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PROFESSOR: Well, today
I'm going to give

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the fourth and final
case study of the course.

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And everything I'm
going to talk about

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is my thesis research
in one form or another.

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So this is work that's
definitely in progress.

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And in a lot of cases,
we haven't really

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drawn conclusions yet.

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So it'll be quite
rough and ready.

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But I hope it'll be informative
and raise some questions

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for you.

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The focus of my
thesis research is--

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well, broadly speaking,
finding approaches

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to manufacturing microfluidic
devices using polymers.

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And for many of you,
I think microfluidics

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will be something you know
at least a little about.

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Essentially, microchips that
manipulate very small volumes

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of fluids to perform various
experimental, or diagnostic, or

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other engineering tasks.

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And we were interested
in developing processes

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and choosing materials that will
help us make these things very

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cheaply so that they can be
used at the point of care

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in the case of diagnostic
devices, and so forth.

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Now, one particular
process that's

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of great interest for
this is the imprinting

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of thermoplastic
polymeric layers.

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Hot embossing is what
we're going to call it.

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And for a start, let
me say why polymers

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are interesting for making
these sorts of devices.

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I think I see
three main reasons.

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Firstly, they're cheap compared
to silicone or glass, which

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are other materials
that you might think

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of as being obvious
candidates to fabricate

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these microscopic fluidic
channels, and valves,

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and pumps, and so forth.

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So polymers are cheap.

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Second thing is, they're
often transparent.

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And that's really important.

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When you have a biological
sample inside this device

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and you're trying to
look at how it behaves

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in response to certain
stimuli, either you're

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exposing it to a dye
that will make cells

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with certain
properties fluoresce.

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You need to see
that fluorescence.

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Or you're prodding
a cell somehow

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to see whether its
stiffness gives you

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information about
its disease state,

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something along these lines.

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Anyway, but transparency
is an important property.

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And thirdly, a lot of plastics
are mechanically tough,

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which makes them highly
suitable to use in the field

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at the point of care,
in doctors' surgeries

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and so forth.

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So these are the three reasons
why polymers are interesting.

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And imprinting them is
interesting as a process,

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because that itself
has the potential

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to be quick and cheap.

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You can imagine a
cycle imprinting

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a thermoplastic polymer
occurring in around a minute.

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And you can choose what kind
of size workpiece you machine.

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You could machine
anything from the size

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of a single microfluidic
chip, all the way up

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to continuous reels
of polymeric film.

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And indeed, the reel to
reel printing approach

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is something that's been
used in industry already

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for quite rudimentary devices.

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3M has a patent on
hot embossing reels

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of thermoplastic polymers.

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And so it's a pretty
flexible process.

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And microfluidics
aren't the only sorts

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of things you might
think of making with it.

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A lot of optical devices
could be made this way.

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You could think of imprinting
refractive elements.

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Or actually 3M's
patent is so that they

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can imprint the reflective
films that are laminated

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onto the front of road signs.

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Imprinted into those films are
many parallel, V-shaped grooves

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that act as corner
[? key ?] reflectors

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so that the street signs reflect
light incident from any angle.

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And so those sorts of
optical applications

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are also pretty crucial.

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But anyway, let me just
describe how the process works.

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What I'm illustrating
here is not

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a role to role printing
process, but something

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where the workpiece is
about the size of a wafer.

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So tens of millimeters
in diameter.

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And first thing we
need is a hard stamp,

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a tool that's been
microfabricated

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using some other process.

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This tool might have
been etched from silicon.

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It might have been
electroplated with nickel.

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It might itself be a polymer,
but one that doesn't soften

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at the processing temperatures.

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Elastomers like PDMS,
polydimethylsiloxane

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are actually quite attractive
as stamp materials.

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So we have this stamp.

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We have two heated
plates to heat

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the stamp and the
workpiece, and a means

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of applying a load normal to
the surface of the workpiece.

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Usually what happens
is the material

00:06:08.080 --> 00:06:11.620
is heated above what's
called its glass transition

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temperature.

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And for anyone who isn't
familiar with this,

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thermoplastics essentially
are composed of an entangled

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network of polymer molecules.

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And there are one
or more temperatures

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for a given polymer at which
those entanglements loosen.

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And the chains can
slide past one another.

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And the stiffness and
the effective viscosity

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of the material around
that temperature

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falls by several
orders of magnitude.

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So above that temperature, it's
highly flexible, easily formed.

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Below that temperature, it's
much stiffer and useable

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as a device.

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So we go above the glass
transition temperature

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to soften it.

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How far we go above is an
important question to answer.

00:07:02.470 --> 00:07:05.470
That's a crucial
parameter to choose.

00:07:05.470 --> 00:07:07.420
We then apply a load.

00:07:07.420 --> 00:07:09.910
That load is going to be
ramped up over some time

00:07:09.910 --> 00:07:11.260
that we have a choice about.

00:07:11.260 --> 00:07:13.420
That might be an
important parameter.

00:07:13.420 --> 00:07:18.250
We hold that load for some time
to allow the material to flow,

00:07:18.250 --> 00:07:20.290
to fill cavities in the stamp.

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And while the load
is still applied,

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we cool down usually,
cool the material

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to below its glass transition
temperature, and finally,

00:07:27.460 --> 00:07:30.160
remove the load.

00:07:30.160 --> 00:07:35.140
And often, that removal step has
a lot of technical challenges

00:07:35.140 --> 00:07:37.390
involved in it,
because of differential

00:07:37.390 --> 00:07:42.430
thermal contraction of
the workpiece in the tool.

00:07:42.430 --> 00:07:44.740
So that gives you
some idea that there

00:07:44.740 --> 00:07:51.610
are at least four parameters
that we need to decide upon,

00:07:51.610 --> 00:07:55.210
temperature, a load,
and two times associated

00:07:55.210 --> 00:07:56.380
with that load.

00:07:56.380 --> 00:07:58.930
There are probably
more parameters

00:07:58.930 --> 00:08:01.820
that we're interested in.

00:08:01.820 --> 00:08:03.370
Now, at this point,
I should also

00:08:03.370 --> 00:08:08.170
mention a rather
similar process that has

00:08:08.170 --> 00:08:09.730
quite different applications.

00:08:09.730 --> 00:08:13.930
And that is thermal nano
imprint lithography.

00:08:13.930 --> 00:08:16.420
This is, essentially,
hot embossing,

00:08:16.420 --> 00:08:21.100
but done on very thin layers of
polymer, thinner than a micron.

00:08:21.100 --> 00:08:25.060
And these layers have been spun
onto a much harder surface,

00:08:25.060 --> 00:08:26.770
usually a silicon wafer.

00:08:26.770 --> 00:08:29.530
And the beauty of
this process is

00:08:29.530 --> 00:08:33.309
that it allows sub
micron features

00:08:33.309 --> 00:08:35.450
to be transferred to the wafer.

00:08:35.450 --> 00:08:38.980
This is, I think, a
really exciting process.

00:08:38.980 --> 00:08:43.150
It has the potential to
revolutionize lithography

00:08:43.150 --> 00:08:48.970
and semiconductor manufacturing,
because the resolution

00:08:48.970 --> 00:08:52.270
with which features
can be transferred

00:08:52.270 --> 00:08:56.080
is not limited by the
wavelength of light.

00:08:56.080 --> 00:08:59.440
Usually you would pattern
a photo resist layer

00:08:59.440 --> 00:09:02.650
with some kind of projection,
optical projection system.

00:09:02.650 --> 00:09:04.810
And we've really got
to the stage where

00:09:04.810 --> 00:09:08.350
critical dimensions
of transistors

00:09:08.350 --> 00:09:12.280
are making that a big challenge,
making the optical lithography

00:09:12.280 --> 00:09:17.120
systems cost tens or hundreds
of millions of dollars.

00:09:17.120 --> 00:09:22.910
So in this case, we have
this spun on polymer layer.

00:09:22.910 --> 00:09:27.580
It's dissolved in an organic
solvent, spun on the solvent.

00:09:27.580 --> 00:09:29.170
It evaporates.

00:09:29.170 --> 00:09:33.220
And then the spun on
layer is a thermoplastic.

00:09:33.220 --> 00:09:34.510
It can be softened.

00:09:34.510 --> 00:09:38.170
You press the the
nano fabricated stamp

00:09:38.170 --> 00:09:39.940
into the wafer.

00:09:39.940 --> 00:09:43.450
And ideally, squeeze
all the material

00:09:43.450 --> 00:09:47.080
from below the individual
features of the stamp.

00:09:47.080 --> 00:09:49.900
Now, in reality,
that's not possible.

00:09:49.900 --> 00:09:52.540
And there is a small
residual polymer

00:09:52.540 --> 00:09:54.170
layer that's left there.

00:09:54.170 --> 00:09:58.810
So you can imagine, once we've
removed the stamp or the mold,

00:09:58.810 --> 00:10:01.780
we have some extremely
thin regions of polymer.

00:10:01.780 --> 00:10:07.150
And then imagine that we want to
pattern, to etch away material

00:10:07.150 --> 00:10:08.860
in the wafer underneath.

00:10:08.860 --> 00:10:14.230
The plasma or the
etching solution

00:10:14.230 --> 00:10:16.420
to which the wafer is
exposed will quite readily

00:10:16.420 --> 00:10:19.060
break through that
residual polymer layer

00:10:19.060 --> 00:10:20.530
and remove the material.

00:10:20.530 --> 00:10:25.030
So these processes are similar.

00:10:25.030 --> 00:10:30.460
In many ways, they actually
often use the same polymers.

00:10:30.460 --> 00:10:35.500
But the boundary conditions, the
mechanics are rather different.

00:10:35.500 --> 00:10:41.860
And so I'll talk a little
bit about nano imprint,

00:10:41.860 --> 00:10:44.050
but mostly the
results that I'm going

00:10:44.050 --> 00:10:48.280
to show you are to do with
micro hot embossing, where

00:10:48.280 --> 00:10:53.440
the workpiece is substantially
thicker than the diameters

00:10:53.440 --> 00:10:56.971
or the depths of the features
that are being patterned.

00:10:56.971 --> 00:11:02.040
AUDIENCE: [INAUDIBLE]
about creating the mold,

00:11:02.040 --> 00:11:05.840
during the mold removal process,
do you have the mold walls

00:11:05.840 --> 00:11:09.450
getting [? dilated? ?] Because
the pattern is getting taken

00:11:09.450 --> 00:11:14.412
off and it might have a
[? dimension ?] [INAUDIBLE]??

00:11:14.412 --> 00:11:16.370
PROFESSOR: Yes, that was
an excellent question.

00:11:16.370 --> 00:11:18.350
You've hit on one of the
most important challenges

00:11:18.350 --> 00:11:19.392
of [INAUDIBLE] embossing.

00:11:19.392 --> 00:11:21.950
And [INAUDIBLE] was
asking, are there problems

00:11:21.950 --> 00:11:25.580
with dimensional stability
of the walls, the side

00:11:25.580 --> 00:11:26.750
walls during de-molding?

00:11:26.750 --> 00:11:29.320
And I'll show you some
results that relate to that.

00:11:29.320 --> 00:11:31.400
So yes, good point.

00:11:31.400 --> 00:11:34.430
Anyhow, as I already
mentioned, there

00:11:34.430 --> 00:11:37.970
are several parameters
to do with the process

00:11:37.970 --> 00:11:43.280
that we need to pick,
temperatures, load times,

00:11:43.280 --> 00:11:46.280
loading durations.

00:11:46.280 --> 00:11:48.650
The range that those
parameters can take

00:11:48.650 --> 00:11:52.250
will be limited by the
capabilities of the machine we

00:11:52.250 --> 00:11:54.473
have, the physical
properties of the polymer

00:11:54.473 --> 00:11:56.390
we're trying to pattern,
what temperature does

00:11:56.390 --> 00:12:00.990
it start to burn, and so forth.

00:12:00.990 --> 00:12:02.750
What about the
material underneath?

00:12:02.750 --> 00:12:04.820
If we're doing nano
imprint lithography,

00:12:04.820 --> 00:12:06.440
are there temperature
constraints

00:12:06.440 --> 00:12:09.366
that the wafer underneath
has to observe?

00:12:09.366 --> 00:12:16.710
So that's what
constrains the process.

00:12:16.710 --> 00:12:21.710
And, of course, we might also
be making engineering decisions

00:12:21.710 --> 00:12:24.320
about what type of
polymer we're going to use

00:12:24.320 --> 00:12:26.690
to achieve a certain end.

00:12:26.690 --> 00:12:29.840
And indeed, we might have some
flexibility in the pattern

00:12:29.840 --> 00:12:31.280
that we are going to emboss.

00:12:31.280 --> 00:12:35.750
We might think about designing
a pattern with an eye

00:12:35.750 --> 00:12:39.260
to manufacturability, something
that will be easier to imprint

00:12:39.260 --> 00:12:40.610
with less variability.

00:12:40.610 --> 00:12:45.170
And that is one of the questions
that I'm trying to answer.

00:12:45.170 --> 00:12:45.986
Mohammed.

00:12:45.986 --> 00:12:48.236
AUDIENCE: [INAUDIBLE] how
do you [INAUDIBLE] the stamp

00:12:48.236 --> 00:12:49.495
[? control? ?]

00:12:49.495 --> 00:12:50.870
PROFESSOR: Right,
well, the stamp

00:12:50.870 --> 00:12:59.360
can be made in a variety
of ways that are usually

00:12:59.360 --> 00:13:02.040
traditional microfabrication.

