n-)?  i am looking
> at enhancement of phos. diffusivities in the presence of 
> arsenic and activation of arsenic in the presence of phos. 

I thought Scott Dunham might know, and he replied:

One of my students investigated diffusion of P in an As background. You can see that work as well as references to prior efforts in his thesis and a paper (F.P. Wittel and S.T. Dunham, APL 66, 1415 (1995)). Both publications are also available on . I am familiar with work by Larsen et al. on diffusion of As in the presence of P (JAP 73, 691 (1993)). You might also refer to some of my other papers for understanding of these interactions at high doping levels (e.g., Dunham and Wu, JAP 78, 2362 (1995)). I am not immediately aware of work on how these interactions affect activation, although I am certainly interested.

Why are obtuse triangles bad?

> do you know anything about the problem of obtuse
> triangles in a grid for device simulation? Why are
> obtuse triangles bad?

It depends where they are. You don't want them near contacts or in the inversion layer. Current can only flow along a grid line. So, if you have a triangle in the channel that points upwards, then the current would be forced up in that direction, which would affect the results. This is the basis for the cartoon at the bottom of the TCAD humor page.

Obtuse triangles can also cause convergence problems, although I think the above issue is more common. Some programs will plot obtuse triangles, but these include 90.1 degree angles, which I don't think are a big problem.

I am currently experimenting with a process-to-device grid translator that produces a lot of obtuse triangles. Here is a warning message from Atlas:

   Mesh statistics:
     Type                non-cylindrical
     Total grid points   935
     Total triangles     1760
     Obtuse triangles    431  (24.4886 %)

   Warning:  Your grid seems to have an excessive percentage of
   obtuse triangles.  Excessive obtuse triangles can cause poor
   convergence and possible loss of accuracy.  The mesh should
   be modified accordingly.

Reply to the above from Valery Axelrad, then at PDF Solutions: don't worry about it, this is a pisces legacy of being scared of obtuse triangles. Many of those are actually in the oxide where they don't matter, most of the ones in silicon are very well shaped, especially the ones in the channel. A lot of those 25% are in the 90.1 degree category, meaning that just looking for a >90 degree count is rather misleading.

Searching some old email, I came up with the following three references on obtuse triangles which might help. I am sure this is more than you needed to know!

From Andy Strachan, Silvaco: On meshing, the general rule is that obtuse triangles in the current path WILL cause problems. Using the discretization scheme for continuity eqns, there can be no current flow along a triangle side opposite an obtuse angle. So obtuse elements MIGHT be OK if the current is not flowing in that direction.

From Chris Bowen, TI: Check the grid for obtuse triangles. Obtuse triangles result in opposite sign coupling coefficients which can cause problems in the iterative solvers. This is especially bad if the obtuse triangle lies on a material interface.

From Tim Thurgate, AMD: Zero coupling means that the coefficient used to calculate fluxes, such as current between those two nodes is zero. Most pairs of nodes have zero coupling which is why the matrix is so sparse. Only those nodes connected by grid lines have nonzero coupling (if the opposite angle is not 90). The nodes opposite an obtuse angle have negative coupling which feeds back in a funny way and messes up convergence. The calculation of current flow is between a node and all adjacent nodes. If the node density is large compared to the variation of solution variables, no problem. But for inversion layers this is impossible. A 90 degree angle opposite the interface nodes forces the current calculation to use the noninterface node. The carrier concentration at this node will be much smaller than the interface nodes and so the current calculation will not be valid.

From: Paul Layman <>
Sent: Friday, June 26, 1998 3:45:31 PM

The problem associated with obtuse triangles is related to the way both the Poisson and current continuity equations are assembled. The volumes associated with each node are determined using the perpendicular bisector of the grid connections between nodes. Provided the angles between the nodes are not obtuse the total volume is same as the sum of all these elements. Also the current flowing out of the edge of one of these volumes is the same as the current flowing into the adjacent volume. If one of the angles is obtuse the volumes constructed using perpendicular bisectors overlap one another. This causes problems with both total volume and current flow between adjacent nodes. Current appears to flow in or out of the simulated device at one of these points. If triangles are only mildly obtuse the error is small. However, very obtuse triangles will cause problems.

Date: 5 Jul 1997 18:10:25 -0500
From: mduane (Michael Duane)
Subject: Student skills/knowledge

> Is there a list of skills and knowledge that you look for when
> hiring a TCAD person?  I'm thinking of software (facility with
> unix, c, c++, perl, are some essential and others desired?)  How
> about characterization?  Should they be able to operate an HP
> 4145?  Know basic characterization techniques, etc.  I assume that
> knowledge of circuit, devices, processes, etc. would be there.  How
> about facility with specific tools (e.g. Suprem, etc.).  I'm not
> looking for a wish list, but with a list of essential skills I
> should make sure that my students leave with - especially the MS
> students who aren't here for a long time.

All the things you list would be on a wishlist.  If you want an
"essential" list, here are a few.  I may add more later.

1) Motivation:  I don't know how to test this very well in a
half-hour interview, but it's the most important thing.  If you
know how to teach this, let me know :)

2) Familiarity with current processing issues.  I think the more
you know about process and devices, the better the modeler you will
be.  To this end, the student should be familiar with some of the
key integration papers from the latest IEDM or VLSI Symposium.

3) TCAD tools - no hard requirements here.  Familiarity with more
than one tool is a plus; as is experience with BOTH process and
device simulators.  Bonus points for knowing how sensitive results
are to changes in the grid.

4) Computer knowledge/interest is of course important, but I don't
have any hard requirements here.

5) Here is a tricky one, especially for PhD's - how to avoid over
specialization.  It's really good to have one or two areas of
expertise that match current industry problems.  This will get you
a lot of interviews.  But if your resume looks too narrow, people
may not want to hire you unless they are interested in that
specific topic.

Date: Mon, 9 Jun 1997 11:35:13 -0500
From: mduane (Michael Duane)
Subject: RE: Opinions about TCAD group organization

> We have not decided a specific software yet but we are evaluating
> SILVACO and TMA right now. I used both of them when I was in
> Winbond Electronics. But in this brand new company, we need to
> re-evaluate them.  My questions concerning TCAD organization are:
> (1) What is the role of this group in a foundry house? What are the
> services this group can provide for each technology?
> (2) What is the structure of this group? How many members?
> (3) How do you assign jobs to engineers in this team? How many
> engineers specially take care of calibration?

tcad vendors like to advertise how "predictive" their software is.
but there are many things you can do with tcad even if it is not
perfectly predictive.  for example, process diagnosis, which is
probably more applicable for a foundry, does not require perfect
calibration. example:  a lot is out of spec - tcad can help
determine the likely causes.  you know that calibration is a
favorite topic of mine.  i think it is extremely difficult to
achieve a "calibrated" set of simulators.  so difficult, that you
should question whether it is worth it.  the vendors will give you
a different reply.

i also think it is important to have tcad experts run the software,
and not to have integration engineers using it part time.
likewise, the more the "tcad expert" knows about integration, the

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