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

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00:00:27,630 --> 00:00:30,000
or it's the first
technical discussion

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00:00:30,000 --> 00:00:32,490
of the actual solar
cell device itself.

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00:00:32,490 --> 00:00:35,140
We talked last
class about the sun

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00:00:35,140 --> 00:00:37,197
and about the nature
of the solar resource.

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00:00:37,197 --> 00:00:39,780
Today we're going to be talking
about the interaction of light

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with matter.

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00:00:40,920 --> 00:00:44,270
In particular, we're
focusing on light absorption.

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00:00:44,270 --> 00:00:47,050
This lecture could alternatively
be called "Light Not Getting

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00:00:47,050 --> 00:00:50,740
Absorbed" or "Optical Losses."

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00:00:50,740 --> 00:00:55,210
Both are important, and both
are related, as we'll see.

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00:00:55,210 --> 00:00:58,980
So this is part of the
fundamentals of the course.

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00:00:58,980 --> 00:01:01,270
Just to situate
ourselves, we're here

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00:01:01,270 --> 00:01:03,645
right now in the fundamentals,
the first third of course.

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00:01:03,645 --> 00:01:05,228
Then we'll talk about
the technologies

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00:01:05,228 --> 00:01:06,490
and the cross-cutting themes.

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00:01:06,490 --> 00:01:07,906
And what we're
going to talk about

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00:01:07,906 --> 00:01:10,330
is extremely important
because it allows us

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00:01:10,330 --> 00:01:12,430
to understand the technologies.

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00:01:12,430 --> 00:01:15,500
Once we begin discussing them
and we discuss cost trade

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00:01:15,500 --> 00:01:19,524
offs of implementing
this particular technique

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00:01:19,524 --> 00:01:21,190
for the way for it
to absorb more light,

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00:01:21,190 --> 00:01:23,920
we can appreciate how
much we can quantify

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00:01:23,920 --> 00:01:27,450
the impact of that
technology development,

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00:01:27,450 --> 00:01:30,232
and we could also later
on ascribe a cost to it,

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00:01:30,232 --> 00:01:34,560
to determine the total
cost benefit analysis.

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00:01:34,560 --> 00:01:37,840
So conversion
efficiency is really

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00:01:37,840 --> 00:01:40,490
what dictates the performance
of the device, the solar cell

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00:01:40,490 --> 00:01:41,550
device.

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00:01:41,550 --> 00:01:46,370
It's how the solar cell device
converts sunlight, the input

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00:01:46,370 --> 00:01:48,680
energy, to some usable
output energy, which

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00:01:48,680 --> 00:01:51,520
is in the form of electricity,
typically, from a solar panel.

40
00:01:51,520 --> 00:01:53,720
so the electricity
coming out of these

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00:01:53,720 --> 00:01:55,780
leads, for instance, right here.

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00:01:55,780 --> 00:02:00,230
And that conversion efficiency,
that simple equation,

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00:02:00,230 --> 00:02:03,340
for most solar cells, can
break down into the following.

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00:02:03,340 --> 00:02:04,340
You have inputs.

45
00:02:04,340 --> 00:02:05,590
Sorry for the small font here.

46
00:02:05,590 --> 00:02:06,850
This reads solar spectrum.

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00:02:06,850 --> 00:02:08,430
That's your input.

48
00:02:08,430 --> 00:02:11,330
Your output, which is
the charge collection,

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00:02:11,330 --> 00:02:13,750
it's a collective charge
coming out of your device,

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00:02:13,750 --> 00:02:16,800
and a bunch of steps in between.

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00:02:16,800 --> 00:02:19,910
So from the solar spectrum,
we have to absorb that light,

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00:02:19,910 --> 00:02:23,110
then we have to excite
charge within the material.

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00:02:23,110 --> 00:02:25,940
Then that charge has to move
around inside the material

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00:02:25,940 --> 00:02:29,210
to get to the metallic
context in the front side.

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00:02:29,210 --> 00:02:32,570
Charge separation has to occur
for there to be a voltage.

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00:02:32,570 --> 00:02:34,890
And finally, the charge
collection process.

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00:02:34,890 --> 00:02:38,620
And so the total
efficiency of this device

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00:02:38,620 --> 00:02:42,547
is the product of each of
these individual processes.

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00:02:42,547 --> 00:02:44,380
And so if you're making
a solar cell device,

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00:02:44,380 --> 00:02:47,450
and I know about a third of you
are based on your background

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00:02:47,450 --> 00:02:51,650
surveys, this diagram right
here will ring true to you.

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00:02:51,650 --> 00:02:53,940
It's Liebig's Law
of the Minimum.

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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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00:02:58,820 --> 00:03:03,640
And the water will flow out
of whatever piece of wood

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00:03:03,640 --> 00:03:04,930
is the shortest.

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00:03:04,930 --> 00:03:07,460
And in the case of
a solar cell device,

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00:03:07,460 --> 00:03:09,840
you can ascribe a
certain name to each

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00:03:09,840 --> 00:03:11,280
of these pieces of wood.

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00:03:11,280 --> 00:03:13,590
We'll learn what each
of those are with time.

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00:03:13,590 --> 00:03:16,060
But one of the big
ones is optical losses.

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00:03:16,060 --> 00:03:19,140
And the optical losses
tend to be rather severe

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00:03:19,140 --> 00:03:21,019
on some of our lab scale cells.

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00:03:21,019 --> 00:03:23,060
So one of the easiest ways
of boosting efficiency

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00:03:23,060 --> 00:03:25,920
is simply to take care
of your optical losses

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00:03:25,920 --> 00:03:29,630
and to minimize the amount of
light reflected or not absorbed

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00:03:29,630 --> 00:03:32,320
into maximizing amount of
life that's actually absorbed.

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00:03:32,320 --> 00:03:33,990
And so to do that,
there are a number

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00:03:33,990 --> 00:03:37,005
of standard techniques and some
cutting edge research areas.

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00:03:37,005 --> 00:03:38,880
And I'll attempt to give
you a broad overview

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00:03:38,880 --> 00:03:41,180
and survey of both,
assuming, of course,

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00:03:41,180 --> 00:03:43,900
you've done your
background reading.

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00:03:43,900 --> 00:03:46,540
So the learning
objectives, the first

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00:03:46,540 --> 00:03:48,290
is to be able to
calculate the reflectance

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00:03:48,290 --> 00:03:51,940
in non-absorption optical
losses of a solar cell.

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00:03:51,940 --> 00:03:54,680
So this is essentially all
the light that's not absorbed.

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00:03:54,680 --> 00:03:57,590
We want to be able
to calculate that.

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00:03:57,590 --> 00:04:00,360
The second is to describe
the physical underpinnings

89
00:04:00,360 --> 00:04:04,900
and the implementations of four
to five-- there are five here.

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00:04:04,900 --> 00:04:06,790
I added one at the end.

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00:04:06,790 --> 00:04:10,330
Four to five advanced methods
of reducing optical losses.

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00:04:10,330 --> 00:04:12,230
So there are
technologies, techniques

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00:04:12,230 --> 00:04:14,870
that we've used that we've
developed over time that we can

94
00:04:14,870 --> 00:04:17,079
use to minimize
the optical losses,

95
00:04:17,079 --> 00:04:20,430
to minimize the amount of
light reflected or not absorbed

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00:04:20,430 --> 00:04:23,280
inside of a solar cell device.

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00:04:23,280 --> 00:04:25,390
So to think of this
pictorially, we

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00:04:25,390 --> 00:04:28,120
can come up with the
following diagram, where

99
00:04:28,120 --> 00:04:31,560
we have some incident energy,
in this case incident light.

100
00:04:31,560 --> 00:04:32,850
Here's our medium.

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00:04:32,850 --> 00:04:34,767
Here's the amount of
light that gets absorbed.

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00:04:34,767 --> 00:04:37,016
Here's the amount of light
that gets transmitted right

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00:04:37,016 --> 00:04:39,340
through that does not get
absorbed within the material

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00:04:39,340 --> 00:04:40,369
upon passing through it.

105
00:04:40,369 --> 00:04:41,910
And there's a certain
amount of light

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00:04:41,910 --> 00:04:44,700
that just gets reflected off
the front of your solar cell

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00:04:44,700 --> 00:04:45,480
device.

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00:04:45,480 --> 00:04:48,900
We want to, obviously,
maximize this part right here.

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00:04:53,260 --> 00:04:55,840
So to begin, we
give a quick review

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00:04:55,840 --> 00:04:58,990
of light, the nature of light.

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00:04:58,990 --> 00:05:02,310
This is going back to the
particle wave duality of light.

112
00:05:02,310 --> 00:05:04,790
It will be useful alternatively
to think about light

113
00:05:04,790 --> 00:05:08,240
as a particle, quant of
light, or to think about light

114
00:05:08,240 --> 00:05:11,380
as a wave, depending on what
light management technique

115
00:05:11,380 --> 00:05:13,200
we're going to be describing.

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00:05:13,200 --> 00:05:16,830
And in particular, I'd
like to just highlight

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00:05:16,830 --> 00:05:18,470
these equations over here.

118
00:05:18,470 --> 00:05:22,330
The notion that one can define
the energy of a photon coming

119
00:05:22,330 --> 00:05:25,250
in, and that photon has
a certain wavelength,

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00:05:25,250 --> 00:05:27,460
a certain frequency, a
certain wave length associated

121
00:05:27,460 --> 00:05:30,510
with it-- frequency and
wavelength-- related,

122
00:05:30,510 --> 00:05:32,030
of course, by the
speed of light,

123
00:05:32,030 --> 00:05:34,970
Planck's constant, and so forth.

124
00:05:34,970 --> 00:05:39,100
So just to situate ourselves
with broad numbers,

125
00:05:39,100 --> 00:05:43,240
so when we dive in and talk
about spatial dimensions

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00:05:43,240 --> 00:05:45,150
in relation to the
wavelength of the light,

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00:05:45,150 --> 00:05:47,880
we're in a situation
where we can actually

128
00:05:47,880 --> 00:05:51,250
have a horse sense, a
common sense, about it.

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00:05:51,250 --> 00:05:53,490
The visible photon
wavelengths are usually

130
00:05:53,490 --> 00:05:54,770
in the hundreds of nanometers.

131
00:05:54,770 --> 00:05:57,980
And the solar spectrum
peaks somewhere around 550,

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00:05:57,980 --> 00:06:00,360
just good numbers
to have in mind.

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00:06:00,360 --> 00:06:03,940
So this was that solar spectrum,
the integrated solar radiance

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00:06:03,940 --> 00:06:05,700
versus wavelength.

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00:06:05,700 --> 00:06:10,020
And the second point
that is equally valid,

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00:06:10,020 --> 00:06:14,322
we can describe the wavelengths
of the incoming light,

137
00:06:14,322 --> 00:06:16,030
wavelengths of the
incoming light lambda,

138
00:06:16,030 --> 00:06:19,390
or we can describe the energies
of the incoming light, this E

139
00:06:19,390 --> 00:06:21,770
sub ph, the energy
of the photons.

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00:06:21,770 --> 00:06:24,410
So just to situate
ourselves again,

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00:06:24,410 --> 00:06:27,830
the visible photon energies
are typically in a range of 0.6

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00:06:27,830 --> 00:06:31,630
to 6 eV, electron volts,
again, with the peak

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00:06:31,630 --> 00:06:34,320
of the solar spectrum at
550 nanometers, somewhere

144
00:06:34,320 --> 00:06:36,260
around 2.3 eV.

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00:06:36,260 --> 00:06:37,430
Good.

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00:06:37,430 --> 00:06:42,590
So a simple thing to keep in
mind, for those high energy

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00:06:42,590 --> 00:06:44,425
particle physicists
in the room, that when

148
00:06:44,425 --> 00:06:45,990
we're talking about
visible light,

149
00:06:45,990 --> 00:06:49,390
we're interacting with a very
specific type of electron

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00:06:49,390 --> 00:06:50,580
inside of our system.

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00:06:50,580 --> 00:06:51,770
It's the valence electrons.

152
00:06:51,770 --> 00:06:54,620
These are the electrons that
are typically most loosely bound

153
00:06:54,620 --> 00:06:56,550
inside of a system
or I would say

154
00:06:56,550 --> 00:07:01,350
in the outer shells of the
atoms within the material.

155
00:07:01,350 --> 00:07:04,140
You're typically not interacting
with core shell electrons

156
00:07:04,140 --> 00:07:05,320
with visible light.

157
00:07:05,320 --> 00:07:06,790
For that, you need x-rays.

158
00:07:06,790 --> 00:07:10,650
So this is just something
to keep in mind.

159
00:07:10,650 --> 00:07:14,125
When we start looking at
the wavelength dependence

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00:07:14,125 --> 00:07:16,670
of absorption inside
of a material,

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00:07:16,670 --> 00:07:20,690
you can have, for example, in
the visible range, a decreasing

162
00:07:20,690 --> 00:07:23,660
depth of penetration of the
light with increasing energy,

163
00:07:23,660 --> 00:07:25,535
whereas with x-rays,
it's the exact opposite.

164
00:07:25,535 --> 00:07:28,076
It's because you're dealing with
different types of electrons

165
00:07:28,076 --> 00:07:29,050
and the material.

166
00:07:29,050 --> 00:07:30,710
So just to situate
ourselves, I know

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00:07:30,710 --> 00:07:33,460
we have a fair number physicists
and chemists in the room.

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00:07:33,460 --> 00:07:37,750
That's a message
geared toward them.

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00:07:37,750 --> 00:07:41,870
Let's describe how light
interacts with matter.

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00:07:41,870 --> 00:07:45,640
And first off, come up
with a few variables.

171
00:07:45,640 --> 00:07:48,690
Define a few units that
will make it easier

172
00:07:48,690 --> 00:07:52,110
for us to understand how light
is interacting with matter.

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00:07:52,110 --> 00:07:53,900
And so here what
I've done for you

174
00:07:53,900 --> 00:07:57,880
is placed the equation that
describes the complex index

175
00:07:57,880 --> 00:08:01,270
of refraction of a material.

176
00:08:01,270 --> 00:08:03,250
What this means,
effectively, you

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00:08:03,250 --> 00:08:06,410
can think about this refractive
index of the material

178
00:08:06,410 --> 00:08:11,250
as being comprised of
two different components.

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00:08:11,250 --> 00:08:13,584
For now, it's going
to be fairly cerebral,

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00:08:13,584 --> 00:08:15,250
but I'm going to
reduce it to practicing

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00:08:15,250 --> 00:08:16,760
in a couple of slides.

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00:08:16,760 --> 00:08:19,020
The real component of
the refractive index--

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00:08:19,020 --> 00:08:22,150
and the refractive index is
material-specific property.

184
00:08:22,150 --> 00:08:23,780
So if I have, for
example, silicon

185
00:08:23,780 --> 00:08:25,430
or if I have silicon
nitride or if I

186
00:08:25,430 --> 00:08:27,180
have a particular
type of glass, it'll

187
00:08:27,180 --> 00:08:29,770
have a particular
refractive index.

188
00:08:29,770 --> 00:08:31,810
It's comprised of a
real component which

189
00:08:31,810 --> 00:08:34,256
indicates the phase velocity
inside of the material

190
00:08:34,256 --> 00:08:35,630
and an imaginary
component, which

191
00:08:35,630 --> 00:08:37,799
can be thought of as an
extinction coefficient.

192
00:08:37,799 --> 00:08:40,360
And it is related
to the attenuation

193
00:08:40,360 --> 00:08:44,690
of the light intensity as it
travels through that material.

194
00:08:44,690 --> 00:08:47,700
The measurements for those who
have already taken measurements

195
00:08:47,700 --> 00:08:50,450
before on a spectroscopic
ellipsometer, this

196
00:08:50,450 --> 00:08:53,921
is how you measure that
parameter up there.

197
00:08:53,921 --> 00:08:55,670
We don't have to dive
too deeply into that

198
00:08:55,670 --> 00:08:56,970
for the purposes of the class.

199
00:08:56,970 --> 00:08:59,340
It's just for background.

200
00:08:59,340 --> 00:09:02,700
Why these values are
important-- these values

201
00:09:02,700 --> 00:09:05,450
here describe the interaction
of light inside of a medium,

202
00:09:05,450 --> 00:09:07,160
inside of a material.

203
00:09:07,160 --> 00:09:09,410
And we use that
information to calculate

204
00:09:09,410 --> 00:09:12,700
engineering relevant parameters
such as reflectance of light

205
00:09:12,700 --> 00:09:14,410
off of a surface.

206
00:09:14,410 --> 00:09:17,920
So if we want to calculate what
is the reflectance of light off

207
00:09:17,920 --> 00:09:20,780
of the silicon right
here, I can calculate it

208
00:09:20,780 --> 00:09:22,550
by knowing these
properties right here,

209
00:09:22,550 --> 00:09:25,260
by knowing the real and
imaginary components

210
00:09:25,260 --> 00:09:30,140
of the refractive index
of silicon, in this case.

211
00:09:30,140 --> 00:09:32,060
And the reason
that's important is

212
00:09:32,060 --> 00:09:35,280
because we want to minimize
reflection off of surfaces.

213
00:09:35,280 --> 00:09:37,000
So I've come up with
the first equation

214
00:09:37,000 --> 00:09:40,850
right here which is describing
the reflectance from air

215
00:09:40,850 --> 00:09:43,530
to a solid, in this
case, from air where

216
00:09:43,530 --> 00:09:46,540
the refractive index
is 1 to a solid,

217
00:09:46,540 --> 00:09:48,720
namely, say for example,
silicon right here

218
00:09:48,720 --> 00:09:53,160
or glass, which has a finite
refractive index typically

219
00:09:53,160 --> 00:09:54,750
greater than 1.

220
00:09:54,750 --> 00:09:57,750
And so I have an equation here
that describes the reflectance.

221
00:09:57,750 --> 00:09:59,390
Let me dive a little
deeper into it

222
00:09:59,390 --> 00:10:01,050
and try to understand
what exactly

223
00:10:01,050 --> 00:10:03,290
that equation is telling me.

