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PROFESSOR: So we have an
interesting class today.

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00:00:28,740 --> 00:00:31,410
We're going to be taking
this IV curve that we've so

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00:00:31,410 --> 00:00:34,300
laboriously set up and
understood-- sorry about that.

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00:00:34,300 --> 00:00:38,110
And now we will subject
it to illumination.

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00:00:38,110 --> 00:00:40,760
So that's the essence
of our lecture today,

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00:00:40,760 --> 00:00:42,710
the diode under illumination.

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00:00:42,710 --> 00:00:45,020
And as part of
today's lecture, we

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00:00:45,020 --> 00:00:46,770
have some wonderful
little kits over there

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00:00:46,770 --> 00:00:48,970
in the corner where
we'll actually be testing

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00:00:48,970 --> 00:00:51,300
IV curves of solar cells.

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00:00:51,300 --> 00:00:53,620
So I hope some of you
brought the computers today,

19
00:00:53,620 --> 00:00:56,480
and if not, we have some extras
up here as well we can use.

20
00:00:56,480 --> 00:00:57,980
So again, just to
situate ourselves.

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00:00:57,980 --> 00:00:59,230
We're here in fundamentals.

22
00:00:59,230 --> 00:01:01,489
We're approaching the end
of our fundamental section,

23
00:01:01,489 --> 00:01:03,530
but we still have a few
really important lectures

24
00:01:03,530 --> 00:01:04,269
to get through.

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00:01:04,269 --> 00:01:05,519
After we get through
the fundamentals,

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00:01:05,519 --> 00:01:06,890
we'll be in a good
position to understand

27
00:01:06,890 --> 00:01:08,473
the different
technologies and finally

28
00:01:08,473 --> 00:01:09,880
the cross-cutting themes.

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00:01:09,880 --> 00:01:12,020
And our goal is to, at
least for the fundamentals,

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00:01:12,020 --> 00:01:13,820
to understand solar
cell conversion

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00:01:13,820 --> 00:01:17,280
efficiency, which is the ratio
of output to input energy.

32
00:01:17,280 --> 00:01:19,100
And for most solar
cells, this breaks down

33
00:01:19,100 --> 00:01:21,610
to the following progression,
from the solar spectrum

34
00:01:21,610 --> 00:01:22,940
to charge collection.

35
00:01:22,940 --> 00:01:25,880
And we're going to be
focusing on charge separation,

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00:01:25,880 --> 00:01:28,240
incorporating elements
of either side

37
00:01:28,240 --> 00:01:30,980
but mostly focused on
charge separation today.

38
00:01:30,980 --> 00:01:33,410
reminding everybody, of
course, that the total system

39
00:01:33,410 --> 00:01:36,180
efficiency is the product of
each individual efficiency.

40
00:01:36,180 --> 00:01:39,520
And if any one of these
is low, the efficiency

41
00:01:39,520 --> 00:01:41,120
for the entire system is low.

42
00:01:41,120 --> 00:01:43,870
And since folks are tired of
looking at this chart by now,

43
00:01:43,870 --> 00:01:48,690
every single lecture I intend
to introduce something new that

44
00:01:48,690 --> 00:01:51,010
follows a similar pattern.

45
00:01:51,010 --> 00:01:54,930
Does anybody recognize
what this is about?

46
00:01:54,930 --> 00:01:59,620
So you have over
here some H2O going

47
00:01:59,620 --> 00:02:02,890
into an oxygen-evolving
complex, and light is coming in,

48
00:02:02,890 --> 00:02:04,640
essentially exciting
up an electron,

49
00:02:04,640 --> 00:02:06,390
which is being stored in
some form of chemical energy.

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00:02:06,390 --> 00:02:06,980
What is that?

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00:02:06,980 --> 00:02:07,480
AUDIENCE: Photosynthesis.

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00:02:07,480 --> 00:02:08,940
PROFESSOR:
Photosynthesis, right?

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00:02:08,940 --> 00:02:15,220
And just like a solar cell,
the photosynthesis conversion

54
00:02:15,220 --> 00:02:17,060
efficiency of the
entire system is

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00:02:17,060 --> 00:02:19,550
dictated by the efficiency
of each individual part.

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00:02:19,550 --> 00:02:22,660
Roughly it can be broken down to
this little pie chart up here.

57
00:02:22,660 --> 00:02:24,620
The total system
efficiency in blue

58
00:02:24,620 --> 00:02:28,060
is somewhere, depending
on the plant, somewhere

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00:02:28,060 --> 00:02:31,430
around 1%, maybe as
high as 7% or 8%,

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00:02:31,430 --> 00:02:33,570
depending on very
specialized plants that

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00:02:33,570 --> 00:02:36,700
are experts at converting
sunlight into usable chemical

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00:02:36,700 --> 00:02:37,460
energy.

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00:02:37,460 --> 00:02:40,600
And that, in part, is largely
due to optical losses.

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00:02:40,600 --> 00:02:43,610
If you can see the absorption
spectrum of chlorophyll,

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00:02:43,610 --> 00:02:45,574
of the different types
of chlorophyll here,

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00:02:45,574 --> 00:02:47,740
you'll see large portions
of the solar spectrum that

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00:02:47,740 --> 00:02:49,810
go underutilized.

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00:02:49,810 --> 00:02:53,190
So again, another system
that's similar to a solar cell,

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00:02:53,190 --> 00:02:56,030
that the total
system efficiency is

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00:02:56,030 --> 00:02:59,680
the product of each individual
component going on here.

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00:02:59,680 --> 00:03:00,180
All right.

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00:03:00,180 --> 00:03:02,670
So now what we're going
to do is just quickly

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00:03:02,670 --> 00:03:05,840
revisit the diode in the dark
and construct the energy band

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00:03:05,840 --> 00:03:09,030
diagram for pn-junction
in the dark.

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00:03:09,030 --> 00:03:11,670
Each of you should have
on your desk these sheets.

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00:03:11,670 --> 00:03:13,170
Oh, we don't have
them on the desks.

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00:03:13,170 --> 00:03:15,222
We need to pass those out.

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00:03:15,222 --> 00:03:17,310
We need to pass those out.

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00:03:17,310 --> 00:03:21,040
So we should have
sheets that describe

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00:03:21,040 --> 00:03:23,670
essentially the equivalent
circuit diagram, the IV

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00:03:23,670 --> 00:03:25,340
characteristics,
and the energy band

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00:03:25,340 --> 00:03:27,930
diagram for our
pn-junction in the dark.

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We laboriously filled
this out last class.

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00:03:30,129 --> 00:03:31,670
We're just going to
refresh ourselves

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00:03:31,670 --> 00:03:33,250
to make sure we're
all on the same page

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00:03:33,250 --> 00:03:34,880
and redo it this class
right at the beginning

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because it's that important.

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00:03:36,160 --> 00:03:37,570
Thank you, thank you,
thank you for those

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00:03:37,570 --> 00:03:39,370
who came to our office
hours and for those

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00:03:39,370 --> 00:03:41,970
who came to the
recitations, and we really

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00:03:41,970 --> 00:03:43,850
tried to get this across.

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00:03:43,850 --> 00:03:45,810
For those who are
still struggling,

93
00:03:45,810 --> 00:03:48,710
let's make sure that you get
this sometime between now

94
00:03:48,710 --> 00:03:50,500
and, say, the next
two weeks because this

95
00:03:50,500 --> 00:03:54,090
will feature
prominently on the exam,

96
00:03:54,090 --> 00:03:56,050
and it's pretty important
for understanding

97
00:03:56,050 --> 00:03:57,620
how a solar cell works.

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00:03:57,620 --> 00:04:01,350
So if you would not mind working
directly with your partner,

99
00:04:01,350 --> 00:04:03,940
the person who's sitting
directly next to you.

100
00:04:03,940 --> 00:04:06,287
Let's walk through
the diode in the dark

101
00:04:06,287 --> 00:04:07,870
and construct the
energy band diagrams

102
00:04:07,870 --> 00:04:09,211
for the diode in the dark.

103
00:04:09,211 --> 00:04:11,210
I'll walk you through it
as soon as you've done.

104
00:04:11,210 --> 00:04:13,600
Maybe I'll give you three
minutes to complete that.

105
00:04:13,600 --> 00:04:16,092
And then we'll progress to
the diode under illumination.

106
00:04:16,092 --> 00:04:17,050
Should be a lot of fun.

107
00:04:23,730 --> 00:04:29,800
I see convergence among several
of you, so let's move forward.

108
00:04:29,800 --> 00:04:32,119
Just to review quickly,
the way I typically

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00:04:32,119 --> 00:04:34,660
think about it, if we set up in
the model circuit right here,

110
00:04:34,660 --> 00:04:36,100
we have our pn-junction.

111
00:04:36,100 --> 00:04:37,705
We have our space-charge
region, also

112
00:04:37,705 --> 00:04:39,580
known as the quasi-neutral
region, also known

113
00:04:39,580 --> 00:04:41,730
as the depletion zone.

114
00:04:41,730 --> 00:04:44,080
So we have this
region right here

115
00:04:44,080 --> 00:04:47,710
that represents the
space-charge region.

116
00:04:47,710 --> 00:04:49,202
So this is in the dark.

117
00:04:49,202 --> 00:04:50,660
Now we have the
energy band diagram

118
00:04:50,660 --> 00:04:54,000
shown right here, where this
dashed blue line represents

119
00:04:54,000 --> 00:04:57,390
the chemical potential, also
called the Fermi energy,

120
00:04:57,390 --> 00:05:01,310
throughout the entire device
right here in cross-section.

121
00:05:01,310 --> 00:05:03,900
And just to be very,
very clear, we've

122
00:05:03,900 --> 00:05:05,470
so far described
the solar cell as

123
00:05:05,470 --> 00:05:07,080
like coming in through the top.

124
00:05:07,080 --> 00:05:09,642
And now we've rotated this
structure by 90 degrees

125
00:05:09,642 --> 00:05:10,850
to represent the pn-junction.

126
00:05:10,850 --> 00:05:12,766
That's been a little
confusing for some folks.

127
00:05:12,766 --> 00:05:15,410
So just to be totally clear,
in a device like this one,

128
00:05:15,410 --> 00:05:17,780
if it were subject
to illumination

129
00:05:17,780 --> 00:05:20,020
you would have light coming
in from the side, right,

130
00:05:20,020 --> 00:05:22,790
either from the p side
or from the n side.

131
00:05:22,790 --> 00:05:24,520
So to transfer this
into what we've

132
00:05:24,520 --> 00:05:27,270
seen so far with the solar
cell devices facing up

133
00:05:27,270 --> 00:05:30,010
toward the sun, you'd have
to rotate this by 90 degrees,

134
00:05:30,010 --> 00:05:30,670
right?

135
00:05:30,670 --> 00:05:32,837
Just to make sure we're all
clear with orientations.

136
00:05:32,837 --> 00:05:34,919
[? Because ?] we have the
Fermi energy right here.

137
00:05:34,919 --> 00:05:37,410
The drift and diffusion currents
for electrons-- electron

138
00:05:37,410 --> 00:05:38,940
diffusion, electron
drift-- there

139
00:05:38,940 --> 00:05:42,052
is an abundance of electrons
over here in the n-type side,

140
00:05:42,052 --> 00:05:44,010
and so they want to
diffuse over to the p-type.

141
00:05:44,010 --> 00:05:46,490
That's why the diffusion
current is pointing left.

142
00:05:46,490 --> 00:05:47,990
Once they do to
a certain degree,

143
00:05:47,990 --> 00:05:50,450
they set up a field,
the electrons and holes,

144
00:05:50,450 --> 00:05:52,100
the mobile charges
set up a field,

145
00:05:52,100 --> 00:05:55,377
and that creates a drift current
that counteracts the diffusion.

146
00:05:55,377 --> 00:05:56,960
And once these two
are in equilibrium,

147
00:05:56,960 --> 00:05:58,876
there's no current flowing
through our device.

148
00:05:58,876 --> 00:06:01,244
That's why current is
equal to 0 right here.

149
00:06:01,244 --> 00:06:02,910
And there's also no
potential difference

150
00:06:02,910 --> 00:06:05,870
because the Fermi energy,
the chemical potential,

151
00:06:05,870 --> 00:06:08,027
is the same on either
side of that device,

152
00:06:08,027 --> 00:06:09,860
and so the voltage
output of that solar cell

153
00:06:09,860 --> 00:06:12,650
would also be 0.