00:13:02.040 --> 00:13:06.770
So one particularly
easy way of doing

00:13:06.770 --> 00:13:10.160
it would be to use a process
called deep reactive ion

00:13:10.160 --> 00:13:11.420
etching.

00:13:11.420 --> 00:13:14.330
And here I'm talking
about micro embossing,

00:13:14.330 --> 00:13:17.480
where the features are several
microns to many microns.

00:13:17.480 --> 00:13:21.860
And essentially, this is just
etching very deep trenches

00:13:21.860 --> 00:13:26.210
into a silicon wafer
using a plasma process.

00:13:26.210 --> 00:13:28.400
I could go into great
detail about how that works,

00:13:28.400 --> 00:13:32.780
but essentially, it's a
fluorine based chemistry.

00:13:32.780 --> 00:13:36.950
The precursor gas is SF6.

00:13:36.950 --> 00:13:41.780
And you build up these
very deep, narrow trenches

00:13:41.780 --> 00:13:47.620
in the silicon wafer
by a series of steps.

00:13:47.620 --> 00:13:51.930
So in fact, you would
start with the silicon

00:13:51.930 --> 00:13:55.050
with a photoresist
mask or something.

00:13:55.050 --> 00:14:01.450
You'd do a brief fluorine based
plasma etch that would remove

00:14:01.450 --> 00:14:03.550
small amounts of material.

00:14:03.550 --> 00:14:06.790
That's roughly isotropic.

00:14:06.790 --> 00:14:08.560
So if you want
vertical sidewalls,

00:14:08.560 --> 00:14:09.940
you've got to do something else.

00:14:09.940 --> 00:14:12.670
And the something
else is depositing

00:14:12.670 --> 00:14:14.800
a polymeric passivation layer.

00:14:14.800 --> 00:14:17.800
So you change the
gas in the chamber

00:14:17.800 --> 00:14:23.080
to C4F8, which creates
what's essentially

00:14:23.080 --> 00:14:26.680
a teflon coating that passivates
the sidewall of the trench

00:14:26.680 --> 00:14:27.580
that's developing.

00:14:27.580 --> 00:14:33.130
Then you go back to the
SF6, build up a new notch,

00:14:33.130 --> 00:14:36.160
and do this many times,
alternate many times.

00:14:36.160 --> 00:14:41.740
So whatever way you
pattern the stamp.

00:14:41.740 --> 00:14:46.900
Silicon actually, as we will see
later, for de-molding reasons,

00:14:46.900 --> 00:14:49.570
is actually a lousy material
to use for the stamp.

00:14:49.570 --> 00:14:54.700
So then you might go one step
further, electroplate nickel

00:14:54.700 --> 00:14:57.670
into that etched wafer,
peel off the nickel,

00:14:57.670 --> 00:14:59.320
and use that as the stamp.

00:14:59.320 --> 00:15:00.490
Much tougher.

00:15:00.490 --> 00:15:04.160
Or you might use
more novel materials,

00:15:04.160 --> 00:15:06.070
things like metallic
glasses, which

00:15:06.070 --> 00:15:11.110
are alloys with an
amorphous structure that are

00:15:11.110 --> 00:15:13.030
both very hard and very tough.

00:15:13.030 --> 00:15:15.800
They would be great
materials for a stamp.

00:15:15.800 --> 00:15:17.800
AUDIENCE: So what
you mentioned--

00:15:17.800 --> 00:15:20.860
you said that you're not
limited to wavelengths

00:15:20.860 --> 00:15:22.790
of the light in this process.

00:15:22.790 --> 00:15:26.440
But however to make the stamp,
then you are limited to--

00:15:26.440 --> 00:15:27.240
PROFESSOR: Yeah.

00:15:27.240 --> 00:15:27.790
AUDIENCE: [INAUDIBLE]

00:15:27.790 --> 00:15:28.800
PROFESSOR: Well, yes.

00:15:28.800 --> 00:15:29.850
AUDIENCE: [INAUDIBLE]
limitation exists.

00:15:29.850 --> 00:15:31.517
PROFESSOR: So what I
just described here

00:15:31.517 --> 00:15:34.000
was for micro embossing.

00:15:34.000 --> 00:15:36.160
I'm sort of describing
two processes

00:15:36.160 --> 00:15:38.860
in parallel that have
great similarities,

00:15:38.860 --> 00:15:40.580
but not in terms of scale.

00:15:40.580 --> 00:15:45.280
So this would be for features
that are a micron or larger.

00:15:45.280 --> 00:15:48.820
If you want to make
sub micron features,

00:15:48.820 --> 00:15:49.960
then you're quite right.

00:15:49.960 --> 00:15:53.000
You need a process that will
let you make a stamp with sub

00:15:53.000 --> 00:15:57.490
micron features, and
electron beam lithography

00:15:57.490 --> 00:16:01.480
is a great candidate for that
where you actually would--

00:16:01.480 --> 00:16:04.120
you would start
with a silicon wafer

00:16:04.120 --> 00:16:10.660
with a 100 nanometer
thick layer of a radiation

00:16:10.660 --> 00:16:11.890
sensitive resist.

00:16:11.890 --> 00:16:15.580
Then you would just actually
steer a focused electron beam

00:16:15.580 --> 00:16:17.830
across the surface, scan
it across the surface

00:16:17.830 --> 00:16:19.840
in the pattern that you wanted.

00:16:19.840 --> 00:16:24.850
And that will give you 5
nanometer resolution or better.

00:16:24.850 --> 00:16:27.730
The trouble is, it takes ages
because it's a serial process.

00:16:27.730 --> 00:16:30.310
You're scanning the
electrons over the surface.

00:16:30.310 --> 00:16:34.150
So once you've made the stamp,
you've paid however many $1,000

00:16:34.150 --> 00:16:34.860
for the stamp.

00:16:34.860 --> 00:16:38.380
You can stamp it in in a
minute into as many substrates

00:16:38.380 --> 00:16:38.950
as you like.

00:16:38.950 --> 00:16:43.540
And that's really the
reason for nano imprint.

00:16:43.540 --> 00:16:47.110
OK, so keep both of
those processes in mind.

00:16:47.110 --> 00:16:50.620
But a lot of the assertions
I'm going to make from now on

00:16:50.620 --> 00:16:55.390
are all about the
micron scale embossing.

00:16:55.390 --> 00:16:58.738
So as I said, there are
lots of different parameters

00:16:58.738 --> 00:17:00.280
we can choose to do
with the process,

00:17:00.280 --> 00:17:02.320
to do with the material
we're embossing,

00:17:02.320 --> 00:17:04.839
to do with the pattern
that we're embossing.

00:17:04.839 --> 00:17:08.230
And the overall
mission that I suppose

00:17:08.230 --> 00:17:12.310
we have is to try to provide
tools for people who are using

00:17:12.310 --> 00:17:16.630
this process to
achieve the desired

00:17:16.630 --> 00:17:25.779
microstructure with as little
time, energy, cost as possible.

00:17:25.779 --> 00:17:28.750
So if you're processing
a certain material,

00:17:28.750 --> 00:17:33.580
can you pick a pattern that will
take 30 seconds to replicate

00:17:33.580 --> 00:17:39.460
instead of a minute at
the available processing

00:17:39.460 --> 00:17:41.150
conditions?

00:17:41.150 --> 00:17:45.460
So that presupposes,
of course, that we

00:17:45.460 --> 00:17:50.680
have some specification on what
satisfactory replication is.

00:17:50.680 --> 00:17:52.300
The most obvious
specification would

00:17:52.300 --> 00:17:54.700
be that every
cavity in the stamp

00:17:54.700 --> 00:17:57.430
has been filled with polymer,
even the narrowest ones.

00:17:57.430 --> 00:18:01.210
That would be a good
specification to use.

00:18:01.210 --> 00:18:03.310
Another good
specification that's

00:18:03.310 --> 00:18:05.920
really important for
nano imprint lithography

00:18:05.920 --> 00:18:10.930
is to make the thickness of
those residual polymer layers

00:18:10.930 --> 00:18:12.850
very uniform.

00:18:12.850 --> 00:18:16.420
And that's important
because it does

00:18:16.420 --> 00:18:20.590
take some time for
the etching process

00:18:20.590 --> 00:18:22.510
to break through
that residual layer.

00:18:25.040 --> 00:18:30.640
And if the residual layer
varies in thickness,

00:18:30.640 --> 00:18:32.950
the time taken to break
through it will be different.

00:18:32.950 --> 00:18:35.770
And then you'll get different
properties of the underlying

00:18:35.770 --> 00:18:36.470
structure.

00:18:36.470 --> 00:18:42.850
So let's say you've imprinted
this 100 nanometer thick

00:18:42.850 --> 00:18:45.070
polymer layer.

00:18:45.070 --> 00:18:50.710
And on this side, the
residual layer is really thin.

00:18:50.710 --> 00:18:53.110
And on this side
it's twice as thick.

00:18:53.110 --> 00:18:58.480
You then expose this
with a fluorine plasma.

00:18:58.480 --> 00:19:02.058
You're trying to etch the
silicon underneath here.

00:19:02.058 --> 00:19:03.850
You're going to end up
with a deeper trench

00:19:03.850 --> 00:19:05.590
here than you are here
because of the time

00:19:05.590 --> 00:19:06.757
it took to get through that.

00:19:06.757 --> 00:19:11.590
So coming up with ways
of designing the stamp so

00:19:11.590 --> 00:19:15.520
that the residual layer ends
up being as uniform as possible

00:19:15.520 --> 00:19:21.880
is a really pressing challenge
actually for this lithography

00:19:21.880 --> 00:19:22.900
technique to be adopted.

00:19:25.930 --> 00:19:30.570
Anyhow, so what we're all about
is simplified modeling tools

00:19:30.570 --> 00:19:32.990
that can be used as
part of the design loop

00:19:32.990 --> 00:19:36.030
that are computationally
efficient enough

00:19:36.030 --> 00:19:41.940
to give results in a
reasonable amount of time,

00:19:41.940 --> 00:19:46.420
and that represent reality well.

00:19:46.420 --> 00:19:50.010
So that implies that we need
some way of characterizing

00:19:50.010 --> 00:19:52.410
the tool that we're using,
the materials that we're

00:19:52.410 --> 00:19:55.560
using efficiently so that
we can get information

00:19:55.560 --> 00:19:57.510
about the physical
properties of these things

00:19:57.510 --> 00:20:00.750
with a minimum of fuss.

00:20:00.750 --> 00:20:05.580
Now, I'm just going to
split the problem up

00:20:05.580 --> 00:20:08.670
into three notional
length scales

00:20:08.670 --> 00:20:12.220
so that we can have a clearer
picture of what's going on.

00:20:12.220 --> 00:20:17.100
And at the largest
length scale you

00:20:17.100 --> 00:20:20.910
can think of variations
in the quality

00:20:20.910 --> 00:20:23.550
of the embossed
features from one side

00:20:23.550 --> 00:20:25.420
of the substrate to the other.

00:20:25.420 --> 00:20:29.340
And that might occur because
the two heated plates that

00:20:29.340 --> 00:20:31.380
are compressing the
stamp and the substrate

00:20:31.380 --> 00:20:32.580
are not perfectly parallel.

00:20:32.580 --> 00:20:34.920
So the pressure's
greater on one side.

00:20:34.920 --> 00:20:40.590
It might be because one of
the plates is bowed or wavy.

00:20:40.590 --> 00:20:43.530
Or it might be to do
simply with the mechanics

00:20:43.530 --> 00:20:45.280
of the substrate itself.

00:20:45.280 --> 00:20:49.410
If that substrate is behaving
as a viscous fluid, say,

00:20:49.410 --> 00:20:53.070
then as you compress that
substrate, that flat, polymer

00:20:53.070 --> 00:20:54.570
substrate, you're
going to expect

00:20:54.570 --> 00:20:58.890
to see, in fact, a parabolic
distribution of pressure

00:20:58.890 --> 00:20:59.820
across it.

00:20:59.820 --> 00:21:05.300
So there are various
things to consider there.

00:21:05.300 --> 00:21:08.860
And then at what I'm going
to call the device scale,

00:21:08.860 --> 00:21:11.800
there are these
pattern dependencies

00:21:11.800 --> 00:21:15.610
where the arrangement
of features on the stamp

00:21:15.610 --> 00:21:20.590
can have a profound effect on
how well defined the features

00:21:20.590 --> 00:21:21.640
end up being.

00:21:21.640 --> 00:21:29.020
And what I've sketched here,
which is really just a sketch,

00:21:29.020 --> 00:21:32.140
it suggests if
there are features

00:21:32.140 --> 00:21:34.970
that are slightly more
closely packed together,

00:21:34.970 --> 00:21:38.620
then they may fill earlier,
or maybe sometimes later

00:21:38.620 --> 00:21:40.660
than regions that are
less densely packed.

00:21:40.660 --> 00:21:42.760
And if that's the
case, then maybe you

00:21:42.760 --> 00:21:45.340
want to put some
design rules in place

00:21:45.340 --> 00:21:49.660
that will constrain the
variation of density

00:21:49.660 --> 00:21:52.600
of features on the stamp.

00:21:52.600 --> 00:21:56.290
Finally, we've got at the
smallest scale effects

00:21:56.290 --> 00:21:58.070
to do with individual features.

00:21:58.070 --> 00:22:00.670
So if an individual
gap is too small, say,

00:22:00.670 --> 00:22:03.100
that's going to be very hard
to force polymer into it.

00:22:03.100 --> 00:22:05.890
And that could be a showstopper.

00:22:05.890 --> 00:22:09.400
So we've got these three
different length scales.