224
00:10:03,290 --> 00:10:07,170
So from the folks who have
studied mechanics, many of you

225
00:10:07,170 --> 00:10:09,190
are mechanical
engineers in the room,

226
00:10:09,190 --> 00:10:11,820
you may recall studying a
problem wherein you have

227
00:10:11,820 --> 00:10:14,130
two springs that are connected.

228
00:10:14,130 --> 00:10:16,390
They have different
spring constants,

229
00:10:16,390 --> 00:10:18,330
different stiffnesses,
shall we say.

230
00:10:18,330 --> 00:10:19,830
And you excite a wave over here.

231
00:10:19,830 --> 00:10:20,840
It travels down.

232
00:10:20,840 --> 00:10:22,930
And when it reaches the
interface between the two,

233
00:10:22,930 --> 00:10:24,346
part of the wave
is reflected back

234
00:10:24,346 --> 00:10:26,140
and part continues through.

235
00:10:26,140 --> 00:10:29,900
The speed of the
wave is changing

236
00:10:29,900 --> 00:10:31,810
as it goes from one
spring to the other,

237
00:10:31,810 --> 00:10:34,530
because the stiffness is
changing of the springs.

238
00:10:34,530 --> 00:10:37,670
And the amount reflected can
be described by this equation

239
00:10:37,670 --> 00:10:40,250
right here, which looks
awfully like the equation

240
00:10:40,250 --> 00:10:42,810
right above it, which is
describing the amount of light

241
00:10:42,810 --> 00:10:44,320
reflected off of an interface.

242
00:10:44,320 --> 00:10:49,500
And in reality, those ends have
a very similar meaning, the n

243
00:10:49,500 --> 00:10:50,270
and the z.

244
00:10:50,270 --> 00:10:51,770
The n, in the case
of light, which

245
00:10:51,770 --> 00:10:53,783
is the real components
of the refractive index.

246
00:10:53,783 --> 00:10:57,710
Mind you, this
parameter right here,

247
00:10:57,710 --> 00:10:59,460
this indicates phase
velocity in material.

248
00:10:59,460 --> 00:11:02,500
It could also be
thought of very loosely

249
00:11:02,500 --> 00:11:04,980
as the ability of an
electromagnetic wave coming

250
00:11:04,980 --> 00:11:08,280
into material to slosh
those electrons around.

251
00:11:08,280 --> 00:11:09,890
Not exactly a
stiffness coefficient,

252
00:11:09,890 --> 00:11:13,100
but it bears some
rough resemblance.

253
00:11:13,100 --> 00:11:16,350
So this is a method for
you to gain a foothold

254
00:11:16,350 --> 00:11:18,780
in this new area
of understanding

255
00:11:18,780 --> 00:11:20,820
the refractive
index of a material

256
00:11:20,820 --> 00:11:24,190
based on something you've
already seen before.

257
00:11:24,190 --> 00:11:26,660
So I would advise
taking this analogy

258
00:11:26,660 --> 00:11:28,770
as far as it will go
until it breaks down.

259
00:11:28,770 --> 00:11:30,840
Push it as far as it goes
until it breaks down.

260
00:11:30,840 --> 00:11:32,830
And you'll see at some
point it actually does,

261
00:11:32,830 --> 00:11:36,820
but it's a useful
place to start.

262
00:11:36,820 --> 00:11:40,020
So I'm going to ask you
a couple of questions.

263
00:11:40,020 --> 00:11:43,712
This might be rather
new for a lot of folks.

264
00:11:43,712 --> 00:11:45,420
But the purpose of
asking these questions

265
00:11:45,420 --> 00:11:46,500
is to get you thinking.

266
00:11:46,500 --> 00:11:49,110
And eventually we'll get
to a point of heightened

267
00:11:49,110 --> 00:11:51,860
understanding as a result.

268
00:11:51,860 --> 00:11:54,300
Tinted windows.

269
00:11:54,300 --> 00:11:57,220
So if you have a
tinted window, what

270
00:11:57,220 --> 00:12:00,010
is typically happening
at that tinted window?

271
00:12:00,010 --> 00:12:03,122
Why can't you see inside?

272
00:12:03,122 --> 00:12:04,580
What would you
imagine is going on?

273
00:12:04,580 --> 00:12:06,510
So let me go back to
this reflectance equation

274
00:12:06,510 --> 00:12:10,000
right here, this one.

275
00:12:10,000 --> 00:12:11,990
How would you modify
a reflectance off

276
00:12:11,990 --> 00:12:13,910
of a window, let's say?

277
00:12:13,910 --> 00:12:16,030
And let's drop the k's for now.

278
00:12:16,030 --> 00:12:19,350
Let's leave those aside and
just focus on this parameter

279
00:12:19,350 --> 00:12:21,660
right here, n minus
1 quantity squared

280
00:12:21,660 --> 00:12:23,560
n plus 1 quantity squared.

281
00:12:23,560 --> 00:12:28,110
What would increase the
reflectance off of that window,

282
00:12:28,110 --> 00:12:29,800
if I have a larger
n or a smaller n?

283
00:12:34,750 --> 00:12:38,660
If I have a bigger n, I
would get bigger reflectance.

284
00:12:38,660 --> 00:12:39,686
Is that right?

285
00:12:39,686 --> 00:12:42,851
r goes up?

286
00:12:42,851 --> 00:12:45,460
Well, you'd have to
plot it out, I guess.

287
00:12:45,460 --> 00:12:49,280
So if I change the refractive
index of the material

288
00:12:49,280 --> 00:12:52,175
that I am working with, I can
change the reflectivity off

289
00:12:52,175 --> 00:12:54,080
of that interface,
off of that surface.

290
00:12:54,080 --> 00:12:55,870
So if I add a
coating, for instance,

291
00:12:55,870 --> 00:12:59,720
to a window that increases
the reflectivity,

292
00:12:59,720 --> 00:13:05,600
then the amount of light that is
able to escape from the inside

293
00:13:05,600 --> 00:13:07,070
to my eyes decreases.

294
00:13:07,070 --> 00:13:10,010
Now, with normal
incident light, there

295
00:13:10,010 --> 00:13:11,810
is a beautiful
symmetry involved.

296
00:13:11,810 --> 00:13:14,710
That is, the amount
reflected off of one side

297
00:13:14,710 --> 00:13:18,960
is equal to the amount of light
reflected off the other side.

298
00:13:18,960 --> 00:13:23,830
So just the same way that
I'm losing the ability

299
00:13:23,830 --> 00:13:26,180
to see inside, the
folks inside are also

300
00:13:26,180 --> 00:13:27,740
losing the ability to see out.

301
00:13:27,740 --> 00:13:29,330
But they can still see out.

302
00:13:29,330 --> 00:13:31,090
Why is that?

303
00:13:31,090 --> 00:13:34,230
Why is it that with
the same reflectivity

304
00:13:34,230 --> 00:13:36,030
they're able to see
outside and I'm not

305
00:13:36,030 --> 00:13:38,321
able to see in through that
tinted window, through that

306
00:13:38,321 --> 00:13:41,630
car, for example, that's driving
by with the tinted glass?

307
00:13:41,630 --> 00:13:44,970
Why can't I see insight but they
can see out, what's going on?

308
00:13:44,970 --> 00:13:46,404
AUDIENCE: [INAUDIBLE].

309
00:13:46,404 --> 00:13:48,070
TONIO BUONASSISI:
Yeah, I hear somebody.

310
00:13:48,070 --> 00:13:49,486
AUDIENCE: The light
on the outside

311
00:13:49,486 --> 00:13:52,256
is much stronger in terms of
an absolute amount of light

312
00:13:52,256 --> 00:13:53,109
being reflected.

313
00:13:53,109 --> 00:13:54,400
TONIO BUONASSISI: Yep, exactly.

314
00:13:54,400 --> 00:13:57,700
So yes, the reflectivity
as a percentage

315
00:13:57,700 --> 00:14:00,247
is the same for both parties.

316
00:14:00,247 --> 00:14:01,830
But the amount of
light, the magnitude

317
00:14:01,830 --> 00:14:04,280
of the light from the
outside, is much, much greater

318
00:14:04,280 --> 00:14:05,580
than it is on the inside.

319
00:14:05,580 --> 00:14:07,620
Can anybody give me
just a gut sense.

320
00:14:07,620 --> 00:14:10,190
If I'm outside on a sunny
day, how much brighter

321
00:14:10,190 --> 00:14:13,180
is it outside versus
inside right here?

322
00:14:13,180 --> 00:14:15,130
Factor of?

323
00:14:15,130 --> 00:14:17,130
AUDIENCE: 100, maybe?

324
00:14:17,130 --> 00:14:19,940
TONIO BUONASSISI: Maybe a factor
of 10, somewhere in that range.

325
00:14:19,940 --> 00:14:22,742
And so when you walk
outside on a sunny day,

326
00:14:22,742 --> 00:14:24,700
you'll notice your eyes
adjusting a little bit.

327
00:14:24,700 --> 00:14:25,727
It'll take a minute.

328
00:14:25,727 --> 00:14:28,060
And when we walk back inside,
it will take a minute here

329
00:14:28,060 --> 00:14:29,460
for your eyes to adjust as well.

330
00:14:29,460 --> 00:14:31,460
That's because of the
difference in intensities.

331
00:14:31,460 --> 00:14:33,880
So if you imagine being
outside of that car

332
00:14:33,880 --> 00:14:40,147
and having 10 times the amount
of light being reflected,

333
00:14:40,147 --> 00:14:42,480
that small amount of light
that is actually transmitting

334
00:14:42,480 --> 00:14:44,680
through the window from the
car to the outside world

335
00:14:44,680 --> 00:14:48,280
will be washed out by the
amount of reflected light.

336
00:14:48,280 --> 00:14:50,460
Whereas if you're
inside the car,

337
00:14:50,460 --> 00:14:52,636
there's a lot of light
coming through that window,

338
00:14:52,636 --> 00:14:54,260
even though a lot of
it gets reflected,

339
00:14:54,260 --> 00:14:56,177
there's still a sizable
amount coming through.

340
00:14:56,177 --> 00:14:57,551
And the amount of
light that gets

341
00:14:57,551 --> 00:14:59,700
reflected off that window
of the internal light

342
00:14:59,700 --> 00:15:02,540
is small in relation to
the outside light that

343
00:15:02,540 --> 00:15:04,360
is being transmitted
through that window.

344
00:15:04,360 --> 00:15:08,897
So it's important to think
about these processes,

345
00:15:08,897 --> 00:15:10,980
both in terms of their
reflectance as a percentage

346
00:15:10,980 --> 00:15:14,880
but also the magnitudes
of the light involved.

347
00:15:14,880 --> 00:15:17,090
What if that glass pane
was flipped around?

348
00:15:17,090 --> 00:15:18,195
Would it change anything?

349
00:15:18,195 --> 00:15:24,960
If I took that glass and just
flipped it, would it change it?

350
00:15:24,960 --> 00:15:28,930
What about the
symmetry argument,

351
00:15:28,930 --> 00:15:32,270
that the amount of light is
reflected, the r reflectance,

352
00:15:32,270 --> 00:15:33,935
is the same from both sides?

353
00:15:33,935 --> 00:15:35,643
AUDIENCE: Is it not
the case that there's

354
00:15:35,643 --> 00:15:37,607
a coating on the outside?

355
00:15:37,607 --> 00:15:41,044
So if the change
in refracted index

356
00:15:41,044 --> 00:15:43,324
is an abrupt change
from the outside looking

357
00:15:43,324 --> 00:15:43,990
at this coating.

358
00:15:43,990 --> 00:15:45,448
Because on the
inside, you're going

359
00:15:45,448 --> 00:15:48,900
through some median glass,
which is more index matched

360
00:15:48,900 --> 00:15:49,900
than the outside.

361
00:15:49,900 --> 00:15:51,350
TONIO BUONASSISI:
Yeah, so I would

362
00:15:51,350 --> 00:15:53,580
advise you to actually walk
through that calculation.

363
00:15:53,580 --> 00:15:56,361
And what you'll find is it
winds up being the same.

364
00:15:56,361 --> 00:15:58,610
And it's because you have
to take all reflectances off

365
00:15:58,610 --> 00:16:01,730
of all these interfaces
into account.

366
00:16:01,730 --> 00:16:05,000
There are, in fact, three
interfaces-- the air,

367
00:16:05,000 --> 00:16:08,400
the glass; the glass, the
anti-reflection coding;

368
00:16:08,400 --> 00:16:10,700
and the anti-reflection
coding, the outside.

369
00:16:10,700 --> 00:16:14,110
This, of course, without getting
into quarter wave effects,

370
00:16:14,110 --> 00:16:18,480
which we'll get into
a minute, there's

371
00:16:18,480 --> 00:16:21,119
some higher order effects that
deal with phase change, which

372
00:16:21,119 --> 00:16:22,410
we haven't discussed right now.

373
00:16:22,410 --> 00:16:25,120
We're just assuming
that all of these layers

374
00:16:25,120 --> 00:16:28,960
are well above the wavelength of
the light in terms of thickness

375
00:16:28,960 --> 00:16:33,890
and that these equations, these
linear equations, are valid.

376
00:16:33,890 --> 00:16:34,670
Very good.

377
00:16:34,670 --> 00:16:37,800
So this is just
to get us situated

378
00:16:37,800 --> 00:16:39,900
with this new concept
of reflectance--

379
00:16:39,900 --> 00:16:43,200
and again, very
powerful equation.

380
00:16:43,200 --> 00:16:45,610
Keep in mind that this
is a very specific form

381
00:16:45,610 --> 00:16:47,491
of the reflectance from
an air into a solid.

382
00:16:47,491 --> 00:16:49,240
If you're going from
a solid into a solid,

383
00:16:49,240 --> 00:16:53,000
you'll add your n1
and your n2, depending

384
00:16:53,000 --> 00:17:00,030
on what material going into and
what material are coming from.

385
00:17:00,030 --> 00:17:04,569
So we're happy to walk through
that perhaps during recitation.

386
00:17:04,569 --> 00:17:06,760
OK, so what we're
going to do now

387
00:17:06,760 --> 00:17:09,344
is we've talked about
reflectance off of surfaces.

388
00:17:09,344 --> 00:17:11,510
What I'd like to do is talk
about a light absorption

389
00:17:11,510 --> 00:17:12,759
inside of a material.

390
00:17:12,759 --> 00:17:15,050
So let's imagine that through
the techniques that we're

391
00:17:15,050 --> 00:17:16,880
going to be discussing
later on in lecture,

392
00:17:16,880 --> 00:17:18,619
we manage to minimize
the amount of reflectance

393
00:17:18,619 --> 00:17:19,700
off the front surface.

394
00:17:19,700 --> 00:17:21,900
And now the light that's
incident on the material

395
00:17:21,900 --> 00:17:24,050
is actually going to go
inside and get absorbed

396
00:17:24,050 --> 00:17:25,630
by the material inside.

397
00:17:25,630 --> 00:17:28,390
We need to be able to understand
how light gets absorbed inside

398
00:17:28,390 --> 00:17:29,380
of matter.

399
00:17:29,380 --> 00:17:33,860
And for that, we apply a very
simple formulation inside

400
00:17:33,860 --> 00:17:37,000
of this class, which is called
Beer-Lambert's Law, which

401
00:17:37,000 --> 00:17:41,630
is a very simple
yet very powerful

402
00:17:41,630 --> 00:17:44,320
formulation that describes not
only the interaction of light

403
00:17:44,320 --> 00:17:45,861
with the solar cell
material but also

404
00:17:45,861 --> 00:17:48,850
light through the
atmosphere, light the water,

405
00:17:48,850 --> 00:17:51,490
many other forms of
optical absorption.

406
00:17:51,490 --> 00:17:55,120
And for that, I'd like to
call Joe up for a quick demo

407
00:17:55,120 --> 00:17:59,690
that he put together that will
allow us to actually plot out

408
00:17:59,690 --> 00:18:00,980
Beer-Lambert's Law.

409
00:18:00,980 --> 00:18:04,180
And I'd like to start
with what I would think

410
00:18:04,180 --> 00:18:05,710
of as a simple hypothesis.

411
00:18:05,710 --> 00:18:07,485
What we're going to
be doing, and Joe

412
00:18:07,485 --> 00:18:09,818
will explain this a minute,
what we're going to be doing

413
00:18:09,818 --> 00:18:13,080
is taking many
sheets of material.

414
00:18:13,080 --> 00:18:15,420
This is just some
polyethylene material,

415
00:18:15,420 --> 00:18:16,830
a little bit discolored.

416
00:18:16,830 --> 00:18:20,356
And we're going to shine a laser
down on to this photodiode.

417
00:18:20,356 --> 00:18:21,980
The photodiode current
will be measured

418
00:18:21,980 --> 00:18:23,730
by this little current
meter right here.

419
00:18:23,730 --> 00:18:27,870
And we'll be inserting these
panes of plastic in the middle.

420
00:18:27,870 --> 00:18:30,590
And as we increase the
thickness of the plastic,

421
00:18:30,590 --> 00:18:32,190
applying good
pressure in between

422
00:18:32,190 --> 00:18:36,530
to minimize the reflectance,
the air gap, for instance--

423
00:18:36,530 --> 00:18:39,490
as we increase the thickness
of the polyethylene,

424
00:18:39,490 --> 00:18:42,140
we will plot the total
transmitted light

425
00:18:42,140 --> 00:18:43,645
as measured by that photodiode.

426
00:18:43,645 --> 00:18:46,890
And so I'm going to come up
with a hypothesis of what's

427
00:18:46,890 --> 00:18:47,844
going to happen.

428
00:18:47,844 --> 00:18:49,260
I'm going to say
that if we double

429
00:18:49,260 --> 00:18:51,870
the thickness of
the polyethylene

430
00:18:51,870 --> 00:18:54,440
that we're going to halve the
amount of light going through.

431
00:18:54,440 --> 00:18:57,260
And if we triple, we're going
to reduce it by a third.

432
00:18:57,260 --> 00:19:00,000
And if we quadruple, we're
going to reduce it by a fourth.

433
00:19:00,000 --> 00:19:02,316
And let's see if the
hypothesis is correct.

