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TONIO BUONASSISI: Today
we're going to talk--

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or it's the first
technical discussion

00:00:30.000 --> 00:00:32.490
of the actual solar
cell device itself.

00:00:32.490 --> 00:00:35.140
We talked last
class about the sun

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and about the nature
of the solar resource.

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Today we're going to be talking
about the interaction of light

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with matter.

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In particular, we're
focusing on light absorption.

00:00:44.270 --> 00:00:47.050
This lecture could alternatively
be called "Light Not Getting

00:00:47.050 --> 00:00:50.740
Absorbed" or "Optical Losses."

00:00:50.740 --> 00:00:55.210
Both are important, and both
are related, as we'll see.

00:00:55.210 --> 00:00:58.980
So this is part of the
fundamentals of the course.

00:00:58.980 --> 00:01:01.270
Just to situate
ourselves, we're here

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right now in the fundamentals,
the first third of course.

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Then we'll talk about
the technologies

00:01:05.228 --> 00:01:06.490
and the cross-cutting themes.

00:01:06.490 --> 00:01:07.906
And what we're
going to talk about

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is extremely important
because it allows us

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to understand the technologies.

00:01:12.430 --> 00:01:15.500
Once we begin discussing them
and we discuss cost trade

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offs of implementing
this particular technique

00:01:19.524 --> 00:01:21.190
for the way for it
to absorb more light,

00:01:21.190 --> 00:01:23.920
we can appreciate how
much we can quantify

00:01:23.920 --> 00:01:27.450
the impact of that
technology development,

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and we could also later
on ascribe a cost to it,

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to determine the total
cost benefit analysis.

00:01:34.560 --> 00:01:37.840
So conversion
efficiency is really

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what dictates the performance
of the device, the solar cell

00:01:40.490 --> 00:01:41.550
device.

00:01:41.550 --> 00:01:46.370
It's how the solar cell device
converts sunlight, the input

00:01:46.370 --> 00:01:48.680
energy, to some usable
output energy, which

00:01:48.680 --> 00:01:51.520
is in the form of electricity,
typically, from a solar panel.

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so the electricity
coming out of these

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leads, for instance, right here.

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And that conversion efficiency,
that simple equation,

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for most solar cells, can
break down into the following.

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You have inputs.

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Sorry for the small font here.

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This reads solar spectrum.

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That's your input.

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Your output, which is
the charge collection,

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it's a collective charge
coming out of your device,

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and a bunch of steps in between.

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So from the solar spectrum,
we have to absorb that light,

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then we have to excite
charge within the material.

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Then that charge has to move
around inside the material

00:02:25.940 --> 00:02:29.210
to get to the metallic
context in the front side.

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Charge separation has to occur
for there to be a voltage.

00:02:32.570 --> 00:02:34.890
And finally, the charge
collection process.

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And so the total
efficiency of this device

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is the product of each of
these individual processes.

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And so if you're making
a solar cell device,

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and I know about a third of you
are based on your background

00:02:47.450 --> 00:02:51.650
surveys, this diagram right
here will ring true to you.

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It's Liebig's Law
of the Minimum.

00:02:53.940 --> 00:02:56.630
What this is
representing is a barrel

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that has water being
dripped into it.

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And the water will flow out
of whatever piece of wood

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is the shortest.

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And in the case of
a solar cell device,

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you can ascribe a
certain name to each

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of these pieces of wood.

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We'll learn what each
of those are with time.

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But one of the big
ones is optical losses.

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And the optical losses
tend to be rather severe

00:03:19.140 --> 00:03:21.019
on some of our lab scale cells.

00:03:21.019 --> 00:03:23.060
So one of the easiest ways
of boosting efficiency

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is simply to take care
of your optical losses

00:03:25.920 --> 00:03:29.630
and to minimize the amount of
light reflected or not absorbed

00:03:29.630 --> 00:03:32.320
into maximizing amount of
life that's actually absorbed.

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And so to do that,
there are a number

00:03:33.990 --> 00:03:37.005
of standard techniques and some
cutting edge research areas.

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And I'll attempt to give
you a broad overview

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and survey of both,
assuming, of course,

00:03:41.180 --> 00:03:43.900
you've done your
background reading.

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So the learning
objectives, the first

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is to be able to
calculate the reflectance

00:03:48.290 --> 00:03:51.940
in non-absorption optical
losses of a solar cell.

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So this is essentially all
the light that's not absorbed.

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We want to be able
to calculate that.

00:03:57.590 --> 00:04:00.360
The second is to describe
the physical underpinnings

00:04:00.360 --> 00:04:04.900
and the implementations of four
to five-- there are five here.

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I added one at the end.

00:04:06.790 --> 00:04:10.330
Four to five advanced methods
of reducing optical losses.

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So there are
technologies, techniques

00:04:12.230 --> 00:04:14.870
that we've used that we've
developed over time that we can

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use to minimize
the optical losses,

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to minimize the amount of
light reflected or not absorbed

00:04:20.430 --> 00:04:23.280
inside of a solar cell device.

00:04:23.280 --> 00:04:25.390
So to think of this
pictorially, we

00:04:25.390 --> 00:04:28.120
can come up with the
following diagram, where

00:04:28.120 --> 00:04:31.560
we have some incident energy,
in this case incident light.

00:04:31.560 --> 00:04:32.850
Here's our medium.

00:04:32.850 --> 00:04:34.767
Here's the amount of
light that gets absorbed.

00:04:34.767 --> 00:04:37.016
Here's the amount of light
that gets transmitted right

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through that does not get
absorbed within the material

00:04:39.340 --> 00:04:40.369
upon passing through it.

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And there's a certain
amount of light

00:04:41.910 --> 00:04:44.700
that just gets reflected off
the front of your solar cell

00:04:44.700 --> 00:04:45.480
device.

00:04:45.480 --> 00:04:48.900
We want to, obviously,
maximize this part right here.

00:04:53.260 --> 00:04:55.840
So to begin, we
give a quick review

00:04:55.840 --> 00:04:58.990
of light, the nature of light.

00:04:58.990 --> 00:05:02.310
This is going back to the
particle wave duality of light.

00:05:02.310 --> 00:05:04.790
It will be useful alternatively
to think about light

00:05:04.790 --> 00:05:08.240
as a particle, quant of
light, or to think about light

00:05:08.240 --> 00:05:11.380
as a wave, depending on what
light management technique

00:05:11.380 --> 00:05:13.200
we're going to be describing.

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And in particular, I'd
like to just highlight

00:05:16.830 --> 00:05:18.470
these equations over here.

00:05:18.470 --> 00:05:22.330
The notion that one can define
the energy of a photon coming

00:05:22.330 --> 00:05:25.250
in, and that photon has
a certain wavelength,

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a certain frequency, a
certain wave length associated

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with it-- frequency and
wavelength-- related,

00:05:30.510 --> 00:05:32.030
of course, by the
speed of light,

00:05:32.030 --> 00:05:34.970
Planck's constant, and so forth.

00:05:34.970 --> 00:05:39.100
So just to situate ourselves
with broad numbers,

00:05:39.100 --> 00:05:43.240
so when we dive in and talk
about spatial dimensions

00:05:43.240 --> 00:05:45.150
in relation to the
wavelength of the light,

00:05:45.150 --> 00:05:47.880
we're in a situation
where we can actually

00:05:47.880 --> 00:05:51.250
have a horse sense, a
common sense, about it.

00:05:51.250 --> 00:05:53.490
The visible photon
wavelengths are usually

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in the hundreds of nanometers.

00:05:54.770 --> 00:05:57.980
And the solar spectrum
peaks somewhere around 550,

00:05:57.980 --> 00:06:00.360
just good numbers
to have in mind.

00:06:00.360 --> 00:06:03.940
So this was that solar spectrum,
the integrated solar radiance

00:06:03.940 --> 00:06:05.700
versus wavelength.

00:06:05.700 --> 00:06:10.020
And the second point
that is equally valid,

00:06:10.020 --> 00:06:14.322
we can describe the wavelengths
of the incoming light,

00:06:14.322 --> 00:06:16.030
wavelengths of the
incoming light lambda,

00:06:16.030 --> 00:06:19.390
or we can describe the energies
of the incoming light, this E

00:06:19.390 --> 00:06:21.770
sub ph, the energy
of the photons.

00:06:21.770 --> 00:06:24.410
So just to situate
ourselves again,

00:06:24.410 --> 00:06:27.830
the visible photon energies
are typically in a range of 0.6

00:06:27.830 --> 00:06:31.630
to 6 eV, electron volts,
again, with the peak

00:06:31.630 --> 00:06:34.320
of the solar spectrum at
550 nanometers, somewhere

00:06:34.320 --> 00:06:36.260
around 2.3 eV.

00:06:36.260 --> 00:06:37.430
Good.

00:06:37.430 --> 00:06:42.590
So a simple thing to keep in
mind, for those high energy

00:06:42.590 --> 00:06:44.425
particle physicists
in the room, that when

00:06:44.425 --> 00:06:45.990
we're talking about
visible light,

00:06:45.990 --> 00:06:49.390
we're interacting with a very
specific type of electron

00:06:49.390 --> 00:06:50.580
inside of our system.

00:06:50.580 --> 00:06:51.770
It's the valence electrons.

00:06:51.770 --> 00:06:54.620
These are the electrons that
are typically most loosely bound

00:06:54.620 --> 00:06:56.550
inside of a system
or I would say

00:06:56.550 --> 00:07:01.350
in the outer shells of the
atoms within the material.

00:07:01.350 --> 00:07:04.140
You're typically not interacting
with core shell electrons

00:07:04.140 --> 00:07:05.320
with visible light.

00:07:05.320 --> 00:07:06.790
For that, you need x-rays.

00:07:06.790 --> 00:07:10.650
So this is just something
to keep in mind.

00:07:10.650 --> 00:07:14.125
When we start looking at
the wavelength dependence

00:07:14.125 --> 00:07:16.670
of absorption inside
of a material,

00:07:16.670 --> 00:07:20.690
you can have, for example, in
the visible range, a decreasing

00:07:20.690 --> 00:07:23.660
depth of penetration of the
light with increasing energy,

00:07:23.660 --> 00:07:25.535
whereas with x-rays,
it's the exact opposite.

00:07:25.535 --> 00:07:28.076
It's because you're dealing with
different types of electrons

00:07:28.076 --> 00:07:29.050
and the material.

00:07:29.050 --> 00:07:30.710
So just to situate
ourselves, I know

00:07:30.710 --> 00:07:33.460
we have a fair number physicists
and chemists in the room.

00:07:33.460 --> 00:07:37.750
That's a message
geared toward them.

00:07:37.750 --> 00:07:41.870
Let's describe how light
interacts with matter.

00:07:41.870 --> 00:07:45.640
And first off, come up
with a few variables.

00:07:45.640 --> 00:07:48.690
Define a few units that
will make it easier

00:07:48.690 --> 00:07:52.110
for us to understand how light
is interacting with matter.

00:07:52.110 --> 00:07:53.900
And so here what
I've done for you

00:07:53.900 --> 00:07:57.880
is placed the equation that
describes the complex index

00:07:57.880 --> 00:08:01.270
of refraction of a material.

00:08:01.270 --> 00:08:03.250
What this means,
effectively, you

00:08:03.250 --> 00:08:06.410
can think about this refractive
index of the material

00:08:06.410 --> 00:08:11.250
as being comprised of
two different components.

00:08:11.250 --> 00:08:13.584
For now, it's going
to be fairly cerebral,

00:08:13.584 --> 00:08:15.250
but I'm going to
reduce it to practicing

00:08:15.250 --> 00:08:16.760
in a couple of slides.

00:08:16.760 --> 00:08:19.020
The real component of
the refractive index--

00:08:19.020 --> 00:08:22.150
and the refractive index is
material-specific property.

00:08:22.150 --> 00:08:23.780
So if I have, for
example, silicon

00:08:23.780 --> 00:08:25.430
or if I have silicon
nitride or if I

00:08:25.430 --> 00:08:27.180
have a particular
type of glass, it'll

00:08:27.180 --> 00:08:29.770
have a particular
refractive index.

00:08:29.770 --> 00:08:31.810
It's comprised of a
real component which

00:08:31.810 --> 00:08:34.256
indicates the phase velocity
inside of the material

00:08:34.256 --> 00:08:35.630
and an imaginary
component, which

00:08:35.630 --> 00:08:37.799
can be thought of as an
extinction coefficient.

00:08:37.799 --> 00:08:40.360
And it is related
to the attenuation

00:08:40.360 --> 00:08:44.690
of the light intensity as it
travels through that material.

00:08:44.690 --> 00:08:47.700
The measurements for those who
have already taken measurements

00:08:47.700 --> 00:08:50.450
before on a spectroscopic
ellipsometer, this

00:08:50.450 --> 00:08:53.921
is how you measure that
parameter up there.

00:08:53.921 --> 00:08:55.670
We don't have to dive
too deeply into that

00:08:55.670 --> 00:08:56.970
for the purposes of the class.

00:08:56.970 --> 00:08:59.340
It's just for background.

00:08:59.340 --> 00:09:02.700
Why these values are
important-- these values

00:09:02.700 --> 00:09:05.450
here describe the interaction
of light inside of a medium,

00:09:05.450 --> 00:09:07.160
inside of a material.

00:09:07.160 --> 00:09:09.410
And we use that
information to calculate

00:09:09.410 --> 00:09:12.700
engineering relevant parameters
such as reflectance of light

00:09:12.700 --> 00:09:14.410
off of a surface.

00:09:14.410 --> 00:09:17.920
So if we want to calculate what
is the reflectance of light off

00:09:17.920 --> 00:09:20.780
of the silicon right
here, I can calculate it

00:09:20.780 --> 00:09:22.550
by knowing these
properties right here,

00:09:22.550 --> 00:09:25.260
by knowing the real and
imaginary components

00:09:25.260 --> 00:09:30.140
of the refractive index
of silicon, in this case.

00:09:30.140 --> 00:09:32.060
And the reason
that's important is

00:09:32.060 --> 00:09:35.280
because we want to minimize
reflection off of surfaces.

00:09:35.280 --> 00:09:37.000
So I've come up with
the first equation

00:09:37.000 --> 00:09:40.850
right here which is describing
the reflectance from air

00:09:40.850 --> 00:09:43.530
to a solid, in this
case, from air where

00:09:43.530 --> 00:09:46.540
the refractive index
is 1 to a solid,

00:09:46.540 --> 00:09:48.720
namely, say for example,
silicon right here

00:09:48.720 --> 00:09:53.160
or glass, which has a finite
refractive index typically

00:09:53.160 --> 00:09:54.750
greater than 1.

00:09:54.750 --> 00:09:57.750
And so I have an equation here
that describes the reflectance.

00:09:57.750 --> 00:09:59.390
Let me dive a little
deeper into it

00:09:59.390 --> 00:10:01.050
and try to understand
what exactly

00:10:01.050 --> 00:10:03.290
that equation is telling me.

00:10:03.290 --> 00:10:07.170
So from the folks who have
studied mechanics, many of you

00:10:07.170 --> 00:10:09.190
are mechanical
engineers in the room,

00:10:09.190 --> 00:10:11.820
you may recall studying a
problem wherein you have

00:10:11.820 --> 00:10:14.130
two springs that are connected.

00:10:14.130 --> 00:10:16.390
They have different
spring constants,

00:10:16.390 --> 00:10:18.330
different stiffnesses,
shall we say.

00:10:18.330 --> 00:10:19.830
And you excite a wave over here.

00:10:19.830 --> 00:10:20.840
It travels down.

00:10:20.840 --> 00:10:22.930
And when it reaches the
interface between the two,

00:10:22.930 --> 00:10:24.346
part of the wave
is reflected back

00:10:24.346 --> 00:10:26.140
and part continues through.

00:10:26.140 --> 00:10:29.900
The speed of the
wave is changing

00:10:29.900 --> 00:10:31.810
as it goes from one
spring to the other,

00:10:31.810 --> 00:10:34.530
because the stiffness is
changing of the springs.

00:10:34.530 --> 00:10:37.670
And the amount reflected can
be described by this equation

00:10:37.670 --> 00:10:40.250
right here, which looks
awfully like the equation

00:10:40.250 --> 00:10:42.810
right above it, which is
describing the amount of light

00:10:42.810 --> 00:10:44.320
reflected off of an interface.

00:10:44.320 --> 00:10:49.500
And in reality, those ends have
a very similar meaning, the n

00:10:49.500 --> 00:10:50.270
and the z.

00:10:50.270 --> 00:10:51.770
The n, in the case
of light, which

00:10:51.770 --> 00:10:53.783
is the real components
of the refractive index.

