1
00:00:00,060 --> 00:00:02,500
The following content is
provided under a Creative

2
00:00:02,500 --> 00:00:04,019
Commons license.

3
00:00:04,019 --> 00:00:06,350
Your support will help
MIT OpenCourseWare

4
00:00:06,350 --> 00:00:10,720
continue to offer high quality
educational resources for free.

5
00:00:10,720 --> 00:00:13,330
To make a donation or
view additional materials

6
00:00:13,330 --> 00:00:17,226
from hundreds of MIT courses,
visit MIT OpenCourseWare

7
00:00:17,226 --> 00:00:17,851
at ocw.mit.edu.

8
00:00:25,715 --> 00:00:27,090
PROFESSOR: What
we're going to be

9
00:00:27,090 --> 00:00:31,460
doing over the next few
days, today and on Tuesday,

10
00:00:31,460 --> 00:00:34,380
is really diving into
the device fundamentals,

11
00:00:34,380 --> 00:00:36,120
and then on Tuesday,
the materials

12
00:00:36,120 --> 00:00:39,830
fundamentals, of how a solar
cell device really works.

13
00:00:39,830 --> 00:00:43,240
And what we've done so
far is skimmed along

14
00:00:43,240 --> 00:00:49,130
at a very high level using
only the necessary physics

15
00:00:49,130 --> 00:00:52,270
and nothing more to describe
how solar cell works.

16
00:00:52,270 --> 00:00:54,960
Because we want to give you
an intuition about solar cell

17
00:00:54,960 --> 00:00:55,700
device operation.

18
00:00:55,700 --> 00:00:57,450
PROFESSOR: The alternative
way of teaching

19
00:00:57,450 --> 00:01:00,700
PV is that we go heavy on
the device physics upfront,

20
00:01:00,700 --> 00:01:04,030
you're completely overloaded,
your RAM is completely full,

21
00:01:04,030 --> 00:01:05,910
and by the time we
actually get to IV curves,

22
00:01:05,910 --> 00:01:07,170
you're completely lost.

23
00:01:07,170 --> 00:01:09,460
So hopefully you have
some intuitive sense now

24
00:01:09,460 --> 00:01:11,210
about how a PV device works.

25
00:01:11,210 --> 00:01:13,640
Now we're going to be
doing some deep dives

26
00:01:13,640 --> 00:01:16,390
into some advanced
concepts so that we really

27
00:01:16,390 --> 00:01:18,620
have a sophisticated
understanding of how

28
00:01:18,620 --> 00:01:19,740
a solar cell works.

29
00:01:19,740 --> 00:01:23,820
So let's dive into the lecture
material for the 1D device

30
00:01:23,820 --> 00:01:27,290
model, we want to be able
to create a one dimensional

31
00:01:27,290 --> 00:01:29,870
model that describes how
a solar cell operates.

32
00:01:29,870 --> 00:01:33,010
So we want to capture all
of the necessary physics

33
00:01:33,010 --> 00:01:35,540
from the materials
and the device

34
00:01:35,540 --> 00:01:37,050
to describe the
IV characteristics

35
00:01:37,050 --> 00:01:38,300
of a solar cell.

36
00:01:38,300 --> 00:01:39,680
So we'll do at
the very beginning

37
00:01:39,680 --> 00:01:41,500
is start a little
bit of nomenclature

38
00:01:41,500 --> 00:01:43,680
so we understand what we're
talking about in terms

39
00:01:43,680 --> 00:01:46,767
of energy conversion efficiency
and quantum efficiency.

40
00:01:46,767 --> 00:01:49,100
And then we'll start describing
the different parameters

41
00:01:49,100 --> 00:01:54,121
that effect energy conversion
efficiency and efficiency here.

42
00:01:54,121 --> 00:01:56,620
So one of the first key concepts
that's very, very important

43
00:01:56,620 --> 00:01:58,980
to understand is that energy
conversion efficiency is not

44
00:01:58,980 --> 00:02:00,521
the same thing as
quantum efficiency.

45
00:02:00,521 --> 00:02:02,570
You'll here these two
terms used quite frequently

46
00:02:02,570 --> 00:02:03,860
the PV community.

47
00:02:03,860 --> 00:02:06,910
Now, I would say we're really
starting to get sophisticated

48
00:02:06,910 --> 00:02:07,950
about their use.

49
00:02:07,950 --> 00:02:11,130
In the very beginning of
the field-- well let's

50
00:02:11,130 --> 00:02:14,390
put it this way, in the
third wave of PV, which

51
00:02:14,390 --> 00:02:19,740
began at around late 1990s
early 2000s, which was really

52
00:02:19,740 --> 00:02:23,090
when, say, some of
the novel materials--

53
00:02:23,090 --> 00:02:26,410
quantum dot-based solar cells,
some modern organic material

54
00:02:26,410 --> 00:02:28,770
based solar cells-- really
started to take off,

55
00:02:28,770 --> 00:02:31,610
there wasn't that sophisticated
of understanding of some

56
00:02:31,610 --> 00:02:33,040
of the nomenclature in PV.

57
00:02:33,040 --> 00:02:35,360
And so terms were used
in a confusing way.

58
00:02:35,360 --> 00:02:37,820
When you read some of the papers
back from the early 2000s,

59
00:02:37,820 --> 00:02:39,130
you might pick up
on some of this.

60
00:02:39,130 --> 00:02:41,530
And So that's why I have this
slide right here describing

61
00:02:41,530 --> 00:02:43,155
very clearly what is
quantum efficiency

62
00:02:43,155 --> 00:02:45,329
and what is energy
conversion efficiency.

63
00:02:45,329 --> 00:02:47,870
So energy conversion efficiency
is pretty easy to understand.

64
00:02:47,870 --> 00:02:49,390
We've been talking
about that all class.

65
00:02:49,390 --> 00:02:50,848
We've been talking
about how photon

66
00:02:50,848 --> 00:02:52,690
comes in with a certain
amount of energy.

67
00:02:52,690 --> 00:02:55,230
And you extract electrons
for your solar cell device

68
00:02:55,230 --> 00:02:56,730
that of a certain
amount of energy.

69
00:02:56,730 --> 00:02:59,188
And that ratio would be the
energy conversion efficiencies,

70
00:02:59,188 --> 00:03:01,520
essentially the
energy coming out

71
00:03:01,520 --> 00:03:03,760
divided by the energy going in.

72
00:03:03,760 --> 00:03:08,570
So if, for example, one
photon comes in with three EV

73
00:03:08,570 --> 00:03:10,770
and generates an electron
hole pair, which is then

74
00:03:10,770 --> 00:03:15,420
extracted from the device with
a voltage of say 0.6 volts,

75
00:03:15,420 --> 00:03:16,920
we would have an
energy conversion

76
00:03:16,920 --> 00:03:20,300
efficiency less than 1,
somewhere around 15% or so.

77
00:03:20,300 --> 00:03:24,280
Whereas if we looked
at quantum efficiency

78
00:03:24,280 --> 00:03:26,960
and define quantum efficiency
as the number of electrons

79
00:03:26,960 --> 00:03:29,820
out per incident
photon, that means

80
00:03:29,820 --> 00:03:32,460
if we have one photon coming
in and one electron coming out

81
00:03:32,460 --> 00:03:37,020
of our device, we have a quantum
efficiency of 1, or 100%.

82
00:03:37,020 --> 00:03:38,970
So quantum efficiency
can be thought

83
00:03:38,970 --> 00:03:40,990
of as collection efficiency.

84
00:03:40,990 --> 00:03:43,450
It means how many electron hole
pairs were generated inside

85
00:03:43,450 --> 00:03:45,200
of the device, and how
many were collected

86
00:03:45,200 --> 00:03:47,022
coming out of the device.

87
00:03:47,022 --> 00:03:48,730
There's a little bit
more to it than that

88
00:03:48,730 --> 00:03:50,479
dealing with reflectivity
off the surface.

89
00:03:50,479 --> 00:03:51,900
I'll get to that slide or two.

90
00:03:51,900 --> 00:03:54,316
But it can be thought of roughly
as collection efficiency,

91
00:03:54,316 --> 00:03:56,540
as whereas energy conversion
efficiency is really

92
00:03:56,540 --> 00:03:58,790
what you think of in terms
of thermodynamic efficiency

93
00:03:58,790 --> 00:04:00,640
of a device.

94
00:04:00,640 --> 00:04:01,730
Why is this important?

95
00:04:01,730 --> 00:04:04,600
Well, there are
papers out there--

96
00:04:04,600 --> 00:04:07,200
this is an old one, I think,
in nature of materials,

97
00:04:07,200 --> 00:04:11,110
if I'm not mistaken,
that started

98
00:04:11,110 --> 00:04:12,420
using a bunch of terms, right.

99
00:04:12,420 --> 00:04:16,649
So under 5 volts
bias and illumination

100
00:04:16,649 --> 00:04:19,940
from a 975 nanometer
laser-- so nothing

101
00:04:19,940 --> 00:04:21,480
like a polychromatic
solar spectrum,

102
00:04:21,480 --> 00:04:23,440
this is a monochromatic
light source--

103
00:04:23,440 --> 00:04:27,800
our detectors show an internal
quantum efficiency of 3%.

104
00:04:27,800 --> 00:04:30,700
The photovoltaic response
under this monochromatic light

105
00:04:30,700 --> 00:04:33,620
results in a maximum open
circuit voltage of so and so,

106
00:04:33,620 --> 00:04:38,150
a short circuit current 350
nanoamps-- very, very tiny--

107
00:04:38,150 --> 00:04:41,040
and a short circuit current
internal quantum efficiency

108
00:04:41,040 --> 00:04:44,090
of 0.006%.

109
00:04:44,090 --> 00:04:45,760
So what they're
talking about here

110
00:04:45,760 --> 00:04:50,780
is a quantum
efficiency of 0.006%.

111
00:04:50,780 --> 00:04:53,150
As we've already done just
by the simple example the 3 V

112
00:04:53,150 --> 00:04:54,941
phonon coming in and
exciting electron hole

113
00:04:54,941 --> 00:04:57,620
pair, quantum efficiency
of 1 but energy conversion

114
00:04:57,620 --> 00:04:59,820
efficiency below
20%, we can already

115
00:04:59,820 --> 00:05:01,990
guess that the energy
conversion efficiency

116
00:05:01,990 --> 00:05:04,630
of a device like this, even
for monochromatic light,

117
00:05:04,630 --> 00:05:07,260
is going to be very low.

118
00:05:07,260 --> 00:05:12,010
So the reason I'm highlighting
this abstract right here

119
00:05:12,010 --> 00:05:16,810
is because it's a great
example of the plethora

120
00:05:16,810 --> 00:05:19,750
of different terms that you
can find in reading a paper.

121
00:05:19,750 --> 00:05:24,170
And if you focus on just a few
of them, like oh, 3%-- wow,

122
00:05:24,170 --> 00:05:26,030
that's awesome, 3%
device efficiency.

123
00:05:26,030 --> 00:05:28,150
No, it's not energy
conversion efficiency.

124
00:05:28,150 --> 00:05:32,630
That's the quantum efficiency
under a very specific bias

125
00:05:32,630 --> 00:05:35,340
condition, reverse bias is
like a photo detector, not

126
00:05:35,340 --> 00:05:38,860
a solar cell, not under
forward bias conditions.

127
00:05:38,860 --> 00:05:41,000
OK, so what does
this really mean,

128
00:05:41,000 --> 00:05:46,240
this 0.006% short circuit
internal quantum efficiency?

129
00:05:46,240 --> 00:05:48,900
Well, we defined our energy
conversion efficiency

130
00:05:48,900 --> 00:05:51,400
or solar conversion efficiency
as power out divided by power

131
00:05:51,400 --> 00:05:52,600
in.

132
00:05:52,600 --> 00:05:55,330
That was done in the
previous lectures.

133
00:05:55,330 --> 00:05:58,680
The power out to would
the power and the current

134
00:05:58,680 --> 00:06:01,120
and the voltage product at the
maximum power point divided

135
00:06:01,120 --> 00:06:03,164
by the solar flux coming in.

136
00:06:03,164 --> 00:06:04,830
And that would be
equivalent to the fill

137
00:06:04,830 --> 00:06:07,371
factor times the short circuit
current times the open circuit

138
00:06:07,371 --> 00:06:08,320
voltage.

139
00:06:08,320 --> 00:06:11,420
And typical values for
energy conversion efficiency

140
00:06:11,420 --> 00:06:14,700
are in the 12% to 20%
range, I would say.

141
00:06:14,700 --> 00:06:17,600
Maybe less than 10% for
emerging technologies.

142
00:06:17,600 --> 00:06:19,700
But these are typical values.

143
00:06:19,700 --> 00:06:23,610
And the solar flux, the
illumination intensity

144
00:06:23,610 --> 00:06:24,490
might vary as well.

145
00:06:24,490 --> 00:06:29,180
But typically we talk about
one sun, or AM 1.5 illumination

146
00:06:29,180 --> 00:06:29,930
conditions, right.

147
00:06:29,930 --> 00:06:32,665
So that's our spectrum
at AM 1.5 conditions,

148
00:06:32,665 --> 00:06:35,060
what we did on
homework number one.

149
00:06:35,060 --> 00:06:38,715
Now the quantum efficiency
has two flavors.

150
00:06:38,715 --> 00:06:40,465
One we'll call external
quantum efficiency

151
00:06:40,465 --> 00:06:42,215
and the other internal
quantum efficiency.

152
00:06:42,215 --> 00:06:43,923
And basically the
difference between them

153
00:06:43,923 --> 00:06:46,240
is the reflectance off the
front surface of the device.

154
00:06:46,240 --> 00:06:49,830
The internal quantum
efficiency essentially

155
00:06:49,830 --> 00:06:51,230
factors out the reflectance.

156
00:06:51,230 --> 00:06:54,670
The external quantum efficiency
is really taking reflectance

157
00:06:54,670 --> 00:06:56,110
into account as well.

158
00:06:56,110 --> 00:06:58,090
So external quantum
efficiency is

159
00:06:58,090 --> 00:07:02,380
defined as electrons out per
photons toward the device.

160
00:07:02,380 --> 00:07:04,520
We say photons in,
but this is really

161
00:07:04,520 --> 00:07:07,519
how many photons are impingent
upon the device itself.

162
00:07:07,519 --> 00:07:09,310
Some of those photons
will be reflected off

163
00:07:09,310 --> 00:07:10,450
the front surface.

164
00:07:10,450 --> 00:07:12,250
Other photons will
go into the device

165
00:07:12,250 --> 00:07:13,659
and generate
electron hole pairs.

166
00:07:13,659 --> 00:07:15,450
Or some will go straight
through the device

167
00:07:15,450 --> 00:07:18,420
and be absorbed in the
back surface or so forth.

168
00:07:18,420 --> 00:07:22,300
So the EQE, external quantum
efficiency, typical peak

169
00:07:22,300 --> 00:07:26,490
values range between
60% and 90% depending

170
00:07:26,490 --> 00:07:30,540
on the reflectivity for
moderate efficiency devices.

171
00:07:30,540 --> 00:07:33,740
So the reason peak
values ranging 60 to 90

172
00:07:33,740 --> 00:07:37,170
is because there's going to
be some band of wavelengths

173
00:07:37,170 --> 00:07:39,660
at which the solar cell
really responds well.

174
00:07:39,660 --> 00:07:42,870
It's really efficient at
converting those photons

175
00:07:42,870 --> 00:07:44,560
into electron hole pairs.

176
00:07:44,560 --> 00:07:47,030
And were the sun-- instead
of a beautiful polychromatic

177
00:07:47,030 --> 00:07:50,310
blackbody emission
source-- if the sun where

178
00:07:50,310 --> 00:07:52,280
a monochromatic
light source tuned

179
00:07:52,280 --> 00:07:54,430
to that particular
wavelength, the solar cell

180
00:07:54,430 --> 00:07:55,910
would be wicked efficient.

181
00:07:55,910 --> 00:07:56,810
But it's not.

182
00:07:56,810 --> 00:08:00,725
So this is why EQE is
an interesting parameter

183
00:08:00,725 --> 00:08:02,770
is because it tells
you the response

184
00:08:02,770 --> 00:08:06,290
of the solar cell to
different spectral conditions.

185
00:08:06,290 --> 00:08:08,780
And that's why we sometimes
call it spectral response

186
00:08:08,780 --> 00:08:10,550
of a solar cell device.

187
00:08:10,550 --> 00:08:12,024
By the way, those
who need notes,

188
00:08:12,024 --> 00:08:13,940
if you would be so kind
as to raise your hand,

189
00:08:13,940 --> 00:08:18,124
Joe will pass them around as
well so we can have enough

190
00:08:18,124 --> 00:08:19,290
for everybody to write down.

191
00:08:22,490 --> 00:08:26,630
Any questions thus far on EQE,
external quantum efficiency,

192
00:08:26,630 --> 00:08:29,850
the difference between QE and
the difference between ECE,

193
00:08:29,850 --> 00:08:35,040
or shall we say, the energy
conversion efficiency?

194
00:08:35,040 --> 00:08:35,539
Okay.

195
00:08:35,539 --> 00:08:37,864
AUDIENCE: Quantum
efficiencies, they also

196
00:08:37,864 --> 00:08:39,570
include [INAUDIBLE]
photons, right?

197
00:08:39,570 --> 00:08:41,638
Or do they just
include photons which

198
00:08:41,638 --> 00:08:43,679
have a potential to make
an electron [INAUDIBLE]?

199
00:08:43,679 --> 00:08:48,170
PROFESSOR: In principle,
QE, or sorry, EQE,

200
00:08:48,170 --> 00:08:51,440
should have EQE as a
function of lambda, really.

201
00:08:51,440 --> 00:08:53,960
And the photon in
is going to be,

202
00:08:53,960 --> 00:08:56,640
obviously, at a certain
wavelength usually.

203
00:08:56,640 --> 00:09:01,600
I've rarely heard EQE given
in a polychromatic sense where

204
00:09:01,600 --> 00:09:03,209
they take an entire
solar spectrum

205
00:09:03,209 --> 00:09:05,000
and measure the quantum
efficiency average.

206
00:09:05,000 --> 00:09:07,940
Usually quantum efficiency
is measured wavelength

207
00:09:07,940 --> 00:09:08,870
by wavelength.

208
00:09:08,870 --> 00:09:12,420
And so you might change
your monochrometer settings

209
00:09:12,420 --> 00:09:14,650
20 or 30 times
over, or even more,

210
00:09:14,650 --> 00:09:16,840
over a quantum efficiency
measurement to really

211
00:09:16,840 --> 00:09:18,700
map out the entire
solar spectrum

212
00:09:18,700 --> 00:09:20,500
from short wavelengths
in the ultraviolet

213
00:09:20,500 --> 00:09:22,060
all the way to longer
wavelength and the infrared.

214
00:09:22,060 --> 00:09:23,226
And you're absolutely right.

215
00:09:23,226 --> 00:09:25,200
Some of those wavelengths,
the photo response

216
00:09:25,200 --> 00:09:27,330
of the solar cell will
be very close to 0

217
00:09:27,330 --> 00:09:29,690
because it just doesn't respond
well at that wavelength.

218
00:09:29,690 --> 00:09:31,340
Maybe the wavelength
is too short

219
00:09:31,340 --> 00:09:33,340
and is being absorbed
by some surface layer.

220
00:09:33,340 --> 00:09:35,839
Or maybe the wavelength is too
long it's just going straight

221
00:09:35,839 --> 00:09:37,730
through [INAUDIBLE] photon.

222
00:09:37,730 --> 00:09:39,700
Whereas energy conversion
efficiency is really

223
00:09:39,700 --> 00:09:45,360
taking the entire solar
spectrum and matching or testing

224
00:09:45,360 --> 00:09:47,750
the energy, the power
coming out of the solar cell

225
00:09:47,750 --> 00:09:49,690
versus the power going in.

226
00:09:49,690 --> 00:09:51,830
So a typical quantum
efficiency curve

227
00:09:51,830 --> 00:09:54,000
might look something like this.