434
00:19:02,316 --> 00:19:03,250
It's not.

435
00:19:03,250 --> 00:19:05,220
But we're going to test it.

436
00:19:05,220 --> 00:19:08,475
And it's a logical
thing you might assume.

437
00:19:08,475 --> 00:19:10,350
And then we'll walk
through a derivation that

438
00:19:10,350 --> 00:19:12,972
will correct our missed logic.

439
00:19:12,972 --> 00:19:13,680
So go ahead, Joe.

440
00:19:13,680 --> 00:19:14,221
Take it away.

441
00:19:14,221 --> 00:19:17,102
JOE: Sure, so if you guys want
to play along, that's fine too.

442
00:19:17,102 --> 00:19:19,060
I know there's lines in
the side of your notes.

443
00:19:19,060 --> 00:19:21,807
You can make little graph
paper, and it comes out

444
00:19:21,807 --> 00:19:23,050
looking really nice.

445
00:19:23,050 --> 00:19:26,117
So basically what we have is a
laser pointed and a photodiode.

446
00:19:26,117 --> 00:19:27,700
And the current out
of this photodiode

447
00:19:27,700 --> 00:19:31,080
is directly proportional to the
light hitting that photodiode.

448
00:19:31,080 --> 00:19:32,802
And it has a quant
efficiency, which

449
00:19:32,802 --> 00:19:34,968
we're going to learn what
that is in a few lectures,

450
00:19:34,968 --> 00:19:35,780
of about 60%.

451
00:19:35,780 --> 00:19:37,980
So of the photons
hitting it, you'll

452
00:19:37,980 --> 00:19:39,567
get a certain number
of electrons out,

453
00:19:39,567 --> 00:19:41,547
and that ratio's 60%.

454
00:19:41,547 --> 00:19:43,172
And so first of all,
we're going to see

455
00:19:43,172 --> 00:19:46,620
what it's like, what
the power of our-- yeah.

456
00:19:46,620 --> 00:19:51,480
So right now we're getting
about 1.32 milliamps.

457
00:19:51,480 --> 00:19:53,200
So Tonio's going to plot that.

458
00:19:53,200 --> 00:19:57,130
Then as we keep increasing and
put one layer of polyethylene,

459
00:19:57,130 --> 00:20:00,005
that drops to 0.75.

460
00:20:00,005 --> 00:20:01,380
TONIO BUONASSISI:
So before we go

461
00:20:01,380 --> 00:20:03,200
onto the next one,
what do people

462
00:20:03,200 --> 00:20:10,110
predict the next dot is going
to drop the total intensity to?

463
00:20:10,110 --> 00:20:13,386
Is it going to be kind of
a linear line like that?

464
00:20:13,386 --> 00:20:15,510
You'd expect it, right,
because you're doubling it.

465
00:20:15,510 --> 00:20:19,680
So you'd expect the intensity
to drop by another factor of 2.

466
00:20:19,680 --> 00:20:21,150
Why not?

467
00:20:21,150 --> 00:20:24,200
Where am I getting
a mistake here?

468
00:20:24,200 --> 00:20:26,225
Somebody says exponential.

469
00:20:26,225 --> 00:20:28,600
There's kind of this sense
that it should be exponential.

470
00:20:28,600 --> 00:20:31,040
What don't we add some
more filter in front,

471
00:20:31,040 --> 00:20:33,830
and we'll see what exactly
this comes out to be.

472
00:20:33,830 --> 00:20:34,747
JOE: This is with two.

473
00:20:34,747 --> 00:20:35,663
TONIO BUONASSISI: Two.

474
00:20:35,663 --> 00:20:36,630
JOE: Now we get 0.43.

475
00:20:36,630 --> 00:20:38,142
TONIO BUONASSISI: 0.43.

476
00:20:38,142 --> 00:20:38,910
OK.

477
00:20:38,910 --> 00:20:39,410
All right.

478
00:20:39,410 --> 00:20:42,070
Why don't we do one more just
to see what sort of trend

479
00:20:42,070 --> 00:20:42,775
we're getting.

480
00:20:42,775 --> 00:20:43,540
Still 0.26.

481
00:20:43,540 --> 00:20:44,276
JOE: 0.26.

482
00:20:44,276 --> 00:20:46,589
TONIO BUONASSISI: 0.26.

483
00:20:46,589 --> 00:20:48,450
Ah, wow.

484
00:20:48,450 --> 00:20:50,870
OK, so it didn't go
in a straight line.

485
00:20:50,870 --> 00:20:52,520
It's actually starting
to curve down.

486
00:20:52,520 --> 00:20:52,640
Cool.

487
00:20:52,640 --> 00:20:53,139
OK.

488
00:20:53,139 --> 00:20:55,022
JOE: And we keep going, 0.16.

489
00:20:55,022 --> 00:20:59,570
TONIO BUONASSISI: 0.16

490
00:20:59,570 --> 00:21:00,970
JOE: 0.10

491
00:21:00,970 --> 00:21:02,884
TONIO BUONASSISI: 0.10.

492
00:21:02,884 --> 00:21:04,230
OK.

493
00:21:04,230 --> 00:21:05,570
Look at that.

494
00:21:05,570 --> 00:21:08,060
What sort of curve is it?

495
00:21:08,060 --> 00:21:09,150
Exponential.

496
00:21:09,150 --> 00:21:10,975
It looks like one at least.

497
00:21:10,975 --> 00:21:12,850
And we can test whether
or not the hypothesis

498
00:21:12,850 --> 00:21:16,870
is correct by an
exponential fit, which

499
00:21:16,870 --> 00:21:18,990
happens to match pretty well.

500
00:21:18,990 --> 00:21:19,792
So--

501
00:21:19,792 --> 00:21:21,500
JOE: Now one other
quick thing you notice

502
00:21:21,500 --> 00:21:24,900
is that if you look at the fit,
the first point's a little bit

503
00:21:24,900 --> 00:21:26,304
higher than that fit.

504
00:21:26,304 --> 00:21:29,790
Anyone have an idea of why
that might be the case?

505
00:21:29,790 --> 00:21:31,920
What are we ignoring
in this experiment?

506
00:21:31,920 --> 00:21:34,145
AUDIENCE: The reflection
is [INAUDIBLE].

507
00:21:34,145 --> 00:21:35,450
JOE: The reflections, yeah.

508
00:21:35,450 --> 00:21:38,350
So in the first one,
you reflect light,

509
00:21:38,350 --> 00:21:40,771
and certain amount
gets transmitted

510
00:21:40,771 --> 00:21:42,976
through that front
surface than absorbs.

511
00:21:42,976 --> 00:21:46,784
And so right now we're ignoring
this is 1 minus r component.

512
00:21:46,784 --> 00:21:48,450
But it's so small
that it really doesn't

513
00:21:48,450 --> 00:21:49,576
matter for this experiment.

514
00:21:49,576 --> 00:21:51,326
These things don't
reflect a lot of light.

515
00:21:54,352 --> 00:21:55,310
TONIO BUONASSISI: Cool.

516
00:21:55,310 --> 00:21:57,324
Well, why don't we
give a quick rondo.

517
00:21:57,324 --> 00:21:58,312
[APPLAUSE]

518
00:21:58,312 --> 00:22:00,191
Well done.

519
00:22:00,191 --> 00:22:01,190
Can I grab one of those?

520
00:22:01,190 --> 00:22:01,430
JOE: Absolutely.

521
00:22:01,430 --> 00:22:02,280
TONIO BUONASSISI:
This is going to be

522
00:22:02,280 --> 00:22:04,180
important for the
immersion scattering demo.

523
00:22:04,180 --> 00:22:05,100
JOE: Oh, sure.

524
00:22:05,100 --> 00:22:06,016
TONIO BUONASSISI: Yep.

525
00:22:06,016 --> 00:22:06,690
Cool.

526
00:22:06,690 --> 00:22:10,970
OK, so we notice that we have
some exponential character

527
00:22:10,970 --> 00:22:14,720
to be decay of the intensity
of the transmitted light

528
00:22:14,720 --> 00:22:16,220
through a medium.

529
00:22:16,220 --> 00:22:19,350
And the amount that's absorbed
is following another trend,

530
00:22:19,350 --> 00:22:21,054
which is just 1 minus that.

531
00:22:21,054 --> 00:22:22,470
So it's the amount
of light that's

532
00:22:22,470 --> 00:22:26,800
absorbed is following a curve
looks something like that.

533
00:22:26,800 --> 00:22:31,770
OK, so let's look through the
formalism of Beer-Lambert Law

534
00:22:31,770 --> 00:22:34,290
and try to understand
why it is that we come up

535
00:22:34,290 --> 00:22:37,310
with that exponential
function right here.

536
00:22:37,310 --> 00:22:42,290
So if we assume that light
is coming in a medium

537
00:22:42,290 --> 00:22:46,340
and light is decaying in
some function to that medium

538
00:22:46,340 --> 00:22:49,024
and a certain amount of
light is transmitted,

539
00:22:49,024 --> 00:22:50,940
we know, of course, from
our little experiment

540
00:22:50,940 --> 00:22:53,120
that it follows some
exponential function.

541
00:22:53,120 --> 00:22:55,157
But how do we justify
that to ourselves?

542
00:22:55,157 --> 00:22:57,240
Well, first off, we're
going to ignore reflections

543
00:22:57,240 --> 00:22:58,647
off the front surface.

544
00:22:58,647 --> 00:22:59,730
We just talked about them.

545
00:22:59,730 --> 00:23:01,070
We can calculate them.

546
00:23:01,070 --> 00:23:03,879
Let's leave that aside for
now as a parallel calculation.

547
00:23:03,879 --> 00:23:05,670
We're just concerning
ourselves with what's

548
00:23:05,670 --> 00:23:07,790
happening inside of the medium.

549
00:23:07,790 --> 00:23:10,390
So if we assume that
the change of intensity

550
00:23:10,390 --> 00:23:13,830
within that medium in each
little delta thickness

551
00:23:13,830 --> 00:23:18,010
is going to be affected by some
sort of scattering intensity

552
00:23:18,010 --> 00:23:21,930
within the medium--
and this sigma here

553
00:23:21,930 --> 00:23:24,020
can refer to a
variety of processes.

554
00:23:24,020 --> 00:23:26,750
That can refer to
absorption events

555
00:23:26,750 --> 00:23:29,770
that result in the
generation of free charge.

556
00:23:29,770 --> 00:23:32,290
They can refer to
absorption events that

557
00:23:32,290 --> 00:23:35,340
just heat the material up
and generate phonons, so

558
00:23:35,340 --> 00:23:36,800
lattice vibrations.

559
00:23:36,800 --> 00:23:39,920
There are a number of processes
embedded in the sigma,

560
00:23:39,920 --> 00:23:42,604
and that's why this formalism
is so powerful, because it

561
00:23:42,604 --> 00:23:45,020
doesn't care really what the
physical nature of that sigma

562
00:23:45,020 --> 00:23:45,640
is.

563
00:23:45,640 --> 00:23:50,140
It just matters that there is
an absorption per unit distance

564
00:23:50,140 --> 00:23:52,320
thickness traveled inside
of the material that

565
00:23:52,320 --> 00:23:54,930
is constant throughout
the entire material.

566
00:23:54,930 --> 00:23:58,750
So the sigma here is independent
of thickness throughout.

567
00:23:58,750 --> 00:24:00,680
And then as you integrate
through, you wind up

568
00:24:00,680 --> 00:24:04,440
with that beautiful exponential
function at the end,

569
00:24:04,440 --> 00:24:08,740
the sigma l times n.

570
00:24:08,740 --> 00:24:11,380
We collapse the n and the
sigma here into an alpha.

571
00:24:11,380 --> 00:24:13,950
That alpha is an
absorption coefficient.

572
00:24:13,950 --> 00:24:17,460
The l is the total length or the
total thickness of this medium

573
00:24:17,460 --> 00:24:18,430
right here.

574
00:24:18,430 --> 00:24:20,700
So if we increase
the total thickness,

575
00:24:20,700 --> 00:24:23,500
we're going to decrease
the total amount of light

576
00:24:23,500 --> 00:24:25,790
coming through via that
exponential function.

577
00:24:25,790 --> 00:24:28,380
The alpha, on the other hand,
is not a geometric parameter.

578
00:24:28,380 --> 00:24:31,240
It's an intrinsic
material parameter.

579
00:24:31,240 --> 00:24:33,379
To put that in terms of
mechanical engineering,

580
00:24:33,379 --> 00:24:35,420
for many of the mechanical
engineers in the room,

581
00:24:35,420 --> 00:24:38,400
you recall from solid
mechanics, 2001,

582
00:24:38,400 --> 00:24:41,370
that you have geometric
parameters that determine, say

583
00:24:41,370 --> 00:24:44,120
for example, structural
response and intrinsic material

584
00:24:44,120 --> 00:24:46,630
parameters like
Young's modulus that

585
00:24:46,630 --> 00:24:49,530
determine the structural
response of a system.

586
00:24:49,530 --> 00:24:51,930
And likewise in
here, in the optical,

587
00:24:51,930 --> 00:24:55,030
shall we say, response, we
have a fundamental intrinsic

588
00:24:55,030 --> 00:24:57,970
material parameter, r alpha,
the absorption coefficient,

589
00:24:57,970 --> 00:25:02,750
and the geometric parameter,
rl, which is the thickness.

590
00:25:02,750 --> 00:25:04,700
And the beauty of
this formalism right

591
00:25:04,700 --> 00:25:07,100
here is that we can
measure, experimentally

592
00:25:07,100 --> 00:25:10,300
just like we did right there,
our alphas for materials.

593
00:25:10,300 --> 00:25:12,220
And so from an
engineering point of view,

594
00:25:12,220 --> 00:25:15,100
we don't really--
to first order,

595
00:25:15,100 --> 00:25:17,582
it doesn't really matter
what sort of scattering

596
00:25:17,582 --> 00:25:19,290
or absorption process
is happening inside

597
00:25:19,290 --> 00:25:21,215
of a material for us
to calculate the amount

598
00:25:21,215 --> 00:25:22,090
of transmitted light.

599
00:25:22,090 --> 00:25:23,760
We just need to know the alpha.

600
00:25:23,760 --> 00:25:27,650
We need to know the optical
absorption coefficient.

601
00:25:27,650 --> 00:25:32,205
This alpha will vary as a
function of wavelength inside

602
00:25:32,205 --> 00:25:33,580
of a material
because, obviously,

603
00:25:33,580 --> 00:25:36,280
the physical absorption
mechanisms are varying

604
00:25:36,280 --> 00:25:37,480
as a function of wavelength.

605
00:25:37,480 --> 00:25:39,740
The resonances with
different electronic states

606
00:25:39,740 --> 00:25:41,642
within the material,
that light, depends

607
00:25:41,642 --> 00:25:43,850
on the energy of the light,
depends on the frequency.

608
00:25:43,850 --> 00:25:45,308
So there's a
wavelength dependence.

609
00:25:47,740 --> 00:25:52,190
Yeah, and that general
equation is the same one that

610
00:25:52,190 --> 00:25:56,010
drives the reduction
of light intensity

611
00:25:56,010 --> 00:25:57,600
as it travels through
the atmosphere.

612
00:25:57,600 --> 00:25:59,517
So if we increase the
atmospheric path length,

613
00:25:59,517 --> 00:26:01,975
we'll be reducing the amount
of light that actually reaches

614
00:26:01,975 --> 00:26:03,400
the surface of the earth.

615
00:26:03,400 --> 00:26:06,120
That's at air mass
two or air mass three,

616
00:26:06,120 --> 00:26:08,430
there's less solar
flux coming down

617
00:26:08,430 --> 00:26:11,231
than at air mass one
or air mass zero.

618
00:26:11,231 --> 00:26:12,730
The alpha, obviously,
is going to be

619
00:26:12,730 --> 00:26:14,110
very different
for our atmosphere

620
00:26:14,110 --> 00:26:17,196
than it was for these
little polyethylene sheets.

621
00:26:17,196 --> 00:26:19,320
Because the nature of the
scattering and absorption

622
00:26:19,320 --> 00:26:21,540
processes are very
different for the atmosphere

623
00:26:21,540 --> 00:26:25,750
than it is for here, the density
of the material and so forth.

624
00:26:25,750 --> 00:26:26,860
Any questions?

625
00:26:26,860 --> 00:26:27,514
Yes?

626
00:26:27,514 --> 00:26:29,170
AUDIENCE: What was n?

627
00:26:29,170 --> 00:26:33,680
TONIO BUONASSISI: So the n,
there's a certain scattering

628
00:26:33,680 --> 00:26:37,040
intensity, and then there's
a certain number density,

629
00:26:37,040 --> 00:26:38,800
for example, of the material.

630
00:26:38,800 --> 00:26:46,210
So this alpha here is, I
would say, density neutral.

631
00:26:46,210 --> 00:26:52,850
What we've done is we have
the alpha encapsulating

632
00:26:52,850 --> 00:26:54,820
the physical parameters
of the material

633
00:26:54,820 --> 00:26:58,860
and the absorption processes
all in one variable,

634
00:26:58,860 --> 00:27:01,080
very nicely and succinctly.

635
00:27:01,080 --> 00:27:03,740
And the only geometric
parameter that is of essence

636
00:27:03,740 --> 00:27:06,840
is really our l.

637
00:27:06,840 --> 00:27:08,840
AUDIENCE: It's called an
absorption coefficient,

638
00:27:08,840 --> 00:27:12,298
but is it more of an
extension coefficient, really?

639
00:27:12,298 --> 00:27:15,969
Because it's kind of confusing
that it includes scattering.

640
00:27:15,969 --> 00:27:18,260
TONIO BUONASSISI: The extension
coefficient, absorption

641
00:27:18,260 --> 00:27:23,750
coefficient, yes,
in solar research,

642
00:27:23,750 --> 00:27:25,820
when we talk about an
absorption coefficient

643
00:27:25,820 --> 00:27:27,570
inside of a material.

644
00:27:27,570 --> 00:27:31,390
Oftentimes we're operating in
a wavelength regime of light

645
00:27:31,390 --> 00:27:33,690
wherein free charge is excited.