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00:06:12,650 --> 00:06:18,164
When we forward bias our device,
now we're forcing a separation,

155
00:06:18,164 --> 00:06:20,455
or we're forcing a separation
of the chemical potential

156
00:06:20,455 --> 00:06:22,770
on either side of the device.

157
00:06:22,770 --> 00:06:26,130
If you connected this
to an external circuit,

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00:06:26,130 --> 00:06:29,470
the electrons would want to flow
from this side to that side.

159
00:06:29,470 --> 00:06:33,320
But since we're forcing this
condition here with a battery,

160
00:06:33,320 --> 00:06:36,360
we are reducing the
barrier height here.

161
00:06:36,360 --> 00:06:38,380
Electrons can now diffuse
over from the n-type

162
00:06:38,380 --> 00:06:40,610
into the p-type
side, and they do.

163
00:06:40,610 --> 00:06:42,650
And the diffusion
current increases.

164
00:06:42,650 --> 00:06:45,680
And that's why we have
current now a positive value.

165
00:06:45,680 --> 00:06:49,440
We've defined the electrons
traveling to the left

166
00:06:49,440 --> 00:06:51,010
as being a positive current.

167
00:06:51,010 --> 00:06:54,510
We have now electrons
traveling from the n-type

168
00:06:54,510 --> 00:06:56,000
to the p-type material.

169
00:06:56,000 --> 00:06:59,114
When we reverse bias our
device, notice the separation

170
00:06:59,114 --> 00:07:00,280
of the quasi-Fermi energies.

171
00:07:00,280 --> 00:07:04,130
Again, we have here
one sign of voltage

172
00:07:04,130 --> 00:07:06,344
because the right side
is higher than the left.

173
00:07:06,344 --> 00:07:08,260
And now the right side
is lower than the left,

174
00:07:08,260 --> 00:07:10,490
so our voltage sign
flips from right

175
00:07:10,490 --> 00:07:13,210
to left over here from
positive to negative values.

176
00:07:13,210 --> 00:07:14,290
So notice the voltage.

177
00:07:14,290 --> 00:07:15,830
And now the current as well.

178
00:07:15,830 --> 00:07:19,220
The drift current will
outweigh the diffusion current

179
00:07:19,220 --> 00:07:23,442
in this particular case because
now the barrier for electrons

180
00:07:23,442 --> 00:07:24,900
to diffuse from
the n to the p-type

181
00:07:24,900 --> 00:07:27,790
is very large they'll have
difficulty going from that side

182
00:07:27,790 --> 00:07:28,820
to that side.

183
00:07:28,820 --> 00:07:31,590
Whereas the drift
current is larger because

184
00:07:31,590 --> 00:07:33,450
of the larger electric field.

185
00:07:33,450 --> 00:07:35,806
And as a result, the drift
current will dominate.

186
00:07:35,806 --> 00:07:37,430
And so now instead
of electrons flowing

187
00:07:37,430 --> 00:07:39,900
from n-type to p-type,
where we had defined

188
00:07:39,900 --> 00:07:42,260
as positive current, electrons
are flowing from p-type

189
00:07:42,260 --> 00:07:45,340
to n-type in that, which we
defined as negative current.

190
00:07:45,340 --> 00:07:47,930
And that's why our
current has changed signs.

191
00:07:47,930 --> 00:07:50,560
Over here, notice that we're
in positive current territory,

192
00:07:50,560 --> 00:07:53,957
and over here, notice we're
in negative current territory.

193
00:07:53,957 --> 00:07:56,290
Also, you'll notice the width
of the space-charge region

194
00:07:56,290 --> 00:07:59,130
changing as we forward and
reverse bias our device.

195
00:07:59,130 --> 00:08:01,530
As the barrier
height decreases, we

196
00:08:01,530 --> 00:08:03,530
have a decrease of the
built-in electric field.

197
00:08:03,530 --> 00:08:05,280
We have a decrease of
the amount of charge

198
00:08:05,280 --> 00:08:06,800
on either side of the junction.

199
00:08:06,800 --> 00:08:09,140
That's why the depletion
width decreases.

200
00:08:09,140 --> 00:08:13,640
And the opposite happens
here under reverse bias.

201
00:08:13,640 --> 00:08:17,690
So getting to the point where
you can set up a pn-junction

202
00:08:17,690 --> 00:08:20,350
and understand how drift
and diffusion currents come

203
00:08:20,350 --> 00:08:21,970
into being in the
first place and then

204
00:08:21,970 --> 00:08:25,700
being able to bias your diode
under different conditions

205
00:08:25,700 --> 00:08:28,240
is a really important
fundamental skill

206
00:08:28,240 --> 00:08:30,280
for understanding how
a solar cell works.

207
00:08:30,280 --> 00:08:30,793
Question.

208
00:08:30,793 --> 00:08:32,542
AUDIENCE: On the forward
and reverse bias,

209
00:08:32,542 --> 00:08:34,434
does the Fermi energy
actually continuous,

210
00:08:34,434 --> 00:08:36,799
or does it actually [INAUDIBLE]?

211
00:08:36,799 --> 00:08:40,965
PROFESSOR: So the Fermi
energy, which we defined here

212
00:08:40,965 --> 00:08:42,482
as the chemical
potential, notice

213
00:08:42,482 --> 00:08:43,940
we're avoiding
talking about what's

214
00:08:43,940 --> 00:08:46,231
happening here in the middle
until a couple of lectures

215
00:08:46,231 --> 00:08:46,910
from now.

216
00:08:46,910 --> 00:08:49,650
That gets into a gray
zone where we talk

217
00:08:49,650 --> 00:08:51,051
about quasi-Fermi energies.

218
00:08:51,051 --> 00:08:53,550
We'll get to that in a minute
or maybe a couple of lectures.

219
00:08:53,550 --> 00:08:57,057
But yes, the Fermi energy in
the extreme sides right here

220
00:08:57,057 --> 00:08:58,473
near the contacts,
so your contact

221
00:08:58,473 --> 00:09:00,806
in your device over here and
your contact in your device

222
00:09:00,806 --> 00:09:02,290
over here, those
Fermi energies are

223
00:09:02,290 --> 00:09:05,370
different on an
absolute energy scale.

224
00:09:05,370 --> 00:09:07,547
So there is an energy
difference when

225
00:09:07,547 --> 00:09:09,880
you're driving the electrons
from one side to the other.

226
00:09:12,780 --> 00:09:14,651
Notice in this case
right here, you

227
00:09:14,651 --> 00:09:16,150
would think that
the electrons would

228
00:09:16,150 --> 00:09:18,120
want to travel through
an external circuit

229
00:09:18,120 --> 00:09:20,411
to come back to this side
because their energy's higher

230
00:09:20,411 --> 00:09:22,240
in this side and
lower over here.

231
00:09:22,240 --> 00:09:25,700
But we're not illuminating
the solar cell yet.

232
00:09:25,700 --> 00:09:27,950
We're biasing it
using a battery.

233
00:09:27,950 --> 00:09:30,515
And this is why we have current
flow coming from this side

234
00:09:30,515 --> 00:09:31,140
into that side.

235
00:09:31,140 --> 00:09:33,870
We're essentially forcing
the electrons from the n-type

236
00:09:33,870 --> 00:09:35,390
into the p-type material.

237
00:09:35,390 --> 00:09:37,490
We're pushing them up
that hill with a battery.

238
00:09:37,490 --> 00:09:41,020
And that's why we have this
diffusion current dominating

239
00:09:41,020 --> 00:09:43,180
in the dark, in the dark.

240
00:09:43,180 --> 00:09:47,160
So we have a current
flowing from right to left.

241
00:09:47,160 --> 00:09:49,150
In the illuminated
case, we'll have

242
00:09:49,150 --> 00:09:52,630
all of our carriers
traveling from left to right.

243
00:09:52,630 --> 00:09:54,330
And in the dark,
this is the only case

244
00:09:54,330 --> 00:09:57,040
in which we have carriers
traveling from right to left.

245
00:09:57,040 --> 00:10:00,050
And it's happening because we're
using that battery in the dark

246
00:10:00,050 --> 00:10:03,300
to change the chemical
potential on either side, which,

247
00:10:03,300 --> 00:10:05,320
in effect, reduces
this barrier height

248
00:10:05,320 --> 00:10:08,940
and allows carriers to diffuse
from the n-type into p-type.

249
00:10:08,940 --> 00:10:11,390
So you can think about
it as forcing carriers

250
00:10:11,390 --> 00:10:13,640
up the junction.

251
00:10:13,640 --> 00:10:15,232
And this is a very
useful technique

252
00:10:15,232 --> 00:10:17,440
because, in effect, what
it's doing in a real device,

253
00:10:17,440 --> 00:10:19,148
when we you have a
two-dimensional device

254
00:10:19,148 --> 00:10:21,020
within homogeneities,
the current

255
00:10:21,020 --> 00:10:24,150
will travel through the weakest
point of that pn-junction.

256
00:10:24,150 --> 00:10:26,230
Wherever the barrier
height is lowest, current

257
00:10:26,230 --> 00:10:28,260
will begin crowding
through that spot.

258
00:10:28,260 --> 00:10:30,800
And so it's a way of
probing or testing

259
00:10:30,800 --> 00:10:35,311
the quality of your junction
characteristic in the dark.

260
00:10:35,311 --> 00:10:35,810
OK.

261
00:10:35,810 --> 00:10:40,870
So this is the basics of
pn-junction in the dark.

262
00:10:40,870 --> 00:10:43,350
Let's flip our page
over and now let's

263
00:10:43,350 --> 00:10:47,550
try to imagine what will happen
under illuminated conditions,

264
00:10:47,550 --> 00:10:50,270
and let's start out
in a very simple case.

265
00:10:50,270 --> 00:10:52,830
We'll assume that the
principle of superposition

266
00:10:52,830 --> 00:10:55,815
applies here, that the
photo-excited carriers--

267
00:10:55,815 --> 00:10:57,940
in other words, when light
shines into our device--

268
00:10:57,940 --> 00:11:00,420
I'm looking at this one right
now or this one right here--

269
00:11:00,420 --> 00:11:03,830
and light's coming in and
generating electron-hole pairs,

270
00:11:03,830 --> 00:11:06,180
essentially exciting
electrons across the band gap

271
00:11:06,180 --> 00:11:09,810
like we described in lecture 3,
so we have carriers now being

272
00:11:09,810 --> 00:11:11,520
excited across
the band gap, what

273
00:11:11,520 --> 00:11:13,060
will happen to
those electrons now

274
00:11:13,060 --> 00:11:14,559
that they're in the
conduction band?

275
00:11:14,559 --> 00:11:16,362
Where will they want to go?

276
00:11:16,362 --> 00:11:17,320
AUDIENCE: To the right.

277
00:11:17,320 --> 00:11:18,450
PROFESSOR: To the right, right?

278
00:11:18,450 --> 00:11:18,950
OK.

279
00:11:18,950 --> 00:11:21,089
So what you'll do
is set up what's

280
00:11:21,089 --> 00:11:22,380
called an illumination current.

281
00:11:22,380 --> 00:11:26,250
Notice now at the bottom
of the second row here,

282
00:11:26,250 --> 00:11:29,020
you have electron diffusion,
electron drift, and IL current.

283
00:11:29,020 --> 00:11:30,992
IL stands for
illumination current.

284
00:11:30,992 --> 00:11:32,450
So you have a third
arrow here that

285
00:11:32,450 --> 00:11:35,390
will have to be
implemented in some way.

286
00:11:35,390 --> 00:11:38,720
And that will-- by the
principle of superposition

287
00:11:38,720 --> 00:11:41,145
you should think what happens
to your IV curve as well.

288
00:11:41,145 --> 00:11:43,520
So let's make an estimate of
what we think should happen,

289
00:11:43,520 --> 00:11:45,228
and then I'll confer
some notes, and then

290
00:11:45,228 --> 00:11:48,334
we'll measure what actually
does happen under illumination.

291
00:11:48,334 --> 00:11:49,500
Why don't we give it a shot?

292
00:11:54,980 --> 00:11:56,550
What does forward
and reverse bias

293
00:11:56,550 --> 00:11:58,690
mean when there's no battery?

294
00:11:58,690 --> 00:12:00,360
This is a very
interesting question.

295
00:12:00,360 --> 00:12:03,390
So once you start illuminating
your solar cell device

296
00:12:03,390 --> 00:12:08,900
and you start injecting carriers
into it, what will happen is,

297
00:12:08,900 --> 00:12:11,429
very naturally,
this band alignment

298
00:12:11,429 --> 00:12:13,220
that you see right
here, this band diagram,

299
00:12:13,220 --> 00:12:16,820
will begin to shift toward
the forward bias condition.

