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PROFESSOR: Well, today I'm going to give
the fourth and final case study of the course.
And everything I'm going to talk about
is my thesis research in one form or another.
So this is work that's definitely in progress.
And in a lot of cases, we haven't really
drawn conclusions yet.
So it'll be quite rough and ready.
But I hope it'll be informative and raise some questions
for you.
The focus of my thesis research is--
well, broadly speaking, finding approaches
to manufacturing microfluidic devices using polymers.
And for many of you, I think microfluidics
will be something you know at least a little about.
Essentially, microchips that manipulate very small volumes
of fluids to perform various experimental, or diagnostic, or
other engineering tasks.
And we were interested in developing processes
and choosing materials that will help us make these things very
cheaply so that they can be used at the point of care
in the case of diagnostic devices, and so forth.
Now, one particular process that's
of great interest for this is the imprinting
of thermoplastic polymeric layers.
Hot embossing is what we're going to call it.
And for a start, let me say why polymers
are interesting for making these sorts of devices.
I think I see three main reasons.
Firstly, they're cheap compared to silicone or glass, which
are other materials that you might think
of as being obvious candidates to fabricate
these microscopic fluidic channels, and valves,
and pumps, and so forth.
So polymers are cheap.
Second thing is, they're often transparent.
And that's really important.
When you have a biological sample inside this device
and you're trying to look at how it behaves
in response to certain stimuli, either you're
exposing it to a dye that will make cells
with certain properties fluoresce.
You need to see that fluorescence.
Or you're prodding a cell somehow
to see whether its stiffness gives you
information about its disease state,
something along these lines.
Anyway, but transparency is an important property.
And thirdly, a lot of plastics are mechanically tough,
which makes them highly suitable to use in the field
at the point of care, in doctors' surgeries
and so forth.
So these are the three reasons why polymers are interesting.
And imprinting them is interesting as a process,
because that itself has the potential
to be quick and cheap.
You can imagine a cycle imprinting
a thermoplastic polymer occurring in around a minute.
And you can choose what kind of size workpiece you machine.
You could machine anything from the size
of a single microfluidic chip, all the way up
to continuous reels of polymeric film.
And indeed, the reel to reel printing approach
is something that's been used in industry already
for quite rudimentary devices.
3M has a patent on hot embossing reels
of thermoplastic polymers.
And so it's a pretty flexible process.
And microfluidics aren't the only sorts
of things you might think of making with it.
A lot of optical devices could be made this way.
You could think of imprinting refractive elements.
Or actually 3M's patent is so that they
can imprint the reflective films that are laminated
onto the front of road signs.
Imprinted into those films are many parallel, V-shaped grooves
that act as corner [? key ?] reflectors
so that the street signs reflect light incident from any angle.
And so those sorts of optical applications
are also pretty crucial.
But anyway, let me just describe how the process works.
What I'm illustrating here is not
a role to role printing process, but something
where the workpiece is about the size of a wafer.
So tens of millimeters in diameter.
And first thing we need is a hard stamp,
a tool that's been microfabricated
using some other process.
This tool might have been etched from silicon.
It might have been electroplated with nickel.
It might itself be a polymer, but one that doesn't soften
at the processing temperatures.
Elastomers like PDMS, polydimethylsiloxane
are actually quite attractive as stamp materials.
So we have this stamp.
We have two heated plates to heat
the stamp and the workpiece, and a means
of applying a load normal to the surface of the workpiece.
Usually what happens is the material
is heated above what's called its glass transition
temperature.
And for anyone who isn't familiar with this,
thermoplastics essentially are composed of an entangled
network of polymer molecules.
And there are one or more temperatures
for a given polymer at which those entanglements loosen.
And the chains can slide past one another.
And the stiffness and the effective viscosity
of the material around that temperature
falls by several orders of magnitude.
So above that temperature, it's highly flexible, easily formed.
Below that temperature, it's much stiffer and useable
as a device.
So we go above the glass transition temperature
to soften it.
How far we go above is an important question to answer.
That's a crucial parameter to choose.
We then apply a load.
That load is going to be ramped up over some time
that we have a choice about.
That might be an important parameter.
We hold that load for some time to allow the material to flow,
to fill cavities in the stamp.
And while the load is still applied,
we cool down usually, cool the material
to below its glass transition temperature, and finally,
remove the load.
And often, that removal step has a lot of technical challenges
involved in it, because of differential
thermal contraction of the workpiece in the tool.
So that gives you some idea that there
are at least four parameters that we need to decide upon,
temperature, a load, and two times associated
with that load.
There are probably more parameters
that we're interested in.
Now, at this point, I should also
mention a rather similar process that has
quite different applications.
And that is thermal nano imprint lithography.
This is, essentially, hot embossing,
but done on very thin layers of polymer, thinner than a micron.
And these layers have been spun onto a much harder surface,
usually a silicon wafer.
And the beauty of this process is
that it allows sub micron features
to be transferred to the wafer.
This is, I think, a really exciting process.
It has the potential to revolutionize lithography
and semiconductor manufacturing, because the resolution
with which features can be transferred
is not limited by the wavelength of light.
Usually you would pattern a photo resist layer
with some kind of projection, optical projection system.
And we've really got to the stage where
critical dimensions of transistors
are making that a big challenge, making the optical lithography
systems cost tens or hundreds of millions of dollars.
So in this case, we have this spun on polymer layer.
It's dissolved in an organic solvent, spun on the solvent.
It evaporates.
And then the spun on layer is a thermoplastic.
It can be softened.
You press the the nano fabricated stamp
into the wafer.
And ideally, squeeze all the material
from below the individual features of the stamp.
Now, in reality, that's not possible.
And there is a small residual polymer
layer that's left there.
So you can imagine, once we've removed the stamp or the mold,
we have some extremely thin regions of polymer.
And then imagine that we want to pattern, to etch away material
in the wafer underneath.