646
00:27:33,690 --> 00:27:37,460
But we can also keep increasing
that the wavelength of light,

647
00:27:37,460 --> 00:27:40,480
say, out to 10 microns, very
long wavelength light, very

648
00:27:40,480 --> 00:27:41,800
low energy light.

649
00:27:41,800 --> 00:27:43,220
And that can excite
free carriers

650
00:27:43,220 --> 00:27:45,340
within the material--
carriers that

651
00:27:45,340 --> 00:27:47,590
are already excited, essentially
excited them further,

652
00:27:47,590 --> 00:27:49,080
without generating
any new free carriers

653
00:27:49,080 --> 00:27:49,850
inside of our material.

654
00:27:49,850 --> 00:27:51,010
So we won't necessarily
be generating

655
00:27:51,010 --> 00:27:52,730
more current by
shedding light on it

656
00:27:52,730 --> 00:27:56,470
but will be absorbing light,
nevertheless, in our material.

657
00:27:56,470 --> 00:27:58,980
So it's important
to keep, let's say,

658
00:27:58,980 --> 00:28:01,460
the underlying
physical processes that

659
00:28:01,460 --> 00:28:02,860
are occurring distinct.

660
00:28:02,860 --> 00:28:04,370
Later on we'll get to that.

661
00:28:04,370 --> 00:28:06,370
For now, it's important
just to, I would say,

662
00:28:06,370 --> 00:28:08,921
recognize that we have
an exponential decay

663
00:28:08,921 --> 00:28:11,420
of the intensity of the light
as it goes through the medium.

664
00:28:11,420 --> 00:28:12,830
And then over the
next few classes,

665
00:28:12,830 --> 00:28:14,790
we're going to get to exactly
what physical processes are

666
00:28:14,790 --> 00:28:15,570
going on.

667
00:28:15,570 --> 00:28:19,620
But I'm glad people are
asking those questions.

668
00:28:19,620 --> 00:28:21,914
OK, so again,
alpha is a function

669
00:28:21,914 --> 00:28:24,330
of the wavelength of light and
the property of the medium.

670
00:28:24,330 --> 00:28:27,060
And let me just
flash up some curves

671
00:28:27,060 --> 00:28:31,360
of alpha versus wavelength
so people have some exposure

672
00:28:31,360 --> 00:28:33,970
to those numbers.

673
00:28:33,970 --> 00:28:37,480
Again, we're talking about
an energy range quite broad

674
00:28:37,480 --> 00:28:41,800
here, from about
6.2 eV to 0.62 eV.

675
00:28:41,800 --> 00:28:43,700
The visible
wavelengths range would

676
00:28:43,700 --> 00:28:45,290
be somewhere in
this regime right

677
00:28:45,290 --> 00:28:47,360
here, so a very limited band.

678
00:28:47,360 --> 00:28:51,950
And the infrared out here,
ultraviolet over here,

679
00:28:51,950 --> 00:28:54,640
and we can see for a variety
of different types of materials

680
00:28:54,640 --> 00:28:57,310
what the absorption
coefficient is.

681
00:28:57,310 --> 00:29:00,060
So here we have germanium.

682
00:29:00,060 --> 00:29:03,690
The red would be crystalline
silicon, gallium arsenide,

683
00:29:03,690 --> 00:29:06,880
indium phosphide, and
amorphous silicon.

684
00:29:06,880 --> 00:29:08,960
So let's do a little
quick calculation

685
00:29:08,960 --> 00:29:10,400
just to get us a little limber.

686
00:29:10,400 --> 00:29:13,040
We're starting to get
into the semester,

687
00:29:13,040 --> 00:29:14,760
so the energy level
starts going down.

688
00:29:14,760 --> 00:29:17,700
What we're going to do is
we're going to pick a value,

689
00:29:17,700 --> 00:29:19,490
say 550 nanometers.

690
00:29:19,490 --> 00:29:21,350
Why did I pick 550 again?

691
00:29:21,350 --> 00:29:23,350
It's near the peak of the
solar spectrum, right?

692
00:29:23,350 --> 00:29:24,300
It matters.

693
00:29:24,300 --> 00:29:26,902
And we're going to look at
two different materials.

694
00:29:26,902 --> 00:29:28,860
We're going to look at
silicon, and we're going

695
00:29:28,860 --> 00:29:30,620
to look at gallium arsenide.

696
00:29:30,620 --> 00:29:32,770
And we're going to
calculate the thickness

697
00:29:32,770 --> 00:29:35,730
necessary to absorb 90%
of the incoming light

698
00:29:35,730 --> 00:29:37,342
at 550 nanometers.

699
00:29:37,342 --> 00:29:39,300
What I want you to do is
turn to your neighbor,

700
00:29:39,300 --> 00:29:41,530
and once again
with your neighbor,

701
00:29:41,530 --> 00:29:43,880
calculate what
thickness of material,

702
00:29:43,880 --> 00:29:46,540
what thickness of gallium
arsenide, the yellow curve,

703
00:29:46,540 --> 00:29:48,820
and what thickness of
silicon, the red curve,

704
00:29:48,820 --> 00:29:52,380
is necessary to absorb
90% of the incoming light

705
00:29:52,380 --> 00:29:54,325
at 550 nanometers.

706
00:29:54,325 --> 00:29:55,990
Why don't you go for it?

707
00:29:55,990 --> 00:29:59,350
I'll give you, say,
a couple minutes.

708
00:30:11,575 --> 00:30:14,190
To make sure people are
setting this up right,

709
00:30:14,190 --> 00:30:18,583
i divided by i0 to absorb
90% of the light, that

710
00:30:18,583 --> 00:30:22,730
would be 0.1, 1 minus 0.9.

711
00:30:22,730 --> 00:30:25,730
OK, so as you're finalizing
your calculations,

712
00:30:25,730 --> 00:30:27,950
I just wanted to make
sure set this up right.

713
00:30:27,950 --> 00:30:30,930
Again, if we're absorbing 90%
of the light, it means only 10%

714
00:30:30,930 --> 00:30:32,670
of the light is going
out the other side.

715
00:30:32,670 --> 00:30:34,810
That means their i is
going to be 1/10 of i0

716
00:30:34,810 --> 00:30:38,330
or i divided by i0 is 0.1.

717
00:30:38,330 --> 00:30:41,050
And then we would take
the log of both sides,

718
00:30:41,050 --> 00:30:45,410
typically, and solve for
our l based on the alphas

719
00:30:45,410 --> 00:30:46,460
that we have here.

720
00:30:46,460 --> 00:30:49,270
Again, units of alpha would
be in inverse centimeters.

721
00:30:49,270 --> 00:30:52,310
And so the l's
that you obtained,

722
00:30:52,310 --> 00:30:54,977
let's go for gallium
arsenide first.

723
00:30:54,977 --> 00:30:56,560
Did anybody manage
to walk all the way

724
00:30:56,560 --> 00:30:58,918
through that calculation?

725
00:30:58,918 --> 00:31:00,380
AUDIENCE: 20 micrometers.

726
00:31:00,380 --> 00:31:01,840
TONIO BUONASSISI:
20 micrometers.

727
00:31:01,840 --> 00:31:04,406
For our gallium arsenide
or for our silicon?

728
00:31:04,406 --> 00:31:05,530
AUDIENCE: Gallium arsenide.

729
00:31:05,530 --> 00:31:06,988
TONIO BUONASSISI:
Gallium arsenide.

730
00:31:06,988 --> 00:31:11,158
Did anybody get any other
numbers for gallium arsenide.

731
00:31:11,158 --> 00:31:12,050
AUDIENCE: 0.4.

732
00:31:12,050 --> 00:31:13,380
TONIO BUONASSISI: 0.4 microns.

733
00:31:13,380 --> 00:31:14,130
Yeah.

734
00:31:14,130 --> 00:31:15,800
That's sounding more
in the ballpark.

735
00:31:15,800 --> 00:31:16,933
Anybody else?

736
00:31:16,933 --> 00:31:17,582
AUDIENCE: 23.

737
00:31:17,582 --> 00:31:18,790
TONIO BUONASSISI: 23 as well.

738
00:31:18,790 --> 00:31:22,310
So I'm getting-- I would have
guessed that the number would

739
00:31:22,310 --> 00:31:24,405
rather small for
gallium arsenide, so

740
00:31:24,405 --> 00:31:29,262
something in the range of,
say, a micron, in that order.

741
00:31:29,262 --> 00:31:31,470
Why don't we give folks
enough time to walk through--

742
00:31:31,470 --> 00:31:33,395
I know I rushed you on
the calculations here.

743
00:31:33,395 --> 00:31:34,728
We have material to get through.

744
00:31:34,728 --> 00:31:37,980
And I wanted to see you
perform under pressure.

745
00:31:37,980 --> 00:31:39,990
But how about the silicon?

746
00:31:39,990 --> 00:31:41,560
Is it larger or smaller?

747
00:31:41,560 --> 00:31:44,030
Let's just for order
of magnitude first

748
00:31:44,030 --> 00:31:46,650
and the general
trend and then try

749
00:31:46,650 --> 00:31:48,340
to pick up the precise number.

750
00:31:48,340 --> 00:31:50,190
For silicon,
crystalline silicon that

751
00:31:50,190 --> 00:31:52,850
is, with an optical
absorption coefficient

752
00:31:52,850 --> 00:31:55,960
and order of magnitude
less than gallium arsenide,

753
00:31:55,960 --> 00:31:59,150
is the thickness needed to
absorb the same amount of light

754
00:31:59,150 --> 00:32:00,481
going to be greater or smaller?

755
00:32:00,481 --> 00:32:01,230
AUDIENCE: Greater.

756
00:32:01,230 --> 00:32:02,313
TONIO BUONASSISI: Greater.

757
00:32:02,313 --> 00:32:03,240
By an--

758
00:32:03,240 --> 00:32:03,590
AUDIENCE: Order of magnitude.

759
00:32:03,590 --> 00:32:04,890
TONIO BUONASSISI: Order
of magnitude, brilliant.

760
00:32:04,890 --> 00:32:05,460
OK.

761
00:32:05,460 --> 00:32:07,293
So whatever number you
got for your gallium,

762
00:32:07,293 --> 00:32:10,560
arsenide you could
translate it fairly easily.

763
00:32:10,560 --> 00:32:12,160
All right, so that was at 550.

764
00:32:12,160 --> 00:32:17,020
And there's a lot of solar
radiation right around 550,

765
00:32:17,020 --> 00:32:19,427
so the numbers that I
have on the top my head

766
00:32:19,427 --> 00:32:21,510
work somewhere out to be
on the order of a micron,

767
00:32:21,510 --> 00:32:23,430
a little less for
gallium arsenide,

768
00:32:23,430 --> 00:32:25,680
somewhere in the order of
10 microns or so for silicon

769
00:32:25,680 --> 00:32:26,550
out here.

770
00:32:26,550 --> 00:32:28,760
But now if we go
out to 800, there's

771
00:32:28,760 --> 00:32:30,500
still a lot of solar
flux out there.

772
00:32:30,500 --> 00:32:33,052
If you recall the solar
spectrum, the folks who

773
00:32:33,052 --> 00:32:35,510
have been doing their homework,
there's still a lot of flux

774
00:32:35,510 --> 00:32:36,640
out around 800.

775
00:32:36,640 --> 00:32:38,931
As a matter of fact, it
continues going all the way out

776
00:32:38,931 --> 00:32:42,135
to here, although decaying
intensity a la black body.

777
00:32:46,120 --> 00:32:49,950
And at 800 nanometers
wavelength light,

778
00:32:49,950 --> 00:32:51,730
the optical
absorption coefficient

779
00:32:51,730 --> 00:32:53,580
is dropped by about
an order of magnitude

780
00:32:53,580 --> 00:32:55,920
relative to the peak
of the solar spectrum.

781
00:32:55,920 --> 00:32:58,920
And that's why most of
these solar cells that you

782
00:32:58,920 --> 00:33:03,364
see of crystalline silicon are
on the order of 100 microns,

783
00:33:03,364 --> 00:33:05,780
typically a little thicker for
some technological reasons,

784
00:33:05,780 --> 00:33:07,738
which we'll get to, make
it difficult to handle

785
00:33:07,738 --> 00:33:09,830
very, very thin stuff.

786
00:33:09,830 --> 00:33:12,200
But if you just assume one
pass through the material,

787
00:33:12,200 --> 00:33:15,090
you'd need about that thickness
to absorb a lot of the light.

788
00:33:15,090 --> 00:33:16,980
And I'll pass around
some of these materials

789
00:33:16,980 --> 00:33:22,150
right here just so you can get
a sense of how thick they are.

790
00:33:22,150 --> 00:33:23,010
Here we go.

791
00:33:23,010 --> 00:33:26,670
Actually, here's
what I'm going to do.

792
00:33:26,670 --> 00:33:28,560
I'm going to take
out the big pieces

793
00:33:28,560 --> 00:33:31,014
and leave the small ones in
here that are already broken.

794
00:33:31,014 --> 00:33:32,930
And you can actually
pick them up if you like.

795
00:33:32,930 --> 00:33:36,200
Just be aware that these
little pieces of silicon

796
00:33:36,200 --> 00:33:38,490
are-- silicon's
brittle material.

797
00:33:38,490 --> 00:33:39,760
It's like glass.

798
00:33:39,760 --> 00:33:41,850
So if you have a little
shard of silicon,

799
00:33:41,850 --> 00:33:44,270
it can poke you just like
a charge of glass can.

800
00:33:44,270 --> 00:33:46,130
So treat it with the
same amount of respect

801
00:33:46,130 --> 00:33:48,889
that you would a very,
very thin piece of glass.

802
00:33:48,889 --> 00:33:50,430
But you can see here
that if you look

803
00:33:50,430 --> 00:33:52,150
at the thickness
of these materials

804
00:33:52,150 --> 00:33:55,440
inside of that little bin, these
are small shards of silicon

805
00:33:55,440 --> 00:33:57,260
solar cell wafers.

806
00:33:57,260 --> 00:34:00,390
Their thicknesses in the
order of 100 microns, those

807
00:34:00,390 --> 00:34:01,970
are particularly thin.

808
00:34:01,970 --> 00:34:03,940
You have other
solar cells that are

809
00:34:03,940 --> 00:34:08,125
170 microns is typical
thickness for silicon.

810
00:34:08,125 --> 00:34:09,500
And for gallium
arsenide, you can

811
00:34:09,500 --> 00:34:11,380
deposit thin films
that are on the order

812
00:34:11,380 --> 00:34:14,537
of a micron thick or less.

813
00:34:14,537 --> 00:34:16,370
You can go down to a
few hundreds nanometers

814
00:34:16,370 --> 00:34:18,328
and still make-- actually
the record efficiency

815
00:34:18,328 --> 00:34:20,710
of gallium arsenide solar
cell is a few hundred

816
00:34:20,710 --> 00:34:22,750
nanometers thick.

817
00:34:22,750 --> 00:34:25,770
And our calculations
right here assumed

818
00:34:25,770 --> 00:34:27,440
one pass through the material.

819
00:34:27,440 --> 00:34:29,050
That's all we gave the light.

820
00:34:29,050 --> 00:34:31,330
We only gave one chance
to go through the material

821
00:34:31,330 --> 00:34:32,940
and get absorbed.

822
00:34:32,940 --> 00:34:36,540
What could you envision would
increase the total amount

823
00:34:36,540 --> 00:34:37,540
of light absorbed?

824
00:34:37,540 --> 00:34:39,670
What could you do to
your solar cell device

825
00:34:39,670 --> 00:34:43,140
to increase the total amount
of light absorbed inside of it?

826
00:34:43,140 --> 00:34:45,000
AUDIENCE: Put anti-relfective
coating on it.

827
00:34:45,000 --> 00:34:47,583
TONIO BUONASSISI: You could put
anti-reflective coating on it.

828
00:34:47,583 --> 00:34:49,125
Let's do something
much more simple.

829
00:34:49,125 --> 00:34:51,000
AUDIENCE: Put reflective
coating on the back.

830
00:34:51,000 --> 00:34:51,909
TONIO BUONASSISI: Reflecting
coating on the back,

831
00:34:51,909 --> 00:34:52,520
absolutely.

832
00:34:52,520 --> 00:34:52,770
Yeah.

833
00:34:52,770 --> 00:34:55,228
So if the light goes through
the solar cell and doesn't get

834
00:34:55,228 --> 00:34:57,512
absorbed, that 10% of the
light that didn't make it,

835
00:34:57,512 --> 00:34:58,970
that's going to
get reflected back.

836
00:34:58,970 --> 00:35:00,934
It's going to get another
chance to go through.

837
00:35:00,934 --> 00:35:03,100
So if you absorb 90% of the
light on the first pass,

838
00:35:03,100 --> 00:35:05,760
you'll absorb 99% of the
light on two bounces, right?

839
00:35:05,760 --> 00:35:07,780
Or in one bounce,
rather, and two trips,

840
00:35:07,780 --> 00:35:10,120
two optical path links
through the material.

841
00:35:10,120 --> 00:35:12,290
And so the term
optical path length

842
00:35:12,290 --> 00:35:15,840
is a very important term
here, because the optical path

843
00:35:15,840 --> 00:35:18,530
length does not have to be
the thickness of the material.

844
00:35:18,530 --> 00:35:21,410
Ideally, the optical path
length through the material

845
00:35:21,410 --> 00:35:24,572
is much, much thicker than
the actual material itself.

846
00:35:24,572 --> 00:35:26,030
And over the next
few slides, we're

847
00:35:26,030 --> 00:35:29,550
going to learn how
we engineer that.

848
00:35:29,550 --> 00:35:34,420
So methods to improve optical
absorption- generally,

849
00:35:34,420 --> 00:35:37,230
these are called light trapping.

850
00:35:37,230 --> 00:35:40,860
Not all of these entail
trapping the light.

851
00:35:40,860 --> 00:35:42,570
Actually, most of them do.

852
00:35:42,570 --> 00:35:44,350
We also call them
light management

853
00:35:44,350 --> 00:35:47,080
as a more general
term that includes

854
00:35:47,080 --> 00:35:51,830
reflection and absorption
inside of the material.