300
00:12:16,820 --> 00:12:17,530
Rationale?

301
00:12:17,530 --> 00:12:18,780
You'll be generating carriers.

302
00:12:18,780 --> 00:12:20,570
They'll be swept over
into this region here.

303
00:12:20,570 --> 00:12:21,860
One way to think
about is that you'll

304
00:12:21,860 --> 00:12:23,969
be increasing the number
of electrons over here

305
00:12:23,969 --> 00:12:26,260
and the number of holes over
here, which will naturally

306
00:12:26,260 --> 00:12:28,430
cause the energy
of those electrons

307
00:12:28,430 --> 00:12:30,430
to increase on this side,
the chemical potential

308
00:12:30,430 --> 00:12:31,910
on this side, to increase.

309
00:12:31,910 --> 00:12:33,660
So one way to think
about it is, as you're

310
00:12:33,660 --> 00:12:36,580
illuminating your solar
cell more and more and more,

311
00:12:36,580 --> 00:12:40,280
you're forcing a forward bias
condition on your device.

312
00:12:40,280 --> 00:12:42,430
To get the solar cell
to go into reverse bias,

313
00:12:42,430 --> 00:12:44,390
you really do need
to bias your device.

314
00:12:44,390 --> 00:12:45,710
You physically need to bias it.

315
00:12:53,590 --> 00:12:54,090
Yeah.

316
00:12:54,090 --> 00:12:56,324
So when I mentioned
illumination current here,

317
00:12:56,324 --> 00:12:58,490
we're really talking about
the electron illumination

318
00:12:58,490 --> 00:13:01,100
current, right, what
direction of travel

319
00:13:01,100 --> 00:13:03,270
the electrons are taking
inside of our system.

320
00:13:03,270 --> 00:13:06,930
So yes, the electrons would be
traveling from left to right.

321
00:13:06,930 --> 00:13:09,500
Very astute observation.

322
00:13:09,500 --> 00:13:12,210
Current is generally described
as a flow of positive charge.

323
00:13:12,210 --> 00:13:18,200
And in the absence of a definer
or, say, electrons or holes,

324
00:13:18,200 --> 00:13:19,952
you rightly could
assume that it would be

325
00:13:19,952 --> 00:13:21,160
the flow of positive charges.

326
00:13:21,160 --> 00:13:22,766
We're assuming electrons
are flowing here

327
00:13:22,766 --> 00:13:23,974
in the illumination. current.

328
00:13:27,360 --> 00:13:28,420
Good.

329
00:13:28,420 --> 00:13:28,920
All right.

330
00:13:28,920 --> 00:13:31,170
So This is very positive.

331
00:13:31,170 --> 00:13:35,410
I see everybody has
settled on the notion

332
00:13:35,410 --> 00:13:38,990
that illumination will
shift our IV curve down.

333
00:13:38,990 --> 00:13:41,660
Because of the way
we've defined current,

334
00:13:41,660 --> 00:13:45,450
that if current flows from
left to right that lands us

335
00:13:45,450 --> 00:13:47,260
in negative current territory.

336
00:13:47,260 --> 00:13:48,520
So that makes sense.

337
00:13:48,520 --> 00:13:50,850
If we shine light
on our system, we

338
00:13:50,850 --> 00:13:53,365
have electrons flowing
from left to right here.

339
00:13:53,365 --> 00:13:54,990
That'll put us into
negative territory.

340
00:13:54,990 --> 00:13:56,820
So that shifts the
entire thing down.

341
00:13:56,820 --> 00:14:00,160
And we would add illumination
current, an arrow pointing

342
00:14:00,160 --> 00:14:02,010
to the right right
here, which would

343
00:14:02,010 --> 00:14:05,410
mean that we would have current
flowing through our device,

344
00:14:05,410 --> 00:14:08,615
but there's still no difference
in the chemical potential

345
00:14:08,615 --> 00:14:09,310
on either side.

346
00:14:09,310 --> 00:14:11,060
There's still a
difference in Fermi energy

347
00:14:11,060 --> 00:14:12,518
in the p-type and
the n-type, which

348
00:14:12,518 --> 00:14:16,670
means our voltage is equal to 0,
which means we're intersecting

349
00:14:16,670 --> 00:14:18,840
the y-axis right
here, and our little x

350
00:14:18,840 --> 00:14:20,870
should be marked
right down here.

351
00:14:20,870 --> 00:14:23,350
So it's really just
a superposition.

352
00:14:23,350 --> 00:14:24,210
Great.

353
00:14:24,210 --> 00:14:24,800
OK.

354
00:14:24,800 --> 00:14:31,610
Now what happens if we
forward bias our device either

355
00:14:31,610 --> 00:14:36,214
because we're adding a resistor
in series to our solar cell?

356
00:14:36,214 --> 00:14:37,630
So instead of a
battery there, you

357
00:14:37,630 --> 00:14:40,300
would replace that
with a resistor.

358
00:14:40,300 --> 00:14:43,280
Or if we're applying a
bias voltage as well,

359
00:14:43,280 --> 00:14:45,255
we could also do that
under illumination.

360
00:14:45,255 --> 00:14:47,380
So we'd still have the
illumination current, right?

361
00:14:47,380 --> 00:14:50,590
And we, through superposition,
shift this entire curve down,

362
00:14:50,590 --> 00:14:54,200
we'd be operating somewhere
in this quadrant right there,

363
00:14:54,200 --> 00:14:55,090
right?

364
00:14:55,090 --> 00:14:58,990
So this we call IV quadrant,
typically I, II, III, IV, IV

365
00:14:58,990 --> 00:14:59,790
quadrant.

366
00:14:59,790 --> 00:15:02,720
This is where power is coming
out of the solar cell device.

367
00:15:02,720 --> 00:15:05,053
Because if we imagine instead
of having a battery there,

368
00:15:05,053 --> 00:15:06,960
we have a resistor,
the electrons

369
00:15:06,960 --> 00:15:08,850
will travel from
the n-type material

370
00:15:08,850 --> 00:15:11,816
through that external load to
get work the p-type material

371
00:15:11,816 --> 00:15:13,690
where the chemical
potential is lower, right,

372
00:15:13,690 --> 00:15:17,010
because they'll desire to
minimize their free energy.

373
00:15:17,010 --> 00:15:19,550
And as a result, they'll
deposit that power

374
00:15:19,550 --> 00:15:22,215
across that resistor,
across that external load,

375
00:15:22,215 --> 00:15:23,840
in order to get back
to this other side

376
00:15:23,840 --> 00:15:26,821
because that's the only path
that they can travel easily,

377
00:15:26,821 --> 00:15:27,320
right?

378
00:15:27,320 --> 00:15:29,170
And so this entire
curve shifts down.

379
00:15:29,170 --> 00:15:32,030
You have your red x somewhere
in the quadrant over here.

380
00:15:32,030 --> 00:15:35,840
And power is flowing
out of the solar cell

381
00:15:35,840 --> 00:15:37,590
across that external load.

382
00:15:37,590 --> 00:15:39,500
So in the next slide,
pretty much everything

383
00:15:39,500 --> 00:15:41,754
is right, except
that, mea culpa,

384
00:15:41,754 --> 00:15:43,420
I forgot to replace
the battery up there

385
00:15:43,420 --> 00:15:44,420
with a little resistor.

386
00:15:44,420 --> 00:15:46,170
So you'll want to correct
that in your notes.

387
00:15:46,170 --> 00:15:48,190
Instead of having the
little batteries up there,

388
00:15:48,190 --> 00:15:50,800
you can replace
those with resistors

389
00:15:50,800 --> 00:15:55,360
or a resistor in series with
a battery, if you prefer.

390
00:15:55,360 --> 00:15:57,840
Since depending on the
illumination condition,

391
00:15:57,840 --> 00:16:00,290
the intensity we may have
natural for a bias condition,

392
00:16:00,290 --> 00:16:02,101
we may need to apply
a bias voltage.

393
00:16:02,101 --> 00:16:02,600
OK.

394
00:16:02,600 --> 00:16:05,200
So we have our IV
characteristic like this.

395
00:16:05,200 --> 00:16:07,750
We have our red x under
forward bias conditions

396
00:16:07,750 --> 00:16:10,310
in the IV quadrant,
denoting that power

397
00:16:10,310 --> 00:16:12,690
would be flowing out of
this solar cell device

398
00:16:12,690 --> 00:16:14,480
under these conditions.

399
00:16:14,480 --> 00:16:17,420
And now the bias is inverted.

400
00:16:17,420 --> 00:16:19,230
We have reverse bias conditions.

401
00:16:19,230 --> 00:16:22,760
And notice that the current
still has the same sign.

402
00:16:22,760 --> 00:16:25,440
So the current is negative
here, negative here,

403
00:16:25,440 --> 00:16:26,300
and negative here.

404
00:16:26,300 --> 00:16:30,070
So the net current is always
flowing in the same direction

405
00:16:30,070 --> 00:16:33,190
in all cases because we have
this illumination current,

406
00:16:33,190 --> 00:16:35,290
because we have this
generation of carriers

407
00:16:35,290 --> 00:16:36,860
inside of the material.

408
00:16:36,860 --> 00:16:37,990
That's pretty cool.

409
00:16:37,990 --> 00:16:41,250
That wasn't the case when we
had the device in the dark.

410
00:16:41,250 --> 00:16:43,740
Here, in the forward
bias conditions,

411
00:16:43,740 --> 00:16:46,690
we're actually forcing carriers
from the n-type material

412
00:16:46,690 --> 00:16:48,930
into the p-type material.

413
00:16:48,930 --> 00:16:51,060
But under illumination,
now we have

414
00:16:51,060 --> 00:16:53,650
all of our carriers
traveling from the p-type

415
00:16:53,650 --> 00:16:55,100
into the n-type.

416
00:16:55,100 --> 00:16:59,270
What's varying is the potential
that the carriers have

417
00:16:59,270 --> 00:17:01,140
and, of course, the
total amount of current.

418
00:17:01,140 --> 00:17:03,940
As you forward bias
more and more and more,

419
00:17:03,940 --> 00:17:08,170
this downhill slope
here decreases, right?

420
00:17:08,170 --> 00:17:11,200
So there's less of a driving
force for the carriers

421
00:17:11,200 --> 00:17:13,410
to be going from the
p-type to the n-type,

422
00:17:13,410 --> 00:17:16,400
and that's why the
current approaches 0.

423
00:17:16,400 --> 00:17:18,859
Eventually at some point, if
you keep forward biasing here,

424
00:17:18,859 --> 00:17:20,500
the current will be 0.

425
00:17:20,500 --> 00:17:22,740
There will be no
net current flow

426
00:17:22,740 --> 00:17:25,357
because there will be no
driving force for the carriers

427
00:17:25,357 --> 00:17:26,940
to go from the p-type
into the n-type.

428
00:17:26,940 --> 00:17:31,110
There will be no
more built-in field.

429
00:17:31,110 --> 00:17:31,870
Kind of cool.

430
00:17:31,870 --> 00:17:32,570
OK.

431
00:17:32,570 --> 00:17:35,950
So now we're beginning to
wrap our heads around what's

432
00:17:35,950 --> 00:17:37,450
happening to the
electrons and holes

433
00:17:37,450 --> 00:17:40,530
during solar cell operation.

434
00:17:40,530 --> 00:17:43,490
Let me put a little bit
of mathematics to this.

435
00:17:43,490 --> 00:17:45,220
These are your IV curves.

436
00:17:45,220 --> 00:17:48,730
The blue is in the dark, and
the red is under illumination.

437
00:17:48,730 --> 00:17:50,915
And we're focused
on this IV quadrant

438
00:17:50,915 --> 00:17:53,165
right here because this is
the quadrant in which power

439
00:17:53,165 --> 00:17:55,070
is coming out of our
solar cell device,

440
00:17:55,070 --> 00:17:56,880
which usable power
is coming out that we

441
00:17:56,880 --> 00:17:58,160
can power an external load.

442
00:17:58,160 --> 00:17:59,360
Why?

443
00:17:59,360 --> 00:18:02,520
Well, first off,
the voltage is such

444
00:18:02,520 --> 00:18:03,979
that we can power
an external load.

445
00:18:03,979 --> 00:18:05,061
We have charge separation.

