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DUANE BONING: Good
morning, everyone,

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and good evening in Singapore.

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Where is everyone?

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AUDIENCE: I think
they are on the way.

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We'll be here in a minute.

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DUANE BONING: OK, I'm going
to go ahead and start.

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What I wanted to do is, I sent a
message around about these team

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guidelines, so--

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our team project guidelines.

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So I'm not going to
go into great detail

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through these slides.

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Hopefully, everybody
is well on the way

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towards identifying a team.

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But I wanted to go
quickly through this

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and then answer
any questions you

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may have on the team projects.

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Quick reminder that the
team projects are about 20%

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of the grade.

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So they are an
important part of this.

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The basic expectation
is, this is

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where you get a chance to
dive deep into the analysis

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and exercising of some of the
kinds of tools and approaches

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we've been talking about
with a set of data.

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Our hope is that you
can find data yourself.

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Through the various
members of the class,

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I think, in one of the
earlier problem sets,

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we asked for your experiences,
perhaps with some past data.

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I think there's
plenty of data around.

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If you are not able to
tap into some past data

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you or colleagues have
generated in the lab,

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in a previous job
that you can share,

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or whatever, you can also
tap into the literature.

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So if you find data
in the literature,

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that is perfectly fine as well.

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And then, in a few
cases, we actually

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have some data from our own
experimentation and research.

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So if you're really stuck, let
me know or let Hayden know.

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And we can try to connect
you up to something.

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I've listed a few topic areas.

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I don't want these
to be limiting.

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But I mean, these are
the main kinds of topics

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we've been dealing
with in the class,

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things like process
diagnosis-- looking at the data

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to detect problems; ways
of optimizing or improving

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the process through design
of experiments, optimization,

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and so on; and then some other
sort of advanced applications,

00:02:35.510 --> 00:02:41.390
things like nested variants,
some of the spatial yield

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modeling, that sort of thing.

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So I think it works well
to have three or even

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four members in the team.

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So the goal is have a
fairly rich data set,

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and have multiple members of the
team applying different kinds

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of analyses to the problem, OK?

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So I think it does
work where you're

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able to identify contributions
from each of the team members.

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But the whole point
of this is actually

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to be able to pick over the
data, talk about the data,

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talk about your
approach to analysis,

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and looking at the problem
with your teammates.

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Thursday, the project
proposal is due.

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This is just one or two pages
describing the basic data,

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the basic problem in
your plan for attack,

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what kinds of analyzes
you hope to do.

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And of course, list who
your team members are

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and what their roles are.

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The goal then is, over the
coming week, and maybe even

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starting, perhaps, even after
class for folks in Singapore,

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on Thursday, and
certainly on Tuesday,

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to have a chance to meet with
me or Dave, if he's available,

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to basically go over your
plan and your analysis

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so far, if you're
partway through it.

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So we'll need to do
that by video conference

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with folks in Singapore.

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If we do it right after
class, we can probably

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try to arrange this facility.

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Otherwise, we'll use the
conference room near the SMA--

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your SMA offices.

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Then the expectations
are two parts.

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There will be a
group presentation.

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By the way, not necessarily
every single member

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of your team needs to present
part of the presentation.

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Trying to have 14 members
in a 15-minute chunk often

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can be kind of a
coordination mess.

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So as a team, you need to
put together a presentation,

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and have one or maybe
two people, most likely,

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presenting some
of those results.

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And then at the end of
that week, on Friday,

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May 16, which is the end of
the term given that we do not

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have a final exam, a
single shared group report

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needs to be submitted.

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These are just some
example topics.

00:05:19.720 --> 00:05:23.440
I'm not sure if those have
been drawn from past semesters

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or not.

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Here's some additional
kinds of suggestions

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that I mentioned--
kinds of analyses

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that might be of interest.

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In the report-- these
are some guidelines

00:05:35.560 --> 00:05:37.720
on what we'd like to
see in the report.

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One note here, and I
haven't posted it yet, is--

00:05:41.350 --> 00:05:48.040
whoops-- is we'd like to
use a common template just

00:05:48.040 --> 00:05:49.660
for the formatting
and guidelines.

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And basically, the
IEEE two-column format

00:05:52.570 --> 00:05:53.840
has worked really nicely.

00:05:53.840 --> 00:05:54.910
We have Word templates.

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I think we even have
LaTeX templates if there's

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anybody who still uses LaTeX.

00:06:00.490 --> 00:06:04.790
I will post that
template on the web.

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What's nice about that is we
can actually then put together

00:06:08.290 --> 00:06:11.350
all of the written reports
from the class into almost

00:06:11.350 --> 00:06:12.640
a little booklet.

00:06:12.640 --> 00:06:17.980
And it almost looks like
a little mini journal,

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or a little mini conference
proceeding, if you will,

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with these reports.

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It also is a nice,
professional looking report.

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So we'll distribute
that as well.

00:06:32.560 --> 00:06:37.230
So finally, I just grabbed,
from the past two or three

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years, some of the titles
from some of the process--

00:06:41.100 --> 00:06:45.120
or team report
and presentations,

00:06:45.120 --> 00:06:47.590
just to give you a little
bit of a sense of the variety

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of kinds of things that we saw.

00:06:49.890 --> 00:06:52.140
So those might
give you some idea.

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By the way, back in 2005,
we were more focused

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on, like, two-person projects
or one-person projects.

00:06:59.670 --> 00:07:01.140
And these were great reports.

00:07:01.140 --> 00:07:05.860
But we did decided that
sharing and interacting

00:07:05.860 --> 00:07:11.490
made things a better
learning experience for all.

00:07:11.490 --> 00:07:13.490
So with that, let me open it up.

00:07:13.490 --> 00:07:16.070
Anybody have questions
on how the team

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reports, team projects, team
presentations need to go?

00:07:21.690 --> 00:07:23.130
I'll try to break--

00:07:23.130 --> 00:07:28.170
does pretty much everybody
have a team in formation?

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Are there people who
kind of are still

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looking for possible partners?

00:07:36.780 --> 00:07:37.800
OK, one or two.

00:07:37.800 --> 00:07:42.430
OK, I'll try to break maybe
five minutes earlier--

00:07:42.430 --> 00:07:46.690
which may mean actually
break on time--

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at the end of class, so could
be a little bit of discussion

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while people are still
face-to-face on that.

00:07:55.480 --> 00:07:56.730
Any other questions on that?

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AUDIENCE: Professor?

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DUANE BONING: Yes.

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AUDIENCE: Just
now, you mentioned

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having a rich set of data.

00:08:07.510 --> 00:08:10.080
So from my understanding,
we are supposed

00:08:10.080 --> 00:08:12.000
to do the experiments ourselves.

00:08:12.000 --> 00:08:15.240
So I would like to know
how big a set of data

00:08:15.240 --> 00:08:16.110
are you expecting?

00:08:18.920 --> 00:08:22.450
DUANE BONING: Well,
my expectation,

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or minimal expectation
I would say,

00:08:25.570 --> 00:08:28.000
is more that you
might be able to tap

00:08:28.000 --> 00:08:32.559
into data that has already
previously been generated.

00:08:32.559 --> 00:08:35.799
It's ambitious,
and I would applaud

00:08:35.799 --> 00:08:41.062
people wanting to go and
generate additional data.

00:08:41.062 --> 00:08:43.270
So we could certainly talk,
and depending on the data

00:08:43.270 --> 00:08:44.650
you have in mind.

00:08:44.650 --> 00:08:47.830
But what I mean by
rich set of data

00:08:47.830 --> 00:08:52.180
is something that will support
enough of the kinds of analyses

00:08:52.180 --> 00:08:55.790
that we've been talking
about through the term.

00:08:55.790 --> 00:08:59.820
So if it's a DOE,
it needs to be,

00:08:59.820 --> 00:09:02.890
you know, probably several
parameters of input,

00:09:02.890 --> 00:09:05.410
several parameters of output.

00:09:05.410 --> 00:09:09.040
Maybe you have some
additional twist to it

00:09:09.040 --> 00:09:13.540
that's kind of interesting
or non-standard that included

00:09:13.540 --> 00:09:16.550
some thorny issues in the data.

00:09:16.550 --> 00:09:19.960
Maybe it's an unbalanced
design, or an imperfect design,

00:09:19.960 --> 00:09:23.470
and you have to try
to accommodate that.

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All I mean is enough
data to do what

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you would like to propose
to do and that we can

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talk about finding acceptable.

00:09:37.920 --> 00:09:42.030
So were you actually looking
at going in and generating

00:09:42.030 --> 00:09:44.778
some data on one of the
processes, or tools,

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or equipment there?

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AUDIENCE: My group haven't
had a discussion yet.

00:09:53.610 --> 00:09:56.408
At first, we talk taught
this as a requirement.

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DUANE BONING: OK, yeah,
so we can follow up

00:09:58.200 --> 00:09:59.700
with Hayden on that.

00:09:59.700 --> 00:10:02.750
I think bonding and that
sort of thing would be great.

00:10:05.800 --> 00:10:07.510
So we won't be too ambitious.

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It will be doable.

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OK, other questions?

00:10:14.270 --> 00:10:14.770
Yeah?

00:10:14.770 --> 00:10:17.920
AUDIENCE: I think
maybe as an example

00:10:17.920 --> 00:10:21.785
of all kind of
manufacturing processes,

00:10:21.785 --> 00:10:28.425
but I have a passed out data for
kind of material engineering.

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Is that OK if I can use
material engineering data?

00:10:36.130 --> 00:10:37.760
DUANE BONING: Sure,
so the question was

00:10:37.760 --> 00:10:43.240
is material engineering
data, mechanical processes,

00:10:43.240 --> 00:10:45.632
mechanical properties,
is that OK?

00:10:45.632 --> 00:10:46.840
And the answer is absolutely.

00:10:46.840 --> 00:10:49.360
I mean, if you look at some
of these past projects,

00:10:49.360 --> 00:10:52.270
you've got everything from
some things that look kind

00:10:52.270 --> 00:10:54.160
of like semiconductor stuff--

00:10:54.160 --> 00:10:56.260
laser diode, it's
not transistors.

00:10:56.260 --> 00:11:00.670
But you have other things
of bending printed circuit

00:11:00.670 --> 00:11:05.500
boards, sheet metal blanket,
surface quality in milling,

00:11:05.500 --> 00:11:06.250
all kinds.

00:11:06.250 --> 00:11:10.960
This is sort of general
manufacturing and general

00:11:10.960 --> 00:11:12.540
processes.

00:11:12.540 --> 00:11:14.180
So that would be
no problem at all.

00:11:14.180 --> 00:11:14.680
Yeah.

00:11:17.400 --> 00:11:18.211
Yeah?

00:11:18.211 --> 00:11:20.616
AUDIENCE: Prof, can you
post more of the reports

00:11:20.616 --> 00:11:23.378
on Stata so we can take a look?

00:11:23.378 --> 00:11:25.670
DUANE BONING: Yeah, I think
what we've done in the past

00:11:25.670 --> 00:11:27.270
is put up some example--

00:11:27.270 --> 00:11:29.483
some of the prior year reports.

00:11:29.483 --> 00:11:30.650
We haven't posted those yet.

00:11:30.650 --> 00:11:33.870
But I'll try to do that today.

00:11:33.870 --> 00:11:37.020
AUDIENCE: Great, thank you.

00:11:37.020 --> 00:11:40.360
DUANE BONING: OK,
any other questions?

00:11:40.360 --> 00:11:42.120
All right, let me switch here.

00:11:45.210 --> 00:11:47.900
So again, what
we're doing now is

00:11:47.900 --> 00:11:50.280
sort of switching to
some case studies.

00:11:50.280 --> 00:11:53.330
There's still, perhaps
in a few of the lectures,

00:11:53.330 --> 00:11:56.480
some new material, if
you will, coming along.

00:11:56.480 --> 00:11:59.630
In this case study--
the first case study--

00:11:59.630 --> 00:12:02.660
I don't think there's actually
that much new in terms

00:12:02.660 --> 00:12:06.230
of methodologies, and so on.

00:12:06.230 --> 00:12:08.900
I just think this is a nice
example, though a little

00:12:08.900 --> 00:12:14.120
dated now, of a fairly
straightforward but thorough

00:12:14.120 --> 00:12:16.910
application of design of
experiments and response

00:12:16.910 --> 00:12:18.570
surface modeling.

00:12:18.570 --> 00:12:24.800
So I also, by the way, posted
the paper for this case study

00:12:24.800 --> 00:12:26.060
on the site as well.

00:12:26.060 --> 00:12:28.580
It's down in the reading
section that goes--

00:12:28.580 --> 00:12:31.820
readings that goes
with the lecture.

00:12:31.820 --> 00:12:34.430
So you'll have to go
and pop off this--

00:12:34.430 --> 00:12:38.310
what is it-- eight or
nine page paper as well.

00:12:38.310 --> 00:12:40.310
I should mention, some
of the other case studies

00:12:40.310 --> 00:12:43.430
will also have papers from
the literature for you

00:12:43.430 --> 00:12:47.480
to grab and read.

00:12:47.480 --> 00:12:51.680
So this case study comes from
semiconductor manufacturing.

00:12:51.680 --> 00:12:53.030
It's a little dated now.

00:12:53.030 --> 00:12:55.670
It goes back to 1991.

00:12:55.670 --> 00:12:57.680
But this was actually
kind of just the time

00:12:57.680 --> 00:13:02.130
when things like statistical
process control, more

00:13:02.130 --> 00:13:04.560
thorough design of experiments,
response surface modeling

00:13:04.560 --> 00:13:09.810
was really finally hitting
the semiconductor industry,

00:13:09.810 --> 00:13:17.500
and really starting to be
more widespread in adoption.

00:13:17.500 --> 00:13:19.317
So I think this is a nice case.

00:13:19.317 --> 00:13:21.150
It's a nice case study
because they actually

00:13:21.150 --> 00:13:25.560
show us the experimental
conditions, the actual data,

00:13:25.560 --> 00:13:29.270
and the actual models
that they generated.

00:13:29.270 --> 00:13:30.980
Some of the things
are a little dated.

00:13:30.980 --> 00:13:35.420
For example, they talk
about 125 millimeter wafers.