228
00:09:54,000 --> 00:09:55,830
Let's walk through the
axes first and then

229
00:09:55,830 --> 00:09:57,130
talk about the curve.

230
00:09:57,130 --> 00:10:01,180
So the axes, we have wavelength
on the x-axis, on the abscissa.

231
00:10:01,180 --> 00:10:03,770
Then on the ordinate, we
have quantum efficiency.

232
00:10:03,770 --> 00:10:05,720
Wavelength is varying
from, let's say,

233
00:10:05,720 --> 00:10:09,630
the ultraviolet to the
infrared and beyond.

234
00:10:09,630 --> 00:10:13,050
Well, beyond the red into the
near infrared and probably

235
00:10:13,050 --> 00:10:15,220
ending somewhere on
the mid-infrared.

236
00:10:15,220 --> 00:10:18,950
And the quantum efficiency
extends from 0 to 1,

237
00:10:18,950 --> 00:10:22,390
in other words from 0% to 100%.

238
00:10:22,390 --> 00:10:26,330
And we have this box that's
represented by this maroon line

239
00:10:26,330 --> 00:10:29,870
right here entitled
Ideal Quantum Efficiency.

240
00:10:29,870 --> 00:10:33,420
And this would be if at the
band gap energy, all of a sudden

241
00:10:33,420 --> 00:10:37,080
our quantum efficiency turned
on to 100% and cut across.

242
00:10:37,080 --> 00:10:39,740
And this was the assumption
that we made in our homework,

243
00:10:39,740 --> 00:10:43,220
that the solar cell device would
respond in this ideal manner.

244
00:10:43,220 --> 00:10:46,580
In reality, at longer
wavelengths here,

245
00:10:46,580 --> 00:10:47,950
what's going on?

246
00:10:47,950 --> 00:10:50,280
Why would there be a decrease
of the quantum efficiency

247
00:10:50,280 --> 00:10:53,080
at longer wavelengths?

248
00:10:53,080 --> 00:10:54,540
What effect is happening there?

249
00:10:54,540 --> 00:10:56,252
AUDIENCE: [INAUDIBLE].

250
00:10:56,252 --> 00:10:59,030
PROFESSOR: Yeah, the absorption
coefficient is dropping.

251
00:10:59,030 --> 00:11:02,020
And this light is starting to
go straight through the device.

252
00:11:02,020 --> 00:11:03,810
There's a growing
fraction of photons

253
00:11:03,810 --> 00:11:06,890
that are not being absorbed
by the solar cell device.

254
00:11:06,890 --> 00:11:09,950
In the very short wavelengths
right here, as I said before,

255
00:11:09,950 --> 00:11:12,210
oftentimes there's
a dead layer right

256
00:11:12,210 --> 00:11:16,470
near the surface of the device
that's impeding good electron

257
00:11:16,470 --> 00:11:20,710
hole pair charge separation
and eventually a collection.

258
00:11:20,710 --> 00:11:22,500
And right here in
the middle, there's

259
00:11:22,500 --> 00:11:25,350
a slow but steady decrease
of the quantum efficiency

260
00:11:25,350 --> 00:11:26,840
typically.

261
00:11:26,840 --> 00:11:30,354
These are photons that are being
absorbed in the absorber layer.

262
00:11:30,354 --> 00:11:32,520
If you think about your
solar cell in cross section,

263
00:11:32,520 --> 00:11:34,190
here's your solar
cell in cross section,

264
00:11:34,190 --> 00:11:35,890
these are photos being
absorbed in the absorber

265
00:11:35,890 --> 00:11:38,265
layer generating electron hole
pairs which are then being

266
00:11:38,265 --> 00:11:40,230
separated by the junction.

267
00:11:40,230 --> 00:11:42,334
And as we go to longer
and longer wavelengths,

268
00:11:42,334 --> 00:11:44,750
if you remember your optical
absorption coefficient begins

269
00:11:44,750 --> 00:11:47,439
dropping, that means that
the penetration depth

270
00:11:47,439 --> 00:11:48,980
of the light, the
average penetration

271
00:11:48,980 --> 00:11:50,840
that the light is increasing.

272
00:11:50,840 --> 00:11:52,930
And so the average distance
that the electron hole

273
00:11:52,930 --> 00:11:56,390
pairs are being generated from
the junction is increasing.

274
00:11:56,390 --> 00:11:58,900
So in other words, as we
go from short wavelengths

275
00:11:58,900 --> 00:12:01,510
to longer wavelengths,
the distance

276
00:12:01,510 --> 00:12:03,540
from which the
electron hole pairs

277
00:12:03,540 --> 00:12:06,760
are being generated from
the junction is increasing.

278
00:12:06,760 --> 00:12:08,820
That means that the electron
hole pairs generated

279
00:12:08,820 --> 00:12:10,570
at these wavelengths
have further

280
00:12:10,570 --> 00:12:13,760
to travel to reach the junction
than those electron hole

281
00:12:13,760 --> 00:12:15,350
pairs generated at
these wavelengths

282
00:12:15,350 --> 00:12:17,590
closer to the front surface.

283
00:12:17,590 --> 00:12:19,800
And since there's a
finite probability

284
00:12:19,800 --> 00:12:23,020
that the electron hole
pair will recombine

285
00:12:23,020 --> 00:12:25,100
as it travels
through the material,

286
00:12:25,100 --> 00:12:29,570
that's why you get this very
slow but steady decrease

287
00:12:29,570 --> 00:12:33,230
of quantum efficiency over
the mid-wavelength range.

288
00:12:33,230 --> 00:12:35,250
And on Tuesday we'll
talk more about that.

289
00:12:38,330 --> 00:12:40,030
Internal quantum efficiency.

290
00:12:40,030 --> 00:12:43,680
So for those who
say, well you know,

291
00:12:43,680 --> 00:12:45,740
there's a certain
delta right here

292
00:12:45,740 --> 00:12:49,930
between 1 and my
maximum response, here

293
00:12:49,930 --> 00:12:51,710
my maximum quantum efficiency.

294
00:12:51,710 --> 00:12:53,900
And I suspect that's
really due to the fact

295
00:12:53,900 --> 00:12:56,410
that a certain
percentage of my photons

296
00:12:56,410 --> 00:12:58,830
are being reflected
off the front surface.

297
00:12:58,830 --> 00:13:00,360
I know how to
calculate reflectance.

298
00:13:00,360 --> 00:13:03,485
We did that in lecture number
two or three, I believe.

299
00:13:03,485 --> 00:13:05,110
So we know how to
calculate reflectance

300
00:13:05,110 --> 00:13:06,170
off the front surface.

301
00:13:06,170 --> 00:13:09,490
We can also measure reflectance
using a spectrophotometer.

302
00:13:09,490 --> 00:13:14,050
And what we can do is normalize
the effect of reflectance out.

303
00:13:14,050 --> 00:13:16,440
By dividing our external
quantum efficiency

304
00:13:16,440 --> 00:13:19,370
by 1 minus R, what in
effect we're doing is

305
00:13:19,370 --> 00:13:21,500
we're normalizing the
effective reflectance

306
00:13:21,500 --> 00:13:22,710
out of our measurement.

307
00:13:22,710 --> 00:13:24,810
So now we're only
considering those photons

308
00:13:24,810 --> 00:13:27,255
they get into the device.

309
00:13:27,255 --> 00:13:29,630
If you want, you can think
about the extreme cases there.

310
00:13:29,630 --> 00:13:33,352
If reflectance is 0, that means
your EQE is equal to your IQE,

311
00:13:33,352 --> 00:13:34,810
your internal
quantum efficiency is

312
00:13:34,810 --> 00:13:37,240
equal to the external
quantum efficiency.

313
00:13:37,240 --> 00:13:40,520
But if reflectance is, say,
50%, if 50% of your photons

314
00:13:40,520 --> 00:13:43,000
are being reflected off the
front surface of your device,

315
00:13:43,000 --> 00:13:44,740
now your IQE is
probably going to be

316
00:13:44,740 --> 00:13:47,950
double your external
quantum efficiency.

317
00:13:47,950 --> 00:13:52,880
And so now this is an
interesting parameter because,

318
00:13:52,880 --> 00:13:55,050
for example, in our lab
scale devices when we're

319
00:13:55,050 --> 00:13:57,510
testing them, oftentimes
we don't optimize

320
00:13:57,510 --> 00:13:58,980
for optical properties.

321
00:13:58,980 --> 00:14:00,700
Sometimes we do,
but many times where

322
00:14:00,700 --> 00:14:03,242
we're focused on the material,
we're focused on the junction,

323
00:14:03,242 --> 00:14:05,533
and we don't bother to put
the perfect entry reflective

324
00:14:05,533 --> 00:14:06,150
coating on it.

325
00:14:06,150 --> 00:14:08,000
It would take too
long to fabricate it.

326
00:14:08,000 --> 00:14:10,160
And so IQE gives
us a good metric

327
00:14:10,160 --> 00:14:11,840
of how the solar
cell is responding

328
00:14:11,840 --> 00:14:14,140
if we were to go
through all the effort

329
00:14:14,140 --> 00:14:17,950
to make the light capture
ideal for our device.

330
00:14:17,950 --> 00:14:18,590
Okay?

331
00:14:18,590 --> 00:14:23,510
And that's why we sometimes
use a report IQE in studies.

332
00:14:23,510 --> 00:14:27,140
And typical peak values
are between 80% and 98%

333
00:14:27,140 --> 00:14:29,250
for moderate efficiency devices.

334
00:14:29,250 --> 00:14:31,560
So it would essentially--
the curve would look

335
00:14:31,560 --> 00:14:33,190
very much like the EQE curve.

336
00:14:33,190 --> 00:14:38,690
It would just be boosted up
by 1 over 1 minus R. Okay?

337
00:14:41,660 --> 00:14:44,010
So any questions so far?

338
00:14:44,010 --> 00:14:46,550
Make sure we're on
the same page here.

339
00:14:46,550 --> 00:14:47,050
Yeah?

340
00:14:47,050 --> 00:14:48,020
AUDIENCE: [INAUDIBLE]?

341
00:14:51,415 --> 00:14:52,460
PROFESSOR: Absolutely.

342
00:14:52,460 --> 00:14:55,650
So IQE is a function
of wavelength.

343
00:14:55,650 --> 00:14:58,190
R, reflectivity, is also
going to be a strong function

344
00:14:58,190 --> 00:15:00,930
of wavelength because
the real component

345
00:15:00,930 --> 00:15:02,534
of the refractive
index is changing

346
00:15:02,534 --> 00:15:03,700
as a function of wavelength.

347
00:15:03,700 --> 00:15:06,920
Yeah, absolutely.

348
00:15:06,920 --> 00:15:09,660
OK, so this gives you a sense.

349
00:15:09,660 --> 00:15:13,190
Sorry for the poor choice of the
reflectivity colors right here.

350
00:15:13,190 --> 00:15:15,500
This baby blue, which is
almost impossible to see,

351
00:15:15,500 --> 00:15:17,520
but I've just traced it
out with my finger, that

352
00:15:17,520 --> 00:15:20,750
denotes the reflectivity
as a function of wavelength

353
00:15:20,750 --> 00:15:23,020
from some data that it
took as a graduate student.

354
00:15:23,020 --> 00:15:28,382
So you have some typical quantum
efficiency curves right here.

355
00:15:28,382 --> 00:15:30,590
And then the quantum efficiency
curves that are shown

356
00:15:30,590 --> 00:15:33,190
are for a pretty
poor quality device.

357
00:15:33,190 --> 00:15:37,900
And in this particular case,
I measured quantum efficiency

358
00:15:37,900 --> 00:15:40,730
under short circuit conditions,
but with different illumination

359
00:15:40,730 --> 00:15:41,820
intensities.

360
00:15:41,820 --> 00:15:44,120
So going from 0 sun
illumination all the way up

361
00:15:44,120 --> 00:15:45,420
to 1 sun illumination.

362
00:15:45,420 --> 00:15:48,620
But the device was still in
short circuit conditions.

363
00:15:48,620 --> 00:15:51,510
So what I was doing, in
effect, was flooding the device

364
00:15:51,510 --> 00:15:53,490
with more and more
and more carriers,

365
00:15:53,490 --> 00:15:57,490
and I got this boost here in
the middle wavelength range.

366
00:15:57,490 --> 00:15:59,189
I still was limited
by my surface.

367
00:15:59,189 --> 00:16:01,730
I was still limited by my band
gap and non-absorption effects

368
00:16:01,730 --> 00:16:02,560
over here.

369
00:16:02,560 --> 00:16:06,700
But in the middle, I was able
to get this boost in performance

370
00:16:06,700 --> 00:16:09,947
simply because I was filling in
trap states inside of material.

371
00:16:09,947 --> 00:16:11,530
This is an advanced
concept that we're

372
00:16:11,530 --> 00:16:14,349
going to get to over
the next few lectures.

373
00:16:14,349 --> 00:16:16,390
But it gives you a sense
of what a QE curve might

374
00:16:16,390 --> 00:16:19,710
look like for device, what the
reflectivity might look like,

375
00:16:19,710 --> 00:16:22,520
and these curves right here
were IQE, or internal quantum

376
00:16:22,520 --> 00:16:24,650
efficiency.

377
00:16:24,650 --> 00:16:28,930
OK, so take efficiency
with a grain of salt.

378
00:16:28,930 --> 00:16:31,680
When you hear somebody
reporting an efficiency value,

379
00:16:31,680 --> 00:16:34,060
ask-- think about what
efficiency is being measured.

380
00:16:34,060 --> 00:16:36,250
Is it energy conversion
efficiency?4 is it quantum

381
00:16:36,250 --> 00:16:37,120
efficiency?

382
00:16:37,120 --> 00:16:38,520
Internal, external?

383
00:16:38,520 --> 00:16:39,507
What wavelengths?

384
00:16:39,507 --> 00:16:41,590
What is the nature of the
light being used, right?

385
00:16:41,590 --> 00:16:45,730
Is a 1 sun illumination source
that has been well calibrated

386
00:16:45,730 --> 00:16:49,550
to within 2% spectral
fidelity, spatial uniformity,

387
00:16:49,550 --> 00:16:50,599
temporal stability?

388
00:16:50,599 --> 00:16:52,390
Is it a really bona
fide good light source?

389
00:16:52,390 --> 00:16:54,690
Or is this some
monochromatic light source

390
00:16:54,690 --> 00:16:56,640
that somebody set up
because they knew, aha,

391
00:16:56,640 --> 00:16:59,560
my solar cell really
responds well to, say,

392
00:16:59,560 --> 00:17:01,570
500 nanometer lights, right?

393
00:17:01,570 --> 00:17:04,339
So I'm going to test my-- I'm
going to report my values right

394
00:17:04,339 --> 00:17:05,800
at that wavelength.

395
00:17:05,800 --> 00:17:09,730
You have to take it
with a grain of salt.

396
00:17:09,730 --> 00:17:10,367
Yeah, exactly.

397
00:17:10,367 --> 00:17:11,950
And what is the
intensity of the light

398
00:17:11,950 --> 00:17:13,280
that's being used as well.

399
00:17:13,280 --> 00:17:15,630
That's very important as
we just saw right over here

400
00:17:15,630 --> 00:17:18,510
because the bulk material is
going to respond differently.

401
00:17:18,510 --> 00:17:20,611
There are certain trap
states for electrons

402
00:17:20,611 --> 00:17:21,569
inside of the material.

403
00:17:21,569 --> 00:17:22,760
And as you add more
and more light,

404
00:17:22,760 --> 00:17:23,810
you're flooding those traps.

405
00:17:23,810 --> 00:17:25,410
They become filled,
and the electrons

406
00:17:25,410 --> 00:17:27,339
can move through the
material more easily.

407
00:17:27,339 --> 00:17:29,940
That's why you get
this boost of response

408
00:17:29,940 --> 00:17:31,690
as you increase the
illumination intensity

409
00:17:31,690 --> 00:17:33,706
in this particular experiment.

410
00:17:33,706 --> 00:17:36,080
So these are all questions
that you should ask yourselves

411
00:17:36,080 --> 00:17:39,130
when you see
quantum efficiency--

412
00:17:39,130 --> 00:17:41,100
internal quantum, external
quantum efficiency

413
00:17:41,100 --> 00:17:45,470
values reported and/or energy
conversion efficiencies.

414
00:17:45,470 --> 00:17:46,840
What is really happening?

415
00:17:46,840 --> 00:17:48,350
What are they measuring?

416
00:17:48,350 --> 00:17:52,580
This right here, a paper out of
Paul Alivisatos' lab from 2002

417
00:17:52,580 --> 00:17:54,950
was, in my humble opinion,
an excellent example

418
00:17:54,950 --> 00:17:57,370
of honest efficiency reporting.

419
00:17:57,370 --> 00:18:02,267
First off, they picked
their highest values and put

420
00:18:02,267 --> 00:18:04,600
their best foot forward, and
said look we have a quantum

421
00:18:04,600 --> 00:18:08,220
efficiency over 54% , and a
monochromatic power conversion

422
00:18:08,220 --> 00:18:14,750
efficiency of 6.9% under very
low intensity light at 515

423
00:18:14,750 --> 00:18:15,500
nanometers, right.

424
00:18:15,500 --> 00:18:17,833
So first off, they put their
best foot forward and said,

425
00:18:17,833 --> 00:18:19,690
under optimal conditions
monochromatic light

426
00:18:19,690 --> 00:18:20,481
that's what we get.

427
00:18:20,481 --> 00:18:24,570
But also under air mass 1.5
global solar conditions,

428
00:18:24,570 --> 00:18:26,540
under the standard
solar spectrum,

429
00:18:26,540 --> 00:18:29,110
we obtained an energy conversion
efficiency, or a power

430
00:18:29,110 --> 00:18:31,910
conversion efficiency of 1.7%.

431
00:18:31,910 --> 00:18:34,170
So both values are put
there out on the table,

432
00:18:34,170 --> 00:18:37,360
and they say look, here's a
characterization of our device.

433
00:18:37,360 --> 00:18:38,620
So I really like this paper.

434
00:18:38,620 --> 00:18:40,590
It was back in 2002
right at the beginning

435
00:18:40,590 --> 00:18:45,190
of the new wave of new
materials in PV, so to speak,

436
00:18:45,190 --> 00:18:48,570
this third wave of PV
in the United States.

437
00:18:48,570 --> 00:18:52,120
And it was a beautiful example
of a really well-reported,

438
00:18:52,120 --> 00:18:55,560
carefully described efficiency.

439
00:18:55,560 --> 00:18:58,370
Any further thoughts
or comments before we

440
00:18:58,370 --> 00:19:00,760
jump on to the next
topics of the day?

441
00:19:00,760 --> 00:19:04,100
AUDIENCE: How do you have
a QE curve for 0 suns,

442
00:19:04,100 --> 00:19:05,564
I noticed on your plot?

443
00:19:05,564 --> 00:19:07,022
Or is that kind of
an extrapolated?

444
00:19:07,022 --> 00:19:11,620
PROFESSOR: Yeah, so this is the
bias condition-- sorry the bias

445
00:19:11,620 --> 00:19:14,960
lighting condition, not the
bias voltage as in battery,

446
00:19:14,960 --> 00:19:18,640
but bias lighting as in
I shine a light source,

447
00:19:18,640 --> 00:19:20,926
a polychromatic light
source at my material.

448
00:19:20,926 --> 00:19:22,550
I believe in that
case it was a halogen

449
00:19:22,550 --> 00:19:26,010
lamp with a series of filters
to simulate the solar spectrum.

450
00:19:26,010 --> 00:19:29,660
And obviously you can't
measure a quantum efficiency

451
00:19:29,660 --> 00:19:32,290
without having some
light involved.

452
00:19:32,290 --> 00:19:35,280
And so the light that was being
generated by the monochrometer

453
00:19:35,280 --> 00:19:39,530
was much lower in intensity
than these illumination

454
00:19:39,530 --> 00:19:40,450
intensities here.

455
00:19:40,450 --> 00:19:42,370
And so it was more of
a perturbation on top

456
00:19:42,370 --> 00:19:43,840
of a steady-state background.