The plasma or the etching solution
to which the wafer is exposed will quite readily
break through that residual polymer layer
and remove the material.
So these processes are similar.
In many ways, they actually often use the same polymers.
But the boundary conditions, the mechanics are rather different.
And so I'll talk a little bit about nano imprint,
but mostly the results that I'm going
to show you are to do with micro hot embossing, where
the workpiece is substantially thicker than the diameters
or the depths of the features that are being patterned.
AUDIENCE: [INAUDIBLE] about creating the mold,
during the mold removal process, do you have the mold walls
getting [? dilated? ?] Because the pattern is getting taken
off and it might have a [? dimension ?] [INAUDIBLE]??
PROFESSOR: Yes, that was an excellent question.
You've hit on one of the most important challenges
of [INAUDIBLE] embossing.
And [INAUDIBLE] was asking, are there problems
with dimensional stability of the walls, the side
walls during de-molding?
And I'll show you some results that relate to that.
So yes, good point.
Anyhow, as I already mentioned, there
are several parameters to do with the process
that we need to pick, temperatures, load times,
loading durations.
The range that those parameters can take
will be limited by the capabilities of the machine we
have, the physical properties of the polymer
we're trying to pattern, what temperature does
it start to burn, and so forth.
What about the material underneath?
If we're doing nano imprint lithography,
are there temperature constraints
that the wafer underneath has to observe?
So that's what constrains the process.
And, of course, we might also be making engineering decisions
about what type of polymer we're going to use
to achieve a certain end.
And indeed, we might have some flexibility in the pattern
that we are going to emboss.
We might think about designing a pattern with an eye
to manufacturability, something that will be easier to imprint
with less variability.
And that is one of the questions that I'm trying to answer.
Mohammed.
AUDIENCE: [INAUDIBLE] how do you [INAUDIBLE] the stamp
[? control? ?]
PROFESSOR: Right, well, the stamp
can be made in a variety of ways that are usually
traditional microfabrication.
So one particularly easy way of doing
it would be to use a process called deep reactive ion
etching.
And here I'm talking about micro embossing,
where the features are several microns to many microns.
And essentially, this is just etching very deep trenches
into a silicon wafer using a plasma process.
I could go into great detail about how that works,
but essentially, it's a fluorine based chemistry.
The precursor gas is SF6.
And you build up these very deep, narrow trenches
in the silicon wafer by a series of steps.
So in fact, you would start with the silicon
with a photoresist mask or something.
You'd do a brief fluorine based plasma etch that would remove
small amounts of material.
That's roughly isotropic.
So if you want vertical sidewalls,
you've got to do something else.
And the something else is depositing
a polymeric passivation layer.
So you change the gas in the chamber
to C4F8, which creates what's essentially
a teflon coating that passivates the sidewall of the trench
that's developing.
Then you go back to the SF6, build up a new notch,
and do this many times, alternate many times.
So whatever way you pattern the stamp.
Silicon actually, as we will see later, for de-molding reasons,
is actually a lousy material to use for the stamp.
So then you might go one step further, electroplate nickel
into that etched wafer, peel off the nickel,
and use that as the stamp.
Much tougher.
Or you might use more novel materials,
things like metallic glasses, which
are alloys with an amorphous structure that are
both very hard and very tough.
They would be great materials for a stamp.
AUDIENCE: So what you mentioned--
you said that you're not limited to wavelengths
of the light in this process.
But however to make the stamp, then you are limited to--
PROFESSOR: Yeah.
AUDIENCE: [INAUDIBLE]
PROFESSOR: Well, yes.
AUDIENCE: [INAUDIBLE] limitation exists.
PROFESSOR: So what I just described here
was for micro embossing.
I'm sort of describing two processes
in parallel that have great similarities,
but not in terms of scale.
So this would be for features that are a micron or larger.
If you want to make sub micron features,
then you're quite right.
You need a process that will let you make a stamp with sub
micron features, and electron beam lithography
is a great candidate for that where you actually would--
you would start with a silicon wafer
with a 100 nanometer thick layer of a radiation
sensitive resist.
Then you would just actually steer a focused electron beam
across the surface, scan it across the surface
in the pattern that you wanted.
And that will give you 5 nanometer resolution or better.
The trouble is, it takes ages because it's a serial process.
You're scanning the electrons over the surface.
So once you've made the stamp, you've paid however many $1,000
for the stamp.
You can stamp it in in a minute into as many substrates
as you like.
And that's really the reason for nano imprint.
OK, so keep both of those processes in mind.
But a lot of the assertions I'm going to make from now on
are all about the micron scale embossing.
So as I said, there are lots of different parameters
we can choose to do with the process,
to do with the material we're embossing,
to do with the pattern that we're embossing.
And the overall mission that I suppose
we have is to try to provide tools for people who are using
this process to achieve the desired
microstructure with as little time, energy, cost as possible.
So if you're processing a certain material,
can you pick a pattern that will take 30 seconds to replicate
instead of a minute at the available processing
conditions?
So that presupposes, of course, that we
have some specification on what satisfactory replication is.
The most obvious specification would
be that every cavity in the stamp
has been filled with polymer, even the narrowest ones.
That would be a good specification to use.
Another good specification that's
really important for nano imprint lithography
is to make the thickness of those residual polymer layers
very uniform.
And that's important because it does
take some time for the etching process
to break through that residual layer.
And if the residual layer varies in thickness,
the time taken to break through it will be different.
And then you'll get different properties of the underlying
structure.
So let's say you've imprinted this 100 nanometer thick
polymer layer.
And on this side, the residual layer is really thin.
And on this side it's twice as thick.
You then expose this with a fluorine plasma.
You're trying to etch the silicon underneath here.
You're going to end up with a deeper trench
here than you are here because of the time
it took to get through that.
So coming up with ways of designing the stamp so
that the residual layer ends up being as uniform as possible
is a really pressing challenge actually for this lithography
technique to be adopted.