446
00:18:05,061 --> 00:18:06,790
The electrons are
accumulated over here.

447
00:18:06,790 --> 00:18:08,456
And they have higher
potential than they

448
00:18:08,456 --> 00:18:10,490
do on the other side,
which means that there's

449
00:18:10,490 --> 00:18:12,865
an incentive for them to go
through the external circuit,

450
00:18:12,865 --> 00:18:15,780
deposit the power across
that external load

451
00:18:15,780 --> 00:18:18,670
to get back to this other side
where their potential is lower,

452
00:18:18,670 --> 00:18:19,170
right?

453
00:18:19,170 --> 00:18:20,560
So the voltage is favorable.

454
00:18:20,560 --> 00:18:22,000
And the current
is also favorable

455
00:18:22,000 --> 00:18:23,670
because now we have
light coming in.

456
00:18:23,670 --> 00:18:27,732
And this generation current is
driving the carriers-- well,

457
00:18:27,732 --> 00:18:29,690
or is creating carriers
here in the p-type that

458
00:18:29,690 --> 00:18:31,523
can then be driven
toward the n-type because

459
00:18:31,523 --> 00:18:33,260
of the built-in field.

460
00:18:33,260 --> 00:18:36,480
So the conditions are just right
under illuminated forward bias

461
00:18:36,480 --> 00:18:40,310
conditions to drive power
through our external load.

462
00:18:40,310 --> 00:18:42,910
Under all other conditions of
operations of the solar cell,

463
00:18:42,910 --> 00:18:45,970
we're putting power into the
device, not getting power out

464
00:18:45,970 --> 00:18:46,990
of it.

465
00:18:46,990 --> 00:18:49,700
This IV quadrant over
here, this forward bias

466
00:18:49,700 --> 00:18:52,670
illuminated case is the only
case in which power is coming,

467
00:18:52,670 --> 00:18:57,190
usable power is coming out of
our solar cell that we can use.

468
00:18:57,190 --> 00:19:00,440
So that's why we focus on
this IV quadrant right here.

469
00:19:00,440 --> 00:19:04,340
The illuminated IV curve
is, to the first order,

470
00:19:04,340 --> 00:19:07,860
is just your dark IV curve
with a superposition, which

471
00:19:07,860 --> 00:19:11,380
we call the illumination
current, I sub L.

472
00:19:11,380 --> 00:19:14,980
And that's what shifts our
entire curve down by this I sub

473
00:19:14,980 --> 00:19:19,380
L right here, so this I sub L,
that one right there or that

474
00:19:19,380 --> 00:19:22,220
right there.

475
00:19:22,220 --> 00:19:23,730
Kind of cool.

476
00:19:23,730 --> 00:19:24,870
All right.

477
00:19:24,870 --> 00:19:28,450
What do we think will happen if
our light intensity goes down

478
00:19:28,450 --> 00:19:29,410
by a factor of 2?

479
00:19:31,970 --> 00:19:34,870
So now if the amount of sunlight
falling on our solar cell

480
00:19:34,870 --> 00:19:37,860
drops by 1/2, what will happen?

481
00:19:37,860 --> 00:19:40,526
What do we predict will happen
based on this right here?

482
00:19:40,526 --> 00:19:41,810
AUDIENCE: [INAUDIBLE].

483
00:19:41,810 --> 00:19:45,010
PROFESSOR: The curve will shift,
the red curve will shift up

484
00:19:45,010 --> 00:19:47,660
by about 1/2, right, because
the illumination current is now

485
00:19:47,660 --> 00:19:49,610
cut in half.

486
00:19:49,610 --> 00:19:54,000
What will happen to the
voltage intersect right here?

487
00:19:54,000 --> 00:19:57,480
What is the relation
between voltage and current?

488
00:19:57,480 --> 00:19:59,260
It's the logarithmic
relation, right?

489
00:19:59,260 --> 00:20:03,590
So it won't necessarily
be cut in half, right?

490
00:20:03,590 --> 00:20:08,450
But it'll be cut by whatever
this would be here, a log of 2.

491
00:20:08,450 --> 00:20:10,230
So OK.

492
00:20:10,230 --> 00:20:14,340
So we're beginning to develop
an intuitive understanding

493
00:20:14,340 --> 00:20:15,950
of where electrons
are flowing inside

494
00:20:15,950 --> 00:20:19,420
of our solar cells in the
dark and under illumination.

495
00:20:19,420 --> 00:20:20,950
In the dark is
important because we

496
00:20:20,950 --> 00:20:22,740
can test our
devices in the dark,

497
00:20:22,740 --> 00:20:25,200
and we can still learn a lot
about our solar cell device

498
00:20:25,200 --> 00:20:27,070
characteristics in the dark.

499
00:20:27,070 --> 00:20:31,000
As well, we can, under forward
bias conditions in the dark,

500
00:20:31,000 --> 00:20:34,460
we can force carriers from
one side of the junction

501
00:20:34,460 --> 00:20:37,416
to the other the wrong way
and probe for weaknesses

502
00:20:37,416 --> 00:20:38,540
in the pn-junction regions.

503
00:20:38,540 --> 00:20:40,660
That's helpful.

504
00:20:40,660 --> 00:20:42,480
And in the
illumination condition,

505
00:20:42,480 --> 00:20:44,820
obviously we're testing the
total amount of power that's

506
00:20:44,820 --> 00:20:46,570
coming out of our device.

507
00:20:46,570 --> 00:20:48,354
So again, this is very
useful because It's

508
00:20:48,354 --> 00:20:49,770
off of this red
curve here that we

509
00:20:49,770 --> 00:20:53,222
defined the efficiency or the
performance of the solar cell.

510
00:20:53,222 --> 00:20:55,170
So what I'll ask
folks to do now is

511
00:20:55,170 --> 00:21:00,860
to-- we'll begin passing
around these little tools.

512
00:21:00,860 --> 00:21:02,440
And I'll ask David
Berney Needleman

513
00:21:02,440 --> 00:21:03,630
to come up to the front.

514
00:21:03,630 --> 00:21:05,230
David is our lab guru.

515
00:21:05,230 --> 00:21:07,180
He's the one who
helped build these,

516
00:21:07,180 --> 00:21:09,650
really was the driving force
behind getting them built.

517
00:21:09,650 --> 00:21:11,777
These are IV testers
that will allow

518
00:21:11,777 --> 00:21:13,860
you to measure the current
voltage characteristics

519
00:21:13,860 --> 00:21:16,600
of solar cells
right here in class.

520
00:21:16,600 --> 00:21:18,937
And he's going to--
well, we'll pass them out

521
00:21:18,937 --> 00:21:20,520
while maybe he comes
to the front here

522
00:21:20,520 --> 00:21:21,645
and explains how they work.

523
00:21:27,650 --> 00:21:31,000
So now that we have the
basic IV curves rolling in,

524
00:21:31,000 --> 00:21:34,050
what I'd like you to
do is modify the height

525
00:21:34,050 --> 00:21:35,330
or the intensity of the light.

526
00:21:35,330 --> 00:21:37,496
And the easiest way to
modify the intensity of light

527
00:21:37,496 --> 00:21:40,600
is to move the light
position up and down.

528
00:21:40,600 --> 00:21:43,120
So modify the
intensity of the light

529
00:21:43,120 --> 00:21:45,730
and see how this
IV curve changes.

530
00:21:45,730 --> 00:21:49,650
Note the y-axis scale,
which might change as well.

531
00:21:49,650 --> 00:21:52,110
It might rescale depending
on the condition.

532
00:21:52,110 --> 00:21:53,730
But note the y-axis
scale and see

533
00:21:53,730 --> 00:21:59,000
how the intercept of
the y-axis is changing

534
00:21:59,000 --> 00:22:00,682
with illumination intensity.

535
00:22:00,682 --> 00:22:01,390
Give that a shot.

536
00:22:08,640 --> 00:22:11,380
All right, folks.

537
00:22:11,380 --> 00:22:13,680
Why don't we circle
back real quick.

538
00:22:13,680 --> 00:22:15,180
This has been a good experiment.

539
00:22:15,180 --> 00:22:19,230
I am very much in favor of
multitasking and browsing.

540
00:22:19,230 --> 00:22:21,459
So if you want to keep your
experiment running over

541
00:22:21,459 --> 00:22:23,250
the course of the
remainder of the lecture,

542
00:22:23,250 --> 00:22:24,791
I will certainly
have nothing opposed

543
00:22:24,791 --> 00:22:27,101
to testing a few different
illumination conditions.

544
00:22:27,101 --> 00:22:29,100
And if there's anything
really, really important

545
00:22:29,100 --> 00:22:31,558
I'm going to emphasize, this
is a really important wake-up,

546
00:22:31,558 --> 00:22:32,740
folks.

547
00:22:32,740 --> 00:22:34,870
The I sub L, just to
really recap here,

548
00:22:34,870 --> 00:22:36,560
we have this ideal
diode equation,

549
00:22:36,560 --> 00:22:39,450
the illumination current coming
in from our light source.

550
00:22:39,450 --> 00:22:41,850
And in our little set-up,
how many batteries

551
00:22:41,850 --> 00:22:42,995
did you see there?

552
00:22:42,995 --> 00:22:43,892
AUDIENCE: One.

553
00:22:43,892 --> 00:22:44,850
PROFESSOR: Look closer.

554
00:22:44,850 --> 00:22:47,239
How many batteries do you
see total in our set-up?

555
00:22:47,239 --> 00:22:48,780
Look especially at
that light source.

556
00:22:48,780 --> 00:22:49,571
Two of them, right?

557
00:22:49,571 --> 00:22:51,930
There's a 9-volt and
a 1.5-volt. All right.

558
00:22:51,930 --> 00:22:54,290
So one of them is
powering the light source.

559
00:22:54,290 --> 00:22:58,860
And we have, as well, bias to
the solar cell device, right?

560
00:22:58,860 --> 00:23:02,380
So we have a bit of a
combination of the last two

561
00:23:02,380 --> 00:23:03,060
slides, right?

562
00:23:03,060 --> 00:23:06,830
In this case, in the dark, we
were biasing our solar cell

563
00:23:06,830 --> 00:23:07,920
using the battery.

564
00:23:07,920 --> 00:23:10,220
And in the illumination
conditions, the light

565
00:23:10,220 --> 00:23:12,860
itself was causing the solar
cell to become forward biased.

566
00:23:12,860 --> 00:23:16,629
But we can add a battery
to sweep the bias

567
00:23:16,629 --> 00:23:17,920
condition of the device, right?

568
00:23:17,920 --> 00:23:20,530
So even though we have a natural
biasing of the solar cell

569
00:23:20,530 --> 00:23:23,080
by the light, we can
force the solar cell

570
00:23:23,080 --> 00:23:25,462
under different operating
conditions with the battery.

571
00:23:25,462 --> 00:23:27,670
And so that's effectively
what's happening right here

572
00:23:27,670 --> 00:23:31,175
is you have a combination
of both simple scenarios

573
00:23:31,175 --> 00:23:33,720
that we just looked
at, and we're

574
00:23:33,720 --> 00:23:36,400
building on those components
to really understand

575
00:23:36,400 --> 00:23:38,520
the larger system.

576
00:23:38,520 --> 00:23:41,550
Why might that be important,
or why might that be realistic?

577
00:23:41,550 --> 00:23:44,450
Well, the light
itself is biasing

578
00:23:44,450 --> 00:23:46,180
that particular
solar cell device.

579
00:23:46,180 --> 00:23:47,940
But that solar cell
might be connected

580
00:23:47,940 --> 00:23:51,755
in series with a bunch of other
solar cells in a module, right?

581
00:23:51,755 --> 00:23:53,130
And those other
solar cells might

582
00:23:53,130 --> 00:23:55,370
be biasing that one solar cell.

583
00:23:55,370 --> 00:23:59,530
So that's why we have to think
about the solar cell device

584
00:23:59,530 --> 00:24:02,700
both from the perspective
of what bias condition is it

585
00:24:02,700 --> 00:24:05,220
under, what illumination
is it under,

586
00:24:05,220 --> 00:24:06,970
and of course, what's
happening around it.

587
00:24:06,970 --> 00:24:08,990
Is it just powering
an external load?

588
00:24:08,990 --> 00:24:10,970
Is there a battery
connected in series to it?

589
00:24:10,970 --> 00:24:13,550
Are there other solar cells
connected in series with it?

590
00:24:13,550 --> 00:24:14,270
OK.