457
00:19:43,840 --> 00:19:46,150
And we ran the measurement
exactly those conditions.

458
00:19:46,150 --> 00:19:47,980
We had a steady-state
background light,

459
00:19:47,980 --> 00:19:51,730
and then we chopped the
monochrometer light coming in ,

460
00:19:51,730 --> 00:19:54,040
and used a lock in amplifier
to track that particular

461
00:19:54,040 --> 00:19:54,710
frequency.

462
00:19:54,710 --> 00:19:56,710
So we were able to detect
the small perturbation

463
00:19:56,710 --> 00:19:58,800
due to the monochromatic
light coming in on top

464
00:19:58,800 --> 00:20:01,580
of the steady background.

465
00:20:01,580 --> 00:20:02,080
Yeah?

466
00:20:02,080 --> 00:20:03,968
AUDIENCE: There's no
international centers

467
00:20:03,968 --> 00:20:06,328
to report efficiency
or convention?

468
00:20:06,328 --> 00:20:07,290
PROFESSOR: There are.

469
00:20:07,290 --> 00:20:09,340
There are conventions,
international conventions,

470
00:20:09,340 --> 00:20:11,900
to report energy
conversion efficiencies.

471
00:20:11,900 --> 00:20:14,800
And I believe there might also
be for quantum efficiencies

472
00:20:14,800 --> 00:20:15,510
as well.

473
00:20:15,510 --> 00:20:16,740
Let me look into that.

474
00:20:16,740 --> 00:20:19,980
Why don't we take note of that
and bring back the precise ASDM

475
00:20:19,980 --> 00:20:21,560
standards next time.

476
00:20:21,560 --> 00:20:25,080
And I believe also there are
other entities like IEC that

477
00:20:25,080 --> 00:20:27,800
have their own systems for it.

478
00:20:27,800 --> 00:20:31,780
There about four
laboratories worldwide

479
00:20:31,780 --> 00:20:37,240
that are authorized to
give standard efficiency

480
00:20:37,240 --> 00:20:37,790
measurements.

481
00:20:37,790 --> 00:20:41,204
So they have very carefully
calibrated quantum efficiency

482
00:20:41,204 --> 00:20:43,120
measurement devices,
very carefully calibrated

483
00:20:43,120 --> 00:20:44,250
solar simulators.

484
00:20:44,250 --> 00:20:48,280
And if you really think you
have a record efficiency cell,

485
00:20:48,280 --> 00:20:50,700
you should get it checked at
one of those laboratories.

486
00:20:50,700 --> 00:20:53,430
You shouldn't just report
what you have coming up

487
00:20:53,430 --> 00:20:54,829
your lab-based system.

488
00:20:54,829 --> 00:20:57,370
You may even want to go around
to a few different labs at MIT

489
00:20:57,370 --> 00:21:00,190
first because one might
have a better calibrated

490
00:21:00,190 --> 00:21:01,500
solar simulator than another.

491
00:21:01,500 --> 00:21:03,210
What we're going
to do now is dive

492
00:21:03,210 --> 00:21:05,460
into some of the
common factors that

493
00:21:05,460 --> 00:21:09,350
cause solar cell IV curves to
deviate from normal ideal diode

494
00:21:09,350 --> 00:21:10,620
model.

495
00:21:10,620 --> 00:21:13,000
We're going to talk about
shunt and series resistance,

496
00:21:13,000 --> 00:21:15,340
recombination
currents-- maybe we'll

497
00:21:15,340 --> 00:21:17,440
get to current crowding,
some other effects.

498
00:21:17,440 --> 00:21:19,315
Basically what we're
doing now in number two,

499
00:21:19,315 --> 00:21:20,731
is we're beginning
to say, OK, now

500
00:21:20,731 --> 00:21:22,280
that we understand
an ideal diode,

501
00:21:22,280 --> 00:21:24,040
now that we have an
ideal picture of how

502
00:21:24,040 --> 00:21:26,820
our solar cell works, let's
bring it down to real life

503
00:21:26,820 --> 00:21:29,232
and talk about all the
things that can go wrong.

504
00:21:29,232 --> 00:21:31,440
Because when you try to make
a solar cell in the lab,

505
00:21:31,440 --> 00:21:32,898
these are the things
that are going

506
00:21:32,898 --> 00:21:35,240
to start nipping at
your heels, so to speak.

507
00:21:35,240 --> 00:21:37,860
So we'll start out with
an equivalent circuit

508
00:21:37,860 --> 00:21:40,590
diagram of a solar cell device.

509
00:21:40,590 --> 00:21:42,500
And this might be
new to some folks,

510
00:21:42,500 --> 00:21:44,930
but it's all stuff
you've seen so far.

511
00:21:44,930 --> 00:21:47,860
What we have over here is
the current generation source

512
00:21:47,860 --> 00:21:51,530
of the solar cell operating
under forward bias conditions,

513
00:21:51,530 --> 00:21:54,800
under illumination, generating
a voltage and a current.

514
00:21:54,800 --> 00:21:56,960
We have a diode
here that prevents

515
00:21:56,960 --> 00:21:58,480
the back flow of
current, and forces

516
00:21:58,480 --> 00:22:02,170
the current to go out through
the external circuit loop.

517
00:22:02,170 --> 00:22:04,695
And it forces it to drive
the external load, which

518
00:22:04,695 --> 00:22:06,820
would be attached to that
little circle over there,

519
00:22:06,820 --> 00:22:08,650
and that other little
circle over there.

520
00:22:08,650 --> 00:22:10,108
So you can imagine
external circuit

521
00:22:10,108 --> 00:22:12,110
attaching itself right there.

522
00:22:12,110 --> 00:22:16,130
So the diode-- if the diode
quality is high, if it's good,

523
00:22:16,130 --> 00:22:18,210
it will prevent the
backflow of current.

524
00:22:18,210 --> 00:22:20,550
If the diode
quality is poor, you

525
00:22:20,550 --> 00:22:23,860
will have so-called leakage
current, current leaking

526
00:22:23,860 --> 00:22:26,179
into the diode back-- if
you want to think about

527
00:22:26,179 --> 00:22:28,720
under forward bias conditions,
here's your solar cell forward

528
00:22:28,720 --> 00:22:29,380
bias.

529
00:22:29,380 --> 00:22:31,620
You have light, your
electrons coming in,

530
00:22:31,620 --> 00:22:34,149
separated by the electric field.

531
00:22:34,149 --> 00:22:35,690
Instead of powering
the external load

532
00:22:35,690 --> 00:22:37,840
and coming back into the
device through the back,

533
00:22:37,840 --> 00:22:40,170
leakage current would be
the electrons going back

534
00:22:40,170 --> 00:22:43,030
up the barrier, going
back into the base

535
00:22:43,030 --> 00:22:46,970
of the device, the
so-called diffusion current.

536
00:22:46,970 --> 00:22:49,510
So this is that diode right
here representing the diffusion

537
00:22:49,510 --> 00:22:52,420
current, or in that
particular case,

538
00:22:52,420 --> 00:22:55,080
in the ideal, the
equivalent circuit diagram,

539
00:22:55,080 --> 00:22:57,390
this is representing the
resistance to diffusion,

540
00:22:57,390 --> 00:22:58,410
if you will.

541
00:22:58,410 --> 00:23:01,270
So we have this voltage
and current being generated

542
00:23:01,270 --> 00:23:04,020
by the solar cell, and
that would be described

543
00:23:04,020 --> 00:23:05,870
by the ideal diode equation.

544
00:23:05,870 --> 00:23:09,310
My apologies, there should be
actually a x of this minus 1

545
00:23:09,310 --> 00:23:09,830
right there.

546
00:23:09,830 --> 00:23:11,621
We should take note of
that and correct it.

547
00:23:11,621 --> 00:23:14,060
I just happened to notice that.

548
00:23:14,060 --> 00:23:16,510
OK, so the ideal diode
equation is right here.

549
00:23:16,510 --> 00:23:19,670
And this is the current
density versus voltage.

550
00:23:19,670 --> 00:23:26,110
So we have in linear
log scale or axes,

551
00:23:26,110 --> 00:23:27,650
we have a straight line.

552
00:23:27,650 --> 00:23:29,590
That would mean
on a linear scale,

553
00:23:29,590 --> 00:23:32,640
we would have an
exponential curve.

554
00:23:32,640 --> 00:23:36,720
So an exponential function,
exponential curve up here,

555
00:23:36,720 --> 00:23:41,950
and a straight line
in linear log scale.

556
00:23:41,950 --> 00:23:43,660
I'm trying to sensitize
you to the two

557
00:23:43,660 --> 00:23:47,330
ways of looking at this,
both a linear scale and a log

558
00:23:47,330 --> 00:23:51,220
scale of current in the y-axis
because both will tell us

559
00:23:51,220 --> 00:23:52,550
something.

560
00:23:52,550 --> 00:23:55,190
From the linear scale up
here in the upper right,

561
00:23:55,190 --> 00:23:58,016
it will be very easy for
us to see the fill factor.

562
00:23:58,016 --> 00:23:59,890
We can just glance at
that curve and see, oh,

563
00:23:59,890 --> 00:24:01,440
it looks really box like.

564
00:24:01,440 --> 00:24:03,310
It must have a
large fill factor.

565
00:24:03,310 --> 00:24:06,550
From this curve down here we
can begin to see deviations

566
00:24:06,550 --> 00:24:07,630
from ideality.

567
00:24:07,630 --> 00:24:10,430
If anything causes this curve
to bend up or down, either

568
00:24:10,430 --> 00:24:11,920
down here or up
here, we're going

569
00:24:11,920 --> 00:24:15,110
to see it really quick
on the log scale.

570
00:24:15,110 --> 00:24:19,450
And that's why looking at the IV
curve in both ways is helpful.

571
00:24:19,450 --> 00:24:23,206
It's a method of diagnosing
the problem quickly.

572
00:24:23,206 --> 00:24:25,830
So what we're going to do now is
to take our equivalent circuit

573
00:24:25,830 --> 00:24:28,780
and begin adding a
few things to it that

574
00:24:28,780 --> 00:24:33,532
represent realistic effects that
we might see in a real device.

575
00:24:33,532 --> 00:24:34,990
So the first thing
that we might do

576
00:24:34,990 --> 00:24:38,090
is say, well listen, a real
device has a finite series

577
00:24:38,090 --> 00:24:39,550
resistance.

578
00:24:39,550 --> 00:24:41,560
And that can come from
a variety of sources.

579
00:24:41,560 --> 00:24:43,590
We'll talk about those
in a few minutes.

580
00:24:43,590 --> 00:24:45,846
But we might add a series
resistance component

581
00:24:45,846 --> 00:24:46,470
right up there.

582
00:24:46,470 --> 00:24:47,299
So let's look back.

583
00:24:47,299 --> 00:24:49,590
I'm going to flip back and
forth between the two slides

584
00:24:49,590 --> 00:24:51,820
just so folks can really
see what the difference is.

585
00:24:51,820 --> 00:24:52,940
This was the ideal case.

586
00:24:52,940 --> 00:24:54,510
That's the with
series resistance,

587
00:24:54,510 --> 00:24:57,910
again ideal with series up
there in the equivalent circuit.

588
00:24:57,910 --> 00:24:58,510
Great.

589
00:24:58,510 --> 00:24:59,384
So what have we done?

590
00:24:59,384 --> 00:25:01,950
Well, we've added a series
resistance component

591
00:25:01,950 --> 00:25:04,490
which is essentially
dropping the voltage output

592
00:25:04,490 --> 00:25:06,320
of our solar cell.

593
00:25:06,320 --> 00:25:07,750
And notice what else happened.

594
00:25:07,750 --> 00:25:09,626
Now we have a
nonlinear equation.

595
00:25:09,626 --> 00:25:11,000
Our current density
is a function

596
00:25:11,000 --> 00:25:13,790
of our current density.

597
00:25:13,790 --> 00:25:19,130
So this is becoming
more difficult to solve

598
00:25:19,130 --> 00:25:20,251
analytically.

599
00:25:20,251 --> 00:25:22,250
And what is happening to
our IV characteristics?

600
00:25:22,250 --> 00:25:25,620
Well, let's look-- we'll go back
once again to our ideal diode

601
00:25:25,620 --> 00:25:26,690
equation right here.

602
00:25:26,690 --> 00:25:29,120
We have a very sharp
box-like IV curve

603
00:25:29,120 --> 00:25:30,360
under the ideal conditions.

604
00:25:30,360 --> 00:25:32,610
Now when we introduce the
series resistance component,

605
00:25:32,610 --> 00:25:36,260
we begin smoothing
out that IV curve.

606
00:25:36,260 --> 00:25:38,180
The fill factor has dropped.

607
00:25:38,180 --> 00:25:38,870
Take a look.

608
00:25:38,870 --> 00:25:41,760
Ideal conditions, sharp,
very large fill factor.

609
00:25:41,760 --> 00:25:43,760
Now we've added the series
resistance component,

610
00:25:43,760 --> 00:25:46,720
the fill factor
has begun dropping.

611
00:25:46,720 --> 00:25:48,390
If we look at it
in log scale, it's

612
00:25:48,390 --> 00:25:51,110
very easy to detect
that series resistance.

613
00:25:51,110 --> 00:25:52,670
We can see it right here.

614
00:25:52,670 --> 00:25:54,270
This used to be
our curve, right?

615
00:25:54,270 --> 00:25:57,590
So again, this was the
ideal case, straight line.

616
00:25:57,590 --> 00:26:00,780
Again, this is log of current
verses linear voltage.

617
00:26:00,780 --> 00:26:03,340
So the x-axis of the two
plots here are the same.

618
00:26:03,340 --> 00:26:05,820
I'm only changing the
y-axis from linear scale

619
00:26:05,820 --> 00:26:07,420
up there to log scale down here.

620
00:26:07,420 --> 00:26:08,420
And notice what happens.

621
00:26:08,420 --> 00:26:10,128
If I add the series
resistance component,

622
00:26:10,128 --> 00:26:13,850
now I begin dropping off.

623
00:26:13,850 --> 00:26:16,410
So this is a telltale sign
when you take an IV curve

624
00:26:16,410 --> 00:26:19,580
and you see that, then you have
some series resistance effect

625
00:26:19,580 --> 00:26:22,290
inside of your external
circuit or your solar cell,

626
00:26:22,290 --> 00:26:24,101
or some combination of the two.

627
00:26:24,101 --> 00:26:24,600
Yes, Ashley?

628
00:26:24,600 --> 00:26:29,090
ASHLEY: So from this curve it
looks the series resistance

629
00:26:29,090 --> 00:26:30,938
really only starts
to have an effect

630
00:26:30,938 --> 00:26:31,790
once you have a higher voltage.

631
00:26:31,790 --> 00:26:32,620
PROFESSOR: Absolutely.

632
00:26:32,620 --> 00:26:35,070
And that, you can begin to
see directly from the equation

633
00:26:35,070 --> 00:26:36,600
right here as well.

634
00:26:36,600 --> 00:26:39,500
Take the limit of low voltage
and the limit of high voltage.

635
00:26:39,500 --> 00:26:44,320
Or another way to put it would
be the high current, really.

636
00:26:44,320 --> 00:26:46,910
And the high current
to voltage ratio

637
00:26:46,910 --> 00:26:49,340
only begins to take on up
at higher voltages because

638
00:26:49,340 --> 00:26:52,580
of the exponential
function of that curve.

639
00:26:52,580 --> 00:26:55,180
So that's a very, very
important and astute observation

640
00:26:55,180 --> 00:26:56,830
that the series
resistance begins

641
00:26:56,830 --> 00:27:00,310
to kill you at high forward
bias voltage conditions.

642
00:27:00,310 --> 00:27:03,550
You hope that you design
your solar cell in such a way

643
00:27:03,550 --> 00:27:05,840
that the series resistance
only really begins

644
00:27:05,840 --> 00:27:09,880
to kick in above the
maximum power point voltage.

645
00:27:09,880 --> 00:27:10,957
That's the goal.

646
00:27:10,957 --> 00:27:13,939
AUDIENCE: This is not
voltage out, this is voltage

647
00:27:13,939 --> 00:27:17,350
applied to the [INAUDIBLE]?

648
00:27:17,350 --> 00:27:19,710
PROFESSOR: This is the
voltage that is being

649
00:27:19,710 --> 00:27:21,915
measured across the solar cell.

650
00:27:21,915 --> 00:27:23,220
AUDIENCE: The output voltage.

651
00:27:23,220 --> 00:27:25,950
PROFESSOR: The
output voltage, yeah.

652
00:27:25,950 --> 00:27:31,160
Yes, you can think of this
as the biasing condition

653
00:27:31,160 --> 00:27:32,650
of your solar cell device.

654
00:27:32,650 --> 00:27:33,910
The two are almost equivalent.

655
00:27:33,910 --> 00:27:35,930
The only difference is you
have that series resistance

656
00:27:35,930 --> 00:27:36,650
in series there.

657
00:27:36,650 --> 00:27:38,316
So you have to be
careful whether you're

658
00:27:38,316 --> 00:27:40,640
talking about the voltage
here at the solar cell itself

659
00:27:40,640 --> 00:27:42,760
across a junction,
or the voltage

660
00:27:42,760 --> 00:27:45,470
coming out of your device that
is effected by that series

661
00:27:45,470 --> 00:27:47,640
resistance as well.

662
00:27:47,640 --> 00:27:50,180
So think of it is
doing that IV sweep

663
00:27:50,180 --> 00:27:52,530
that we did in
class the other day.

664
00:27:52,530 --> 00:27:54,590
So you're taking the IV
sweep of your device,

665
00:27:54,590 --> 00:27:58,050
and you're seeing the impact
of the series resistance

666
00:27:58,050 --> 00:28:01,190
in the output voltage you're
measuring of your solar cell

667
00:28:01,190 --> 00:28:03,500
device, just like
we did in class.

668
00:28:03,500 --> 00:28:06,540
So again, series resistance
will effect you at some point.

669
00:28:06,540 --> 00:28:07,960
It is almost inevitable.

670
00:28:07,960 --> 00:28:10,250
But you have to design
your solar cell such

671
00:28:10,250 --> 00:28:12,855
that it effects you only
after the maximum power point.

672
00:28:15,620 --> 00:28:17,900
Likewise, we're going to
introduce another resistance

673
00:28:17,900 --> 00:28:20,080
term inside of our equivalent
circuit diagram, what

674
00:28:20,080 --> 00:28:21,610
we call a shunt resistance.

675
00:28:21,610 --> 00:28:23,140
Let me back up one step here.

676
00:28:23,140 --> 00:28:25,280
This was just a
series resistance,

677
00:28:25,280 --> 00:28:28,440
now I've added a shunt
resistance term here as well.

678
00:28:28,440 --> 00:28:34,560
And whereas we wanted our series
resistance to be small, right?

679
00:28:34,560 --> 00:28:39,180
The smaller our series
resistance, the less

680
00:28:39,180 --> 00:28:42,230
this effect would be, the more
ideal this curve would be.

681
00:28:42,230 --> 00:28:44,970
We want our shunt
resistance to be large,

682
00:28:44,970 --> 00:28:48,450
because we want to prevent the
current from flowing inside

683
00:28:48,450 --> 00:28:52,291
of the device back to the base.

684
00:28:52,291 --> 00:28:53,790
Instead, we want
the current to flow

685
00:28:53,790 --> 00:28:55,350
through the external circuit.

686
00:28:55,350 --> 00:28:57,620
So we want the shunt
resistance to be large.

687
00:28:57,620 --> 00:28:59,820
In other words, we don't
want our solar cell device

688
00:28:59,820 --> 00:29:01,590
to full of shunts.

689
00:29:01,590 --> 00:29:02,670
That's pretty obvious.

690
00:29:02,670 --> 00:29:06,020
OK, so what does shunt
resistance do to you?