Anyhow, so what we're all about is simplified modeling tools
that can be used as part of the design loop
that are computationally efficient enough
to give results in a reasonable amount of time,
and that represent reality well.
So that implies that we need some way of characterizing
the tool that we're using, the materials that we're
using efficiently so that we can get information
about the physical properties of these things
with a minimum of fuss.
Now, I'm just going to split the problem up
into three notional length scales
so that we can have a clearer picture of what's going on.
And at the largest length scale you
can think of variations in the quality
of the embossed features from one side
of the substrate to the other.
And that might occur because the two heated plates that
are compressing the stamp and the substrate
are not perfectly parallel.
So the pressure's greater on one side.
It might be because one of the plates is bowed or wavy.
Or it might be to do simply with the mechanics
of the substrate itself.
If that substrate is behaving as a viscous fluid, say,
then as you compress that substrate, that flat, polymer
substrate, you're going to expect
to see, in fact, a parabolic distribution of pressure
across it.
So there are various things to consider there.
And then at what I'm going to call the device scale,
there are these pattern dependencies
where the arrangement of features on the stamp
can have a profound effect on how well defined the features
end up being.
And what I've sketched here, which is really just a sketch,
it suggests if there are features
that are slightly more closely packed together,
then they may fill earlier, or maybe sometimes later
than regions that are less densely packed.
And if that's the case, then maybe you
want to put some design rules in place
that will constrain the variation of density
of features on the stamp.
Finally, we've got at the smallest scale effects
to do with individual features.
So if an individual gap is too small, say,
that's going to be very hard to force polymer into it.
And that could be a showstopper.
So we've got these three different length scales.
I've alluded to these sorts of problems,
bowing of the patterns, non parallelism of the patterns.
They relate to the substrate scale effects.
This shows one particular substrate that we embossed.
This is a square of PMMA, which is acrylic,
which is about 100 millimeters square.
We embossed with a wafer that had been uniformly patterned
with some silicon posts, roughly 100 microns in diameter.
And we just use this as a probe to look
at our embossing machine and see how uniform a pattern could
be produced.
Now, aside from the fact that huge chunks of the silicon
wafer broke off during de-molding--
and that's a good illustration of some of the problems that we
face--
we were able to look at the topography of the pattern
at different locations on the wafer.
We did that using an interferometer,
scanning from above, measuring the topography.
And so we were able to see various things,
that the emboss depth was higher on this side than on this side.
Then near the edge of the wafer the embossed features
tailed off in height.
And so these are the sorts of things
that we need to come up with ways of predicting
so that we can counteract them.
Anyway, what I'm going to concentrate on
for the rest of this talk, in fact, is pattern
dependent non uniformity, which is, in many ways,
the most challenging to deal with.
Effects to do with the edge of the wafer
become important when you're trying to eke out one or two
extra devices.
You're trying to save a little bit of material.
But if the actual design of the device--
there may be many devices across a wafer.
If the design of the individual device is faulty
and it will never replicate properly,
then you're in real trouble.
So trying to get an understanding
of what patterns will form well and what patterns will not
is crucial.
And so although we are working towards a unified way
of dealing with this, I'm just going
to talk mostly about the pattern dependencies now.
So I've mentioned all of these different questions that
need to be answered, factors that need to be chosen when
you're designing a new process.
And some of them are going to be continuous variables,
and some of them will be discrete choices.
And it's not absolutely clear which will be which.
I've really split the decisions up
into three categories, the decisions
you have to make about the pattern
you're going to emboss, what are the shapes of the features?
Rectangles, circles, triangles, how big they are,
and how they are oriented on the stamp?
And that can be important when you're
starting to think about radial thermal contraction
of the parts, or about anisotropic material
properties.
So there you've got-- you know, size is a continuous variable,
and the feature shape you might think
of as being a discrete choice.
When it comes to the substrate itself,
then you've got to decide on the material.
Various materials soften at different temperatures.
Some of them exhibit a range of temperatures over which they
behave rather like a rubber.
Others don't really have much of a rubbery region.
They just flow very easily as soon
as you're above the glass transition temperature.
So that's a decision that has to be made.
And in micro embossing, often you're
picking between a variety of off the shelf substrates, PMMA,
plexiglass, polycarbonate, materials like this,
where these are technical grade materials.
They're molecular weight.
In other words, the average length of the polymer chains
is not necessarily well documented or well defined.
So in that sense, your material choice
might be a discrete decision.
On the other hand, if you're spinning the polymer
onto the wafer, and you're dissolving it,
then you do have the option of choosing the molecular weight,
and therefore, defining the viscosity as essentially
a continuous variable.
So those are things that might need to be thought about.
And, of course, there's the thickness.
Either how thickly do you spin this resistor?
And that, a lot of research in the field
demonstrates the optimal thickness
is a strong function of what pattern you're
trying to emboss, how many voids there are in the stamp.
So the thickness of that might be important,
and also the thickness in micro embossing
where the substrate is a millimeter thick, say.
That's also a decision that has to be made.
So and the third category, of course,
is the process parameters, the temperature, pressure,
hold time, and so forth.
Now, there's an awful lot of variables there.
And if one were to just take a purely empirical approach
and try doing a full factorial or a fractional factorial
exploration of the space, it would
start to look pretty much like a nightmare.
And luckily, we don't have to stumble around in the dark,
because we do already have some reasonably
good physical intuition about how these materials behave.
And, of course, there's a huge research field
to do with characterizing these bulk materials,
building theoretical models of how they behave,
fitting data to those models.
And I'm sure mechanical engineers here
will be familiar with this sort of way of describing polymers
in a simplified manner, where you build up a model.
In this case, this is a one dimensional model
that sums up the viscoelastic behavior of the polymer using
a combination of springs, elastic, nondissipative
elements.
And these elements here are dashpots, which are essentially
viscous components and damp.
Yes, exactly, they dissipate energy.
So the various stiffnesses and dissipation factors
for the springs and dashpots may be non-linear functions
of temperature.