00:22:09.400 --> 00:22:13.000
I've alluded to these
sorts of problems,

00:22:13.000 --> 00:22:18.730
bowing of the patterns, non
parallelism of the patterns.

00:22:18.730 --> 00:22:20.920
They relate to the
substrate scale effects.

00:22:24.110 --> 00:22:31.310
This shows one particular
substrate that we embossed.

00:22:31.310 --> 00:22:35.990
This is a square of
PMMA, which is acrylic,

00:22:35.990 --> 00:22:39.060
which is about 100
millimeters square.

00:22:39.060 --> 00:22:43.190
We embossed with a wafer that
had been uniformly patterned

00:22:43.190 --> 00:22:48.380
with some silicon posts,
roughly 100 microns in diameter.

00:22:48.380 --> 00:22:51.230
And we just use this
as a probe to look

00:22:51.230 --> 00:22:56.480
at our embossing machine and
see how uniform a pattern could

00:22:56.480 --> 00:22:57.230
be produced.

00:22:57.230 --> 00:23:00.560
Now, aside from the fact that
huge chunks of the silicon

00:23:00.560 --> 00:23:02.447
wafer broke off
during de-molding--

00:23:02.447 --> 00:23:05.030
and that's a good illustration
of some of the problems that we

00:23:05.030 --> 00:23:06.140
face--

00:23:06.140 --> 00:23:12.530
we were able to look at the
topography of the pattern

00:23:12.530 --> 00:23:14.600
at different locations
on the wafer.

00:23:14.600 --> 00:23:17.900
We did that using
an interferometer,

00:23:17.900 --> 00:23:21.410
scanning from above,
measuring the topography.

00:23:21.410 --> 00:23:25.220
And so we were able
to see various things,

00:23:25.220 --> 00:23:29.720
that the emboss depth was higher
on this side than on this side.

00:23:29.720 --> 00:23:34.760
Then near the edge of the
wafer the embossed features

00:23:34.760 --> 00:23:37.260
tailed off in height.

00:23:37.260 --> 00:23:38.780
And so these are
the sorts of things

00:23:38.780 --> 00:23:43.460
that we need to come up
with ways of predicting

00:23:43.460 --> 00:23:47.270
so that we can counteract them.

00:23:47.270 --> 00:23:54.530
Anyway, what I'm going
to concentrate on

00:23:54.530 --> 00:23:57.500
for the rest of this
talk, in fact, is pattern

00:23:57.500 --> 00:24:04.520
dependent non uniformity,
which is, in many ways,

00:24:04.520 --> 00:24:07.670
the most challenging
to deal with.

00:24:07.670 --> 00:24:09.590
Effects to do with
the edge of the wafer

00:24:09.590 --> 00:24:13.430
become important when you're
trying to eke out one or two

00:24:13.430 --> 00:24:14.420
extra devices.

00:24:14.420 --> 00:24:16.780
You're trying to save a
little bit of material.

00:24:16.780 --> 00:24:20.990
But if the actual
design of the device--

00:24:20.990 --> 00:24:22.880
there may be many
devices across a wafer.

00:24:22.880 --> 00:24:25.670
If the design of the
individual device is faulty

00:24:25.670 --> 00:24:27.320
and it will never
replicate properly,

00:24:27.320 --> 00:24:28.990
then you're in real trouble.

00:24:28.990 --> 00:24:30.950
So trying to get
an understanding

00:24:30.950 --> 00:24:34.580
of what patterns will form
well and what patterns will not

00:24:34.580 --> 00:24:36.440
is crucial.

00:24:36.440 --> 00:24:43.760
And so although we are
working towards a unified way

00:24:43.760 --> 00:24:45.260
of dealing with
this, I'm just going

00:24:45.260 --> 00:24:50.000
to talk mostly about the
pattern dependencies now.

00:24:50.000 --> 00:24:56.780
So I've mentioned all of
these different questions that

00:24:56.780 --> 00:25:01.040
need to be answered, factors
that need to be chosen when

00:25:01.040 --> 00:25:03.080
you're designing a new process.

00:25:03.080 --> 00:25:07.430
And some of them are going
to be continuous variables,

00:25:07.430 --> 00:25:09.560
and some of them will
be discrete choices.

00:25:09.560 --> 00:25:15.530
And it's not absolutely
clear which will be which.

00:25:15.530 --> 00:25:17.210
I've really split
the decisions up

00:25:17.210 --> 00:25:19.453
into three categories,
the decisions

00:25:19.453 --> 00:25:20.870
you have to make
about the pattern

00:25:20.870 --> 00:25:24.290
you're going to emboss, what
are the shapes of the features?

00:25:24.290 --> 00:25:29.070
Rectangles, circles,
triangles, how big they are,

00:25:29.070 --> 00:25:32.270
and how they are
oriented on the stamp?

00:25:32.270 --> 00:25:34.850
And that can be
important when you're

00:25:34.850 --> 00:25:37.970
starting to think about
radial thermal contraction

00:25:37.970 --> 00:25:41.090
of the parts, or about
anisotropic material

00:25:41.090 --> 00:25:41.710
properties.

00:25:41.710 --> 00:25:47.150
So there you've got-- you know,
size is a continuous variable,

00:25:47.150 --> 00:25:49.460
and the feature
shape you might think

00:25:49.460 --> 00:25:52.130
of as being a discrete choice.

00:25:52.130 --> 00:25:56.370
When it comes to the
substrate itself,

00:25:56.370 --> 00:25:58.770
then you've got to
decide on the material.

00:25:58.770 --> 00:26:02.710
Various materials soften
at different temperatures.

00:26:02.710 --> 00:26:08.430
Some of them exhibit a range
of temperatures over which they

00:26:08.430 --> 00:26:10.380
behave rather like a rubber.

00:26:10.380 --> 00:26:13.470
Others don't really have
much of a rubbery region.

00:26:13.470 --> 00:26:15.330
They just flow
very easily as soon

00:26:15.330 --> 00:26:17.560
as you're above the glass
transition temperature.

00:26:17.560 --> 00:26:20.490
So that's a decision
that has to be made.

00:26:20.490 --> 00:26:23.700
And in micro
embossing, often you're

00:26:23.700 --> 00:26:30.120
picking between a variety of
off the shelf substrates, PMMA,

00:26:30.120 --> 00:26:33.510
plexiglass, polycarbonate,
materials like this,

00:26:33.510 --> 00:26:36.540
where these are technical
grade materials.

00:26:36.540 --> 00:26:38.740
They're molecular weight.

00:26:38.740 --> 00:26:41.430
In other words, the average
length of the polymer chains

00:26:41.430 --> 00:26:44.770
is not necessarily well
documented or well defined.

00:26:44.770 --> 00:26:46.530
So in that sense,
your material choice

00:26:46.530 --> 00:26:49.030
might be a discrete decision.

00:26:49.030 --> 00:26:51.870
On the other hand, if
you're spinning the polymer

00:26:51.870 --> 00:26:54.180
onto the wafer, and
you're dissolving it,

00:26:54.180 --> 00:26:59.310
then you do have the option of
choosing the molecular weight,

00:26:59.310 --> 00:27:02.460
and therefore, defining the
viscosity as essentially

00:27:02.460 --> 00:27:03.850
a continuous variable.

00:27:03.850 --> 00:27:07.140
So those are things that might
need to be thought about.

00:27:07.140 --> 00:27:08.940
And, of course,
there's the thickness.

00:27:08.940 --> 00:27:13.560
Either how thickly do
you spin this resistor?

00:27:13.560 --> 00:27:17.280
And that, a lot of
research in the field

00:27:17.280 --> 00:27:20.910
demonstrates the
optimal thickness

00:27:20.910 --> 00:27:23.250
is a strong function
of what pattern you're

00:27:23.250 --> 00:27:27.160
trying to emboss, how many
voids there are in the stamp.

00:27:27.160 --> 00:27:29.520
So the thickness of
that might be important,

00:27:29.520 --> 00:27:34.000
and also the thickness
in micro embossing

00:27:34.000 --> 00:27:37.980
where the substrate is
a millimeter thick, say.

00:27:37.980 --> 00:27:41.210
That's also a decision
that has to be made.

00:27:41.210 --> 00:27:43.662
So and the third
category, of course,

00:27:43.662 --> 00:27:45.870
is the process parameters,
the temperature, pressure,

00:27:45.870 --> 00:27:49.350
hold time, and so forth.

00:27:52.370 --> 00:27:56.570
Now, there's an awful
lot of variables there.

00:27:56.570 --> 00:28:00.580
And if one were to just take
a purely empirical approach

00:28:00.580 --> 00:28:05.710
and try doing a full factorial
or a fractional factorial

00:28:05.710 --> 00:28:08.230
exploration of the
space, it would

00:28:08.230 --> 00:28:11.470
start to look pretty
much like a nightmare.

00:28:11.470 --> 00:28:15.820
And luckily, we don't have to
stumble around in the dark,

00:28:15.820 --> 00:28:19.450
because we do already
have some reasonably

00:28:19.450 --> 00:28:22.810
good physical intuition about
how these materials behave.

00:28:22.810 --> 00:28:27.070
And, of course, there's
a huge research field

00:28:27.070 --> 00:28:30.320
to do with characterizing
these bulk materials,

00:28:30.320 --> 00:28:33.490
building theoretical
models of how they behave,

00:28:33.490 --> 00:28:36.610
fitting data to those models.

00:28:36.610 --> 00:28:40.990
And I'm sure mechanical
engineers here

00:28:40.990 --> 00:28:48.940
will be familiar with this sort
of way of describing polymers

00:28:48.940 --> 00:28:55.880
in a simplified manner,
where you build up a model.

00:28:55.880 --> 00:28:58.180
In this case, this is
a one dimensional model

00:28:58.180 --> 00:29:03.580
that sums up the viscoelastic
behavior of the polymer using

00:29:03.580 --> 00:29:07.660
a combination of springs,
elastic, nondissipative

00:29:07.660 --> 00:29:08.170
elements.

00:29:08.170 --> 00:29:13.300
And these elements here are
dashpots, which are essentially

00:29:13.300 --> 00:29:14.890
viscous components and damp.

00:29:14.890 --> 00:29:17.500
Yes, exactly, they
dissipate energy.

00:29:17.500 --> 00:29:24.310
So the various stiffnesses
and dissipation factors

00:29:24.310 --> 00:29:29.620
for the springs and dashpots
may be non-linear functions

00:29:29.620 --> 00:29:30.610
of temperature.

00:29:30.610 --> 00:29:33.170
They may be non-linear
functions of strain rate,

00:29:33.170 --> 00:29:35.350
and, in fact, almost always are.

00:29:35.350 --> 00:29:39.190
And so there are
many theses that

00:29:39.190 --> 00:29:43.240
have been written trying to
characterize these materials.

00:29:43.240 --> 00:29:49.180
And building on those
experimental approaches

00:29:49.180 --> 00:29:50.980
are simulation models.

00:29:50.980 --> 00:29:56.060
There are finite element
models of these polymers that

00:29:56.060 --> 00:29:58.420
have been lovingly built up.

00:29:58.420 --> 00:30:03.725
And so with enough
information about the polymer

00:30:03.725 --> 00:30:06.100
with a detailed model of the
stamp that you were thinking

00:30:06.100 --> 00:30:09.040
of embossing, and
knowing something

00:30:09.040 --> 00:30:12.430
about the dimensional tolerances
of the machine you have,

00:30:12.430 --> 00:30:18.610
you could do a simulation
and perhaps predict

00:30:18.610 --> 00:30:20.470
what was going to happen.

00:30:20.470 --> 00:30:22.450
The trouble is, it would
probably take years.

00:30:22.450 --> 00:30:28.600
Because when you start
having microscale patterns

00:30:28.600 --> 00:30:34.030
that you're trying to emboss,
the computational burden

00:30:34.030 --> 00:30:38.680
of using these full nonlinear,
finite, deformation polymer

00:30:38.680 --> 00:30:40.510
models becomes immense.

00:30:40.510 --> 00:30:44.320
And that's great if you have
one particular device that

00:30:44.320 --> 00:30:46.090
absolutely must be perfect.

00:30:46.090 --> 00:30:49.840
However, what we're interested
in doing in our research

00:30:49.840 --> 00:30:51.580
is finding some sort
of middle ground

00:30:51.580 --> 00:30:55.360
between the empirical
approach and the really

00:30:55.360 --> 00:30:59.950
rigorous, thorough,
theoretical approach

00:30:59.950 --> 00:31:03.650
that's based on a highly
controlled set of experiments.

00:31:03.650 --> 00:31:07.720
And so the idea is to find
approximate descriptions

00:31:07.720 --> 00:31:12.720
for the material that
are efficient to run,

00:31:12.720 --> 00:31:17.570
efficient to simulate patterns,
wafers that have thousands

00:31:17.570 --> 00:31:20.100
of features across them.

00:31:20.100 --> 00:31:27.710
So let's start to think
about how we can build out

00:31:27.710 --> 00:31:29.600
the bare bones of a
model that are going

00:31:29.600 --> 00:31:34.430
to inform the experiments that
we do about this embossing

00:31:34.430 --> 00:31:35.700
process.

00:31:35.700 --> 00:31:42.620
Now, what I've done here-- and
I won't go into laborious detail

00:31:42.620 --> 00:31:46.670
about, but essentially, this
is just building intuition

00:31:46.670 --> 00:31:48.560
about one particular polymer.

00:31:48.560 --> 00:31:52.490
This is a model for
polymethylmethacrylate,

00:31:52.490 --> 00:31:54.710
plexiglass, acrylic,
call it what

00:31:54.710 --> 00:31:59.060
you will, which a student
at MIT has recently

00:31:59.060 --> 00:32:02.900
written a thesis about, doing
compression experiments of it,

00:32:02.900 --> 00:32:07.340
building up a highly
faithful model of it.