00:10:53.783 --> 00:10:57.710
Mind you, this
parameter right here,

00:10:57.710 --> 00:10:59.460
this indicates phase
velocity in material.

00:10:59.460 --> 00:11:02.500
It could also be
thought of very loosely

00:11:02.500 --> 00:11:04.980
as the ability of an
electromagnetic wave coming

00:11:04.980 --> 00:11:08.280
into material to slosh
those electrons around.

00:11:08.280 --> 00:11:09.890
Not exactly a
stiffness coefficient,

00:11:09.890 --> 00:11:13.100
but it bears some
rough resemblance.

00:11:13.100 --> 00:11:16.350
So this is a method for
you to gain a foothold

00:11:16.350 --> 00:11:18.780
in this new area
of understanding

00:11:18.780 --> 00:11:20.820
the refractive
index of a material

00:11:20.820 --> 00:11:24.190
based on something you've
already seen before.

00:11:24.190 --> 00:11:26.660
So I would advise
taking this analogy

00:11:26.660 --> 00:11:28.770
as far as it will go
until it breaks down.

00:11:28.770 --> 00:11:30.840
Push it as far as it goes
until it breaks down.

00:11:30.840 --> 00:11:32.830
And you'll see at some
point it actually does,

00:11:32.830 --> 00:11:36.820
but it's a useful
place to start.

00:11:36.820 --> 00:11:40.020
So I'm going to ask you
a couple of questions.

00:11:40.020 --> 00:11:43.712
This might be rather
new for a lot of folks.

00:11:43.712 --> 00:11:45.420
But the purpose of
asking these questions

00:11:45.420 --> 00:11:46.500
is to get you thinking.

00:11:46.500 --> 00:11:49.110
And eventually we'll get
to a point of heightened

00:11:49.110 --> 00:11:51.860
understanding as a result.

00:11:51.860 --> 00:11:54.300
Tinted windows.

00:11:54.300 --> 00:11:57.220
So if you have a
tinted window, what

00:11:57.220 --> 00:12:00.010
is typically happening
at that tinted window?

00:12:00.010 --> 00:12:03.122
Why can't you see inside?

00:12:03.122 --> 00:12:04.580
What would you
imagine is going on?

00:12:04.580 --> 00:12:06.510
So let me go back to
this reflectance equation

00:12:06.510 --> 00:12:10.000
right here, this one.

00:12:10.000 --> 00:12:11.990
How would you modify
a reflectance off

00:12:11.990 --> 00:12:13.910
of a window, let's say?

00:12:13.910 --> 00:12:16.030
And let's drop the k's for now.

00:12:16.030 --> 00:12:19.350
Let's leave those aside and
just focus on this parameter

00:12:19.350 --> 00:12:21.660
right here, n minus
1 quantity squared

00:12:21.660 --> 00:12:23.560
n plus 1 quantity squared.

00:12:23.560 --> 00:12:28.110
What would increase the
reflectance off of that window,

00:12:28.110 --> 00:12:29.800
if I have a larger
n or a smaller n?

00:12:34.750 --> 00:12:38.660
If I have a bigger n, I
would get bigger reflectance.

00:12:38.660 --> 00:12:39.686
Is that right?

00:12:39.686 --> 00:12:42.851
r goes up?

00:12:42.851 --> 00:12:45.460
Well, you'd have to
plot it out, I guess.

00:12:45.460 --> 00:12:49.280
So if I change the refractive
index of the material

00:12:49.280 --> 00:12:52.175
that I am working with, I can
change the reflectivity off

00:12:52.175 --> 00:12:54.080
of that interface,
off of that surface.

00:12:54.080 --> 00:12:55.870
So if I add a
coating, for instance,

00:12:55.870 --> 00:12:59.720
to a window that increases
the reflectivity,

00:12:59.720 --> 00:13:05.600
then the amount of light that is
able to escape from the inside

00:13:05.600 --> 00:13:07.070
to my eyes decreases.

00:13:07.070 --> 00:13:10.010
Now, with normal
incident light, there

00:13:10.010 --> 00:13:11.810
is a beautiful
symmetry involved.

00:13:11.810 --> 00:13:14.710
That is, the amount
reflected off of one side

00:13:14.710 --> 00:13:18.960
is equal to the amount of light
reflected off the other side.

00:13:18.960 --> 00:13:23.830
So just the same way that
I'm losing the ability

00:13:23.830 --> 00:13:26.180
to see inside, the
folks inside are also

00:13:26.180 --> 00:13:27.740
losing the ability to see out.

00:13:27.740 --> 00:13:29.330
But they can still see out.

00:13:29.330 --> 00:13:31.090
Why is that?

00:13:31.090 --> 00:13:34.230
Why is it that with
the same reflectivity

00:13:34.230 --> 00:13:36.030
they're able to see
outside and I'm not

00:13:36.030 --> 00:13:38.321
able to see in through that
tinted window, through that

00:13:38.321 --> 00:13:41.630
car, for example, that's driving
by with the tinted glass?

00:13:41.630 --> 00:13:44.970
Why can't I see insight but they
can see out, what's going on?

00:13:44.970 --> 00:13:46.404
AUDIENCE: [INAUDIBLE].

00:13:46.404 --> 00:13:48.070
TONIO BUONASSISI:
Yeah, I hear somebody.

00:13:48.070 --> 00:13:49.486
AUDIENCE: The light
on the outside

00:13:49.486 --> 00:13:52.256
is much stronger in terms of
an absolute amount of light

00:13:52.256 --> 00:13:53.109
being reflected.

00:13:53.109 --> 00:13:54.400
TONIO BUONASSISI: Yep, exactly.

00:13:54.400 --> 00:13:57.700
So yes, the reflectivity
as a percentage

00:13:57.700 --> 00:14:00.247
is the same for both parties.

00:14:00.247 --> 00:14:01.830
But the amount of
light, the magnitude

00:14:01.830 --> 00:14:04.280
of the light from the
outside, is much, much greater

00:14:04.280 --> 00:14:05.580
than it is on the inside.

00:14:05.580 --> 00:14:07.620
Can anybody give me
just a gut sense.

00:14:07.620 --> 00:14:10.190
If I'm outside on a sunny
day, how much brighter

00:14:10.190 --> 00:14:13.180
is it outside versus
inside right here?

00:14:13.180 --> 00:14:15.130
Factor of?

00:14:15.130 --> 00:14:17.130
AUDIENCE: 100, maybe?

00:14:17.130 --> 00:14:19.940
TONIO BUONASSISI: Maybe a factor
of 10, somewhere in that range.

00:14:19.940 --> 00:14:22.742
And so when you walk
outside on a sunny day,

00:14:22.742 --> 00:14:24.700
you'll notice your eyes
adjusting a little bit.

00:14:24.700 --> 00:14:25.727
It'll take a minute.

00:14:25.727 --> 00:14:28.060
And when we walk back inside,
it will take a minute here

00:14:28.060 --> 00:14:29.460
for your eyes to adjust as well.

00:14:29.460 --> 00:14:31.460
That's because of the
difference in intensities.

00:14:31.460 --> 00:14:33.880
So if you imagine being
outside of that car

00:14:33.880 --> 00:14:40.147
and having 10 times the amount
of light being reflected,

00:14:40.147 --> 00:14:42.480
that small amount of light
that is actually transmitting

00:14:42.480 --> 00:14:44.680
through the window from the
car to the outside world

00:14:44.680 --> 00:14:48.280
will be washed out by the
amount of reflected light.

00:14:48.280 --> 00:14:50.460
Whereas if you're
inside the car,

00:14:50.460 --> 00:14:52.636
there's a lot of light
coming through that window,

00:14:52.636 --> 00:14:54.260
even though a lot of
it gets reflected,

00:14:54.260 --> 00:14:56.177
there's still a sizable
amount coming through.

00:14:56.177 --> 00:14:57.551
And the amount of
light that gets

00:14:57.551 --> 00:14:59.700
reflected off that window
of the internal light

00:14:59.700 --> 00:15:02.540
is small in relation to
the outside light that

00:15:02.540 --> 00:15:04.360
is being transmitted
through that window.

00:15:04.360 --> 00:15:08.897
So it's important to think
about these processes,

00:15:08.897 --> 00:15:10.980
both in terms of their
reflectance as a percentage

00:15:10.980 --> 00:15:14.880
but also the magnitudes
of the light involved.

00:15:14.880 --> 00:15:17.090
What if that glass pane
was flipped around?

00:15:17.090 --> 00:15:18.195
Would it change anything?

00:15:18.195 --> 00:15:24.960
If I took that glass and just
flipped it, would it change it?

00:15:24.960 --> 00:15:28.930
What about the
symmetry argument,

00:15:28.930 --> 00:15:32.270
that the amount of light is
reflected, the r reflectance,

00:15:32.270 --> 00:15:33.935
is the same from both sides?

00:15:33.935 --> 00:15:35.643
AUDIENCE: Is it not
the case that there's

00:15:35.643 --> 00:15:37.607
a coating on the outside?

00:15:37.607 --> 00:15:41.044
So if the change
in refracted index

00:15:41.044 --> 00:15:43.324
is an abrupt change
from the outside looking

00:15:43.324 --> 00:15:43.990
at this coating.

00:15:43.990 --> 00:15:45.448
Because on the
inside, you're going

00:15:45.448 --> 00:15:48.900
through some median glass,
which is more index matched

00:15:48.900 --> 00:15:49.900
than the outside.

00:15:49.900 --> 00:15:51.350
TONIO BUONASSISI:
Yeah, so I would

00:15:51.350 --> 00:15:53.580
advise you to actually walk
through that calculation.

00:15:53.580 --> 00:15:56.361
And what you'll find is it
winds up being the same.

00:15:56.361 --> 00:15:58.610
And it's because you have
to take all reflectances off

00:15:58.610 --> 00:16:01.730
of all these interfaces
into account.

00:16:01.730 --> 00:16:05.000
There are, in fact, three
interfaces-- the air,

00:16:05.000 --> 00:16:08.400
the glass; the glass, the
anti-reflection coding;

00:16:08.400 --> 00:16:10.700
and the anti-reflection
coding, the outside.

00:16:10.700 --> 00:16:14.110
This, of course, without getting
into quarter wave effects,

00:16:14.110 --> 00:16:18.480
which we'll get into
a minute, there's

00:16:18.480 --> 00:16:21.119
some higher order effects that
deal with phase change, which

00:16:21.119 --> 00:16:22.410
we haven't discussed right now.

00:16:22.410 --> 00:16:25.120
We're just assuming
that all of these layers

00:16:25.120 --> 00:16:28.960
are well above the wavelength of
the light in terms of thickness

00:16:28.960 --> 00:16:33.890
and that these equations, these
linear equations, are valid.

00:16:33.890 --> 00:16:34.670
Very good.

00:16:34.670 --> 00:16:37.800
So this is just
to get us situated

00:16:37.800 --> 00:16:39.900
with this new concept
of reflectance--

00:16:39.900 --> 00:16:43.200
and again, very
powerful equation.

00:16:43.200 --> 00:16:45.610
Keep in mind that this
is a very specific form

00:16:45.610 --> 00:16:47.491
of the reflectance from
an air into a solid.

00:16:47.491 --> 00:16:49.240
If you're going from
a solid into a solid,

00:16:49.240 --> 00:16:53.000
you'll add your n1
and your n2, depending

00:16:53.000 --> 00:17:00.030
on what material going into and
what material are coming from.

00:17:00.030 --> 00:17:04.569
So we're happy to walk through
that perhaps during recitation.

00:17:04.569 --> 00:17:06.760
OK, so what we're
going to do now

00:17:06.760 --> 00:17:09.344
is we've talked about
reflectance off of surfaces.

00:17:09.344 --> 00:17:11.510
What I'd like to do is talk
about a light absorption

00:17:11.510 --> 00:17:12.759
inside of a material.

00:17:12.759 --> 00:17:15.050
So let's imagine that through
the techniques that we're

00:17:15.050 --> 00:17:16.880
going to be discussing
later on in lecture,

00:17:16.880 --> 00:17:18.619
we manage to minimize
the amount of reflectance

00:17:18.619 --> 00:17:19.700
off the front surface.

00:17:19.700 --> 00:17:21.900
And now the light that's
incident on the material

00:17:21.900 --> 00:17:24.050
is actually going to go
inside and get absorbed

00:17:24.050 --> 00:17:25.630
by the material inside.

00:17:25.630 --> 00:17:28.390
We need to be able to understand
how light gets absorbed inside

00:17:28.390 --> 00:17:29.380
of matter.

00:17:29.380 --> 00:17:33.860
And for that, we apply a very
simple formulation inside

00:17:33.860 --> 00:17:37.000
of this class, which is called
Beer-Lambert's Law, which

00:17:37.000 --> 00:17:41.630
is a very simple
yet very powerful

00:17:41.630 --> 00:17:44.320
formulation that describes not
only the interaction of light

00:17:44.320 --> 00:17:45.861
with the solar cell
material but also

00:17:45.861 --> 00:17:48.850
light through the
atmosphere, light the water,

00:17:48.850 --> 00:17:51.490
many other forms of
optical absorption.

00:17:51.490 --> 00:17:55.120
And for that, I'd like to
call Joe up for a quick demo

00:17:55.120 --> 00:17:59.690
that he put together that will
allow us to actually plot out

00:17:59.690 --> 00:18:00.980
Beer-Lambert's Law.

00:18:00.980 --> 00:18:04.180
And I'd like to start
with what I would think

00:18:04.180 --> 00:18:05.710
of as a simple hypothesis.

00:18:05.710 --> 00:18:07.485
What we're going to
be doing, and Joe

00:18:07.485 --> 00:18:09.818
will explain this a minute,
what we're going to be doing

00:18:09.818 --> 00:18:13.080
is taking many
sheets of material.

00:18:13.080 --> 00:18:15.420
This is just some
polyethylene material,

00:18:15.420 --> 00:18:16.830
a little bit discolored.

00:18:16.830 --> 00:18:20.356
And we're going to shine a laser
down on to this photodiode.

00:18:20.356 --> 00:18:21.980
The photodiode current
will be measured

00:18:21.980 --> 00:18:23.730
by this little current
meter right here.

00:18:23.730 --> 00:18:27.870
And we'll be inserting these
panes of plastic in the middle.

00:18:27.870 --> 00:18:30.590
And as we increase the
thickness of the plastic,

00:18:30.590 --> 00:18:32.190
applying good
pressure in between

00:18:32.190 --> 00:18:36.530
to minimize the reflectance,
the air gap, for instance--

00:18:36.530 --> 00:18:39.490
as we increase the thickness
of the polyethylene,

00:18:39.490 --> 00:18:42.140
we will plot the total
transmitted light

00:18:42.140 --> 00:18:43.645
as measured by that photodiode.

00:18:43.645 --> 00:18:46.890
And so I'm going to come up
with a hypothesis of what's

00:18:46.890 --> 00:18:47.844
going to happen.

00:18:47.844 --> 00:18:49.260
I'm going to say
that if we double

00:18:49.260 --> 00:18:51.870
the thickness of
the polyethylene

00:18:51.870 --> 00:18:54.440
that we're going to halve the
amount of light going through.

00:18:54.440 --> 00:18:57.260
And if we triple, we're going
to reduce it by a third.

00:18:57.260 --> 00:19:00.000
And if we quadruple, we're
going to reduce it by a fourth.

00:19:00.000 --> 00:19:02.316
And let's see if the
hypothesis is correct.

00:19:02.316 --> 00:19:03.250
It's not.

00:19:03.250 --> 00:19:05.220
But we're going to test it.

00:19:05.220 --> 00:19:08.475
And it's a logical
thing you might assume.

00:19:08.475 --> 00:19:10.350
And then we'll walk
through a derivation that

00:19:10.350 --> 00:19:12.972
will correct our missed logic.

00:19:12.972 --> 00:19:13.680
So go ahead, Joe.

00:19:13.680 --> 00:19:14.221
Take it away.

00:19:14.221 --> 00:19:17.102
JOE: Sure, so if you guys want
to play along, that's fine too.

00:19:17.102 --> 00:19:19.060
I know there's lines in
the side of your notes.

00:19:19.060 --> 00:19:21.807
You can make little graph
paper, and it comes out

00:19:21.807 --> 00:19:23.050
looking really nice.

00:19:23.050 --> 00:19:26.117
So basically what we have is a
laser pointed and a photodiode.

00:19:26.117 --> 00:19:27.700
And the current out
of this photodiode

00:19:27.700 --> 00:19:31.080
is directly proportional to the
light hitting that photodiode.