They may be non-linear functions of strain rate,
and, in fact, almost always are.
And so there are many theses that
have been written trying to characterize these materials.
And building on those experimental approaches
are simulation models.
There are finite element models of these polymers that
have been lovingly built up.
And so with enough information about the polymer
with a detailed model of the stamp that you were thinking
of embossing, and knowing something
about the dimensional tolerances of the machine you have,
you could do a simulation and perhaps predict
what was going to happen.
The trouble is, it would probably take years.
Because when you start having microscale patterns
that you're trying to emboss, the computational burden
of using these full nonlinear, finite, deformation polymer
models becomes immense.
And that's great if you have one particular device that
absolutely must be perfect.
However, what we're interested in doing in our research
is finding some sort of middle ground
between the empirical approach and the really
rigorous, thorough, theoretical approach
that's based on a highly controlled set of experiments.
And so the idea is to find approximate descriptions
for the material that are efficient to run,
efficient to simulate patterns, wafers that have thousands
of features across them.
So let's start to think about how we can build out
the bare bones of a model that are going
to inform the experiments that we do about this embossing
process.
Now, what I've done here-- and I won't go into laborious detail
about, but essentially, this is just building intuition
about one particular polymer.
This is a model for polymethylmethacrylate,
plexiglass, acrylic, call it what
you will, which a student at MIT has recently
written a thesis about, doing compression experiments of it,
building up a highly faithful model of it.
But there's a one dimensional implementation of that model
that we can run.
We can look at what happens when you give it various load
profiles over time and look at the stresses and the strains
in each of those components of the model over time.
So what I've done here is I've just
done two what are essentially thought experiments.
The left hand column of graphs shows
what happens if the material is heated above its glass
transition temperature and then given
a 1 and 1/2 megapascal compressive load which
is held for 10 seconds.
That load is maintained while the temperature is reduced
below the glass transmission.
The glass transition here is about 105 degrees C.
So then we looked at how the model responded to that.
There's a compressive strain, of course.
There are stresses built up in the left hand
branch of that model, this spring and this dashpot.
And there are stresses in the right hand side as well.
And essentially what this shows is that most of the deformation
is frozen in place, frozen by this
cooling below glass transition.
So when the load is removed, this amount of strain
remains, this P amount here.
However, if you don't cool down before you remove the load,
and that's what is shown on the right,
then we see this recovery.
We see the material springing back,
almost to its original shape.
And so there's a very small residual compressive strain
in that case.
And just looking at a distance, from a distance
at this simulation, which is done
at a particular temperature, 140 degrees C, essentially
the material is behaving in a springlike way predominantly.
Most of the deformation is recovered
without cooling it to freeze that deformation in place.
And you could run similar thought experiments
at different temperatures, different strain
rates with the model and get an impression of how much of that
deformation is recovered when the temperature is
kept at its elevated level when you remove the load.
And so loosely speaking, if most of the deformation
is recovered at high temperature,
we would describe the material as being rubbery over here.
This is a plot essentially of the ratio
of that strain to that strain, P over Q,
as a function of temperature and peak compressive stress.
If that ratio is large, we call it rubbery.
If the ratio is small, in other words,
if there's been a lot of plastic deformation
that doesn't spring back upon unloading,
then we would sort of classify the material
as being in a glassy state.
And sometimes glassy is useful to you.
Sometimes rubbery is preferable.
So in any case, this sort of intuition building
is helpful to us in that it begins
to give us a starting point for a physical model that
will let us choose what experiments we're going to do,
and will let us build quick, efficient simulations.
And so for that particular temperature that I looked at
in detail, if you wanted the simplest possible model
of the polymer, you might just think
of making the model a linear, elastic model, where
the Young's modulus was a function of temperature.
And there are many shortcomings of that.
If you hold the load for long enough,
then there will of course be plastic flow that's permanent.
And the material is not linear elastic.
It changes its stiffness as the strain increases.
But we might as well start simple and see if it works.
It gives us information about what types of features
replicate and what do not.
So that's what we initially started with.
And the idea is that increasing the temperature
reduces that modulus by three or four orders of magnitude.
We form the shape, and then we cool down
to freeze that topography in place.
And what this is going to let us do
is predict, for an arbitrary stamp design,
what the shape of the embossed part will be,
what its surface topography will be for a chosen temperature
and pressure for embossing.
And here's the computational approach that we decided upon.
And this is really quick to run.
The idea is that we want to describe
how the surface of the material responds to a point load.
And if the material were linear elastic,
and if it were substantially thicker
than the dimensions of the features of interest,
then the topography in response to a point load
would effectively go as one over the radial distance
from the point where the load is applied.
And that's a standard contact mechanics result.
But we're talking about computing
approximate topographies.
And this is going to be done in a discretized way, where
we split the surface of the polymer
into a series of square elements so we can translate this point
load response into the response of the surface
to unit pressure, applied over one element
of our discretized surface.
So this is the plane of the surface of the wafer,
the surface of the polymer.
And we are trying to express how far that part of the surface
goes down when you apply unit pressure here.
And that's the answer.
So we tried this with some very simple geometries,
lots of parallel channels that we had etched into silicon.
They were about 20 microns deep, these silicon channels,
and on the order of 120 microns in pitch.
There are many channels going across the screen.
But what we show here is on the left,
scanning electron micrographs of cross sections
through those embossed structures, where
a variety of different loads have been applied.
And the loads were held for less than a minute.
So it's our working assumption here
that all the deformation was to do
with the rubbery behavior of the material,
and there wasn't really enough time for plastic flow to occur.
So we're just using our zero [INAUDIBLE] model
to figure out what the Young's modulus of the material
was essentially.
There's one parameter that we fit in doing this simulation.
And that is the Young's modulus.
Here are simulations done using that model.
So we're roughly capturing the shape.
And it seems to all stack up if we
choose this Young's modulus, 5 mega pascals at 130 degrees C.