00:13:35.420 --> 00:13:37.910
So this was 5-inch
wafer processing,

00:13:37.910 --> 00:13:39.650
which is kind of a weird size.

00:13:39.650 --> 00:13:43.640
But it also-- we're up to 300
millimeter, 12-inch wafers.

00:13:43.640 --> 00:13:45.380
So it shows the march of--

00:13:45.380 --> 00:13:47.730
progress of technology.

00:13:47.730 --> 00:13:51.440
However, CVD and CVD
of blanket tungsten

00:13:51.440 --> 00:13:54.420
is still heavily used
and very integral.

00:13:54.420 --> 00:13:56.910
So it's still a
relevant process.

00:13:56.910 --> 00:14:00.830
So what I want to do in looking
at this case is go through,

00:14:00.830 --> 00:14:03.140
talk a little bit
about the background

00:14:03.140 --> 00:14:05.750
of tungsten CVD, things
that aren't in the paper

00:14:05.750 --> 00:14:08.630
but may give you a
little bit of a feel on--

00:14:08.630 --> 00:14:12.050
more of a feel on the
process; talk a little bit

00:14:12.050 --> 00:14:16.250
about the preliminary work
that they did looking back

00:14:16.250 --> 00:14:20.330
at the prior paper
that they cite;

00:14:20.330 --> 00:14:22.460
and then we'll go through
the experimental design

00:14:22.460 --> 00:14:26.780
that they performed to try
to optimize this tungsten CVD

00:14:26.780 --> 00:14:30.030
process, to understand it,
model it, and then optimize it.

00:14:30.030 --> 00:14:31.490
So we'll look at the data.

00:14:31.490 --> 00:14:35.780
We'll do some RSM
analysis, or mostly looking

00:14:35.780 --> 00:14:39.170
at their analysis in the paper.

00:14:39.170 --> 00:14:43.190
But assuming I have time at
the end, and I think I will,

00:14:43.190 --> 00:14:44.060
I'll switch over.

00:14:44.060 --> 00:14:47.660
And we'll use-- play around
with JUMP a little bit with that

00:14:47.660 --> 00:14:52.250
same data set, and show you a
few of the kinds of analyses

00:14:52.250 --> 00:14:58.310
that are possible with that
tool, both for regression--

00:14:58.310 --> 00:15:00.110
some of the stepwise
regression that's

00:15:00.110 --> 00:15:02.670
referred to in the paper--

00:15:02.670 --> 00:15:04.310
and then some of
the neat tools that

00:15:04.310 --> 00:15:08.330
actually in the interactive
capabilities of JUMP

00:15:08.330 --> 00:15:10.710
for optimization.

00:15:10.710 --> 00:15:13.490
Now throughout this,
think a little bit

00:15:13.490 --> 00:15:18.147
about where you see weaknesses,
or alternative ideas,

00:15:18.147 --> 00:15:18.980
or things like that.

00:15:18.980 --> 00:15:20.522
Because at the end,
I might ask, what

00:15:20.522 --> 00:15:22.490
are some of your
ideas of things you

00:15:22.490 --> 00:15:25.220
think might have been
interesting, or important

00:15:25.220 --> 00:15:27.410
to try or to improve on this.

00:15:27.410 --> 00:15:29.710
So have that in mind.

00:15:29.710 --> 00:15:31.400
Where do you think
they did a good job?

00:15:31.400 --> 00:15:34.310
Where do you think
they did a weaker job?

00:15:34.310 --> 00:15:36.200
What might you suggest?

00:15:36.200 --> 00:15:41.370
And I'll ask you that
question at the end, OK?

00:15:41.370 --> 00:15:43.260
So let me talk a little
bit about tungsten,

00:15:43.260 --> 00:15:46.510
and in particular,
tungsten plugs.

00:15:46.510 --> 00:15:52.860
So tungsten, here, is
generally used as a conductor

00:15:52.860 --> 00:15:55.080
in semiconductor fabrication.

00:15:55.080 --> 00:15:57.690
It's not a great
conductor, meaning

00:15:57.690 --> 00:16:02.250
it's often a little bit higher
resistivity than other metals,

00:16:02.250 --> 00:16:07.110
like aluminum or, now, copper.

00:16:07.110 --> 00:16:10.530
However, it continues
to be heavily used

00:16:10.530 --> 00:16:13.080
for contacts and plugs.

00:16:13.080 --> 00:16:17.880
So contacts are the holes
that are drilled between--

00:16:17.880 --> 00:16:22.290
into an insulating layer
from the first level of metal

00:16:22.290 --> 00:16:25.710
down to the underlying silicon.

00:16:25.710 --> 00:16:30.060
Plugs are the same idea, but at
other levels of interconnect.

00:16:30.060 --> 00:16:34.560
So you would have a plug
from metal one to metal two,

00:16:34.560 --> 00:16:37.530
or metal two to metal
three, and so on.

00:16:37.530 --> 00:16:39.540
Terminology is not
completely uniform.

00:16:39.540 --> 00:16:43.370
But that's the
typical terminology.

00:16:46.610 --> 00:16:49.070
The examples drawn
from this paper,

00:16:49.070 --> 00:16:52.400
they talk about tungsten
plugs in conjunction

00:16:52.400 --> 00:16:54.110
with aluminum interconnect.

00:16:54.110 --> 00:16:56.370
And they're actually
mostly focused, I think,

00:16:56.370 --> 00:16:59.180
on tungsten between--

00:16:59.180 --> 00:17:03.660
or tungsten contacts, with the
idea that in older technology,

00:17:03.660 --> 00:17:05.569
in fact, you didn't
need to drill and form

00:17:05.569 --> 00:17:09.140
separate plugs between layers.

00:17:09.140 --> 00:17:12.079
You could just allow, say,
an aluminum deposition

00:17:12.079 --> 00:17:16.040
to go in and fill that
layer, and then etch off

00:17:16.040 --> 00:17:18.619
where you didn't want it.

00:17:18.619 --> 00:17:20.540
With scaling, it
became pretty much

00:17:20.540 --> 00:17:23.359
essential to be able to
form the plugs separately

00:17:23.359 --> 00:17:24.770
from the interconnect.

00:17:24.770 --> 00:17:29.810
So then, tungsten was used to
fill those plugs between metal

00:17:29.810 --> 00:17:31.340
layers, as well.

00:17:31.340 --> 00:17:33.680
As we've gone to
copper interconnect,

00:17:33.680 --> 00:17:40.280
tungsten still appears in most
advanced technologies, now

00:17:40.280 --> 00:17:46.960
primarily just as the first
level of contact from a copper

00:17:46.960 --> 00:17:49.180
interconnect down
to the silicon.

00:17:49.180 --> 00:17:54.250
So it is still used, and
extensions where it may not

00:17:54.250 --> 00:18:01.100
purely be tungsten plugs, but
it may also be, in some cases,

00:18:01.100 --> 00:18:04.340
some local interconnect.

00:18:04.340 --> 00:18:06.710
So you can, down very
close to the silicon,

00:18:06.710 --> 00:18:08.690
form little straps
or other sorts

00:18:08.690 --> 00:18:14.710
of local tungsten-based short--
very short-run interconnect

00:18:14.710 --> 00:18:18.090
to form electrical connections.

00:18:18.090 --> 00:18:22.470
Now, the important part of
tungsten-- why it's used--

00:18:22.470 --> 00:18:30.420
is that it also can be
formally filled, and can,

00:18:30.420 --> 00:18:33.030
especially with chemical
vapor deposition,

00:18:33.030 --> 00:18:37.320
or plasma processing, can
fill fairly small holes.

00:18:37.320 --> 00:18:43.920
So the basic idea or progression
in a tungsten deposition

00:18:43.920 --> 00:18:48.690
is you primarily get
conformal deposition.

00:18:48.690 --> 00:18:57.780
So in time, the gases that are
present in the plasma chamber

00:18:57.780 --> 00:19:00.810
and reactor interface
with the surface

00:19:00.810 --> 00:19:06.430
form reactions, and basically
build up in a conformal way

00:19:06.430 --> 00:19:12.270
to fill the plug.

00:19:12.270 --> 00:19:13.860
Now, you want to do
this in a way that

00:19:13.860 --> 00:19:18.210
does not result in seams
or voids in the middle.

00:19:18.210 --> 00:19:20.400
So that can be a
little bit tricky.

00:19:20.400 --> 00:19:22.680
But that can be
done in such a way

00:19:22.680 --> 00:19:26.685
that one avoids those plugs.

00:19:29.810 --> 00:19:33.950
Now, the way this paper
uses tungsten plugs is

00:19:33.950 --> 00:19:38.330
with a process they refer
to as plasma etchback.

00:19:38.330 --> 00:19:42.130
So if I do that conformal
deposition, finally,

00:19:42.130 --> 00:19:49.090
to this the surface, now I've
got the tungsten not only in

00:19:49.090 --> 00:19:51.670
the plug, but I've also got
all this excess tungsten

00:19:51.670 --> 00:19:55.630
out here in the neighboring
regions that I want to remove.

00:19:55.630 --> 00:20:00.820
And the idea of etchback was
that through that deposition

00:20:00.820 --> 00:20:04.870
process, I filled the
surface, but I leave,

00:20:04.870 --> 00:20:08.620
essentially, a nearly
planar surface that now,

00:20:08.620 --> 00:20:13.240
if I just etch uniformly
back that whole surface,

00:20:13.240 --> 00:20:19.150
I can remove down to the
underlying interface metal

00:20:19.150 --> 00:20:22.480
or interface layer,
or the oxide,

00:20:22.480 --> 00:20:26.810
and leave the metal just in
the plug where I wanted it.

00:20:26.810 --> 00:20:30.260
In the paper, they
refer to using this as--

00:20:30.260 --> 00:20:34.580
using plasma etchback to
do this uniform etchback.

00:20:34.580 --> 00:20:37.730
In modern processing,
this step has pretty much

00:20:37.730 --> 00:20:40.430
been replaced with
CMP, because that

00:20:40.430 --> 00:20:43.640
has a much higher
controllability,

00:20:43.640 --> 00:20:47.000
and gets around an
important limitation that's

00:20:47.000 --> 00:20:51.650
kind of pictured here
in this diagram having

00:20:51.650 --> 00:20:55.070
to do with very tight
constraints on uniformity

00:20:55.070 --> 00:20:57.110
with a plasma etchback.

00:20:57.110 --> 00:21:01.280
The basic issue with
uniformity is if I, in fact,

00:21:01.280 --> 00:21:06.140
have deposition that results
in different thicknesses--

00:21:06.140 --> 00:21:09.890
either in different locations
within the chip or in different

00:21:09.890 --> 00:21:11.840
chips across the wafer--

00:21:11.840 --> 00:21:15.140
and I uniformly
etchback, first off,

00:21:15.140 --> 00:21:19.310
if I only etchback this
amount in both regions,

00:21:19.310 --> 00:21:22.010
then I have not completely
removed what I needed to

00:21:22.010 --> 00:21:23.430
in the other regions.

00:21:23.430 --> 00:21:26.030
So I have to make sure
I do enough over-etch

00:21:26.030 --> 00:21:29.840
to at least clear off and make
sure I don't have any shorts

00:21:29.840 --> 00:21:31.400
anywhere on the wafer.

00:21:31.400 --> 00:21:33.320
And when you do
that, to make sure

00:21:33.320 --> 00:21:37.760
that I'm down to the surface
in the thickest area,

00:21:37.760 --> 00:21:43.190
you get over-etch lossage
in the thinnest regions.

00:21:43.190 --> 00:21:45.510
So you have a fairly
tight constraint then

00:21:45.510 --> 00:21:48.590
on what the thickness
uniformity is,

00:21:48.590 --> 00:21:52.860
as well as the etch uniformity,
in order to achieve that, OK?

00:21:52.860 --> 00:21:55.530
So the paper does talk a
bit-- and in fact, we'll

00:21:55.530 --> 00:21:59.850
see later, explicitly models
the wafer uniformity as one

00:21:59.850 --> 00:22:03.870
of the outputs in order to try
to understand, as they play

00:22:03.870 --> 00:22:05.490
with some of the
process conditions,

00:22:05.490 --> 00:22:07.770
how uniformity is
going to be affected

00:22:07.770 --> 00:22:10.570
by their choice of
these conditions.

00:22:13.410 --> 00:22:16.260
There's a couple of other
interesting aspects of plasma

00:22:16.260 --> 00:22:22.350
etchback that are important,
as well, in particular,

00:22:22.350 --> 00:22:29.870
help inform the modeling
that this paper undertakes.

00:22:29.870 --> 00:22:33.080
And that has to do
with surface roughness.

00:22:33.080 --> 00:22:37.460
So not only will these sorts
of features, this topography

00:22:37.460 --> 00:22:39.770
like that little dimple there--

00:22:39.770 --> 00:22:43.040
but also, if the
surface of the film--

00:22:43.040 --> 00:22:47.380
the deposited film-- is rough,
and I do a uniform plasma

00:22:47.380 --> 00:22:51.950
etchback, sort of a
vertical plasma etchback,

00:22:51.950 --> 00:22:55.640
that surface roughness
can in fact then--

00:22:55.640 --> 00:22:56.900
this is rough.

00:22:56.900 --> 00:23:01.040
That, in truth,
may be transmitted

00:23:01.040 --> 00:23:05.180
to the final
surface of the plug.

00:23:05.180 --> 00:23:08.330
So another important parameter
that they will be explicitly

00:23:08.330 --> 00:23:11.030
modeling is tungsten--

00:23:11.030 --> 00:23:15.780
the deposited
tungsten roughness.

00:23:15.780 --> 00:23:18.390
And generally, less
rough is better.

00:23:18.390 --> 00:23:20.400
It's going to give a
better surface quality,

00:23:20.400 --> 00:23:23.700
less prone to defects,
more uniform in resistance,

00:23:23.700 --> 00:23:25.710
and so on.

00:23:25.710 --> 00:23:29.410
That, by the way, is another
reason for switching to CMP.

00:23:29.410 --> 00:23:33.780
CMP planarizes-- can
deal with not only

00:23:33.780 --> 00:23:39.010
this kind of surface
topography on a large scale,

00:23:39.010 --> 00:23:42.720
but it also smooths the surface
on sort of the atomic scale.