00:19:31.080 --> 00:19:32.802
And it has a quant
efficiency, which

00:19:32.802 --> 00:19:34.968
we're going to learn what
that is in a few lectures,

00:19:34.968 --> 00:19:35.780
of about 60%.

00:19:35.780 --> 00:19:37.980
So of the photons
hitting it, you'll

00:19:37.980 --> 00:19:39.567
get a certain number
of electrons out,

00:19:39.567 --> 00:19:41.547
and that ratio's 60%.

00:19:41.547 --> 00:19:43.172
And so first of all,
we're going to see

00:19:43.172 --> 00:19:46.620
what it's like, what
the power of our-- yeah.

00:19:46.620 --> 00:19:51.480
So right now we're getting
about 1.32 milliamps.

00:19:51.480 --> 00:19:53.200
So Tonio's going to plot that.

00:19:53.200 --> 00:19:57.130
Then as we keep increasing and
put one layer of polyethylene,

00:19:57.130 --> 00:20:00.005
that drops to 0.75.

00:20:00.005 --> 00:20:01.380
TONIO BUONASSISI:
So before we go

00:20:01.380 --> 00:20:03.200
onto the next one,
what do people

00:20:03.200 --> 00:20:10.110
predict the next dot is going
to drop the total intensity to?

00:20:10.110 --> 00:20:13.386
Is it going to be kind of
a linear line like that?

00:20:13.386 --> 00:20:15.510
You'd expect it, right,
because you're doubling it.

00:20:15.510 --> 00:20:19.680
So you'd expect the intensity
to drop by another factor of 2.

00:20:19.680 --> 00:20:21.150
Why not?

00:20:21.150 --> 00:20:24.200
Where am I getting
a mistake here?

00:20:24.200 --> 00:20:26.225
Somebody says exponential.

00:20:26.225 --> 00:20:28.600
There's kind of this sense
that it should be exponential.

00:20:28.600 --> 00:20:31.040
What don't we add some
more filter in front,

00:20:31.040 --> 00:20:33.830
and we'll see what exactly
this comes out to be.

00:20:33.830 --> 00:20:34.747
JOE: This is with two.

00:20:34.747 --> 00:20:35.663
TONIO BUONASSISI: Two.

00:20:35.663 --> 00:20:36.630
JOE: Now we get 0.43.

00:20:36.630 --> 00:20:38.142
TONIO BUONASSISI: 0.43.

00:20:38.142 --> 00:20:38.910
OK.

00:20:38.910 --> 00:20:39.410
All right.

00:20:39.410 --> 00:20:42.070
Why don't we do one more just
to see what sort of trend

00:20:42.070 --> 00:20:42.775
we're getting.

00:20:42.775 --> 00:20:43.540
Still 0.26.

00:20:43.540 --> 00:20:44.276
JOE: 0.26.

00:20:44.276 --> 00:20:46.589
TONIO BUONASSISI: 0.26.

00:20:46.589 --> 00:20:48.450
Ah, wow.

00:20:48.450 --> 00:20:50.870
OK, so it didn't go
in a straight line.

00:20:50.870 --> 00:20:52.520
It's actually starting
to curve down.

00:20:52.520 --> 00:20:52.640
Cool.

00:20:52.640 --> 00:20:53.139
OK.

00:20:53.139 --> 00:20:55.022
JOE: And we keep going, 0.16.

00:20:55.022 --> 00:20:59.570
TONIO BUONASSISI: 0.16

00:20:59.570 --> 00:21:00.970
JOE: 0.10

00:21:00.970 --> 00:21:02.884
TONIO BUONASSISI: 0.10.

00:21:02.884 --> 00:21:04.230
OK.

00:21:04.230 --> 00:21:05.570
Look at that.

00:21:05.570 --> 00:21:08.060
What sort of curve is it?

00:21:08.060 --> 00:21:09.150
Exponential.

00:21:09.150 --> 00:21:10.975
It looks like one at least.

00:21:10.975 --> 00:21:12.850
And we can test whether
or not the hypothesis

00:21:12.850 --> 00:21:16.870
is correct by an
exponential fit, which

00:21:16.870 --> 00:21:18.990
happens to match pretty well.

00:21:18.990 --> 00:21:19.792
So--

00:21:19.792 --> 00:21:21.500
JOE: Now one other
quick thing you notice

00:21:21.500 --> 00:21:24.900
is that if you look at the fit,
the first point's a little bit

00:21:24.900 --> 00:21:26.304
higher than that fit.

00:21:26.304 --> 00:21:29.790
Anyone have an idea of why
that might be the case?

00:21:29.790 --> 00:21:31.920
What are we ignoring
in this experiment?

00:21:31.920 --> 00:21:34.145
AUDIENCE: The reflection
is [INAUDIBLE].

00:21:34.145 --> 00:21:35.450
JOE: The reflections, yeah.

00:21:35.450 --> 00:21:38.350
So in the first one,
you reflect light,

00:21:38.350 --> 00:21:40.771
and certain amount
gets transmitted

00:21:40.771 --> 00:21:42.976
through that front
surface than absorbs.

00:21:42.976 --> 00:21:46.784
And so right now we're ignoring
this is 1 minus r component.

00:21:46.784 --> 00:21:48.450
But it's so small
that it really doesn't

00:21:48.450 --> 00:21:49.576
matter for this experiment.

00:21:49.576 --> 00:21:51.326
These things don't
reflect a lot of light.

00:21:54.352 --> 00:21:55.310
TONIO BUONASSISI: Cool.

00:21:55.310 --> 00:21:57.324
Well, why don't we
give a quick rondo.

00:21:57.324 --> 00:21:58.312
[APPLAUSE]

00:21:58.312 --> 00:22:00.191
Well done.

00:22:00.191 --> 00:22:01.190
Can I grab one of those?

00:22:01.190 --> 00:22:01.430
JOE: Absolutely.

00:22:01.430 --> 00:22:02.280
TONIO BUONASSISI:
This is going to be

00:22:02.280 --> 00:22:04.180
important for the
immersion scattering demo.

00:22:04.180 --> 00:22:05.100
JOE: Oh, sure.

00:22:05.100 --> 00:22:06.016
TONIO BUONASSISI: Yep.

00:22:06.016 --> 00:22:06.690
Cool.

00:22:06.690 --> 00:22:10.970
OK, so we notice that we have
some exponential character

00:22:10.970 --> 00:22:14.720
to be decay of the intensity
of the transmitted light

00:22:14.720 --> 00:22:16.220
through a medium.

00:22:16.220 --> 00:22:19.350
And the amount that's absorbed
is following another trend,

00:22:19.350 --> 00:22:21.054
which is just 1 minus that.

00:22:21.054 --> 00:22:22.470
So it's the amount
of light that's

00:22:22.470 --> 00:22:26.800
absorbed is following a curve
looks something like that.

00:22:26.800 --> 00:22:31.770
OK, so let's look through the
formalism of Beer-Lambert Law

00:22:31.770 --> 00:22:34.290
and try to understand
why it is that we come up

00:22:34.290 --> 00:22:37.310
with that exponential
function right here.

00:22:37.310 --> 00:22:42.290
So if we assume that light
is coming in a medium

00:22:42.290 --> 00:22:46.340
and light is decaying in
some function to that medium

00:22:46.340 --> 00:22:49.024
and a certain amount of
light is transmitted,

00:22:49.024 --> 00:22:50.940
we know, of course, from
our little experiment

00:22:50.940 --> 00:22:53.120
that it follows some
exponential function.

00:22:53.120 --> 00:22:55.157
But how do we justify
that to ourselves?

00:22:55.157 --> 00:22:57.240
Well, first off, we're
going to ignore reflections

00:22:57.240 --> 00:22:58.647
off the front surface.

00:22:58.647 --> 00:22:59.730
We just talked about them.

00:22:59.730 --> 00:23:01.070
We can calculate them.

00:23:01.070 --> 00:23:03.879
Let's leave that aside for
now as a parallel calculation.

00:23:03.879 --> 00:23:05.670
We're just concerning
ourselves with what's

00:23:05.670 --> 00:23:07.790
happening inside of the medium.

00:23:07.790 --> 00:23:10.390
So if we assume that
the change of intensity

00:23:10.390 --> 00:23:13.830
within that medium in each
little delta thickness

00:23:13.830 --> 00:23:18.010
is going to be affected by some
sort of scattering intensity

00:23:18.010 --> 00:23:21.930
within the medium--
and this sigma here

00:23:21.930 --> 00:23:24.020
can refer to a
variety of processes.

00:23:24.020 --> 00:23:26.750
That can refer to
absorption events

00:23:26.750 --> 00:23:29.770
that result in the
generation of free charge.

00:23:29.770 --> 00:23:32.290
They can refer to
absorption events that

00:23:32.290 --> 00:23:35.340
just heat the material up
and generate phonons, so

00:23:35.340 --> 00:23:36.800
lattice vibrations.

00:23:36.800 --> 00:23:39.920
There are a number of processes
embedded in the sigma,

00:23:39.920 --> 00:23:42.604
and that's why this formalism
is so powerful, because it

00:23:42.604 --> 00:23:45.020
doesn't care really what the
physical nature of that sigma

00:23:45.020 --> 00:23:45.640
is.

00:23:45.640 --> 00:23:50.140
It just matters that there is
an absorption per unit distance

00:23:50.140 --> 00:23:52.320
thickness traveled inside
of the material that

00:23:52.320 --> 00:23:54.930
is constant throughout
the entire material.

00:23:54.930 --> 00:23:58.750
So the sigma here is independent
of thickness throughout.

00:23:58.750 --> 00:24:00.680
And then as you integrate
through, you wind up

00:24:00.680 --> 00:24:04.440
with that beautiful exponential
function at the end,

00:24:04.440 --> 00:24:08.740
the sigma l times n.

00:24:08.740 --> 00:24:11.380
We collapse the n and the
sigma here into an alpha.

00:24:11.380 --> 00:24:13.950
That alpha is an
absorption coefficient.

00:24:13.950 --> 00:24:17.460
The l is the total length or the
total thickness of this medium

00:24:17.460 --> 00:24:18.430
right here.

00:24:18.430 --> 00:24:20.700
So if we increase
the total thickness,

00:24:20.700 --> 00:24:23.500
we're going to decrease
the total amount of light

00:24:23.500 --> 00:24:25.790
coming through via that
exponential function.

00:24:25.790 --> 00:24:28.380
The alpha, on the other hand,
is not a geometric parameter.

00:24:28.380 --> 00:24:31.240
It's an intrinsic
material parameter.

00:24:31.240 --> 00:24:33.379
To put that in terms of
mechanical engineering,

00:24:33.379 --> 00:24:35.420
for many of the mechanical
engineers in the room,

00:24:35.420 --> 00:24:38.400
you recall from solid
mechanics, 2001,

00:24:38.400 --> 00:24:41.370
that you have geometric
parameters that determine, say

00:24:41.370 --> 00:24:44.120
for example, structural
response and intrinsic material

00:24:44.120 --> 00:24:46.630
parameters like
Young's modulus that

00:24:46.630 --> 00:24:49.530
determine the structural
response of a system.

00:24:49.530 --> 00:24:51.930
And likewise in
here, in the optical,

00:24:51.930 --> 00:24:55.030
shall we say, response, we
have a fundamental intrinsic

00:24:55.030 --> 00:24:57.970
material parameter, r alpha,
the absorption coefficient,

00:24:57.970 --> 00:25:02.750
and the geometric parameter,
rl, which is the thickness.

00:25:02.750 --> 00:25:04.700
And the beauty of
this formalism right

00:25:04.700 --> 00:25:07.100
here is that we can
measure, experimentally

00:25:07.100 --> 00:25:10.300
just like we did right there,
our alphas for materials.

00:25:10.300 --> 00:25:12.220
And so from an
engineering point of view,

00:25:12.220 --> 00:25:15.100
we don't really--
to first order,

00:25:15.100 --> 00:25:17.582
it doesn't really matter
what sort of scattering

00:25:17.582 --> 00:25:19.290
or absorption process
is happening inside

00:25:19.290 --> 00:25:21.215
of a material for us
to calculate the amount

00:25:21.215 --> 00:25:22.090
of transmitted light.

00:25:22.090 --> 00:25:23.760
We just need to know the alpha.

00:25:23.760 --> 00:25:27.650
We need to know the optical
absorption coefficient.

00:25:27.650 --> 00:25:32.205
This alpha will vary as a
function of wavelength inside

00:25:32.205 --> 00:25:33.580
of a material
because, obviously,

00:25:33.580 --> 00:25:36.280
the physical absorption
mechanisms are varying

00:25:36.280 --> 00:25:37.480
as a function of wavelength.

00:25:37.480 --> 00:25:39.740
The resonances with
different electronic states

00:25:39.740 --> 00:25:41.642
within the material,
that light, depends

00:25:41.642 --> 00:25:43.850
on the energy of the light,
depends on the frequency.

00:25:43.850 --> 00:25:45.308
So there's a
wavelength dependence.

00:25:47.740 --> 00:25:52.190
Yeah, and that general
equation is the same one that

00:25:52.190 --> 00:25:56.010
drives the reduction
of light intensity

00:25:56.010 --> 00:25:57.600
as it travels through
the atmosphere.

00:25:57.600 --> 00:25:59.517
So if we increase the
atmospheric path length,

00:25:59.517 --> 00:26:01.975
we'll be reducing the amount
of light that actually reaches

00:26:01.975 --> 00:26:03.400
the surface of the earth.

00:26:03.400 --> 00:26:06.120
That's at air mass
two or air mass three,

00:26:06.120 --> 00:26:08.430
there's less solar
flux coming down

00:26:08.430 --> 00:26:11.231
than at air mass one
or air mass zero.

00:26:11.231 --> 00:26:12.730
The alpha, obviously,
is going to be

00:26:12.730 --> 00:26:14.110
very different
for our atmosphere

00:26:14.110 --> 00:26:17.196
than it was for these
little polyethylene sheets.

00:26:17.196 --> 00:26:19.320
Because the nature of the
scattering and absorption

00:26:19.320 --> 00:26:21.540
processes are very
different for the atmosphere

00:26:21.540 --> 00:26:25.750
than it is for here, the density
of the material and so forth.

00:26:25.750 --> 00:26:26.860
Any questions?

00:26:26.860 --> 00:26:27.514
Yes?

00:26:27.514 --> 00:26:29.170
AUDIENCE: What was n?

00:26:29.170 --> 00:26:33.680
TONIO BUONASSISI: So the n,
there's a certain scattering

00:26:33.680 --> 00:26:37.040
intensity, and then there's
a certain number density,

00:26:37.040 --> 00:26:38.800
for example, of the material.

00:26:38.800 --> 00:26:46.210
So this alpha here is, I
would say, density neutral.

00:26:46.210 --> 00:26:52.850
What we've done is we have
the alpha encapsulating

00:26:52.850 --> 00:26:54.820
the physical parameters
of the material

00:26:54.820 --> 00:26:58.860
and the absorption processes
all in one variable,

00:26:58.860 --> 00:27:01.080
very nicely and succinctly.

00:27:01.080 --> 00:27:03.740
And the only geometric
parameter that is of essence

00:27:03.740 --> 00:27:06.840
is really our l.

00:27:06.840 --> 00:27:08.840
AUDIENCE: It's called an
absorption coefficient,

00:27:08.840 --> 00:27:12.298
but is it more of an
extension coefficient, really?

00:27:12.298 --> 00:27:15.969
Because it's kind of confusing
that it includes scattering.

00:27:15.969 --> 00:27:18.260
TONIO BUONASSISI: The extension
coefficient, absorption

00:27:18.260 --> 00:27:23.750
coefficient, yes,
in solar research,

00:27:23.750 --> 00:27:25.820
when we talk about an
absorption coefficient

00:27:25.820 --> 00:27:27.570
inside of a material.

00:27:27.570 --> 00:27:31.390
Oftentimes we're operating in
a wavelength regime of light

00:27:31.390 --> 00:27:33.690
wherein free charge is excited.

00:27:33.690 --> 00:27:37.460
But we can also keep increasing
that the wavelength of light,

00:27:37.460 --> 00:27:40.480
say, out to 10 microns, very
long wavelength light, very

00:27:40.480 --> 00:27:41.800
low energy light.

00:27:41.800 --> 00:27:43.220
And that can excite
free carriers

00:27:43.220 --> 00:27:45.340
within the material--
carriers that

00:27:45.340 --> 00:27:47.590
are already excited, essentially
excited them further,

00:27:47.590 --> 00:27:49.080
without generating
any new free carriers

00:27:49.080 --> 00:27:49.850
inside of our material.