591
00:24:14,270 --> 00:24:14,780
Yes, Ashley?

592
00:24:14,780 --> 00:24:19,920
AUDIENCE: So I don't understand
still why having a load

593
00:24:19,920 --> 00:24:23,730
would bias the device.

594
00:24:23,730 --> 00:24:26,450
PROFESSOR: So let's imagine
under illumination conditions

595
00:24:26,450 --> 00:24:28,280
right here, what I'm
going to do very,

596
00:24:28,280 --> 00:24:33,700
very quickly is replace this
battery manually in my slides,

597
00:24:33,700 --> 00:24:37,460
if PowerPoint auto save will
allow me, with a resistor.

598
00:24:37,460 --> 00:24:41,680
So if you'll excuse my
quick introduction here

599
00:24:41,680 --> 00:24:43,550
of the resistor.

600
00:24:43,550 --> 00:24:48,380
Now, sorry about the
little artistic license.

601
00:24:48,380 --> 00:24:48,880
OK.

602
00:24:48,880 --> 00:24:50,400
So now I have my resistor here.

603
00:24:50,400 --> 00:24:53,780
And my illumination is
coming into the device

604
00:24:53,780 --> 00:24:56,880
from-- say one of the sides is
generating electron-hole pairs.

605
00:24:56,880 --> 00:24:59,260
I have a multiplicity of
electrons that have now

606
00:24:59,260 --> 00:25:01,282
gone down the hill, right?

607
00:25:01,282 --> 00:25:03,490
It's more energetically
favorable for these electrons

608
00:25:03,490 --> 00:25:04,630
to be on the other side.

609
00:25:04,630 --> 00:25:05,588
And what has that done?

610
00:25:05,588 --> 00:25:07,610
It's raised the chemical
potential of this side.

611
00:25:07,610 --> 00:25:10,616
It's difficult for them
to get back the other way.

612
00:25:10,616 --> 00:25:11,990
It's not impossible,
but it could

613
00:25:11,990 --> 00:25:14,620
be more easy for them to flow
through an external circuit

614
00:25:14,620 --> 00:25:16,032
to get back to the other side.

615
00:25:16,032 --> 00:25:17,990
And as they flow through
that external circuit,

616
00:25:17,990 --> 00:25:20,620
they're depositing their energy
across that external circuit.

617
00:25:20,620 --> 00:25:21,670
What energy?

618
00:25:21,670 --> 00:25:24,100
Well, it's the
potential difference

619
00:25:24,100 --> 00:25:27,460
from this side to that side.

620
00:25:27,460 --> 00:25:30,470
So that's why the solar
cell can be thought of, as

621
00:25:30,470 --> 00:25:32,650
in forward bias conditions,
under illumination

622
00:25:32,650 --> 00:25:34,500
with an external
load attached to it.

623
00:25:34,500 --> 00:25:38,110
Of course, the load has to
be well-matched to the output

624
00:25:38,110 --> 00:25:39,176
of the solar cell device.

625
00:25:39,176 --> 00:25:41,675
AUDIENCE: And is the biasing
because there is a voltage drop

626
00:25:41,675 --> 00:25:42,805
across the resistor?

627
00:25:42,805 --> 00:25:43,430
PROFESSOR: Yes.

628
00:25:43,430 --> 00:25:45,550
The biasing is because
you have a shift

629
00:25:45,550 --> 00:25:48,970
in the chemical potential of
this side up relative to-- you

630
00:25:48,970 --> 00:25:51,797
have a shift of the n-type side
higher than the p-type side.

631
00:25:51,797 --> 00:25:52,380
That's a bias.

632
00:25:52,380 --> 00:25:55,170
Anytime you have a difference
in the chemical potential

633
00:25:55,170 --> 00:25:57,930
in one terminal versus the other
terminal of your solar cell,

634
00:25:57,930 --> 00:25:58,774
you have a bias.

635
00:25:58,774 --> 00:26:00,190
Whether that's
generated by light,

636
00:26:00,190 --> 00:26:02,260
whether it's generated
by a battery, right,

637
00:26:02,260 --> 00:26:05,030
whether it's the energy input
to create that bias is coming

638
00:26:05,030 --> 00:26:08,050
from the sun or if it's coming
from an external battery,

639
00:26:08,050 --> 00:26:09,410
that's a matter of detail.

640
00:26:09,410 --> 00:26:11,665
AUDIENCE: So is the sun
forward biasing the cell?

641
00:26:11,665 --> 00:26:12,290
PROFESSOR: Yes.

642
00:26:12,290 --> 00:26:13,664
One can think about this as--

643
00:26:13,664 --> 00:26:16,039
AUDIENCE: I thought you were
talking about the difference

644
00:26:16,039 --> 00:26:17,460
between light and the LE-- OK.

645
00:26:17,460 --> 00:26:17,540
PROFESSOR: Oh.

646
00:26:17,540 --> 00:26:20,000
So the LED, in this case, could
forward bias your device, too.

647
00:26:20,000 --> 00:26:21,083
I mean, it's just photons.

648
00:26:21,083 --> 00:26:22,870
Photons are forward
biasing the device.

649
00:26:22,870 --> 00:26:25,127
AUDIENCE: So then can
some ever reverse bias?

650
00:26:25,127 --> 00:26:25,710
PROFESSOR: No.

651
00:26:25,710 --> 00:26:28,320
That would be very
difficult. What you could do,

652
00:26:28,320 --> 00:26:30,320
though, is have a bunch
of solar cells connected

653
00:26:30,320 --> 00:26:32,210
in series with this
one, right, that

654
00:26:32,210 --> 00:26:33,449
are producing forward power.

655
00:26:33,449 --> 00:26:35,240
You could shade this
device, and then power

656
00:26:35,240 --> 00:26:37,190
could be flowing backward
through it, right?

657
00:26:37,190 --> 00:26:39,150
In other words, it could
be in the dark right

658
00:26:39,150 --> 00:26:42,007
here, in a dark condition.

659
00:26:42,007 --> 00:26:43,840
And you could be in a
reverse bias condition

660
00:26:43,840 --> 00:26:47,005
just because of the way the
other solar cells around it

661
00:26:47,005 --> 00:26:49,533
are behaving, if you have a
shaded solar cell, for example,

662
00:26:49,533 --> 00:26:50,105
in a module.

663
00:26:50,105 --> 00:26:52,540
So imagine a seagull lands
and kind of covers up

664
00:26:52,540 --> 00:26:54,280
one of the cells.

665
00:26:54,280 --> 00:26:58,460
That will be under reverse bias,
and that could present problems

666
00:26:58,460 --> 00:27:02,580
if the solar cell can't
withstand the reverse bias.

667
00:27:02,580 --> 00:27:04,240
No, this is a very
ideal condition.

668
00:27:04,240 --> 00:27:06,859
What happens in the real world
is that at some reverse bias

669
00:27:06,859 --> 00:27:08,400
condition, you'll
just have biased it

670
00:27:08,400 --> 00:27:10,390
so much that electrons will
be able to tunnel through

671
00:27:10,390 --> 00:27:12,390
from the p-type into
the n-type right here.

672
00:27:12,390 --> 00:27:14,796
The electrons in the valence
band will be able to tunnel

673
00:27:14,796 --> 00:27:16,170
through into the
conduction band.

674
00:27:16,170 --> 00:27:18,710
And what happens to this
IV curve is it goes zoom,

675
00:27:18,710 --> 00:27:19,960
begins dropping.

676
00:27:19,960 --> 00:27:24,280
So if the solar
cell reverse bias--

677
00:27:24,280 --> 00:27:27,190
let's see, the
reverse bias current,

678
00:27:27,190 --> 00:27:30,262
or the current at reverse bias
voltage, is not low enough,

679
00:27:30,262 --> 00:27:31,970
in other words, if
the pn-junction is not

680
00:27:31,970 --> 00:27:34,630
strong enough, you could
have a catastrophic failure

681
00:27:34,630 --> 00:27:37,487
of your module by just
shading one of your cells.

682
00:27:37,487 --> 00:27:39,320
Thankfully, this is one
of the testings that

683
00:27:39,320 --> 00:27:41,800
are done with the
solar simulator

684
00:27:41,800 --> 00:27:43,250
to prevent that failure mode.

685
00:27:43,250 --> 00:27:43,990
AUDIENCE: OK.

686
00:27:43,990 --> 00:27:44,864
PROFESSOR: All right.

687
00:27:44,864 --> 00:27:47,091
I'll entertain deeper
dives with questions.

688
00:27:47,091 --> 00:27:48,590
I'll try to keep
the lecture focused

689
00:27:48,590 --> 00:27:50,220
on the broader general topics.

690
00:27:50,220 --> 00:27:53,950
But if somebody is
interested in learning more,

691
00:27:53,950 --> 00:27:55,901
I'm happy to kind
of dive into there.

692
00:27:55,901 --> 00:27:56,400
All right.

693
00:27:56,400 --> 00:27:59,220
So readings are
strongly encouraged.

694
00:27:59,220 --> 00:28:01,500
I have interacted
with several of you.

695
00:28:01,500 --> 00:28:03,930
Joe has interacted
with probably 3n,

696
00:28:03,930 --> 00:28:06,680
n being the number of people
I've interacted with so far,

697
00:28:06,680 --> 00:28:10,430
and really tried to impart
the wisdom of pn-junctions.

698
00:28:10,430 --> 00:28:12,917
So please, please, please
come to us if still

699
00:28:12,917 --> 00:28:14,250
things are going over your head.

700
00:28:14,250 --> 00:28:17,940
You should be able to explain to
your roommates exactly what is

701
00:28:17,940 --> 00:28:19,430
going on in a pn-junction.

702
00:28:19,430 --> 00:28:22,144
Define parameters that
determine solar cell efficiency.

703
00:28:22,144 --> 00:28:23,560
So now we have a
qualitative sense

704
00:28:23,560 --> 00:28:26,250
about where current is flowing,
where electrons are moving

705
00:28:26,250 --> 00:28:29,585
around, what defines
the power output, how

706
00:28:29,585 --> 00:28:31,960
the power output is changing
with illumination condition.

707
00:28:31,960 --> 00:28:33,834
We're getting an intuitive
sense of all this.

708
00:28:33,834 --> 00:28:35,960
Let's start putting
some discrete variables

709
00:28:35,960 --> 00:28:37,370
to all of that.

710
00:28:37,370 --> 00:28:40,880
And there are a bunch of
two-letter or three-letter

711
00:28:40,880 --> 00:28:43,732
acronyms with some subscripts
here that we'll get to know

712
00:28:43,732 --> 00:28:45,190
and we'll become
very familiar with

713
00:28:45,190 --> 00:28:47,120
over the next few lectures.

714
00:28:47,120 --> 00:28:51,640
So how is solar cell conversion
efficiency determined

715
00:28:51,640 --> 00:28:53,280
from that illuminated IV curve?

716
00:28:53,280 --> 00:28:54,770
That's our first question.

717
00:28:54,770 --> 00:28:59,380
And what I'm going to do
is start with our source

718
00:28:59,380 --> 00:29:00,590
IV curve right here.

719
00:29:00,590 --> 00:29:02,330
This is just the IV quadrant.

720
00:29:02,330 --> 00:29:02,830
OK?

721
00:29:02,830 --> 00:29:05,950
So notice the
current starts at 0

722
00:29:05,950 --> 00:29:07,520
and goes to some negative value.

723
00:29:07,520 --> 00:29:09,170
So we're looking
in the IV quadrant.

724
00:29:09,170 --> 00:29:11,570
Voltage is going from
0 to a positive value.

725
00:29:11,570 --> 00:29:13,130
So again, IV quadrant.

726
00:29:13,130 --> 00:29:16,870
We have our ideal
diode equation here.

727
00:29:16,870 --> 00:29:18,450
And oh, notice one thing.

728
00:29:18,450 --> 00:29:22,230
I just changed I to
J. What just happened?

729
00:29:22,230 --> 00:29:24,650
Well, I and J look very
similar, but they're, in fact,

730
00:29:24,650 --> 00:29:26,460
two different variables.

731
00:29:26,460 --> 00:29:30,090
Most often, PV researchers
will report a current density,

732
00:29:30,090 --> 00:29:32,990
in other words, a current
per unit area instead

733
00:29:32,990 --> 00:29:35,780
of the actual current coming
out of a solar cell device.

734
00:29:35,780 --> 00:29:38,707
So what you've been
measuring here off of the DAC

735
00:29:38,707 --> 00:29:41,040
has been current, total current
output from that device.