00:23:42.720 --> 00:23:49.140
And so you tend to get
much, much higher quality

00:23:49.140 --> 00:23:51.390
final plugs.

00:23:51.390 --> 00:23:54.140
OK, any questions
on basic tungsten--

00:23:54.140 --> 00:23:56.670
a little lesson
on tungsten plugs.

00:23:56.670 --> 00:23:58.920
So let's talk a little bit
about the process equipment

00:23:58.920 --> 00:24:00.810
and the process
parameters that are

00:24:00.810 --> 00:24:02.950
going to be in this case study.

00:24:02.950 --> 00:24:05.130
This is a schematic
cross section

00:24:05.130 --> 00:24:08.670
of an Applied Materials
Precision 5000 reactor

00:24:08.670 --> 00:24:10.920
configured for tungsten CVD.

00:24:10.920 --> 00:24:14.222
By the way, this
is a classic tool.

00:24:14.222 --> 00:24:22.220
The P5000-- AMaP P5000, there's
one of these in the Smithsonian

00:24:22.220 --> 00:24:24.750
Institute.

00:24:24.750 --> 00:24:27.660
It was the tool that made
Applied Materials what

00:24:27.660 --> 00:24:29.500
it is today.

00:24:29.500 --> 00:24:32.910
It was one of the first
single-wafer processing

00:24:32.910 --> 00:24:36.600
tools that really
gave good control

00:24:36.600 --> 00:24:41.100
over the atmospheric conditions
for deposition, for etching,

00:24:41.100 --> 00:24:43.050
these sorts of things.

00:24:43.050 --> 00:24:47.630
So we're seeing a glimpse back
into history here even looking

00:24:47.630 --> 00:24:48.800
at this cross section.

00:24:48.800 --> 00:24:52.880
By the way P5000's are still
in use all over the place.

00:24:52.880 --> 00:24:54.110
We have some--

00:24:54.110 --> 00:24:59.330
I guess just one in MTL, I
think mostly for etching.

00:24:59.330 --> 00:25:03.950
But even in some FABs
I still run into them.

00:25:03.950 --> 00:25:06.740
They've been scaled
up, and improved,

00:25:06.740 --> 00:25:10.880
and configured-- changed
in configuration,

00:25:10.880 --> 00:25:12.540
but they are still around.

00:25:12.540 --> 00:25:15.680
So the basic idea
here is that the wafer

00:25:15.680 --> 00:25:21.990
will sit here on a susceptor
in this plasma reactor--

00:25:21.990 --> 00:25:25.830
this low pressure
plasma reactor.

00:25:25.830 --> 00:25:28.050
In fact, there
are usually pins--

00:25:28.050 --> 00:25:29.580
I think three or four pins--

00:25:29.580 --> 00:25:30.990
that hold the wafer.

00:25:30.990 --> 00:25:34.080
The robot loads the
wafer in onto these pins.

00:25:34.080 --> 00:25:35.650
And then the pins--

00:25:35.650 --> 00:25:37.650
these lift fingers
here, I guess--

00:25:37.650 --> 00:25:38.400
recede.

00:25:38.400 --> 00:25:41.550
And the wafer then
sits on the susceptor.

00:25:41.550 --> 00:25:46.140
This susceptor is
optically heated.

00:25:46.140 --> 00:25:47.550
So there are these heat lamps.

00:25:47.550 --> 00:25:50.550
I think there's something
like 1,000 watt heat

00:25:50.550 --> 00:25:54.210
lamps in this configuration
that heat up and hold

00:25:54.210 --> 00:25:59.970
the temperature of the whole
platen, the whole susceptor.

00:25:59.970 --> 00:26:05.250
There's then gas flow
coming in from a gas feed.

00:26:05.250 --> 00:26:07.380
There's a little
mixing chamber in here

00:26:07.380 --> 00:26:10.470
so that you can mix different
combinations of different gas

00:26:10.470 --> 00:26:11.130
flows.

00:26:11.130 --> 00:26:15.240
And then it goes
through a shower head.

00:26:15.240 --> 00:26:17.430
This thing right
here is typically

00:26:17.430 --> 00:26:20.430
referred to as a shower head.

00:26:20.430 --> 00:26:22.680
And you can imagine,
it's basically

00:26:22.680 --> 00:26:24.130
like a shower head
in your shower.

00:26:24.130 --> 00:26:25.830
It's got holes in
it that basically

00:26:25.830 --> 00:26:28.710
allow the gases to
flow through, hopefully

00:26:28.710 --> 00:26:32.130
in a fairly uniform
distribution across the surface

00:26:32.130 --> 00:26:33.590
of the wafer.

00:26:33.590 --> 00:26:36.260
And then there's
a vacuum control,

00:26:36.260 --> 00:26:42.750
and a number of different vacuum
outlets for the gases to flow.

00:26:42.750 --> 00:26:44.370
So some of the key inputs--

00:26:44.370 --> 00:26:48.360
there's lots and lots of knobs
to control on these equipment.

00:26:48.360 --> 00:26:53.160
Some of the key inputs that
are used in this study--

00:26:53.160 --> 00:26:54.660
in the paper that
we're looking at--

00:26:54.660 --> 00:26:59.970
are gap space temperature, H2
pressure, and WF6 pressure.

00:26:59.970 --> 00:27:04.770
So the gap space
refers to, I believe,

00:27:04.770 --> 00:27:07.650
essentially the height
of this susceptor.

00:27:07.650 --> 00:27:10.530
One can play with the
distance between the gas

00:27:10.530 --> 00:27:15.990
inflow and the wafer, moving
it between, say, 2 to 4

00:27:15.990 --> 00:27:17.430
or 5 inches.

00:27:17.430 --> 00:27:20.620
And that changes a number of
the plasma characteristics.

00:27:20.620 --> 00:27:24.390
It changes perhaps some of
the gas flow characteristics.

00:27:24.390 --> 00:27:27.550
It may also change some of
the thermal characteristics.

00:27:27.550 --> 00:27:31.650
So it is a control parameter
that is not entirely obvious

00:27:31.650 --> 00:27:35.910
up front how it affects the
growth of-- or deposition

00:27:35.910 --> 00:27:37.860
of this tungsten.

00:27:37.860 --> 00:27:40.530
So that's going to be one
of the parameters that needs

00:27:40.530 --> 00:27:43.165
to be empirically studied.

00:27:43.165 --> 00:27:44.790
Certainly, temperature
is going to have

00:27:44.790 --> 00:27:49.650
a very strong effect in this
process on things like growth

00:27:49.650 --> 00:27:53.460
rate, perhaps also the surface
morphology or the roughness

00:27:53.460 --> 00:27:56.880
of the film, the amount of
incorporation of tungsten,

00:27:56.880 --> 00:27:59.550
and the ultimate
resistivity of the film--

00:27:59.550 --> 00:28:01.440
those sorts of parameters.

00:28:01.440 --> 00:28:08.610
And then, both hydrogen and
tungsten hexafluoride gas flow

00:28:08.610 --> 00:28:14.700
pressures will also be
clearly of influence

00:28:14.700 --> 00:28:19.240
in rate resistivity and so on.

00:28:19.240 --> 00:28:22.170
So this is kind of a neat
paper, because they actually

00:28:22.170 --> 00:28:25.950
are measuring about eight
different parameters

00:28:25.950 --> 00:28:28.420
and modeling each of them.

00:28:28.420 --> 00:28:32.640
So it's kind of a four input,
eight output kind of DOE.

00:28:32.640 --> 00:28:35.173
So just to go through some of
these parameters, many of them

00:28:35.173 --> 00:28:36.840
are pretty obvious,
but a couple of them

00:28:36.840 --> 00:28:40.620
I want to explain a little
bit more so that you have

00:28:40.620 --> 00:28:42.390
a good feel for what they are.

00:28:42.390 --> 00:28:46.110
Deposition rate, I think
that's pretty obvious.

00:28:46.110 --> 00:28:49.650
Generally, you would like
to have a fairly high rate.

00:28:49.650 --> 00:28:51.690
It's going to make
the process time

00:28:51.690 --> 00:28:56.220
as short as possible, efficiency
in the tool use, and so on.

00:28:56.220 --> 00:28:59.610
The paper mentions wanting
to have about 500 nanometers

00:28:59.610 --> 00:29:05.300
a minute-type rates
with these processes.

00:29:05.300 --> 00:29:09.050
The resistivity
value-- or rho here--

00:29:09.050 --> 00:29:11.570
generally, you kind of
want a low resistance,

00:29:11.570 --> 00:29:14.210
or a low resistivity film.

00:29:14.210 --> 00:29:16.370
An interesting twist
here is, depending

00:29:16.370 --> 00:29:21.320
on the application, the
actual resistivity you want

00:29:21.320 --> 00:29:25.440
and whether it's all that
low actually changes.

00:29:25.440 --> 00:29:28.250
So for example, if you're
using it as a short run metal

00:29:28.250 --> 00:29:33.500
wire, pretty much all the time,
low resistance is important.

00:29:33.500 --> 00:29:36.710
But it turns out, interestingly,
when you use tungsten plugs

00:29:36.710 --> 00:29:39.500
in conjunction with
aluminum layers,

00:29:39.500 --> 00:29:41.480
you may actually want
the tungsten plug

00:29:41.480 --> 00:29:45.680
to be a little bit higher
resistance than the aluminum

00:29:45.680 --> 00:29:50.810
itself, so that, because it's a
very small, constrained spatial

00:29:50.810 --> 00:29:56.120
area, the higher resistance
causes the current flow

00:29:56.120 --> 00:29:58.880
to spread out a little
bit more uniformly,

00:29:58.880 --> 00:30:01.520
and actually improves the
reliability of these tungsten

00:30:01.520 --> 00:30:02.540
plugs.

00:30:02.540 --> 00:30:06.200
So you'd actually like to
understand what the resistance

00:30:06.200 --> 00:30:08.240
is and be able to tune that in.

00:30:08.240 --> 00:30:11.420
So that's going to motivate
some of the modeling

00:30:11.420 --> 00:30:12.530
that that's done here.

00:30:12.530 --> 00:30:16.510
It's not always purely a
lower resistance is better.

00:30:20.280 --> 00:30:24.330
RS uniformity refers to
sheet resistance uniformity.

00:30:24.330 --> 00:30:32.400
This is the ohms per
square of sheet resistance,

00:30:32.400 --> 00:30:35.460
but then a uniformity
number calculated

00:30:35.460 --> 00:30:38.340
for that measured
sheet resistance

00:30:38.340 --> 00:30:40.530
across the entire wafer.

00:30:40.530 --> 00:30:43.980
And so you want a
very good uniformity.

00:30:43.980 --> 00:30:48.450
The 3% non-uniformity number
is the deviation-- percentage

00:30:48.450 --> 00:30:50.610
deviation of the thickness.

00:30:50.610 --> 00:30:53.280
Sort of one standard
deviation over mean

00:30:53.280 --> 00:30:55.350
is what they're referring
to in here, I believe,

00:30:55.350 --> 00:30:56.940
for this uniformity.

00:30:56.940 --> 00:30:58.860
And again, one of
the motivations

00:30:58.860 --> 00:31:03.950
there is that uniformity
in the plasma etchback,

00:31:03.950 --> 00:31:06.360
you want to avoid
recess of these plugs

00:31:06.360 --> 00:31:10.020
in some region which can make
it difficult for the subsequent

00:31:10.020 --> 00:31:14.350
aluminum to reach down in and
actually contact those recessed

00:31:14.350 --> 00:31:14.850
plugs.

00:31:17.760 --> 00:31:22.050
Film stress is another
important parameter.

00:31:22.050 --> 00:31:24.390
Let me see if I've got
other slides on that.

00:31:24.390 --> 00:31:25.440
No, not much.

00:31:28.940 --> 00:31:33.200
Essentially, there is
a volumetric mismatch

00:31:33.200 --> 00:31:36.170
to the deposited
tungsten compared

00:31:36.170 --> 00:31:39.350
to the underlying
silicon substrate wafer.

00:31:39.350 --> 00:31:40.850
And in fact, what
you'd typically

00:31:40.850 --> 00:31:44.120
find is that the
wafer will undergo--

00:31:44.120 --> 00:31:46.190
or be in tensile stress.

00:31:46.190 --> 00:31:50.990
So basically, there's more
volume in the deposited film.

00:31:50.990 --> 00:31:54.950
And it's causing a thick--

00:31:54.950 --> 00:32:00.090
a layer, depending on the
thickness of the layer--

00:32:00.090 --> 00:32:02.870
in fact, in the design, they're
talking about two different

00:32:02.870 --> 00:32:04.670
thicknesses that they explore--

00:32:04.670 --> 00:32:07.500
that causes the wafer to bow.

00:32:07.500 --> 00:32:12.280
So I've got a film that wants
to spread out a little bit more,

00:32:12.280 --> 00:32:14.370
especially at lower
temperature compared

00:32:14.370 --> 00:32:16.560
to the temperature
of processing.

00:32:16.560 --> 00:32:21.030
And that wafer bow
is a nice indicator

00:32:21.030 --> 00:32:24.960
of intrinsic internal
stress in those films.

00:32:24.960 --> 00:32:29.100
In general, you don't
want stress mismatches

00:32:29.100 --> 00:32:32.290
between different
layers on your wafer,

00:32:32.290 --> 00:32:35.190
because that means there's
sort of this excess energy

00:32:35.190 --> 00:32:37.690
around that would like
to release itself.

00:32:37.690 --> 00:32:39.570
And one way it
releases itself is

00:32:39.570 --> 00:32:42.750
by having those
layers delaminate, OK?

00:32:42.750 --> 00:32:48.570
So a reliability concern is
to try to avoid very high

00:32:48.570 --> 00:32:52.950
stresses in order to support
subsequent processing

00:32:52.950 --> 00:32:58.110
and long-term reliability of
the material on the wafer.

00:32:58.110 --> 00:33:01.040
So they are making some
measurements of film stress.