00:27:49.850 --> 00:27:51.010
So we won't necessarily
be generating

00:27:51.010 --> 00:27:52.730
more current by
shedding light on it

00:27:52.730 --> 00:27:56.470
but will be absorbing light,
nevertheless, in our material.

00:27:56.470 --> 00:27:58.980
So it's important
to keep, let's say,

00:27:58.980 --> 00:28:01.460
the underlying
physical processes that

00:28:01.460 --> 00:28:02.860
are occurring distinct.

00:28:02.860 --> 00:28:04.370
Later on we'll get to that.

00:28:04.370 --> 00:28:06.370
For now, it's important
just to, I would say,

00:28:06.370 --> 00:28:08.921
recognize that we have
an exponential decay

00:28:08.921 --> 00:28:11.420
of the intensity of the light
as it goes through the medium.

00:28:11.420 --> 00:28:12.830
And then over the
next few classes,

00:28:12.830 --> 00:28:14.790
we're going to get to exactly
what physical processes are

00:28:14.790 --> 00:28:15.570
going on.

00:28:15.570 --> 00:28:19.620
But I'm glad people are
asking those questions.

00:28:19.620 --> 00:28:21.914
OK, so again,
alpha is a function

00:28:21.914 --> 00:28:24.330
of the wavelength of light and
the property of the medium.

00:28:24.330 --> 00:28:27.060
And let me just
flash up some curves

00:28:27.060 --> 00:28:31.360
of alpha versus wavelength
so people have some exposure

00:28:31.360 --> 00:28:33.970
to those numbers.

00:28:33.970 --> 00:28:37.480
Again, we're talking about
an energy range quite broad

00:28:37.480 --> 00:28:41.800
here, from about
6.2 eV to 0.62 eV.

00:28:41.800 --> 00:28:43.700
The visible
wavelengths range would

00:28:43.700 --> 00:28:45.290
be somewhere in
this regime right

00:28:45.290 --> 00:28:47.360
here, so a very limited band.

00:28:47.360 --> 00:28:51.950
And the infrared out here,
ultraviolet over here,

00:28:51.950 --> 00:28:54.640
and we can see for a variety
of different types of materials

00:28:54.640 --> 00:28:57.310
what the absorption
coefficient is.

00:28:57.310 --> 00:29:00.060
So here we have germanium.

00:29:00.060 --> 00:29:03.690
The red would be crystalline
silicon, gallium arsenide,

00:29:03.690 --> 00:29:06.880
indium phosphide, and
amorphous silicon.

00:29:06.880 --> 00:29:08.960
So let's do a little
quick calculation

00:29:08.960 --> 00:29:10.400
just to get us a little limber.

00:29:10.400 --> 00:29:13.040
We're starting to get
into the semester,

00:29:13.040 --> 00:29:14.760
so the energy level
starts going down.

00:29:14.760 --> 00:29:17.700
What we're going to do is
we're going to pick a value,

00:29:17.700 --> 00:29:19.490
say 550 nanometers.

00:29:19.490 --> 00:29:21.350
Why did I pick 550 again?

00:29:21.350 --> 00:29:23.350
It's near the peak of the
solar spectrum, right?

00:29:23.350 --> 00:29:24.300
It matters.

00:29:24.300 --> 00:29:26.902
And we're going to look at
two different materials.

00:29:26.902 --> 00:29:28.860
We're going to look at
silicon, and we're going

00:29:28.860 --> 00:29:30.620
to look at gallium arsenide.

00:29:30.620 --> 00:29:32.770
And we're going to
calculate the thickness

00:29:32.770 --> 00:29:35.730
necessary to absorb 90%
of the incoming light

00:29:35.730 --> 00:29:37.342
at 550 nanometers.

00:29:37.342 --> 00:29:39.300
What I want you to do is
turn to your neighbor,

00:29:39.300 --> 00:29:41.530
and once again
with your neighbor,

00:29:41.530 --> 00:29:43.880
calculate what
thickness of material,

00:29:43.880 --> 00:29:46.540
what thickness of gallium
arsenide, the yellow curve,

00:29:46.540 --> 00:29:48.820
and what thickness of
silicon, the red curve,

00:29:48.820 --> 00:29:52.380
is necessary to absorb
90% of the incoming light

00:29:52.380 --> 00:29:54.325
at 550 nanometers.

00:29:54.325 --> 00:29:55.990
Why don't you go for it?

00:29:55.990 --> 00:29:59.350
I'll give you, say,
a couple minutes.

00:30:11.575 --> 00:30:14.190
To make sure people are
setting this up right,

00:30:14.190 --> 00:30:18.583
i divided by i0 to absorb
90% of the light, that

00:30:18.583 --> 00:30:22.730
would be 0.1, 1 minus 0.9.

00:30:22.730 --> 00:30:25.730
OK, so as you're finalizing
your calculations,

00:30:25.730 --> 00:30:27.950
I just wanted to make
sure set this up right.

00:30:27.950 --> 00:30:30.930
Again, if we're absorbing 90%
of the light, it means only 10%

00:30:30.930 --> 00:30:32.670
of the light is going
out the other side.

00:30:32.670 --> 00:30:34.810
That means their i is
going to be 1/10 of i0

00:30:34.810 --> 00:30:38.330
or i divided by i0 is 0.1.

00:30:38.330 --> 00:30:41.050
And then we would take
the log of both sides,

00:30:41.050 --> 00:30:45.410
typically, and solve for
our l based on the alphas

00:30:45.410 --> 00:30:46.460
that we have here.

00:30:46.460 --> 00:30:49.270
Again, units of alpha would
be in inverse centimeters.

00:30:49.270 --> 00:30:52.310
And so the l's
that you obtained,

00:30:52.310 --> 00:30:54.977
let's go for gallium
arsenide first.

00:30:54.977 --> 00:30:56.560
Did anybody manage
to walk all the way

00:30:56.560 --> 00:30:58.918
through that calculation?

00:30:58.918 --> 00:31:00.380
AUDIENCE: 20 micrometers.

00:31:00.380 --> 00:31:01.840
TONIO BUONASSISI:
20 micrometers.

00:31:01.840 --> 00:31:04.406
For our gallium arsenide
or for our silicon?

00:31:04.406 --> 00:31:05.530
AUDIENCE: Gallium arsenide.

00:31:05.530 --> 00:31:06.988
TONIO BUONASSISI:
Gallium arsenide.

00:31:06.988 --> 00:31:11.158
Did anybody get any other
numbers for gallium arsenide.

00:31:11.158 --> 00:31:12.050
AUDIENCE: 0.4.

00:31:12.050 --> 00:31:13.380
TONIO BUONASSISI: 0.4 microns.

00:31:13.380 --> 00:31:14.130
Yeah.

00:31:14.130 --> 00:31:15.800
That's sounding more
in the ballpark.

00:31:15.800 --> 00:31:16.933
Anybody else?

00:31:16.933 --> 00:31:17.582
AUDIENCE: 23.

00:31:17.582 --> 00:31:18.790
TONIO BUONASSISI: 23 as well.

00:31:18.790 --> 00:31:22.310
So I'm getting-- I would have
guessed that the number would

00:31:22.310 --> 00:31:24.405
rather small for
gallium arsenide, so

00:31:24.405 --> 00:31:29.262
something in the range of,
say, a micron, in that order.

00:31:29.262 --> 00:31:31.470
Why don't we give folks
enough time to walk through--

00:31:31.470 --> 00:31:33.395
I know I rushed you on
the calculations here.

00:31:33.395 --> 00:31:34.728
We have material to get through.

00:31:34.728 --> 00:31:37.980
And I wanted to see you
perform under pressure.

00:31:37.980 --> 00:31:39.990
But how about the silicon?

00:31:39.990 --> 00:31:41.560
Is it larger or smaller?

00:31:41.560 --> 00:31:44.030
Let's just for order
of magnitude first

00:31:44.030 --> 00:31:46.650
and the general
trend and then try

00:31:46.650 --> 00:31:48.340
to pick up the precise number.

00:31:48.340 --> 00:31:50.190
For silicon,
crystalline silicon that

00:31:50.190 --> 00:31:52.850
is, with an optical
absorption coefficient

00:31:52.850 --> 00:31:55.960
and order of magnitude
less than gallium arsenide,

00:31:55.960 --> 00:31:59.150
is the thickness needed to
absorb the same amount of light

00:31:59.150 --> 00:32:00.481
going to be greater or smaller?

00:32:00.481 --> 00:32:01.230
AUDIENCE: Greater.

00:32:01.230 --> 00:32:02.313
TONIO BUONASSISI: Greater.

00:32:02.313 --> 00:32:03.240
By an--

00:32:03.240 --> 00:32:03.590
AUDIENCE: Order of magnitude.

00:32:03.590 --> 00:32:04.890
TONIO BUONASSISI: Order
of magnitude, brilliant.

00:32:04.890 --> 00:32:05.460
OK.

00:32:05.460 --> 00:32:07.293
So whatever number you
got for your gallium,

00:32:07.293 --> 00:32:10.560
arsenide you could
translate it fairly easily.

00:32:10.560 --> 00:32:12.160
All right, so that was at 550.

00:32:12.160 --> 00:32:17.020
And there's a lot of solar
radiation right around 550,

00:32:17.020 --> 00:32:19.427
so the numbers that I
have on the top my head

00:32:19.427 --> 00:32:21.510
work somewhere out to be
on the order of a micron,

00:32:21.510 --> 00:32:23.430
a little less for
gallium arsenide,

00:32:23.430 --> 00:32:25.680
somewhere in the order of
10 microns or so for silicon

00:32:25.680 --> 00:32:26.550
out here.

00:32:26.550 --> 00:32:28.760
But now if we go
out to 800, there's

00:32:28.760 --> 00:32:30.500
still a lot of solar
flux out there.

00:32:30.500 --> 00:32:33.052
If you recall the solar
spectrum, the folks who

00:32:33.052 --> 00:32:35.510
have been doing their homework,
there's still a lot of flux

00:32:35.510 --> 00:32:36.640
out around 800.

00:32:36.640 --> 00:32:38.931
As a matter of fact, it
continues going all the way out

00:32:38.931 --> 00:32:42.135
to here, although decaying
intensity a la black body.

00:32:46.120 --> 00:32:49.950
And at 800 nanometers
wavelength light,

00:32:49.950 --> 00:32:51.730
the optical
absorption coefficient

00:32:51.730 --> 00:32:53.580
is dropped by about
an order of magnitude

00:32:53.580 --> 00:32:55.920
relative to the peak
of the solar spectrum.

00:32:55.920 --> 00:32:58.920
And that's why most of
these solar cells that you

00:32:58.920 --> 00:33:03.364
see of crystalline silicon are
on the order of 100 microns,

00:33:03.364 --> 00:33:05.780
typically a little thicker for
some technological reasons,

00:33:05.780 --> 00:33:07.738
which we'll get to, make
it difficult to handle

00:33:07.738 --> 00:33:09.830
very, very thin stuff.

00:33:09.830 --> 00:33:12.200
But if you just assume one
pass through the material,

00:33:12.200 --> 00:33:15.090
you'd need about that thickness
to absorb a lot of the light.

00:33:15.090 --> 00:33:16.980
And I'll pass around
some of these materials

00:33:16.980 --> 00:33:22.150
right here just so you can get
a sense of how thick they are.

00:33:22.150 --> 00:33:23.010
Here we go.

00:33:23.010 --> 00:33:26.670
Actually, here's
what I'm going to do.

00:33:26.670 --> 00:33:28.560
I'm going to take
out the big pieces

00:33:28.560 --> 00:33:31.014
and leave the small ones in
here that are already broken.

00:33:31.014 --> 00:33:32.930
And you can actually
pick them up if you like.

00:33:32.930 --> 00:33:36.200
Just be aware that these
little pieces of silicon

00:33:36.200 --> 00:33:38.490
are-- silicon's
brittle material.

00:33:38.490 --> 00:33:39.760
It's like glass.

00:33:39.760 --> 00:33:41.850
So if you have a little
shard of silicon,

00:33:41.850 --> 00:33:44.270
it can poke you just like
a charge of glass can.

00:33:44.270 --> 00:33:46.130
So treat it with the
same amount of respect

00:33:46.130 --> 00:33:48.889
that you would a very,
very thin piece of glass.

00:33:48.889 --> 00:33:50.430
But you can see here
that if you look

00:33:50.430 --> 00:33:52.150
at the thickness
of these materials

00:33:52.150 --> 00:33:55.440
inside of that little bin, these
are small shards of silicon

00:33:55.440 --> 00:33:57.260
solar cell wafers.

00:33:57.260 --> 00:34:00.390
Their thicknesses in the
order of 100 microns, those

00:34:00.390 --> 00:34:01.970
are particularly thin.

00:34:01.970 --> 00:34:03.940
You have other
solar cells that are

00:34:03.940 --> 00:34:08.125
170 microns is typical
thickness for silicon.

00:34:08.125 --> 00:34:09.500
And for gallium
arsenide, you can

00:34:09.500 --> 00:34:11.380
deposit thin films
that are on the order

00:34:11.380 --> 00:34:14.537
of a micron thick or less.

00:34:14.537 --> 00:34:16.370
You can go down to a
few hundreds nanometers

00:34:16.370 --> 00:34:18.328
and still make-- actually
the record efficiency

00:34:18.328 --> 00:34:20.710
of gallium arsenide solar
cell is a few hundred

00:34:20.710 --> 00:34:22.750
nanometers thick.

00:34:22.750 --> 00:34:25.770
And our calculations
right here assumed

00:34:25.770 --> 00:34:27.440
one pass through the material.

00:34:27.440 --> 00:34:29.050
That's all we gave the light.

00:34:29.050 --> 00:34:31.330
We only gave one chance
to go through the material

00:34:31.330 --> 00:34:32.940
and get absorbed.

00:34:32.940 --> 00:34:36.540
What could you envision would
increase the total amount

00:34:36.540 --> 00:34:37.540
of light absorbed?

00:34:37.540 --> 00:34:39.670
What could you do to
your solar cell device

00:34:39.670 --> 00:34:43.140
to increase the total amount
of light absorbed inside of it?

00:34:43.140 --> 00:34:45.000
AUDIENCE: Put anti-relfective
coating on it.

00:34:45.000 --> 00:34:47.583
TONIO BUONASSISI: You could put
anti-reflective coating on it.

00:34:47.583 --> 00:34:49.125
Let's do something
much more simple.

00:34:49.125 --> 00:34:51.000
AUDIENCE: Put reflective
coating on the back.

00:34:51.000 --> 00:34:51.909
TONIO BUONASSISI: Reflecting
coating on the back,

00:34:51.909 --> 00:34:52.520
absolutely.

00:34:52.520 --> 00:34:52.770
Yeah.

00:34:52.770 --> 00:34:55.228
So if the light goes through
the solar cell and doesn't get

00:34:55.228 --> 00:34:57.512
absorbed, that 10% of the
light that didn't make it,

00:34:57.512 --> 00:34:58.970
that's going to
get reflected back.

00:34:58.970 --> 00:35:00.934
It's going to get another
chance to go through.

00:35:00.934 --> 00:35:03.100
So if you absorb 90% of the
light on the first pass,

00:35:03.100 --> 00:35:05.760
you'll absorb 99% of the
light on two bounces, right?

00:35:05.760 --> 00:35:07.780
Or in one bounce,
rather, and two trips,

00:35:07.780 --> 00:35:10.120
two optical path links
through the material.

00:35:10.120 --> 00:35:12.290
And so the term
optical path length

00:35:12.290 --> 00:35:15.840
is a very important term
here, because the optical path

00:35:15.840 --> 00:35:18.530
length does not have to be
the thickness of the material.

00:35:18.530 --> 00:35:21.410
Ideally, the optical path
length through the material

00:35:21.410 --> 00:35:24.572
is much, much thicker than
the actual material itself.

00:35:24.572 --> 00:35:26.030
And over the next
few slides, we're

00:35:26.030 --> 00:35:29.550
going to learn how
we engineer that.

00:35:29.550 --> 00:35:34.420
So methods to improve optical
absorption- generally,

00:35:34.420 --> 00:35:37.230
these are called light trapping.

00:35:37.230 --> 00:35:40.860
Not all of these entail
trapping the light.

00:35:40.860 --> 00:35:42.570
Actually, most of them do.

00:35:42.570 --> 00:35:44.350
We also call them
light management

00:35:44.350 --> 00:35:47.080
as a more general
term that includes

00:35:47.080 --> 00:35:51.830
reflection and absorption
inside of the material.