So that's all very well.
But having these parallel channels
doesn't give us too much information
for a given experiment.
So we have to think quite carefully
about what type of characterization patterns
to use in these experiments.
We're trying to think of ways of doing
a minimal number of experiments that
will give us as much physical information as possible.
And what we came up with was this.
Here is a plan of the surface of a silicon stamp that we etched.
And it's a square array of various patches of features.
Some of them are parallel channels.
Some of them are square holes.
And we have parallel channels running in both directions.
So for every line to space ratio of channels,
there's one set running horizontally somewhere,
one set running vertically.
And they were arranged in a random order across the stamp.
Now, there's one twist to this, which
is that because we do our simulation using
a discrete Fourier transform, a fast Fourier transform,
the representation of the space that we're simulating
is assumed to be periodic in space.
So we accommodate that by actually making the pattern
periodic.
What I show here is one replicate of the pattern.
And this is about 4 millimeters in diameter.
But, in fact, what we do is we have--
I suppose on the stamp we have a 3x3 array where
what I've shown on the screen is contained in this region.
So it's pseudo periodic from the point of view
of the material surrounding it.
The material's a millimeter thick.
This is 4 millimeters.
And so what's going on at the edge here
looks exactly the same to the material
as this material sees over here.
And that makes the simulation match up with the experiments
nicely.
So we etch this stamp.
We choose some embossing conditions,
press it into the substrate, and use
white light scanning interferometry
to measure the surface topography.
The smallest features in this particular stamp
are 5 micron in diameter.
What we're also doing now actually
is a set of experiments where we've scaled down this pattern
100-fold to make a nano imprint lithography
stamp of the same pattern.
And so we're trying to tie all the mechanics together and see
if similar effects occur at the nanoscale.
Anyhow, in the bottom left here is a composite map
of the surface, where the red colors show that the higher
topography is where more material has penetrated further
into the stamp cavities.
And on the right here are eight cross-sections
through that topography, labeled one, two, eight.
Experimental data is shown in black, underneath.
And the prediction of the linear elastic model,
with only one fitted parameter, the Young's modulus,
is shown in red.
And you can see that there's remarkable correspondence
between the two.
We get both a prediction of how far on average material
penetrates cavities of a given diameter.
And also, we do capture these interactions of patterns
of different densities.
You can see, for example, let's say--
well, I guess this is a good example.
Here you're seeing many instances of a given trench
diameter, but trenches that are closer to different patterns
feel less far than those that are in the center of the patch.
And this is all captured reasonably
well by this rubbery model of the polymer.
So looks like we've got the basis here
for doing efficient simulations.
You can run that simulation in 20 seconds in Matlab,
and it's giving you, I think, probably
95% of the information a full finite element simulation
would give you, as far as topography is concerned.
So we can also abstract our experimental results
and view them in simpler ways.
And one way of doing that is to look
within each region of features and measure
the peak penetration of material into the cavity.
So we just measure the range of heights
within the central 80% of the area of each patch of features.
And then plot that peak penetration
against some parameter.
In this case, I plotted the pattern density,
which is the ratio of the cavity width to the cavity pitch.
And the different colors in this graph
represent different feature pitches.
So the pitch being the distance from one cavity to the next.
And what I show is the elastic model matching up pretty well
with the experimental results.
Of course, you might think that this
is leading towards the possibility of non dimensional
groups to describe features and how they fill,
and putting down design rules that would tell you
how to scale the embossing pressure
as your pattern's scaled down, and these sorts of things.
So this is a great way of viewing the results
and getting intuition about them.
Of course, as you increase the pressure and material starts
to touch the tops of the stamp cavities,
this straight line breaks down, of course.
And the red symbols show what happens
when the pressure is increased to a stage where the larger
cavities fill.
What you can also do is use a series of these experiments
to get material properties as a function of temperature
or of some other parameter.
And that's exactly what we did here,
by doing a series of embossing tests
at different temperatures.
And the gradient of that line penetration to pressure
will be inversely proportional to the effective elastic
modulus of the material.
So we did that.
We got out these values for the Young's modulus
against temperature.
And luckily, they match up really
nicely with a model for Young's modulus
that was derived from bulk compression experiments, that
was just done in a big and strong load
frame using bulk materials.
So you could start to see how, with careful choice of test
embossing patterns, we can get a lot of information out
of a new material quite quickly, scale information,
strain rate information perhaps, temperature information.
And really, one of the big challenges here
is deciding what are the embossing tests you're
going to do, what combination of temperatures and pressures
are you going to go for first that will give you the most
information?
Now, I said before that this rubbery model is really
only useful if the whole time is comparatively short.
And often that's the case.
You want the cycle time to be as short as possible.
So if you can get the material into a state
where you press hard enough, you get
the deformation almost instantaneously,
then that's great.
But in a lot of cases, you can't do that,
and you do get this plastic flow.
So what I show here is the evolution
of an embossed topography over time
as we hold the load at high temperature.
The black symbols down here show what
happens if you start cooling the material
down as soon as the load reaches its peak.
So the material is bowing into the cavities,
but hasn't gone very far.
And then right up here, you've waited for 10 minutes.
And all but the smallest features
have at least touched the tops of the cavities.
Of course, this y-axis is showing the peak penetration.
So it's the distance from the top
of the feature to the bottom.
And it tells you nothing about whether the corners
of the features have been filled.
But this is a reasonably useful measurement.
Now, the question is, can we adapt our simple model
to capture this viscoelastic behavior
without increasing the computational burden very much?
And well, the next thing you might think of doing
is adding a linear dashpot into the system.
And maybe it's linear.
That would be the first thing to try.
Maybe you do need to capture the idea of a yield stress as well.
And maybe you need to capture the idea of a strain rate
dependence, which in PMMA is such
that the yield stress increases substantially
with strain rates above about 10 to the minus 2 per second.
So, in fact, we just tried adding in a linear dashpot.