736
00:29:41,040 --> 00:29:42,670
And it might be a
really tiny number,

737
00:29:42,670 --> 00:29:44,170
and it might be
difficult to compare

738
00:29:44,170 --> 00:29:45,644
against other-sized devices.

739
00:29:45,644 --> 00:29:47,310
And so what solar
cell researchers often

740
00:29:47,310 --> 00:29:49,268
do is they say, OK, let's
normalize the current

741
00:29:49,268 --> 00:29:51,150
by the area to get
a current density.

742
00:29:51,150 --> 00:29:53,190
And we'll call
current density J,

743
00:29:53,190 --> 00:29:56,210
and we'll call current I, right?

744
00:29:56,210 --> 00:29:57,710
So for calculating
power, we'll have

745
00:29:57,710 --> 00:30:00,830
to use I. We'll have
to multiply I times V.

746
00:30:00,830 --> 00:30:04,170
But if we're just looking at
one solar cell versus another,

747
00:30:04,170 --> 00:30:06,870
we can use J as a very
convenient way of comparing

748
00:30:06,870 --> 00:30:09,270
one solar cell versus another.

749
00:30:09,270 --> 00:30:10,020
Cool.

750
00:30:10,020 --> 00:30:10,520
OK.

751
00:30:10,520 --> 00:30:13,380
So the illuminated IV curve
looks something like this,

752
00:30:13,380 --> 00:30:13,880
right?

753
00:30:13,880 --> 00:30:15,040
It's in the IV quadrant.

754
00:30:15,040 --> 00:30:17,206
It goes out a certain amount,
then it the curves up.

755
00:30:17,206 --> 00:30:20,020
We just determined
that here in class.

756
00:30:20,020 --> 00:30:22,420
And that's essentially
the ideal diode equation

757
00:30:22,420 --> 00:30:26,240
with a superposition term,
this J sub L right there.

758
00:30:26,240 --> 00:30:28,650
So let's parse through this.

759
00:30:28,650 --> 00:30:31,040
We have the
y-intercept over here.

760
00:30:31,040 --> 00:30:34,060
At the y-intercept,
there is maximum current

761
00:30:34,060 --> 00:30:36,510
flowing through the
circuit but no power

762
00:30:36,510 --> 00:30:38,765
because voltage is equal to 0.

763
00:30:38,765 --> 00:30:41,140
So remember, the Fermi energy
is the same on either side.

764
00:30:41,140 --> 00:30:42,639
The chemical
potentials are the same

765
00:30:42,639 --> 00:30:43,860
on either side of the device.

766
00:30:43,860 --> 00:30:46,670
So there's no energy gain
of the electron traveling

767
00:30:46,670 --> 00:30:50,757
through the external circuit,
but there's a maximum current.

768
00:30:50,757 --> 00:30:52,840
And no power flowing through
that external circuit

769
00:30:52,840 --> 00:30:54,590
because there's no
potential to be dropped

770
00:30:54,590 --> 00:30:56,870
across the external resistor.

771
00:30:56,870 --> 00:30:58,860
The opposite happens
over here at this point

772
00:30:58,860 --> 00:31:01,660
called Voc, which we'll
call open-circuit voltage.

773
00:31:01,660 --> 00:31:04,670
The oc stands for open
circuit, V, voltage.

774
00:31:04,670 --> 00:31:07,130
Open-circuit voltage is just
as you would think it is.

775
00:31:07,130 --> 00:31:09,900
When your solar cell is in
an open circuit, when you--

776
00:31:09,900 --> 00:31:11,290
say you took a
pair of scissors--

777
00:31:11,290 --> 00:31:13,380
please don't this--
and cut the leads so

778
00:31:13,380 --> 00:31:16,110
that your solar cell
wasn't outputting

779
00:31:16,110 --> 00:31:17,770
the current through
an external load,

780
00:31:17,770 --> 00:31:21,540
there would be a bias voltage
built up across the p and the n

781
00:31:21,540 --> 00:31:22,810
side of the solar cell.

782
00:31:22,810 --> 00:31:25,249
And it would be
the maximum voltage

783
00:31:25,249 --> 00:31:27,290
that could be supported
by that solar cell device

784
00:31:27,290 --> 00:31:28,539
under illumination conditions.

785
00:31:28,539 --> 00:31:30,690
That's the open-circuit
voltage, open circuit

786
00:31:30,690 --> 00:31:33,010
because there's
no current, again,

787
00:31:33,010 --> 00:31:34,810
traveling through
the external circuit.

788
00:31:34,810 --> 00:31:38,460
That's why current
is 0, open circuit.

789
00:31:38,460 --> 00:31:40,507
And voltage because
this is-- well,

790
00:31:40,507 --> 00:31:42,090
it's an interesting
point because it's

791
00:31:42,090 --> 00:31:45,420
the maximum voltage here
represented in the IV quadrant.

792
00:31:45,420 --> 00:31:49,140
And somewhere in between the
point of open-circuit voltage

793
00:31:49,140 --> 00:31:51,714
and short-circuit current--
short-circuit current,

794
00:31:51,714 --> 00:31:53,880
again, because you're short
circuiting your device--

795
00:31:53,880 --> 00:31:55,395
current is flowing through,
but there's no resistor.

796
00:31:55,395 --> 00:31:56,436
There's no external load.

797
00:31:56,436 --> 00:31:58,810
There's no power being
deposited on external load.

798
00:31:58,810 --> 00:32:00,380
Somewhere between these
two extreme conditions

799
00:32:00,380 --> 00:32:02,879
where there's no power flowing
through the external circuit,

800
00:32:02,879 --> 00:32:04,440
you have a maximum
power point where

801
00:32:04,440 --> 00:32:06,981
there is a power being deposited
across your external circuit

802
00:32:06,981 --> 00:32:08,510
and a lot of it, right?

803
00:32:08,510 --> 00:32:10,160
That's the maximum power point.

804
00:32:10,160 --> 00:32:12,135
This is the point at
which the solar cell

805
00:32:12,135 --> 00:32:15,170
is producing the maximum
amount of power output.

806
00:32:15,170 --> 00:32:18,590
And to represent that
slightly differently, what

807
00:32:18,590 --> 00:32:21,900
I've done-- so if I were
to take current times

808
00:32:21,900 --> 00:32:24,870
voltage right here
using IV quadrant data,

809
00:32:24,870 --> 00:32:26,921
my power would be
a negative number.

810
00:32:26,921 --> 00:32:27,420
Why?

811
00:32:27,420 --> 00:32:29,220
Because voltage is
positive, but current

812
00:32:29,220 --> 00:32:30,387
is a negative number, right?

813
00:32:30,387 --> 00:32:32,720
So I'd multiply a positive
and negative number together,

814
00:32:32,720 --> 00:32:35,210
you get a negative number,
and that just sounds weird.

815
00:32:35,210 --> 00:32:37,210
Who talks about power
output from solar cells

816
00:32:37,210 --> 00:32:38,270
being negative?

817
00:32:38,270 --> 00:32:41,160
It almost sounds like power's
going into the device.

818
00:32:41,160 --> 00:32:43,330
So this is another
convention that you're

819
00:32:43,330 --> 00:32:45,830
going to have to get used to
is looking at the IV curve

820
00:32:45,830 --> 00:32:47,750
in the I quadrant.

821
00:32:47,750 --> 00:32:50,229
So all we've done
is taken the y-axis

822
00:32:50,229 --> 00:32:51,520
and multiplied by a negative 1.

823
00:32:51,520 --> 00:32:55,030
So we flipped it up, right?

824
00:32:55,030 --> 00:32:56,235
So bear with me here.

825
00:32:56,235 --> 00:32:58,300
It's a bit tricky to keep
all this in your RAM.

826
00:32:58,300 --> 00:33:01,040
But here's our short-circuit
current point now.

827
00:33:01,040 --> 00:33:02,910
Here's our open-circuit
voltage point.

828
00:33:02,910 --> 00:33:05,180
Our IV curve now
is pointed down.

829
00:33:05,180 --> 00:33:07,640
Before it was going up because
we were in the IV quadrant.

830
00:33:07,640 --> 00:33:09,370
Now, we flipped,
essentially just

831
00:33:09,370 --> 00:33:11,980
done a-- we've done a flip
vertical, if you will,

832
00:33:11,980 --> 00:33:16,100
on our IV curve, and we have
our current increasing here

833
00:33:16,100 --> 00:33:17,944
going to higher bias voltages.

834
00:33:17,944 --> 00:33:20,360
Now we can take the product
of the voltage and the current

835
00:33:20,360 --> 00:33:22,309
to determine the
power, and we obtain

836
00:33:22,309 --> 00:33:24,350
a curve that looks very
much like this blue curve

837
00:33:24,350 --> 00:33:26,200
right here that you can see.

838
00:33:26,200 --> 00:33:29,280
And the maximum power point
is truth in advertising.

839
00:33:29,280 --> 00:33:30,960
It's at the maximum power.

840
00:33:30,960 --> 00:33:33,390
It's where this blue
curve reaches a maximum.

841
00:33:33,390 --> 00:33:35,910
That is the maximum power
point of the solar cell device.

842
00:33:35,910 --> 00:33:38,070
That is where the solar
cell is outputting

843
00:33:38,070 --> 00:33:40,720
the maximum amount of power.

844
00:33:40,720 --> 00:33:42,230
And so at this
maximum power point,

845
00:33:42,230 --> 00:33:45,070
there is a voltage and a current
associated with it that you can

846
00:33:45,070 --> 00:33:46,890
read right off the IV curve.

847
00:33:46,890 --> 00:33:51,310
And this we call Jmp, or current
density at the maximum power

848
00:33:51,310 --> 00:33:55,500
point, and Vmp, which is the
voltage at the maximum power

849
00:33:55,500 --> 00:33:57,310
point.

850
00:33:57,310 --> 00:33:59,490
So, so far, we've learned
essentially four variables

851
00:33:59,490 --> 00:33:59,990
here.

852
00:33:59,990 --> 00:34:04,130
We have our Jsc, our
Voc, and our Jmp,

853
00:34:04,130 --> 00:34:07,830
and our Vmp at that
data point right there.

854
00:34:07,830 --> 00:34:11,286
Questions, since I
know you have them.

855
00:34:11,286 --> 00:34:13,436
AUDIENCE: To ensure that
the device is working

856
00:34:13,436 --> 00:34:17,808
in the maximum power point,
does an external voltage have

857
00:34:17,808 --> 00:34:19,659
to be applied to it?

858
00:34:19,659 --> 00:34:21,469
PROFESSOR: So to ensure
that the solar cell

859
00:34:21,469 --> 00:34:24,550
device is operating right
here, a couple of things

860
00:34:24,550 --> 00:34:25,489
need to happen.

861
00:34:25,489 --> 00:34:27,659
You need to have the right
illumination conditions,

862
00:34:27,659 --> 00:34:29,639
and you need to
have the right load.

863
00:34:29,639 --> 00:34:31,650
So the two need to be
matched to each other.

864
00:34:31,650 --> 00:34:32,303
Absolutely.

865
00:34:32,303 --> 00:34:34,219
And that's where some
of the power electronics

866
00:34:34,219 --> 00:34:36,715
come into play.

867
00:34:36,715 --> 00:34:37,215
Yeah?

868
00:34:37,215 --> 00:34:39,171
AUDIENCE: So in the
last problem set,

869
00:34:39,171 --> 00:34:44,305
where [INAUDIBLE], we assumed
that output voltage would

870
00:34:44,305 --> 00:34:46,329
be [INAUDIBLE] volts.

871
00:34:46,329 --> 00:34:46,995
PROFESSOR: Yeah.

872
00:34:46,995 --> 00:34:49,790
AUDIENCE: Is that, in
general, a safe assumption

873
00:34:49,790 --> 00:34:51,464
for [INAUDIBLE] solar cell?

874
00:34:51,464 --> 00:34:52,380
PROFESSOR: Yeah, yeah.

875
00:34:52,380 --> 00:34:55,320
So it's a very interesting
question regarding the homework

876
00:34:55,320 --> 00:34:55,820
question.

877
00:34:55,820 --> 00:34:58,540
Let me repeat it so that
the microphone can hear it.

878
00:34:58,540 --> 00:35:01,670
The homework question
in the last homework,

879
00:35:01,670 --> 00:35:05,040
there was one question
that inquired,

880
00:35:05,040 --> 00:35:07,160
assume that the voltage
at the maximum power point

881
00:35:07,160 --> 00:35:12,130
is the band gap voltage
equivalent minus 0.5 volts.