00:35:51.830 --> 00:35:54.305
So the very simplest thing we
can do on the front surface--

00:35:54.305 --> 00:35:55.680
so what we're
going to do is take

00:35:55.680 --> 00:35:59.271
this step by step, as light
goes into the solar cell

00:35:59.271 --> 00:36:01.520
from the front side, we're
going to take step by step,

00:36:01.520 --> 00:36:04.050
what can we do to improve
the amount of light that

00:36:04.050 --> 00:36:05.150
is absorbed?

00:36:05.150 --> 00:36:08.114
The first thing that we can do
is texturize our front surface.

00:36:08.114 --> 00:36:10.030
If we don't have texture
on our front surface,

00:36:10.030 --> 00:36:12.240
if it's absolutely
flat, what we call

00:36:12.240 --> 00:36:17.110
specular surface-- specular
coming from the root mirror.

00:36:17.110 --> 00:36:20.880
In Latin languages, for example,
Italian specchio is mirror.

00:36:20.880 --> 00:36:24.800
So a flat silicon substrate,
a specular surface,

00:36:24.800 --> 00:36:27.344
would reflect some
finite amount of light.

00:36:27.344 --> 00:36:29.010
And we can calculate
that now because we

00:36:29.010 --> 00:36:31.090
know that it relates
to the real component

00:36:31.090 --> 00:36:33.380
of the refractive
index of the material.

00:36:33.380 --> 00:36:35.480
Now if we texturize
our surface--

00:36:35.480 --> 00:36:39.580
this is representing kind of
a pyramid type texturization.

00:36:39.580 --> 00:36:43.260
If the light comes in
and some fraction doesn't

00:36:43.260 --> 00:36:45.152
go into the material--
there's some component

00:36:45.152 --> 00:36:47.360
of that ray that's going
into the material over here,

00:36:47.360 --> 00:36:48.900
but we're ignoring
it in this drawing.

00:36:48.900 --> 00:36:50.316
We're just focusing
on the lights,

00:36:50.316 --> 00:36:52.450
the rays that get reflected.

00:36:52.450 --> 00:36:54.330
That beam that
gets reflected off,

00:36:54.330 --> 00:36:56.502
instead of just going
back out toward the sun,

00:36:56.502 --> 00:36:58.210
it's now going toward
the material again.

00:36:58.210 --> 00:37:01.020
So it has a second chance
of getting absorbed.

00:37:01.020 --> 00:37:03.630
So you just went--
for example, let's say

00:37:03.630 --> 00:37:05.790
if you have a 10%
reflectivity on the surface,

00:37:05.790 --> 00:37:07.775
you went from a 10%
reflectivity over here

00:37:07.775 --> 00:37:10.800
to a 1% reflectivity over here.

00:37:10.800 --> 00:37:13.840
Because now you have the total
amount of light that gets

00:37:13.840 --> 00:37:20.060
reflected is 1 minus 0.9 squared
as opposed to 1 minus 0.9

00:37:20.060 --> 00:37:21.071
to the 1.

00:37:21.071 --> 00:37:23.320
In this case right here, the
amount of light that gets

00:37:23.320 --> 00:37:26.620
reflected, assuming
its 10% reflective,

00:37:26.620 --> 00:37:30.977
would be 1 minus
0.9, so 10% of light.

00:37:30.977 --> 00:37:32.810
And over here, the
amount of light that gets

00:37:32.810 --> 00:37:37.540
reflected would be 1 minus
0.9 quantity squared, so 1%

00:37:37.540 --> 00:37:38.870
instead of 10%.

00:37:38.870 --> 00:37:41.460
So texturization
increases the probability

00:37:41.460 --> 00:37:43.470
that light will
enter the device.

00:37:43.470 --> 00:37:47.250
And what it also does-- this
is a secondary benefit--

00:37:47.250 --> 00:37:50.220
is it increases the path length,
the effective path length,

00:37:50.220 --> 00:37:51.676
of the incoming light.

00:37:51.676 --> 00:37:53.800
And the way to understand
that particular phenomena

00:37:53.800 --> 00:37:55.710
is called Snell's Law.

00:37:55.710 --> 00:37:58.985
Well, even in the absence
of Snell's Law-- no,

00:37:58.985 --> 00:37:59.610
let's go there.

00:37:59.610 --> 00:38:01.010
Let's go there.

00:38:01.010 --> 00:38:03.000
So we have a texturized
front surface.

00:38:03.000 --> 00:38:04.400
What's happening?

00:38:04.400 --> 00:38:08.110
Well, as the material goes
from one medium to another,

00:38:08.110 --> 00:38:10.220
the refractive index changes.

00:38:10.220 --> 00:38:12.690
We discussed this right at
the beginning of lecture.

00:38:12.690 --> 00:38:17.272
So the way in which the
electromagnetic wave oscillates

00:38:17.272 --> 00:38:18.730
the electrons
instead of the system

00:38:18.730 --> 00:38:20.900
is changing from one
medium to another,

00:38:20.900 --> 00:38:23.990
let's say from air into the
solar cell device from air

00:38:23.990 --> 00:38:27.560
into our silicon, for
example, right here.

00:38:27.560 --> 00:38:30.630
Now, we can ascribe the
refractive indices to air

00:38:30.630 --> 00:38:32.830
and to our silicon like so.

00:38:32.830 --> 00:38:36.770
And the light path
will obey what

00:38:36.770 --> 00:38:39.240
is called Snell's Law,
which is the product

00:38:39.240 --> 00:38:42.400
of the refractive index and
sine of that angle, the angle

00:38:42.400 --> 00:38:44.670
relative to the surface normal.

00:38:44.670 --> 00:38:46.290
So a simple way to
think about this

00:38:46.290 --> 00:38:50.270
is when the light goes from a
low index of refraction medium

00:38:50.270 --> 00:38:54.080
to a high index of refraction
medium, light bends

00:38:54.080 --> 00:38:57.287
toward or away from the normal?

00:38:57.287 --> 00:38:58.870
So if I'm going from
air into silicon,

00:38:58.870 --> 00:39:00.940
light would bend toward
the normal, right?

00:39:00.940 --> 00:39:04.180
So here my theta 1 is going
to be greater than theta 2.

00:39:04.180 --> 00:39:07.480
My light has bent toward the
normal, if this is my silicon

00:39:07.480 --> 00:39:10.590
and this white stuff
over here is my air.

00:39:10.590 --> 00:39:12.050
So light came in.

00:39:12.050 --> 00:39:13.760
It encountered the surface.

00:39:13.760 --> 00:39:17.380
The theta 1 was defined
as the angle of the light

00:39:17.380 --> 00:39:18.750
relative to the surface normal.

00:39:18.750 --> 00:39:20.100
That was my theta 1.

00:39:20.100 --> 00:39:22.450
My theta 2 is going to
be given as the ratio

00:39:22.450 --> 00:39:23.720
of the refractive indices.

00:39:23.720 --> 00:39:26.140
And because the refractive
index of silicon

00:39:26.140 --> 00:39:29.110
is going to be greater
than that of air,

00:39:29.110 --> 00:39:30.930
light would bend
toward the normal.

00:39:30.930 --> 00:39:34.000
And so what I have on a
macroscopic view over here,

00:39:34.000 --> 00:39:36.660
if this is my surface
texture, light was coming in,

00:39:36.660 --> 00:39:37.760
it's now bent.

00:39:37.760 --> 00:39:39.810
And so the effective
optical path length

00:39:39.810 --> 00:39:42.450
is now larger than the
thickness of my device.

00:39:42.450 --> 00:39:44.320
It's kind of cool.

00:39:44.320 --> 00:39:49.390
So there are two benefits to
texturizing your front surface.

00:39:49.390 --> 00:39:53.200
One is you have an additional
pass, additional bounce,

00:39:53.200 --> 00:39:55.290
an additional encounter
with the material.

00:39:55.290 --> 00:39:58.439
So that reflected light gets
another chance to go in.

00:39:58.439 --> 00:39:59.980
And the second
benefit is that you're

00:39:59.980 --> 00:40:01.410
able to increase
the optical path

00:40:01.410 --> 00:40:08.720
length by the delta in
refractive indices and the fact

00:40:08.720 --> 00:40:11.445
that the path of the
light will be Snell's Law.

00:40:11.445 --> 00:40:15.480
Now another really interesting
aside of Snell's Law

00:40:15.480 --> 00:40:19.970
is that if light is trying to
go from a high index medium

00:40:19.970 --> 00:40:22.090
to a low index medium,
and if it's coming in

00:40:22.090 --> 00:40:24.980
at a very oblique
angle like this,

00:40:24.980 --> 00:40:27.000
if you run through
Snell's Law, you

00:40:27.000 --> 00:40:28.250
don't get an angle coming out.

00:40:28.250 --> 00:40:29.850
It actually falls
along the surface

00:40:29.850 --> 00:40:32.730
or actually bounces back in most
often, depending on the angle.

00:40:32.730 --> 00:40:35.142
And you have what is called
total internal reflection,

00:40:35.142 --> 00:40:36.600
which is this case
right over here.

00:40:36.600 --> 00:40:39.400
That little bounce,
that friendly bounce,

00:40:39.400 --> 00:40:42.990
of the light that went in
bounced off the back side

00:40:42.990 --> 00:40:44.840
and then was reflected back in.

00:40:44.840 --> 00:40:47.060
That's a total internal
reflection event.

00:40:47.060 --> 00:40:49.780
And that happens
in solar modules.

00:40:49.780 --> 00:40:52.070
Right here, when light
comes in, bounces off

00:40:52.070 --> 00:40:54.080
of the white back
skin right here,

00:40:54.080 --> 00:40:56.790
and then gets scattered
off at an angle,

00:40:56.790 --> 00:40:58.710
it can have a total
internal reflection off

00:40:58.710 --> 00:41:00.520
of the front surface
glass and have

00:41:00.520 --> 00:41:03.960
a second chance of getting back
into the solar cells inside.

00:41:03.960 --> 00:41:07.100
So that's one of the reasons
why you see this white spacing,

00:41:07.100 --> 00:41:09.280
the white colored material,
in between the cells,

00:41:09.280 --> 00:41:11.642
is that the light gets
reflected off of there.

00:41:11.642 --> 00:41:13.600
It doesn't make it very
aesthetically pleasing.

00:41:13.600 --> 00:41:15.100
You might want it
to look all black.

00:41:15.100 --> 00:41:17.224
And if you do want it to
look all black, what would

00:41:17.224 --> 00:41:17.870
you do instead?

00:41:23.120 --> 00:41:25.830
Instead of changing the back
skin, what other component

00:41:25.830 --> 00:41:27.520
might you change?

00:41:27.520 --> 00:41:28.510
AUDIENCE: The front.

00:41:28.510 --> 00:41:29.150
TONIO BUONASSISI:
The front, right?

00:41:29.150 --> 00:41:32.010
You might change the nature
of the anti-reflection coating

00:41:32.010 --> 00:41:33.320
on the glass.

00:41:33.320 --> 00:41:36.160
We'll get anti-reflection
coatings in a minute.

00:41:36.160 --> 00:41:38.107
So even if the
panel looks black,

00:41:38.107 --> 00:41:39.940
there are some really
aesthetically pleasing

00:41:39.940 --> 00:41:42.023
solar panels out there
that look completely black.

00:41:42.023 --> 00:41:43.600
They may still have
white back skin,

00:41:43.600 --> 00:41:46.095
but the glass is just very
good at absorbing that light

00:41:46.095 --> 00:41:48.560
and preventing it from escaping.

00:41:48.560 --> 00:41:52.360
OK, so to engineer front and
back surface reflectances,

00:41:52.360 --> 00:41:54.090
you really have to
carefully select

00:41:54.090 --> 00:41:56.050
your refractive indices
and your materials

00:41:56.050 --> 00:41:57.980
if you put on either side.

00:41:57.980 --> 00:42:01.370
And it's very important--
extremely important.

00:42:01.370 --> 00:42:05.230
To make a long story short, the
record efficiency solar cell

00:42:05.230 --> 00:42:09.380
that was announced this past
year in gallium arsenide

00:42:09.380 --> 00:42:13.630
was achieved because of
good light management.

00:42:13.630 --> 00:42:18.620
And we'll explain how that came
about perhaps towards lectures,

00:42:18.620 --> 00:42:21.000
maybe lectures eight or nine.

00:42:21.000 --> 00:42:23.400
So I'm going to play a
little game with you, which

00:42:23.400 --> 00:42:25.570
is to look at a swimming pool.

00:42:25.570 --> 00:42:27.550
This is a pool
filled with water,

00:42:27.550 --> 00:42:29.890
which is refractive index 1.3.

00:42:29.890 --> 00:42:30.990
Air is 1.

00:42:30.990 --> 00:42:33.010
And so that's the normal
view, what we have.

00:42:33.010 --> 00:42:35.580
Light bends toward
the normal, right?

00:42:35.580 --> 00:42:38.870
And so you're able to
look down inside the pool

00:42:38.870 --> 00:42:41.416
that stuff that is not
in your line of sight,

00:42:41.416 --> 00:42:42.790
not in your direct
line of sight.

00:42:42.790 --> 00:42:44.930
That's because when you
look down, the ray of light

00:42:44.930 --> 00:42:46.388
is traveling like
this and it bends

00:42:46.388 --> 00:42:49.740
toward the normal and
likewise symmetric.

00:42:49.740 --> 00:42:52.360
So you're seeing
material down there.

00:42:52.360 --> 00:42:56.310
What change of
property would give you

00:42:56.310 --> 00:42:57.530
these two images over here.

00:42:57.530 --> 00:42:58.820
Let me give you a hint.

00:42:58.820 --> 00:43:01.760
In one of those two images,
the refractive index

00:43:01.760 --> 00:43:04.680
of the medium inside
the pool is not 1.3.

00:43:04.680 --> 00:43:08.286
It's 0.9.

00:43:08.286 --> 00:43:09.760
It's 0.9.

00:43:09.760 --> 00:43:14.900
And in another one of these
two, the refractive index

00:43:14.900 --> 00:43:18.340
of the medium is actually
going to be negative.

00:43:18.340 --> 00:43:21.750
We'll call it a negative
refractive index material,

00:43:21.750 --> 00:43:23.550
a negative index material.

00:43:23.550 --> 00:43:25.892
So which of these two
do you think is which?

00:43:25.892 --> 00:43:27.350
Why don't you turn
to your neighbor

00:43:27.350 --> 00:43:29.910
quickly and chat about it
without peeking at your lecture

00:43:29.910 --> 00:43:30.410
notes.

00:43:45.010 --> 00:43:48.860
So let me walk through, as you
begin honing in on your answers

00:43:48.860 --> 00:43:49.640
here.

00:43:49.640 --> 00:43:52.370
Think about what would
happen to the reflectivity

00:43:52.370 --> 00:43:54.860
of that front
surface of the water

00:43:54.860 --> 00:43:59.130
and what would happen to the
angle that the light travels,

00:43:59.130 --> 00:44:02.340
or the angle of refraction
of bending, shall

00:44:02.340 --> 00:44:05.240
you say, as the light goes
from one medium to another.

00:44:05.240 --> 00:44:10.596
So if we go to a refractive
index material of minus 1.3,

00:44:10.596 --> 00:44:12.220
will we change the
reflectivity at all?

00:44:15.884 --> 00:44:20.990
It depends, but the
answers here are shown,

00:44:20.990 --> 00:44:22.472
for this particular system.

00:44:22.472 --> 00:44:24.180
It would require
sitting down and walking

00:44:24.180 --> 00:44:26.469
through the equations,
but in essence

00:44:26.469 --> 00:44:29.010
right here, with the pool filled
with the negative refractive

00:44:29.010 --> 00:44:32.690
index material, you're
really affecting

00:44:32.690 --> 00:44:36.100
the angle at which light
is coming out of the pool.

00:44:36.100 --> 00:44:39.680
Here you can see the corner
of the pool, which you

00:44:39.680 --> 00:44:41.090
shouldn't even be able to see.

00:44:41.090 --> 00:44:42.840
It's just that the
light traveled this way

00:44:42.840 --> 00:44:45.620
and then came back because it
was a negative refractive index

00:44:45.620 --> 00:44:46.370
material.

00:44:46.370 --> 00:44:48.532
Light actually did something
like this, zoop, zoop.

00:44:48.532 --> 00:44:49.740
AUDIENCE: What's in the pool?

00:44:49.740 --> 00:44:51.400
TONIO BUONASSISI: Oh,
that's just a corner.

00:44:51.400 --> 00:44:52.400
So what is in that pool?

00:44:52.400 --> 00:44:54.420
That is a computer
generated graphic.

00:44:54.420 --> 00:44:56.410
This is not a real pool.

00:44:56.410 --> 00:44:58.730
There exists negative
refractive index materials

00:44:58.730 --> 00:45:01.640
but not in that volume yet.