00:33:01.040 --> 00:33:03.430
In fact, the way they make
this measurement, I believe--

00:33:03.430 --> 00:33:04.440
if I remember right--

00:33:04.440 --> 00:33:07.200
is they measure the wafer bow.

00:33:07.200 --> 00:33:13.320
And then, based on assumed
numbers for the Young's modulus

00:33:13.320 --> 00:33:16.890
and perhaps the thickness--
they may measure the thickness

00:33:16.890 --> 00:33:18.900
separately--

00:33:18.900 --> 00:33:21.630
they basically
calculate or estimate

00:33:21.630 --> 00:33:24.090
what the film stress is.

00:33:24.090 --> 00:33:24.590
Yeah?

00:33:24.590 --> 00:33:28.170
AUDIENCE: And that's
originally CTE mismatch?

00:33:28.170 --> 00:33:30.510
DUANE BONING: I believe
that it is CTE mismatch,

00:33:30.510 --> 00:33:33.220
that in some sense, at
whatever temperature

00:33:33.220 --> 00:33:36.810
you're doing, if you
could deposit the film

00:33:36.810 --> 00:33:39.070
and keep the wafer at
300 degrees, or 100

00:33:39.070 --> 00:33:42.090
and whatever it is,
at that point in time,

00:33:42.090 --> 00:33:44.190
I don't believe
the wafer undergoes

00:33:44.190 --> 00:33:47.910
or experiences much stress
during this deposition.

00:33:47.910 --> 00:33:53.130
But then, it's a temperature
expansion difference.

00:33:53.130 --> 00:33:54.690
I'm not entirely sure of that.

00:33:54.690 --> 00:33:57.150
It's possible that the
simple incorporation

00:33:57.150 --> 00:34:02.740
at the time of deposition
also has some stress.

00:34:02.740 --> 00:34:05.340
But really, we're talking
about intrinsic stress that--

00:34:05.340 --> 00:34:13.168
or extrinsic stress that remains
at the end of processing.

00:34:13.168 --> 00:34:17.045
You know any more
on that, Hayden?

00:34:17.045 --> 00:34:20.350
AUDIENCE: Sounds reasonable.

00:34:20.350 --> 00:34:23.620
I mean, there are
situations where

00:34:23.620 --> 00:34:28.480
you're depositing an
epitaxial layer of, say,

00:34:28.480 --> 00:34:34.270
a semiconductor, that has a very
clearly defined lattice, whose

00:34:34.270 --> 00:34:37.000
picture is mismatched with
the substrate underneath.

00:34:37.000 --> 00:34:38.980
In that case, there's a--

00:34:38.980 --> 00:34:44.500
I guess a definite
built-in stress

00:34:44.500 --> 00:34:46.239
that's going to result
in that deposition

00:34:46.239 --> 00:34:49.230
but isn't connected with
thermal contraction.

00:34:49.230 --> 00:34:55.940
But I would have thought,
in this situation,

00:34:55.940 --> 00:34:59.330
it's mostly to do with
the presence of impurity

00:34:59.330 --> 00:35:04.400
is changing the CTE of the
deposited layer that stretched.

00:35:06.918 --> 00:35:07.710
DUANE BONING: Good.

00:35:10.350 --> 00:35:13.050
The fifth parameter that
they measure and model

00:35:13.050 --> 00:35:14.820
is step coverage.

00:35:14.820 --> 00:35:19.350
And so here, that refers
to essentially how good

00:35:19.350 --> 00:35:21.510
the deposition process is--

00:35:21.510 --> 00:35:23.130
I know you've read here--

00:35:23.130 --> 00:35:26.580
in filling these features.

00:35:26.580 --> 00:35:30.720
Now, if all of your features
are exactly the same size,

00:35:30.720 --> 00:35:33.100
then that's a little bit easier.

00:35:33.100 --> 00:35:35.130
So if all you're doing
is filling contacts

00:35:35.130 --> 00:35:38.040
of exactly the same
size, then you've

00:35:38.040 --> 00:35:40.890
got a nice, well-defined
number for step coverage.

00:35:40.890 --> 00:35:43.680
And that's really what they're
doing in this application.

00:35:43.680 --> 00:35:48.510
But I should mention that these
kind of conformal depositions

00:35:48.510 --> 00:35:52.970
can actually be a very
strong challenge for dealing

00:35:52.970 --> 00:35:55.580
with patterns or features
of different sizes.

00:35:55.580 --> 00:36:00.260
So you can imagine, for example,
having some contacts here,

00:36:00.260 --> 00:36:04.220
having some structures that
might in fact be lines,

00:36:04.220 --> 00:36:06.620
and then having some
other structures

00:36:06.620 --> 00:36:09.200
that are in fact
very wide lines.

00:36:09.200 --> 00:36:12.450
And now, if I can
formally fill, I

00:36:12.450 --> 00:36:18.000
might be able to fill
the narrow structures,

00:36:18.000 --> 00:36:21.870
but the wider ones will not
necessarily fill completely.

00:36:21.870 --> 00:36:25.350
I won't have excellent
step coverage.

00:36:25.350 --> 00:36:32.250
Now, I believe what they're
doing in this paper is really

00:36:32.250 --> 00:36:36.150
just looking locally
after the deposition,

00:36:36.150 --> 00:36:40.040
and looking to see sort of
what percentage of volume

00:36:40.040 --> 00:36:44.060
is missing in that little
indentation resulting

00:36:44.060 --> 00:36:49.010
from the conformal deposition,
and looking for fairly high--

00:36:49.010 --> 00:36:52.100
near 100%-- step coverage,
so that there's not

00:36:52.100 --> 00:36:58.340
a missing percentage of the
feature compared to, say, one

00:36:58.340 --> 00:37:02.390
of these large structures that
might have a very high missing

00:37:02.390 --> 00:37:03.830
volume.

00:37:03.830 --> 00:37:07.430
Generally, they're able to
achieve fairly high step

00:37:07.430 --> 00:37:08.040
coverages.

00:37:08.040 --> 00:37:10.340
So that's not one of
the critical output

00:37:10.340 --> 00:37:12.760
parameters in this process.

00:37:12.760 --> 00:37:15.570
Now, also shown on this
picture, and maybe a little bit

00:37:15.570 --> 00:37:16.810
hard for you to see--

00:37:16.810 --> 00:37:18.240
it's also in the paper.

00:37:18.240 --> 00:37:22.830
But on the right, you see
a top down photograph,

00:37:22.830 --> 00:37:27.360
or SEM micrograph, of
the surface structure.

00:37:27.360 --> 00:37:30.430
And it gives you a sense, a
little bit, of two things.

00:37:30.430 --> 00:37:34.740
One is there's a lot of
surface morphology going on,

00:37:34.740 --> 00:37:36.390
surface roughness.

00:37:36.390 --> 00:37:38.490
But the other basic
thing that happens

00:37:38.490 --> 00:37:43.320
is, as you're depositing
these materials,

00:37:43.320 --> 00:37:47.910
they are lining up in sort of
a polycrystalline kind of way.

00:37:47.910 --> 00:37:51.480
You do get some local
self-organization.

00:37:51.480 --> 00:37:55.170
And you can see that also
over here on the left side.

00:37:55.170 --> 00:37:57.780
If you kind of see,
there's little crystals,

00:37:57.780 --> 00:37:59.430
or little threads.

00:37:59.430 --> 00:38:02.220
And in here, you
can see a little bit

00:38:02.220 --> 00:38:03.830
of the polycrystalline
structure.

00:38:03.830 --> 00:38:05.580
And that's actually
one of the things that

00:38:05.580 --> 00:38:07.410
gives that surface roughness.

00:38:07.410 --> 00:38:11.190
It's not surface roughness
on the atom by atom level.

00:38:11.190 --> 00:38:14.880
It's really these
preferential growth directions

00:38:14.880 --> 00:38:19.980
in some of these grains, if
you will, as they're growing.

00:38:24.470 --> 00:38:26.600
Only two or three
more parameters here.

00:38:26.600 --> 00:38:28.730
Another one-- and this
is kind of neat, I think,

00:38:28.730 --> 00:38:31.880
because it's a
nice parameter that

00:38:31.880 --> 00:38:33.200
contrasts with the other ones.

00:38:33.200 --> 00:38:34.500
The other ones are--

00:38:34.500 --> 00:38:35.000
let's see.

00:38:35.000 --> 00:38:38.330
Most of these-- things like
step coverage, film stress,

00:38:38.330 --> 00:38:40.940
uniformity, resistance
uniformity-- those

00:38:40.940 --> 00:38:44.660
are parameters of the final
wafer or the intermediate wafer

00:38:44.660 --> 00:38:47.180
state that you want to achieve.

00:38:47.180 --> 00:38:50.990
Deposition rate
and WF6 conversion

00:38:50.990 --> 00:38:53.645
are both more
manufacturing parameters.

00:38:53.645 --> 00:38:56.090
In some sense, they don't
really matter to the final wafer

00:38:56.090 --> 00:38:56.590
product.

00:38:56.590 --> 00:39:00.500
But they can matter a great
deal for the cost efficiency

00:39:00.500 --> 00:39:03.090
or the time efficiency
of the process.

00:39:03.090 --> 00:39:08.570
So WF6 conversion is what
percentage of the incoming gas

00:39:08.570 --> 00:39:12.860
is actually resulting
in the deposited film.

00:39:12.860 --> 00:39:19.810
So you might have only
1% of the tungsten going

00:39:19.810 --> 00:39:23.800
onto the wafer and 99%
going out the exhaust pipe.

00:39:23.800 --> 00:39:25.240
That's terrible waste.

00:39:25.240 --> 00:39:28.120
It may have some
environmental implications,

00:39:28.120 --> 00:39:31.450
but it also has a lot
of cost implications.

00:39:31.450 --> 00:39:35.800
Because tungsten hexafluoride
is not a cheap gas--

00:39:35.800 --> 00:39:37.600
very, very highly purified.

00:39:37.600 --> 00:39:40.060
So I like this paper
in terms of they're

00:39:40.060 --> 00:39:44.320
actually trying to track,
and keep track of, and model

00:39:44.320 --> 00:39:47.260
the WF6 conversion rate,
and try to optimize

00:39:47.260 --> 00:39:50.720
that parameter also.

00:39:50.720 --> 00:39:53.690
Then finally, a couple
more parameters here.

00:39:53.690 --> 00:39:57.830
Reflectance is basically
an optical reflectance,

00:39:57.830 --> 00:40:01.430
percentage of light
reflected kind of measurement

00:40:01.430 --> 00:40:04.230
of the surface topography.

00:40:04.230 --> 00:40:06.710
So that's how they're trying
to estimate or correlate

00:40:06.710 --> 00:40:09.500
to the roughness of
the surface film.

00:40:09.500 --> 00:40:12.680
And then finally, another
manufacturing parameter

00:40:12.680 --> 00:40:16.130
is reproducibility,
not just wafer

00:40:16.130 --> 00:40:22.430
uniformity one wafer at a
time, but wafer to wafer

00:40:22.430 --> 00:40:25.560
repeatability or
reproducibility of the process.

00:40:25.560 --> 00:40:28.370
So they are actually making,
in this case, I think,

00:40:28.370 --> 00:40:33.620
the assumption that pretty
much all of these processes

00:40:33.620 --> 00:40:38.160
are more or less
similarly repeatable.

00:40:38.160 --> 00:40:41.700
But they want to estimate how
repeatable the process is.

00:40:41.700 --> 00:40:43.260
And we'll see that in their DOE.

00:40:43.260 --> 00:40:45.720
They're going to basically
do some replicate

00:40:45.720 --> 00:40:49.260
at one of the design points,
and use that to estimate

00:40:49.260 --> 00:40:52.150
reproducibility.

00:40:52.150 --> 00:40:54.150
So they're not
going in and trying

00:40:54.150 --> 00:40:59.200
to estimate where the
noise or the variance

00:40:59.200 --> 00:41:01.630
is minimum across
their operating space.

00:41:01.630 --> 00:41:08.540
They're actually assuming
that that's similar, OK?

00:41:08.540 --> 00:41:10.730
So here's what they
do in the paper.

00:41:10.730 --> 00:41:13.760
Their goals are to build
response surface models--

00:41:13.760 --> 00:41:16.880
just classic response
surface models.

00:41:16.880 --> 00:41:19.220
And then, as I said,
the reproducibility

00:41:19.220 --> 00:41:22.340
is really focused just on
the center point designs

00:41:22.340 --> 00:41:24.890
and applying that
throughout the entire space.

00:41:24.890 --> 00:41:28.010
And then, they want to use
these response surface models.

00:41:28.010 --> 00:41:31.570
They want to qualitatively
understand some of the trends--

00:41:31.570 --> 00:41:34.570
very good engineering
use, trying to understand

00:41:34.570 --> 00:41:36.040
from an engineering point.

00:41:36.040 --> 00:41:40.840
And then, they also want to use
these models in an optimization

00:41:40.840 --> 00:41:44.290
kind of loop to try to
drive towards satisfaction

00:41:44.290 --> 00:41:49.720
of multiple limits
or goals on those--

00:41:49.720 --> 00:41:52.510
what was it-- seven or
eight output parameters.

00:41:55.080 --> 00:41:57.510
Now, the paper does
refer to some prior work

00:41:57.510 --> 00:41:59.160
on screening experiments.

00:41:59.160 --> 00:42:07.010
In fact, these Precision
5000 tools and most FAB tools

00:42:07.010 --> 00:42:10.190
probably have,
literally in some cases,

00:42:10.190 --> 00:42:18.260
dozens of control settings, some
subset of which, maybe only 15,

00:42:18.260 --> 00:42:20.360
are easily settable
electronically.

00:42:20.360 --> 00:42:23.630
And another 15 might be more
mechanical, or other more

00:42:23.630 --> 00:42:25.170
permanent adjustments.

00:42:25.170 --> 00:42:27.920
But there's a huge space
of possible parameters.

00:42:27.920 --> 00:42:31.610
The paper just refers to
prior screening experiments

00:42:31.610 --> 00:42:34.620
to narrow down to
these four parameters.

00:42:34.620 --> 00:42:37.760
So I don't want you to think
that they knew automatically,

00:42:37.760 --> 00:42:40.220
up front, what four parameters
they wanted to play with.