691
00:29:06,020 --> 00:29:07,790
Well, if we compare
the IV curves

692
00:29:07,790 --> 00:29:10,630
once again between
the solar cell just

693
00:29:10,630 --> 00:29:16,090
with the series resistance, we
had a very low forward current

694
00:29:16,090 --> 00:29:18,380
here under low forward
bias conditions.

695
00:29:18,380 --> 00:29:21,420
If we have a very
poor shunt-- if we

696
00:29:21,420 --> 00:29:24,502
have a plethora of shunt
pathways in our device,

697
00:29:24,502 --> 00:29:26,710
we're going to get current
flowing through our device

698
00:29:26,710 --> 00:29:29,710
even at low bias conditions.

699
00:29:29,710 --> 00:29:31,620
That's because the
pn-junction is weak.

700
00:29:31,620 --> 00:29:33,820
And even though we have a
very large field in there,

701
00:29:33,820 --> 00:29:36,010
there are some regions where the
field is much smaller because

702
00:29:36,010 --> 00:29:37,720
of the shunt pathway,
and current is going

703
00:29:37,720 --> 00:29:38,680
to be flowing through there.

704
00:29:38,680 --> 00:29:40,140
Diffusion current
will be flowing

705
00:29:40,140 --> 00:29:42,130
through that shunt pathway.

706
00:29:42,130 --> 00:29:45,640
So think of this as being
a very strong diode, right.

707
00:29:45,640 --> 00:29:47,100
In the absence of
shunt resistance,

708
00:29:47,100 --> 00:29:48,308
you have a very strong diode.

709
00:29:48,308 --> 00:29:51,440
You have in your p-type
region and your n,

710
00:29:51,440 --> 00:29:53,840
and that large
barrier is preventing

711
00:29:53,840 --> 00:29:56,300
the diffusion of electrons
back into the device.

712
00:29:56,300 --> 00:29:58,280
It's preventing
this from rising.

713
00:29:58,280 --> 00:30:00,050
It's keeping it low.

714
00:30:00,050 --> 00:30:03,540
And that can only happen
when the pn-junction barrier

715
00:30:03,540 --> 00:30:06,280
is uniform throughout
your entire device.

716
00:30:06,280 --> 00:30:07,870
If you have one
region if your device

717
00:30:07,870 --> 00:30:10,245
that is poor that
has a shunt pathway,

718
00:30:10,245 --> 00:30:12,870
maybe you have a piece of metal
that fired through the junction

719
00:30:12,870 --> 00:30:15,830
and is making good ohmic
contact to both sides.

720
00:30:15,830 --> 00:30:18,090
If you have a shunt
pathway, now the current

721
00:30:18,090 --> 00:30:21,090
can flow even under
small bias conditions.

722
00:30:21,090 --> 00:30:23,340
The diffusion current can
flow into your device.

723
00:30:23,340 --> 00:30:27,900
And that, of course, drops
on the linear log scale

724
00:30:27,900 --> 00:30:30,260
right up here, you
hardly detect it.

725
00:30:30,260 --> 00:30:32,090
Notice, if we go back
and forth between

726
00:30:32,090 --> 00:30:34,230
with and without
shunt resistance,

727
00:30:34,230 --> 00:30:36,010
you can hardly
detect it right here

728
00:30:36,010 --> 00:30:39,070
until you start getting to some
really leaky diodes, in which

729
00:30:39,070 --> 00:30:42,770
case you begin to impact
your fill factor as well.

730
00:30:42,770 --> 00:30:48,970
So shunt resistance is important
for a solar cell device

731
00:30:48,970 --> 00:30:51,750
that it not be too, too high.

732
00:30:51,750 --> 00:30:53,500
Because at some
point it does begin

733
00:30:53,500 --> 00:30:55,770
impacting your fill factor.

734
00:30:55,770 --> 00:30:58,060
Sorry, the shunt resistance
not be too, too low.

735
00:30:58,060 --> 00:31:00,492
Yes, your shunt resistance
can't be too, too low

736
00:31:00,492 --> 00:31:01,950
because at some
point it will begin

737
00:31:01,950 --> 00:31:03,980
impacting your fill factor.

738
00:31:03,980 --> 00:31:06,330
But more importantly,
shunt resistance

739
00:31:06,330 --> 00:31:09,030
is usually indicative
of some localized

740
00:31:09,030 --> 00:31:11,190
failure in your pn-junction.

741
00:31:11,190 --> 00:31:12,940
It's usually not
homogeneously distributed

742
00:31:12,940 --> 00:31:14,260
throughout the
entire pn-junction.

743
00:31:14,260 --> 00:31:16,259
Maybe your first solar
cell device you ever make

744
00:31:16,259 --> 00:31:17,506
might be effected by that.

745
00:31:17,506 --> 00:31:18,880
But as you get
better and better,

746
00:31:18,880 --> 00:31:22,170
you'll start making
higher quality junctions.

747
00:31:22,170 --> 00:31:24,460
And usually the
shunt resistance is

748
00:31:24,460 --> 00:31:26,330
indicative of one little spot.

749
00:31:26,330 --> 00:31:28,350
And what happens at
that one little spot?

750
00:31:28,350 --> 00:31:31,790
Well, current is flowing in
from the entire emitter region

751
00:31:31,790 --> 00:31:35,537
into that one little shunt and
locally heating up your device.

752
00:31:35,537 --> 00:31:37,870
And so that's why people worry
about shunts in industry,

753
00:31:37,870 --> 00:31:40,078
is because if you have
current crowding into that one

754
00:31:40,078 --> 00:31:42,580
little spot, it's heating
up, it's becoming a hotspot,

755
00:31:42,580 --> 00:31:44,880
and it can even melt the
encapsulated materials

756
00:31:44,880 --> 00:31:45,750
in your module.

757
00:31:45,750 --> 00:31:49,730
Perhaps even create a fire
in extreme conditions.

758
00:31:49,730 --> 00:31:53,990
And so when you test
the solar cell devices,

759
00:31:53,990 --> 00:31:58,400
typically the IV tester will
measure the shunt resistance

760
00:31:58,400 --> 00:32:00,080
in a solar cell by
looking at what's

761
00:32:00,080 --> 00:32:02,780
happening under very small
bias conditions right here,

762
00:32:02,780 --> 00:32:04,680
and comparing it
against the healthy cell

763
00:32:04,680 --> 00:32:06,000
that it would expect.

764
00:32:06,000 --> 00:32:09,750
And if it finds cells with
high shunt leakage current,

765
00:32:09,750 --> 00:32:11,800
in other words, low
shunt resistance,

766
00:32:11,800 --> 00:32:14,370
it will advise the
tester and sorter

767
00:32:14,370 --> 00:32:16,400
to throw out those
cells, and so they'll

768
00:32:16,400 --> 00:32:19,160
be put into the scrap pile.

769
00:32:19,160 --> 00:32:22,090
And so the shunt resistance
manifests itself right here

770
00:32:22,090 --> 00:32:25,665
in the ideal diode equation
in this term right there.

771
00:32:25,665 --> 00:32:27,730
And so it's essentially
an add-on term

772
00:32:27,730 --> 00:32:32,000
after your exponential,
looking something like this.

773
00:32:32,000 --> 00:32:35,041
Essentially, at low
bias conditions,

774
00:32:35,041 --> 00:32:36,790
you can extrapolate
this point right here,

775
00:32:36,790 --> 00:32:38,320
determine the slope
of that point,

776
00:32:38,320 --> 00:32:40,085
and find the shunt resistance.

777
00:32:43,190 --> 00:32:46,100
And likewise, you'll notice
that the shunt resistance really

778
00:32:46,100 --> 00:32:49,232
isn't impacting you up here.

779
00:32:49,232 --> 00:32:51,190
The shunt resistance
really isn't impacting you

780
00:32:51,190 --> 00:32:52,960
at higher forward
bias conditions.

781
00:32:52,960 --> 00:32:55,535
That's mostly series resistance
in the illumination current

782
00:32:55,535 --> 00:32:58,520
that's overwhelming
any shunt pathway.

783
00:32:58,520 --> 00:32:59,286
Ashley, yeah?

784
00:32:59,286 --> 00:33:01,941
ASHLEY: Do you know
for, I don't know,

785
00:33:01,941 --> 00:33:03,316
a high-quality
manufacturer, what

786
00:33:03,316 --> 00:33:06,597
percentage of produced cells
get tossed because [INAUDIBLE].

787
00:33:06,597 --> 00:33:07,430
PROFESSOR: Very low.

788
00:33:07,430 --> 00:33:12,450
The manufacturing yields of
a well-oiled manufacturing

789
00:33:12,450 --> 00:33:14,780
line- I say oiled in
a figurative sense.

790
00:33:14,780 --> 00:33:17,420
We're not typically-- yeah,
some of the parts, I suppose,

791
00:33:17,420 --> 00:33:19,260
use oil.

792
00:33:19,260 --> 00:33:22,170
In a well-functioning
manufacturing line,

793
00:33:22,170 --> 00:33:26,610
the yields are upwards of
95% for cell fabrication.

794
00:33:26,610 --> 00:33:28,340
So it's a very small percentage.

795
00:33:28,340 --> 00:33:29,770
You typically see
this when you're

796
00:33:29,770 --> 00:33:31,610
developing a new process.

797
00:33:31,610 --> 00:33:33,317
And that's why I'm
informing all of you

798
00:33:33,317 --> 00:33:35,900
about this is because we're all
developing new processes here,

799
00:33:35,900 --> 00:33:36,400
right?

800
00:33:36,400 --> 00:33:38,540
We're all working on
new solar cell devices.

801
00:33:38,540 --> 00:33:42,290
And it's very important to be
aware of what's going wrong

802
00:33:42,290 --> 00:33:44,920
in your device, not just that
you're getting a low efficiency

803
00:33:44,920 --> 00:33:47,561
because this is the first
step to troubleshooting.

804
00:33:47,561 --> 00:33:48,060
Yep?

805
00:33:48,060 --> 00:33:48,758
AUDIENCE: [INAUDIBLE]
but why is it

806
00:33:48,758 --> 00:33:50,424
bad that we have a
high current density?

807
00:33:50,424 --> 00:33:52,409
[INAUDIBLE] current
density [INAUDIBLE]?

808
00:33:52,409 --> 00:33:54,950
PROFESSOR: Why is it bad that
we have a high current density?

809
00:33:54,950 --> 00:33:56,408
Why don't we go
back to simple case

810
00:33:56,408 --> 00:33:59,560
right here where we have a
series instance, for instance,

811
00:33:59,560 --> 00:34:00,070
right?

812
00:34:00,070 --> 00:34:03,170
And so at, say, 0.5
volts forward bias,

813
00:34:03,170 --> 00:34:06,410
we now have with the
series resistance, a higher

814
00:34:06,410 --> 00:34:08,550
forward currend-- we'll
call a dark forward current

815
00:34:08,550 --> 00:34:10,420
because we're measuring
this in the dark.

816
00:34:10,420 --> 00:34:12,030
That's why we have 0 here.

817
00:34:12,030 --> 00:34:13,489
And it's forward
current, meaning

818
00:34:13,489 --> 00:34:16,400
it's like a diffusion current
going from the emitter

819
00:34:16,400 --> 00:34:18,420
back into the base.

820
00:34:18,420 --> 00:34:20,679
And so we have a higher
dark forward current here

821
00:34:20,679 --> 00:34:22,730
in the dark with the
series resistance,

822
00:34:22,730 --> 00:34:25,210
then if we didn't have the
series resistance, right?

823
00:34:25,210 --> 00:34:26,210
So let me do that again.

824
00:34:26,210 --> 00:34:28,699
We're up here at,
say, 1 times 10

825
00:34:28,699 --> 00:34:30,580
to minus 2 milliamps
per square centimeter,

826
00:34:30,580 --> 00:34:34,969
whereas before we were
down at around a quarter.

827
00:34:34,969 --> 00:34:36,590
So why is that bad?

828
00:34:36,590 --> 00:34:38,880
That's bad because when we
illuminate our solar cell

829
00:34:38,880 --> 00:34:41,780
device, we are going to be
shifting that curve down,

830
00:34:41,780 --> 00:34:44,070
and that's going to reduce
the total current output

831
00:34:44,070 --> 00:34:46,199
at the maximum power point.

832
00:34:46,199 --> 00:34:49,020
So anything that goes up here
when it's shifted or transposed

833
00:34:49,020 --> 00:34:51,590
by a finite fixed
amount, it will

834
00:34:51,590 --> 00:34:55,940
be closer to the 0 point of
current than it used to be.

835
00:34:55,940 --> 00:34:57,280
That's why it's bad.

836
00:34:57,280 --> 00:35:00,470
So anything that
increases that blue curve

837
00:35:00,470 --> 00:35:02,330
and shifts it up in
the dark is going

838
00:35:02,330 --> 00:35:03,950
to be bad for our solar cell.

839
00:35:03,950 --> 00:35:06,720
In an ideal case, we want
our dark forward current

840
00:35:06,720 --> 00:35:08,400
to be as small as possible.

841
00:35:08,400 --> 00:35:12,002
We want our J0 to be
as tiny as possible

842
00:35:12,002 --> 00:35:13,210
for a good solar cell device.

843
00:35:16,678 --> 00:35:17,178
OK.

844
00:35:20,160 --> 00:35:24,550
Good let me show you dynamically
what happens in a solar cell.

845
00:35:24,550 --> 00:35:26,190
Oops, sorry about that.

846
00:35:26,190 --> 00:35:26,940
Here we go.

847
00:35:26,940 --> 00:35:30,680
So this is a PV CD-ROM
again in a beautiful example

848
00:35:30,680 --> 00:35:34,030
of, in this particular case,
looks like series resistance.

849
00:35:34,030 --> 00:35:36,320
So now we're at 1
ohm series resistance

850
00:35:36,320 --> 00:35:37,970
for the entire device.

851
00:35:37,970 --> 00:35:40,240
The ideal solar cell
is shown in red.

852
00:35:40,240 --> 00:35:43,392
The IV curve for the ideal
solar cell is shown in red.

853
00:35:43,392 --> 00:35:44,850
It would be a short
circuit current

854
00:35:44,850 --> 00:35:47,120
of 35 milliamps per
square centimeter,

855
00:35:47,120 --> 00:35:49,970
an open circuit voltage
of 624 millivolts,

856
00:35:49,970 --> 00:35:53,160
and a fill factor of
83%, ideal solar cell.

857
00:35:53,160 --> 00:35:57,490
The real solar cell now with 1
ohm series resistance, the fill

858
00:35:57,490 --> 00:36:03,340
factor has dropped by
5% absolute down to 78%.

859
00:36:03,340 --> 00:36:06,004
And now I'm going to
increase the fill factor.

860
00:36:06,004 --> 00:36:07,920
What would you expect
to happen to that curve?

861
00:36:10,900 --> 00:36:11,820
Flattens, right?

862
00:36:11,820 --> 00:36:13,240
The fill factor drops.

863
00:36:13,240 --> 00:36:15,740
So let me start increasing the
series resistance by manually

864
00:36:15,740 --> 00:36:17,200
dragging this forward.

865
00:36:17,200 --> 00:36:23,910
So now we're at around
2, 3, 4, 5, 7, 8, 9, 10.

866
00:36:23,910 --> 00:36:27,000
So now we're at 10
ohms series resistance.

867
00:36:27,000 --> 00:36:28,970
That means we have
a large resistance

868
00:36:28,970 --> 00:36:30,890
inside of our solar cell
device at some point.

869
00:36:30,890 --> 00:36:34,072
And our fill factor has
now dropped precipitously.

870
00:36:34,072 --> 00:36:35,530
And if you remember
that efficiency

871
00:36:35,530 --> 00:36:38,520
is proportional to fill,
factor that means we

872
00:36:38,520 --> 00:36:40,410
have a problem with our device.

873
00:36:40,410 --> 00:36:42,860
We're really dropping
the maximum power point.

874
00:36:42,860 --> 00:36:44,870
We're really dropping
the operating point

875
00:36:44,870 --> 00:36:46,520
of our solar cell.

876
00:36:46,520 --> 00:36:50,220
So if you were to do
an extreme condition,

877
00:36:50,220 --> 00:36:52,640
you might have so
much series resistance

878
00:36:52,640 --> 00:36:55,560
that your IV curve looks
like a straight line,

879
00:36:55,560 --> 00:36:57,250
you have an ohmic resistor now.

880
00:36:57,250 --> 00:37:00,340
The resistance component
is swamping out

881
00:37:00,340 --> 00:37:03,100
any diode-like behavior
of your solar cell.

882
00:37:03,100 --> 00:37:04,537
And that's why you have a line.

883
00:37:04,537 --> 00:37:06,620
Likewise, you're dropping
the total current output

884
00:37:06,620 --> 00:37:08,360
of your device,
right, because you

885
00:37:08,360 --> 00:37:09,860
have a resistor in
series now that's

886
00:37:09,860 --> 00:37:11,400
preventing the current flow.

887
00:37:11,400 --> 00:37:15,580
OK, so that's, again,
an extreme case of what

888
00:37:15,580 --> 00:37:17,840
can happen in a
shunt resistance.

889
00:37:17,840 --> 00:37:19,690
Let me show you that as well.

890
00:37:19,690 --> 00:37:23,890
So we have another beautiful
example shunt resistance here.

891
00:37:23,890 --> 00:37:26,610
Now we start out with a
very high shunt resistance,

892
00:37:26,610 --> 00:37:29,170
because in our equivalent
circuit diagram,

893
00:37:29,170 --> 00:37:32,100
if we go back up here,
we have a large barrier

894
00:37:32,100 --> 00:37:34,930
that prevents the current
from flowing back internally

895
00:37:34,930 --> 00:37:36,142
inside of the device.

896
00:37:36,142 --> 00:37:37,600
The current is
forced to go outside

897
00:37:37,600 --> 00:37:38,808
through the external circuit.

898
00:37:38,808 --> 00:37:41,640
But as we drop that red
shunt resistance component

899
00:37:41,640 --> 00:37:44,700
right there, as we
decrease the magnitude

900
00:37:44,700 --> 00:37:46,800
of the shunt resistance,
we will allow the current

901
00:37:46,800 --> 00:37:48,190
to flow inside of the device.

902
00:37:48,190 --> 00:37:49,750
Now we have internal
current loops,

903
00:37:49,750 --> 00:37:52,208
and that means that we no longer
are forcing the current go

904
00:37:52,208 --> 00:37:54,270
outside through the
external circuit.

905
00:37:54,270 --> 00:37:58,140
And somewhere around
between 1,000 and 100 ohms

906
00:37:58,140 --> 00:37:59,820
for our shunt
resistance, we really

907
00:37:59,820 --> 00:38:01,490
begin to see that
drop in fill factor.

908
00:38:01,490 --> 00:38:03,300
And as expected,
it's really begin

909
00:38:03,300 --> 00:38:07,610
to impact us at the lower bias
voltages down here like we saw.

910
00:38:07,610 --> 00:38:10,440
And at some point, we
drop the shunt resistance

911
00:38:10,440 --> 00:38:14,530
so much that now the voltage
across our solar cell

912
00:38:14,530 --> 00:38:17,510
is even suffering
because there's not

913
00:38:17,510 --> 00:38:20,740
enough separation
of charge sustained

914
00:38:20,740 --> 00:38:25,110
to make that voltage large
because the current is being

915
00:38:25,110 --> 00:38:27,330
shunted back inside the device.

916
00:38:27,330 --> 00:38:31,310
And again, we have what appears
to be very linear IV curve.

917
00:38:31,310 --> 00:38:33,525
So you can see when you
measure your solar cell

918
00:38:33,525 --> 00:38:37,110
and you test it, and you get
a linear IV curve instead

919
00:38:37,110 --> 00:38:38,810
of that nice
exponential, you have

920
00:38:38,810 --> 00:38:40,935
to do a little bit of
troubleshooting to figure out

921
00:38:40,935 --> 00:38:42,191
what exactly is going on.

922
00:38:42,191 --> 00:38:42,690
OK.

923
00:38:45,430 --> 00:38:47,380
Good.

924
00:38:47,380 --> 00:38:49,850
So key concepts so far.