So what this does, in effect, is takes the point load
response associated with purely rubbery,
purely linear elastic behavior, which would be like this,
and scales it by a factor that's related to the time
the load is applied.
And all that's saying is imagine this was viscoelastic.
You applied a point load you get some instantaneous deformation.
But over time, I'm saying this surface is just scaling down.
All the points are staying in the same ratio of height,
but it's just scaling down.
And we assume that that scale factor
was proportional to the hold time,
but you might not assume that.
You might say, well, what if there's actually
a sort of limiting strain where the polymer network is
as stretched out as it is it can be for a particular load?
And in that case, you would have I guess strain against time
would asymptotically approach some limiting value that
was related to that spring.
And that would also be quite easy to compute.
You compute a topography at the start of the whole thing,
a topography that would be associated with infinite time,
and then maybe interpolate using an exponential function
of hold time.
But anyway, we just went with a linear scaling.
And it seems to work remarkably well.
For these particular conditions, 110 degrees C,
which is a few degrees above glass transition.
So we're definitely in a region where plastic flow
is significant, is important.
And what we see, these are the top experimental data,
3D plot of the measurements taken
using optical interferometry on the left for less than a
minute holding time, loading duration,
and on the right when we left that load in place for 10
minutes.
So you can see that obviously over time the narrower features
start to fill.
And the simulation, to a reasonable extent,
has captured that.
And in fact, the shortcoming of the simulation
is that it underestimates how quickly the narrower
features fill for the parameters that we fit.
And so that is definitely an imperfect model,
but it's pretty useful, I think, for getting
a first cut of a simulation.
So, of course, now that we've got this characterization idea,
we can apply that to different materials.
And we did it with this cyclic olefin polymer, ZEONOR,
which is a thermoplastic.
This one softens around 135 degrees
C. It has quite a few advantages over PMMA.
Although, it's more expensive, it
doesn't absorb water as readily, which
is pretty relevant to microfluidic devices.
It transmits light to shorter wavelengths, which is relevant
when you're exciting fluorescent tags
inside the chip with UV light.
And so it's useful to be able to characterize
these new materials as they come along,
and when you don't necessarily have an unlimited supply
of the material.
So again, this is a plot of peak penetration
against cavity diameter.
And although most of the data sit
on a roughly straight line, when you have cavity
diameter being a large proportion of the pitch,
in other words, there are very narrow--
hello.
There are very narrow walls of the stamp material pressing
into the polymer, that's when the penetration does
seem to deviate from this straight line.
So anyway, now, I've shown you results from a few
carefully chosen operating points.
And I showed a set of results where
only temperature was varied.
And I showed some for ZEONOR that
was only one temperature, one hold time, one load.
And we need to start thinking about what combination
of operating parameters would we want
to deploy if we knew nothing about a material
except for its approximate glass transition temperature?
What would we want to vary first?
And so you might think about doing
some sort of fractional factorial experiments
where your variables of interest were those connected
with the process, the temperature, the load, the hold
time, the time over which the load is applied.
And that, indeed, is what I did with a third material,
another brand of cyclic olefin polymer called TOPAS.
And this is a material that softens around 85 degrees C.
And so we did a 2 to the 4 minus 1 fractional factorial
where the four parameters were embossing temperature,
peak embossing force, hold time, and the time
over which the load was ramped up to its peak.
And the astute among you will notice that these variables are
not going to be independent, because the average load
over the loading time will contribute to the hold time.
So it's a rough and ready set of experiments.
But nevertheless, it gives you some idea of what we might do.
And here we have, again, cavity penetration results
as a function of cavity width for different feature pitches.
The top plot is for features of a pitch of 100 microns.
And this is for 50 and 25.
And you see that, again, we have this nice trend where
the peak penetration increases up to a maximum value.
That maximum value is the height of the cavities in the stamp.
And you'll also notice that I've put these little black dots
on the graph as well.
And those are the measured heights of the stamp cavities.
So you can see that actually the heights of the stamp cavities
fall off for the narrower cavities.
And that's associated with the etching process that's used.
The actual plasma etch that makes
the trenches in the silicon stamp
has a harder time etching the narrower trenches.
But it's a good sanity check that we're actually
measuring the penetration of polymer into the cavities.
Now, here are some 3D plots of results.
This in the top left, this is essentially our standard,
our center point run set of parameters
where for a 4 minute hold time you
get a reasonably good filling of most of the feature sizes,
but it's not perfect.
So we can get an idea of process variability.
This is a set of parameters that was really
no use at all, 100 newtons.
We haven't even leveled out the non-parallelism in the machine.
And one side of the substrate was contacted with the stamp,
and the other was not.
So there's a lot of missing data here.
And at 100 C, 900 Newtons, 8 minutes,
we pretty much got complete filling
of most of the features.
So what we also did, I should have
mentioned it randomized the order of the samples
and interspersed these center point runs.
Mohammed.
AUDIENCE: [INAUDIBLE] with feature sizes [INAUDIBLE]
small, that forces [INAUDIBLE] [? 100 ?] Newtons,
does it damage the stamp?
PROFESSOR: In these experiments we haven't damaged the stamp.
Actually, the compressive stresses
experienced by the silicon are nowhere near enough.
I mean, to break the tensile strength of silicon
is over 100 mega pascals.
But actually where the danger arises when
you're cooling the substrate.
And we'll get onto that.
But it's really the lateral forces
applied to the protruding stamp features that are dangerous,
because they create moments on the features,
and can cause cracks at the base of the feature
as it propagates.
So good question.
All right, so anyway, interspersed center point runs.
And then what we've done to provide some basis
for a test of significance of the effects
is to take the average of these peak penetrations.
So we've just taken the mean over all feature
sizes, and orientations, and everything,
and put it down here.
And so you can do an ANOVA.
And you can look at the significance
of various effects.
And actually we get the impression--
I mean, certainly temperature, force, and hold time
is significant.
That is exactly what we expected.