00:42:42.982 --> 00:42:45.440
There is a reference if you
want to go try to track it down

00:42:45.440 --> 00:42:47.190
for their prior work.

00:42:47.190 --> 00:42:50.150
It's actually in some
obscure conference thing,

00:42:50.150 --> 00:42:53.670
so it's hard to find.

00:42:53.670 --> 00:42:57.060
So the details exactly of what
they did in their screening

00:42:57.060 --> 00:42:58.710
are not entirely clear.

00:42:58.710 --> 00:43:01.110
But the point is, they
probably did something

00:43:01.110 --> 00:43:06.240
like a fractional factorial--
a highly fractionalized

00:43:06.240 --> 00:43:09.660
factorial kind of
design to explore

00:43:09.660 --> 00:43:13.020
the space of just trying
to see what parameters are

00:43:13.020 --> 00:43:17.100
significant, what influence--
what input parameters influence

00:43:17.100 --> 00:43:19.830
the outputs that
they were of concern,

00:43:19.830 --> 00:43:23.850
and then narrow that down to
just these four parameters

00:43:23.850 --> 00:43:27.480
that they wanted to do a second
set of experiments-- which

00:43:27.480 --> 00:43:30.630
is what's in this paper-- that
are focused on response surface

00:43:30.630 --> 00:43:34.110
modeling, OK?

00:43:34.110 --> 00:43:36.960
There's another
interesting, subtle point

00:43:36.960 --> 00:43:41.950
that pops up in the
description of the paper.

00:43:41.950 --> 00:43:45.430
Some of these parameters,
things like sheet resistance--

00:43:45.430 --> 00:43:47.800
sheet resistance
is resistivity--

00:43:50.760 --> 00:43:55.190
is it divided by per square--

00:43:55.190 --> 00:44:01.690
the pure resistivity divided
by the thickness of the film,

00:44:01.690 --> 00:44:03.820
so that the thickness
of the deposited film

00:44:03.820 --> 00:44:09.320
will change the RS
measure on the wafer.

00:44:09.320 --> 00:44:12.650
What that means is, to do a
fair comparison just of truly

00:44:12.650 --> 00:44:18.440
the resistivity of the film, or
to estimate that, you actually

00:44:18.440 --> 00:44:24.460
want to grow all of your films
to about the same thickness.

00:44:24.460 --> 00:44:27.130
Well, if the deposition
rate is a parameter

00:44:27.130 --> 00:44:29.380
that you don't necessarily
know, and you're trying

00:44:29.380 --> 00:44:30.900
to model, how do you do that?

00:44:34.000 --> 00:44:36.810
So in other words, if I run
for a fixed period of time--

00:44:36.810 --> 00:44:41.310
maybe I run for 60 seconds on
each of these design points--

00:44:41.310 --> 00:44:43.560
but I have deposition
rates that are

00:44:43.560 --> 00:44:46.630
different by a
factor of 2, 5, 10,

00:44:46.630 --> 00:44:49.020
I'm going to get widely
varying thicknesses.

00:44:49.020 --> 00:44:51.750
And therefore, when I make
some of these simple sheet

00:44:51.750 --> 00:44:57.410
resistance measurements, that's
going to be very, very tricky.

00:44:57.410 --> 00:45:01.070
Furthermore, if my
thickness is varying

00:45:01.070 --> 00:45:03.260
it makes a basis for
comparison of many

00:45:03.260 --> 00:45:06.000
of these other
parameters really hard.

00:45:06.000 --> 00:45:07.890
How about film stress?

00:45:07.890 --> 00:45:09.750
Well, is it a film
stress that I'm

00:45:09.750 --> 00:45:11.610
seeing because of the
thickness difference,

00:45:11.610 --> 00:45:17.580
or is it truly intrinsic
film stress in the layer?

00:45:17.580 --> 00:45:19.910
So what they've done is been--

00:45:19.910 --> 00:45:21.810
and I think this is very cool--

00:45:21.810 --> 00:45:23.150
they were very careful.

00:45:23.150 --> 00:45:25.550
And they say that
they are doing this

00:45:25.550 --> 00:45:28.400
to where all films are
grown to about 1 micron

00:45:28.400 --> 00:45:32.040
thickness in this DOE.

00:45:32.040 --> 00:45:35.470
What's sneaky is, I think
to actually do this--

00:45:35.470 --> 00:45:37.890
which is also good,
because that is really

00:45:37.890 --> 00:45:42.170
the thickness that's close
to their target application.

00:45:42.170 --> 00:45:45.350
What's a little bit sneaky is to
do that, I think they basically

00:45:45.350 --> 00:45:50.690
had to do prior runs, maybe
at each individual DOE point,

00:45:50.690 --> 00:45:55.340
to do the run,
measure the thickness,

00:45:55.340 --> 00:45:58.730
estimate the growth
rate, and then adjust

00:45:58.730 --> 00:46:04.470
the time for the real DOE run
on each of the design points.

00:46:04.470 --> 00:46:07.400
So I think that there's
a whole extra duplicate

00:46:07.400 --> 00:46:09.500
set of experiments
that they're not

00:46:09.500 --> 00:46:16.650
talking about that were done in
order to be able to normalize

00:46:16.650 --> 00:46:20.790
and get a very nice set
of experiments in here

00:46:20.790 --> 00:46:22.350
that they could
talk about and be

00:46:22.350 --> 00:46:26.610
able to use to make the
right kinds of optimization

00:46:26.610 --> 00:46:27.877
and judgment.

00:46:27.877 --> 00:46:29.460
So it's kind of an
interesting lesson.

00:46:29.460 --> 00:46:32.730
I think there may often be
additional experimentation

00:46:32.730 --> 00:46:36.210
around your main
DOE that you have

00:46:36.210 --> 00:46:43.050
to do in order for your main DOE
to really be a good, clean DOE.

00:46:43.050 --> 00:46:46.650
Now, it's possible that maybe
their screening experiment

00:46:46.650 --> 00:46:49.920
gave them some information
to be able to do

00:46:49.920 --> 00:46:54.360
a rough estimate-- a good enough
estimate of deposition rate.

00:46:54.360 --> 00:46:56.580
So it's possible they were
able to get that benefit

00:46:56.580 --> 00:47:00.950
from their prior screening DOE.

00:47:00.950 --> 00:47:03.020
OK, here's their
experimental design.

00:47:03.020 --> 00:47:05.030
What they're going to do
is a central composite

00:47:05.030 --> 00:47:10.800
with five levels at each design
point, which is pretty cool.

00:47:10.800 --> 00:47:13.120
I think that's better
than the three levels.

00:47:13.120 --> 00:47:17.410
What's one reason that you might
like five levels rather than

00:47:17.410 --> 00:47:20.360
three, especially if you want to
build, say, quadratic response

00:47:20.360 --> 00:47:21.100
surface models?

00:47:27.550 --> 00:47:29.510
We haven't explicitly
done this before,

00:47:29.510 --> 00:47:34.270
but for example,
on quiz two, you

00:47:34.270 --> 00:47:37.060
were going from a linear
model to a quadratic model

00:47:37.060 --> 00:47:40.240
and asking questions
about lack of fit.

00:47:40.240 --> 00:47:46.010
In order to say whether a
linear model had lack of fit,

00:47:46.010 --> 00:47:50.960
I needed a third design point
so that I could say, well,

00:47:50.960 --> 00:47:53.420
does that third design
point give me indication

00:47:53.420 --> 00:47:55.370
that the linear model
is not sufficient?

00:47:55.370 --> 00:47:59.660
If I do three levels and
build a quadratic model,

00:47:59.660 --> 00:48:02.240
and I want to ask the
question, is a quadratic model

00:48:02.240 --> 00:48:06.860
sufficient, or is there a lack
of fit in the quadratic model,

00:48:06.860 --> 00:48:11.235
can I do that with
just three data points?

00:48:15.210 --> 00:48:16.020
No, right?

00:48:16.020 --> 00:48:20.080
You can fit a quadratic
to three data points.

00:48:20.080 --> 00:48:25.750
So you won't detect if there's
some other structure going on.

00:48:25.750 --> 00:48:28.890
So in order to be able to
do a lack-of-fit analysis up

00:48:28.890 --> 00:48:32.790
to seeing if a quadratic
model exhibits,

00:48:32.790 --> 00:48:36.450
then you need at least
additional levels implicitly

00:48:36.450 --> 00:48:37.600
somewhere in the design.

00:48:37.600 --> 00:48:40.570
So that's kind of a neat
thing that they do here.

00:48:40.570 --> 00:48:42.390
So what they've
done is normalized

00:48:42.390 --> 00:48:43.630
all of their factors.

00:48:43.630 --> 00:48:46.950
There are four factors here--
space, temperature, and so on.

00:48:46.950 --> 00:48:49.320
Again, not just two--

00:48:49.320 --> 00:48:52.110
in their case, not just two
of them, minus 1 plus 1.

00:48:52.110 --> 00:48:55.650
But they use, with their
five levels, a minus 2

00:48:55.650 --> 00:48:57.840
to plus 2 normalization.

00:48:57.840 --> 00:48:59.040
But essentially.

00:48:59.040 --> 00:49:04.200
They're doing up to five levels
on each of their parameters.

00:49:04.200 --> 00:49:05.970
And so they're using
coded variables

00:49:05.970 --> 00:49:11.620
that we'll see in the later
tables just like we're used to.

00:49:11.620 --> 00:49:14.730
Now, of course,
the other benefit

00:49:14.730 --> 00:49:17.460
of doing a screening
experiment is

00:49:17.460 --> 00:49:19.830
that also helps give
you some information

00:49:19.830 --> 00:49:24.390
about reasonable design space
for picking the range that you

00:49:24.390 --> 00:49:25.915
want to explore
these parameters in.

00:49:25.915 --> 00:49:27.540
Otherwise, they
probably would have had

00:49:27.540 --> 00:49:31.350
to just go by prior experience.

00:49:31.350 --> 00:49:34.920
But that's another advantage
of doing sort of this two-stage

00:49:34.920 --> 00:49:39.570
experimentation with screening
followed by a more extensive--

00:49:39.570 --> 00:49:44.110
either a new DOE, or adding
to the screening DOE.

00:49:44.110 --> 00:49:47.020
So they're going to be building
second order polynomial

00:49:47.020 --> 00:49:51.880
models, that is to say quadratic
models with both interactions

00:49:51.880 --> 00:49:53.800
and then square terms--

00:49:53.800 --> 00:49:57.107
just square terms in
individual parameters.

00:49:57.107 --> 00:49:58.690
And they also mention
that they're not

00:49:58.690 --> 00:50:02.620
going to do any transformations
of the output variables,

00:50:02.620 --> 00:50:04.555
such as a log or an inverse.

00:50:07.800 --> 00:50:12.880
OK, so we've already talked, I
think, about those two points.

00:50:12.880 --> 00:50:17.110
So in the paper, they show the
variable test level is coded.

00:50:17.110 --> 00:50:20.290
Here's, again, our four
inputs and the trials.

00:50:20.290 --> 00:50:25.890
And if you look,
you can start to get

00:50:25.890 --> 00:50:29.760
a very nice sense of what this
central composite looks like.

00:50:29.760 --> 00:50:33.050
What they're
essentially doing here--

00:50:33.050 --> 00:50:36.800
breaking it up into, let's call
it, three different segments

00:50:36.800 --> 00:50:38.990
of design points.

00:50:38.990 --> 00:50:40.440
What are these design points?

00:50:40.440 --> 00:50:41.840
What do those correspond to?

00:50:48.325 --> 00:50:48.950
There's a term.

00:50:48.950 --> 00:50:51.065
We refer to those kind
of design points as?

00:51:02.730 --> 00:51:04.480
Where does one of those
design points lie?

00:51:08.140 --> 00:51:11.530
Take trial number one, right?

00:51:11.530 --> 00:51:14.860
It's way out, minus
2 on the space axis

00:51:14.860 --> 00:51:19.900
and holding the others at their
median or their nominal value,

00:51:19.900 --> 00:51:21.460
right?

00:51:21.460 --> 00:51:25.540
So that's out on the
end of one of the axes.

00:51:25.540 --> 00:51:28.880
Then the plus 2 minus 2,
that's the other end of this.

00:51:28.880 --> 00:51:32.680
So those are our axial points
in a central composite design.

00:51:37.850 --> 00:51:41.150
They're sort of the classic
hold everything else constant,

00:51:41.150 --> 00:51:43.140
vary one parameter at a time.

00:51:43.140 --> 00:51:45.140
So they are giving
you unambiguous sense

00:51:45.140 --> 00:51:48.050
of what that one
parameter is doing,

00:51:48.050 --> 00:51:52.040
but not able to capture
interactions, and so on.

00:51:52.040 --> 00:51:57.932
They're also exploring sort of
the outer limits of the design.

00:51:57.932 --> 00:51:58.890
How about these points?

00:52:07.630 --> 00:52:10.054
How many of them are there?

00:52:10.054 --> 00:52:14.140
Looks like there are 16 of them.

00:52:14.140 --> 00:52:16.330
Corner points, exactly.

00:52:16.330 --> 00:52:19.030
So those are all
corner combinations

00:52:19.030 --> 00:52:21.370
of four parameters--

00:52:21.370 --> 00:52:24.760
4 squared, 16 different corners.

00:52:24.760 --> 00:52:27.190
And then finally,
these are easy.

00:52:27.190 --> 00:52:28.730
What are these?

00:52:28.730 --> 00:52:30.260
Center points, right.

00:52:30.260 --> 00:52:34.480
And so I don't know whether
they have seven replicates.

00:52:34.480 --> 00:52:37.660
So the other points are
unreplicated, by the way.

00:52:37.660 --> 00:52:40.570
So you might be a little
bit susceptible to outliers

00:52:40.570 --> 00:52:42.070
in some of the other points.

00:52:42.070 --> 00:52:44.200
But they have a fairly
reasonable number--

00:52:44.200 --> 00:52:46.330
seven replicates at the center.

00:52:46.330 --> 00:52:51.010
So that'll allow some
more or less reasonable

00:52:51.010 --> 00:52:53.890
estimate of some of
the reproducibility--

00:52:53.890 --> 00:52:57.335
some of the inherent
variances in the process.