925
00:38:49,850 --> 00:38:52,590
We can add the effects
of parallel resistance.

926
00:38:52,590 --> 00:38:54,720
What we typically refer
to a shunt resistance

927
00:38:54,720 --> 00:38:56,500
is also called
parallel resistance

928
00:38:56,500 --> 00:39:01,080
because it appears in
parallel with the diode inside

929
00:39:01,080 --> 00:39:02,540
of the device, right.

930
00:39:02,540 --> 00:39:06,040
So we can have a parallel or
shunt resistance and series

931
00:39:06,040 --> 00:39:07,550
resistance in our devices.

932
00:39:07,550 --> 00:39:09,580
And as an advanced
concept, I really

933
00:39:09,580 --> 00:39:11,780
wanted to expose
you once, and we

934
00:39:11,780 --> 00:39:15,680
can talk more about this in
office hours, to the notion

935
00:39:15,680 --> 00:39:20,180
that in addition to just
having one saturation current,

936
00:39:20,180 --> 00:39:23,010
you could envision difference
saturation currents coming

937
00:39:23,010 --> 00:39:25,060
from different regions of
your solar cell device.

938
00:39:25,060 --> 00:39:26,690
Let me walk you through that.

939
00:39:26,690 --> 00:39:32,240
Under low bias conditions where
we have a large built in field,

940
00:39:32,240 --> 00:39:34,130
and we have very
low bias conditions.

941
00:39:34,130 --> 00:39:36,660
Before bias, obviously the
field is going to be decreasing,

942
00:39:36,660 --> 00:39:38,826
the barrier height's going
to be decreasing as well.

943
00:39:38,826 --> 00:39:40,580
So under low forward
bias conditions,

944
00:39:40,580 --> 00:39:42,660
current is going to have a hard
time getting all the way up

945
00:39:42,660 --> 00:39:44,850
into the base and recombining
inside of the base,

946
00:39:44,850 --> 00:39:47,308
but some of the current could
recombine in the space charge

947
00:39:47,308 --> 00:39:48,630
region of our device.

948
00:39:48,630 --> 00:39:50,900
And that's why under low
forward bias conditions,

949
00:39:50,900 --> 00:39:54,390
we might have what is called a
J02 current, or recombination

950
00:39:54,390 --> 00:39:56,180
current in the
space-charge region.

951
00:39:56,180 --> 00:39:58,770
And then there are high
forward bias conditions when

952
00:39:58,770 --> 00:40:01,410
a lot of the carriers can
diffuse into the bulk,

953
00:40:01,410 --> 00:40:03,100
and recombine
inside of the bulk,

954
00:40:03,100 --> 00:40:06,040
we might be driven by different
recombination mechanisms,

955
00:40:06,040 --> 00:40:07,370
bulk recombination mechaniss.

956
00:40:07,370 --> 00:40:09,490
So that's sometimes
where you see

957
00:40:09,490 --> 00:40:12,620
what is called a two-diode
model for a solar cell.

958
00:40:12,620 --> 00:40:14,347
And the two-diode
model for a solar cell

959
00:40:14,347 --> 00:40:16,180
would look very much
like this, except you'd

960
00:40:16,180 --> 00:40:20,099
have two diodes one
right next to the other.

961
00:40:20,099 --> 00:40:22,640
One that would effect you at
low bias conditions, another one

962
00:40:22,640 --> 00:40:24,060
at large bias conditions.

963
00:40:24,060 --> 00:40:25,610
You might see this
in your research.

964
00:40:25,610 --> 00:40:27,485
It's really an advanced
concept more targeted

965
00:40:27,485 --> 00:40:30,050
towards the graduate
students here.

966
00:40:30,050 --> 00:40:31,880
Another thing you
might see pop up

967
00:40:31,880 --> 00:40:35,240
is this ideality factor
showing up right down here.

968
00:40:35,240 --> 00:40:37,850
The ideality factor
is a slope factor.

969
00:40:37,850 --> 00:40:40,630
What that means is--
here if we go back

970
00:40:40,630 --> 00:40:43,300
to this, if you change
your ideality factor,

971
00:40:43,300 --> 00:40:45,830
you're changing the
slope in log scale.

972
00:40:45,830 --> 00:40:48,416
It'd still be a straight line,
but if your ideality factor

973
00:40:48,416 --> 00:40:50,290
increases, you would
get something like this.

974
00:40:50,290 --> 00:40:53,350
If it decreases, the slope
would increase, right?

975
00:40:53,350 --> 00:40:56,190
Because you have the
equation dependent on 1

976
00:40:56,190 --> 00:40:58,190
over this parameter.

977
00:40:58,190 --> 00:41:00,840
So the ideality
factor is important

978
00:41:00,840 --> 00:41:03,760
as well because it indicates the
type of recombination mechanism

979
00:41:03,760 --> 00:41:05,410
that's driving
the current inside

980
00:41:05,410 --> 00:41:06,650
of that region of the device.

981
00:41:06,650 --> 00:41:09,220
If anybody ever comes across
this in their research,

982
00:41:09,220 --> 00:41:10,090
come talk to me.

983
00:41:10,090 --> 00:41:12,850
I'd be happy point to
the right directions.

984
00:41:12,850 --> 00:41:16,270
Or you could look up the
thesis of Keith McIntosh

985
00:41:16,270 --> 00:41:18,530
from University of
New South Wales.

986
00:41:18,530 --> 00:41:20,550
Excellent, excellent
thesis entitled,

987
00:41:20,550 --> 00:41:24,780
"Humps, Lumps and Bumps:
Three Dimensional Effects

988
00:41:24,780 --> 00:41:27,030
of the Current Voltage Curve
of Silicon Solar Cells."

989
00:41:27,030 --> 00:41:29,700
Some of which might apply as
well to other material systems

990
00:41:29,700 --> 00:41:30,706
as well.

991
00:41:30,706 --> 00:41:32,330
And you can tell
where the lumps, humps

992
00:41:32,330 --> 00:41:33,205
and bumps comes from.

993
00:41:33,205 --> 00:41:36,420
It's really these lumps, humps
and bumps in the IV curve

994
00:41:36,420 --> 00:41:37,920
he's talking about.

995
00:41:37,920 --> 00:41:40,360
Excellent read,
very good thesis.

996
00:41:40,360 --> 00:41:43,660
Highly recommended for those
who want to look into their IV

997
00:41:43,660 --> 00:41:44,710
curves a little bit more.

998
00:41:44,710 --> 00:41:46,640
It's kind of like looking
to the tea leaves, right?

999
00:41:46,640 --> 00:41:48,080
Because there are
a number of things

1000
00:41:48,080 --> 00:41:49,580
that can be effecting
the IV curves.

1001
00:41:49,580 --> 00:41:53,720
We'll get to some of
those on Tuesday as well.

1002
00:41:53,720 --> 00:41:57,520
These are IV curves,
again in log scale

1003
00:41:57,520 --> 00:42:01,279
on the ordinate, linear
scale on the abscissa.

1004
00:42:01,279 --> 00:42:02,820
You notice there's
little commas here

1005
00:42:02,820 --> 00:42:07,120
because I took this data in
Germany so the decimal place is

1006
00:42:07,120 --> 00:42:08,980
written as a comma.

1007
00:42:08,980 --> 00:42:13,860
The IV curves vary in
shape and in style.

1008
00:42:13,860 --> 00:42:17,040
Let's look at this one
right here, this black one.

1009
00:42:17,040 --> 00:42:19,790
It starts up like this, and
then it goes flat for a while,

1010
00:42:19,790 --> 00:42:22,070
and then it becomes series
resistance dominated way up

1011
00:42:22,070 --> 00:42:24,110
at higher bias voltages.

1012
00:42:24,110 --> 00:42:27,650
Whereas this blue curve
right here, this one again,

1013
00:42:27,650 --> 00:42:30,050
you have the effect of shunt
resistance at lower buys

1014
00:42:30,050 --> 00:42:31,020
voltages.

1015
00:42:31,020 --> 00:42:34,340
Then you have one diode,
two diodes, and eventually

1016
00:42:34,340 --> 00:42:36,910
the series resistance
component coming in as well.

1017
00:42:36,910 --> 00:42:40,393
Or perhaps it's a
large shunt as well.

1018
00:42:40,393 --> 00:42:42,976
You don't really know until you
start fitting it, and modeling

1019
00:42:42,976 --> 00:42:45,059
it, and maybe measuring
the temperature dependence

1020
00:42:45,059 --> 00:42:46,230
and so forth.

1021
00:42:46,230 --> 00:42:50,400
So this gives you a
sense of the real life

1022
00:42:50,400 --> 00:42:52,820
diode IV curves that
you might get over

1023
00:42:52,820 --> 00:42:56,490
the course of your research,
and it gives you some tools

1024
00:42:56,490 --> 00:42:58,490
to use to begin parsing
through and figuring out

1025
00:42:58,490 --> 00:43:00,250
what's going wrong.

1026
00:43:00,250 --> 00:43:01,510
Let's talk about that.

1027
00:43:01,510 --> 00:43:03,340
Let's talk about
solving problems.

1028
00:43:03,340 --> 00:43:04,300
So fill factor.

1029
00:43:04,300 --> 00:43:05,770
What can impact the fill factor?

1030
00:43:05,770 --> 00:43:09,210
Well, we talked about the
need for a high fill factor

1031
00:43:09,210 --> 00:43:10,940
to produce a high power cell.

1032
00:43:10,940 --> 00:43:12,110
Very easy to understand.

1033
00:43:12,110 --> 00:43:16,270
The larger the fill factor, the
larger the maximum power point.

1034
00:43:16,270 --> 00:43:19,300
If you have a low fill factor,
your maximum power point

1035
00:43:19,300 --> 00:43:20,570
is going to drop.

1036
00:43:20,570 --> 00:43:22,430
Let me show you back and forth.

1037
00:43:22,430 --> 00:43:26,420
Good device, bad device, large
fill factor, low fill factor,

1038
00:43:26,420 --> 00:43:31,080
high maximum power point,
lower maximum power point.

1039
00:43:31,080 --> 00:43:32,870
OK, we talked about this.

1040
00:43:32,870 --> 00:43:36,270
OK, so causes of shunt
resistance, physical causes.

1041
00:43:36,270 --> 00:43:38,150
I alluded to this
earlier, but let's imagine

1042
00:43:38,150 --> 00:43:40,780
you have that weak spot
in your pn-junction.

1043
00:43:40,780 --> 00:43:43,270
This is meant to represent
pn-junction in two dimensions

1044
00:43:43,270 --> 00:43:44,120
now.

1045
00:43:44,120 --> 00:43:46,770
So, so far we've only taken
a cross section like this.

1046
00:43:46,770 --> 00:43:49,632
Now you have a
real device in 2D.

1047
00:43:49,632 --> 00:43:51,090
And what this is
meant to represent

1048
00:43:51,090 --> 00:43:53,880
to some local weakness
in the pn-junction.

1049
00:43:53,880 --> 00:43:57,640
And the current is now flowing
through that local weakness.

1050
00:43:57,640 --> 00:44:01,680
So that's a representation
in a 2D energy band diagram

1051
00:44:01,680 --> 00:44:09,880
E versus x versus y of a
shunt in realistic conditions.

1052
00:44:09,880 --> 00:44:13,170
So shunt series resistance,
on the other hand,

1053
00:44:13,170 --> 00:44:15,426
we talked about the effect
of high series resistance,

1054
00:44:15,426 --> 00:44:17,050
and we're going to
calculate the series

1055
00:44:17,050 --> 00:44:18,257
resistance for a solar cell.

1056
00:44:18,257 --> 00:44:19,840
In part, because
this is asked for you

1057
00:44:19,840 --> 00:44:20,650
on your homework assignment.

1058
00:44:20,650 --> 00:44:22,108
At least the graduate
students have

1059
00:44:22,108 --> 00:44:24,260
a problem pertaining to this.

1060
00:44:24,260 --> 00:44:26,960
So let's talk about the
different components

1061
00:44:26,960 --> 00:44:28,190
of series resistance.

1062
00:44:28,190 --> 00:44:31,000
We have a bulk current and
then a lateral current inside

1063
00:44:31,000 --> 00:44:32,590
of a typical solar cell device.

1064
00:44:32,590 --> 00:44:36,240
So sunlight comes in, shines,
generates electron hole pairs.

1065
00:44:36,240 --> 00:44:39,700
These electrons will diffuse
to the junction region,

1066
00:44:39,700 --> 00:44:41,690
and then they'll drift
across the junction,

1067
00:44:41,690 --> 00:44:44,560
wind up in this emitter
front surface region.

1068
00:44:44,560 --> 00:44:47,890
And eventually through lateral
diffusion reach the context

1069
00:44:47,890 --> 00:44:49,730
and be pulled out of the device.

1070
00:44:49,730 --> 00:44:53,229
So we have to consider these
two different components,

1071
00:44:53,229 --> 00:44:55,770
and pretty much the current all
the way from the back contact

1072
00:44:55,770 --> 00:44:57,000
to the front contact.

1073
00:44:57,000 --> 00:45:00,060
Any one of those things could
contribute to series resistance

1074
00:45:00,060 --> 00:45:01,860
in an additive sense.

1075
00:45:01,860 --> 00:45:04,190
So to put that pictorially,
we have bulk resistance,

1076
00:45:04,190 --> 00:45:06,280
emitter sheet resistance,
the contact resistance,

1077
00:45:06,280 --> 00:45:09,160
and in line losses
out of plane as we

1078
00:45:09,160 --> 00:45:13,370
travel along those front
contact metallization.

1079
00:45:13,370 --> 00:45:15,320
So bulk resistance.

1080
00:45:15,320 --> 00:45:18,280
This is another way to state
how to choose an absorber

1081
00:45:18,280 --> 00:45:19,630
thickness.

1082
00:45:19,630 --> 00:45:22,699
So we've talked about
choosing absorber thicknesses,

1083
00:45:22,699 --> 00:45:24,490
in other words, we've
talked about choosing

1084
00:45:24,490 --> 00:45:26,190
the thickness of our
solar cell device

1085
00:45:26,190 --> 00:45:28,270
based on how much light
we want to capture,

1086
00:45:28,270 --> 00:45:30,450
based on the optical
absorption coefficients.

1087
00:45:30,450 --> 00:45:31,660
Well guess what?

1088
00:45:31,660 --> 00:45:33,380
This is a
co-optimization problem.

1089
00:45:33,380 --> 00:45:35,520
We also have to worry
about the finite resistance

1090
00:45:35,520 --> 00:45:37,090
of the bulk
material, and we have

1091
00:45:37,090 --> 00:45:39,080
to spec the
thickness accordingly

1092
00:45:39,080 --> 00:45:42,120
so that we don't wind up with
too thick of a bulk material

1093
00:45:42,120 --> 00:45:44,930
and the series resistance
component will be too large.

1094
00:45:44,930 --> 00:45:47,352
So how to choose the
appropriate absorber thickness.

1095
00:45:47,352 --> 00:45:48,810
Let's talk about
that for a minute.

1096
00:45:48,810 --> 00:45:53,490
So you can measure a parameter
in the bulk called resistivity.

1097
00:45:53,490 --> 00:45:56,780
Resistivity will be given
as a function of q, which

1098
00:45:56,780 --> 00:46:01,350
is the charge, u, which is the
carrier mobility, which means

1099
00:46:01,350 --> 00:46:04,530
how easy is it for that carrier
to move around the lattice,

1100
00:46:04,530 --> 00:46:06,064
and n being the carry density.

1101
00:46:06,064 --> 00:46:07,230
So let's think that through.

1102
00:46:07,230 --> 00:46:09,589
Resistivity-- if our
carrier density goes up,

1103
00:46:09,589 --> 00:46:11,630
if we have more carriers
to transport the charge,

1104
00:46:11,630 --> 00:46:12,900
the resistive should go down.

1105
00:46:12,900 --> 00:46:13,730
That makes sense.

1106
00:46:13,730 --> 00:46:14,450
Check.

1107
00:46:14,450 --> 00:46:16,991
If the mobility goes up, meaning
it's easier for the carriers

1108
00:46:16,991 --> 00:46:20,000
to move around the lattice, then
the resistivity should go down.

1109
00:46:20,000 --> 00:46:20,500
Check.

1110
00:46:20,500 --> 00:46:23,120
OK, so that makes
good, intuitive sense.

1111
00:46:23,120 --> 00:46:25,980
Now the base resistance, in
other words, the resistance

1112
00:46:25,980 --> 00:46:29,650
that we should have as current
travels across the base,

1113
00:46:29,650 --> 00:46:32,200
across the absorber of our
material, which we also call

1114
00:46:32,200 --> 00:46:33,880
the base of our solar cell.

1115
00:46:33,880 --> 00:46:37,620
So as the total resistance, as
current goes across the base,

1116
00:46:37,620 --> 00:46:41,530
should be given as Rho, which
is a fundamental material

1117
00:46:41,530 --> 00:46:45,040
parameter combined with some
geometric parameters that

1118
00:46:45,040 --> 00:46:47,540
define the size
of our solar cell.

1119
00:46:47,540 --> 00:46:50,200
So l is going to be the length
of the conductive of path

1120
00:46:50,200 --> 00:46:53,070
which typically would be given
as the thickness of the device,

1121
00:46:53,070 --> 00:46:55,100
and A is the area
of current flow.

1122
00:46:55,100 --> 00:46:58,970
In other words, the dimension or
size of our solar cell device.

1123
00:46:58,970 --> 00:47:01,040
So to minimize
base resistance, we

1124
00:47:01,040 --> 00:47:03,540
want to have a very
thin solar cell device.

1125
00:47:03,540 --> 00:47:04,290
But wait a second.

1126
00:47:04,290 --> 00:47:05,670
If we make it very
thin, then what happens?

1127
00:47:05,670 --> 00:47:06,476
AUDIENCE: [INAUDIBLE].

1128
00:47:06,476 --> 00:47:07,600
PROFESSOR: You get
less absorption.

1129
00:47:07,600 --> 00:47:09,570
So you have to make
it a certain thickness

1130
00:47:09,570 --> 00:47:11,232
to get a good enough absorption.

1131
00:47:11,232 --> 00:47:12,190
Then we can compensate.

1132
00:47:12,190 --> 00:47:14,080
If we still need to drop
the base resistance,

1133
00:47:14,080 --> 00:47:17,560
we can increase the
area of the base.

1134
00:47:17,560 --> 00:47:19,850
And so far that
makes good sense.

1135
00:47:19,850 --> 00:47:22,550
There's nothing else
tugging for the area

1136
00:47:22,550 --> 00:47:24,700
to be the other
direction, right?

1137
00:47:24,700 --> 00:47:28,720
So we can make this solar
cell infinitely large, thick

1138
00:47:28,720 --> 00:47:30,460
as we want to be to
absorb all the light.

1139
00:47:30,460 --> 00:47:32,019
Great, OK.

1140
00:47:32,019 --> 00:47:33,560
Hold on to that
thought because we're

1141
00:47:33,560 --> 00:47:35,601
going to have another
constraining parameter that

1142
00:47:35,601 --> 00:47:37,980
pushes us in the opposite
way in a few slides.

1143
00:47:37,980 --> 00:47:40,490
All right, so the
emitter sheet resistance.

1144
00:47:40,490 --> 00:47:43,570
In other words, how to design
front contact metallization.

1145
00:47:43,570 --> 00:47:46,780
Emitter sheet resistance
refers to the resistance

1146
00:47:46,780 --> 00:47:48,700
of lateral current
that the carriers

1147
00:47:48,700 --> 00:47:50,410
will experience as
they move laterally

1148
00:47:50,410 --> 00:47:52,360
to reach the front contacts.

1149
00:47:52,360 --> 00:47:55,770
And again, we go back to this
fundamental material parameter

1150
00:47:55,770 --> 00:47:58,880
where we have resistivity
as a function of mobility,

1151
00:47:58,880 --> 00:48:01,520
and total dopant concentration.

1152
00:48:01,520 --> 00:48:04,190
Sorry, for some reason, I used
the big N here and a little n

1153
00:48:04,190 --> 00:48:04,910
on the previous slide.