00:32:07.340 --> 00:32:10.730
But there's a one dimensional
implementation of that model

00:32:10.730 --> 00:32:12.020
that we can run.

00:32:12.020 --> 00:32:15.000
We can look at what happens
when you give it various load

00:32:15.000 --> 00:32:20.180
profiles over time and look at
the stresses and the strains

00:32:20.180 --> 00:32:26.120
in each of those components
of the model over time.

00:32:26.120 --> 00:32:30.880
So what I've done
here is I've just

00:32:30.880 --> 00:32:34.030
done two what are essentially
thought experiments.

00:32:34.030 --> 00:32:40.150
The left hand column
of graphs shows

00:32:40.150 --> 00:32:44.380
what happens if the material
is heated above its glass

00:32:44.380 --> 00:32:48.910
transition temperature
and then given

00:32:48.910 --> 00:32:53.140
a 1 and 1/2 megapascal
compressive load which

00:32:53.140 --> 00:32:56.350
is held for 10 seconds.

00:32:56.350 --> 00:32:59.950
That load is maintained while
the temperature is reduced

00:32:59.950 --> 00:33:03.190
below the glass transmission.

00:33:03.190 --> 00:33:06.880
The glass transition here
is about 105 degrees C.

00:33:06.880 --> 00:33:11.870
So then we looked at how
the model responded to that.

00:33:11.870 --> 00:33:14.710
There's a compressive
strain, of course.

00:33:14.710 --> 00:33:17.320
There are stresses built
up in the left hand

00:33:17.320 --> 00:33:20.380
branch of that model, this
spring and this dashpot.

00:33:20.380 --> 00:33:23.360
And there are stresses in
the right hand side as well.

00:33:23.360 --> 00:33:27.820
And essentially what this shows
is that most of the deformation

00:33:27.820 --> 00:33:30.790
is frozen in place,
frozen by this

00:33:30.790 --> 00:33:32.480
cooling below glass transition.

00:33:32.480 --> 00:33:35.260
So when the load is removed,
this amount of strain

00:33:35.260 --> 00:33:38.310
remains, this P amount here.

00:33:38.310 --> 00:33:43.690
However, if you don't cool down
before you remove the load,

00:33:43.690 --> 00:33:45.610
and that's what is
shown on the right,

00:33:45.610 --> 00:33:47.830
then we see this recovery.

00:33:47.830 --> 00:33:50.050
We see the material
springing back,

00:33:50.050 --> 00:33:52.300
almost to its original shape.

00:33:52.300 --> 00:33:56.380
And so there's a very small
residual compressive strain

00:33:56.380 --> 00:33:57.310
in that case.

00:33:57.310 --> 00:34:01.450
And just looking at a
distance, from a distance

00:34:01.450 --> 00:34:04.060
at this simulation,
which is done

00:34:04.060 --> 00:34:09.400
at a particular temperature,
140 degrees C, essentially

00:34:09.400 --> 00:34:13.449
the material is behaving in a
springlike way predominantly.

00:34:13.449 --> 00:34:15.820
Most of the deformation
is recovered

00:34:15.820 --> 00:34:19.929
without cooling it to freeze
that deformation in place.

00:34:19.929 --> 00:34:24.760
And you could run similar
thought experiments

00:34:24.760 --> 00:34:27.159
at different temperatures,
different strain

00:34:27.159 --> 00:34:32.020
rates with the model and get an
impression of how much of that

00:34:32.020 --> 00:34:37.060
deformation is recovered
when the temperature is

00:34:37.060 --> 00:34:41.440
kept at its elevated level
when you remove the load.

00:34:41.440 --> 00:34:45.295
And so loosely speaking,
if most of the deformation

00:34:45.295 --> 00:34:47.170
is recovered at
high temperature,

00:34:47.170 --> 00:34:50.620
we would describe the material
as being rubbery over here.

00:34:50.620 --> 00:34:53.320
This is a plot
essentially of the ratio

00:34:53.320 --> 00:34:58.180
of that strain to
that strain, P over Q,

00:34:58.180 --> 00:35:03.490
as a function of temperature
and peak compressive stress.

00:35:03.490 --> 00:35:05.830
If that ratio is large,
we call it rubbery.

00:35:05.830 --> 00:35:08.030
If the ratio is
small, in other words,

00:35:08.030 --> 00:35:10.750
if there's been a lot
of plastic deformation

00:35:10.750 --> 00:35:12.970
that doesn't spring
back upon unloading,

00:35:12.970 --> 00:35:16.320
then we would sort of
classify the material

00:35:16.320 --> 00:35:18.100
as being in a glassy state.

00:35:18.100 --> 00:35:21.700
And sometimes glassy
is useful to you.

00:35:21.700 --> 00:35:23.500
Sometimes rubbery is preferable.

00:35:23.500 --> 00:35:31.000
So in any case, this sort
of intuition building

00:35:31.000 --> 00:35:35.050
is helpful to us
in that it begins

00:35:35.050 --> 00:35:39.490
to give us a starting point
for a physical model that

00:35:39.490 --> 00:35:42.580
will let us choose what
experiments we're going to do,

00:35:42.580 --> 00:35:45.670
and will let us build quick,
efficient simulations.

00:35:45.670 --> 00:35:51.760
And so for that particular
temperature that I looked at

00:35:51.760 --> 00:35:55.000
in detail, if you wanted
the simplest possible model

00:35:55.000 --> 00:35:56.500
of the polymer, you
might just think

00:35:56.500 --> 00:36:00.820
of making the model a
linear, elastic model, where

00:36:00.820 --> 00:36:03.350
the Young's modulus was a
function of temperature.

00:36:03.350 --> 00:36:06.040
And there are many
shortcomings of that.

00:36:06.040 --> 00:36:07.910
If you hold the load
for long enough,

00:36:07.910 --> 00:36:11.950
then there will of course be
plastic flow that's permanent.

00:36:11.950 --> 00:36:16.180
And the material is
not linear elastic.

00:36:16.180 --> 00:36:19.240
It changes its stiffness
as the strain increases.

00:36:19.240 --> 00:36:24.080
But we might as well start
simple and see if it works.

00:36:24.080 --> 00:36:26.660
It gives us information
about what types of features

00:36:26.660 --> 00:36:28.280
replicate and what do not.

00:36:28.280 --> 00:36:32.550
So that's what we
initially started with.

00:36:32.550 --> 00:36:36.950
And the idea is that
increasing the temperature

00:36:36.950 --> 00:36:42.000
reduces that modulus by three
or four orders of magnitude.

00:36:42.000 --> 00:36:44.510
We form the shape,
and then we cool down

00:36:44.510 --> 00:36:48.660
to freeze that
topography in place.

00:36:48.660 --> 00:36:54.020
And what this is
going to let us do

00:36:54.020 --> 00:36:59.120
is predict, for an
arbitrary stamp design,

00:36:59.120 --> 00:37:03.500
what the shape of the
embossed part will be,

00:37:03.500 --> 00:37:08.660
what its surface topography
will be for a chosen temperature

00:37:08.660 --> 00:37:11.780
and pressure for embossing.

00:37:11.780 --> 00:37:19.460
And here's the computational
approach that we decided upon.

00:37:19.460 --> 00:37:23.710
And this is really quick to run.

00:37:23.710 --> 00:37:27.490
The idea is that
we want to describe

00:37:27.490 --> 00:37:33.310
how the surface of the material
responds to a point load.

00:37:33.310 --> 00:37:37.720
And if the material
were linear elastic,

00:37:37.720 --> 00:37:41.440
and if it were
substantially thicker

00:37:41.440 --> 00:37:47.270
than the dimensions of
the features of interest,

00:37:47.270 --> 00:37:50.800
then the topography in
response to a point load

00:37:50.800 --> 00:37:56.470
would effectively go as one
over the radial distance

00:37:56.470 --> 00:37:58.490
from the point where
the load is applied.

00:37:58.490 --> 00:38:03.820
And that's a standard
contact mechanics result.

00:38:03.820 --> 00:38:07.630
But we're talking
about computing

00:38:07.630 --> 00:38:10.237
approximate topographies.

00:38:10.237 --> 00:38:12.570
And this is going to be done
in a discretized way, where

00:38:12.570 --> 00:38:15.960
we split the surface
of the polymer

00:38:15.960 --> 00:38:22.500
into a series of square elements
so we can translate this point

00:38:22.500 --> 00:38:25.380
load response into the
response of the surface

00:38:25.380 --> 00:38:30.420
to unit pressure,
applied over one element

00:38:30.420 --> 00:38:32.130
of our discretized surface.

00:38:32.130 --> 00:38:35.100
So this is the plane of
the surface of the wafer,

00:38:35.100 --> 00:38:37.380
the surface of the polymer.

00:38:37.380 --> 00:38:41.490
And we are trying to express
how far that part of the surface

00:38:41.490 --> 00:38:44.460
goes down when you apply
unit pressure here.

00:38:44.460 --> 00:38:46.410
And that's the answer.

00:38:49.280 --> 00:38:55.220
So we tried this with some
very simple geometries,

00:38:55.220 --> 00:38:59.750
lots of parallel channels that
we had etched into silicon.

00:38:59.750 --> 00:39:05.120
They were about 20 microns
deep, these silicon channels,

00:39:05.120 --> 00:39:12.080
and on the order of
120 microns in pitch.

00:39:12.080 --> 00:39:18.570
There are many channels
going across the screen.

00:39:18.570 --> 00:39:21.770
But what we show
here is on the left,

00:39:21.770 --> 00:39:26.720
scanning electron
micrographs of cross sections

00:39:26.720 --> 00:39:29.390
through those embossed
structures, where

00:39:29.390 --> 00:39:31.670
a variety of different
loads have been applied.

00:39:31.670 --> 00:39:35.660
And the loads were held
for less than a minute.

00:39:35.660 --> 00:39:38.480
So it's our working
assumption here

00:39:38.480 --> 00:39:42.050
that all the
deformation was to do

00:39:42.050 --> 00:39:44.390
with the rubbery
behavior of the material,

00:39:44.390 --> 00:39:48.150
and there wasn't really enough
time for plastic flow to occur.

00:39:48.150 --> 00:39:51.740
So we're just using our
zero [INAUDIBLE] model

00:39:51.740 --> 00:39:56.390
to figure out what the Young's
modulus of the material

00:39:56.390 --> 00:39:57.140
was essentially.

00:39:57.140 --> 00:40:01.670
There's one parameter that we
fit in doing this simulation.

00:40:01.670 --> 00:40:03.500
And that is the Young's modulus.

00:40:03.500 --> 00:40:06.900
Here are simulations
done using that model.

00:40:06.900 --> 00:40:11.180
So we're roughly
capturing the shape.

00:40:11.180 --> 00:40:13.100
And it seems to
all stack up if we

00:40:13.100 --> 00:40:19.610
choose this Young's modulus, 5
mega pascals at 130 degrees C.

00:40:19.610 --> 00:40:20.840
So that's all very well.

00:40:20.840 --> 00:40:23.840
But having these
parallel channels

00:40:23.840 --> 00:40:25.550
doesn't give us too
much information

00:40:25.550 --> 00:40:26.880
for a given experiment.

00:40:26.880 --> 00:40:31.190
So we have to think
quite carefully

00:40:31.190 --> 00:40:34.550
about what type of
characterization patterns

00:40:34.550 --> 00:40:36.830
to use in these experiments.

00:40:36.830 --> 00:40:39.590
We're trying to think
of ways of doing

00:40:39.590 --> 00:40:41.270
a minimal number
of experiments that

00:40:41.270 --> 00:40:43.910
will give us as much physical
information as possible.

00:40:43.910 --> 00:40:47.150
And what we came
up with was this.

00:40:47.150 --> 00:40:54.380
Here is a plan of the surface of
a silicon stamp that we etched.

00:40:54.380 --> 00:41:02.120
And it's a square array of
various patches of features.

00:41:02.120 --> 00:41:04.100
Some of them are
parallel channels.

00:41:04.100 --> 00:41:06.830
Some of them are square holes.

00:41:06.830 --> 00:41:10.320
And we have parallel channels
running in both directions.

00:41:10.320 --> 00:41:14.150
So for every line to
space ratio of channels,

00:41:14.150 --> 00:41:16.670
there's one set running
horizontally somewhere,

00:41:16.670 --> 00:41:18.200
one set running vertically.

00:41:18.200 --> 00:41:25.040
And they were arranged in a
random order across the stamp.

00:41:27.550 --> 00:41:30.970
Now, there's one
twist to this, which

00:41:30.970 --> 00:41:37.390
is that because we do
our simulation using

00:41:37.390 --> 00:41:41.200
a discrete Fourier transform,
a fast Fourier transform,

00:41:41.200 --> 00:41:47.320
the representation of the
space that we're simulating

00:41:47.320 --> 00:41:51.920
is assumed to be
periodic in space.

00:41:51.920 --> 00:41:57.815
So we accommodate that by
actually making the pattern

00:41:57.815 --> 00:41:58.315
periodic.

00:42:04.740 --> 00:42:10.720
What I show here is one
replicate of the pattern.

00:42:10.720 --> 00:42:14.640
And this is about 4
millimeters in diameter.

00:42:14.640 --> 00:42:18.520
But, in fact, what
we do is we have--

00:42:18.520 --> 00:42:25.512
I suppose on the stamp
we have a 3x3 array where

00:42:25.512 --> 00:42:29.190
what I've shown on the screen
is contained in this region.