855
00:35:51,830 --> 00:35:54,305
So the very simplest thing we
can do on the front surface--

856
00:35:54,305 --> 00:35:55,680
so what we're
going to do is take

857
00:35:55,680 --> 00:35:59,271
this step by step, as light
goes into the solar cell

858
00:35:59,271 --> 00:36:01,520
from the front side, we're
going to take step by step,

859
00:36:01,520 --> 00:36:04,050
what can we do to improve
the amount of light that

860
00:36:04,050 --> 00:36:05,150
is absorbed?

861
00:36:05,150 --> 00:36:08,114
The first thing that we can do
is texturize our front surface.

862
00:36:08,114 --> 00:36:10,030
If we don't have texture
on our front surface,

863
00:36:10,030 --> 00:36:12,240
if it's absolutely
flat, what we call

864
00:36:12,240 --> 00:36:17,110
specular surface-- specular
coming from the root mirror.

865
00:36:17,110 --> 00:36:20,880
In Latin languages, for example,
Italian specchio is mirror.

866
00:36:20,880 --> 00:36:24,800
So a flat silicon substrate,
a specular surface,

867
00:36:24,800 --> 00:36:27,344
would reflect some
finite amount of light.

868
00:36:27,344 --> 00:36:29,010
And we can calculate
that now because we

869
00:36:29,010 --> 00:36:31,090
know that it relates
to the real component

870
00:36:31,090 --> 00:36:33,380
of the refractive
index of the material.

871
00:36:33,380 --> 00:36:35,480
Now if we texturize
our surface--

872
00:36:35,480 --> 00:36:39,580
this is representing kind of
a pyramid type texturization.

873
00:36:39,580 --> 00:36:43,260
If the light comes in
and some fraction doesn't

874
00:36:43,260 --> 00:36:45,152
go into the material--
there's some component

875
00:36:45,152 --> 00:36:47,360
of that ray that's going
into the material over here,

876
00:36:47,360 --> 00:36:48,900
but we're ignoring
it in this drawing.

877
00:36:48,900 --> 00:36:50,316
We're just focusing
on the lights,

878
00:36:50,316 --> 00:36:52,450
the rays that get reflected.

879
00:36:52,450 --> 00:36:54,330
That beam that
gets reflected off,

880
00:36:54,330 --> 00:36:56,502
instead of just going
back out toward the sun,

881
00:36:56,502 --> 00:36:58,210
it's now going toward
the material again.

882
00:36:58,210 --> 00:37:01,020
So it has a second chance
of getting absorbed.

883
00:37:01,020 --> 00:37:03,630
So you just went--
for example, let's say

884
00:37:03,630 --> 00:37:05,790
if you have a 10%
reflectivity on the surface,

885
00:37:05,790 --> 00:37:07,775
you went from a 10%
reflectivity over here

886
00:37:07,775 --> 00:37:10,800
to a 1% reflectivity over here.

887
00:37:10,800 --> 00:37:13,840
Because now you have the total
amount of light that gets

888
00:37:13,840 --> 00:37:20,060
reflected is 1 minus 0.9 squared
as opposed to 1 minus 0.9

889
00:37:20,060 --> 00:37:21,071
to the 1.

890
00:37:21,071 --> 00:37:23,320
In this case right here, the
amount of light that gets

891
00:37:23,320 --> 00:37:26,620
reflected, assuming
its 10% reflective,

892
00:37:26,620 --> 00:37:30,977
would be 1 minus
0.9, so 10% of light.

893
00:37:30,977 --> 00:37:32,810
And over here, the
amount of light that gets

894
00:37:32,810 --> 00:37:37,540
reflected would be 1 minus
0.9 quantity squared, so 1%

895
00:37:37,540 --> 00:37:38,870
instead of 10%.

896
00:37:38,870 --> 00:37:41,460
So texturization
increases the probability

897
00:37:41,460 --> 00:37:43,470
that light will
enter the device.

898
00:37:43,470 --> 00:37:47,250
And what it also does-- this
is a secondary benefit--

899
00:37:47,250 --> 00:37:50,220
is it increases the path length,
the effective path length,

900
00:37:50,220 --> 00:37:51,676
of the incoming light.

901
00:37:51,676 --> 00:37:53,800
And the way to understand
that particular phenomena

902
00:37:53,800 --> 00:37:55,710
is called Snell's Law.

903
00:37:55,710 --> 00:37:58,985
Well, even in the absence
of Snell's Law-- no,

904
00:37:58,985 --> 00:37:59,610
let's go there.

905
00:37:59,610 --> 00:38:01,010
Let's go there.

906
00:38:01,010 --> 00:38:03,000
So we have a texturized
front surface.

907
00:38:03,000 --> 00:38:04,400
What's happening?

908
00:38:04,400 --> 00:38:08,110
Well, as the material goes
from one medium to another,

909
00:38:08,110 --> 00:38:10,220
the refractive index changes.

910
00:38:10,220 --> 00:38:12,690
We discussed this right at
the beginning of lecture.

911
00:38:12,690 --> 00:38:17,272
So the way in which the
electromagnetic wave oscillates

912
00:38:17,272 --> 00:38:18,730
the electrons
instead of the system

913
00:38:18,730 --> 00:38:20,900
is changing from one
medium to another,

914
00:38:20,900 --> 00:38:23,990
let's say from air into the
solar cell device from air

915
00:38:23,990 --> 00:38:27,560
into our silicon, for
example, right here.

916
00:38:27,560 --> 00:38:30,630
Now, we can ascribe the
refractive indices to air

917
00:38:30,630 --> 00:38:32,830
and to our silicon like so.

918
00:38:32,830 --> 00:38:36,770
And the light path
will obey what

919
00:38:36,770 --> 00:38:39,240
is called Snell's Law,
which is the product

920
00:38:39,240 --> 00:38:42,400
of the refractive index and
sine of that angle, the angle

921
00:38:42,400 --> 00:38:44,670
relative to the surface normal.

922
00:38:44,670 --> 00:38:46,290
So a simple way to
think about this

923
00:38:46,290 --> 00:38:50,270
is when the light goes from a
low index of refraction medium

924
00:38:50,270 --> 00:38:54,080
to a high index of refraction
medium, light bends

925
00:38:54,080 --> 00:38:57,287
toward or away from the normal?

926
00:38:57,287 --> 00:38:58,870
So if I'm going from
air into silicon,

927
00:38:58,870 --> 00:39:00,940
light would bend toward
the normal, right?

928
00:39:00,940 --> 00:39:04,180
So here my theta 1 is going
to be greater than theta 2.

929
00:39:04,180 --> 00:39:07,480
My light has bent toward the
normal, if this is my silicon

930
00:39:07,480 --> 00:39:10,590
and this white stuff
over here is my air.

931
00:39:10,590 --> 00:39:12,050
So light came in.

932
00:39:12,050 --> 00:39:13,760
It encountered the surface.

933
00:39:13,760 --> 00:39:17,380
The theta 1 was defined
as the angle of the light

934
00:39:17,380 --> 00:39:18,750
relative to the surface normal.

935
00:39:18,750 --> 00:39:20,100
That was my theta 1.

936
00:39:20,100 --> 00:39:22,450
My theta 2 is going to
be given as the ratio

937
00:39:22,450 --> 00:39:23,720
of the refractive indices.

938
00:39:23,720 --> 00:39:26,140
And because the refractive
index of silicon

939
00:39:26,140 --> 00:39:29,110
is going to be greater
than that of air,

940
00:39:29,110 --> 00:39:30,930
light would bend
toward the normal.

941
00:39:30,930 --> 00:39:34,000
And so what I have on a
macroscopic view over here,

942
00:39:34,000 --> 00:39:36,660
if this is my surface
texture, light was coming in,

943
00:39:36,660 --> 00:39:37,760
it's now bent.

944
00:39:37,760 --> 00:39:39,810
And so the effective
optical path length

945
00:39:39,810 --> 00:39:42,450
is now larger than the
thickness of my device.

946
00:39:42,450 --> 00:39:44,320
It's kind of cool.

947
00:39:44,320 --> 00:39:49,390
So there are two benefits to
texturizing your front surface.

948
00:39:49,390 --> 00:39:53,200
One is you have an additional
pass, additional bounce,

949
00:39:53,200 --> 00:39:55,290
an additional encounter
with the material.

950
00:39:55,290 --> 00:39:58,439
So that reflected light gets
another chance to go in.

951
00:39:58,439 --> 00:39:59,980
And the second
benefit is that you're

952
00:39:59,980 --> 00:40:01,410
able to increase
the optical path

953
00:40:01,410 --> 00:40:08,720
length by the delta in
refractive indices and the fact

954
00:40:08,720 --> 00:40:11,445
that the path of the
light will be Snell's Law.

955
00:40:11,445 --> 00:40:15,480
Now another really interesting
aside of Snell's Law

956
00:40:15,480 --> 00:40:19,970
is that if light is trying to
go from a high index medium

957
00:40:19,970 --> 00:40:22,090
to a low index medium,
and if it's coming in

958
00:40:22,090 --> 00:40:24,980
at a very oblique
angle like this,

959
00:40:24,980 --> 00:40:27,000
if you run through
Snell's Law, you

960
00:40:27,000 --> 00:40:28,250
don't get an angle coming out.

961
00:40:28,250 --> 00:40:29,850
It actually falls
along the surface

962
00:40:29,850 --> 00:40:32,730
or actually bounces back in most
often, depending on the angle.

963
00:40:32,730 --> 00:40:35,142
And you have what is called
total internal reflection,

964
00:40:35,142 --> 00:40:36,600
which is this case
right over here.

965
00:40:36,600 --> 00:40:39,400
That little bounce,
that friendly bounce,

966
00:40:39,400 --> 00:40:42,990
of the light that went in
bounced off the back side

967
00:40:42,990 --> 00:40:44,840
and then was reflected back in.

968
00:40:44,840 --> 00:40:47,060
That's a total internal
reflection event.

969
00:40:47,060 --> 00:40:49,780
And that happens
in solar modules.

970
00:40:49,780 --> 00:40:52,070
Right here, when light
comes in, bounces off

971
00:40:52,070 --> 00:40:54,080
of the white back
skin right here,

972
00:40:54,080 --> 00:40:56,790
and then gets scattered
off at an angle,

973
00:40:56,790 --> 00:40:58,710
it can have a total
internal reflection off

974
00:40:58,710 --> 00:41:00,520
of the front surface
glass and have

975
00:41:00,520 --> 00:41:03,960
a second chance of getting back
into the solar cells inside.

976
00:41:03,960 --> 00:41:07,100
So that's one of the reasons
why you see this white spacing,

977
00:41:07,100 --> 00:41:09,280
the white colored material,
in between the cells,

978
00:41:09,280 --> 00:41:11,642
is that the light gets
reflected off of there.

979
00:41:11,642 --> 00:41:13,600
It doesn't make it very
aesthetically pleasing.

980
00:41:13,600 --> 00:41:15,100
You might want it
to look all black.

981
00:41:15,100 --> 00:41:17,224
And if you do want it to
look all black, what would

982
00:41:17,224 --> 00:41:17,870
you do instead?

983
00:41:23,120 --> 00:41:25,830
Instead of changing the back
skin, what other component

984
00:41:25,830 --> 00:41:27,520
might you change?

985
00:41:27,520 --> 00:41:28,510
AUDIENCE: The front.

986
00:41:28,510 --> 00:41:29,150
TONIO BUONASSISI:
The front, right?

987
00:41:29,150 --> 00:41:32,010
You might change the nature
of the anti-reflection coating

988
00:41:32,010 --> 00:41:33,320
on the glass.

989
00:41:33,320 --> 00:41:36,160
We'll get anti-reflection
coatings in a minute.

990
00:41:36,160 --> 00:41:38,107
So even if the
panel looks black,

991
00:41:38,107 --> 00:41:39,940
there are some really
aesthetically pleasing

992
00:41:39,940 --> 00:41:42,023
solar panels out there
that look completely black.

993
00:41:42,023 --> 00:41:43,600
They may still have
white back skin,

994
00:41:43,600 --> 00:41:46,095
but the glass is just very
good at absorbing that light

995
00:41:46,095 --> 00:41:48,560
and preventing it from escaping.

996
00:41:48,560 --> 00:41:52,360
OK, so to engineer front and
back surface reflectances,

997
00:41:52,360 --> 00:41:54,090
you really have to
carefully select

998
00:41:54,090 --> 00:41:56,050
your refractive indices
and your materials

999
00:41:56,050 --> 00:41:57,980
if you put on either side.

1000
00:41:57,980 --> 00:42:01,370
And it's very important--
extremely important.

1001
00:42:01,370 --> 00:42:05,230
To make a long story short, the
record efficiency solar cell

1002
00:42:05,230 --> 00:42:09,380
that was announced this past
year in gallium arsenide

1003
00:42:09,380 --> 00:42:13,630
was achieved because of
good light management.

1004
00:42:13,630 --> 00:42:18,620
And we'll explain how that came
about perhaps towards lectures,

1005
00:42:18,620 --> 00:42:21,000
maybe lectures eight or nine.

1006
00:42:21,000 --> 00:42:23,400
So I'm going to play a
little game with you, which

1007
00:42:23,400 --> 00:42:25,570
is to look at a swimming pool.

1008
00:42:25,570 --> 00:42:27,550
This is a pool
filled with water,

1009
00:42:27,550 --> 00:42:29,890
which is refractive index 1.3.

1010
00:42:29,890 --> 00:42:30,990
Air is 1.

1011
00:42:30,990 --> 00:42:33,010
And so that's the normal
view, what we have.

1012
00:42:33,010 --> 00:42:35,580
Light bends toward
the normal, right?

1013
00:42:35,580 --> 00:42:38,870
And so you're able to
look down inside the pool

1014
00:42:38,870 --> 00:42:41,416
that stuff that is not
in your line of sight,

1015
00:42:41,416 --> 00:42:42,790
not in your direct
line of sight.

1016
00:42:42,790 --> 00:42:44,930
That's because when you
look down, the ray of light

1017
00:42:44,930 --> 00:42:46,388
is traveling like
this and it bends

1018
00:42:46,388 --> 00:42:49,740
toward the normal and
likewise symmetric.

1019
00:42:49,740 --> 00:42:52,360
So you're seeing
material down there.

1020
00:42:52,360 --> 00:42:56,310
What change of
property would give you

1021
00:42:56,310 --> 00:42:57,530
these two images over here.

1022
00:42:57,530 --> 00:42:58,820
Let me give you a hint.

1023
00:42:58,820 --> 00:43:01,760
In one of those two images,
the refractive index

1024
00:43:01,760 --> 00:43:04,680
of the medium inside
the pool is not 1.3.

1025
00:43:04,680 --> 00:43:08,286
It's 0.9.

1026
00:43:08,286 --> 00:43:09,760
It's 0.9.

1027
00:43:09,760 --> 00:43:14,900
And in another one of these
two, the refractive index

1028
00:43:14,900 --> 00:43:18,340
of the medium is actually
going to be negative.

1029
00:43:18,340 --> 00:43:21,750
We'll call it a negative
refractive index material,

1030
00:43:21,750 --> 00:43:23,550
a negative index material.

1031
00:43:23,550 --> 00:43:25,892
So which of these two
do you think is which?

1032
00:43:25,892 --> 00:43:27,350
Why don't you turn
to your neighbor

1033
00:43:27,350 --> 00:43:29,910
quickly and chat about it
without peeking at your lecture

1034
00:43:29,910 --> 00:43:30,410
notes.

1035
00:43:45,010 --> 00:43:48,860
So let me walk through, as you
begin honing in on your answers

1036
00:43:48,860 --> 00:43:49,640
here.

1037
00:43:49,640 --> 00:43:52,370
Think about what would
happen to the reflectivity

1038
00:43:52,370 --> 00:43:54,860
of that front
surface of the water

1039
00:43:54,860 --> 00:43:59,130
and what would happen to the
angle that the light travels,

1040
00:43:59,130 --> 00:44:02,340
or the angle of refraction
of bending, shall

1041
00:44:02,340 --> 00:44:05,240
you say, as the light goes
from one medium to another.

1042
00:44:05,240 --> 00:44:10,596
So if we go to a refractive
index material of minus 1.3,

1043
00:44:10,596 --> 00:44:12,220
will we change the
reflectivity at all?

1044
00:44:15,884 --> 00:44:20,990
It depends, but the
answers here are shown,

1045
00:44:20,990 --> 00:44:22,472
for this particular system.

1046
00:44:22,472 --> 00:44:24,180
It would require
sitting down and walking

1047
00:44:24,180 --> 00:44:26,469
through the equations,
but in essence

1048
00:44:26,469 --> 00:44:29,010
right here, with the pool filled
with the negative refractive

1049
00:44:29,010 --> 00:44:32,690
index material, you're
really affecting

1050
00:44:32,690 --> 00:44:36,100
the angle at which light
is coming out of the pool.

1051
00:44:36,100 --> 00:44:39,680
Here you can see the corner
of the pool, which you

1052
00:44:39,680 --> 00:44:41,090
shouldn't even be able to see.

1053
00:44:41,090 --> 00:44:42,840
It's just that the
light traveled this way

1054
00:44:42,840 --> 00:44:45,620
and then came back because it
was a negative refractive index

1055
00:44:45,620 --> 00:44:46,370
material.

1056
00:44:46,370 --> 00:44:48,532
Light actually did something
like this, zoop, zoop.

1057
00:44:48,532 --> 00:44:49,740
AUDIENCE: What's in the pool?

1058
00:44:49,740 --> 00:44:51,400
TONIO BUONASSISI: Oh,
that's just a corner.

1059
00:44:51,400 --> 00:44:52,400
So what is in that pool?

1060
00:44:52,400 --> 00:44:54,420
That is a computer
generated graphic.

1061
00:44:54,420 --> 00:44:56,410
This is not a real pool.

1062
00:44:56,410 --> 00:44:58,730
There exists negative
refractive index materials

1063
00:44:58,730 --> 00:45:01,640
but not in that volume yet.