882
00:35:12,130 --> 00:35:15,240
And the rationale for that
assumption is as follows.

883
00:35:15,240 --> 00:35:17,680
The open-circuit
voltage, this point,

884
00:35:17,680 --> 00:35:23,290
is generally between 0.35 and
0.4 volts minus the band gap,

885
00:35:23,290 --> 00:35:24,750
or lower than the band gap.

886
00:35:24,750 --> 00:35:27,150
So you have the band gap
energy minus 0.4 volts.

887
00:35:27,150 --> 00:35:29,820
And I can show you a
very nice little paper

888
00:35:29,820 --> 00:35:30,995
that describes why that is.

889
00:35:30,995 --> 00:35:32,640
It essentially has
to do, in part,

890
00:35:32,640 --> 00:35:35,830
with losses inside of the solar
cell at thermodynamic limits

891
00:35:35,830 --> 00:35:37,880
of conversion inside of
the solar cell device.

892
00:35:37,880 --> 00:35:39,560
Then what we've
done is we've done

893
00:35:39,560 --> 00:35:42,090
another additional discounting
from the Voc to the maximum

894
00:35:42,090 --> 00:35:47,310
power point, which we've assumed
is around 0.1, maybe 0.2 volts.

895
00:35:47,310 --> 00:35:49,507
Notice the shape of the
IV curve right here.

896
00:35:49,507 --> 00:35:51,090
The maximum power
point is interesting

897
00:35:51,090 --> 00:35:53,006
because the voltage at
the maximum power point

898
00:35:53,006 --> 00:35:55,990
is almost the Voc,
in a good device.

899
00:35:55,990 --> 00:35:57,940
And the current at the
maximum power point

900
00:35:57,940 --> 00:36:00,560
is almost Jsc, but not quite.

901
00:36:00,560 --> 00:36:01,380
All right?

902
00:36:01,380 --> 00:36:04,335
So the discounting from the
Voc to the maximum power

903
00:36:04,335 --> 00:36:08,040
point voltage is not that
much, as is the discounting

904
00:36:08,040 --> 00:36:10,480
from the short-circuit
current to the maximum power

905
00:36:10,480 --> 00:36:12,640
point in a good device.

906
00:36:12,640 --> 00:36:15,850
In a bad device, this
maximum power point

907
00:36:15,850 --> 00:36:17,710
here could be dragged
all way down here.

908
00:36:17,710 --> 00:36:20,335
You could have an IV curve that
looked something more like this

909
00:36:20,335 --> 00:36:23,310
instead, almost like a
resistor, at which point

910
00:36:23,310 --> 00:36:26,699
the maximum power output would
be a lot less, a lot less

911
00:36:26,699 --> 00:36:28,240
than what's shown
here in blue curve.

912
00:36:31,660 --> 00:36:32,350
Cool.

913
00:36:32,350 --> 00:36:32,850
All right.

914
00:36:32,850 --> 00:36:35,010
So let's continue moving on.

915
00:36:35,010 --> 00:36:37,160
The efficiency of
the solar cell.

916
00:36:37,160 --> 00:36:42,290
Eta, this Greek letter eta, is
our power out versus power in.

917
00:36:42,290 --> 00:36:45,390
Our power in is the
illumination intensity

918
00:36:45,390 --> 00:36:48,100
given in units of watts
per meter squared.

919
00:36:48,100 --> 00:36:51,140
So we calculated this in our
very first homework assignment

920
00:36:51,140 --> 00:36:54,100
and realized that the AM
1.5 spectrum is around

921
00:36:54,100 --> 00:36:56,560
1,000 watts per meter squared.

922
00:36:56,560 --> 00:36:58,980
So that's our input
power right here.

923
00:37:02,090 --> 00:37:05,840
Our output power is the
voltage at the maximum power

924
00:37:05,840 --> 00:37:07,522
point times--
whoopsy-- times the

925
00:37:07,522 --> 00:37:08,980
current at the
maximum power point,

926
00:37:08,980 --> 00:37:10,960
not the current
density, the current

927
00:37:10,960 --> 00:37:12,232
at the maximum power point.

928
00:37:12,232 --> 00:37:13,940
So take this current
density and multiply

929
00:37:13,940 --> 00:37:16,460
by area, and that's
effectively-- the units

930
00:37:16,460 --> 00:37:19,040
work out better that way.

931
00:37:19,040 --> 00:37:21,960
So it would be either V times
I at the maximum power point

932
00:37:21,960 --> 00:37:25,259
or V times J times the area,
the area of the device,

933
00:37:25,259 --> 00:37:27,550
the area of the solar cell,
at the maximum power point.

934
00:37:27,550 --> 00:37:30,870
And that's the total power out.

935
00:37:30,870 --> 00:37:32,130
Actually, yeah, yeah.

936
00:37:32,130 --> 00:37:35,412
So as long as the units are
in units of watts per meter

937
00:37:35,412 --> 00:37:37,870
squared-- yeah, down here-- if
this is not total watts but,

938
00:37:37,870 --> 00:37:39,536
watts per meter
squared, you could still

939
00:37:39,536 --> 00:37:41,200
use current density.

940
00:37:41,200 --> 00:37:42,670
Those units would
still work out.

941
00:37:42,670 --> 00:37:45,890
So be very careful whether
you use total power in

942
00:37:45,890 --> 00:37:48,650
or normalized by unit
area power, right?

943
00:37:48,650 --> 00:37:50,440
Just keep track of your units.

944
00:37:50,440 --> 00:37:52,850
Don't do like the professor.

945
00:37:52,850 --> 00:37:53,410
OK.

946
00:37:53,410 --> 00:37:56,530
So we have efficiency here
as power out versus power in,

947
00:37:56,530 --> 00:38:00,030
the power out being the maximum
power point power and the power

948
00:38:00,030 --> 00:38:02,199
in being the illumination
from the sun.

949
00:38:02,199 --> 00:38:03,240
Now we're really talking.

950
00:38:03,240 --> 00:38:05,379
This is starting to get
interesting because it's

951
00:38:05,379 --> 00:38:06,170
beginning to click.

952
00:38:06,170 --> 00:38:08,050
Pieces from lecture
number 2 come together

953
00:38:08,050 --> 00:38:09,314
with what we're seeing now.

954
00:38:09,314 --> 00:38:11,605
So this is solar cell output
power at the maximum power

955
00:38:11,605 --> 00:38:13,230
point and sunlight coming in.

956
00:38:13,230 --> 00:38:14,380
OK.

957
00:38:14,380 --> 00:38:16,850
So what I'm going
to do next is I'm

958
00:38:16,850 --> 00:38:18,470
going to take this
maximum power point

959
00:38:18,470 --> 00:38:23,050
and I'm going to draw a box
that starts at the origin here,

960
00:38:23,050 --> 00:38:28,650
and the kitty-corner
corner of my box

961
00:38:28,650 --> 00:38:31,160
is going to end at the
maximum power point.

962
00:38:31,160 --> 00:38:33,640
So it'll have some
rectilinear shape that

963
00:38:33,640 --> 00:38:35,650
will comprise the
maximum power point

964
00:38:35,650 --> 00:38:39,550
and 0, 0, the origin,
as two of its corners.

965
00:38:39,550 --> 00:38:42,030
And that box looks like
this blue one right here.

966
00:38:42,030 --> 00:38:45,120
The area of that box
is Jmp times Vmp.

967
00:38:47,670 --> 00:38:48,300
OK?

968
00:38:48,300 --> 00:38:50,550
And notice I have
another box around here.

969
00:38:50,550 --> 00:38:54,780
I have this clear box
that starts at the Voc

970
00:38:54,780 --> 00:38:57,120
point and the Jsc point.

971
00:38:57,120 --> 00:39:00,770
And now I have two rectilinear
shapes, this blue one

972
00:39:00,770 --> 00:39:03,470
and the clear one right
here, the bigger one.

973
00:39:03,470 --> 00:39:08,820
The bigger one has an
area of Jsc times Voc.

974
00:39:08,820 --> 00:39:10,570
And I'm going to define
a parameter called

975
00:39:10,570 --> 00:39:14,180
fill factor, which will be
the ratio of these two areas,

976
00:39:14,180 --> 00:39:17,510
the ratio of those two boxes,
the Vmp times Jmp divided

977
00:39:17,510 --> 00:39:20,470
by the Voc and Jsc.

978
00:39:20,470 --> 00:39:23,840
If this is 1, which is
virtually impossible to do,

979
00:39:23,840 --> 00:39:25,840
but if this were 1, it
would mean that these two

980
00:39:25,840 --> 00:39:27,510
boxes were the same size.

981
00:39:27,510 --> 00:39:29,840
And the current and voltage
at the maximum power points

982
00:39:29,840 --> 00:39:32,530
would be the current
and voltage under

983
00:39:32,530 --> 00:39:35,850
short-circuit and open-circuit
conditions respectively.

984
00:39:35,850 --> 00:39:41,840
In real life, this blue box
is smaller than the square box

985
00:39:41,840 --> 00:39:42,860
right over here.

986
00:39:42,860 --> 00:39:48,120
And so the Jmp Vmp product is
less than the Jsc Voc product.

987
00:39:48,120 --> 00:39:50,310
And by consequence
as well, the Jmp

988
00:39:50,310 --> 00:39:54,610
is less than the Jsc,
Vmp is less than Voc.

989
00:39:54,610 --> 00:39:58,470
So the ratio of the two boxes
is defined as the fill factor.

990
00:39:58,470 --> 00:40:02,550
The fill factor indicates
the quality of your diode.

991
00:40:02,550 --> 00:40:04,830
If your fill factor
is very poor,

992
00:40:04,830 --> 00:40:07,565
that means that that sun right
over there at its maximum power

993
00:40:07,565 --> 00:40:10,060
point is being dragged
toward the origin.

994
00:40:10,060 --> 00:40:11,980
That means that the
area of this blue box

995
00:40:11,980 --> 00:40:16,160
is growing smaller relative
to the area of this clear box.

996
00:40:16,160 --> 00:40:18,730
The fill factor is going down.

997
00:40:18,730 --> 00:40:22,900
That means you're filling less
of this maximum square box

998
00:40:22,900 --> 00:40:27,340
function defined by the Voc Jsc.

999
00:40:27,340 --> 00:40:28,280
OK.

1000
00:40:28,280 --> 00:40:32,950
So we have defined efficiency
as power out divided

1001
00:40:32,950 --> 00:40:36,120
by power in, power out
being the current voltage

1002
00:40:36,120 --> 00:40:38,180
product of the maximum
power point divided

1003
00:40:38,180 --> 00:40:40,820
by the solar
insulation, fill factor

1004
00:40:40,820 --> 00:40:46,320
being defined as the ratio
of Vmp Imp product divided

1005
00:40:46,320 --> 00:40:49,360
by Voc Ioc product.

1006
00:40:49,360 --> 00:40:52,450
Notice that here I've written
this in terms of total current,

1007
00:40:52,450 --> 00:40:54,260
here in terms of
current density.

1008
00:40:54,260 --> 00:40:56,064
The areas essentially
just cancel out

1009
00:40:56,064 --> 00:40:58,480
because you have an area in
the numerator and denominator.

1010
00:40:58,480 --> 00:40:59,000
They cancel.

1011
00:40:59,000 --> 00:41:01,650
These ratios should
be identical.

1012
00:41:01,650 --> 00:41:05,210
Thus we obtain an expression
for the efficiency in terms

1013
00:41:05,210 --> 00:41:09,280
of fill factor, Voc, and Ioc.

1014
00:41:09,280 --> 00:41:12,430
Simply by using this fill
factor definition right here,

1015
00:41:12,430 --> 00:41:14,450
what I've done is
I've multiplied

1016
00:41:14,450 --> 00:41:16,650
this side of the
equation-- let's just

1017
00:41:16,650 --> 00:41:18,620
focus right here--
where we have fill

1018
00:41:18,620 --> 00:41:22,470
factor equals Vmp times Imp
divided by Voc times Ioc.

1019
00:41:22,470 --> 00:41:25,070
I moved the denominator
up to the side

1020
00:41:25,070 --> 00:41:28,140
over here, multiplied it by fill
factor, and that's my Vmp Imp.