1154
00:48:04,910 --> 00:48:05,910
But it's the same thing.

1155
00:48:05,910 --> 00:48:07,050
It's carrier density.

1156
00:48:07,050 --> 00:48:09,914
So again, our resistivity is
a function of carrier mobility

1157
00:48:09,914 --> 00:48:12,330
and carrier concentration, how
easy it is for the carriers

1158
00:48:12,330 --> 00:48:15,200
to move, and how many
of them are there.

1159
00:48:15,200 --> 00:48:17,830
For a thin layer,
a sheet resistance

1160
00:48:17,830 --> 00:48:21,200
can be described as the
integral of the resistivity

1161
00:48:21,200 --> 00:48:23,780
by the thickness of that layer.

1162
00:48:23,780 --> 00:48:26,990
Or to put it more simply,
if you have a uniform layer,

1163
00:48:26,990 --> 00:48:31,380
you simply multiply the
denominator here by thickness.

1164
00:48:31,380 --> 00:48:33,580
So this can be thought
in the following way.

1165
00:48:33,580 --> 00:48:39,830
If we have a thicker emitter,
we will be dropping the emitter

1166
00:48:39,830 --> 00:48:41,090
sheet resistance.

1167
00:48:41,090 --> 00:48:44,680
We will be dropping the
resistance component

1168
00:48:44,680 --> 00:48:47,324
that carriers experience as they
travel laterally through this.

1169
00:48:47,324 --> 00:48:48,990
And that makes sense
because, in effect,

1170
00:48:48,990 --> 00:48:51,260
as we increase the thickness
of this emitter region,

1171
00:48:51,260 --> 00:48:53,885
we're increasing the total cross
sectional area for the charges

1172
00:48:53,885 --> 00:48:56,620
to travel through.

1173
00:48:56,620 --> 00:48:58,560
So folks with me so far.

1174
00:48:58,560 --> 00:49:02,310
For the emitter sheet
resistance to be low,

1175
00:49:02,310 --> 00:49:05,220
we need the thickness
to be good enough,

1176
00:49:05,220 --> 00:49:07,300
the thickness to
be thick enough,

1177
00:49:07,300 --> 00:49:09,220
the carrier density
to be high enough,

1178
00:49:09,220 --> 00:49:11,170
and the mobility
to be large enough.

1179
00:49:11,170 --> 00:49:14,350
And oftentimes, the
resistivity of a material, you

1180
00:49:14,350 --> 00:49:17,060
might spend months trying
to optimize the resistivity

1181
00:49:17,060 --> 00:49:18,590
of your emitter region.

1182
00:49:18,590 --> 00:49:20,290
For those doing
thin film materials,

1183
00:49:20,290 --> 00:49:22,990
you might be working on
zinc oxide, aluminum doped,

1184
00:49:22,990 --> 00:49:25,100
or fluorine doped zinc
oxide, for instance.

1185
00:49:25,100 --> 00:49:28,570
And after months of tuning
the temperature and the oxygen

1186
00:49:28,570 --> 00:49:30,650
partial pressure during
the deposition process,

1187
00:49:30,650 --> 00:49:32,690
you're there and you
have what you have.

1188
00:49:32,690 --> 00:49:34,690
You have a certain carrier
density and a certain mobility.

1189
00:49:34,690 --> 00:49:37,230
And you can't do much more than
vary the geometric parameter

1190
00:49:37,230 --> 00:49:39,120
varying the thickness.

1191
00:49:39,120 --> 00:49:41,600
So what next?

1192
00:49:41,600 --> 00:49:44,560
If my thickness is
too big on my emitter,

1193
00:49:44,560 --> 00:49:46,390
if my thickness is
too big, I'm going

1194
00:49:46,390 --> 00:49:49,110
to be absorbing all of my
short wavelengths photons

1195
00:49:49,110 --> 00:49:52,460
in the front surface
of my device.

1196
00:49:52,460 --> 00:49:55,080
And maybe the current
collection probability

1197
00:49:55,080 --> 00:49:59,750
from that layer up here,
that has a very high carrier

1198
00:49:59,750 --> 00:50:02,240
density, is not going to be
as large-- in other words,

1199
00:50:02,240 --> 00:50:04,490
the current collection
efficiency won't be as large as

1200
00:50:04,490 --> 00:50:07,344
if I generated the carriers
here in the bulk because

1201
00:50:07,344 --> 00:50:09,010
of an effect called
Auger recombination,

1202
00:50:09,010 --> 00:50:10,830
which we'll get
to a few lectures.

1203
00:50:10,830 --> 00:50:13,170
So this front
surface region here

1204
00:50:13,170 --> 00:50:16,110
oftentimes is considered a
dead layer to a solar cell.

1205
00:50:16,110 --> 00:50:18,960
Its electrical properties
are very, very poor.

1206
00:50:18,960 --> 00:50:21,270
So if I make this
layer too thick,

1207
00:50:21,270 --> 00:50:25,110
sure I get rid of my emitter
sheet resistance term.

1208
00:50:25,110 --> 00:50:27,780
But at the same time I'm
killing my quantum efficiency

1209
00:50:27,780 --> 00:50:29,472
in the short wavelengths.

1210
00:50:29,472 --> 00:50:31,680
Because I'm not able to
absorb those short wavelength

1211
00:50:31,680 --> 00:50:34,890
photons and convert them
efficiently into electron hole

1212
00:50:34,890 --> 00:50:37,740
pairs.

1213
00:50:37,740 --> 00:50:39,660
So this is a story
about co-optimization

1214
00:50:39,660 --> 00:50:41,940
of different device parameters.

1215
00:50:41,940 --> 00:50:43,780
So let's keep this
thought for a minute.

1216
00:50:43,780 --> 00:50:46,526
And let's now try to
calculate the total power loss

1217
00:50:46,526 --> 00:50:48,650
due to the emitter sheet
resistance, because now we

1218
00:50:48,650 --> 00:50:52,450
have this weird unit
of ohms per square.

1219
00:50:52,450 --> 00:50:53,450
In reality, it's ohms.

1220
00:50:53,450 --> 00:50:55,650
But when we think about
emitter sheet resistance,

1221
00:50:55,650 --> 00:50:57,680
we're thinking about a
square of the material.

1222
00:50:57,680 --> 00:50:59,100
We have units of
ohms per square,

1223
00:50:59,100 --> 00:51:00,900
square being a
unit-less parameter.

1224
00:51:00,900 --> 00:51:03,440
So it has, let's
see, resistivity

1225
00:51:03,440 --> 00:51:07,074
had units of ohm centimeter,
we divided our resistivity

1226
00:51:07,074 --> 00:51:08,740
by our thickness of
that emitter region,

1227
00:51:08,740 --> 00:51:10,910
so our units became ohms.

1228
00:51:10,910 --> 00:51:13,840
And ohms per square here is
the units typically given

1229
00:51:13,840 --> 00:51:15,730
for emitter sheet resistance.

1230
00:51:15,730 --> 00:51:20,580
And now we have to convert this
into some meaningful parameter

1231
00:51:20,580 --> 00:51:22,149
for actual solar cell device.

1232
00:51:22,149 --> 00:51:24,190
So if we want the calculate
the fraction of power

1233
00:51:24,190 --> 00:51:27,430
lost due to this emitter
sheet resistance,

1234
00:51:27,430 --> 00:51:29,180
it's fairly straightforward.

1235
00:51:29,180 --> 00:51:32,500
We would have to think
about the current.

1236
00:51:32,500 --> 00:51:34,740
Since power is I
squared R, we have

1237
00:51:34,740 --> 00:51:37,270
to think about the current as
a function of the resistance,

1238
00:51:37,270 --> 00:51:37,769
right?

1239
00:51:37,769 --> 00:51:39,350
As a function of
the position here,

1240
00:51:39,350 --> 00:51:45,170
we're integrating over y, y
being the lateral dimension.

1241
00:51:45,170 --> 00:51:48,170
And we're integrating-- imagine
the separation between contacts

1242
00:51:48,170 --> 00:51:50,870
is S. So here's one
contact metal finger.

1243
00:51:50,870 --> 00:51:52,610
Here's the next
contact metal finger.

1244
00:51:52,610 --> 00:51:54,720
It's extracting charge
from the material.

1245
00:51:54,720 --> 00:51:58,160
And we have a certain distance,
S, right here between them.

1246
00:51:58,160 --> 00:52:00,014
So the maximum distance
that the current

1247
00:52:00,014 --> 00:52:01,430
would travel in
principle would be

1248
00:52:01,430 --> 00:52:03,842
S divided by 2, since
any current that

1249
00:52:03,842 --> 00:52:05,800
reaches the emitter over
here will be collected

1250
00:52:05,800 --> 00:52:08,650
by this contact grid, and
any electrons reaching

1251
00:52:08,650 --> 00:52:11,130
the emitter over here will
collected by that contact grid

1252
00:52:11,130 --> 00:52:12,880
finger.

1253
00:52:12,880 --> 00:52:14,694
OK, so now we have our current.

1254
00:52:14,694 --> 00:52:16,235
We can translate
that into here where

1255
00:52:16,235 --> 00:52:20,670
we have our b, b being
the vertical dimension,

1256
00:52:20,670 --> 00:52:24,190
y being the horizontal
dimension here.

1257
00:52:24,190 --> 00:52:26,927
And we would get this
equation coming out right

1258
00:52:26,927 --> 00:52:29,260
in the other side, which is
a function of the separation

1259
00:52:29,260 --> 00:52:32,740
of our contact metallization
fingers to the cubed,

1260
00:52:32,740 --> 00:52:34,640
to the third power.

1261
00:52:34,640 --> 00:52:37,770
So the power loss coming
from the solar cell device,

1262
00:52:37,770 --> 00:52:40,120
as we separate our
contact metallization

1263
00:52:40,120 --> 00:52:46,460
by small amount, this power loss
is going to go up very quickly.

1264
00:52:46,460 --> 00:52:49,230
That's a really deep
point to recognize here

1265
00:52:49,230 --> 00:52:51,020
because what this
means, in effect, is

1266
00:52:51,020 --> 00:52:53,860
that we can lose a lot of power
very quickly in our solar cell

1267
00:52:53,860 --> 00:52:57,340
device if we place our contact
fingers too far apart, due

1268
00:52:57,340 --> 00:53:00,270
to this emitter sheet
resistance effect,

1269
00:53:00,270 --> 00:53:03,860
due to the row sub s,
which is our emitter sheet

1270
00:53:03,860 --> 00:53:07,840
resistance right here.

1271
00:53:07,840 --> 00:53:12,142
OK, so then if we divide the
power loss by the maximum power

1272
00:53:12,142 --> 00:53:15,750
point, we essentially get
a normalized power loss.

1273
00:53:15,750 --> 00:53:18,440
And so if we want to,
say, limit this ratio

1274
00:53:18,440 --> 00:53:21,220
to a certain fraction,
say 4% of total power

1275
00:53:21,220 --> 00:53:23,632
is lost due to emitter
sheet resistance, now we

1276
00:53:23,632 --> 00:53:25,090
can define the
geometric parameter,

1277
00:53:25,090 --> 00:53:27,090
the distance between
the contact metal

1278
00:53:27,090 --> 00:53:29,270
that we need to do
an actual solar cell.

1279
00:53:29,270 --> 00:53:31,900
And if you run through
the calculations

1280
00:53:31,900 --> 00:53:36,350
with a typical set of parameters
for a silicon-based solar cell,

1281
00:53:36,350 --> 00:53:40,420
you'll find out that your
metallization fingers should

1282
00:53:40,420 --> 00:53:42,340
be separated on the
order of 4 millimeters.

1283
00:53:42,340 --> 00:53:44,339
And if you remember the
real solar cell devices

1284
00:53:44,339 --> 00:53:45,880
that you saw embedded
in that module,

1285
00:53:45,880 --> 00:53:49,140
the separation of the fingers
is just about 4 millimeters.

1286
00:53:49,140 --> 00:53:52,200
So this is where that finger
separation comes from.

1287
00:53:52,200 --> 00:53:55,226
In one case, you'd want to have
your fingers spaced really,

1288
00:53:55,226 --> 00:53:57,350
really close together to
minimize the emitter sheet

1289
00:53:57,350 --> 00:53:58,094
resistance.

1290
00:53:58,094 --> 00:54:00,510
But on the other hand, if you
place your fingers too close

1291
00:54:00,510 --> 00:54:02,176
together, your shading
the front surface

1292
00:54:02,176 --> 00:54:03,920
of your solar cell
with metal and light's

1293
00:54:03,920 --> 00:54:06,562
not going to get in to
generate electron hole pairs.

1294
00:54:06,562 --> 00:54:08,020
So that's the
optimization function

1295
00:54:08,020 --> 00:54:09,520
that's run right there.

1296
00:54:09,520 --> 00:54:11,870
Wow, so far I'm
counting three or four

1297
00:54:11,870 --> 00:54:14,000
of these different
parameters tugging

1298
00:54:14,000 --> 00:54:15,370
in different directions, right?

1299
00:54:15,370 --> 00:54:18,540
So you can begin to sense how
constrained the solar cell

1300
00:54:18,540 --> 00:54:21,130
device is in terms
of optimization

1301
00:54:21,130 --> 00:54:22,860
of all these parameters,
and how easy it

1302
00:54:22,860 --> 00:54:25,460
is to make a very low
efficiency device as a result,

1303
00:54:25,460 --> 00:54:28,930
how difficult it is to make
a high efficiency device.

1304
00:54:28,930 --> 00:54:31,515
So this is interesting.

1305
00:54:31,515 --> 00:54:33,640
So we have now the spacing,
the appropriate spacing

1306
00:54:33,640 --> 00:54:35,810
between fingers.

1307
00:54:35,810 --> 00:54:38,010
It's about 4 millimeters.

1308
00:54:38,010 --> 00:54:41,220
Which means if we're going to
be making a solar cell device,

1309
00:54:41,220 --> 00:54:44,370
say a thin film solar cell
device on a sheet of glass

1310
00:54:44,370 --> 00:54:46,897
with some transparent conducting
materials [INAUDIBLE],

1311
00:54:46,897 --> 00:54:48,480
and then we have our
source of device,

1312
00:54:48,480 --> 00:54:51,160
and we have their front surface
here, and we have, let's say,

1313
00:54:51,160 --> 00:54:53,580
something else on
top, we have to limit

1314
00:54:53,580 --> 00:54:55,510
how wide we make that device.

1315
00:54:55,510 --> 00:54:59,730
Otherwise, we could be
limited by our sheet

1316
00:54:59,730 --> 00:55:03,520
resistance in, say, the zinc
oxide layer of our device.

1317
00:55:03,520 --> 00:55:07,370
And this is interesting
now because previously

1318
00:55:07,370 --> 00:55:10,170
for the bulk resistance--
let's think back over

1319
00:55:10,170 --> 00:55:11,290
to our bulk resistance.

1320
00:55:11,290 --> 00:55:14,430
We wanted our area to be large
because we wanted to minimize

1321
00:55:14,430 --> 00:55:16,330
the bulk resistance.

1322
00:55:16,330 --> 00:55:21,045
Now we want the area to be small
so that we minimize our emitter

1323
00:55:21,045 --> 00:55:22,840
sheet resistance.

1324
00:55:22,840 --> 00:55:24,929
So you can see how
the current traveling

1325
00:55:24,929 --> 00:55:26,970
in two orthogonal directions
inside of our device

1326
00:55:26,970 --> 00:55:29,070
is really causing us
problems because we're

1327
00:55:29,070 --> 00:55:31,700
having to optimize
the same parameter

1328
00:55:31,700 --> 00:55:35,010
in different
directions for each.

1329
00:55:35,010 --> 00:55:36,181
It's tricky.

1330
00:55:36,181 --> 00:55:37,680
And I'm providing
you the tools here

1331
00:55:37,680 --> 00:55:40,170
to be able to sit
down and calculate out

1332
00:55:40,170 --> 00:55:42,270
what is the optimal
thickness, what

1333
00:55:42,270 --> 00:55:44,799
is the optimal thickness of
your emitter, of your base,

1334
00:55:44,799 --> 00:55:47,340
and what is the optimal lateral
dimensions of your solar cell

1335
00:55:47,340 --> 00:55:50,630
device to simultaneously
minimize your bulk resistance

1336
00:55:50,630 --> 00:55:53,700
and your emitter resistance
instead of a device.

1337
00:55:53,700 --> 00:55:56,770
And you can do it all now with
equations that I just gave you.

1338
00:55:56,770 --> 00:55:58,320
So it's pretty cool.

1339
00:55:58,320 --> 00:56:00,438
At least to first order.

1340
00:56:00,438 --> 00:56:02,670
AUDIENCE: How did you
define B, again, in that?

1341
00:56:02,670 --> 00:56:03,836
PROFESSOR: Yeah, absolutely.

1342
00:56:03,836 --> 00:56:05,520
So B was a vertical dimension.

1343
00:56:05,520 --> 00:56:07,670
B is just given as
the distance here.

1344
00:56:07,670 --> 00:56:09,950
Yeah.

1345
00:56:09,950 --> 00:56:11,559
AUDIENCE: And that's
going across like

1346
00:56:11,559 --> 00:56:12,850
if you look down on your model?

1347
00:56:12,850 --> 00:56:15,141
PROFESSOR:Yeah, you're looking
down on your solar cell.

1348
00:56:15,141 --> 00:56:19,268
So the pn-junction would be
planar to this view right here.

1349
00:56:19,268 --> 00:56:21,490
AUDIENCE: [INAUDIBLE]?

1350
00:56:21,490 --> 00:56:23,065
PROFESSOR: Yep.

1351
00:56:23,065 --> 00:56:24,965
It's a bird's eye view
on the solar cell.

1352
00:56:29,060 --> 00:56:32,190
Any other questions?

1353
00:56:32,190 --> 00:56:36,450
OK, so contact resistance.

1354
00:56:36,450 --> 00:56:40,150
This is the next thing that
can kill a solar cell device.

1355
00:56:40,150 --> 00:56:43,200
Contact resistance-- we
want to minimize the contact

1356
00:56:43,200 --> 00:56:45,100
resistance, but the
first step to minimizing

1357
00:56:45,100 --> 00:56:49,020
is to measure, to know what your
contact resistance really is.

1358
00:56:49,020 --> 00:56:51,990
And one simple way to
measure contact resistance

1359
00:56:51,990 --> 00:56:55,120
is to take a cross section
of your solar cell device.

1360
00:56:55,120 --> 00:56:58,650
We have deposited, say,
four metal fingers on it,

1361
00:56:58,650 --> 00:57:00,850
and they're appropriately
spaced by, I don't know,

1362
00:57:00,850 --> 00:57:03,050
how many millimeters or so.

1363
00:57:03,050 --> 00:57:05,790
So you have a certain
contact resistance right here

1364
00:57:05,790 --> 00:57:10,210
between the metal and your
semiconductor material that's

1365
00:57:10,210 --> 00:57:14,170
denoted as R sub C. And then
there's a certain emitter

1366
00:57:14,170 --> 00:57:19,110
resistance that we just talked
about, R sub em right here.

1367
00:57:19,110 --> 00:57:25,060
And if you were to measure the
current passing through here

1368
00:57:25,060 --> 00:57:26,970
to here, or another
way to say it

1369
00:57:26,970 --> 00:57:29,360
is, the resistance for current
to pass from this point

1370
00:57:29,360 --> 00:57:32,620
to that point, you
might get, let's say,

1371
00:57:32,620 --> 00:57:34,970
this data point right here,
a total resistance value

1372
00:57:34,970 --> 00:57:40,460
of some value, and a distance
between the two probes of, say,

1373
00:57:40,460 --> 00:57:44,430
1 times d sub f we're
d sub f is the unit

1374
00:57:44,430 --> 00:57:48,790
distance between two adjacent
contact metallization fingers.

1375
00:57:48,790 --> 00:57:51,060
Now if we measure the
resistance between this point

1376
00:57:51,060 --> 00:57:53,810
and that point, we might
wind up with that data point

1377
00:57:53,810 --> 00:57:55,700
right here.