1064
00:45:01,640 --> 00:45:07,690
These are relatively small
things and very much a study

1065
00:45:07,690 --> 00:45:08,880
in fundamental science.

1066
00:45:08,880 --> 00:45:12,760
So in this case
right here, we have

1067
00:45:12,760 --> 00:45:17,220
less of an acute bending
of our angle of light.

1068
00:45:17,220 --> 00:45:19,610
So we don't get to see quite
as many features right here

1069
00:45:19,610 --> 00:45:20,660
toward the edge.

1070
00:45:20,660 --> 00:45:24,130
And the reflectivity
has changed as a result

1071
00:45:24,130 --> 00:45:29,252
of having drastically modified
our reflection condition.

1072
00:45:29,252 --> 00:45:31,460
AUDIENCE: Why does the
reflectivity seem to have gone

1073
00:45:31,460 --> 00:45:35,070
up and the index has gone down?

1074
00:45:35,070 --> 00:45:37,420
TONIO BUONASSISI: In
that particular case?

1075
00:45:37,420 --> 00:45:39,710
I think what they were getting
at-- this is coming off

1076
00:45:39,710 --> 00:45:40,460
of an SPI website.

1077
00:45:40,460 --> 00:45:42,460
I think what they were
getting at is mostly just

1078
00:45:42,460 --> 00:45:44,020
a change in the reflectivity.

1079
00:45:44,020 --> 00:45:48,110
So they were trying to emphasize
that you were modifying

1080
00:45:48,110 --> 00:45:50,630
the reflection off the
surface in addition

1081
00:45:50,630 --> 00:45:53,640
to the angle at which the
light was exiting the material.

1082
00:45:53,640 --> 00:45:58,580
I'm going to come back to
Snell's Law in a minute.

1083
00:45:58,580 --> 00:46:02,060
But for the time being,
I want to move on

1084
00:46:02,060 --> 00:46:05,450
to the next concept here,
which is Lambertian reflector.

1085
00:46:05,450 --> 00:46:09,210
You'll hear this topic or this
word thrown around quite a lot

1086
00:46:09,210 --> 00:46:10,770
in the solar cell community.

1087
00:46:10,770 --> 00:46:13,760
And it's used rather liberally
to mean a lot of things.

1088
00:46:13,760 --> 00:46:17,890
Although in optics, it has
a very specific meaning.

1089
00:46:17,890 --> 00:46:20,410
So I'm going to show you
that very specific meaning

1090
00:46:20,410 --> 00:46:24,100
and then describe for you
what it has very loosely come

1091
00:46:24,100 --> 00:46:25,620
to mean in the solar industry.

1092
00:46:25,620 --> 00:46:28,440
So a diffuse
Lambertian reflector

1093
00:46:28,440 --> 00:46:32,610
will follow a reflectance
that follows a cosine theta

1094
00:46:32,610 --> 00:46:33,920
dependence.

1095
00:46:33,920 --> 00:46:36,530
So if you have light
coming into a sample,

1096
00:46:36,530 --> 00:46:39,330
the surface normal, and
the outgoing light ray

1097
00:46:39,330 --> 00:46:41,410
form an angle theta.

1098
00:46:41,410 --> 00:46:43,240
And if the two are
perfectly aligned,

1099
00:46:43,240 --> 00:46:45,390
you get a lot of reflectance
off of that angle.

1100
00:46:45,390 --> 00:46:47,500
If the two are perpendicular
to one another,

1101
00:46:47,500 --> 00:46:49,830
you get zero reflectance
in that angle.

1102
00:46:49,830 --> 00:46:53,130
And so the reflectance parallel
to the surface here is zero.

1103
00:46:53,130 --> 00:46:55,720
In everywhere in between,
the magnitude of reflectance

1104
00:46:55,720 --> 00:46:57,480
is varying as consine theta.

1105
00:46:57,480 --> 00:47:01,730
That's the, I would
say, pedantic definition

1106
00:47:01,730 --> 00:47:03,550
of an Lambertian reflector.

1107
00:47:03,550 --> 00:47:04,990
Often in the solar
industry you'll

1108
00:47:04,990 --> 00:47:07,960
hear people, probably because
of a lack of optics background,

1109
00:47:07,960 --> 00:47:10,470
just call any randomly
reflecting surface

1110
00:47:10,470 --> 00:47:12,220
a Lambertian scatter.

1111
00:47:12,220 --> 00:47:15,400
It's a very loosely used term.

1112
00:47:15,400 --> 00:47:18,990
And it is wrong by the
book, but nevertheless, it's

1113
00:47:18,990 --> 00:47:22,930
one of these things that
live on in our industry.

1114
00:47:22,930 --> 00:47:26,190
So the difference between
a specular reflector,

1115
00:47:26,190 --> 00:47:28,470
the one that we've just
been analyzing right now,

1116
00:47:28,470 --> 00:47:30,880
and a Lambertian reflector,
is that typically the way

1117
00:47:30,880 --> 00:47:35,490
these are made is that you
do have a random texture

1118
00:47:35,490 --> 00:47:36,380
on your surface.

1119
00:47:36,380 --> 00:47:38,921
And that's probably where the
origin of this misunderstanding

1120
00:47:38,921 --> 00:47:39,900
comes about.

1121
00:47:39,900 --> 00:47:42,445
We don't get a
random reflectance

1122
00:47:42,445 --> 00:47:44,730
of the light coming off,
but the surface itself

1123
00:47:44,730 --> 00:47:46,440
can be rather texturized.

1124
00:47:46,440 --> 00:47:49,420
So, for example, if you suspect
that this little material

1125
00:47:49,420 --> 00:47:52,110
right here might behave
like a Lambertian scatter,

1126
00:47:52,110 --> 00:47:56,332
you might put it inside of
a tool and rotate the angle

1127
00:47:56,332 --> 00:47:58,040
and measure the amount
of reflected light

1128
00:47:58,040 --> 00:48:00,680
as a function of the angle
to determine whether or not

1129
00:48:00,680 --> 00:48:03,510
it follows this cosine
theta dependence.

1130
00:48:03,510 --> 00:48:07,510
And the reason it's important
is because the back skins

1131
00:48:07,510 --> 00:48:11,619
of our solar modules can quite
often be Lambertian scatters.

1132
00:48:11,619 --> 00:48:13,160
And we have a certain
amount of light

1133
00:48:13,160 --> 00:48:15,140
that comes off at
some angle here

1134
00:48:15,140 --> 00:48:17,760
that will get trapped by a
total internal reflection

1135
00:48:17,760 --> 00:48:19,250
inside of a modules.

1136
00:48:19,250 --> 00:48:23,790
So if, instead of having
macroscopic pyramids right

1137
00:48:23,790 --> 00:48:26,780
here, you had very, very
small pyramids-- still not

1138
00:48:26,780 --> 00:48:29,370
sub-wavelength, but
smaller features,

1139
00:48:29,370 --> 00:48:32,340
for example, the texturization
on the back skin right here.

1140
00:48:32,340 --> 00:48:34,260
An it managed to
scatter the light

1141
00:48:34,260 --> 00:48:35,920
at a particular
angle that got caught

1142
00:48:35,920 --> 00:48:37,380
by total internal reflection.

1143
00:48:37,380 --> 00:48:39,900
Macroscopically, we might be
able to describe the scattering

1144
00:48:39,900 --> 00:48:42,800
behavior of that surface
as Lambertian scatter.

1145
00:48:42,800 --> 00:48:45,950
But it's those waves, those
rays that are bouncing off

1146
00:48:45,950 --> 00:48:48,260
at those large angles
that are causing

1147
00:48:48,260 --> 00:48:52,390
the total internal
reflection event.

1148
00:48:52,390 --> 00:48:55,595
And so the notion of
a Lambertian scatter

1149
00:48:55,595 --> 00:48:58,660
is important on the backsides
of solar cell devices.

1150
00:48:58,660 --> 00:49:04,410
We would obviously wants to even
change the scattering profile.

1151
00:49:04,410 --> 00:49:07,482
We wouldn't want necessarily
specular reflectance.

1152
00:49:07,482 --> 00:49:09,940
We might want to maximize the
amount of light reflected off

1153
00:49:09,940 --> 00:49:12,170
at particular angles.

1154
00:49:12,170 --> 00:49:14,320
And there is, of
course, research

1155
00:49:14,320 --> 00:49:18,050
being done to figure out
how to make light do that.

1156
00:49:18,050 --> 00:49:20,790
I'll show you one example
at the very end of lecture,

1157
00:49:20,790 --> 00:49:23,670
a paper that was just
published in Science last week,

1158
00:49:23,670 --> 00:49:25,380
as an example.

1159
00:49:25,380 --> 00:49:27,380
And so these
scattering centers off

1160
00:49:27,380 --> 00:49:29,315
the backs of the
rear sides of cells

1161
00:49:29,315 --> 00:49:31,440
would operate more or less
in the following manner.

1162
00:49:31,440 --> 00:49:32,980
You'd have incoming light.

1163
00:49:32,980 --> 00:49:35,360
Let's ignore front
surface texturing for now.

1164
00:49:35,360 --> 00:49:36,980
Let's just focus
on the backside.

1165
00:49:36,980 --> 00:49:39,770
And if you have some random, as
we call it, a random reflector,

1166
00:49:39,770 --> 00:49:43,135
a randomly texturized reflector
on the back that reflects off

1167
00:49:43,135 --> 00:49:45,860
in, say, a Lambertian
fashion, you'll

1168
00:49:45,860 --> 00:49:48,430
have some fraction of
that light scattered off

1169
00:49:48,430 --> 00:49:53,170
at an angle that is large
enough relative to the surface

1170
00:49:53,170 --> 00:49:57,740
normal that it is trapped by
total internal reflection.

1171
00:49:57,740 --> 00:50:01,090
And you don't only have
to texture your back skin.

1172
00:50:01,090 --> 00:50:03,034
You can also texture
the bus bars.

1173
00:50:03,034 --> 00:50:05,200
The bus bars are these
little metal wires right here

1174
00:50:05,200 --> 00:50:07,709
that are collecting the charge
from each of the solar cells.

1175
00:50:07,709 --> 00:50:09,750
And they're connecting
essentially the front side

1176
00:50:09,750 --> 00:50:11,580
of one cell to the
backside of the next.

1177
00:50:11,580 --> 00:50:13,000
If you want to think about it
as the cathode to the anode,

1178
00:50:13,000 --> 00:50:14,791
cathode to the anode,
cathode to the anode,

1179
00:50:14,791 --> 00:50:17,130
stringing all these
cells together in series.

1180
00:50:17,130 --> 00:50:19,110
And this metal right here
is just really shiny,

1181
00:50:19,110 --> 00:50:22,070
and it's reflecting light
right back out into space.

1182
00:50:22,070 --> 00:50:25,330
What if we instead were to
texture that metal so that when

1183
00:50:25,330 --> 00:50:27,320
laser light shined on it
a certain amount would

1184
00:50:27,320 --> 00:50:29,250
be reflected off at an
angle and then caught

1185
00:50:29,250 --> 00:50:30,290
by total internal reflection.

1186
00:50:30,290 --> 00:50:32,331
And that's exactly what
you're seeing right here.

1187
00:50:32,331 --> 00:50:34,400
The light bounced here
on a textured bus bar,

1188
00:50:34,400 --> 00:50:36,560
bounced off of the glass
more or less around here

1189
00:50:36,560 --> 00:50:38,710
halfway, and then
got a second chance

1190
00:50:38,710 --> 00:50:40,297
to enter the cell over here.

1191
00:50:40,297 --> 00:50:41,880
Obviously some of
it is reflecting off

1192
00:50:41,880 --> 00:50:43,090
so we can see it.

1193
00:50:43,090 --> 00:50:44,480
But a lot of it's going in.

1194
00:50:44,480 --> 00:50:46,492
And that little
innovation right there,

1195
00:50:46,492 --> 00:50:47,950
which was developed
in the building

1196
00:50:47,950 --> 00:50:50,470
right next door by
Professor Ely Sachs,

1197
00:50:50,470 --> 00:50:53,290
can gain module performances
somewhere on the order

1198
00:50:53,290 --> 00:50:55,430
of a few percent relative.

1199
00:50:55,430 --> 00:50:57,430
So that might not
sound like a whole lot,

1200
00:50:57,430 --> 00:51:01,930
but if you're a $100 billion
industry, 1% is a lot of money.

1201
00:51:01,930 --> 00:51:05,040
So it does add up.

1202
00:51:05,040 --> 00:51:08,410
So that goes back to the
total internal reflection.

1203
00:51:08,410 --> 00:51:14,620
So there is a limit to
all of this texturization.

1204
00:51:14,620 --> 00:51:18,350
There's a limit to how much
we can trap light simply

1205
00:51:18,350 --> 00:51:23,930
by modifying or
corrugating the surfaces

1206
00:51:23,930 --> 00:51:27,060
to enhance the optical path
length with these types

1207
00:51:27,060 --> 00:51:32,220
of bounces using Snell's
Law and of course

1208
00:51:32,220 --> 00:51:33,870
the general
reflectivity equations.

1209
00:51:33,870 --> 00:51:37,470
And a gentleman by the name
of Eli Yablonovitch, who's

1210
00:51:37,470 --> 00:51:40,690
now a professor in Berkeley
calculated these parameters

1211
00:51:40,690 --> 00:51:45,130
I think back in 1982 and
came up with an upper limit

1212
00:51:45,130 --> 00:51:46,740
to the optical path length.

1213
00:51:46,740 --> 00:51:50,460
He, after a long
series of calculations,

1214
00:51:50,460 --> 00:51:53,990
derived an expression
for the maximum increase

1215
00:51:53,990 --> 00:51:56,710
of the optical path length
due to surface texturing,

1216
00:51:56,710 --> 00:51:59,080
which was 4n squared.

1217
00:51:59,080 --> 00:52:01,640
And the Yablonovitch
limit to this day

1218
00:52:01,640 --> 00:52:05,870
is a pretty good litmus
test for the ability

1219
00:52:05,870 --> 00:52:07,250
of a material to trap light.

1220
00:52:07,250 --> 00:52:09,430
So if you have
silicon, for instance,

1221
00:52:09,430 --> 00:52:12,030
with a refractive
index of, let's say,

1222
00:52:12,030 --> 00:52:15,690
in the infrared some around
3.6, your Yablonovitch limit

1223
00:52:15,690 --> 00:52:18,530
is around 50, which means
that you can increase

1224
00:52:18,530 --> 00:52:20,860
the optical path
length by a factor 50,

1225
00:52:20,860 --> 00:52:24,570
relative to the thickness
of your material.

1226
00:52:24,570 --> 00:52:26,180
If you have an organic
material, which

1227
00:52:26,180 --> 00:52:29,800
has a refractive index typically
of around maximum 2, then

1228
00:52:29,800 --> 00:52:32,460
that would be squared, 16,
somewhere in that range.

1229
00:52:32,460 --> 00:52:35,264
You can increase probably
in the order of 20

1230
00:52:35,264 --> 00:52:37,180
the optical path length
inside of the material

1231
00:52:37,180 --> 00:52:38,930
through texturization.

1232
00:52:38,930 --> 00:52:42,180
So this is a useful
parameter for those

1233
00:52:42,180 --> 00:52:43,890
who are doing research
in photovoltaics,

1234
00:52:43,890 --> 00:52:45,480
the graduate
students especially.

1235
00:52:45,480 --> 00:52:47,590
And so I think the
graduate students

1236
00:52:47,590 --> 00:52:49,840
will have a question at some
point on the Yablonovitch

1237
00:52:49,840 --> 00:52:51,610
limit.

1238
00:52:51,610 --> 00:52:55,480
And so that's a useful
parameter to keep in your mind.

1239
00:52:55,480 --> 00:53:00,320
Let me touch upon a few other
forms of trapping light.

1240
00:53:00,320 --> 00:53:02,970
We've so far just
assumed that light

1241
00:53:02,970 --> 00:53:07,340
behaves like a
continuous wave, doesn't

1242
00:53:07,340 --> 00:53:09,900
interfere with anything,
doesn't interfere with itself.

1243
00:53:09,900 --> 00:53:14,907
Now we're going to discuss some
anti-reflection effects which

1244
00:53:14,907 --> 00:53:16,740
derives from the notion
that light is a wave

1245
00:53:16,740 --> 00:53:20,470
and can constructively and
destructively interfere.

1246
00:53:20,470 --> 00:53:25,300
What we have right here is
a layer of another material

1247
00:53:25,300 --> 00:53:27,820
with a refractive
index, say n1, which

1248
00:53:27,820 --> 00:53:30,070
is in between our
n0 which is at air

1249
00:53:30,070 --> 00:53:31,800
and our n2 is the
absorber material,

1250
00:53:31,800 --> 00:53:33,580
let's say the silicon.

1251
00:53:33,580 --> 00:53:35,357
So we have a grading
of refractive indices

1252
00:53:35,357 --> 00:53:37,190
going from air, our
anti-reflection coating,

1253
00:53:37,190 --> 00:53:38,270
to silicon.

1254
00:53:38,270 --> 00:53:40,895
And right over here we have
a certain thickness, d1.

1255
00:53:40,895 --> 00:53:43,890
And over here we have a
certain thickness, d2.

1256
00:53:43,890 --> 00:53:47,760
So what is happening
in these two images?

1257
00:53:47,760 --> 00:53:51,540
Let me show you with another,
a little bit more clear figure,

1258
00:53:51,540 --> 00:53:53,680
coming from our
beloved Wikipedia,

1259
00:53:53,680 --> 00:53:56,140
and then go back to that
other image right there.

1260
00:53:56,140 --> 00:53:59,710
So what's happening is we
have an incoming wave that

1261
00:53:59,710 --> 00:54:02,110
for some reason is
ignoring Snell's Law.

1262
00:54:02,110 --> 00:54:02,949
It's beyond me.

1263
00:54:02,949 --> 00:54:04,990
But anyway, the wave is
going in a straight line.

1264
00:54:04,990 --> 00:54:07,470
It should be bending toward
the surface norm, obviously.