1021
00:41:28,140 --> 00:41:30,100
Now, I go back to
that top equation

1022
00:41:30,100 --> 00:41:32,480
and say my Vmp Imp is now
going to be substituted

1023
00:41:32,480 --> 00:41:35,260
by fill factor
times Voc times Ioc,

1024
00:41:35,260 --> 00:41:37,853
and that's how I get to
this equation right here.

1025
00:41:37,853 --> 00:41:38,719
Why?

1026
00:41:38,719 --> 00:41:41,010
Why do I go through the effort
of this little numerical

1027
00:41:41,010 --> 00:41:42,050
manipulation?

1028
00:41:42,050 --> 00:41:44,900
I do it because these
parameters right here

1029
00:41:44,900 --> 00:41:48,790
are fairly easy to measure
using the solar simulator

1030
00:41:48,790 --> 00:41:50,580
that you just put together.

1031
00:41:50,580 --> 00:41:54,440
So I can measure the point
at which my voltage is

1032
00:41:54,440 --> 00:41:55,530
at open-circuit condition.

1033
00:41:55,530 --> 00:41:59,000
I can measure the current
at short-circuit condition.

1034
00:41:59,000 --> 00:42:01,670
And simply by taking the
ratio of those boxes,

1035
00:42:01,670 --> 00:42:04,160
I can determine what my
fill factor is as well.

1036
00:42:04,160 --> 00:42:10,660
And these break down roughly
into the current is going

1037
00:42:10,660 --> 00:42:13,372
to be a function roughly--
again, I'm really painting

1038
00:42:13,372 --> 00:42:15,330
broad brush strokes here--
the current is going

1039
00:42:15,330 --> 00:42:18,480
to be roughly a function of
illumination condition and bulk

1040
00:42:18,480 --> 00:42:20,380
material quality.

1041
00:42:20,380 --> 00:42:23,690
The Voc will be roughly a
function of the interface

1042
00:42:23,690 --> 00:42:25,050
and the diode characteristics.

1043
00:42:25,050 --> 00:42:26,809
And the fill factor
is going to be

1044
00:42:26,809 --> 00:42:28,850
a function of the interface
diode characteristics

1045
00:42:28,850 --> 00:42:31,647
but also of the resistances
within the device.

1046
00:42:31,647 --> 00:42:33,355
And so from an
engineering point of view,

1047
00:42:33,355 --> 00:42:37,420
when we break the solar cell
output down into these three

1048
00:42:37,420 --> 00:42:40,280
parameters so that we can
better understand what's

1049
00:42:40,280 --> 00:42:43,040
going wrong with our solar cell.

1050
00:42:43,040 --> 00:42:45,457
If we have everything
lumped in terms of Vmp Imp,

1051
00:42:45,457 --> 00:42:47,540
it becomes a little bit
more obscure to figure out

1052
00:42:47,540 --> 00:42:50,290
what exactly is going wrong
with our solar cell device.

1053
00:42:50,290 --> 00:42:51,607
Ashley?

1054
00:42:51,607 --> 00:42:53,232
AUDIENCE: You said
the fill factor also

1055
00:42:53,232 --> 00:42:55,162
an easily measurable parameter?

1056
00:42:55,162 --> 00:42:57,620
PROFESSOR: So the fill factor
you would measure essentially

1057
00:42:57,620 --> 00:43:00,830
by doing the little analysis
we just did right here.

1058
00:43:00,830 --> 00:43:01,880
Yeah, exactly.

1059
00:43:01,880 --> 00:43:04,560
So you'd have to do a
voltage current sweep.

1060
00:43:04,560 --> 00:43:05,060
Mm-hmm.

1061
00:43:08,630 --> 00:43:09,260
Coolness.

1062
00:43:09,260 --> 00:43:09,890
OK.

1063
00:43:09,890 --> 00:43:12,840
So we have an expression
for efficiency

1064
00:43:12,840 --> 00:43:17,640
in terms of fill factor, Voc,
Ioc and our incoming power.

1065
00:43:17,640 --> 00:43:20,000
So power out, this
right here again

1066
00:43:20,000 --> 00:43:23,910
is power out,
divided by power in.

1067
00:43:23,910 --> 00:43:26,110
Why does efficiency matter?

1068
00:43:26,110 --> 00:43:28,140
Why do we care so
much about efficiency?

1069
00:43:28,140 --> 00:43:31,920
Well, the conversion
efficiency determines

1070
00:43:31,920 --> 00:43:34,910
the area of solar cells needed
to produce a certain peak

1071
00:43:34,910 --> 00:43:37,100
power, or to think
of it differently,

1072
00:43:37,100 --> 00:43:39,540
the area of solar panels
that is necessary to produce

1073
00:43:39,540 --> 00:43:42,010
a certain energy per unit time.

1074
00:43:42,010 --> 00:43:44,815
And many costs scale with area.

1075
00:43:44,815 --> 00:43:47,612
You have glass, encapsulants,
the absorbent materials

1076
00:43:47,612 --> 00:43:49,320
within the solar cell
devices themselves,

1077
00:43:49,320 --> 00:43:51,300
the metals that are
used to make contacts,

1078
00:43:51,300 --> 00:43:53,365
the labor that's used
to install the panels.

1079
00:43:53,365 --> 00:43:55,101
If you have a larger
panel area, you

1080
00:43:55,101 --> 00:43:56,350
need more labor to install it.

1081
00:43:56,350 --> 00:43:58,475
The aluminum and racking
and framing materials that

1082
00:43:58,475 --> 00:44:02,380
go into holding the panels up
in the field either on a roof

1083
00:44:02,380 --> 00:44:03,620
or out in the field.

1084
00:44:03,620 --> 00:44:06,710
So efficiency affects
pretty much everything

1085
00:44:06,710 --> 00:44:08,960
but the inverter and possibly
some of the soft costs

1086
00:44:08,960 --> 00:44:09,585
of the project.

1087
00:44:09,585 --> 00:44:11,390
That includes the
architect and the people

1088
00:44:11,390 --> 00:44:16,030
who you pay to handle the money,
financing, and the lawyers

1089
00:44:16,030 --> 00:44:16,610
perhaps.

1090
00:44:16,610 --> 00:44:20,050
So pretty much all of the
real material and labor costs

1091
00:44:20,050 --> 00:44:22,210
are scaling with area.

1092
00:44:22,210 --> 00:44:24,970
And so efficiency determines
that to a large degree,

1093
00:44:24,970 --> 00:44:26,830
and hence it's a
highly-leveraged way

1094
00:44:26,830 --> 00:44:28,560
to reduce the costs
of solar energy.

1095
00:44:28,560 --> 00:44:30,120
If you do a
sensitivity analysis,

1096
00:44:30,120 --> 00:44:33,000
which you will do in the second
and third parts of the class,

1097
00:44:33,000 --> 00:44:34,610
and look at the costs
of solar and how

1098
00:44:34,610 --> 00:44:35,984
it scales with
efficiency, you'll

1099
00:44:35,984 --> 00:44:38,890
see that efficiency is one
of the determining factors

1100
00:44:38,890 --> 00:44:41,090
for cost in a solar cell device.

1101
00:44:41,090 --> 00:44:42,770
And that's why we
focus on it a lot.

1102
00:44:42,770 --> 00:44:45,940
To put it into perspective,
if the efficiency up there is

1103
00:44:45,940 --> 00:44:48,500
determined by the output
power versus the input power,

1104
00:44:48,500 --> 00:44:51,770
if we had 100% conversion
efficiency, which is impossible

1105
00:44:51,770 --> 00:44:54,420
to achieve, thermodynamically
impossible to achieve,

1106
00:44:54,420 --> 00:44:57,117
we would produce a certain
amount of energy per unit time,

1107
00:44:57,117 --> 00:44:59,200
or a certain amount of
peak power, with this panel

1108
00:44:59,200 --> 00:44:59,970
right there.

1109
00:44:59,970 --> 00:45:02,580
Say that's the size of
our field installation.

1110
00:45:02,580 --> 00:45:04,830
If we had a 33%
efficiency cell, which

1111
00:45:04,830 --> 00:45:07,030
is closer to the
space-grade solar cells,

1112
00:45:07,030 --> 00:45:09,810
we'd need three times
that area, so three

1113
00:45:09,810 --> 00:45:12,380
times the encapsulants, three
times the glass, three times

1114
00:45:12,380 --> 00:45:14,260
the labor to install it.

1115
00:45:14,260 --> 00:45:20,230
And if we had a 20%
efficiency, say, high end

1116
00:45:20,230 --> 00:45:22,311
but still commercial
solar module,

1117
00:45:22,311 --> 00:45:24,060
not something you'd
need to get from NASA,

1118
00:45:24,060 --> 00:45:27,840
but something that you
could buy from a supplier,

1119
00:45:27,840 --> 00:45:30,050
you'd need five times that area.

1120
00:45:30,050 --> 00:45:33,490
Whereas if you had a 10%
efficiency module, which

1121
00:45:33,490 --> 00:45:36,130
is more approaching the
area of some relatively

1122
00:45:36,130 --> 00:45:40,102
inexpensive solar cells, you
would need 10 times that area.

1123
00:45:40,102 --> 00:45:41,560
So if you're doing
a cost analysis,

1124
00:45:41,560 --> 00:45:43,130
this is why efficiency matters.

1125
00:45:43,130 --> 00:45:45,110
It might still be
cheaper to use this

1126
00:45:45,110 --> 00:45:47,230
instead of to use
this over here.

1127
00:45:47,230 --> 00:45:50,070
That might very well be more
expensive when you do the math

1128
00:45:50,070 --> 00:45:52,130
and figure out how much it
costs to deposit those materials

1129
00:45:52,130 --> 00:45:53,680
with a very low
throughput deposition

1130
00:45:53,680 --> 00:45:55,510
process and very high cost.

1131
00:45:55,510 --> 00:45:57,190
It might still be,
but it might not.

1132
00:45:57,190 --> 00:45:59,590
The material costs might
end up whopping you.

1133
00:45:59,590 --> 00:46:02,980
And so a simple equation that
calculates all these parameters

1134
00:46:02,980 --> 00:46:05,830
in, the material costs,
the module efficiency,

1135
00:46:05,830 --> 00:46:07,830
essentially the material
[? and  labor ?] costs,

1136
00:46:07,830 --> 00:46:10,457
are being calculated in dollars
per meter squared, just saying,

1137
00:46:10,457 --> 00:46:12,540
how many dollars go into
producing a meter squared

1138
00:46:12,540 --> 00:46:13,760
of this material?

1139
00:46:13,760 --> 00:46:15,490
And the efficiency is over here.

1140
00:46:15,490 --> 00:46:18,370
And this is just a very
simple back-of-the-envelope

1141
00:46:18,370 --> 00:46:22,020
calculation type of way of
estimating the cost of a solar

1142
00:46:22,020 --> 00:46:22,930
system.

1143
00:46:22,930 --> 00:46:26,410
So if you say, OK, I'm
willing to pay more

1144
00:46:26,410 --> 00:46:29,910
for a high-efficiency cell
because I'm using less area,

1145
00:46:29,910 --> 00:46:32,580
you can use this
type of calculation

1146
00:46:32,580 --> 00:46:34,397
to get to the answer quickly.

1147
00:46:34,397 --> 00:46:36,480
It's not a levelized cost
of electricity analysis.

1148
00:46:36,480 --> 00:46:38,560
It's not using
discounted capital flows

1149
00:46:38,560 --> 00:46:40,686
and so forth, which we'll
get to later on in class.

1150
00:46:40,686 --> 00:46:42,601
This is a really
back-of-the-envelope envelope

1151
00:46:42,601 --> 00:46:44,790
engineering approach to
estimating costs of a solar

1152
00:46:44,790 --> 00:46:47,060
system.

1153
00:46:47,060 --> 00:46:50,220
So I think this is a
great place to stop.

1154
00:46:50,220 --> 00:46:53,240
And if anybody has a pitch
concerning their project

1155
00:46:53,240 --> 00:46:55,550
ideas, class project ideas,
I'd like to invite them

1156
00:46:55,550 --> 00:46:57,980
to the front now.

1157
00:46:57,980 --> 00:47:00,220
The class project, mind
you, is really the capstone

1158
00:47:00,220 --> 00:47:03,670
of this class, 2.626, 2.627.

1159
00:47:03,670 --> 00:47:07,189
So if you have an idea, a fun
idea, for a class project,

1160
00:47:07,189 --> 00:47:09,730
I'd invite you to give a pitch
up here at the front of class,

1161
00:47:09,730 --> 00:47:14,000
or you're welcome to send it on
an email to the class listserv.