00:42:29.190 --> 00:42:32.760
So it's pseudo periodic
from the point of view

00:42:32.760 --> 00:42:34.170
of the material surrounding it.

00:42:34.170 --> 00:42:35.760
The material's a
millimeter thick.

00:42:35.760 --> 00:42:37.440
This is 4 millimeters.

00:42:37.440 --> 00:42:41.730
And so what's going
on at the edge here

00:42:41.730 --> 00:42:44.250
looks exactly the
same to the material

00:42:44.250 --> 00:42:47.310
as this material sees over here.

00:42:47.310 --> 00:42:51.390
And that makes the simulation
match up with the experiments

00:42:51.390 --> 00:42:51.910
nicely.

00:42:51.910 --> 00:42:54.570
So we etch this stamp.

00:42:54.570 --> 00:42:57.240
We choose some
embossing conditions,

00:42:57.240 --> 00:43:00.420
press it into the
substrate, and use

00:43:00.420 --> 00:43:03.300
white light scanning
interferometry

00:43:03.300 --> 00:43:05.520
to measure the
surface topography.

00:43:05.520 --> 00:43:07.830
The smallest features
in this particular stamp

00:43:07.830 --> 00:43:12.060
are 5 micron in diameter.

00:43:12.060 --> 00:43:14.070
What we're also
doing now actually

00:43:14.070 --> 00:43:16.860
is a set of experiments where
we've scaled down this pattern

00:43:16.860 --> 00:43:19.950
100-fold to make a nano
imprint lithography

00:43:19.950 --> 00:43:21.750
stamp of the same pattern.

00:43:21.750 --> 00:43:27.630
And so we're trying to tie all
the mechanics together and see

00:43:27.630 --> 00:43:31.980
if similar effects
occur at the nanoscale.

00:43:31.980 --> 00:43:38.400
Anyhow, in the bottom left
here is a composite map

00:43:38.400 --> 00:43:42.780
of the surface, where the red
colors show that the higher

00:43:42.780 --> 00:43:47.190
topography is where more
material has penetrated further

00:43:47.190 --> 00:43:50.400
into the stamp cavities.

00:43:50.400 --> 00:43:54.540
And on the right here
are eight cross-sections

00:43:54.540 --> 00:43:59.400
through that topography,
labeled one, two, eight.

00:43:59.400 --> 00:44:01.950
Experimental data is shown
in black, underneath.

00:44:01.950 --> 00:44:06.480
And the prediction of
the linear elastic model,

00:44:06.480 --> 00:44:10.500
with only one fitted
parameter, the Young's modulus,

00:44:10.500 --> 00:44:11.410
is shown in red.

00:44:11.410 --> 00:44:15.810
And you can see that there's
remarkable correspondence

00:44:15.810 --> 00:44:17.580
between the two.

00:44:17.580 --> 00:44:23.730
We get both a prediction of
how far on average material

00:44:23.730 --> 00:44:27.240
penetrates cavities
of a given diameter.

00:44:27.240 --> 00:44:31.440
And also, we do capture these
interactions of patterns

00:44:31.440 --> 00:44:32.470
of different densities.

00:44:32.470 --> 00:44:37.180
You can see, for
example, let's say--

00:44:37.180 --> 00:44:39.840
well, I guess this
is a good example.

00:44:39.840 --> 00:44:45.900
Here you're seeing many
instances of a given trench

00:44:45.900 --> 00:44:51.340
diameter, but trenches that are
closer to different patterns

00:44:51.340 --> 00:44:54.010
feel less far than those that
are in the center of the patch.

00:44:54.010 --> 00:44:57.310
And this is all
captured reasonably

00:44:57.310 --> 00:45:03.240
well by this rubbery
model of the polymer.

00:45:03.240 --> 00:45:06.800
So looks like we've
got the basis here

00:45:06.800 --> 00:45:12.800
for doing efficient simulations.

00:45:12.800 --> 00:45:16.250
You can run that simulation
in 20 seconds in Matlab,

00:45:16.250 --> 00:45:19.430
and it's giving you,
I think, probably

00:45:19.430 --> 00:45:23.060
95% of the information a full
finite element simulation

00:45:23.060 --> 00:45:27.450
would give you, as far as
topography is concerned.

00:45:27.450 --> 00:45:33.320
So we can also abstract
our experimental results

00:45:33.320 --> 00:45:36.690
and view them in simpler ways.

00:45:36.690 --> 00:45:40.070
And one way of doing
that is to look

00:45:40.070 --> 00:45:44.060
within each region of
features and measure

00:45:44.060 --> 00:45:47.660
the peak penetration of
material into the cavity.

00:45:47.660 --> 00:45:50.720
So we just measure
the range of heights

00:45:50.720 --> 00:45:55.400
within the central 80% of the
area of each patch of features.

00:45:55.400 --> 00:45:58.760
And then plot that
peak penetration

00:45:58.760 --> 00:46:02.030
against some parameter.

00:46:02.030 --> 00:46:04.740
In this case, I plotted
the pattern density,

00:46:04.740 --> 00:46:09.320
which is the ratio of the cavity
width to the cavity pitch.

00:46:09.320 --> 00:46:12.200
And the different
colors in this graph

00:46:12.200 --> 00:46:15.260
represent different
feature pitches.

00:46:15.260 --> 00:46:20.690
So the pitch being the distance
from one cavity to the next.

00:46:20.690 --> 00:46:28.220
And what I show is the elastic
model matching up pretty well

00:46:28.220 --> 00:46:30.530
with the experimental results.

00:46:33.500 --> 00:46:37.250
Of course, you might
think that this

00:46:37.250 --> 00:46:40.310
is leading towards the
possibility of non dimensional

00:46:40.310 --> 00:46:43.940
groups to describe
features and how they fill,

00:46:43.940 --> 00:46:48.170
and putting down design
rules that would tell you

00:46:48.170 --> 00:46:49.970
how to scale the
embossing pressure

00:46:49.970 --> 00:46:52.530
as your pattern's scaled down,
and these sorts of things.

00:46:52.530 --> 00:46:56.660
So this is a great way
of viewing the results

00:46:56.660 --> 00:46:59.430
and getting
intuition about them.

00:46:59.430 --> 00:47:02.630
Of course, as you increase the
pressure and material starts

00:47:02.630 --> 00:47:06.620
to touch the tops of
the stamp cavities,

00:47:06.620 --> 00:47:09.740
this straight line
breaks down, of course.

00:47:09.740 --> 00:47:12.710
And the red symbols
show what happens

00:47:12.710 --> 00:47:16.820
when the pressure is increased
to a stage where the larger

00:47:16.820 --> 00:47:17.570
cavities fill.

00:47:20.090 --> 00:47:23.720
What you can also do is use
a series of these experiments

00:47:23.720 --> 00:47:27.830
to get material properties
as a function of temperature

00:47:27.830 --> 00:47:29.330
or of some other parameter.

00:47:29.330 --> 00:47:31.250
And that's exactly
what we did here,

00:47:31.250 --> 00:47:34.580
by doing a series
of embossing tests

00:47:34.580 --> 00:47:36.080
at different temperatures.

00:47:36.080 --> 00:47:40.910
And the gradient of that
line penetration to pressure

00:47:40.910 --> 00:47:44.210
will be inversely proportional
to the effective elastic

00:47:44.210 --> 00:47:46.050
modulus of the material.

00:47:46.050 --> 00:47:47.540
So we did that.

00:47:47.540 --> 00:47:51.440
We got out these values
for the Young's modulus

00:47:51.440 --> 00:47:52.580
against temperature.

00:47:52.580 --> 00:47:55.700
And luckily, they
match up really

00:47:55.700 --> 00:48:00.620
nicely with a model
for Young's modulus

00:48:00.620 --> 00:48:04.250
that was derived from bulk
compression experiments, that

00:48:04.250 --> 00:48:06.290
was just done in a
big and strong load

00:48:06.290 --> 00:48:09.140
frame using bulk materials.

00:48:09.140 --> 00:48:16.790
So you could start to see how,
with careful choice of test

00:48:16.790 --> 00:48:20.060
embossing patterns, we can
get a lot of information out

00:48:20.060 --> 00:48:25.310
of a new material quite
quickly, scale information,

00:48:25.310 --> 00:48:28.670
strain rate information perhaps,
temperature information.

00:48:28.670 --> 00:48:31.700
And really, one of the
big challenges here

00:48:31.700 --> 00:48:35.780
is deciding what are the
embossing tests you're

00:48:35.780 --> 00:48:38.510
going to do, what combination
of temperatures and pressures

00:48:38.510 --> 00:48:41.840
are you going to go for first
that will give you the most

00:48:41.840 --> 00:48:44.180
information?

00:48:44.180 --> 00:48:49.850
Now, I said before that
this rubbery model is really

00:48:49.850 --> 00:48:54.500
only useful if the whole
time is comparatively short.

00:48:54.500 --> 00:48:59.700
And often that's the case.

00:48:59.700 --> 00:49:02.290
You want the cycle time to
be as short as possible.

00:49:02.290 --> 00:49:06.320
So if you can get the
material into a state

00:49:06.320 --> 00:49:08.180
where you press
hard enough, you get

00:49:08.180 --> 00:49:10.440
the deformation almost
instantaneously,

00:49:10.440 --> 00:49:11.810
then that's great.

00:49:11.810 --> 00:49:14.090
But in a lot of cases,
you can't do that,

00:49:14.090 --> 00:49:16.350
and you do get
this plastic flow.

00:49:16.350 --> 00:49:20.300
So what I show here
is the evolution

00:49:20.300 --> 00:49:23.060
of an embossed
topography over time

00:49:23.060 --> 00:49:27.110
as we hold the load
at high temperature.

00:49:27.110 --> 00:49:29.420
The black symbols
down here show what

00:49:29.420 --> 00:49:32.090
happens if you start
cooling the material

00:49:32.090 --> 00:49:34.200
down as soon as the
load reaches its peak.

00:49:34.200 --> 00:49:38.060
So the material is
bowing into the cavities,

00:49:38.060 --> 00:49:39.720
but hasn't gone very far.

00:49:39.720 --> 00:49:43.820
And then right up here,
you've waited for 10 minutes.

00:49:43.820 --> 00:49:46.490
And all but the
smallest features

00:49:46.490 --> 00:49:49.700
have at least touched
the tops of the cavities.

00:49:49.700 --> 00:49:54.210
Of course, this y-axis is
showing the peak penetration.

00:49:54.210 --> 00:49:56.660
So it's the distance
from the top

00:49:56.660 --> 00:49:59.780
of the feature to the bottom.

00:49:59.780 --> 00:50:02.420
And it tells you nothing
about whether the corners

00:50:02.420 --> 00:50:04.070
of the features
have been filled.

00:50:04.070 --> 00:50:08.720
But this is a reasonably
useful measurement.

00:50:08.720 --> 00:50:12.740
Now, the question is, can
we adapt our simple model

00:50:12.740 --> 00:50:15.650
to capture this
viscoelastic behavior

00:50:15.650 --> 00:50:19.310
without increasing the
computational burden very much?

00:50:19.310 --> 00:50:23.120
And well, the next thing
you might think of doing

00:50:23.120 --> 00:50:26.900
is adding a linear
dashpot into the system.

00:50:26.900 --> 00:50:29.438
And maybe it's linear.

00:50:29.438 --> 00:50:30.980
That would be the
first thing to try.

00:50:30.980 --> 00:50:34.910
Maybe you do need to capture the
idea of a yield stress as well.

00:50:34.910 --> 00:50:38.330
And maybe you need to capture
the idea of a strain rate

00:50:38.330 --> 00:50:42.350
dependence, which
in PMMA is such

00:50:42.350 --> 00:50:46.250
that the yield stress
increases substantially

00:50:46.250 --> 00:50:49.930
with strain rates above about
10 to the minus 2 per second.

00:50:49.930 --> 00:50:57.320
So, in fact, we just tried
adding in a linear dashpot.

00:50:57.320 --> 00:51:06.720
So what this does, in effect,
is takes the point load

00:51:06.720 --> 00:51:10.350
response associated
with purely rubbery,

00:51:10.350 --> 00:51:14.850
purely linear elastic behavior,
which would be like this,

00:51:14.850 --> 00:51:20.130
and scales it by a factor
that's related to the time

00:51:20.130 --> 00:51:21.600
the load is applied.

00:51:21.600 --> 00:51:25.950
And all that's saying is
imagine this was viscoelastic.

00:51:25.950 --> 00:51:30.060
You applied a point load you get
some instantaneous deformation.

00:51:30.060 --> 00:51:36.210
But over time, I'm saying this
surface is just scaling down.

00:51:36.210 --> 00:51:40.140
All the points are staying
in the same ratio of height,

00:51:40.140 --> 00:51:42.090
but it's just scaling down.

00:51:42.090 --> 00:51:49.230
And we assume that
that scale factor

00:51:49.230 --> 00:51:51.360
was proportional
to the hold time,

00:51:51.360 --> 00:51:52.770
but you might not assume that.

00:51:52.770 --> 00:51:58.170
You might say, well,
what if there's actually

00:51:58.170 --> 00:52:03.600
a sort of limiting strain
where the polymer network is

00:52:03.600 --> 00:52:07.200
as stretched out as it is it
can be for a particular load?

00:52:07.200 --> 00:52:13.080
And in that case, you would
have I guess strain against time

00:52:13.080 --> 00:52:17.280
would asymptotically approach
some limiting value that

00:52:17.280 --> 00:52:18.750
was related to that spring.

00:52:18.750 --> 00:52:21.070
And that would also be
quite easy to compute.