1378
00:57:55,700 --> 00:57:58,040
And if we measure the
resistance between this point

1379
00:57:58,040 --> 00:58:00,440
and that point-- we already
did that-- to this point

1380
00:58:00,440 --> 00:58:02,880
and that point, we might
wind up with that data point

1381
00:58:02,880 --> 00:58:04,896
right here, and so forth.

1382
00:58:04,896 --> 00:58:05,770
And what's happening?

1383
00:58:05,770 --> 00:58:08,500
Well, as a current
goes into the device,

1384
00:58:08,500 --> 00:58:12,150
it passes once through the
contact resistance, a certain n

1385
00:58:12,150 --> 00:58:16,680
times R sub em, n being the
number of metallization,

1386
00:58:16,680 --> 00:58:20,591
number pops, the number of
times we travel distance df.

1387
00:58:20,591 --> 00:58:22,090
And then it goes
out the other side,

1388
00:58:22,090 --> 00:58:25,260
again traveling through
the contact resistance.

1389
00:58:25,260 --> 00:58:30,230
So the slope of this line here
should be equal to the emitter

1390
00:58:30,230 --> 00:58:32,100
resistance.

1391
00:58:32,100 --> 00:58:36,360
And the offset, the
intercept at x equals 0 here,

1392
00:58:36,360 --> 00:58:38,767
the intercept should be 2
times the contact resistance.

1393
00:58:38,767 --> 00:58:40,850
Because in principle, that
would be the equivalent

1394
00:58:40,850 --> 00:58:43,767
of current going in and going
back out through this contact

1395
00:58:43,767 --> 00:58:45,600
resistance right here,
through the same one,

1396
00:58:45,600 --> 00:58:47,466
not traveling at all
through the emitter.

1397
00:58:47,466 --> 00:58:49,340
Obviously since that's
impossible to measure,

1398
00:58:49,340 --> 00:58:51,298
we have to determine that
through extrapolation

1399
00:58:51,298 --> 00:58:53,435
back to the y-axis.

1400
00:58:53,435 --> 00:58:57,289
So this so-called TLM method,
the transmission line method,

1401
00:58:57,289 --> 00:58:59,330
is a method that is used
to determine the contact

1402
00:58:59,330 --> 00:59:02,530
resistance of a
solar cell device.

1403
00:59:02,530 --> 00:59:04,660
You could either
perform it linearly

1404
00:59:04,660 --> 00:59:08,590
in this fashion right
here, or using a circular,

1405
00:59:08,590 --> 00:59:11,020
essentially an array
of concentric circles.

1406
00:59:11,020 --> 00:59:14,060
And the latter method is
typically preferred, especially

1407
00:59:14,060 --> 00:59:16,480
in thin film devices.

1408
00:59:16,480 --> 00:59:19,560
So this is how you measure
the contact resistance.

1409
00:59:19,560 --> 00:59:21,350
And then there are line losses.

1410
00:59:21,350 --> 00:59:23,420
So what can-- let me back
up one step-- what can

1411
00:59:23,420 --> 00:59:24,990
effect the contact resistance?

1412
00:59:24,990 --> 00:59:26,960
Typically, what effects
contact resistance

1413
00:59:26,960 --> 00:59:31,060
is the atomic interface
between your metal

1414
00:59:31,060 --> 00:59:32,770
and your semiconductor,
whether it's

1415
00:59:32,770 --> 00:59:35,180
an organic or an
inorganic semiconductor.

1416
00:59:35,180 --> 00:59:35,920
Bless you.

1417
00:59:35,920 --> 00:59:40,770
So the interface here is
what determines the contact

1418
00:59:40,770 --> 00:59:42,940
resistance, typically.

1419
00:59:42,940 --> 00:59:45,440
And of course,
the dopant density

1420
00:59:45,440 --> 00:59:49,320
within your semiconductor.

1421
00:59:49,320 --> 00:59:51,920
So components of the series
resistance in the line losses.

1422
00:59:51,920 --> 00:59:55,880
So line losses are
essentially the losses

1423
00:59:55,880 --> 00:59:58,810
in the contact metallization
lines out of plane.

1424
00:59:58,810 --> 01:00:03,400
What can cause a resistance in
the contact metallization line?

1425
01:00:03,400 --> 01:00:06,140
Well, intuitively we know that,
OK if the line is too small,

1426
01:00:06,140 --> 01:00:08,380
if the cross section
that line is too tiny,

1427
01:00:08,380 --> 01:00:12,240
then there's going to be a high
resistance to current travel

1428
01:00:12,240 --> 01:00:13,270
along that line.

1429
01:00:13,270 --> 01:00:14,430
And indeed that's the case.

1430
01:00:14,430 --> 01:00:16,280
Whoa, we have the
same exact equation

1431
01:00:16,280 --> 01:00:17,940
as we had for our
base resistance.

1432
01:00:17,940 --> 01:00:19,900
Now it's applied to the line,
because in principle it's

1433
01:00:19,900 --> 01:00:20,524
the same thing.

1434
01:00:20,524 --> 01:00:22,860
We have current traveling
through in one direction

1435
01:00:22,860 --> 01:00:25,850
along a constrained
cross sectional

1436
01:00:25,850 --> 01:00:28,220
area, a certain distance,
a certain length.

1437
01:00:28,220 --> 01:00:30,800
So we have now a resistivity
given by the metal

1438
01:00:30,800 --> 01:00:33,360
obviously, because now we're
talking about the metal itself,

1439
01:00:33,360 --> 01:00:34,610
not the semiconductor anymore.

1440
01:00:34,610 --> 01:00:36,460
Currents traveling
along the contact metal

1441
01:00:36,460 --> 01:00:39,260
so that the row becomes the
resistivity of the metal, the A

1442
01:00:39,260 --> 01:00:41,940
becomes a cross sectional
area of the contact finger,

1443
01:00:41,940 --> 01:00:44,380
and the l is the length
of the conductive path.

1444
01:00:44,380 --> 01:00:46,640
In other words, how
long does the current

1445
01:00:46,640 --> 01:00:48,440
have to travel along
that contact metal

1446
01:00:48,440 --> 01:00:51,040
before it reaches a
highway, a bus bar, one

1447
01:00:51,040 --> 01:00:55,460
those really thick strips of
metal on our social device,

1448
01:00:55,460 --> 01:00:56,980
in which case it's home free.

1449
01:00:56,980 --> 01:01:01,350
So the R, the row rather,
the metal resistivity,

1450
01:01:01,350 --> 01:01:06,090
resistivities of several
metals and non-metal materials

1451
01:01:06,090 --> 01:01:07,510
are given here.

1452
01:01:07,510 --> 01:01:10,850
That's typically why you see
silver contact metallization

1453
01:01:10,850 --> 01:01:13,730
used for solar cells.

1454
01:01:13,730 --> 01:01:15,840
It's because it has a very
low resistivity, which

1455
01:01:15,840 --> 01:01:19,489
means that the resistance
line losses will be small.

1456
01:01:19,489 --> 01:01:21,030
Now, what is the
problem with silver?

1457
01:01:21,030 --> 01:01:23,200
Does anybody know what
percentage of the world's

1458
01:01:23,200 --> 01:01:26,160
silver right now manufactured
each year is currently

1459
01:01:26,160 --> 01:01:29,507
being used for contact
metallization on solar cells?

1460
01:01:29,507 --> 01:01:30,090
Take a number.

1461
01:01:30,090 --> 01:01:30,589
Guess.

1462
01:01:30,589 --> 01:01:31,326
AUDIENCE: 30.

1463
01:01:31,326 --> 01:01:34,690
PROFESSOR: A little lower, but
in that order of magnitude.

1464
01:01:34,690 --> 01:01:36,150
So he said 30.

1465
01:01:36,150 --> 01:01:39,300
Somewhere upwards of 10%,
right, would be your guess?

1466
01:01:39,300 --> 01:01:41,450
So around 10%.

1467
01:01:41,450 --> 01:01:44,980
And of course PV is growing
at a cumulative annual growth

1468
01:01:44,980 --> 01:01:47,500
rate in the several 10s
of percents per year.

1469
01:01:47,500 --> 01:01:49,600
So silver utilization
is expected

1470
01:01:49,600 --> 01:01:50,960
to continue to increase.

1471
01:01:50,960 --> 01:01:54,820
So either we mine
more silver, or we

1472
01:01:54,820 --> 01:01:57,770
venture to another
contact metal material.

1473
01:01:57,770 --> 01:01:59,990
And that's why you see
folks looking into copper.

1474
01:01:59,990 --> 01:02:02,130
Nickel, which is similar
in electronic structure.

1475
01:02:02,130 --> 01:02:05,050
It's one element to the left of
copper on the periodic table,

1476
01:02:05,050 --> 01:02:07,470
and another metal alternatives.

1477
01:02:07,470 --> 01:02:07,970
Yes?

1478
01:02:07,970 --> 01:02:09,345
AUDIENCE: Yeah,
where does nickel

1479
01:02:09,345 --> 01:02:10,712
fall on the resistivity chart?

1480
01:02:10,712 --> 01:02:12,160
PROFESSOR: I have to give
you the exact number,

1481
01:02:12,160 --> 01:02:14,409
but if I were to venture a
guess, what you're noticing

1482
01:02:14,409 --> 01:02:18,070
over here are several
of the metals that fall

1483
01:02:18,070 --> 01:02:19,770
in the noble metal category.

1484
01:02:19,770 --> 01:02:23,820
These are far to the
right on the 3D series.

1485
01:02:23,820 --> 01:02:25,840
So if you picture the
periodic table again,

1486
01:02:25,840 --> 01:02:29,110
far in the 3D series you
have that d-shell orbital

1487
01:02:29,110 --> 01:02:30,500
completely filled.

1488
01:02:30,500 --> 01:02:32,410
And those outermost
electrons are then

1489
01:02:32,410 --> 01:02:34,582
screened by all the other
electrons in the system

1490
01:02:34,582 --> 01:02:35,540
and very loosely bound.

1491
01:02:35,540 --> 01:02:38,265
And so you can remove the
electrons fairly easily.

1492
01:02:38,265 --> 01:02:41,830
It's one of the reasons why
these elements in that class

1493
01:02:41,830 --> 01:02:44,685
have a higher conductivity,
a lower resistivity.

1494
01:02:44,685 --> 01:02:45,540
Yeah, question?

1495
01:02:45,540 --> 01:02:47,956
AUDIENCE: Copper doesn't seem
that much worse that silver.

1496
01:02:47,956 --> 01:02:49,689
[INAUDIBLE].

1497
01:02:49,689 --> 01:02:52,580
PROFESSOR: So, yes, absolutely.

1498
01:02:52,580 --> 01:02:54,770
Copper doesn't seem so
much worse than silver.

1499
01:02:54,770 --> 01:02:58,800
So the contact
metallization pastes to date

1500
01:02:58,800 --> 01:03:00,970
have mostly been using silver.

1501
01:03:00,970 --> 01:03:03,980
Copper can oxidize
fairly easily.

1502
01:03:03,980 --> 01:03:06,290
So that's one
downside of copper.

1503
01:03:06,290 --> 01:03:10,070
Another problem with copper is
that it's a very fast diffuser.

1504
01:03:10,070 --> 01:03:12,000
It's very tiny.

1505
01:03:12,000 --> 01:03:13,850
And so the elastic
strain energy turn

1506
01:03:13,850 --> 01:03:16,800
as it tries to move through
a lattice is very small.

1507
01:03:16,800 --> 01:03:19,049
And as a result, it goes deep.

1508
01:03:19,049 --> 01:03:20,840
So when you fire your
contact metallization

1509
01:03:20,840 --> 01:03:22,930
when you create the
contact between your metal

1510
01:03:22,930 --> 01:03:24,400
and your semiconductor
underneath,

1511
01:03:24,400 --> 01:03:28,140
you run the risk of having
atoms diffuse into your device

1512
01:03:28,140 --> 01:03:30,370
and hurting the
efficiency, hurting

1513
01:03:30,370 --> 01:03:32,569
the ability of the solar
cell to collect carriers.

1514
01:03:32,569 --> 01:03:34,110
We'll are more about
that on Tuesday.

1515
01:03:34,110 --> 01:03:35,610
AUDIENCE: So it
becomes an impurity.

1516
01:03:35,610 --> 01:03:37,690
PROFESSOR: Yeah, exactly.
it becomes an impurity.

1517
01:03:37,690 --> 01:03:39,590
In this case, unintentional.

1518
01:03:39,590 --> 01:03:42,100
So just remember
where the contact

1519
01:03:42,100 --> 01:03:43,400
is right here in the emitter.

1520
01:03:43,400 --> 01:03:45,720
OK, if it diffuses into
the emitter, it's OK.

1521
01:03:45,720 --> 01:03:48,140
The electrons at this point
are the majority carriers.

1522
01:03:48,140 --> 01:03:50,690
But if the metal diffuses
all the way into the bulk,

1523
01:03:50,690 --> 01:03:54,467
the electrons inside of the bulk
in here are minority carriers.

1524
01:03:54,467 --> 01:03:57,050
And they can be impacted by the
presence of that copper there.

1525
01:04:00,170 --> 01:04:02,760
All right, so I wanted to
get through at least one

1526
01:04:02,760 --> 01:04:06,562
more point to really set
us up well on Tuesday.

1527
01:04:06,562 --> 01:04:08,270
We want to be able to
calculate the Fermi

1528
01:04:08,270 --> 01:04:10,145
energy of a solar cell
as a function of dopan

1529
01:04:10,145 --> 01:04:13,240
concentration, illumination
condition and temperature.

1530
01:04:13,240 --> 01:04:15,780
So, so far we've really
talked about the Fermi energy,

1531
01:04:15,780 --> 01:04:18,620
the chemical potential inside
of a solar cell in hand wavy

1532
01:04:18,620 --> 01:04:19,420
terms.

1533
01:04:19,420 --> 01:04:21,150
We've talked about
general trends,

1534
01:04:21,150 --> 01:04:23,510
about how as we add more
electrons to our system,

1535
01:04:23,510 --> 01:04:25,640
say by doping, we shift
the Fermi energy up

1536
01:04:25,640 --> 01:04:28,450
because the average ensemble
energy of the electrons

1537
01:04:28,450 --> 01:04:29,930
is increasing.

1538
01:04:29,930 --> 01:04:32,370
But now we're going to be
calculating it and determining

1539
01:04:32,370 --> 01:04:33,590
how to calculate it.

1540
01:04:33,590 --> 01:04:36,730
So the question is
calculating Fermi energy.

1541
01:04:36,730 --> 01:04:38,820
So let's introduce
a new concept here.

1542
01:04:38,820 --> 01:04:42,200
So far we've talked about
and energy band diagram,

1543
01:04:42,200 --> 01:04:44,274
and drawn our valence
band, and drawn

1544
01:04:44,274 --> 01:04:45,690
our conduction
band, and of course

1545
01:04:45,690 --> 01:04:46,970
the band gap in between them.

1546
01:04:46,970 --> 01:04:49,261
We've drawn the valence band
and conduction bands as it

1547
01:04:49,261 --> 01:04:51,555
they were just continuum
density of states,

1548
01:04:51,555 --> 01:04:53,180
as if they were just
these blocks where

1549
01:04:53,180 --> 01:04:55,280
electrons could pile in.

1550
01:04:55,280 --> 01:04:59,939
In reality we have what's
called a density of states

1551
01:04:59,939 --> 01:05:01,730
in the valence band
and a density of states

1552
01:05:01,730 --> 01:05:03,060
in the conduction band.

1553
01:05:03,060 --> 01:05:05,442
If you want to think
about electrons as cars,

1554
01:05:05,442 --> 01:05:07,150
the density of states
could be considered

1555
01:05:07,150 --> 01:05:10,840
the number of parking
spaces there are

1556
01:05:10,840 --> 01:05:12,780
per floor in a parking garage.

1557
01:05:12,780 --> 01:05:15,424
As you increase the energy in
the case of a parking garage,

1558
01:05:15,424 --> 01:05:16,840
you increase your
potential energy

1559
01:05:16,840 --> 01:05:19,030
as you move your car
higher and higher.

1560
01:05:19,030 --> 01:05:21,530
In here, you would be increasing
the energy of the electrons

1561
01:05:21,530 --> 01:05:22,850
as you go higher and higher.

1562
01:05:22,850 --> 01:05:24,641
The increase in the
energy of holes as they

1563
01:05:24,641 --> 01:05:25,810
go lower and lower.

1564
01:05:25,810 --> 01:05:29,820
So we have a certain density of
states that is allowed inside

1565
01:05:29,820 --> 01:05:31,030
of our semiconductor.

1566
01:05:31,030 --> 01:05:33,330
And there's a very
small density of states

1567
01:05:33,330 --> 01:05:34,941
right at the band edge.

1568
01:05:34,941 --> 01:05:36,440
And that density
of states typically

1569
01:05:36,440 --> 01:05:40,850
increases as you go deeper
and deeper into the bands.

1570
01:05:40,850 --> 01:05:45,950
So now at absolute
zero, and the person

1571
01:05:45,950 --> 01:05:47,830
who probably knows more
about absolute zero

1572
01:05:47,830 --> 01:05:49,288
than anybody else
here in this room

1573
01:05:49,288 --> 01:05:51,694
is Kristy Simmons in the
back, who for her Ph.D.

1574
01:05:51,694 --> 01:05:53,610
Would work on very low
temperature experiments

1575
01:05:53,610 --> 01:05:56,540
down into the, what, 10s
of millikelvin range.

1576
01:05:56,540 --> 01:05:59,910
10s of millikelvin range--
it's very, very cold.

1577
01:05:59,910 --> 01:06:03,920
And then if you cool
things down a lot,

1578
01:06:03,920 --> 01:06:05,530
all the electrons
that were excited

1579
01:06:05,530 --> 01:06:08,660
will drop down, say, into
the valence band right here.

1580
01:06:08,660 --> 01:06:11,726
And what this is represented
is as a filled valence band

1581
01:06:11,726 --> 01:06:12,225
right there.

1582
01:06:12,225 --> 01:06:14,887
And as you begin
heating your system up,

1583
01:06:14,887 --> 01:06:16,970
some of the electrons will
have the thermal energy

1584
01:06:16,970 --> 01:06:19,070
to be excited
across the band gap.

1585
01:06:19,070 --> 01:06:20,990
So thermally excited
electrons here

1586
01:06:20,990 --> 01:06:23,740
represented in your
conduction band.

1587
01:06:23,740 --> 01:06:25,510
[WHISPERING]

1588
01:06:25,510 --> 01:06:27,990
So we have a certain number
of thermally excited electrons

1589
01:06:27,990 --> 01:06:33,001
here up into the
conduction band.

1590
01:06:33,001 --> 01:06:38,490
Oh, and these carriers we'll
call intrinsic carriers

1591
01:06:38,490 --> 01:06:40,664
because they're not
added by dopans.

1592
01:06:40,664 --> 01:06:42,580
We're not adding anything
to the semiconductor

1593
01:06:42,580 --> 01:06:44,954
to create dopans to
generate new carriers.

1594
01:06:44,954 --> 01:06:46,620
There are intrinsic
carries because they

1595
01:06:46,620 --> 01:06:49,960
came from the valence band,
went up to the conduction band.

1596
01:06:49,960 --> 01:06:52,440
So if we plot intrinsic
carrier concentration

1597
01:06:52,440 --> 01:06:54,960
as a function of
temperature, we see

1598
01:06:54,960 --> 01:06:56,690
a curve that looks like this.

1599
01:06:56,690 --> 01:06:58,630
And it follows this
expression right here,

1600
01:06:58,630 --> 01:07:01,677
which is called in an Arrhenius
equation in a generic form.

1601
01:07:01,677 --> 01:07:04,010
In this case it would be
intrinsic carrier concentration

1602
01:07:04,010 --> 01:07:05,420
as a function of temperature.