The question down here is, well, at the 5% level, loading rate,
the time over which that load is ramped up
is not appearing quite to be significant.
But you know, we don't know, because we
didn't make a very judicious choice of aliasing
arrangements.
We don't know whether that's really at the 7% level
significant that loading time is a relevant factor,
or whether it's the interaction of temperature, force, and hold
time.
Just thinking about this intuitively,
you do expect the interactions to be important.
You expect the product of temperature and force
to be relevant, or some non-linear combination
of the two parameters, just because a temperature
imparts a strain rate for a given force.
So increasing the force will increase the strain rate
and so forth.
So anyway.
And also, as we probably would have expected,
there's significant curvature in the results.
And harking back to that graph of modulus against temperature,
that's exactly what we would expect.
Actually, I should have highlighted when I showed you
this graph that there are trade offs to be made in picking
these operating parameters.
On the one hand, you might say I don't
want to heat the material any hotter than is necessary.
I'd rather just press as hard as I need to,
and maybe operate at 120, 115 degrees
C where I can deform the material.
And then because I'm not at a very high temperature, when
I cool down, there isn't going to be very much
differential thermal contraction of the stamp on the substrate.
So I won't have big residual stresses,
and I won't risk breaking the stamp.
Now, that would be a really logical thing to say.
And from a process control perspective,
however, you can see that this may not be a very good place
to operate, where modulus is highly
sensitive to temperature.
And our personal experience with lab apparatus-- and this
is probably different in industry.
But controlling the temperature is fairly difficult.
I mean, this is quite an optimistic error bar,
in fact, to put on the temperature.
So that's, I think, a really relevant consideration
for choosing hot embossing parameters, how sensitive we
are to temperature.
AUDIENCE: [? Given ?] the temperature readouts,
plus minus 1 degree?
PROFESSOR: That's what I estimated
for that particular machine, yeah.
And I think that there are also big challenges
to do with temperature uniformity across [INAUDIBLE]..
Yeah, that's really something that people are looking at.
So, in fact, the side of the industry that's more advanced
is really the nano imprint lithography side,
more so than the micro embossing side.
And in that case, it's more attractive to go
to very high temperatures, to make the material behave more
like a viscous fluid than like a rubbery material
or a viscoelastic.
So then temperature variation isn't so much of an issue.
So you're right down in the 4 megapascal range.
So but yes, good point, absolutely.
Now, yes, there's one really interesting thing
about these results.
And I mentioned that I had two sets of each feature size.
And one was oriented vertically on the stamp, and one
horizontally.
And I just put those on there on the off chance
that there was anisotropy in the materials.
And it turns out, with this TOPAS sample, which
is a gift from the supplier, there
is really strong anisotropy.
And so you can see that the filled in symbols
are for an arbitrarily defined orientation, 90 degrees,
and the open symbols for 0 degrees.
So turning the feature through 90 degrees
gives you this really big difference in penetration.
And these results are based on five replicates.
You can see the error bars there at one standard deviation
of the five replicate results.
And there's definitely a significant anisotropy.
Whether that's to do with residual stress in the cast
sheet, alignment of the polymer chains
because of some feature of its processing, I mean,
you can start to see that if materials like this
have such a big orientation dependence,
and that is so dependent on how they've been processed,
you can't necessarily know the whole processing history
of what you're supplied.
It will be useful to have these quick checks
of the properties of materials that are given to you.
And you wouldn't be able to get that information just
by a bulk compression experiment.
So these carefully designed test patterns are really important.
I should say that this is anisotropy in the material,
not in the stamp.
Because if we rotate the stamp relative to the sample,
the results reverse.
So it's definitely in the material.
Anyhow, that was for TOPAS.
And I showed you a few slides ago what
happens when hold time is relevant,
when you've got plastic flow.
And we saw that the introduction of this linear dashpot,
the scaling of the point load response function
was a reasonably good way of capturing that.
What we're working on now is this ability
to capture yield stress to iron out
some of the shortcomings of the model, the fact
that those narrower features actually filled more
than the model predicted.
And the other thing that we're trying to do
is extend this simulation approach to thin substrates
for the nano imprint lithography case,
where this type of point load response function
isn't correct.
The features are the same size roughly
as the thickness of the substrate.
You have to start thinking about lateral transported material.
And that's quite an exciting topic.
Now, we had a couple of good questions about damage
to the stamp and de-molding issues.
And this is perhaps the biggest impediment
to the use of imprinting, a microscale structure.
There's not that much of a problem for nano imprint.
But microscale structures, it's crucial.
And here are some examples of problems that have occurred
during cooling and de-molding.
This is an SEM picture of a PMMA component
that has been embossed with a hexagonal post.
This was made from silicon, in fact.
And if you imagine the substrate being
mostly on this side of the feature, cooled under load,
the polymer having at least 10 times the thermal expansion
coefficient as silicon, it has pushed itself
against the sides of the features.
And when we de-mold, we get these really substantial
ridges.
I think this was embossed at 130 degree C, 20 degrees
above the glass transition.
And so what we haven't yet worked out
is whether these contact stresses
are large enough actually to push
the stamp off the substrate, or whether it's just
elastic potential energy stored in the polymer
that causes this ridge to spring up when you peel
the stamp off the substrate.
Here are some optical micrographs
showing a similar problem, a triangular hole
embossed into a polymer substrate.
The material is contracted from right
to left relative to the stamp feature.
And in fact, sometimes we see these shards
of polymer being sheared off, and again, a hole where
there's been a few tens of microns relative contraction.
AUDIENCE: I'm curious, is there any sort of like lubricant
that you can use to increase the load?
PROFESSOR: There are products you
can get that you can spray onto the mold,
or, indeed, treatments that can be given to the mold
to reduce the coefficient of friction
between the mold and the substrate.
That won't reduce the magnitude of the lateral force.
That's to do with Young's modulus and the coefficient
of thermal expansion.