00:45:01.640 --> 00:45:07.690
These are relatively small
things and very much a study

00:45:07.690 --> 00:45:08.880
in fundamental science.

00:45:08.880 --> 00:45:12.760
So in this case
right here, we have

00:45:12.760 --> 00:45:17.220
less of an acute bending
of our angle of light.

00:45:17.220 --> 00:45:19.610
So we don't get to see quite
as many features right here

00:45:19.610 --> 00:45:20.660
toward the edge.

00:45:20.660 --> 00:45:24.130
And the reflectivity
has changed as a result

00:45:24.130 --> 00:45:29.252
of having drastically modified
our reflection condition.

00:45:29.252 --> 00:45:31.460
AUDIENCE: Why does the
reflectivity seem to have gone

00:45:31.460 --> 00:45:35.070
up and the index has gone down?

00:45:35.070 --> 00:45:37.420
TONIO BUONASSISI: In
that particular case?

00:45:37.420 --> 00:45:39.710
I think what they were getting
at-- this is coming off

00:45:39.710 --> 00:45:40.460
of an SPI website.

00:45:40.460 --> 00:45:42.460
I think what they were
getting at is mostly just

00:45:42.460 --> 00:45:44.020
a change in the reflectivity.

00:45:44.020 --> 00:45:48.110
So they were trying to emphasize
that you were modifying

00:45:48.110 --> 00:45:50.630
the reflection off the
surface in addition

00:45:50.630 --> 00:45:53.640
to the angle at which the
light was exiting the material.

00:45:53.640 --> 00:45:58.580
I'm going to come back to
Snell's Law in a minute.

00:45:58.580 --> 00:46:02.060
But for the time being,
I want to move on

00:46:02.060 --> 00:46:05.450
to the next concept here,
which is Lambertian reflector.

00:46:05.450 --> 00:46:09.210
You'll hear this topic or this
word thrown around quite a lot

00:46:09.210 --> 00:46:10.770
in the solar cell community.

00:46:10.770 --> 00:46:13.760
And it's used rather liberally
to mean a lot of things.

00:46:13.760 --> 00:46:17.890
Although in optics, it has
a very specific meaning.

00:46:17.890 --> 00:46:20.410
So I'm going to show you
that very specific meaning

00:46:20.410 --> 00:46:24.100
and then describe for you
what it has very loosely come

00:46:24.100 --> 00:46:25.620
to mean in the solar industry.

00:46:25.620 --> 00:46:28.440
So a diffuse
Lambertian reflector

00:46:28.440 --> 00:46:32.610
will follow a reflectance
that follows a cosine theta

00:46:32.610 --> 00:46:33.920
dependence.

00:46:33.920 --> 00:46:36.530
So if you have light
coming into a sample,

00:46:36.530 --> 00:46:39.330
the surface normal, and
the outgoing light ray

00:46:39.330 --> 00:46:41.410
form an angle theta.

00:46:41.410 --> 00:46:43.240
And if the two are
perfectly aligned,

00:46:43.240 --> 00:46:45.390
you get a lot of reflectance
off of that angle.

00:46:45.390 --> 00:46:47.500
If the two are perpendicular
to one another,

00:46:47.500 --> 00:46:49.830
you get zero reflectance
in that angle.

00:46:49.830 --> 00:46:53.130
And so the reflectance parallel
to the surface here is zero.

00:46:53.130 --> 00:46:55.720
In everywhere in between,
the magnitude of reflectance

00:46:55.720 --> 00:46:57.480
is varying as consine theta.

00:46:57.480 --> 00:47:01.730
That's the, I would
say, pedantic definition

00:47:01.730 --> 00:47:03.550
of an Lambertian reflector.

00:47:03.550 --> 00:47:04.990
Often in the solar
industry you'll

00:47:04.990 --> 00:47:07.960
hear people, probably because
of a lack of optics background,

00:47:07.960 --> 00:47:10.470
just call any randomly
reflecting surface

00:47:10.470 --> 00:47:12.220
a Lambertian scatter.

00:47:12.220 --> 00:47:15.400
It's a very loosely used term.

00:47:15.400 --> 00:47:18.990
And it is wrong by the
book, but nevertheless, it's

00:47:18.990 --> 00:47:22.930
one of these things that
live on in our industry.

00:47:22.930 --> 00:47:26.190
So the difference between
a specular reflector,

00:47:26.190 --> 00:47:28.470
the one that we've just
been analyzing right now,

00:47:28.470 --> 00:47:30.880
and a Lambertian reflector,
is that typically the way

00:47:30.880 --> 00:47:35.490
these are made is that you
do have a random texture

00:47:35.490 --> 00:47:36.380
on your surface.

00:47:36.380 --> 00:47:38.921
And that's probably where the
origin of this misunderstanding

00:47:38.921 --> 00:47:39.900
comes about.

00:47:39.900 --> 00:47:42.445
We don't get a
random reflectance

00:47:42.445 --> 00:47:44.730
of the light coming off,
but the surface itself

00:47:44.730 --> 00:47:46.440
can be rather texturized.

00:47:46.440 --> 00:47:49.420
So, for example, if you suspect
that this little material

00:47:49.420 --> 00:47:52.110
right here might behave
like a Lambertian scatter,

00:47:52.110 --> 00:47:56.332
you might put it inside of
a tool and rotate the angle

00:47:56.332 --> 00:47:58.040
and measure the amount
of reflected light

00:47:58.040 --> 00:48:00.680
as a function of the angle
to determine whether or not

00:48:00.680 --> 00:48:03.510
it follows this cosine
theta dependence.

00:48:03.510 --> 00:48:07.510
And the reason it's important
is because the back skins

00:48:07.510 --> 00:48:11.619
of our solar modules can quite
often be Lambertian scatters.

00:48:11.619 --> 00:48:13.160
And we have a certain
amount of light

00:48:13.160 --> 00:48:15.140
that comes off at
some angle here

00:48:15.140 --> 00:48:17.760
that will get trapped by a
total internal reflection

00:48:17.760 --> 00:48:19.250
inside of a modules.

00:48:19.250 --> 00:48:23.790
So if, instead of having
macroscopic pyramids right

00:48:23.790 --> 00:48:26.780
here, you had very, very
small pyramids-- still not

00:48:26.780 --> 00:48:29.370
sub-wavelength, but
smaller features,

00:48:29.370 --> 00:48:32.340
for example, the texturization
on the back skin right here.

00:48:32.340 --> 00:48:34.260
An it managed to
scatter the light

00:48:34.260 --> 00:48:35.920
at a particular
angle that got caught

00:48:35.920 --> 00:48:37.380
by total internal reflection.

00:48:37.380 --> 00:48:39.900
Macroscopically, we might be
able to describe the scattering

00:48:39.900 --> 00:48:42.800
behavior of that surface
as Lambertian scatter.

00:48:42.800 --> 00:48:45.950
But it's those waves, those
rays that are bouncing off

00:48:45.950 --> 00:48:48.260
at those large angles
that are causing

00:48:48.260 --> 00:48:52.390
the total internal
reflection event.

00:48:52.390 --> 00:48:55.595
And so the notion of
a Lambertian scatter

00:48:55.595 --> 00:48:58.660
is important on the backsides
of solar cell devices.

00:48:58.660 --> 00:49:04.410
We would obviously wants to even
change the scattering profile.

00:49:04.410 --> 00:49:07.482
We wouldn't want necessarily
specular reflectance.

00:49:07.482 --> 00:49:09.940
We might want to maximize the
amount of light reflected off

00:49:09.940 --> 00:49:12.170
at particular angles.

00:49:12.170 --> 00:49:14.320
And there is, of
course, research

00:49:14.320 --> 00:49:18.050
being done to figure out
how to make light do that.

00:49:18.050 --> 00:49:20.790
I'll show you one example
at the very end of lecture,

00:49:20.790 --> 00:49:23.670
a paper that was just
published in Science last week,

00:49:23.670 --> 00:49:25.380
as an example.

00:49:25.380 --> 00:49:27.380
And so these
scattering centers off

00:49:27.380 --> 00:49:29.315
the backs of the
rear sides of cells

00:49:29.315 --> 00:49:31.440
would operate more or less
in the following manner.

00:49:31.440 --> 00:49:32.980
You'd have incoming light.

00:49:32.980 --> 00:49:35.360
Let's ignore front
surface texturing for now.

00:49:35.360 --> 00:49:36.980
Let's just focus
on the backside.

00:49:36.980 --> 00:49:39.770
And if you have some random, as
we call it, a random reflector,

00:49:39.770 --> 00:49:43.135
a randomly texturized reflector
on the back that reflects off

00:49:43.135 --> 00:49:45.860
in, say, a Lambertian
fashion, you'll

00:49:45.860 --> 00:49:48.430
have some fraction of
that light scattered off

00:49:48.430 --> 00:49:53.170
at an angle that is large
enough relative to the surface

00:49:53.170 --> 00:49:57.740
normal that it is trapped by
total internal reflection.

00:49:57.740 --> 00:50:01.090
And you don't only have
to texture your back skin.

00:50:01.090 --> 00:50:03.034
You can also texture
the bus bars.

00:50:03.034 --> 00:50:05.200
The bus bars are these
little metal wires right here

00:50:05.200 --> 00:50:07.709
that are collecting the charge
from each of the solar cells.

00:50:07.709 --> 00:50:09.750
And they're connecting
essentially the front side

00:50:09.750 --> 00:50:11.580
of one cell to the
backside of the next.

00:50:11.580 --> 00:50:13.000
If you want to think about it
as the cathode to the anode,

00:50:13.000 --> 00:50:14.791
cathode to the anode,
cathode to the anode,

00:50:14.791 --> 00:50:17.130
stringing all these
cells together in series.

00:50:17.130 --> 00:50:19.110
And this metal right here
is just really shiny,

00:50:19.110 --> 00:50:22.070
and it's reflecting light
right back out into space.

00:50:22.070 --> 00:50:25.330
What if we instead were to
texture that metal so that when

00:50:25.330 --> 00:50:27.320
laser light shined on it
a certain amount would

00:50:27.320 --> 00:50:29.250
be reflected off at an
angle and then caught

00:50:29.250 --> 00:50:30.290
by total internal reflection.

00:50:30.290 --> 00:50:32.331
And that's exactly what
you're seeing right here.

00:50:32.331 --> 00:50:34.400
The light bounced here
on a textured bus bar,

00:50:34.400 --> 00:50:36.560
bounced off of the glass
more or less around here

00:50:36.560 --> 00:50:38.710
halfway, and then
got a second chance

00:50:38.710 --> 00:50:40.297
to enter the cell over here.

00:50:40.297 --> 00:50:41.880
Obviously some of
it is reflecting off

00:50:41.880 --> 00:50:43.090
so we can see it.

00:50:43.090 --> 00:50:44.480
But a lot of it's going in.

00:50:44.480 --> 00:50:46.492
And that little
innovation right there,

00:50:46.492 --> 00:50:47.950
which was developed
in the building

00:50:47.950 --> 00:50:50.470
right next door by
Professor Ely Sachs,

00:50:50.470 --> 00:50:53.290
can gain module performances
somewhere on the order

00:50:53.290 --> 00:50:55.430
of a few percent relative.

00:50:55.430 --> 00:50:57.430
So that might not
sound like a whole lot,

00:50:57.430 --> 00:51:01.930
but if you're a $100 billion
industry, 1% is a lot of money.

00:51:01.930 --> 00:51:05.040
So it does add up.

00:51:05.040 --> 00:51:08.410
So that goes back to the
total internal reflection.

00:51:08.410 --> 00:51:14.620
So there is a limit to
all of this texturization.

00:51:14.620 --> 00:51:18.350
There's a limit to how much
we can trap light simply

00:51:18.350 --> 00:51:23.930
by modifying or
corrugating the surfaces

00:51:23.930 --> 00:51:27.060
to enhance the optical path
length with these types

00:51:27.060 --> 00:51:32.220
of bounces using Snell's
Law and of course

00:51:32.220 --> 00:51:33.870
the general
reflectivity equations.

00:51:33.870 --> 00:51:37.470
And a gentleman by the name
of Eli Yablonovitch, who's

00:51:37.470 --> 00:51:40.690
now a professor in Berkeley
calculated these parameters

00:51:40.690 --> 00:51:45.130
I think back in 1982 and
came up with an upper limit

00:51:45.130 --> 00:51:46.740
to the optical path length.

00:51:46.740 --> 00:51:50.460
He, after a long
series of calculations,

00:51:50.460 --> 00:51:53.990
derived an expression
for the maximum increase

00:51:53.990 --> 00:51:56.710
of the optical path length
due to surface texturing,

00:51:56.710 --> 00:51:59.080
which was 4n squared.

00:51:59.080 --> 00:52:01.640
And the Yablonovitch
limit to this day

00:52:01.640 --> 00:52:05.870
is a pretty good litmus
test for the ability

00:52:05.870 --> 00:52:07.250
of a material to trap light.

00:52:07.250 --> 00:52:09.430
So if you have
silicon, for instance,

00:52:09.430 --> 00:52:12.030
with a refractive
index of, let's say,

00:52:12.030 --> 00:52:15.690
in the infrared some around
3.6, your Yablonovitch limit

00:52:15.690 --> 00:52:18.530
is around 50, which means
that you can increase

00:52:18.530 --> 00:52:20.860
the optical path
length by a factor 50,

00:52:20.860 --> 00:52:24.570
relative to the thickness
of your material.

00:52:24.570 --> 00:52:26.180
If you have an organic
material, which

00:52:26.180 --> 00:52:29.800
has a refractive index typically
of around maximum 2, then

00:52:29.800 --> 00:52:32.460
that would be squared, 16,
somewhere in that range.

00:52:32.460 --> 00:52:35.264
You can increase probably
in the order of 20

00:52:35.264 --> 00:52:37.180
the optical path length
inside of the material

00:52:37.180 --> 00:52:38.930
through texturization.

00:52:38.930 --> 00:52:42.180
So this is a useful
parameter for those

00:52:42.180 --> 00:52:43.890
who are doing research
in photovoltaics,

00:52:43.890 --> 00:52:45.480
the graduate
students especially.

00:52:45.480 --> 00:52:47.590
And so I think the
graduate students

00:52:47.590 --> 00:52:49.840
will have a question at some
point on the Yablonovitch

00:52:49.840 --> 00:52:51.610
limit.

00:52:51.610 --> 00:52:55.480
And so that's a useful
parameter to keep in your mind.

00:52:55.480 --> 00:53:00.320
Let me touch upon a few other
forms of trapping light.

00:53:00.320 --> 00:53:02.970
We've so far just
assumed that light

00:53:02.970 --> 00:53:07.340
behaves like a
continuous wave, doesn't

00:53:07.340 --> 00:53:09.900
interfere with anything,
doesn't interfere with itself.

00:53:09.900 --> 00:53:14.907
Now we're going to discuss some
anti-reflection effects which

00:53:14.907 --> 00:53:16.740
derives from the notion
that light is a wave

00:53:16.740 --> 00:53:20.470
and can constructively and
destructively interfere.

00:53:20.470 --> 00:53:25.300
What we have right here is
a layer of another material

00:53:25.300 --> 00:53:27.820
with a refractive
index, say n1, which

00:53:27.820 --> 00:53:30.070
is in between our
n0 which is at air

00:53:30.070 --> 00:53:31.800
and our n2 is the
absorber material,

00:53:31.800 --> 00:53:33.580
let's say the silicon.

00:53:33.580 --> 00:53:35.357
So we have a grading
of refractive indices

00:53:35.357 --> 00:53:37.190
going from air, our
anti-reflection coating,

00:53:37.190 --> 00:53:38.270
to silicon.

00:53:38.270 --> 00:53:40.895
And right over here we have
a certain thickness, d1.

00:53:40.895 --> 00:53:43.890
And over here we have a
certain thickness, d2.

00:53:43.890 --> 00:53:47.760
So what is happening
in these two images?

00:53:47.760 --> 00:53:51.540
Let me show you with another,
a little bit more clear figure,

00:53:51.540 --> 00:53:53.680
coming from our
beloved Wikipedia,

00:53:53.680 --> 00:53:56.140
and then go back to that
other image right there.

00:53:56.140 --> 00:53:59.710
So what's happening is we
have an incoming wave that

00:53:59.710 --> 00:54:02.110
for some reason is
ignoring Snell's Law.

00:54:02.110 --> 00:54:02.949
It's beyond me.

00:54:02.949 --> 00:54:04.990
But anyway, the wave is
going in a straight line.

00:54:04.990 --> 00:54:07.470
It should be bending toward
the surface norm, obviously.