1265
00:54:07,470 --> 00:54:11,290
But we have reflections
off of this interface

1266
00:54:11,290 --> 00:54:14,190
and this interface right here.

1267
00:54:14,190 --> 00:54:19,530
And because the
thickness of this layer

1268
00:54:19,530 --> 00:54:22,360
is in the order
of lambda over 4,

1269
00:54:22,360 --> 00:54:24,090
that means that the
wave that's going in

1270
00:54:24,090 --> 00:54:26,131
will be phase shifted
relative to the wave that's

1271
00:54:26,131 --> 00:54:28,650
reflected off the front surface,
first by lambda over 4 then

1272
00:54:28,650 --> 00:54:30,610
2 times lambda over
4, in other words,

1273
00:54:30,610 --> 00:54:33,530
lambda over 2, which means that
the two waves are out of phase

1274
00:54:33,530 --> 00:54:36,510
by lambda over 2, which means
that they will destructively

1275
00:54:36,510 --> 00:54:38,512
interfere.

1276
00:54:38,512 --> 00:54:39,720
The peak will be at a trough.

1277
00:54:39,720 --> 00:54:41,695
The trough will be at a peak.

1278
00:54:41,695 --> 00:54:44,320
So the two waves will are going
to be destructively interfering

1279
00:54:44,320 --> 00:54:45,180
when they come out.

1280
00:54:45,180 --> 00:54:47,096
If you add these two
together, due to the wave

1281
00:54:47,096 --> 00:54:51,170
nature of light, you get
suppressed reflectance.

1282
00:54:51,170 --> 00:54:53,800
And that's a really
interesting property.

1283
00:54:53,800 --> 00:54:56,630
You can begin varying the
thickness of this layer,

1284
00:54:56,630 --> 00:54:59,270
and of course changing the
nature of the reflected light.

1285
00:54:59,270 --> 00:55:01,735
You can constructively
interfere if you like

1286
00:55:01,735 --> 00:55:04,440
and enhance the amount
of reflected light

1287
00:55:04,440 --> 00:55:07,770
as a result of this
interference effect.

1288
00:55:07,770 --> 00:55:11,050
Obviously, in most solar cells,
we want to suppress reflection.

1289
00:55:11,050 --> 00:55:12,800
And so we go to great
lengths to make sure

1290
00:55:12,800 --> 00:55:16,200
that this thickness as well
as the refractive index

1291
00:55:16,200 --> 00:55:23,880
of the material is optimized
for a particular system.

1292
00:55:23,880 --> 00:55:29,020
And so without going
into the hairy math,

1293
00:55:29,020 --> 00:55:33,494
to calculate this right here,
it's definitely possible.

1294
00:55:33,494 --> 00:55:35,410
It's definitely something
that should be done.

1295
00:55:35,410 --> 00:55:37,618
And I believe the graduate
students have it assigned.

1296
00:55:37,618 --> 00:55:39,490
It's the very last
problem in the homework.

1297
00:55:39,490 --> 00:55:43,690
But for a very simple kind of
conceptual understanding that

1298
00:55:43,690 --> 00:55:45,860
is wavelength
independent, if we want

1299
00:55:45,860 --> 00:55:50,030
to minimize the reflectance at
a particular wavelength, let's

1300
00:55:50,030 --> 00:55:53,570
call it at a lambda
0, which is the photon

1301
00:55:53,570 --> 00:55:56,700
wavelength at the peak
of the solar spectrum,

1302
00:55:56,700 --> 00:55:59,549
we have to design the thickness
of our anti-reflection coating

1303
00:55:59,549 --> 00:56:01,090
to satisfy that
equation right there,

1304
00:56:01,090 --> 00:56:02,640
essentially lambda over 4.

1305
00:56:02,640 --> 00:56:04,772
That's the phase
shift we want upon one

1306
00:56:04,772 --> 00:56:06,230
pass of the
anti-reflection coating

1307
00:56:06,230 --> 00:56:08,000
so that two passes,
when it goes through

1308
00:56:08,000 --> 00:56:09,440
and then back,
it's phase shifted

1309
00:56:09,440 --> 00:56:11,630
relative to the surface
reflected light by lambda

1310
00:56:11,630 --> 00:56:15,390
over 2, divided by n, n
being the refractive index

1311
00:56:15,390 --> 00:56:16,830
of the material.

1312
00:56:16,830 --> 00:56:20,234
Obviously the frequency of
light is staying the same

1313
00:56:20,234 --> 00:56:21,900
as it goes from one
material to another.

1314
00:56:21,900 --> 00:56:25,040
But the wavelength
would be changing.

1315
00:56:25,040 --> 00:56:28,250
So that's why the n
parameter appears right here

1316
00:56:28,250 --> 00:56:29,580
in this equation.

1317
00:56:29,580 --> 00:56:32,350
The t is the thickness of the
optimal anti-reflection coating

1318
00:56:32,350 --> 00:56:33,470
thickness.

1319
00:56:33,470 --> 00:56:38,425
So just to give us a
sense, kind of an estimate,

1320
00:56:38,425 --> 00:56:40,550
and to give us some confidence
in these engineering

1321
00:56:40,550 --> 00:56:42,720
methods, what I'd
like you to do is

1322
00:56:42,720 --> 00:56:47,390
to calculate the thickness of an
ideal anti-reflective coating.

1323
00:56:47,390 --> 00:56:49,730
This anti-reflective coating
right here on these cells--

1324
00:56:49,730 --> 00:56:51,855
I apologize, they also have
the metal on the front,

1325
00:56:51,855 --> 00:56:54,280
so it's a little difficult to
distinguish between the two.

1326
00:56:54,280 --> 00:56:58,260
But in my right hand, this one,
I have a piece of bare silicon.

1327
00:56:58,260 --> 00:57:00,610
And you can see it's
rather reflective.

1328
00:57:00,610 --> 00:57:03,180
In my left hand
over here, I have

1329
00:57:03,180 --> 00:57:05,690
a piece of silicon with
an anti-reflective coating

1330
00:57:05,690 --> 00:57:08,146
as well some contact
metalization on the front.

1331
00:57:08,146 --> 00:57:09,770
So that's why you
see those grid lines.

1332
00:57:09,770 --> 00:57:11,700
But it looks very blue.

1333
00:57:11,700 --> 00:57:13,497
It looks very blue
because the cell

1334
00:57:13,497 --> 00:57:15,830
is absorbing very well at the
peak of the solar spectrum

1335
00:57:15,830 --> 00:57:18,180
which is in the yellow.

1336
00:57:18,180 --> 00:57:23,320
So calculate for me what
is the optimal thickness

1337
00:57:23,320 --> 00:57:26,110
of an anti-reflection
coating of silicon nitride?

1338
00:57:26,110 --> 00:57:29,010
And we'll give it a
refractive index of, say, 2.1.

1339
00:57:29,010 --> 00:57:31,360
Let me see if those
numbers make sense,

1340
00:57:31,360 --> 00:57:35,640
so refractive index of silicon
nitride somewhere around 550.

1341
00:57:35,640 --> 00:57:38,160
Let's call it 2, just
make our lives simple.

1342
00:57:38,160 --> 00:57:41,730
And the peak of the solar
spectrum we'll again call 550.

1343
00:57:41,730 --> 00:57:43,584
So why don't we run
the numbers quickly.

1344
00:57:43,584 --> 00:57:44,834
What should that thickness be?

1345
00:57:54,983 --> 00:57:56,524
AUDIENCE: Tonio,
I'm sorry, could you

1346
00:57:56,524 --> 00:57:57,852
repeat the constant again?

1347
00:57:57,852 --> 00:57:58,810
TONIO BUONASSISI: Sure.

1348
00:57:58,810 --> 00:58:03,210
So the n, the refractive
index, is going to be around 2

1349
00:58:03,210 --> 00:58:04,690
for silicon nitride.

1350
00:58:04,690 --> 00:58:07,400
So we're going from air, which
is around refractive index one,

1351
00:58:07,400 --> 00:58:10,810
to silicon nitride, the silicon.

1352
00:58:10,810 --> 00:58:14,500
And the peak of the solar
spectrum, our lambda 0,

1353
00:58:14,500 --> 00:58:16,530
which is the photon
wavelength at the peak

1354
00:58:16,530 --> 00:58:20,740
of the solar spectrum in vacuum
or in air, is 550 nanometers.

1355
00:58:26,950 --> 00:58:29,760
So what thicknesses are
folks coming up with?

1356
00:58:29,760 --> 00:58:31,200
Order of magnitude.

1357
00:58:31,200 --> 00:58:32,200
AUDIENCE: 70 nanometers.

1358
00:58:32,200 --> 00:58:33,533
TONIO BUONASSISI: 70 nanometers.

1359
00:58:33,533 --> 00:58:37,420
That's almost spot on
to the actual thickness,

1360
00:58:37,420 --> 00:58:39,670
to somewhere on the
order between 70 to 80

1361
00:58:39,670 --> 00:58:42,380
nanometer typically.

1362
00:58:42,380 --> 00:58:46,210
You're telling me that
something that is 1/1,000,

1363
00:58:46,210 --> 00:58:49,540
the thickness of my hair,
is deposited on the surface

1364
00:58:49,540 --> 00:58:53,060
of this wafer and is
absorbing all this light?

1365
00:58:53,060 --> 00:58:54,256
That's pretty cool.

1366
00:58:54,256 --> 00:58:55,630
And it's not
absorbing the light.

1367
00:58:55,630 --> 00:58:56,870
The anti-reflective
coating is not

1368
00:58:56,870 --> 00:58:58,280
absorbing the light,
which is really important.

1369
00:58:58,280 --> 00:58:59,779
We want the solar
cell underneath it

1370
00:58:59,779 --> 00:59:00,890
to be absorbing the light.

1371
00:59:00,890 --> 00:59:03,440
The anti-reflection coding
is enabling the light

1372
00:59:03,440 --> 00:59:07,790
to be absorbed because it's
suppressing the reflectance.

1373
00:59:07,790 --> 00:59:10,120
The reflected modes at
that particular wavelength

1374
00:59:10,120 --> 00:59:13,900
are suppressed because of
the destructive interference.

1375
00:59:13,900 --> 00:59:15,410
That's cool.

1376
00:59:15,410 --> 00:59:18,530
I really get a kick out of
anti-reflective coatings.

1377
00:59:18,530 --> 00:59:22,070
So they're 70 nanometers thick.

1378
00:59:22,070 --> 00:59:24,780
And you gain quite a lot in
terms of cell performance.

1379
00:59:27,560 --> 00:59:30,850
I'll show you some slides to
drive that point home in a bit.

1380
00:59:34,600 --> 00:59:37,600
This is really really briefly--
I'll post these slides online

1381
00:59:37,600 --> 00:59:39,320
so you can have access to them.

1382
00:59:39,320 --> 00:59:42,560
If you use the matrix
transfer method,

1383
00:59:42,560 --> 00:59:46,880
as described beautifully in
[? Gonchen's ?] textbook,

1384
00:59:46,880 --> 00:59:50,280
you can calculate the
amount of light reflected

1385
00:59:50,280 --> 00:59:54,360
across a broad spectral
range for a given thickness

1386
00:59:54,360 --> 00:59:55,600
of anti-reflection coding.

1387
00:59:55,600 --> 00:59:57,500
So what we did right
now was to calculate

1388
00:59:57,500 --> 01:00:00,370
a suppression of the light
at a particular wavelength.

1389
01:00:00,370 --> 01:00:02,920
But you can also calculate
with the tools that

1390
01:00:02,920 --> 01:00:06,890
are available to
you the reflectance

1391
01:00:06,890 --> 01:00:09,140
of your particular device
over a broader wavelength.

1392
01:00:09,140 --> 01:00:11,090
Range and that's pretty
cool because now you

1393
01:00:11,090 --> 01:00:14,520
can begin, say, multiplying
this function right

1394
01:00:14,520 --> 01:00:17,540
here against your solar
spectrum and begin

1395
01:00:17,540 --> 01:00:21,000
to calculate the total amount
of light entering your sample

1396
01:00:21,000 --> 01:00:22,960
and the total energy
entering your sample.

1397
01:00:22,960 --> 01:00:25,420
Equations, brilliant.

1398
01:00:25,420 --> 01:00:27,730
The important thing
to note here is

1399
01:00:27,730 --> 01:00:30,550
that it really, really matters.

1400
01:00:30,550 --> 01:00:32,970
This is silicon under
glass right here,

1401
01:00:32,970 --> 01:00:35,730
for example, typical solar
cell material in blue.

1402
01:00:35,730 --> 01:00:37,320
It's better than
the bare silicon.

1403
01:00:37,320 --> 01:00:40,550
Why is it better than the bare
silicon, silicon under glass?

1404
01:00:40,550 --> 01:00:42,500
Glass has a refractive
index of 1.5 or so.

1405
01:00:45,886 --> 01:00:48,316
AUDIENCE: The index matching.

1406
01:00:48,316 --> 01:00:52,690
You go from pairs 1 to 2.3
and then to [INAUDIBLE].

1407
01:00:52,690 --> 01:00:56,277
The difference is small
between the classes.

1408
01:00:56,277 --> 01:00:57,360
TONIO BUONASSISI: Exactly.

1409
01:00:57,360 --> 01:00:58,900
So if we recall
that equation that

1410
01:00:58,900 --> 01:01:00,400
described the amount
of reflectance,

1411
01:01:00,400 --> 01:01:04,260
there was that-- what was it--
n1 minus n2 quantity squared,

1412
01:01:04,260 --> 01:01:04,760
right?

1413
01:01:04,760 --> 01:01:07,210
So the bigger the delta
between the ends, the bigger

1414
01:01:07,210 --> 01:01:08,710
the difference in
refractive indices

1415
01:01:08,710 --> 01:01:10,330
between material one
and material two,

1416
01:01:10,330 --> 01:01:12,890
the more the reflectance is
going to be off that interface.

1417
01:01:12,890 --> 01:01:15,460
And so you can begin
reducing reflectance off

1418
01:01:15,460 --> 01:01:18,530
of a stack of light
going both ways

1419
01:01:18,530 --> 01:01:22,730
by grading the refractive
index of the material.

1420
01:01:22,730 --> 01:01:26,380
And that, of course, changes the
reflectance in both directions.

1421
01:01:26,380 --> 01:01:29,489
And so you get a reduction
in the total amount

1422
01:01:29,489 --> 01:01:31,780
of reflected light when you
put the silicon under glass

1423
01:01:31,780 --> 01:01:35,620
because glass has a refractive
index somewhere between air

1424
01:01:35,620 --> 01:01:37,750
and silicon.

1425
01:01:37,750 --> 01:01:39,480
And then you get a
further reduction

1426
01:01:39,480 --> 01:01:43,370
of the reflectance when you
have an anti-reflection coating

1427
01:01:43,370 --> 01:01:45,730
with a refractive index
somewhere around--

1428
01:01:45,730 --> 01:01:47,830
for this particular
system, silicon again

1429
01:01:47,830 --> 01:01:49,570
has a higher refractive index.

1430
01:01:49,570 --> 01:01:52,300
This used in anti-reflective
coating of a refractive index

1431
01:01:52,300 --> 01:01:56,710
of 2.3 of some
thickness, probably

1432
01:01:56,710 --> 01:01:59,800
somewhere around--
let's see, it'd

1433
01:01:59,800 --> 01:02:03,520
be greater or smaller,
probably around 65,

1434
01:02:03,520 --> 01:02:05,610
75 nanometer
somewhere that range.

1435
01:02:05,610 --> 01:02:08,630
So what this is
saying is that you

1436
01:02:08,630 --> 01:02:11,350
can minimize the
reflection of light

1437
01:02:11,350 --> 01:02:13,080
off of the front
surface of your sample

1438
01:02:13,080 --> 01:02:15,990
by using an intelligent
combination of the very

1439
01:02:15,990 --> 01:02:18,040
first equation that we're
exposed to in the class

1440
01:02:18,040 --> 01:02:20,480
today, which was the
reflected light as a function

1441
01:02:20,480 --> 01:02:22,646
of refractive index, so
essentially refractive index

1442
01:02:22,646 --> 01:02:25,490
matching and secondly, by
engineering by engineering

1443
01:02:25,490 --> 01:02:28,220
an anti-reflective
coating, which oftentimes

1444
01:02:28,220 --> 01:02:29,690
in the lingo of
solar cell science

1445
01:02:29,690 --> 01:02:32,540
we call it an ARC, an
anti-reflective coating.

1446
01:02:32,540 --> 01:02:36,430
And those two things combined
give us very low reflection

1447
01:02:36,430 --> 01:02:39,190
off of the front surface.

1448
01:02:39,190 --> 01:02:47,000
Probably 5% of our R&D
cells that we make at MIT

1449
01:02:47,000 --> 01:02:49,640
use these sorts of
technologies, which are pretty

1450
01:02:49,640 --> 01:02:51,210
standard in the industry.

1451
01:02:51,210 --> 01:02:54,650
And you can see what
the hit is, right?

1452
01:02:54,650 --> 01:02:56,610
Let's see, if I'm just
using a bare material,

1453
01:02:56,610 --> 01:02:58,770
if I'm getting 30%
reflection, I'm

1454
01:02:58,770 --> 01:03:04,010
getting a 30% drop in the
current output of my device.

1455
01:03:04,010 --> 01:03:05,680
That's pretty significant.

1456
01:03:05,680 --> 01:03:08,560
So these are simple ways to
improve performance of devices.

1457
01:03:11,430 --> 01:03:15,160
If you want to become
fancy and actually do

1458
01:03:15,160 --> 01:03:19,080
what's called a ray tracing
to calculate the path of light

1459
01:03:19,080 --> 01:03:22,110
through a medium, there
is software available

1460
01:03:22,110 --> 01:03:24,950
that will take all of
what we've discussed today

1461
01:03:24,950 --> 01:03:26,570
and calculate it
for you so you don't

1462
01:03:26,570 --> 01:03:30,750
have to walk through
the expressions

1463
01:03:30,750 --> 01:03:32,000
that we just walked through.

1464
01:03:32,000 --> 01:03:35,000
It is easy.