But yes, it will potentially make it easier
once that lateral force is exerted to pull the stamp out.
However, it's not-- the problem isn't all to do with friction.
Sometimes you have-- either your stamp is imperfectly made,
and there's a negative draft.
I mean, I exaggerate, but if that were the stamp and that
were the polymer, that's a problem
that people run into quite a lot.
And then if the stamp has been made
by deep, reactive ion etching where
there's this cyclic etching process,
and there are these little, sub micron scallops,
you're susceptible to mechanical locking.
And there's plastic deformation of the polymer
as you pull it off.
So it's a good point.
Yes, and actually, one thing that does work quite well
is to leave the Teflon polymeric coating on the silicon
after etching.
And that does do quite a lot.
It has a very limited lifetime, though.
Anyway, the point of saying all this
is, as I alluded to a few minutes ago,
you might think of reducing the temperature
swing to a small a value as you can
so that amount of thermal contraction is restricted.
You might even think of removing the load slightly
above the glass transition temperature.
And if you're in a region where some
of the deformation, or most of the deformation
is actually plastic, which is true in a region
about 10 degrees above glass transition for PMMA--
if you can exploit the material properties to avoid
having a big temperature swing, then that
could potentially be very exciting.
And together with Matt Dirks, who's
in the lab for manufacturing and productivity,
we looked into this a couple of years ago,
and found that if we control the temperature really carefully,
then it was promising.
If you de-mold at 50 degrees C, so well below glass transition,
and then pull the stamp off-- this is a cross-section through
the part--
then you get this horrendous ridge
on the side of the part nearer the edge,
the side of the feature nearer the edge of the part.
If you de-mold, say, well above glass transition, 120,
you get this blue line.
So you get some bowing of the base of the feature where
material has sprung back.
And you get splaying of the sidewalls.
And this was repeatable over many samples.
However, if we can hit 110 degrees C on the nose,
we get a nice, flat feature.
We get nice, flat sidewalls.
And we get no ridge at all.
And that would be great.
But again, that's the thing.
Can you, in a production setting,
make it 110, and not 115 or 120?
And that, I think, is probably possible to achieve,
but would increase the cost of the apparatus.
So this is definitely something to be aware of.
Another thing that is of importance
is that the risk of the whole part
bowing if the de-molding temperature is too high.
We've observed problems with that.
So that needs to be thought of as well.
Here we can see also that if you're
going to remove the load at or above the glass transition
temperature, you have to pull out the stamp,
cool it down jolly quickly.
Because otherwise the part will start to contract back
to its original flat surface.
And so you leave it for 10 minutes,
things start to look pretty poor.
OK, that is an overview of about half of my thesis.
And since we're at half past 9:00, I think we should stop.
But are there any questions from anyone?
If not, then I guess the floor is open for questions
about the projects.
PROFESSOR: [INAUDIBLE] mention one thing [INAUDIBLE]..
I think later today, hopefully, or by tomorrow at the latest,
I'll post the tentative schedule for what
groups will be presenting on each of Tuesday and Thursday.
It will be in the normal class period.
So we'll plan for that.
And I'll have some other instructions,
like it'll be best, if possible, to send those presentations
to me a little bit early.
I see we do have a USB port.
So it's possible we can add up the presentations on the fly.
I don't know quite how well that works out in Singapore.
We'll have to figure that out as well.
But be alert.
Some of you, based on random draw,
will be doing presentations on Tuesday.
And some groups will be doing that on Thursday.
Are there questions?
AUDIENCE: Is there a rough guideline
for how long the IEEE letter should be?
PROFESSOR: Oh, the IEEE paper?
AUDIENCE: Yeah.
PROFESSOR: I think typically--
whatever it takes to do a reasonable job.
I think something typically on the order
of six, seven, eight pages is, I think,
what we often saw in the past.
Sometimes it might be a little bit shorter,
depending on how much background you have.
So I don't have a strict page guideline.
Good.
Any questions in Singapore on that?
OK, great.
AUDIENCE: Professor.
PROFESSOR: Yes.
AUDIENCE: We have a question for our project.
We actually have two questions.
So one question is that we have two outputs in our--
can you hear me?
PROFESSOR: Yeah, speak up a little bit.
AUDIENCE: OK, so one question is that we have two outputs,
and then we are measuring the data.
But these two outputs, they are negatively correlated.
And our objective is to maximize one output
and minimize the other output.
So we understand that we can do it separately
in our optimization.
But when we want to sort of create
a combined an objective function and optimize these two
together, as they come from the same set of inputs, how can
we do that?
PROFESSOR: Yeah, so the classic approach there
is it's a trade off.
Right?
One or the other.
And what you typically do is apply a weight
to the two alternatives.
So you have a different numeric weight
based on your engineering importance, or the customer
importance, or whatever of the two effects.
So you have one function that combines, say,
squared deviations in the two outputs,
but with a different weight on the two outputs.
AUDIENCE: OK, I see.
PROFESSOR: OK?
You're all set?
AUDIENCE: We have another question actually.
PROFESSOR: Oh, OK.
AUDIENCE: I have one more question.
It's regarding the email you sent us.
So we were told that we can explore one factor [INAUDIBLE]
strategy.
We are not quite sure what strategy you are referring to.
Is it studying the output and one input at a time?
Or is it more like stepwise regression?
PROFESSOR: No, I'm referring to the optimization approach,
the One Factor At a Time, OFAT, that Professor Dan [? Frey ?]
talked about in his lecture.
So where you explore the corners.
You look and see if you've improved it or not,
to decide if you keep that move.
And then once you do make a move,
then you randomly decide which next corner
to experimentally try.
So you've actually got the data already done from a DOE.
But now you can pretend you were actually
running the experiment just one experimental point at a time
using the OFAT approach.
And I think that would be interesting
for online optimization to compare also to response
surface modeling optimization.
AUDIENCE: OK.
All right, thanks.
PROFESSOR: Great, all right.
See you guys later.