00:52:21.070 --> 00:52:25.540
You compute a topography at
the start of the whole thing,

00:52:25.540 --> 00:52:28.770
a topography that would be
associated with infinite time,

00:52:28.770 --> 00:52:32.460
and then maybe interpolate
using an exponential function

00:52:32.460 --> 00:52:33.200
of hold time.

00:52:33.200 --> 00:52:37.200
But anyway, we just went
with a linear scaling.

00:52:37.200 --> 00:52:41.010
And it seems to work
remarkably well.

00:52:41.010 --> 00:52:43.890
For these particular
conditions, 110 degrees C,

00:52:43.890 --> 00:52:47.710
which is a few degrees
above glass transition.

00:52:47.710 --> 00:52:55.230
So we're definitely in a
region where plastic flow

00:52:55.230 --> 00:52:58.200
is significant, is important.

00:52:58.200 --> 00:53:04.050
And what we see, these are
the top experimental data,

00:53:04.050 --> 00:53:06.600
3D plot of the
measurements taken

00:53:06.600 --> 00:53:11.070
using optical interferometry
on the left for less than a

00:53:11.070 --> 00:53:13.800
minute holding time,
loading duration,

00:53:13.800 --> 00:53:17.100
and on the right when we left
that load in place for 10

00:53:17.100 --> 00:53:18.310
minutes.

00:53:18.310 --> 00:53:21.540
So you can see that obviously
over time the narrower features

00:53:21.540 --> 00:53:22.950
start to fill.

00:53:22.950 --> 00:53:27.450
And the simulation, to
a reasonable extent,

00:53:27.450 --> 00:53:29.200
has captured that.

00:53:29.200 --> 00:53:31.590
And in fact, the shortcoming
of the simulation

00:53:31.590 --> 00:53:34.740
is that it underestimates
how quickly the narrower

00:53:34.740 --> 00:53:38.340
features fill for the
parameters that we fit.

00:53:38.340 --> 00:53:44.250
And so that is definitely
an imperfect model,

00:53:44.250 --> 00:53:48.420
but it's pretty useful,
I think, for getting

00:53:48.420 --> 00:53:53.070
a first cut of a simulation.

00:53:53.070 --> 00:54:01.470
So, of course, now that we've
got this characterization idea,

00:54:01.470 --> 00:54:03.480
we can apply that to
different materials.

00:54:03.480 --> 00:54:08.430
And we did it with this
cyclic olefin polymer, ZEONOR,

00:54:08.430 --> 00:54:11.220
which is a thermoplastic.

00:54:11.220 --> 00:54:13.650
This one softens
around 135 degrees

00:54:13.650 --> 00:54:20.940
C. It has quite a few
advantages over PMMA.

00:54:20.940 --> 00:54:22.560
Although, it's
more expensive, it

00:54:22.560 --> 00:54:24.720
doesn't absorb water
as readily, which

00:54:24.720 --> 00:54:29.070
is pretty relevant to
microfluidic devices.

00:54:29.070 --> 00:54:33.270
It transmits light to shorter
wavelengths, which is relevant

00:54:33.270 --> 00:54:37.050
when you're exciting
fluorescent tags

00:54:37.050 --> 00:54:39.780
inside the chip with UV light.

00:54:39.780 --> 00:54:43.650
And so it's useful to
be able to characterize

00:54:43.650 --> 00:54:45.480
these new materials
as they come along,

00:54:45.480 --> 00:54:48.360
and when you don't necessarily
have an unlimited supply

00:54:48.360 --> 00:54:49.240
of the material.

00:54:49.240 --> 00:54:53.970
So again, this is a
plot of peak penetration

00:54:53.970 --> 00:54:55.650
against cavity diameter.

00:54:55.650 --> 00:55:00.150
And although most
of the data sit

00:55:00.150 --> 00:55:04.200
on a roughly straight
line, when you have cavity

00:55:04.200 --> 00:55:06.520
diameter being a large
proportion of the pitch,

00:55:06.520 --> 00:55:08.145
in other words, there
are very narrow--

00:55:10.800 --> 00:55:12.030
hello.

00:55:12.030 --> 00:55:19.020
There are very narrow walls
of the stamp material pressing

00:55:19.020 --> 00:55:25.230
into the polymer, that's
when the penetration does

00:55:25.230 --> 00:55:28.030
seem to deviate from
this straight line.

00:55:28.030 --> 00:55:38.240
So anyway, now, I've shown
you results from a few

00:55:38.240 --> 00:55:42.620
carefully chosen
operating points.

00:55:42.620 --> 00:55:45.020
And I showed a set
of results where

00:55:45.020 --> 00:55:46.610
only temperature was varied.

00:55:46.610 --> 00:55:50.600
And I showed some
for ZEONOR that

00:55:50.600 --> 00:55:54.980
was only one temperature,
one hold time, one load.

00:55:54.980 --> 00:55:58.610
And we need to start thinking
about what combination

00:55:58.610 --> 00:56:01.070
of operating parameters
would we want

00:56:01.070 --> 00:56:05.270
to deploy if we knew
nothing about a material

00:56:05.270 --> 00:56:07.940
except for its approximate
glass transition temperature?

00:56:07.940 --> 00:56:12.110
What would we want
to vary first?

00:56:12.110 --> 00:56:15.260
And so you might
think about doing

00:56:15.260 --> 00:56:18.350
some sort of fractional
factorial experiments

00:56:18.350 --> 00:56:23.750
where your variables of
interest were those connected

00:56:23.750 --> 00:56:26.270
with the process, the
temperature, the load, the hold

00:56:26.270 --> 00:56:29.030
time, the time over which
the load is applied.

00:56:29.030 --> 00:56:35.120
And that, indeed, is what I
did with a third material,

00:56:35.120 --> 00:56:40.610
another brand of cyclic
olefin polymer called TOPAS.

00:56:40.610 --> 00:56:48.380
And this is a material that
softens around 85 degrees C.

00:56:48.380 --> 00:56:53.450
And so we did a 2 to the 4
minus 1 fractional factorial

00:56:53.450 --> 00:56:58.550
where the four parameters
were embossing temperature,

00:56:58.550 --> 00:57:03.590
peak embossing force,
hold time, and the time

00:57:03.590 --> 00:57:07.550
over which the load was
ramped up to its peak.

00:57:07.550 --> 00:57:13.730
And the astute among you will
notice that these variables are

00:57:13.730 --> 00:57:18.110
not going to be independent,
because the average load

00:57:18.110 --> 00:57:21.540
over the loading time will
contribute to the hold time.

00:57:21.540 --> 00:57:27.800
So it's a rough and
ready set of experiments.

00:57:27.800 --> 00:57:32.090
But nevertheless, it gives you
some idea of what we might do.

00:57:32.090 --> 00:57:40.160
And here we have, again,
cavity penetration results

00:57:40.160 --> 00:57:44.150
as a function of cavity width
for different feature pitches.

00:57:44.150 --> 00:57:49.460
The top plot is for features
of a pitch of 100 microns.

00:57:49.460 --> 00:57:51.260
And this is for 50 and 25.

00:57:51.260 --> 00:57:55.580
And you see that, again, we
have this nice trend where

00:57:55.580 --> 00:58:01.970
the peak penetration increases
up to a maximum value.

00:58:01.970 --> 00:58:06.470
That maximum value is the height
of the cavities in the stamp.

00:58:06.470 --> 00:58:12.080
And you'll also notice that
I've put these little black dots

00:58:12.080 --> 00:58:13.350
on the graph as well.

00:58:13.350 --> 00:58:18.180
And those are the measured
heights of the stamp cavities.

00:58:18.180 --> 00:58:21.590
So you can see that actually the
heights of the stamp cavities

00:58:21.590 --> 00:58:25.880
fall off for the
narrower cavities.

00:58:25.880 --> 00:58:33.680
And that's associated with the
etching process that's used.

00:58:33.680 --> 00:58:35.660
The actual plasma
etch that makes

00:58:35.660 --> 00:58:38.210
the trenches in
the silicon stamp

00:58:38.210 --> 00:58:40.220
has a harder time etching
the narrower trenches.

00:58:40.220 --> 00:58:43.310
But it's a good sanity
check that we're actually

00:58:43.310 --> 00:58:47.450
measuring the penetration of
polymer into the cavities.

00:58:47.450 --> 00:58:53.930
Now, here are some
3D plots of results.

00:58:53.930 --> 00:58:59.700
This in the top left, this
is essentially our standard,

00:58:59.700 --> 00:59:03.050
our center point run
set of parameters

00:59:03.050 --> 00:59:04.640
where for a 4
minute hold time you

00:59:04.640 --> 00:59:07.098
get a reasonably good filling
of most of the feature sizes,

00:59:07.098 --> 00:59:08.220
but it's not perfect.

00:59:08.220 --> 00:59:12.900
So we can get an idea
of process variability.

00:59:12.900 --> 00:59:15.380
This is a set of
parameters that was really

00:59:15.380 --> 00:59:18.710
no use at all, 100 newtons.

00:59:18.710 --> 00:59:26.180
We haven't even leveled out the
non-parallelism in the machine.

00:59:26.180 --> 00:59:29.540
And one side of the substrate
was contacted with the stamp,

00:59:29.540 --> 00:59:30.510
and the other was not.

00:59:30.510 --> 00:59:32.660
So there's a lot of
missing data here.

00:59:32.660 --> 00:59:36.560
And at 100 C, 900
Newtons, 8 minutes,

00:59:36.560 --> 00:59:38.480
we pretty much got
complete filling

00:59:38.480 --> 00:59:39.590
of most of the features.

00:59:39.590 --> 00:59:48.350
So what we also
did, I should have

00:59:48.350 --> 00:59:51.380
mentioned it randomized
the order of the samples

00:59:51.380 --> 00:59:54.330
and interspersed these
center point runs.

00:59:54.330 --> 00:59:54.830
Mohammed.

00:59:54.830 --> 00:59:57.140
AUDIENCE: [INAUDIBLE] with
feature sizes [INAUDIBLE]

00:59:57.140 --> 01:00:00.680
small, that forces
[INAUDIBLE] [? 100 ?] Newtons,

01:00:00.680 --> 01:00:02.210
does it damage the stamp?

01:00:04.760 --> 01:00:07.750
PROFESSOR: In these experiments
we haven't damaged the stamp.

01:00:11.750 --> 01:00:14.540
Actually, the
compressive stresses

01:00:14.540 --> 01:00:19.400
experienced by the silicon
are nowhere near enough.

01:00:19.400 --> 01:00:24.470
I mean, to break the
tensile strength of silicon

01:00:24.470 --> 01:00:26.120
is over 100 mega pascals.

01:00:26.120 --> 01:00:29.180
But actually where
the danger arises when

01:00:29.180 --> 01:00:30.440
you're cooling the substrate.

01:00:30.440 --> 01:00:32.240
And we'll get onto that.

01:00:32.240 --> 01:00:36.710
But it's really
the lateral forces

01:00:36.710 --> 01:00:40.190
applied to the protruding stamp
features that are dangerous,

01:00:40.190 --> 01:00:43.820
because they create
moments on the features,

01:00:43.820 --> 01:00:46.542
and can cause cracks at
the base of the feature

01:00:46.542 --> 01:00:47.250
as it propagates.

01:00:47.250 --> 01:00:50.370
So good question.

01:00:50.370 --> 01:00:53.190
All right, so anyway,
interspersed center point runs.

01:00:53.190 --> 01:00:56.250
And then what we've done
to provide some basis

01:00:56.250 --> 01:00:59.070
for a test of significance
of the effects

01:00:59.070 --> 01:01:03.750
is to take the average of
these peak penetrations.

01:01:03.750 --> 01:01:06.090
So we've just taken the
mean over all feature

01:01:06.090 --> 01:01:07.950
sizes, and orientations,
and everything,

01:01:07.950 --> 01:01:11.260
and put it down here.

01:01:11.260 --> 01:01:13.560
And so you can do an ANOVA.

01:01:13.560 --> 01:01:15.060
And you can look
at the significance

01:01:15.060 --> 01:01:17.300
of various effects.

01:01:17.300 --> 01:01:23.830
And actually we get
the impression--

01:01:23.830 --> 01:01:26.040
I mean, certainly temperature,
force, and hold time

01:01:26.040 --> 01:01:26.730
is significant.

01:01:26.730 --> 01:01:30.270
That is exactly
what we expected.

01:01:30.270 --> 01:01:38.070
The question down here is, well,
at the 5% level, loading rate,

01:01:38.070 --> 01:01:40.740
the time over which
that load is ramped up

01:01:40.740 --> 01:01:44.230
is not appearing quite
to be significant.

01:01:44.230 --> 01:01:49.800
But you know, we
don't know, because we

01:01:49.800 --> 01:01:54.390
didn't make a very
judicious choice of aliasing

01:01:54.390 --> 01:01:55.980
arrangements.

01:01:55.980 --> 01:02:00.330
We don't know whether that's
really at the 7% level

01:02:00.330 --> 01:02:04.920
significant that loading
time is a relevant factor,

01:02:04.920 --> 01:02:07.560
or whether it's the interaction
of temperature, force, and hold

01:02:07.560 --> 01:02:08.460
time.

01:02:08.460 --> 01:02:10.500
Just thinking about
this intuitively,

01:02:10.500 --> 01:02:13.020
you do expect the
interactions to be important.

01:02:13.020 --> 01:02:16.710
You expect the product
of temperature and force

01:02:16.710 --> 01:02:21.510
to be relevant, or some
non-linear combination

01:02:21.510 --> 01:02:26.970
of the two parameters,
just because a temperature

01:02:26.970 --> 01:02:30.930
imparts a strain rate
for a given force.