00:54:07.470 --> 00:54:11.290
But we have reflections
off of this interface

00:54:11.290 --> 00:54:14.190
and this interface right here.

00:54:14.190 --> 00:54:19.530
And because the
thickness of this layer

00:54:19.530 --> 00:54:22.360
is in the order
of lambda over 4,

00:54:22.360 --> 00:54:24.090
that means that the
wave that's going in

00:54:24.090 --> 00:54:26.131
will be phase shifted
relative to the wave that's

00:54:26.131 --> 00:54:28.650
reflected off the front surface,
first by lambda over 4 then

00:54:28.650 --> 00:54:30.610
2 times lambda over
4, in other words,

00:54:30.610 --> 00:54:33.530
lambda over 2, which means that
the two waves are out of phase

00:54:33.530 --> 00:54:36.510
by lambda over 2, which means
that they will destructively

00:54:36.510 --> 00:54:38.512
interfere.

00:54:38.512 --> 00:54:39.720
The peak will be at a trough.

00:54:39.720 --> 00:54:41.695
The trough will be at a peak.

00:54:41.695 --> 00:54:44.320
So the two waves will are going
to be destructively interfering

00:54:44.320 --> 00:54:45.180
when they come out.

00:54:45.180 --> 00:54:47.096
If you add these two
together, due to the wave

00:54:47.096 --> 00:54:51.170
nature of light, you get
suppressed reflectance.

00:54:51.170 --> 00:54:53.800
And that's a really
interesting property.

00:54:53.800 --> 00:54:56.630
You can begin varying the
thickness of this layer,

00:54:56.630 --> 00:54:59.270
and of course changing the
nature of the reflected light.

00:54:59.270 --> 00:55:01.735
You can constructively
interfere if you like

00:55:01.735 --> 00:55:04.440
and enhance the amount
of reflected light

00:55:04.440 --> 00:55:07.770
as a result of this
interference effect.

00:55:07.770 --> 00:55:11.050
Obviously, in most solar cells,
we want to suppress reflection.

00:55:11.050 --> 00:55:12.800
And so we go to great
lengths to make sure

00:55:12.800 --> 00:55:16.200
that this thickness as well
as the refractive index

00:55:16.200 --> 00:55:23.880
of the material is optimized
for a particular system.

00:55:23.880 --> 00:55:29.020
And so without going
into the hairy math,

00:55:29.020 --> 00:55:33.494
to calculate this right here,
it's definitely possible.

00:55:33.494 --> 00:55:35.410
It's definitely something
that should be done.

00:55:35.410 --> 00:55:37.618
And I believe the graduate
students have it assigned.

00:55:37.618 --> 00:55:39.490
It's the very last
problem in the homework.

00:55:39.490 --> 00:55:43.690
But for a very simple kind of
conceptual understanding that

00:55:43.690 --> 00:55:45.860
is wavelength
independent, if we want

00:55:45.860 --> 00:55:50.030
to minimize the reflectance at
a particular wavelength, let's

00:55:50.030 --> 00:55:53.570
call it at a lambda
0, which is the photon

00:55:53.570 --> 00:55:56.700
wavelength at the peak
of the solar spectrum,

00:55:56.700 --> 00:55:59.549
we have to design the thickness
of our anti-reflection coating

00:55:59.549 --> 00:56:01.090
to satisfy that
equation right there,

00:56:01.090 --> 00:56:02.640
essentially lambda over 4.

00:56:02.640 --> 00:56:04.772
That's the phase
shift we want upon one

00:56:04.772 --> 00:56:06.230
pass of the
anti-reflection coating

00:56:06.230 --> 00:56:08.000
so that two passes,
when it goes through

00:56:08.000 --> 00:56:09.440
and then back,
it's phase shifted

00:56:09.440 --> 00:56:11.630
relative to the surface
reflected light by lambda

00:56:11.630 --> 00:56:15.390
over 2, divided by n, n
being the refractive index

00:56:15.390 --> 00:56:16.830
of the material.

00:56:16.830 --> 00:56:20.234
Obviously the frequency of
light is staying the same

00:56:20.234 --> 00:56:21.900
as it goes from one
material to another.

00:56:21.900 --> 00:56:25.040
But the wavelength
would be changing.

00:56:25.040 --> 00:56:28.250
So that's why the n
parameter appears right here

00:56:28.250 --> 00:56:29.580
in this equation.

00:56:29.580 --> 00:56:32.350
The t is the thickness of the
optimal anti-reflection coating

00:56:32.350 --> 00:56:33.470
thickness.

00:56:33.470 --> 00:56:38.425
So just to give us a
sense, kind of an estimate,

00:56:38.425 --> 00:56:40.550
and to give us some confidence
in these engineering

00:56:40.550 --> 00:56:42.720
methods, what I'd
like you to do is

00:56:42.720 --> 00:56:47.390
to calculate the thickness of an
ideal anti-reflective coating.

00:56:47.390 --> 00:56:49.730
This anti-reflective coating
right here on these cells--

00:56:49.730 --> 00:56:51.855
I apologize, they also have
the metal on the front,

00:56:51.855 --> 00:56:54.280
so it's a little difficult to
distinguish between the two.

00:56:54.280 --> 00:56:58.260
But in my right hand, this one,
I have a piece of bare silicon.

00:56:58.260 --> 00:57:00.610
And you can see it's
rather reflective.

00:57:00.610 --> 00:57:03.180
In my left hand
over here, I have

00:57:03.180 --> 00:57:05.690
a piece of silicon with
an anti-reflective coating

00:57:05.690 --> 00:57:08.146
as well some contact
metalization on the front.

00:57:08.146 --> 00:57:09.770
So that's why you
see those grid lines.

00:57:09.770 --> 00:57:11.700
But it looks very blue.

00:57:11.700 --> 00:57:13.497
It looks very blue
because the cell

00:57:13.497 --> 00:57:15.830
is absorbing very well at the
peak of the solar spectrum

00:57:15.830 --> 00:57:18.180
which is in the yellow.

00:57:18.180 --> 00:57:23.320
So calculate for me what
is the optimal thickness

00:57:23.320 --> 00:57:26.110
of an anti-reflection
coating of silicon nitride?

00:57:26.110 --> 00:57:29.010
And we'll give it a
refractive index of, say, 2.1.

00:57:29.010 --> 00:57:31.360
Let me see if those
numbers make sense,

00:57:31.360 --> 00:57:35.640
so refractive index of silicon
nitride somewhere around 550.

00:57:35.640 --> 00:57:38.160
Let's call it 2, just
make our lives simple.

00:57:38.160 --> 00:57:41.730
And the peak of the solar
spectrum we'll again call 550.

00:57:41.730 --> 00:57:43.584
So why don't we run
the numbers quickly.

00:57:43.584 --> 00:57:44.834
What should that thickness be?

00:57:54.983 --> 00:57:56.524
AUDIENCE: Tonio,
I'm sorry, could you

00:57:56.524 --> 00:57:57.852
repeat the constant again?

00:57:57.852 --> 00:57:58.810
TONIO BUONASSISI: Sure.

00:57:58.810 --> 00:58:03.210
So the n, the refractive
index, is going to be around 2

00:58:03.210 --> 00:58:04.690
for silicon nitride.

00:58:04.690 --> 00:58:07.400
So we're going from air, which
is around refractive index one,

00:58:07.400 --> 00:58:10.810
to silicon nitride, the silicon.

00:58:10.810 --> 00:58:14.500
And the peak of the solar
spectrum, our lambda 0,

00:58:14.500 --> 00:58:16.530
which is the photon
wavelength at the peak

00:58:16.530 --> 00:58:20.740
of the solar spectrum in vacuum
or in air, is 550 nanometers.

00:58:26.950 --> 00:58:29.760
So what thicknesses are
folks coming up with?

00:58:29.760 --> 00:58:31.200
Order of magnitude.

00:58:31.200 --> 00:58:32.200
AUDIENCE: 70 nanometers.

00:58:32.200 --> 00:58:33.533
TONIO BUONASSISI: 70 nanometers.

00:58:33.533 --> 00:58:37.420
That's almost spot on
to the actual thickness,

00:58:37.420 --> 00:58:39.670
to somewhere on the
order between 70 to 80

00:58:39.670 --> 00:58:42.380
nanometer typically.

00:58:42.380 --> 00:58:46.210
You're telling me that
something that is 1/1,000,

00:58:46.210 --> 00:58:49.540
the thickness of my hair,
is deposited on the surface

00:58:49.540 --> 00:58:53.060
of this wafer and is
absorbing all this light?

00:58:53.060 --> 00:58:54.256
That's pretty cool.

00:58:54.256 --> 00:58:55.630
And it's not
absorbing the light.

00:58:55.630 --> 00:58:56.870
The anti-reflective
coating is not

00:58:56.870 --> 00:58:58.280
absorbing the light,
which is really important.

00:58:58.280 --> 00:58:59.779
We want the solar
cell underneath it

00:58:59.779 --> 00:59:00.890
to be absorbing the light.

00:59:00.890 --> 00:59:03.440
The anti-reflection coding
is enabling the light

00:59:03.440 --> 00:59:07.790
to be absorbed because it's
suppressing the reflectance.

00:59:07.790 --> 00:59:10.120
The reflected modes at
that particular wavelength

00:59:10.120 --> 00:59:13.900
are suppressed because of
the destructive interference.

00:59:13.900 --> 00:59:15.410
That's cool.

00:59:15.410 --> 00:59:18.530
I really get a kick out of
anti-reflective coatings.

00:59:18.530 --> 00:59:22.070
So they're 70 nanometers thick.

00:59:22.070 --> 00:59:24.780
And you gain quite a lot in
terms of cell performance.

00:59:27.560 --> 00:59:30.850
I'll show you some slides to
drive that point home in a bit.

00:59:34.600 --> 00:59:37.600
This is really really briefly--
I'll post these slides online

00:59:37.600 --> 00:59:39.320
so you can have access to them.

00:59:39.320 --> 00:59:42.560
If you use the matrix
transfer method,

00:59:42.560 --> 00:59:46.880
as described beautifully in
[? Gonchen's ?] textbook,

00:59:46.880 --> 00:59:50.280
you can calculate the
amount of light reflected

00:59:50.280 --> 00:59:54.360
across a broad spectral
range for a given thickness

00:59:54.360 --> 00:59:55.600
of anti-reflection coding.

00:59:55.600 --> 00:59:57.500
So what we did right
now was to calculate

00:59:57.500 --> 01:00:00.370
a suppression of the light
at a particular wavelength.

01:00:00.370 --> 01:00:02.920
But you can also calculate
with the tools that

01:00:02.920 --> 01:00:06.890
are available to
you the reflectance

01:00:06.890 --> 01:00:09.140
of your particular device
over a broader wavelength.

01:00:09.140 --> 01:00:11.090
Range and that's pretty
cool because now you

01:00:11.090 --> 01:00:14.520
can begin, say, multiplying
this function right

01:00:14.520 --> 01:00:17.540
here against your solar
spectrum and begin

01:00:17.540 --> 01:00:21.000
to calculate the total amount
of light entering your sample

01:00:21.000 --> 01:00:22.960
and the total energy
entering your sample.

01:00:22.960 --> 01:00:25.420
Equations, brilliant.

01:00:25.420 --> 01:00:27.730
The important thing
to note here is

01:00:27.730 --> 01:00:30.550
that it really, really matters.

01:00:30.550 --> 01:00:32.970
This is silicon under
glass right here,

01:00:32.970 --> 01:00:35.730
for example, typical solar
cell material in blue.

01:00:35.730 --> 01:00:37.320
It's better than
the bare silicon.

01:00:37.320 --> 01:00:40.550
Why is it better than the bare
silicon, silicon under glass?

01:00:40.550 --> 01:00:42.500
Glass has a refractive
index of 1.5 or so.

01:00:45.886 --> 01:00:48.316
AUDIENCE: The index matching.

01:00:48.316 --> 01:00:52.690
You go from pairs 1 to 2.3
and then to [INAUDIBLE].

01:00:52.690 --> 01:00:56.277
The difference is small
between the classes.

01:00:56.277 --> 01:00:57.360
TONIO BUONASSISI: Exactly.

01:00:57.360 --> 01:00:58.900
So if we recall
that equation that

01:00:58.900 --> 01:01:00.400
described the amount
of reflectance,

01:01:00.400 --> 01:01:04.260
there was that-- what was it--
n1 minus n2 quantity squared,

01:01:04.260 --> 01:01:04.760
right?

01:01:04.760 --> 01:01:07.210
So the bigger the delta
between the ends, the bigger

01:01:07.210 --> 01:01:08.710
the difference in
refractive indices

01:01:08.710 --> 01:01:10.330
between material one
and material two,

01:01:10.330 --> 01:01:12.890
the more the reflectance is
going to be off that interface.

01:01:12.890 --> 01:01:15.460
And so you can begin
reducing reflectance off

01:01:15.460 --> 01:01:18.530
of a stack of light
going both ways

01:01:18.530 --> 01:01:22.730
by grading the refractive
index of the material.

01:01:22.730 --> 01:01:26.380
And that, of course, changes the
reflectance in both directions.

01:01:26.380 --> 01:01:29.489
And so you get a reduction
in the total amount

01:01:29.489 --> 01:01:31.780
of reflected light when you
put the silicon under glass

01:01:31.780 --> 01:01:35.620
because glass has a refractive
index somewhere between air

01:01:35.620 --> 01:01:37.750
and silicon.

01:01:37.750 --> 01:01:39.480
And then you get a
further reduction

01:01:39.480 --> 01:01:43.370
of the reflectance when you
have an anti-reflection coating

01:01:43.370 --> 01:01:45.730
with a refractive index
somewhere around--

01:01:45.730 --> 01:01:47.830
for this particular
system, silicon again

01:01:47.830 --> 01:01:49.570
has a higher refractive index.

01:01:49.570 --> 01:01:52.300
This used in anti-reflective
coating of a refractive index

01:01:52.300 --> 01:01:56.710
of 2.3 of some
thickness, probably

01:01:56.710 --> 01:01:59.800
somewhere around--
let's see, it'd

01:01:59.800 --> 01:02:03.520
be greater or smaller,
probably around 65,

01:02:03.520 --> 01:02:05.610
75 nanometer
somewhere that range.

01:02:05.610 --> 01:02:08.630
So what this is
saying is that you

01:02:08.630 --> 01:02:11.350
can minimize the
reflection of light

01:02:11.350 --> 01:02:13.080
off of the front
surface of your sample

01:02:13.080 --> 01:02:15.990
by using an intelligent
combination of the very

01:02:15.990 --> 01:02:18.040
first equation that we're
exposed to in the class

01:02:18.040 --> 01:02:20.480
today, which was the
reflected light as a function

01:02:20.480 --> 01:02:22.646
of refractive index, so
essentially refractive index

01:02:22.646 --> 01:02:25.490
matching and secondly, by
engineering by engineering

01:02:25.490 --> 01:02:28.220
an anti-reflective
coating, which oftentimes

01:02:28.220 --> 01:02:29.690
in the lingo of
solar cell science

01:02:29.690 --> 01:02:32.540
we call it an ARC, an
anti-reflective coating.

01:02:32.540 --> 01:02:36.430
And those two things combined
give us very low reflection

01:02:36.430 --> 01:02:39.190
off of the front surface.

01:02:39.190 --> 01:02:47.000
Probably 5% of our R&D
cells that we make at MIT

01:02:47.000 --> 01:02:49.640
use these sorts of
technologies, which are pretty

01:02:49.640 --> 01:02:51.210
standard in the industry.

01:02:51.210 --> 01:02:54.650
And you can see what
the hit is, right?

01:02:54.650 --> 01:02:56.610
Let's see, if I'm just
using a bare material,

01:02:56.610 --> 01:02:58.770
if I'm getting 30%
reflection, I'm

01:02:58.770 --> 01:03:04.010
getting a 30% drop in the
current output of my device.

01:03:04.010 --> 01:03:05.680
That's pretty significant.

01:03:05.680 --> 01:03:08.560
So these are simple ways to
improve performance of devices.

01:03:11.430 --> 01:03:15.160
If you want to become
fancy and actually do

01:03:15.160 --> 01:03:19.080
what's called a ray tracing
to calculate the path of light

01:03:19.080 --> 01:03:22.110
through a medium, there
is software available

01:03:22.110 --> 01:03:24.950
that will take all of
what we've discussed today

01:03:24.950 --> 01:03:26.570
and calculate it
for you so you don't

01:03:26.570 --> 01:03:30.750
have to walk through
the expressions

01:03:30.750 --> 01:03:32.000
that we just walked through.

01:03:32.000 --> 01:03:35.000
It is easy.