00:53:01.820 --> 00:53:06.980
They say, by the way, that those
replicates generally result

00:53:06.980 --> 00:53:14.120
in about 1 1/2% to 5% 1 sigma
range in the output parameters.

00:53:14.120 --> 00:53:17.163
The paper says they did
a randomized run order.

00:53:17.163 --> 00:53:18.080
Why would you do that?

00:53:24.110 --> 00:53:25.360
Why not just run--

00:53:25.360 --> 00:53:28.120
you've got trial 1,
et cetera, et cetera.

00:53:28.120 --> 00:53:32.930
Why not just run all the
way down to trial number 31

00:53:32.930 --> 00:53:35.396
in this order?

00:53:35.396 --> 00:53:37.272
AUDIENCE: To be independent.

00:53:37.272 --> 00:53:38.487
To be independent

00:53:38.487 --> 00:53:39.820
DUANE BONING: To be independent.

00:53:42.650 --> 00:53:46.080
Independent of what?

00:53:46.080 --> 00:53:48.410
AUDIENCE: Different
pressure, different pressure.

00:53:54.682 --> 00:53:56.140
DUANE BONING: I
think you're right.

00:53:56.140 --> 00:53:58.630
But as you changes
parameters, we're

00:53:58.630 --> 00:54:00.880
only playing with
these four parameters.

00:54:00.880 --> 00:54:03.400
But there might still be noise--
other noise in the process,

00:54:03.400 --> 00:54:05.510
or drifts like we talked about.

00:54:05.510 --> 00:54:08.200
And it turns out, in many of
these deposition processes,

00:54:08.200 --> 00:54:12.320
you actually have to worry about
possible drifts, in that you

00:54:12.320 --> 00:54:16.580
may get film buildup on the
inside of the reactor that,

00:54:16.580 --> 00:54:20.010
over time, might change a little
bit the deposition process.

00:54:20.010 --> 00:54:25.460
So by randomizing the run order,
you're randomizing the output,

00:54:25.460 --> 00:54:27.950
and converting-- if
there is a trend,

00:54:27.950 --> 00:54:33.410
you basically convert that
systematic trend into noise.

00:54:33.410 --> 00:54:36.140
It may still
perturb your values,

00:54:36.140 --> 00:54:38.660
but now, it does it
kind of distributed

00:54:38.660 --> 00:54:41.630
in a random fashion
across all of your output.

00:54:41.630 --> 00:54:44.420
And it will add to the noise--

00:54:44.420 --> 00:54:47.900
change the
reproducibility values.

00:54:47.900 --> 00:54:50.510
But at least then,
it's not fooling you

00:54:50.510 --> 00:54:53.990
in a systematic way.

00:54:53.990 --> 00:54:58.610
If there is that kind of other
drift, it will not confuse you

00:54:58.610 --> 00:55:01.370
or alias with some
other parameter.

00:55:04.210 --> 00:55:08.220
I have one minor
annoyance in the paper.

00:55:08.220 --> 00:55:14.670
And so if you're writing papers
and you do a randomized run,

00:55:14.670 --> 00:55:17.160
tell me what the run
order actually was.

00:55:17.160 --> 00:55:19.050
If you're telling me
the data, I would love

00:55:19.050 --> 00:55:20.580
to actually know the run order.

00:55:20.580 --> 00:55:23.520
Because then, when I do
residual analysis and look

00:55:23.520 --> 00:55:26.340
at the residuals as
a function of time,

00:55:26.340 --> 00:55:30.810
I can actually go in and
see if there was perhaps

00:55:30.810 --> 00:55:33.300
a systematic time drift.

00:55:33.300 --> 00:55:38.580
And it really doesn't cost
much to do that in ink space

00:55:38.580 --> 00:55:39.910
in the paper.

00:55:39.910 --> 00:55:42.420
So for example,
here they had trial.

00:55:42.420 --> 00:55:44.670
Some papers, you
will actually see,

00:55:44.670 --> 00:55:48.270
they go in and might put
a number sort of right

00:55:48.270 --> 00:55:51.510
beside it in parentheses
or something like that,

00:55:51.510 --> 00:55:55.650
or another column in the table
or whatever, that tells me run

00:55:55.650 --> 00:55:58.890
order, not just trial number.

00:55:58.890 --> 00:56:04.450
So do that if you write
papers with data in it.

00:56:04.450 --> 00:56:07.060
They also say they did
some outlier analysis.

00:56:07.060 --> 00:56:09.820
They don't really
say what that was.

00:56:09.820 --> 00:56:12.800
But they do note it in the data.

00:56:12.800 --> 00:56:14.110
And by the way--

00:56:14.110 --> 00:56:17.260
oh, I may not have put
this on the site yet.

00:56:17.260 --> 00:56:21.530
I will also add the spreadsheet
with this basic data.

00:56:21.530 --> 00:56:24.490
So if you want to grab this
later and play with the data,

00:56:24.490 --> 00:56:27.220
and do some of your own
response surface model fits

00:56:27.220 --> 00:56:32.090
with JUMP or some of the
other tools, you can do that.

00:56:32.090 --> 00:56:34.360
Here's the output--
trial number,

00:56:34.360 --> 00:56:36.895
and then each of the
seven different outputs--

00:56:36.895 --> 00:56:39.260
so these are the seven
different outputs--

00:56:39.260 --> 00:56:43.760
and basically just the
raw, measured data.

00:56:43.760 --> 00:56:47.470
They also may have
asterisked or footnoted

00:56:47.470 --> 00:56:49.480
a few of these, which
is a good practice.

00:56:49.480 --> 00:56:55.320
They said, you know, weird
things like "indicates entries

00:56:55.320 --> 00:56:58.710
determined to be outliers."

00:56:58.710 --> 00:57:00.870
Or if they knew
something weird happened

00:57:00.870 --> 00:57:02.940
with the measurement
of that particular data

00:57:02.940 --> 00:57:07.320
point or that entire row,
they would note that.

00:57:07.320 --> 00:57:10.655
That can be really critical when
you're interpreting the data.

00:57:10.655 --> 00:57:12.780
And then, what they've done
down here at the bottom

00:57:12.780 --> 00:57:18.480
is simply calculated things
like the standard deviation

00:57:18.480 --> 00:57:21.360
across all of those.

00:57:21.360 --> 00:57:25.510
I think that's across
just the replicate runs.

00:57:25.510 --> 00:57:28.540
You can see that
underneath here.

00:57:28.540 --> 00:57:32.400
Yeah, OK, so it
gives you a sense

00:57:32.400 --> 00:57:34.800
of the percentage variance--

00:57:34.800 --> 00:57:40.240
1 sigma percentage variance in
each of the output parameters.

00:57:40.240 --> 00:57:41.896
Yes, question?

00:57:41.896 --> 00:57:44.900
AUDIENCE: One of the
entries has an issue.

00:57:44.900 --> 00:57:50.170
Doesn't that mean the
whole row has an issue?

00:57:50.170 --> 00:57:53.120
So shouldn't that
whole row be discarded.

00:57:53.120 --> 00:57:58.400
How can you, for example in
round six, have an issue in,

00:57:58.400 --> 00:58:01.520
let's say, 8.1, and
say this looks weird?

00:58:01.520 --> 00:58:05.730
And they're not going
to use it in the row.

00:58:05.730 --> 00:58:09.260
DUANE BONING: Yeah, so the
question for folks in Singapore

00:58:09.260 --> 00:58:14.560
is, how can you have just
an issue with one element

00:58:14.560 --> 00:58:16.880
and not an issue
with the whole row?

00:58:16.880 --> 00:58:19.720
Basically, I think it comes
down to some engineering

00:58:19.720 --> 00:58:22.090
knowledge on what the
issue might actually be.

00:58:22.090 --> 00:58:24.610
So in particular,
if you're worried

00:58:24.610 --> 00:58:28.270
that there's something
wrong with the measurement,

00:58:28.270 --> 00:58:30.910
then that does not necessarily
contaminate your measurements

00:58:30.910 --> 00:58:35.370
of other columns.

00:58:35.370 --> 00:58:37.380
If you think it's
really an indicator

00:58:37.380 --> 00:58:44.180
that the whole run, or the whole
trial, was messed up somehow,

00:58:44.180 --> 00:58:44.990
then I agree.

00:58:44.990 --> 00:58:49.010
You would probably want
to omit that entire run

00:58:49.010 --> 00:58:52.040
from your whole table,
or maybe repeat that run.

00:58:52.040 --> 00:58:54.130
In this case, with
single-wafer processing,

00:58:54.130 --> 00:58:55.662
it's probably an
easy thing to do.

00:58:55.662 --> 00:58:56.870
AUDIENCE: I guess the second.

00:58:56.870 --> 00:59:00.990
If we were experiments that
we heard that's an issue.

00:59:00.990 --> 00:59:06.870
One of the numbers looks funky.

00:59:06.870 --> 00:59:11.010
The fact-- and we want to
eliminate that whole row.

00:59:11.010 --> 00:59:13.510
What does that mean
for our experiment

00:59:13.510 --> 00:59:15.860
if there's, for example,
like, we only-- we

00:59:15.860 --> 00:59:17.610
didn't replicate
the center point,

00:59:17.610 --> 00:59:19.560
and now we don't
have a center point.

00:59:19.560 --> 00:59:21.810
DUANE BONING: Yeah, so the
other question is if you do

00:59:21.810 --> 00:59:24.000
have a bad data row,
how does that mess

00:59:24.000 --> 00:59:25.680
up your data analysis?

00:59:25.680 --> 00:59:29.550
And the answer is depending
on the kind of DOE

00:59:29.550 --> 00:59:33.480
that you have, and the kinds
of analysis that you apply,

00:59:33.480 --> 00:59:36.900
you can be more or less robust
to those kinds of missing data

00:59:36.900 --> 00:59:37.830
points.

00:59:37.830 --> 00:59:41.640
One of the nice things about
a central composite design,

00:59:41.640 --> 00:59:45.840
and especially one where they've
got kind of these five levels,

00:59:45.840 --> 00:59:50.670
is if you do that in conjunction
with response surface

00:59:50.670 --> 00:59:54.030
modeling-- regression
modeling in particular,

00:59:54.030 --> 00:59:56.130
the numerical
regression modeling--

00:59:56.130 --> 01:00:00.210
you're fairly well off if you
have a few missing data points.

01:00:00.210 --> 01:00:02.010
It would throw you
for a loop and some

01:00:02.010 --> 01:00:05.340
of the shorthand formation of
contrasts that we talked about.

01:00:05.340 --> 01:00:07.890
Because then, your
typical averaging

01:00:07.890 --> 01:00:10.800
that's implicit in some
of those are wrong.

01:00:10.800 --> 01:00:14.220
So you've got to be a little--
but if you do regression

01:00:14.220 --> 01:00:19.240
modeling in conjunction
with a fairly rich--

01:00:19.240 --> 01:00:22.510
sort of extra data points
are lurking in there,

01:00:22.510 --> 01:00:24.850
extra degrees of freedom
are lurking in there,

01:00:24.850 --> 01:00:27.910
that'd still allow you
to reliably fit models.

01:00:33.500 --> 01:00:37.460
So the paper says the ANOVA is
performed but it is not shown.

01:00:37.460 --> 01:00:39.320
I want to see the ANOVA table!

01:00:39.320 --> 01:00:42.540
So, well, we can basically
generate those on our own.

01:00:42.540 --> 01:00:47.970
And so in this case, if the
paper has the raw data in it,

01:00:47.970 --> 01:00:50.000
I think it's OK that they
didn't show the ANOVA,

01:00:50.000 --> 01:00:51.830
because I can regenerate that.

01:00:51.830 --> 01:00:53.900
Papers I hate are they
don't show you the data

01:00:53.900 --> 01:00:55.400
and they don't
show you the ANOVA,

01:00:55.400 --> 01:00:58.430
and so you don't know
really what the noise was,

01:00:58.430 --> 01:01:01.730
you don't know
significances of parameters,

01:01:01.730 --> 01:01:03.500
you don't know
which parameters--

01:01:03.500 --> 01:01:05.330
often, they won't
tell you, really,

01:01:05.330 --> 01:01:09.470
the significance level that
was used to accept a model, all

01:01:09.470 --> 01:01:10.740
of those sorts of things.

01:01:10.740 --> 01:01:12.560
So in this case, I'm
happy with the paper,

01:01:12.560 --> 01:01:15.830
because I've got the raw data.

01:01:15.830 --> 01:01:20.600
They claim that each of the
model is significant at 99.9%

01:01:20.600 --> 01:01:21.660
significance level.

01:01:21.660 --> 01:01:27.270
That's just their p value on
the F test for the whole model.

01:01:27.270 --> 01:01:29.420
So these are very--

01:01:29.420 --> 01:01:32.450
at least there is some
parameter that is significant

01:01:32.450 --> 01:01:34.430
and influencing the output.

01:01:34.430 --> 01:01:37.700
They report also r
squared, which is nice.

01:01:37.700 --> 01:01:41.150
And for most of the
models, they are really

01:01:41.150 --> 01:01:45.290
quite high-- in the
0.88 0.97 range.

01:01:45.290 --> 01:01:54.490
The lowest one was
resistivity at about 0.79.

01:01:54.490 --> 01:01:56.230
They also report
some lack of fit.

01:01:56.230 --> 01:01:59.020
I mentioned a little bit
of evidence of lack of fit

01:01:59.020 --> 01:02:01.660
for uniformity and reflectance.

01:02:01.660 --> 01:02:07.360
This lack of fit for sheet
resistance uniformity

01:02:07.360 --> 01:02:09.250
is really interesting.

01:02:09.250 --> 01:02:13.630
And in fact, so interesting that
I think, a week from today--

01:02:13.630 --> 01:02:15.790
if Dave is talking on Thursday--

01:02:15.790 --> 01:02:21.640
I will spend a whole lecture on
modeling of uniformity response

01:02:21.640 --> 01:02:24.430
surface modeling
approaches, spatial modeling

01:02:24.430 --> 01:02:27.460
approaches appropriate
for uniformity.