01:02:30.930 --> 01:02:33.930
So increasing the force will
increase the strain rate

01:02:33.930 --> 01:02:34.700
and so forth.

01:02:34.700 --> 01:02:35.385
So anyway.

01:02:38.530 --> 01:02:42.670
And also, as we probably
would have expected,

01:02:42.670 --> 01:02:45.040
there's significant
curvature in the results.

01:02:45.040 --> 01:02:51.070
And harking back to that graph
of modulus against temperature,

01:02:51.070 --> 01:02:54.850
that's exactly what
we would expect.

01:02:54.850 --> 01:02:57.940
Actually, I should have
highlighted when I showed you

01:02:57.940 --> 01:03:05.740
this graph that there are trade
offs to be made in picking

01:03:05.740 --> 01:03:08.140
these operating parameters.

01:03:08.140 --> 01:03:11.290
On the one hand, you
might say I don't

01:03:11.290 --> 01:03:14.170
want to heat the material
any hotter than is necessary.

01:03:14.170 --> 01:03:17.820
I'd rather just press
as hard as I need to,

01:03:17.820 --> 01:03:21.970
and maybe operate
at 120, 115 degrees

01:03:21.970 --> 01:03:24.520
C where I can
deform the material.

01:03:27.160 --> 01:03:31.150
And then because I'm not at
a very high temperature, when

01:03:31.150 --> 01:03:33.250
I cool down, there isn't
going to be very much

01:03:33.250 --> 01:03:35.890
differential thermal contraction
of the stamp on the substrate.

01:03:35.890 --> 01:03:37.700
So I won't have big
residual stresses,

01:03:37.700 --> 01:03:39.200
and I won't risk
breaking the stamp.

01:03:39.200 --> 01:03:42.580
Now, that would be a really
logical thing to say.

01:03:42.580 --> 01:03:46.000
And from a process
control perspective,

01:03:46.000 --> 01:03:49.300
however, you can see that this
may not be a very good place

01:03:49.300 --> 01:03:51.790
to operate, where
modulus is highly

01:03:51.790 --> 01:03:53.440
sensitive to temperature.

01:03:53.440 --> 01:04:00.190
And our personal experience
with lab apparatus-- and this

01:04:00.190 --> 01:04:01.720
is probably different
in industry.

01:04:01.720 --> 01:04:06.020
But controlling the temperature
is fairly difficult.

01:04:06.020 --> 01:04:09.612
I mean, this is quite
an optimistic error bar,

01:04:09.612 --> 01:04:11.070
in fact, to put on
the temperature.

01:04:11.070 --> 01:04:17.570
So that's, I think, a really
relevant consideration

01:04:17.570 --> 01:04:21.130
for choosing hot embossing
parameters, how sensitive we

01:04:21.130 --> 01:04:24.598
are to temperature.

01:04:24.598 --> 01:04:26.556
AUDIENCE: [? Given ?]
the temperature readouts,

01:04:26.556 --> 01:04:28.900
plus minus 1 degree?

01:04:28.900 --> 01:04:31.000
PROFESSOR: That's
what I estimated

01:04:31.000 --> 01:04:33.460
for that particular
machine, yeah.

01:04:33.460 --> 01:04:37.510
And I think that there
are also big challenges

01:04:37.510 --> 01:04:39.760
to do with temperature
uniformity across [INAUDIBLE]..

01:04:39.760 --> 01:04:43.850
Yeah, that's really something
that people are looking at.

01:04:43.850 --> 01:04:50.950
So, in fact, the side of the
industry that's more advanced

01:04:50.950 --> 01:04:53.170
is really the nano
imprint lithography side,

01:04:53.170 --> 01:04:55.440
more so than the
micro embossing side.

01:04:55.440 --> 01:05:00.490
And in that case, it's
more attractive to go

01:05:00.490 --> 01:05:03.790
to very high temperatures, to
make the material behave more

01:05:03.790 --> 01:05:07.240
like a viscous fluid than
like a rubbery material

01:05:07.240 --> 01:05:08.860
or a viscoelastic.

01:05:08.860 --> 01:05:13.840
So then temperature variation
isn't so much of an issue.

01:05:13.840 --> 01:05:17.050
So you're right down in
the 4 megapascal range.

01:05:17.050 --> 01:05:21.590
So but yes, good
point, absolutely.

01:05:21.590 --> 01:05:26.320
Now, yes, there's one
really interesting thing

01:05:26.320 --> 01:05:27.760
about these results.

01:05:27.760 --> 01:05:33.520
And I mentioned that I had
two sets of each feature size.

01:05:33.520 --> 01:05:36.400
And one was oriented vertically
on the stamp, and one

01:05:36.400 --> 01:05:37.610
horizontally.

01:05:37.610 --> 01:05:41.320
And I just put those on
there on the off chance

01:05:41.320 --> 01:05:43.450
that there was anisotropy
in the materials.

01:05:43.450 --> 01:05:46.180
And it turns out, with
this TOPAS sample, which

01:05:46.180 --> 01:05:48.010
is a gift from the
supplier, there

01:05:48.010 --> 01:05:50.380
is really strong anisotropy.

01:05:50.380 --> 01:05:56.440
And so you can see that
the filled in symbols

01:05:56.440 --> 01:06:02.710
are for an arbitrarily defined
orientation, 90 degrees,

01:06:02.710 --> 01:06:04.850
and the open symbols
for 0 degrees.

01:06:04.850 --> 01:06:07.360
So turning the feature
through 90 degrees

01:06:07.360 --> 01:06:11.800
gives you this really big
difference in penetration.

01:06:11.800 --> 01:06:18.025
And these results are
based on five replicates.

01:06:18.025 --> 01:06:21.130
You can see the error bars
there at one standard deviation

01:06:21.130 --> 01:06:23.950
of the five replicate results.

01:06:23.950 --> 01:06:28.000
And there's definitely a
significant anisotropy.

01:06:28.000 --> 01:06:35.050
Whether that's to do with
residual stress in the cast

01:06:35.050 --> 01:06:37.930
sheet, alignment of
the polymer chains

01:06:37.930 --> 01:06:43.390
because of some feature
of its processing, I mean,

01:06:43.390 --> 01:06:45.750
you can start to see that
if materials like this

01:06:45.750 --> 01:06:49.230
have such a big
orientation dependence,

01:06:49.230 --> 01:06:54.100
and that is so dependent on
how they've been processed,

01:06:54.100 --> 01:06:56.420
you can't necessarily know
the whole processing history

01:06:56.420 --> 01:06:57.420
of what you're supplied.

01:06:57.420 --> 01:07:01.140
It will be useful to
have these quick checks

01:07:01.140 --> 01:07:04.440
of the properties of materials
that are given to you.

01:07:04.440 --> 01:07:07.800
And you wouldn't be able to
get that information just

01:07:07.800 --> 01:07:10.770
by a bulk compression
experiment.

01:07:10.770 --> 01:07:14.430
So these carefully designed test
patterns are really important.

01:07:14.430 --> 01:07:17.370
I should say that this is
anisotropy in the material,

01:07:17.370 --> 01:07:18.160
not in the stamp.

01:07:18.160 --> 01:07:24.000
Because if we rotate the
stamp relative to the sample,

01:07:24.000 --> 01:07:25.140
the results reverse.

01:07:25.140 --> 01:07:28.770
So it's definitely
in the material.

01:07:28.770 --> 01:07:34.310
Anyhow, that was for TOPAS.

01:07:34.310 --> 01:07:37.190
And I showed you a
few slides ago what

01:07:37.190 --> 01:07:41.630
happens when hold
time is relevant,

01:07:41.630 --> 01:07:43.040
when you've got plastic flow.

01:07:43.040 --> 01:07:48.800
And we saw that the introduction
of this linear dashpot,

01:07:48.800 --> 01:07:51.740
the scaling of the point
load response function

01:07:51.740 --> 01:07:55.250
was a reasonably good
way of capturing that.

01:07:55.250 --> 01:07:58.520
What we're working on
now is this ability

01:07:58.520 --> 01:08:01.872
to capture yield
stress to iron out

01:08:01.872 --> 01:08:03.830
some of the shortcomings
of the model, the fact

01:08:03.830 --> 01:08:06.680
that those narrower features
actually filled more

01:08:06.680 --> 01:08:09.460
than the model predicted.

01:08:09.460 --> 01:08:14.520
And the other thing
that we're trying to do

01:08:14.520 --> 01:08:18.060
is extend this simulation
approach to thin substrates

01:08:18.060 --> 01:08:20.220
for the nano imprint
lithography case,

01:08:20.220 --> 01:08:23.250
where this type of point
load response function

01:08:23.250 --> 01:08:24.960
isn't correct.

01:08:24.960 --> 01:08:27.600
The features are the
same size roughly

01:08:27.600 --> 01:08:29.399
as the thickness
of the substrate.

01:08:29.399 --> 01:08:32.819
You have to start thinking about
lateral transported material.

01:08:32.819 --> 01:08:36.149
And that's quite
an exciting topic.

01:08:36.149 --> 01:08:40.170
Now, we had a couple of
good questions about damage

01:08:40.170 --> 01:08:42.960
to the stamp and
de-molding issues.

01:08:42.960 --> 01:08:49.770
And this is perhaps
the biggest impediment

01:08:49.770 --> 01:08:53.250
to the use of imprinting,
a microscale structure.

01:08:53.250 --> 01:08:56.460
There's not that much of a
problem for nano imprint.

01:08:56.460 --> 01:08:59.460
But microscale
structures, it's crucial.

01:08:59.460 --> 01:09:04.890
And here are some examples of
problems that have occurred

01:09:04.890 --> 01:09:06.340
during cooling and de-molding.

01:09:06.340 --> 01:09:11.850
This is an SEM picture
of a PMMA component

01:09:11.850 --> 01:09:15.390
that has been embossed
with a hexagonal post.

01:09:15.390 --> 01:09:18.460
This was made from
silicon, in fact.

01:09:18.460 --> 01:09:25.439
And if you imagine
the substrate being

01:09:25.439 --> 01:09:31.020
mostly on this side of the
feature, cooled under load,

01:09:31.020 --> 01:09:35.520
the polymer having at least
10 times the thermal expansion

01:09:35.520 --> 01:09:40.890
coefficient as silicon,
it has pushed itself

01:09:40.890 --> 01:09:42.970
against the sides
of the features.

01:09:42.970 --> 01:09:46.950
And when we de-mold, we get
these really substantial

01:09:46.950 --> 01:09:48.029
ridges.

01:09:48.029 --> 01:09:52.350
I think this was embossed
at 130 degree C, 20 degrees

01:09:52.350 --> 01:09:55.140
above the glass transition.

01:09:55.140 --> 01:09:59.850
And so what we
haven't yet worked out

01:09:59.850 --> 01:10:05.220
is whether these
contact stresses

01:10:05.220 --> 01:10:07.020
are large enough
actually to push

01:10:07.020 --> 01:10:15.170
the stamp off the substrate,
or whether it's just

01:10:15.170 --> 01:10:19.760
elastic potential energy
stored in the polymer

01:10:19.760 --> 01:10:22.650
that causes this ridge to
spring up when you peel

01:10:22.650 --> 01:10:26.600
the stamp off the substrate.

01:10:26.600 --> 01:10:28.020
Here are some
optical micrographs

01:10:28.020 --> 01:10:32.240
showing a similar
problem, a triangular hole

01:10:32.240 --> 01:10:35.180
embossed into a
polymer substrate.

01:10:35.180 --> 01:10:36.920
The material is
contracted from right

01:10:36.920 --> 01:10:39.200
to left relative to
the stamp feature.

01:10:39.200 --> 01:10:42.170
And in fact, sometimes
we see these shards

01:10:42.170 --> 01:10:48.860
of polymer being sheared
off, and again, a hole where

01:10:48.860 --> 01:10:53.540
there's been a few tens of
microns relative contraction.

01:10:53.540 --> 01:10:56.630
AUDIENCE: I'm curious, is there
any sort of like lubricant

01:10:56.630 --> 01:11:00.490
that you can use to
increase the load?

01:11:00.490 --> 01:11:04.760
PROFESSOR: There
are products you

01:11:04.760 --> 01:11:07.490
can get that you can
spray onto the mold,

01:11:07.490 --> 01:11:10.070
or, indeed, treatments that
can be given to the mold

01:11:10.070 --> 01:11:11.900
to reduce the
coefficient of friction

01:11:11.900 --> 01:11:16.370
between the mold
and the substrate.

01:11:16.370 --> 01:11:23.150
That won't reduce the
magnitude of the lateral force.

01:11:23.150 --> 01:11:26.270
That's to do with Young's
modulus and the coefficient

01:11:26.270 --> 01:11:27.470
of thermal expansion.

01:11:27.470 --> 01:11:32.120
But yes, it will
potentially make it easier

01:11:32.120 --> 01:11:37.130
once that lateral force is
exerted to pull the stamp out.

01:11:37.130 --> 01:11:40.700
However, it's not-- the problem
isn't all to do with friction.

01:11:40.700 --> 01:11:45.230
Sometimes you have-- either
your stamp is imperfectly made,

01:11:45.230 --> 01:11:48.330
and there's a negative draft.

01:11:48.330 --> 01:11:51.920
I mean, I exaggerate, but if
that were the stamp and that

01:11:51.920 --> 01:11:53.810
were the polymer,
that's a problem

01:11:53.810 --> 01:11:55.610
that people run
into quite a lot.