01:03:35.000 --> 01:03:37.110
In other words, you
plug something in.

01:03:37.110 --> 01:03:38.160
You get some ray traces.

01:03:38.160 --> 01:03:40.830
You can calculate reflectance
and so forth, transmittance.

01:03:40.830 --> 01:03:43.424
But it's as smart as
what you put into it.

01:03:43.424 --> 01:03:45.590
It's really important to
understand the fundamentals

01:03:45.590 --> 01:03:48.590
behind any simulation software
because you will get out

01:03:48.590 --> 01:03:50.410
of it what you put into it.

01:03:50.410 --> 01:03:52.840
You will not be able to
pick up on obvious things

01:03:52.840 --> 01:03:55.890
that you might of--
for example, double

01:03:55.890 --> 01:03:57.390
clicked on this
little material here

01:03:57.390 --> 01:04:01.290
and find the real component of
the refractive index completely

01:04:01.290 --> 01:04:02.130
wrong.

01:04:02.130 --> 01:04:03.854
And you might not notice it.

01:04:03.854 --> 01:04:05.270
You might not pick
up on it if you

01:04:05.270 --> 01:04:07.600
don't have some good
intuition which is

01:04:07.600 --> 01:04:09.410
grounded in the fundamentals.

01:04:09.410 --> 01:04:11.880
And so it's important
that you understand

01:04:11.880 --> 01:04:13.250
what we've presented today.

01:04:13.250 --> 01:04:15.624
It's important you understand
the reading and, of course,

01:04:15.624 --> 01:04:19.290
do the p-set as well to really
drive those fundamentals home.

01:04:19.290 --> 01:04:23.450
So to kind of put a big umbrella
over the entire lecture,

01:04:23.450 --> 01:04:28.630
light management ensures
that the absorbtance is high.

01:04:28.630 --> 01:04:31.790
The absorbtance would
be, essentially,

01:04:31.790 --> 01:04:33.833
the amount of light
getting absorbed inside

01:04:33.833 --> 01:04:38.160
of the material, normalized by
the amount of light going in,

01:04:38.160 --> 01:04:39.370
so 1 minus r.

01:04:39.370 --> 01:04:43.910
So we want to ensure that
light enters the absorber.

01:04:43.910 --> 01:04:45.516
We want to minimize reflection.

01:04:45.516 --> 01:04:48.015
We want to ensure good light
trapping inside of the absorber

01:04:48.015 --> 01:04:50.930
as well, the absorber
being the material,

01:04:50.930 --> 01:04:53.347
our photovoltaic material, the
ones absorbing the sunlight

01:04:53.347 --> 01:04:55.388
and ultimately going to
be generating the charge.

01:04:55.388 --> 01:04:56.540
So we call it the absorber.

01:04:56.540 --> 01:04:58.540
So we want to ensure good
light trapping inside it.

01:04:58.540 --> 01:05:00.414
We want to ensure the
maximum amount of light

01:05:00.414 --> 01:05:01.780
gets trapped inside.

01:05:01.780 --> 01:05:04.662
We want to maximize the
optical path length within it.

01:05:04.662 --> 01:05:06.120
And we want to
minimize reflectance

01:05:06.120 --> 01:05:08.280
off the front surface.

01:05:08.280 --> 01:05:10.530
There are fancier ways of
light management as well

01:05:10.530 --> 01:05:12.570
that don't involve light
trapping necessarily

01:05:12.570 --> 01:05:16.930
but light manipulation or even
semiconductor manipulation.

01:05:16.930 --> 01:05:20.600
You can, for instance,
change the wave length

01:05:20.600 --> 01:05:23.370
of the incoming light.

01:05:23.370 --> 01:05:25.000
One very simple
example of this is

01:05:25.000 --> 01:05:27.750
when you shine, say for
example, red light on a phosphor

01:05:27.750 --> 01:05:30.290
and then it glows
green in the dark.

01:05:30.290 --> 01:05:32.250
That's a wavelength
change-- maybe not red.

01:05:32.250 --> 01:05:35.650
You'd probably have to shine
blue to have it glow green.

01:05:35.650 --> 01:05:38.125
That's an example of a
spectral down converter where

01:05:38.125 --> 01:05:39.500
it's taking a
higher energy light

01:05:39.500 --> 01:05:41.782
and converting it into
lower energy light.

01:05:41.782 --> 01:05:43.240
Likewise, there
are folks out there

01:05:43.240 --> 01:05:45.570
trying to do spectral up
converters where they take

01:05:45.570 --> 01:05:48.210
two lower energy photons
then somehow convert that

01:05:48.210 --> 01:05:50.280
into a higher energy photon.

01:05:50.280 --> 01:05:52.970
And so since our
absorption coefficient

01:05:52.970 --> 01:05:54.740
is dependent on
wavelength, if we're

01:05:54.740 --> 01:05:57.350
able to shift the wavelength
of the light around

01:05:57.350 --> 01:05:59.540
by engineering materials
near the surface,

01:05:59.540 --> 01:06:01.230
we can enhance
absorption as well.

01:06:01.230 --> 01:06:03.470
That is a form-- a valid
form-- of light management.

01:06:03.470 --> 01:06:05.780
It has additional
benefits as well.

01:06:05.780 --> 01:06:08.330
If we can eliminate the longer
wavelength stuff out here,

01:06:08.330 --> 01:06:11.760
which is heat, performance
of most solar cell

01:06:11.760 --> 01:06:13.570
suffers when they get hot.

01:06:13.570 --> 01:06:15.300
And we'll learn why
that is about five

01:06:15.300 --> 01:06:16.700
or 10 lectures from now.

01:06:16.700 --> 01:06:19.190
And so if we manage to
do spectral up converting

01:06:19.190 --> 01:06:22.660
or reflect that long wavelength
light away from our device,

01:06:22.660 --> 01:06:24.526
we can improve
performance there as well.

01:06:24.526 --> 01:06:26.150
That's another form
of light management

01:06:26.150 --> 01:06:30.370
that doesn't necessarily
involve light trapping.

01:06:30.370 --> 01:06:34.050
So again, I wanted
to really emphasize

01:06:34.050 --> 01:06:36.990
that light management
is necessary devices.

01:06:36.990 --> 01:06:39.837
This is no light
trapping, the blue curve,

01:06:39.837 --> 01:06:42.420
and with light trapping, light
trapping being essentially just

01:06:42.420 --> 01:06:45.495
an engineered coating
on the backside,

01:06:45.495 --> 01:06:47.620
on the backside of your
device, of lights coming in

01:06:47.620 --> 01:06:48.209
through here.

01:06:48.209 --> 01:06:49.750
I've engineered a
coating on the back

01:06:49.750 --> 01:06:52.660
to reflect the light back so
that it gets a second bounce

01:06:52.660 --> 01:06:53.594
through the material.

01:06:53.594 --> 01:06:55.010
I've engineered
the front surface,

01:06:55.010 --> 01:06:57.860
texturized it so that we have
not only the benefit of two

01:06:57.860 --> 01:07:00.930
bounces, double the
chance of light going in,

01:07:00.930 --> 01:07:04.370
but also the Snell's
Law working in our favor

01:07:04.370 --> 01:07:06.410
and increasing the
optical pathway.

01:07:06.410 --> 01:07:12.082
And so all told, the one
reason why this boost is so big

01:07:12.082 --> 01:07:14.290
right here is because I'm
increasing the optical path

01:07:14.290 --> 01:07:15.710
length, the effective
optical path

01:07:15.710 --> 01:07:18.770
length, relative to the
thickness of my material.

01:07:18.770 --> 01:07:22.610
And as a result, I'm getting
a much larger current output.

01:07:22.610 --> 01:07:24.902
I'm generating many
more free carriers

01:07:24.902 --> 01:07:25.860
instead of my material.

01:07:25.860 --> 01:07:27.720
I'm absorbing much
more light inside

01:07:27.720 --> 01:07:31.827
of my material, just a very
simple calculation versus cell

01:07:31.827 --> 01:07:32.800
thickness.

01:07:32.800 --> 01:07:34.841
And obviously the thicker
and thicker and thicker

01:07:34.841 --> 01:07:38.065
you go in your device, the
less important this becomes.

01:07:38.065 --> 01:07:40.190
Because the less important
light trapping-- I mean,

01:07:40.190 --> 01:07:41.600
you have the entire thickness.

01:07:41.600 --> 01:07:44.560
I can absorb the majority
of the light in one pass.

01:07:44.560 --> 01:07:48.730
But if you have
a thinner device,

01:07:48.730 --> 01:07:50.106
it really begins to matter.

01:07:50.106 --> 01:07:51.480
Once the thickness
of your device

01:07:51.480 --> 01:07:54.684
starts approaching the
optical absorption, or 1

01:07:54.684 --> 01:07:56.600
over the optical absorption
coefficient, which

01:07:56.600 --> 01:07:59.250
is the extension
length, then it really

01:07:59.250 --> 01:08:02.390
begins to matter in
the absorption length.

01:08:02.390 --> 01:08:05.170
Light trapping can still matter
for thick devices, though.

01:08:05.170 --> 01:08:10.830
Because if you manage to make
the light essentially refract

01:08:10.830 --> 01:08:14.330
or bend, if you will, so that
it travels near the surface,

01:08:14.330 --> 01:08:16.270
the distance that
those excited carriers

01:08:16.270 --> 01:08:18.454
have to travel to be
collected is shorter.

01:08:18.454 --> 01:08:21.240
And so you can get an additional
benefit from thicker devices

01:08:21.240 --> 01:08:22.823
by engineering light
trapping as well.

01:08:25.350 --> 01:08:27.535
OK, any questions about this?

01:08:27.535 --> 01:08:30.175
This is kind of important.

01:08:30.175 --> 01:08:32.300
This is why we spent all
this time in lecture today

01:08:32.300 --> 01:08:35.810
talking about light management
is because of this plot right

01:08:35.810 --> 01:08:36.970
here.

01:08:36.970 --> 01:08:40.140
That's why.

01:08:40.140 --> 01:08:42.250
I just wanted to show
you a cross section

01:08:42.250 --> 01:08:43.679
of very high efficiency device.

01:08:43.679 --> 01:08:45.220
This is one of the
highest efficiency

01:08:45.220 --> 01:08:47.040
silicon-based devices
are out there.

01:08:47.040 --> 01:08:51.550
And we have these
so-called backside mirror,

01:08:51.550 --> 01:08:54.540
which is really just a layer
of dielectric material,

01:08:54.540 --> 01:08:56.420
typically, that
reflects the light off

01:08:56.420 --> 01:08:58.469
of that interface
using the equation

01:08:58.469 --> 01:09:00.260
that we saw at the very
beginning of class,

01:09:00.260 --> 01:09:05.500
the r equal to [INAUDIBLE]
n minus 1 quantity squared

01:09:05.500 --> 01:09:09.770
divided by open parentheses
n plus 1 quantity squared.

01:09:09.770 --> 01:09:12.680
So that's benefiting here from
the change of refractive index

01:09:12.680 --> 01:09:15.060
going through your silicon
to that dielectric material

01:09:15.060 --> 01:09:17.609
in the back.

01:09:17.609 --> 01:09:19.420
They definitely take
good advantage of it.

01:09:19.420 --> 01:09:20.420
Where you have
your metal, you're

01:09:20.420 --> 01:09:21.439
going to be absorbing the light.

01:09:21.439 --> 01:09:23.730
Or you have a higher probability
of absorbing the light

01:09:23.730 --> 01:09:26.470
than you would if you had
a dielectric semiconductor

01:09:26.470 --> 01:09:27.630
interface.

01:09:27.630 --> 01:09:29.950
So the device design can
get pretty complicated

01:09:29.950 --> 01:09:32.740
for these super high
efficiency devices.

01:09:32.740 --> 01:09:36.149
And they're worried quite a bit
about trapping, other things

01:09:36.149 --> 01:09:36.649
as well.

01:09:36.649 --> 01:09:38.630
AUDIENCE: Coefficient,
is that one there?

01:09:38.630 --> 01:09:40.490
TONIO BUONASSISI:
This one right here?

01:09:40.490 --> 01:09:46.890
In the lab, 24.2%, in commercial
production, 22% and change.

01:09:46.890 --> 01:09:50.580
22.4%, I think.

01:09:50.580 --> 01:09:53.200
Just to throw some
last things out there

01:09:53.200 --> 01:09:55.790
since we're five
minutes to closure.

01:09:55.790 --> 01:09:59.880
Snell's Law assumes that there's
no phase shift of the light

01:09:59.880 --> 01:10:02.174
as it transfers from
one medium to another.

01:10:02.174 --> 01:10:03.715
If you introduce a
phase shift-- this

01:10:03.715 --> 01:10:06.015
is just a paper published
in Science last week

01:10:06.015 --> 01:10:08.670
by our friends over at
Harvard, Federico Capasso.

01:10:08.670 --> 01:10:10.660
If you introduce a
phase shift of the light

01:10:10.660 --> 01:10:12.368
as it goes through
one medium or another,

01:10:12.368 --> 01:10:14.280
now you can start
doing some fun things.

01:10:14.280 --> 01:10:18.530
If you introduce a constant
phase shift gradient

01:10:18.530 --> 01:10:21.540
throughout the surface of a
material, let's say right here,

01:10:21.540 --> 01:10:23.970
then you can cause
each node, each point

01:10:23.970 --> 01:10:27.140
within your material, to
lag by an increasing amount,

01:10:27.140 --> 01:10:29.900
so that your wave
front now bends.

01:10:29.900 --> 01:10:33.410
You can think of these as kind
of a Huygen wavefront forming

01:10:33.410 --> 01:10:35.950
as a result of these
small nodes here.

01:10:35.950 --> 01:10:38.570
And if you can tailor
the phase independently

01:10:38.570 --> 01:10:41.805
at each one of these points, you
can cause an increasing delay

01:10:41.805 --> 01:10:43.209
as you go across.

01:10:43.209 --> 01:10:45.000
And that will cause
the light, essentially,

01:10:45.000 --> 01:10:48.290
if you trace through the
points of maximum intensity,

01:10:48.290 --> 01:10:51.432
say the pink, you'll see
that the light is bent.

01:10:51.432 --> 01:10:52.390
And that's pretty cool.

01:10:52.390 --> 01:10:56.100
Because now we
can, in principle,

01:10:56.100 --> 01:10:58.475
if this is hot off the press--
and then of course there's

01:10:58.475 --> 01:11:00.974
a whole flurry of researchers
out there trying to figure out

01:11:00.974 --> 01:11:02.840
how to use this
to our advantage,

01:11:02.840 --> 01:11:06.040
but with anomalous refraction,
in principle, now you

01:11:06.040 --> 01:11:08.430
can tailor the angle at
which light bends inside

01:11:08.430 --> 01:11:09.490
of the material.

01:11:09.490 --> 01:11:11.620
Perhaps you can even exceed
the Yablonovitch limit

01:11:11.620 --> 01:11:14.424
inside of the material
as a result of this.

01:11:14.424 --> 01:11:15.590
And so it's really exciting.

01:11:15.590 --> 01:11:17.421
There's stuff
coming up every day.

01:11:17.421 --> 01:11:18.170
This is the point.

01:11:18.170 --> 01:11:20.760
There's stuff coming out every
day on light trapping and light

01:11:20.760 --> 01:11:23.640
management.

01:11:23.640 --> 01:11:25.870
Mostly it's for
photonic devices.

01:11:25.870 --> 01:11:28.980
But they can be transferred
over into solar cells as well.

01:11:28.980 --> 01:11:30.820
So it's going to
keep your eyes open.

01:11:30.820 --> 01:11:34.210
And another example
of the photon up/down

01:11:34.210 --> 01:11:39.230
converters, there's
recent reports in SPIE,

01:11:39.230 --> 01:11:42.030
a lot of interest in
the optics community.

01:11:42.030 --> 01:11:46.650
There was a TR35 award
given to a person who

01:11:46.650 --> 01:11:48.290
studying this topic.

01:11:48.290 --> 01:11:51.863
So it is, as well, a
very exciting and up

01:11:51.863 --> 01:11:52.970
and coming field.

01:11:52.970 --> 01:11:55.670
Again, the opportunities
there of manipulating

01:11:55.670 --> 01:11:59.530
light are large, are vast.

01:11:59.530 --> 01:12:03.150
So the laws, if you
will, that constrain us,

01:12:03.150 --> 01:12:05.750
that we've discussed
today in class,

01:12:05.750 --> 01:12:09.180
don't let that
constrain your thinking.

01:12:09.180 --> 01:12:10.700
That's my final message.

01:12:10.700 --> 01:12:12.250
Thanks.