01:02:27.460 --> 01:02:31.150
The preview is, think of
the calculations that go

01:02:31.150 --> 01:02:33.730
into a wafer level uniformity--

01:02:33.730 --> 01:02:36.595
you know, the
calculation of that.

01:02:36.595 --> 01:02:38.470
You might measure-- I
think they're measuring

01:02:38.470 --> 01:02:40.870
49 points across the wafer.

01:02:40.870 --> 01:02:44.170
They're forming sums
of squared deviations

01:02:44.170 --> 01:02:47.440
and then taking a square root,
and then perhaps normalizing

01:02:47.440 --> 01:02:49.660
by some mean.

01:02:49.660 --> 01:02:53.680
Does that sound like a
set of linear operations?

01:02:53.680 --> 01:02:57.520
No, there's a lot of implicit
non-linearity lurking

01:02:57.520 --> 01:03:01.450
just in the calculation
of that metric.

01:03:01.450 --> 01:03:06.430
And so it's not surprising that
there's quadratic lack of fit,

01:03:06.430 --> 01:03:09.130
or inability of
a quadratic model

01:03:09.130 --> 01:03:12.250
to deal with a
uniformity metric--

01:03:12.250 --> 01:03:13.960
a spatial uniformity metric.

01:03:13.960 --> 01:03:16.870
And we'll talk more
about that next week.

01:03:16.870 --> 01:03:21.250
But, so they do
mention this at least.

01:03:21.250 --> 01:03:24.940
They also mention some potential
lack of fit in reflectance.

01:03:24.940 --> 01:03:26.800
I don't have an
explanation for that.

01:03:26.800 --> 01:03:31.220
They conjecture it's due to
a very small pure error term,

01:03:31.220 --> 01:03:35.320
so that you're able to detect,
with pretty fine resolution,

01:03:35.320 --> 01:03:39.850
if there's any subtle
non-quadratic trends.

01:03:39.850 --> 01:03:42.490
But they're not
concerned with it.

01:03:42.490 --> 01:03:45.650
They still feel that they
have very good models.

01:03:45.650 --> 01:03:47.830
It's also the case
that there may

01:03:47.830 --> 01:03:51.480
be transformations
that could be applied

01:03:51.480 --> 01:03:53.310
to improve these models.

01:03:53.310 --> 01:03:57.180
And that also, for
this sheet resistivity,

01:03:57.180 --> 01:03:59.760
or sheet resistance
measurement, there

01:03:59.760 --> 01:04:01.770
might be natural
transformations that you

01:04:01.770 --> 01:04:03.710
might think that apply.

01:04:03.710 --> 01:04:08.390
In fact, if this is related
to things like resistance

01:04:08.390 --> 01:04:15.260
divided by a thickness, and the
thickness grows linearly with--

01:04:15.260 --> 01:04:19.580
maybe you have a linear
dependence on growth rate

01:04:19.580 --> 01:04:21.200
or something like
that, there may

01:04:21.200 --> 01:04:25.280
be inherent in there some one
over kinds of transformations

01:04:25.280 --> 01:04:27.650
that might actually
be a better thing

01:04:27.650 --> 01:04:30.320
to do, to take that
sheet resistance,

01:04:30.320 --> 01:04:34.070
invert it, and model the
inverse of sheet resistance

01:04:34.070 --> 01:04:36.492
as a function of the
input parameters.

01:04:36.492 --> 01:04:37.950
So you could play
around with that.

01:04:37.950 --> 01:04:40.010
And actually, that's a
fun thing to play around

01:04:40.010 --> 01:04:41.210
with some of these models.

01:04:41.210 --> 01:04:44.730
They didn't do
that, but you could.

01:04:44.730 --> 01:04:47.060
And then they do show
the regression models.

01:04:47.060 --> 01:04:48.675
Here's the output.

01:04:48.675 --> 01:04:50.300
These are the regression
coefficients--

01:04:50.300 --> 01:04:53.280
all of the linear terms,
and the cross terms,

01:04:53.280 --> 01:04:54.392
and the square terms.

01:04:54.392 --> 01:04:55.850
And what they've
done in this table

01:04:55.850 --> 01:05:01.340
is report the fit for just
the significant terms.

01:05:01.340 --> 01:05:04.278
If the coefficient
was determined

01:05:04.278 --> 01:05:06.320
in their stepwise regression
to be insignificant,

01:05:06.320 --> 01:05:09.040
they've left it off.

01:05:09.040 --> 01:05:11.690
I don't think they
actually told us

01:05:11.690 --> 01:05:14.030
what their criteria
for inclusion--

01:05:14.030 --> 01:05:18.590
what their significance
level cut off was in here.

01:05:18.590 --> 01:05:20.790
So that would be a good
thing to do as well.

01:05:20.790 --> 01:05:26.030
But you can see, lots of models,
lots of second order terms.

01:05:26.030 --> 01:05:30.710
These are interactions--
b1,1; b,2,2; b3,3; b--

01:05:30.710 --> 01:05:32.810
those are our pure square terms.

01:05:32.810 --> 01:05:34.560
And then these are interactions.

01:05:34.560 --> 01:05:37.920
So there's a fair amount
of square activity going on

01:05:37.920 --> 01:05:40.810
as well as interactions.

01:05:40.810 --> 01:05:42.880
They also then use
those fit models

01:05:42.880 --> 01:05:46.060
to start to form contour plots.

01:05:46.060 --> 01:05:49.690
And this is how they start to
make some engineering judgment

01:05:49.690 --> 01:05:51.200
about different trends.

01:05:51.200 --> 01:05:54.090
So they would plot--

01:05:54.090 --> 01:05:57.160
realize, they've got four
inputs and seven outputs.

01:05:57.160 --> 01:05:59.670
You can't possibly have a--

01:05:59.670 --> 01:06:02.397
whatever-- four-dimensional
dimensional input space

01:06:02.397 --> 01:06:03.480
is very hard to visualize.

01:06:03.480 --> 01:06:07.092
So what you resort
to are typically

01:06:07.092 --> 01:06:08.550
sort of two-dimensional
plots where

01:06:08.550 --> 01:06:12.570
you might plot one output
or two outputs as a contour.

01:06:12.570 --> 01:06:15.870
So in this particular plot,
the solid line, I believe,

01:06:15.870 --> 01:06:19.220
is growth rate.

01:06:19.220 --> 01:06:23.360
And the dashed line
here is WF6 conversion.

01:06:26.530 --> 01:06:30.790
And you can start to get a
feel for as, for example,

01:06:30.790 --> 01:06:34.330
the WF6 pressure and the
temperature change what

01:06:34.330 --> 01:06:37.160
trends you get in those two
parameters and what trade

01:06:37.160 --> 01:06:39.380
offs you get in
those two parameters.

01:06:39.380 --> 01:06:43.660
So things like as the
temperature increases--

01:06:43.660 --> 01:06:46.060
so temperature
increasing this way--

01:06:46.060 --> 01:06:51.510
the growth rate
kind of increases.

01:06:51.510 --> 01:06:55.210
So the growth rate
is the solid line.

01:06:55.210 --> 01:06:58.890
So pretty directly
with temperature,

01:06:58.890 --> 01:07:01.410
that looks like a fairly
strong direct impact,

01:07:01.410 --> 01:07:05.520
as you might expect with a
chemically dependent kind

01:07:05.520 --> 01:07:07.090
of process.

01:07:07.090 --> 01:07:09.960
So they can start to get a feel
for what some of these trends

01:07:09.960 --> 01:07:13.770
are, and look at what, for
example, has the biggest

01:07:13.770 --> 01:07:19.290
impact on growth rate
of these parameters,

01:07:19.290 --> 01:07:23.400
and which have either
insignificant or small

01:07:23.400 --> 01:07:26.700
in magnitude kinds of effects.

01:07:26.700 --> 01:07:30.060
Now, they can also start
to do things like overlay

01:07:30.060 --> 01:07:33.510
requirements or
conditions on these

01:07:33.510 --> 01:07:36.750
to start to understand the
feasible operating space

01:07:36.750 --> 01:07:39.220
for process design
and optimization.

01:07:39.220 --> 01:07:41.790
So for example, if
your growth rate

01:07:41.790 --> 01:07:45.720
had to be 500 nanometers
per minute or higher,

01:07:45.720 --> 01:07:48.555
you might then have--

01:07:48.555 --> 01:07:51.090
kind of shading on this
plot, you would say,

01:07:51.090 --> 01:07:54.120
OK, I really need
to be above that 500

01:07:54.120 --> 01:07:57.760
nanometer per minute contour.

01:07:57.760 --> 01:08:01.600
And that tells me where I need
to be, at least with respect

01:08:01.600 --> 01:08:06.140
to those two parameters in terms
of feasible operating space.

01:08:06.140 --> 01:08:08.290
So already, it tells
you a lot just looking

01:08:08.290 --> 01:08:10.660
at these plots of where you
might need to be in order

01:08:10.660 --> 01:08:13.180
to achieve your multiple goals.

01:08:13.180 --> 01:08:16.270
It may not give you a
numerical optimum point.

01:08:16.270 --> 01:08:19.450
But all by itself, lots
of looking at the data

01:08:19.450 --> 01:08:22.450
and plotting of the
data is really valuable.

01:08:22.450 --> 01:08:25.510
And they do that for not
only growth rate in WF6,

01:08:25.510 --> 01:08:29.830
but things like
resistivity, reflectance.

01:08:29.830 --> 01:08:32.290
They start to look and
see is the overall design

01:08:32.290 --> 01:08:34.960
going to be feasible,
what has the biggest

01:08:34.960 --> 01:08:38.859
effect on morphology,
those sorts of things.

01:08:41.520 --> 01:08:45.330
We found if you look
at their contour plots,

01:08:45.330 --> 01:08:48.990
most of these contour
plots are reasonably--

01:08:48.990 --> 01:08:54.790
these are nice,
semilinear kinds of plots.

01:08:54.790 --> 01:08:59.399
Their uniformity plot,
these look bizarre--

01:08:59.399 --> 01:09:01.380
very complex surfaces.

01:09:01.380 --> 01:09:06.240
And again, that's a reflection
that this uniformity metric,

01:09:06.240 --> 01:09:09.510
the spatial uniformity metric,
is a very complex function

01:09:09.510 --> 01:09:10.800
of the input parameters.

01:09:14.500 --> 01:09:17.200
What they then do, finally,
to round out the paper,

01:09:17.200 --> 01:09:19.100
is talk a little bit
about optimization.

01:09:19.100 --> 01:09:22.510
So what they will
have is, some of those

01:09:22.510 --> 01:09:25.899
limits-- like I said, for
example, on the growth rate,

01:09:25.899 --> 01:09:28.689
I guess it wasn't a
500 nanometer cut off.

01:09:28.689 --> 01:09:30.970
They needed at
least 300 nanometer.

01:09:30.970 --> 01:09:32.649
But they would
like to get that--

01:09:32.649 --> 01:09:34.359
higher is better.

01:09:34.359 --> 01:09:38.649
And they would basically have
different lower or upper bounds

01:09:38.649 --> 01:09:42.609
on each of the other
parameters, as well as desires

01:09:42.609 --> 01:09:46.330
to sort of hit either targets
or make those bigger or smaller.

01:09:46.330 --> 01:09:48.130
Now, they don't really
describe very much

01:09:48.130 --> 01:09:54.220
what their optimization
procedure is.

01:09:54.220 --> 01:09:56.890
All they do is report
that using the model,

01:09:56.890 --> 01:10:00.340
they were able to achieve
the following best

01:10:00.340 --> 01:10:05.800
condition, which they report
and are very satisfied with--

01:10:05.800 --> 01:10:08.980
so things like
very high, 99% step

01:10:08.980 --> 01:10:16.100
coverage, improved or
fairly good conversion rate,

01:10:16.100 --> 01:10:17.208
and so on.

01:10:17.208 --> 01:10:19.750
So that's actually one of the
fun things one could play with,

01:10:19.750 --> 01:10:21.700
I think, with the
actual data, is

01:10:21.700 --> 01:10:25.630
apply some of the hill climbing
or other kinds of optimization

01:10:25.630 --> 01:10:28.850
algorithms to this data.

01:10:28.850 --> 01:10:32.330
They do note in the paper
that some of these constraints

01:10:32.330 --> 01:10:36.050
or limits do not greatly
reduce their factor space.

01:10:36.050 --> 01:10:40.760
They do not constrain
where they need to operate.

01:10:40.760 --> 01:10:43.737
And that gives them lots
of latitude to be able to--

01:10:43.737 --> 01:10:44.570
that's a good thing.

01:10:44.570 --> 01:10:46.790
It gives them latitude to
play with those parameters

01:10:46.790 --> 01:10:52.670
to achieve perhaps
some other goals.

01:10:52.670 --> 01:10:56.150
OK, so what I want to do
in the last six minutes

01:10:56.150 --> 01:10:57.590
is switch over here.

01:11:01.050 --> 01:11:03.340
So are we ready to do a switch?

01:11:03.340 --> 01:11:04.590
Because what I want to do is--

01:11:04.590 --> 01:11:06.700
AUDIENCE: Why don't
you drop a pin there?

01:11:06.700 --> 01:11:07.408
DUANE BONING: OK.

01:11:18.370 --> 01:11:23.660
OK, what's that number?

01:11:23.660 --> 01:11:25.190
So what I'm going
to be doing here

01:11:25.190 --> 01:11:31.390
is basically showing you some
JUMP analysis of this data.

01:11:39.780 --> 01:11:41.190
Oh, dear.

01:11:41.190 --> 01:11:42.300
Maybe I'm not online.

01:12:14.850 --> 01:12:16.850
So what I've
basically done is just

01:12:16.850 --> 01:12:20.510
sucked in the raw data
and their input conditions

01:12:20.510 --> 01:12:21.740
and their output conditions.

01:12:21.740 --> 01:12:23.360
And we'll play with two things.

01:12:23.360 --> 01:12:27.160
I just want to give you a little
bit of a glimpse here of--

01:12:27.160 --> 01:12:28.160
AUDIENCE: We can't hear.

01:12:28.160 --> 01:12:31.226
DUANE BONING: OK, excellent.

01:12:41.660 --> 01:12:44.600
OK, can you see
that in Singapore?