1465
01:03:35,000 --> 01:03:37,110
In other words, you
plug something in.

1466
01:03:37,110 --> 01:03:38,160
You get some ray traces.

1467
01:03:38,160 --> 01:03:40,830
You can calculate reflectance
and so forth, transmittance.

1468
01:03:40,830 --> 01:03:43,424
But it's as smart as
what you put into it.

1469
01:03:43,424 --> 01:03:45,590
It's really important to
understand the fundamentals

1470
01:03:45,590 --> 01:03:48,590
behind any simulation software
because you will get out

1471
01:03:48,590 --> 01:03:50,410
of it what you put into it.

1472
01:03:50,410 --> 01:03:52,840
You will not be able to
pick up on obvious things

1473
01:03:52,840 --> 01:03:55,890
that you might of--
for example, double

1474
01:03:55,890 --> 01:03:57,390
clicked on this
little material here

1475
01:03:57,390 --> 01:04:01,290
and find the real component of
the refractive index completely

1476
01:04:01,290 --> 01:04:02,130
wrong.

1477
01:04:02,130 --> 01:04:03,854
And you might not notice it.

1478
01:04:03,854 --> 01:04:05,270
You might not pick
up on it if you

1479
01:04:05,270 --> 01:04:07,600
don't have some good
intuition which is

1480
01:04:07,600 --> 01:04:09,410
grounded in the fundamentals.

1481
01:04:09,410 --> 01:04:11,880
And so it's important
that you understand

1482
01:04:11,880 --> 01:04:13,250
what we've presented today.

1483
01:04:13,250 --> 01:04:15,624
It's important you understand
the reading and, of course,

1484
01:04:15,624 --> 01:04:19,290
do the p-set as well to really
drive those fundamentals home.

1485
01:04:19,290 --> 01:04:23,450
So to kind of put a big umbrella
over the entire lecture,

1486
01:04:23,450 --> 01:04:28,630
light management ensures
that the absorbtance is high.

1487
01:04:28,630 --> 01:04:31,790
The absorbtance would
be, essentially,

1488
01:04:31,790 --> 01:04:33,833
the amount of light
getting absorbed inside

1489
01:04:33,833 --> 01:04:38,160
of the material, normalized by
the amount of light going in,

1490
01:04:38,160 --> 01:04:39,370
so 1 minus r.

1491
01:04:39,370 --> 01:04:43,910
So we want to ensure that
light enters the absorber.

1492
01:04:43,910 --> 01:04:45,516
We want to minimize reflection.

1493
01:04:45,516 --> 01:04:48,015
We want to ensure good light
trapping inside of the absorber

1494
01:04:48,015 --> 01:04:50,930
as well, the absorber
being the material,

1495
01:04:50,930 --> 01:04:53,347
our photovoltaic material, the
ones absorbing the sunlight

1496
01:04:53,347 --> 01:04:55,388
and ultimately going to
be generating the charge.

1497
01:04:55,388 --> 01:04:56,540
So we call it the absorber.

1498
01:04:56,540 --> 01:04:58,540
So we want to ensure good
light trapping inside it.

1499
01:04:58,540 --> 01:05:00,414
We want to ensure the
maximum amount of light

1500
01:05:00,414 --> 01:05:01,780
gets trapped inside.

1501
01:05:01,780 --> 01:05:04,662
We want to maximize the
optical path length within it.

1502
01:05:04,662 --> 01:05:06,120
And we want to
minimize reflectance

1503
01:05:06,120 --> 01:05:08,280
off the front surface.

1504
01:05:08,280 --> 01:05:10,530
There are fancier ways of
light management as well

1505
01:05:10,530 --> 01:05:12,570
that don't involve light
trapping necessarily

1506
01:05:12,570 --> 01:05:16,930
but light manipulation or even
semiconductor manipulation.

1507
01:05:16,930 --> 01:05:20,600
You can, for instance,
change the wave length

1508
01:05:20,600 --> 01:05:23,370
of the incoming light.

1509
01:05:23,370 --> 01:05:25,000
One very simple
example of this is

1510
01:05:25,000 --> 01:05:27,750
when you shine, say for
example, red light on a phosphor

1511
01:05:27,750 --> 01:05:30,290
and then it glows
green in the dark.

1512
01:05:30,290 --> 01:05:32,250
That's a wavelength
change-- maybe not red.

1513
01:05:32,250 --> 01:05:35,650
You'd probably have to shine
blue to have it glow green.

1514
01:05:35,650 --> 01:05:38,125
That's an example of a
spectral down converter where

1515
01:05:38,125 --> 01:05:39,500
it's taking a
higher energy light

1516
01:05:39,500 --> 01:05:41,782
and converting it into
lower energy light.

1517
01:05:41,782 --> 01:05:43,240
Likewise, there
are folks out there

1518
01:05:43,240 --> 01:05:45,570
trying to do spectral up
converters where they take

1519
01:05:45,570 --> 01:05:48,210
two lower energy photons
then somehow convert that

1520
01:05:48,210 --> 01:05:50,280
into a higher energy photon.

1521
01:05:50,280 --> 01:05:52,970
And so since our
absorption coefficient

1522
01:05:52,970 --> 01:05:54,740
is dependent on
wavelength, if we're

1523
01:05:54,740 --> 01:05:57,350
able to shift the wavelength
of the light around

1524
01:05:57,350 --> 01:05:59,540
by engineering materials
near the surface,

1525
01:05:59,540 --> 01:06:01,230
we can enhance
absorption as well.

1526
01:06:01,230 --> 01:06:03,470
That is a form-- a valid
form-- of light management.

1527
01:06:03,470 --> 01:06:05,780
It has additional
benefits as well.

1528
01:06:05,780 --> 01:06:08,330
If we can eliminate the longer
wavelength stuff out here,

1529
01:06:08,330 --> 01:06:11,760
which is heat, performance
of most solar cell

1530
01:06:11,760 --> 01:06:13,570
suffers when they get hot.

1531
01:06:13,570 --> 01:06:15,300
And we'll learn why
that is about five

1532
01:06:15,300 --> 01:06:16,700
or 10 lectures from now.

1533
01:06:16,700 --> 01:06:19,190
And so if we manage to
do spectral up converting

1534
01:06:19,190 --> 01:06:22,660
or reflect that long wavelength
light away from our device,

1535
01:06:22,660 --> 01:06:24,526
we can improve
performance there as well.

1536
01:06:24,526 --> 01:06:26,150
That's another form
of light management

1537
01:06:26,150 --> 01:06:30,370
that doesn't necessarily
involve light trapping.

1538
01:06:30,370 --> 01:06:34,050
So again, I wanted
to really emphasize

1539
01:06:34,050 --> 01:06:36,990
that light management
is necessary devices.

1540
01:06:36,990 --> 01:06:39,837
This is no light
trapping, the blue curve,

1541
01:06:39,837 --> 01:06:42,420
and with light trapping, light
trapping being essentially just

1542
01:06:42,420 --> 01:06:45,495
an engineered coating
on the backside,

1543
01:06:45,495 --> 01:06:47,620
on the backside of your
device, of lights coming in

1544
01:06:47,620 --> 01:06:48,209
through here.

1545
01:06:48,209 --> 01:06:49,750
I've engineered a
coating on the back

1546
01:06:49,750 --> 01:06:52,660
to reflect the light back so
that it gets a second bounce

1547
01:06:52,660 --> 01:06:53,594
through the material.

1548
01:06:53,594 --> 01:06:55,010
I've engineered
the front surface,

1549
01:06:55,010 --> 01:06:57,860
texturized it so that we have
not only the benefit of two

1550
01:06:57,860 --> 01:07:00,930
bounces, double the
chance of light going in,

1551
01:07:00,930 --> 01:07:04,370
but also the Snell's
Law working in our favor

1552
01:07:04,370 --> 01:07:06,410
and increasing the
optical pathway.

1553
01:07:06,410 --> 01:07:12,082
And so all told, the one
reason why this boost is so big

1554
01:07:12,082 --> 01:07:14,290
right here is because I'm
increasing the optical path

1555
01:07:14,290 --> 01:07:15,710
length, the effective
optical path

1556
01:07:15,710 --> 01:07:18,770
length, relative to the
thickness of my material.

1557
01:07:18,770 --> 01:07:22,610
And as a result, I'm getting
a much larger current output.

1558
01:07:22,610 --> 01:07:24,902
I'm generating many
more free carriers

1559
01:07:24,902 --> 01:07:25,860
instead of my material.

1560
01:07:25,860 --> 01:07:27,720
I'm absorbing much
more light inside

1561
01:07:27,720 --> 01:07:31,827
of my material, just a very
simple calculation versus cell

1562
01:07:31,827 --> 01:07:32,800
thickness.

1563
01:07:32,800 --> 01:07:34,841
And obviously the thicker
and thicker and thicker

1564
01:07:34,841 --> 01:07:38,065
you go in your device, the
less important this becomes.

1565
01:07:38,065 --> 01:07:40,190
Because the less important
light trapping-- I mean,

1566
01:07:40,190 --> 01:07:41,600
you have the entire thickness.

1567
01:07:41,600 --> 01:07:44,560
I can absorb the majority
of the light in one pass.

1568
01:07:44,560 --> 01:07:48,730
But if you have
a thinner device,

1569
01:07:48,730 --> 01:07:50,106
it really begins to matter.

1570
01:07:50,106 --> 01:07:51,480
Once the thickness
of your device

1571
01:07:51,480 --> 01:07:54,684
starts approaching the
optical absorption, or 1

1572
01:07:54,684 --> 01:07:56,600
over the optical absorption
coefficient, which

1573
01:07:56,600 --> 01:07:59,250
is the extension
length, then it really

1574
01:07:59,250 --> 01:08:02,390
begins to matter in
the absorption length.

1575
01:08:02,390 --> 01:08:05,170
Light trapping can still matter
for thick devices, though.

1576
01:08:05,170 --> 01:08:10,830
Because if you manage to make
the light essentially refract

1577
01:08:10,830 --> 01:08:14,330
or bend, if you will, so that
it travels near the surface,

1578
01:08:14,330 --> 01:08:16,270
the distance that
those excited carriers

1579
01:08:16,270 --> 01:08:18,454
have to travel to be
collected is shorter.

1580
01:08:18,454 --> 01:08:21,240
And so you can get an additional
benefit from thicker devices

1581
01:08:21,240 --> 01:08:22,823
by engineering light
trapping as well.

1582
01:08:25,350 --> 01:08:27,535
OK, any questions about this?

1583
01:08:27,535 --> 01:08:30,175
This is kind of important.

1584
01:08:30,175 --> 01:08:32,300
This is why we spent all
this time in lecture today

1585
01:08:32,300 --> 01:08:35,810
talking about light management
is because of this plot right

1586
01:08:35,810 --> 01:08:36,970
here.

1587
01:08:36,970 --> 01:08:40,140
That's why.

1588
01:08:40,140 --> 01:08:42,250
I just wanted to show
you a cross section

1589
01:08:42,250 --> 01:08:43,679
of very high efficiency device.

1590
01:08:43,679 --> 01:08:45,220
This is one of the
highest efficiency

1591
01:08:45,220 --> 01:08:47,040
silicon-based devices
are out there.

1592
01:08:47,040 --> 01:08:51,550
And we have these
so-called backside mirror,

1593
01:08:51,550 --> 01:08:54,540
which is really just a layer
of dielectric material,

1594
01:08:54,540 --> 01:08:56,420
typically, that
reflects the light off

1595
01:08:56,420 --> 01:08:58,469
of that interface
using the equation

1596
01:08:58,469 --> 01:09:00,260
that we saw at the very
beginning of class,

1597
01:09:00,260 --> 01:09:05,500
the r equal to [INAUDIBLE]
n minus 1 quantity squared

1598
01:09:05,500 --> 01:09:09,770
divided by open parentheses
n plus 1 quantity squared.

1599
01:09:09,770 --> 01:09:12,680
So that's benefiting here from
the change of refractive index

1600
01:09:12,680 --> 01:09:15,060
going through your silicon
to that dielectric material

1601
01:09:15,060 --> 01:09:17,609
in the back.

1602
01:09:17,609 --> 01:09:19,420
They definitely take
good advantage of it.

1603
01:09:19,420 --> 01:09:20,420
Where you have
your metal, you're

1604
01:09:20,420 --> 01:09:21,439
going to be absorbing the light.

1605
01:09:21,439 --> 01:09:23,730
Or you have a higher probability
of absorbing the light

1606
01:09:23,730 --> 01:09:26,470
than you would if you had
a dielectric semiconductor

1607
01:09:26,470 --> 01:09:27,630
interface.

1608
01:09:27,630 --> 01:09:29,950
So the device design can
get pretty complicated

1609
01:09:29,950 --> 01:09:32,740
for these super high
efficiency devices.

1610
01:09:32,740 --> 01:09:36,149
And they're worried quite a bit
about trapping, other things

1611
01:09:36,149 --> 01:09:36,649
as well.

1612
01:09:36,649 --> 01:09:38,630
AUDIENCE: Coefficient,
is that one there?

1613
01:09:38,630 --> 01:09:40,490
TONIO BUONASSISI:
This one right here?

1614
01:09:40,490 --> 01:09:46,890
In the lab, 24.2%, in commercial
production, 22% and change.

1615
01:09:46,890 --> 01:09:50,580
22.4%, I think.

1616
01:09:50,580 --> 01:09:53,200
Just to throw some
last things out there

1617
01:09:53,200 --> 01:09:55,790
since we're five
minutes to closure.

1618
01:09:55,790 --> 01:09:59,880
Snell's Law assumes that there's
no phase shift of the light

1619
01:09:59,880 --> 01:10:02,174
as it transfers from
one medium to another.

1620
01:10:02,174 --> 01:10:03,715
If you introduce a
phase shift-- this

1621
01:10:03,715 --> 01:10:06,015
is just a paper published
in Science last week

1622
01:10:06,015 --> 01:10:08,670
by our friends over at
Harvard, Federico Capasso.

1623
01:10:08,670 --> 01:10:10,660
If you introduce a
phase shift of the light

1624
01:10:10,660 --> 01:10:12,368
as it goes through
one medium or another,

1625
01:10:12,368 --> 01:10:14,280
now you can start
doing some fun things.

1626
01:10:14,280 --> 01:10:18,530
If you introduce a constant
phase shift gradient

1627
01:10:18,530 --> 01:10:21,540
throughout the surface of a
material, let's say right here,

1628
01:10:21,540 --> 01:10:23,970
then you can cause
each node, each point

1629
01:10:23,970 --> 01:10:27,140
within your material, to
lag by an increasing amount,

1630
01:10:27,140 --> 01:10:29,900
so that your wave
front now bends.

1631
01:10:29,900 --> 01:10:33,410
You can think of these as kind
of a Huygen wavefront forming

1632
01:10:33,410 --> 01:10:35,950
as a result of these
small nodes here.

1633
01:10:35,950 --> 01:10:38,570
And if you can tailor
the phase independently

1634
01:10:38,570 --> 01:10:41,805
at each one of these points, you
can cause an increasing delay

1635
01:10:41,805 --> 01:10:43,209
as you go across.

1636
01:10:43,209 --> 01:10:45,000
And that will cause
the light, essentially,

1637
01:10:45,000 --> 01:10:48,290
if you trace through the
points of maximum intensity,

1638
01:10:48,290 --> 01:10:51,432
say the pink, you'll see
that the light is bent.

1639
01:10:51,432 --> 01:10:52,390
And that's pretty cool.

1640
01:10:52,390 --> 01:10:56,100
Because now we
can, in principle,

1641
01:10:56,100 --> 01:10:58,475
if this is hot off the press--
and then of course there's

1642
01:10:58,475 --> 01:11:00,974
a whole flurry of researchers
out there trying to figure out

1643
01:11:00,974 --> 01:11:02,840
how to use this
to our advantage,

1644
01:11:02,840 --> 01:11:06,040
but with anomalous refraction,
in principle, now you

1645
01:11:06,040 --> 01:11:08,430
can tailor the angle at
which light bends inside

1646
01:11:08,430 --> 01:11:09,490
of the material.

1647
01:11:09,490 --> 01:11:11,620
Perhaps you can even exceed
the Yablonovitch limit

1648
01:11:11,620 --> 01:11:14,424
inside of the material
as a result of this.

1649
01:11:14,424 --> 01:11:15,590
And so it's really exciting.

1650
01:11:15,590 --> 01:11:17,421
There's stuff
coming up every day.

1651
01:11:17,421 --> 01:11:18,170
This is the point.

1652
01:11:18,170 --> 01:11:20,760
There's stuff coming out every
day on light trapping and light

1653
01:11:20,760 --> 01:11:23,640
management.

1654
01:11:23,640 --> 01:11:25,870
Mostly it's for
photonic devices.

1655
01:11:25,870 --> 01:11:28,980
But they can be transferred
over into solar cells as well.

1656
01:11:28,980 --> 01:11:30,820
So it's going to
keep your eyes open.

1657
01:11:30,820 --> 01:11:34,210
And another example
of the photon up/down

1658
01:11:34,210 --> 01:11:39,230
converters, there's
recent reports in SPIE,

1659
01:11:39,230 --> 01:11:42,030
a lot of interest in
the optics community.

1660
01:11:42,030 --> 01:11:46,650
There was a TR35 award
given to a person who

1661
01:11:46,650 --> 01:11:48,290
studying this topic.

1662
01:11:48,290 --> 01:11:51,863
So it is, as well, a
very exciting and up

1663
01:11:51,863 --> 01:11:52,970
and coming field.

1664
01:11:52,970 --> 01:11:55,670
Again, the opportunities
there of manipulating

1665
01:11:55,670 --> 01:11:59,530
light are large, are vast.

1666
01:11:59,530 --> 01:12:03,150
So the laws, if you
will, that constrain us,

1667
01:12:03,150 --> 01:12:05,750
that we've discussed
today in class,

1668
01:12:05,750 --> 01:12:09,180
don't let that
constrain your thinking.

1669
01:12:09,180 --> 01:12:10,700
That's my final message.

1670
01:12:10,700 --> 01:12:12,250
Thanks.