01:11:55.610 --> 01:11:57.740
And then if the
stamp has been made

01:11:57.740 --> 01:11:59.420
by deep, reactive
ion etching where

01:11:59.420 --> 01:12:02.810
there's this cyclic
etching process,

01:12:02.810 --> 01:12:06.710
and there are these little,
sub micron scallops,

01:12:06.710 --> 01:12:10.040
you're susceptible to
mechanical locking.

01:12:10.040 --> 01:12:13.298
And there's plastic
deformation of the polymer

01:12:13.298 --> 01:12:14.090
as you pull it off.

01:12:14.090 --> 01:12:16.700
So it's a good point.

01:12:16.700 --> 01:12:19.790
Yes, and actually, one thing
that does work quite well

01:12:19.790 --> 01:12:26.390
is to leave the Teflon
polymeric coating on the silicon

01:12:26.390 --> 01:12:27.260
after etching.

01:12:27.260 --> 01:12:29.360
And that does do quite a lot.

01:12:29.360 --> 01:12:31.040
It has a very limited
lifetime, though.

01:12:33.920 --> 01:12:37.310
Anyway, the point
of saying all this

01:12:37.310 --> 01:12:41.270
is, as I alluded to
a few minutes ago,

01:12:41.270 --> 01:12:46.460
you might think of
reducing the temperature

01:12:46.460 --> 01:12:48.680
swing to a small
a value as you can

01:12:48.680 --> 01:12:53.640
so that amount of thermal
contraction is restricted.

01:12:53.640 --> 01:12:57.680
You might even think of
removing the load slightly

01:12:57.680 --> 01:13:00.190
above the glass
transition temperature.

01:13:00.190 --> 01:13:03.470
And if you're in a
region where some

01:13:03.470 --> 01:13:06.020
of the deformation, or
most of the deformation

01:13:06.020 --> 01:13:09.470
is actually plastic,
which is true in a region

01:13:09.470 --> 01:13:12.710
about 10 degrees above
glass transition for PMMA--

01:13:12.710 --> 01:13:17.540
if you can exploit the
material properties to avoid

01:13:17.540 --> 01:13:19.700
having a big temperature
swing, then that

01:13:19.700 --> 01:13:21.320
could potentially
be very exciting.

01:13:21.320 --> 01:13:24.230
And together with
Matt Dirks, who's

01:13:24.230 --> 01:13:27.560
in the lab for manufacturing
and productivity,

01:13:27.560 --> 01:13:30.890
we looked into this a
couple of years ago,

01:13:30.890 --> 01:13:37.670
and found that if we control the
temperature really carefully,

01:13:37.670 --> 01:13:39.880
then it was promising.

01:13:39.880 --> 01:13:44.750
If you de-mold at 50 degrees C,
so well below glass transition,

01:13:44.750 --> 01:13:50.870
and then pull the stamp off--
this is a cross-section through

01:13:50.870 --> 01:13:52.190
the part--

01:13:52.190 --> 01:13:54.710
then you get this
horrendous ridge

01:13:54.710 --> 01:13:57.440
on the side of the
part nearer the edge,

01:13:57.440 --> 01:14:00.320
the side of the feature
nearer the edge of the part.

01:14:00.320 --> 01:14:05.570
If you de-mold, say, well
above glass transition, 120,

01:14:05.570 --> 01:14:07.520
you get this blue line.

01:14:07.520 --> 01:14:11.180
So you get some bowing of
the base of the feature where

01:14:11.180 --> 01:14:13.640
material has sprung back.

01:14:13.640 --> 01:14:16.100
And you get splaying
of the sidewalls.

01:14:16.100 --> 01:14:19.550
And this was repeatable
over many samples.

01:14:19.550 --> 01:14:22.520
However, if we can hit
110 degrees C on the nose,

01:14:22.520 --> 01:14:23.840
we get a nice, flat feature.

01:14:23.840 --> 01:14:25.040
We get nice, flat sidewalls.

01:14:25.040 --> 01:14:27.240
And we get no ridge at all.

01:14:27.240 --> 01:14:29.450
And that would be great.

01:14:29.450 --> 01:14:31.850
But again, that's the thing.

01:14:31.850 --> 01:14:35.240
Can you, in a
production setting,

01:14:35.240 --> 01:14:38.270
make it 110, and not 115 or 120?

01:14:38.270 --> 01:14:42.650
And that, I think, is
probably possible to achieve,

01:14:42.650 --> 01:14:45.818
but would increase the
cost of the apparatus.

01:14:45.818 --> 01:14:51.600
So this is definitely
something to be aware of.

01:14:51.600 --> 01:14:55.880
Another thing that
is of importance

01:14:55.880 --> 01:14:58.280
is that the risk
of the whole part

01:14:58.280 --> 01:15:01.260
bowing if the de-molding
temperature is too high.

01:15:01.260 --> 01:15:04.380
We've observed
problems with that.

01:15:04.380 --> 01:15:07.280
So that needs to be
thought of as well.

01:15:07.280 --> 01:15:11.600
Here we can see
also that if you're

01:15:11.600 --> 01:15:15.950
going to remove the load at
or above the glass transition

01:15:15.950 --> 01:15:19.370
temperature, you have
to pull out the stamp,

01:15:19.370 --> 01:15:20.930
cool it down jolly quickly.

01:15:20.930 --> 01:15:25.310
Because otherwise the part
will start to contract back

01:15:25.310 --> 01:15:27.900
to its original flat surface.

01:15:27.900 --> 01:15:30.110
And so you leave
it for 10 minutes,

01:15:30.110 --> 01:15:32.120
things start to
look pretty poor.

01:15:35.750 --> 01:15:42.860
OK, that is an overview of
about half of my thesis.

01:15:42.860 --> 01:15:45.650
And since we're at half past
9:00, I think we should stop.

01:15:45.650 --> 01:15:51.170
But are there any
questions from anyone?

01:15:51.170 --> 01:15:56.873
If not, then I guess the
floor is open for questions

01:15:56.873 --> 01:15:57.665
about the projects.

01:16:00.990 --> 01:16:03.240
PROFESSOR: [INAUDIBLE]
mention one thing [INAUDIBLE]..

01:16:06.580 --> 01:16:11.290
I think later today, hopefully,
or by tomorrow at the latest,

01:16:11.290 --> 01:16:14.770
I'll post the tentative
schedule for what

01:16:14.770 --> 01:16:19.940
groups will be presenting on
each of Tuesday and Thursday.

01:16:19.940 --> 01:16:22.640
It will be in the
normal class period.

01:16:22.640 --> 01:16:24.647
So we'll plan for that.

01:16:24.647 --> 01:16:26.230
And I'll have some
other instructions,

01:16:26.230 --> 01:16:32.170
like it'll be best, if possible,
to send those presentations

01:16:32.170 --> 01:16:33.430
to me a little bit early.

01:16:33.430 --> 01:16:36.940
I see we do have a USB port.

01:16:36.940 --> 01:16:42.560
So it's possible we can add up
the presentations on the fly.

01:16:42.560 --> 01:16:45.190
I don't know quite how well
that works out in Singapore.

01:16:45.190 --> 01:16:47.000
We'll have to figure
that out as well.

01:16:47.000 --> 01:16:48.310
But be alert.

01:16:48.310 --> 01:16:51.790
Some of you, based
on random draw,

01:16:51.790 --> 01:16:54.280
will be doing
presentations on Tuesday.

01:16:54.280 --> 01:16:57.550
And some groups will be
doing that on Thursday.

01:16:57.550 --> 01:16:58.450
Are there questions?

01:16:58.450 --> 01:16:59.950
AUDIENCE: Is there
a rough guideline

01:16:59.950 --> 01:17:02.240
for how long the IEEE
letter should be?

01:17:02.240 --> 01:17:04.375
PROFESSOR: Oh, the IEEE paper?

01:17:04.375 --> 01:17:07.060
AUDIENCE: Yeah.

01:17:07.060 --> 01:17:08.830
PROFESSOR: I think typically--

01:17:08.830 --> 01:17:11.980
whatever it takes to
do a reasonable job.

01:17:11.980 --> 01:17:14.230
I think something
typically on the order

01:17:14.230 --> 01:17:18.250
of six, seven, eight
pages is, I think,

01:17:18.250 --> 01:17:20.330
what we often saw in the past.

01:17:20.330 --> 01:17:22.370
Sometimes it might be
a little bit shorter,

01:17:22.370 --> 01:17:24.760
depending on how much
background you have.

01:17:24.760 --> 01:17:28.060
So I don't have a
strict page guideline.

01:17:31.440 --> 01:17:31.940
Good.

01:17:31.940 --> 01:17:36.340
Any questions in
Singapore on that?

01:17:36.340 --> 01:17:37.367
OK, great.

01:17:37.367 --> 01:17:38.200
AUDIENCE: Professor.

01:17:38.200 --> 01:17:38.825
PROFESSOR: Yes.

01:17:38.825 --> 01:17:42.050
AUDIENCE: We have a
question for our project.

01:17:42.050 --> 01:17:45.970
We actually have two questions.

01:17:45.970 --> 01:17:51.990
So one question is that we
have two outputs in our--

01:17:51.990 --> 01:17:53.220
can you hear me?

01:17:53.220 --> 01:17:56.220
PROFESSOR: Yeah,
speak up a little bit.

01:17:56.220 --> 01:18:01.080
AUDIENCE: OK, so one question
is that we have two outputs,

01:18:01.080 --> 01:18:03.600
and then we are
measuring the data.

01:18:03.600 --> 01:18:07.470
But these two outputs, they
are negatively correlated.

01:18:07.470 --> 01:18:11.250
And our objective is
to maximize one output

01:18:11.250 --> 01:18:13.320
and minimize the other output.

01:18:13.320 --> 01:18:15.195
So we understand that
we can do it separately

01:18:15.195 --> 01:18:17.970
in our optimization.

01:18:17.970 --> 01:18:19.935
But when we want
to sort of create

01:18:19.935 --> 01:18:24.510
a combined an objective
function and optimize these two

01:18:24.510 --> 01:18:28.920
together, as they come from
the same set of inputs, how can

01:18:28.920 --> 01:18:30.363
we do that?

01:18:30.363 --> 01:18:32.280
PROFESSOR: Yeah, so the
classic approach there

01:18:32.280 --> 01:18:33.990
is it's a trade off.

01:18:33.990 --> 01:18:34.590
Right?

01:18:34.590 --> 01:18:35.890
One or the other.

01:18:35.890 --> 01:18:40.260
And what you typically
do is apply a weight

01:18:40.260 --> 01:18:42.760
to the two alternatives.

01:18:42.760 --> 01:18:44.370
So you have a different
numeric weight

01:18:44.370 --> 01:18:49.920
based on your engineering
importance, or the customer

01:18:49.920 --> 01:18:53.200
importance, or whatever
of the two effects.

01:18:53.200 --> 01:18:56.880
So you have one function
that combines, say,

01:18:56.880 --> 01:18:59.760
squared deviations
in the two outputs,

01:18:59.760 --> 01:19:01.755
but with a different
weight on the two outputs.

01:19:04.290 --> 01:19:06.170
AUDIENCE: OK, I see.

01:19:19.130 --> 01:19:20.106
PROFESSOR: OK?

01:19:20.106 --> 01:19:22.567
You're all set?

01:19:22.567 --> 01:19:24.400
AUDIENCE: We have another
question actually.

01:19:24.400 --> 01:19:26.212
PROFESSOR: Oh, OK.

01:19:26.212 --> 01:19:27.670
AUDIENCE: I have
one more question.

01:19:27.670 --> 01:19:31.510
It's regarding the
email you sent us.

01:19:31.510 --> 01:19:35.560
So we were told that we can
explore one factor [INAUDIBLE]

01:19:35.560 --> 01:19:37.430
strategy.

01:19:37.430 --> 01:19:42.370
We are not quite sure what
strategy you are referring to.

01:19:42.370 --> 01:19:46.510
Is it studying the output
and one input at a time?

01:19:46.510 --> 01:19:49.210
Or is it more like
stepwise regression?

01:19:49.210 --> 01:19:54.520
PROFESSOR: No, I'm referring
to the optimization approach,

01:19:54.520 --> 01:19:59.860
the One Factor At a Time, OFAT,
that Professor Dan [? Frey ?]

01:19:59.860 --> 01:20:04.220
talked about in his lecture.

01:20:04.220 --> 01:20:06.400
So where you
explore the corners.

01:20:06.400 --> 01:20:09.520
You look and see if
you've improved it or not,

01:20:09.520 --> 01:20:11.710
to decide if you keep that move.

01:20:11.710 --> 01:20:13.720
And then once you
do make a move,

01:20:13.720 --> 01:20:16.750
then you randomly
decide which next corner

01:20:16.750 --> 01:20:19.270
to experimentally try.

01:20:19.270 --> 01:20:24.550
So you've actually got the
data already done from a DOE.

01:20:24.550 --> 01:20:27.010
But now you can pretend
you were actually

01:20:27.010 --> 01:20:31.480
running the experiment just one
experimental point at a time

01:20:31.480 --> 01:20:33.640
using the OFAT approach.

01:20:33.640 --> 01:20:36.010
And I think that
would be interesting

01:20:36.010 --> 01:20:41.330
for online optimization to
compare also to response

01:20:41.330 --> 01:20:45.070
surface modeling optimization.

01:20:45.070 --> 01:20:46.420
AUDIENCE: OK.

01:20:46.420 --> 01:20:47.560
All right, thanks.

01:20:47.560 --> 01:20:49.390
PROFESSOR: Great, all right.

01:20:49.390 --> 01:20:51.360
See you guys later.