01:12:44.600 --> 01:12:45.440
Excellent.

01:12:45.440 --> 01:12:47.840
All right, I'm psyched.

01:12:47.840 --> 01:12:49.940
OK, so what I've done
here is use JUMP--

01:12:49.940 --> 01:12:53.310
JUMP 7 in fact, which is a
more recent version than I'm

01:12:53.310 --> 01:12:53.810
used to.

01:12:53.810 --> 01:12:55.935
So some of the controls
are a little bit different.

01:12:55.935 --> 01:12:59.250
By the way, I don't know if
you played with JUMP before.

01:12:59.250 --> 01:13:03.290
As you're looking
at your projects,

01:13:03.290 --> 01:13:06.200
there is a 30-day
free trial license

01:13:06.200 --> 01:13:07.970
of the full version of JUMP.

01:13:07.970 --> 01:13:11.300
So you can download
the trial version

01:13:11.300 --> 01:13:13.820
if you want-- if you
want to grab it and play

01:13:13.820 --> 01:13:20.217
with it, especially
for the project.

01:13:20.217 --> 01:13:22.300
I believe there's also an
academic version that's,

01:13:22.300 --> 01:13:24.910
like, $50 for a year
license or something, which

01:13:24.910 --> 01:13:25.810
is pretty nice.

01:13:25.810 --> 01:13:30.140
Because the commercial version
is hundreds of dollars.

01:13:30.140 --> 01:13:31.590
So it's a nice package.

01:13:31.590 --> 01:13:34.320
So all I did is I
sucked in the inputs.

01:13:34.320 --> 01:13:37.260
These are our four
input conditions here,

01:13:37.260 --> 01:13:40.020
and then our growth rate
and output conditions.

01:13:40.020 --> 01:13:42.300
And I would always encourage
you, as a first step,

01:13:42.300 --> 01:13:44.190
to explore your data.

01:13:44.190 --> 01:13:45.360
Just look at it.

01:13:45.360 --> 01:13:46.980
See if it makes sense.

01:13:46.980 --> 01:13:52.130
Do univariate plot of outputs
as a function of inputs.

01:13:52.130 --> 01:13:54.540
And by the way, there's
some very cool things

01:13:54.540 --> 01:13:58.200
like scatterplot
3D, where you might

01:13:58.200 --> 01:14:02.670
take three of these
parameters and plot them

01:14:02.670 --> 01:14:04.870
against each other.

01:14:04.870 --> 01:14:07.560
And so you get cool
things like this

01:14:07.560 --> 01:14:13.140
that give you a picture of
the scatterplot as a function

01:14:13.140 --> 01:14:14.610
of those three inputs.

01:14:14.610 --> 01:14:17.220
Or I guess this is a
scatterplot of three

01:14:17.220 --> 01:14:18.750
outputs versus each other.

01:14:18.750 --> 01:14:21.540
See if there's some correlation
between these outputs.

01:14:21.540 --> 01:14:25.030
You can do it one output as
a function of two others,

01:14:25.030 --> 01:14:25.660
and so on.

01:14:25.660 --> 01:14:29.210
So one of the nice things
I like about JUMP--

01:14:29.210 --> 01:14:32.120
and you should look for it in
a good interactive package--

01:14:32.120 --> 01:14:33.740
is that interaction.

01:14:33.740 --> 01:14:36.380
You can actually interact with
the data, one of the things

01:14:36.380 --> 01:14:38.790
that Excel is not good at.

01:14:38.790 --> 01:14:43.570
So other tools like MATLAB
are good at this as well.

01:14:43.570 --> 01:14:48.020
OK, so having done that, another
thing I like about JUMP is it

01:14:48.020 --> 01:14:53.460
allows you to highlight
what are bad data points.

01:14:53.460 --> 01:14:56.300
So I don't-- I can deal with
missing data points in JUMP.

01:14:56.300 --> 01:14:59.965
So I've pulled those
from the paper as well.

01:14:59.965 --> 01:15:01.340
And then I can
start to do things

01:15:01.340 --> 01:15:04.170
like build regression models.

01:15:04.170 --> 01:15:05.900
So there are graph--

01:15:05.900 --> 01:15:11.130
whoops, I'm sorry--
analyze fit model.

01:15:11.130 --> 01:15:14.900
So here, I might say, OK, I
want to build a model for--

01:15:14.900 --> 01:15:16.880
I'll just pick one
for the moment--

01:15:16.880 --> 01:15:21.020
growth rate as a function of
these four input parameters.

01:15:21.020 --> 01:15:23.450
And I can do things
like, say, I really

01:15:23.450 --> 01:15:27.260
am doing a response surface
model up to polynomial degree

01:15:27.260 --> 01:15:28.190
2.

01:15:28.190 --> 01:15:31.890
And it builds for
me the template,

01:15:31.890 --> 01:15:33.830
if you will, for all
of the interaction

01:15:33.830 --> 01:15:36.278
terms, the square terms,
all of those things

01:15:36.278 --> 01:15:37.820
that if you were
doing this in Excel,

01:15:37.820 --> 01:15:42.560
you would have to yourself
build those fictitious input

01:15:42.560 --> 01:15:43.620
parameters.

01:15:43.620 --> 01:15:45.260
But here, I'm
basically telling it

01:15:45.260 --> 01:15:48.830
directly what the structure
of the model I want to fit is.

01:15:48.830 --> 01:15:50.330
And one thing that
we haven't talked

01:15:50.330 --> 01:15:52.940
a lot about that I
wanted to highlight

01:15:52.940 --> 01:15:56.300
is how to go about
building the model.

01:15:56.300 --> 01:15:58.880
I could go ahead and
do a full ANOVA--

01:15:58.880 --> 01:16:02.000
a full regression in ANOVA--
and look at each of the terms

01:16:02.000 --> 01:16:05.420
and decide what's
significant and what's not.

01:16:05.420 --> 01:16:11.660
There is a stepwise version
of that same process

01:16:11.660 --> 01:16:17.780
where, essentially, what we do
is, one parameter at a time,

01:16:17.780 --> 01:16:18.860
add--

01:16:18.860 --> 01:16:20.000
AUDIENCE: Hi, Prof, sorry.

01:16:20.000 --> 01:16:23.336
Yes We just lost the connection.

01:16:23.336 --> 01:16:25.652
We can't see a screen anymore.

01:16:32.015 --> 01:16:33.800
DUANE BONING: I
wonder if I lost my--

01:16:37.950 --> 01:16:39.570
can you see it just--

01:16:39.570 --> 01:16:41.330
maybe we'll just transmit.

01:16:41.330 --> 01:16:45.529
I'll try-- it's not
accepting the net meeting.

01:16:45.529 --> 01:16:47.196
AUDIENCE: I can put
it through the Codex

01:16:47.196 --> 01:16:48.570
so they can see it
one their screen.

01:16:48.570 --> 01:16:49.740
DUANE BONING: Yeah,
it won't look as good.

01:16:49.740 --> 01:16:51.595
But let's at least
do that since we only

01:16:51.595 --> 01:16:52.720
have a couple more minutes.

01:16:52.720 --> 01:16:55.440
AUDIENCE: I can't do anything
about your net component.

01:16:55.440 --> 01:16:57.490
DUANE BONING: Yeah, that's fine.

01:16:57.490 --> 01:17:00.780
So we're just going to project
so you can see kind of crudely

01:17:00.780 --> 01:17:01.770
on the screen.

01:17:01.770 --> 01:17:04.620
But the basic idea of
this stepwise regression

01:17:04.620 --> 01:17:07.590
is that you can set
the significance

01:17:07.590 --> 01:17:10.560
level for accepting
a model parameter.

01:17:10.560 --> 01:17:12.820
And then, one step at a time--

01:17:12.820 --> 01:17:15.060
so for example,
if I do this step,

01:17:15.060 --> 01:17:18.840
it's pulling in additional
coefficients that

01:17:18.840 --> 01:17:22.600
are of acceptable significance.

01:17:22.600 --> 01:17:25.320
And in fact, I think the
probability, to enter,

01:17:25.320 --> 01:17:28.380
it needs to be set to 0.25.

01:17:28.380 --> 01:17:31.500
This is 75%
confidence level needs

01:17:31.500 --> 01:17:34.740
to be achieved in order
to accept the model.

01:17:34.740 --> 01:17:36.420
And I can keep stepping through.

01:17:36.420 --> 01:17:40.290
And it iteratively is
basically making determinations

01:17:40.290 --> 01:17:43.980
based on my setting
of significance values

01:17:43.980 --> 01:17:48.520
to pull in or
discard model terms.

01:17:48.520 --> 01:17:50.550
And if it discards a
model term, then it

01:17:50.550 --> 01:17:53.190
takes those degrees of
freedom, throws them back

01:17:53.190 --> 01:17:56.760
into the error term,
not purely as a function

01:17:56.760 --> 01:18:00.330
of the replicate
error, but it does

01:18:00.330 --> 01:18:04.230
this kind of stepwise
multiple regression

01:18:04.230 --> 01:18:06.850
in order to build
the overall model.

01:18:06.850 --> 01:18:08.460
So here you can
see, for example,

01:18:08.460 --> 01:18:13.140
for this particular
output of growth rate,

01:18:13.140 --> 01:18:15.900
you can see which terms
end up being significant.

01:18:15.900 --> 01:18:18.390
You've got things like
temperature squared,

01:18:18.390 --> 01:18:22.230
and temperature H2
pressure interactions.

01:18:22.230 --> 01:18:25.890
OK, doing that, you can then
accept one of these models

01:18:25.890 --> 01:18:32.490
and build another
column in JUMP that

01:18:32.490 --> 01:18:35.580
is, in fact, the
prediction formula for one

01:18:35.580 --> 01:18:36.640
of these parameters.

01:18:36.640 --> 01:18:39.360
So for example, this might
be the prediction formula

01:18:39.360 --> 01:18:40.410
for growth rate.

01:18:40.410 --> 01:18:43.750
It now has that
polynomial model in it.

01:18:43.750 --> 01:18:46.740
And one of the cool things about
JUMP, just so that it's there

01:18:46.740 --> 01:18:48.900
and then you can
play with it, are

01:18:48.900 --> 01:18:53.010
you can also now start to go
in and do things like profiler

01:18:53.010 --> 01:18:57.240
or contour profiler for
optimization and exploration

01:18:57.240 --> 01:18:59.230
of that design space.

01:18:59.230 --> 01:19:03.150
So doing a simple
one-parameter profiler,

01:19:03.150 --> 01:19:07.950
I might say, OK, I want to
profile growth rate and row.

01:19:07.950 --> 01:19:12.370
I'll just do those
two parameters.

01:19:12.370 --> 01:19:14.680
And what I've got is
this prediction profiler

01:19:14.680 --> 01:19:17.950
that has the two outputs.

01:19:17.950 --> 01:19:21.430
Growth rate is the
first row, and--

01:19:21.430 --> 01:19:22.180
whatever it was.

01:19:22.180 --> 01:19:24.945
Was it-- I can't remember
what the second one was.

01:19:24.945 --> 01:19:26.320
It's a little hard
to see there--

01:19:26.320 --> 01:19:27.340
formula row.

01:19:27.340 --> 01:19:30.850
OK, so the resistance and
the growth rate as a function

01:19:30.850 --> 01:19:33.440
of each of the
individual parameters.

01:19:33.440 --> 01:19:36.070
So this is the
univariate dependence

01:19:36.070 --> 01:19:39.230
depending on my current
operating point.

01:19:39.230 --> 01:19:41.110
And then I can move
that operating point

01:19:41.110 --> 01:19:44.990
and see how the other
parameters change.

01:19:44.990 --> 01:19:50.550
So as I change temperature, how
does that affect my outputs?

01:19:50.550 --> 01:19:51.930
OK, so it's kind of fun.

01:19:51.930 --> 01:19:56.220
You can play around and see
how those things happen.

01:19:56.220 --> 01:19:59.630
You can also do,
essentially, close

01:19:59.630 --> 01:20:02.810
to what they did in the
paper, and do contour plot

01:20:02.810 --> 01:20:04.010
explorations.

01:20:04.010 --> 01:20:08.360
So I might, for example,
do those same parameters--

01:20:10.940 --> 01:20:13.340
yeah, that's fine--
and actually,

01:20:13.340 --> 01:20:20.000
now, plot the current operating
point, the response of growth

01:20:20.000 --> 01:20:24.770
rate, row, resistance,
uniformity in the design space

01:20:24.770 --> 01:20:26.870
so that I can see how
those things change

01:20:26.870 --> 01:20:30.230
as I change my gap
spacing or my temperature.

01:20:30.230 --> 01:20:33.920
And I can also apply
things like the limits.

01:20:33.920 --> 01:20:38.720
Maybe I have a low limit
of 500 for the growth rate.

01:20:38.720 --> 01:20:40.940
I need, again, 500 nanometers.

01:20:40.940 --> 01:20:45.860
And what it does, it'll start
to shade out unallowable regions

01:20:45.860 --> 01:20:48.870
to achieve those kinds of goals.

01:20:48.870 --> 01:20:50.810
So this is just a
nice, interactive tool

01:20:50.810 --> 01:20:56.030
that lets you do that kind
of dynamic exploration

01:20:56.030 --> 01:20:58.470
of the optimal space.

01:20:58.470 --> 01:21:03.980
So I'll put that data
up on the web as well.

01:21:03.980 --> 01:21:05.850
And you can play around with it.

01:21:05.850 --> 01:21:09.380
But this is kind of
where I'll leave it

01:21:09.380 --> 01:21:11.720
for you to explore
more if you want to

01:21:11.720 --> 01:21:16.550
with JUMP, either on this data,
or perhaps more efficiently,

01:21:16.550 --> 01:21:18.440
on your team project data.

01:21:18.440 --> 01:21:20.840
But wanted to get
this case study

01:21:20.840 --> 01:21:22.610
so some of the capabilities.

01:21:22.610 --> 01:21:24.980
So I think with that,
I'm going to break.

01:21:24.980 --> 01:21:27.050
And we can chat a
little bit if people

01:21:27.050 --> 01:21:30.500
have questions about team
projects and whatnot.