1603
01:07:05,420 --> 01:07:07,140
We'd have to substitute
this big N here

1604
01:07:07,140 --> 01:07:08,639
for intrinsic carrier
concentration,

1605
01:07:08,639 --> 01:07:10,230
some exponential
prefactor, and then

1606
01:07:10,230 --> 01:07:12,940
an activation energy,
the activation energy

1607
01:07:12,940 --> 01:07:16,210
being the energy needed to
create that free carrier.

1608
01:07:16,210 --> 01:07:18,030
The band gap energy
in this case.

1609
01:07:18,030 --> 01:07:20,780
The activation energy
divided by KbT,

1610
01:07:20,780 --> 01:07:23,680
the KbT being Boltzmann's
constant times

1611
01:07:23,680 --> 01:07:25,440
temperature in Kelvin.

1612
01:07:25,440 --> 01:07:28,550
Now, if we plot the same
functions that we just saw

1613
01:07:28,550 --> 01:07:32,460
in the previous slide a little
differently, we plot 1 over T--

1614
01:07:32,460 --> 01:07:34,920
see 1 over T right
-- and there--

1615
01:07:34,920 --> 01:07:37,520
and we plot the
log of this value.

1616
01:07:37,520 --> 01:07:41,160
So again, log of this value, we
can read the activation energy

1617
01:07:41,160 --> 01:07:43,159
off of the slope of this graph.

1618
01:07:43,159 --> 01:07:45,450
So that's why you typically
see Arrhenius plots plotted

1619
01:07:45,450 --> 01:07:48,459
in this way-- 1 over T
verses log of parameter--

1620
01:07:48,459 --> 01:07:50,750
because you can read the
activation energy straight off

1621
01:07:50,750 --> 01:07:51,291
of the graph.

1622
01:07:51,291 --> 01:07:54,040
It becomes very easy to see
the carrier concentration.

1623
01:07:54,040 --> 01:08:00,080
So again, at absolute
zero we have,

1624
01:08:00,080 --> 01:08:02,050
here the valence band
completely filled,

1625
01:08:02,050 --> 01:08:04,710
the conduction band completely
empty in our semiconductor.

1626
01:08:04,710 --> 01:08:07,650
And the probability of
occupancy of a state

1627
01:08:07,650 --> 01:08:10,490
inside of our semiconductor
is given by this box function

1628
01:08:10,490 --> 01:08:11,980
right here.

1629
01:08:11,980 --> 01:08:14,790
Now let's look at what
happens when we heat this up.

1630
01:08:14,790 --> 01:08:17,700
When we heat the sample
up, some of the electrons

1631
01:08:17,700 --> 01:08:20,422
that were in the higher energy
states are going to be excited.

1632
01:08:20,422 --> 01:08:22,380
So they used to be here
in lower energy states.

1633
01:08:22,380 --> 01:08:24,588
They are going to be excited
to higher energy states.

1634
01:08:24,588 --> 01:08:26,939
In the area of this
little shape right here

1635
01:08:26,939 --> 01:08:29,010
is equal to the area
of that little shape

1636
01:08:29,010 --> 01:08:30,859
right here because of
conservation of number

1637
01:08:30,859 --> 01:08:33,149
of electrons in our system.

1638
01:08:33,149 --> 01:08:36,920
If we multiply this by
the density of states,

1639
01:08:36,920 --> 01:08:39,950
this is the density of states in
the valence band minimized here

1640
01:08:39,950 --> 01:08:41,381
at the band edges,
and increasing

1641
01:08:41,381 --> 01:08:43,506
as we go deeper into the
bands for the valence band

1642
01:08:43,506 --> 01:08:44,569
and the conduction band.

1643
01:08:44,569 --> 01:08:46,910
So we take our probability
distribution function,

1644
01:08:46,910 --> 01:08:48,920
multiply it by the
density of states,

1645
01:08:48,920 --> 01:08:52,569
and we get the occupied density
of states in our semiconductor.

1646
01:08:52,569 --> 01:08:56,090
So now we see that there's some
number of missing electrons

1647
01:08:56,090 --> 01:08:57,590
that are now in the
conduction band.

1648
01:08:57,590 --> 01:09:00,040
They used to be in the valence
band at very low temperature.

1649
01:09:00,040 --> 01:09:01,665
But now as we increase
the temperature,

1650
01:09:01,665 --> 01:09:03,420
they've had the thermal
energy to excite

1651
01:09:03,420 --> 01:09:07,580
across given this probability
distribution function.

1652
01:09:07,580 --> 01:09:09,920
And these carriers are
now free to conduct

1653
01:09:09,920 --> 01:09:12,310
charge inside of our system.

1654
01:09:12,310 --> 01:09:14,350
So what do we do
with this framework,

1655
01:09:14,350 --> 01:09:15,710
with this understanding?

1656
01:09:15,710 --> 01:09:18,974
Well, we can look
at this function

1657
01:09:18,974 --> 01:09:21,390
here and ask ourselves, what
is the name of that function.

1658
01:09:21,390 --> 01:09:23,430
It's called the
Fermi-Dirac distribution,

1659
01:09:23,430 --> 01:09:26,439
and it's given by this
equation right here.

1660
01:09:26,439 --> 01:09:28,910
We'll notice in the
Fermi Dirac distribution,

1661
01:09:28,910 --> 01:09:33,200
we'll notice that this
equation approximates

1662
01:09:33,200 --> 01:09:37,590
to an exponential equation as
we move further and further away

1663
01:09:37,590 --> 01:09:40,060
from the Fermi energy, the
Fermi energy being defined

1664
01:09:40,060 --> 01:09:41,143
as this energy right here.

1665
01:09:41,143 --> 01:09:43,680
If we move further way down
here, or further way up here,

1666
01:09:43,680 --> 01:09:46,370
this starts looking an awful
lot like an exponential.

1667
01:09:46,370 --> 01:09:49,319
Meaning this right here
and this right here

1668
01:09:49,319 --> 01:09:53,149
start looking like
exponential functions.

1669
01:09:53,149 --> 01:09:57,240
OK, so let's do a quick
little Gedanken experiment is

1670
01:09:57,240 --> 01:09:59,170
a quick little thought
experiment, about what

1671
01:09:59,170 --> 01:10:01,760
happens when we heat
up a semiconductor.

1672
01:10:01,760 --> 01:10:05,300
And how would this impact, how
these free carriers right here

1673
01:10:05,300 --> 01:10:11,610
impact the noise, say, in a
camera, in a CCD-based camera.

1674
01:10:11,610 --> 01:10:14,407
A charge couple display
camera, which functions not

1675
01:10:14,407 --> 01:10:15,990
so different from a
solar cell device,

1676
01:10:15,990 --> 01:10:18,200
except that it's biased
a little differently

1677
01:10:18,200 --> 01:10:19,575
than an actual
solar cell device.

1678
01:10:19,575 --> 01:10:21,450
But it could be like
a pn-junction, p-i-n,

1679
01:10:21,450 --> 01:10:22,770
to be more precise.

1680
01:10:22,770 --> 01:10:26,400
So we have our little
camera right here,

1681
01:10:26,400 --> 01:10:30,420
and the camera's
typically placed inside

1682
01:10:30,420 --> 01:10:33,970
of a liquid nitrogen dewar if
we want very high performance.

1683
01:10:33,970 --> 01:10:36,670
These are not your
typical handheld cameras

1684
01:10:36,670 --> 01:10:38,630
that you would use for
shots in the street.

1685
01:10:38,630 --> 01:10:41,630
These are cameras that we use
in the laboratory for detecting

1686
01:10:41,630 --> 01:10:45,660
very faint signals inside of
our semiconductor systems.

1687
01:10:45,660 --> 01:10:48,470
And we typically cool
our cameras down.

1688
01:10:48,470 --> 01:10:49,290
Why?

1689
01:10:49,290 --> 01:10:51,530
Because we want to
minimize the density

1690
01:10:51,530 --> 01:10:54,354
of these intrinsic carriers.

1691
01:10:54,354 --> 01:10:56,270
Because any photon that
comes into our system,

1692
01:10:56,270 --> 01:10:58,270
we want to be able to
count it and to detect it.

1693
01:10:58,270 --> 01:11:00,120
And not have to detect
a very small signal

1694
01:11:00,120 --> 01:11:02,360
on top of a large background
noise of thermally

1695
01:11:02,360 --> 01:11:04,780
excited carriers.

1696
01:11:04,780 --> 01:11:08,210
In a solar cell device, the
intrinsic carrier concentration

1697
01:11:08,210 --> 01:11:13,037
is typically much, much less
than the dopant concentration.

1698
01:11:13,037 --> 01:11:14,620
So the intrinsic
carrier concentration

1699
01:11:14,620 --> 01:11:16,640
matters less for
our semiconductors

1700
01:11:16,640 --> 01:11:19,580
than it does for a photo
detector like this.

1701
01:11:19,580 --> 01:11:21,080
And that's why,
thankfully, we don't

1702
01:11:21,080 --> 01:11:24,470
have to cool our solar
cells with liquid nitrogen.

1703
01:11:24,470 --> 01:11:28,880
So in terms of have
intrinsic carries,

1704
01:11:28,880 --> 01:11:31,080
let's dwell there just
a little bit longer.

1705
01:11:31,080 --> 01:11:33,560
Transistors are made of
what semiconductor material

1706
01:11:33,560 --> 01:11:38,250
to have less electronic
noise to experience?

1707
01:11:38,250 --> 01:11:41,120
OK, so what semiconductor
material, germanium or silicon,

1708
01:11:41,120 --> 01:11:43,780
would experience less electronic
noise at room temperature?

1709
01:11:43,780 --> 01:11:45,260
And let me give you a hint.

1710
01:11:45,260 --> 01:11:47,950
Silicon has a band
gap of 1.1 eV.

1711
01:11:47,950 --> 01:11:50,290
Germanium has a
band gap of 0.67 eV.

1712
01:11:50,290 --> 01:11:54,020
Which of the two is going to
have greater electronic noise

1713
01:11:54,020 --> 01:11:55,087
at room temperature?

1714
01:11:55,087 --> 01:11:55,920
AUDIENCE: Germanium.

1715
01:11:55,920 --> 01:11:58,240
PROFESSOR: Germanium because
it has smaller band gap,

1716
01:11:58,240 --> 01:12:01,405
it's going to be easier
for the carriers-- we

1717
01:12:01,405 --> 01:12:04,030
go all the way back here-- it's
going to be easier for carriers

1718
01:12:04,030 --> 01:12:06,584
to hop across because
the band gap is smaller.

1719
01:12:06,584 --> 01:12:08,750
Another way to look at it
is on the Arrhenius plots,

1720
01:12:08,750 --> 01:12:10,200
you'll have a higher
carrier concentration

1721
01:12:10,200 --> 01:12:12,570
because your slope is smaller,
your activation energy

1722
01:12:12,570 --> 01:12:13,570
is smaller.

1723
01:12:13,570 --> 01:12:15,347
And as a result,
you'll have a higher--

1724
01:12:15,347 --> 01:12:17,930
if the band gap shrinks-- you'll
have a higher carrier density

1725
01:12:17,930 --> 01:12:19,240
here in the conduction band.

1726
01:12:19,240 --> 01:12:21,410
Let me show you that
in pictorial form.

1727
01:12:21,410 --> 01:12:23,770
So this is the silicon band gap.

1728
01:12:23,770 --> 01:12:27,530
This is the density of thermally
excited carriers for silicon.

1729
01:12:27,530 --> 01:12:28,830
Now we shrink the band gap.

1730
01:12:28,830 --> 01:12:29,779
Boom, we shrunk it.

1731
01:12:29,779 --> 01:12:31,945
Same probability distribution
function because we're

1732
01:12:31,945 --> 01:12:33,784
at the same temperature.

1733
01:12:33,784 --> 01:12:35,200
But now we have a
smaller band gap

1734
01:12:35,200 --> 01:12:38,340
so we have a higher
density of free carriers.

1735
01:12:38,340 --> 01:12:41,020
And true story, germanium
was one of the first crystals

1736
01:12:41,020 --> 01:12:46,000
to be purified during the
early days of semiconductors,

1737
01:12:46,000 --> 01:12:49,190
and silicon was
following germanium.

1738
01:12:49,190 --> 01:12:51,320
And silicon was
ultimately chosen

1739
01:12:51,320 --> 01:12:53,907
as the material of
choice for transistors

1740
01:12:53,907 --> 01:12:56,240
because the intrinsic carrier
concentration of germanium

1741
01:12:56,240 --> 01:12:58,780
was just too high for
most applications.

1742
01:12:58,780 --> 01:13:01,030
And so you can see the
intrinsic carrier concentration

1743
01:13:01,030 --> 01:13:03,900
at room temperature of
silicon is around 10 to the 10

1744
01:13:03,900 --> 01:13:06,900
whereas for germanium is
around 10 to the 13, three

1745
01:13:06,900 --> 01:13:08,780
orders of magnitude higher.

1746
01:13:08,780 --> 01:13:09,810
So, yes, question?

1747
01:13:09,810 --> 01:13:10,800
AUDIENCE: [INAUDIBLE]?

1748
01:13:22,185 --> 01:13:24,690
PROFESSOR: Yeah, it
would be most costly.

1749
01:13:24,690 --> 01:13:26,000
Absolutely.

1750
01:13:26,000 --> 01:13:27,959
And so you do see solar
cells like Concentrics

1751
01:13:27,959 --> 01:13:29,500
is one company that's
commercializing

1752
01:13:29,500 --> 01:13:31,130
gallium arsenide-based
solar cells.

1753
01:13:31,130 --> 01:13:34,530
But they have to concentrate the
sunlight into very small area

1754
01:13:34,530 --> 01:13:38,040
devices because the devices cost
so much to make per unit area.

1755
01:13:38,040 --> 01:13:41,851
So they take cheap plastic and
concentrate the sunlight down.

1756
01:13:41,851 --> 01:13:43,350
Yeah, and here's a
gallium arsenide.

1757
01:13:43,350 --> 01:13:44,700
The intrinsic
carrier concentration

1758
01:13:44,700 --> 01:13:46,074
is even less than
that of silicon

1759
01:13:46,074 --> 01:13:50,540
because the band gap is
1.4 eV instead of 1.1.

1760
01:13:50,540 --> 01:13:52,810
OK, so I think this is
a good place to stop.

1761
01:13:52,810 --> 01:13:55,010
I'm still not through
all the material.

1762
01:13:55,010 --> 01:13:56,780
Oh, we wanted to do one demo.

1763
01:13:56,780 --> 01:13:57,430
JOE: Yeah.

1764
01:13:57,430 --> 01:14:00,213
PROFESSOR: Do you want to do
it first thing next lecture?

1765
01:14:00,213 --> 01:14:01,059
JOE: That's fine.

1766
01:14:01,059 --> 01:14:01,905
We've got five more minutes.

1767
01:14:01,905 --> 01:14:04,000
Ah, we do have five more
minutes before 10 after.

1768
01:14:04,000 --> 01:14:05,715
OK, why don't we do
a quick demo then.

1769
01:14:05,715 --> 01:14:07,950
So what we're going to
do as Joe sets this up,

1770
01:14:07,950 --> 01:14:11,240
is I'll verbally describe
what's going to happen here.

1771
01:14:11,240 --> 01:14:14,670
We are going to
take this-- actually

1772
01:14:14,670 --> 01:14:17,670
let me go back to be Fermi-Dirac
distribution function.

1773
01:14:17,670 --> 01:14:20,190
This function right here,
as we increase temperature,

1774
01:14:20,190 --> 01:14:21,300
what happens to this?

1775
01:14:21,300 --> 01:14:26,850
This will look more and
more, shall we say, flat.

1776
01:14:26,850 --> 01:14:28,350
It won't actually
go flat, but it'll

1777
01:14:28,350 --> 01:14:30,320
become more and more
diagonal opposed

1778
01:14:30,320 --> 01:14:32,460
to box-like in function.

1779
01:14:32,460 --> 01:14:34,840
What that means is the
density of carriers,

1780
01:14:34,840 --> 01:14:37,720
the density of free carriers
will increase with temperature.

1781
01:14:37,720 --> 01:14:39,560
And because of the
Arrhenius dependence

1782
01:14:39,560 --> 01:14:41,650
here, we have an
exponential increase

1783
01:14:41,650 --> 01:14:44,400
of the number of free
carriers with temperature.

1784
01:14:44,400 --> 01:14:46,960
Because the function
right around this region

1785
01:14:46,960 --> 01:14:49,780
right here, which impacts
the electron concentration,

1786
01:14:49,780 --> 01:14:52,404
the conduction band,
this small portion

1787
01:14:52,404 --> 01:14:53,820
of the Fermi-Dirac
equation can be

1788
01:14:53,820 --> 01:14:55,750
approximated by an exponential.

1789
01:14:55,750 --> 01:14:57,350
If we have an
increasing temperature,

1790
01:14:57,350 --> 01:15:00,560
we should have a drastically
increasing carrier density.

1791
01:15:00,560 --> 01:15:02,790
And let's see if
that's indeed the case.

1792
01:15:02,790 --> 01:15:05,850
What we have is a piece
of intrinsic silicon just

1793
01:15:05,850 --> 01:15:08,260
with a battery
pack attached so we

1794
01:15:08,260 --> 01:15:12,697
have a field across that
piece of intrinsic silicon.

1795
01:15:12,697 --> 01:15:13,196
Whoops.

1796
01:15:13,196 --> 01:15:14,340
Here we go.

1797
01:15:14,340 --> 01:15:15,769
And we are going
to apply, again,

1798
01:15:15,769 --> 01:15:17,810
that field across the
intrinsic piece of silicon.

1799
01:15:17,810 --> 01:15:20,070
A certain current
will flow through it.

1800
01:15:20,070 --> 01:15:22,020
And then Joe has a
heat gun, so he's

1801
01:15:22,020 --> 01:15:24,610
going to heat up
the silicon and see

1802
01:15:24,610 --> 01:15:29,040
what happens as the Fermi-Dirac
equation here is effected

1803
01:15:29,040 --> 01:15:31,800
by temperature, we should
have an increasing density

1804
01:15:31,800 --> 01:15:33,710
of carriers in the
conduction band.

1805
01:15:33,710 --> 01:15:36,280
So let's see if that's
indeed the case.

1806
01:15:36,280 --> 01:15:39,210
Can somebody read off what the
current is currently measuring

1807
01:15:39,210 --> 01:15:41,038
there on our current meter?

1808
01:15:41,038 --> 01:15:43,180
AUDIENCE: It's about
9.8 microamps right now.

1809
01:15:43,180 --> 01:15:44,460
PROFESSOR: 9.8 microamps.

1810
01:15:44,460 --> 01:15:47,390
So this battery pack
of 3 volts right here

1811
01:15:47,390 --> 01:15:51,790
is it is forcing a
current of 9.8 microamps

1812
01:15:51,790 --> 01:15:54,160
across that little
slab of silicon that

1813
01:15:54,160 --> 01:15:55,740
is sitted right here.

1814
01:15:55,740 --> 01:15:57,490
And so Joe is going
to apply the heat gun,

1815
01:15:57,490 --> 01:16:00,470
and if none of the
contacts pop off,

1816
01:16:00,470 --> 01:16:01,840
let's see what will happen.

1817
01:16:01,840 --> 01:16:04,744
So we expect the
resistivity to go what?

1818
01:16:04,744 --> 01:16:05,660
AUDIENCE: [INAUDIBLE].

1819
01:16:05,660 --> 01:16:06,570
PROFESSOR: Down.

1820
01:16:06,570 --> 01:16:09,200
And the conductivity to go up.

1821
01:16:09,200 --> 01:16:12,380
All right, so let's see here.

1822
01:16:15,630 --> 01:16:18,640
So what's happening there folks?

1823
01:16:18,640 --> 01:16:19,940
It's going up?

1824
01:16:19,940 --> 01:16:22,238
So that's the --

1825
01:16:22,238 --> 01:16:24,388
JOE: So it went up to
around 50 microamps,

1826
01:16:24,388 --> 01:16:27,625
and can see it's dropping rather
dramatically now [INAUDIBLE].

1827
01:16:27,625 --> 01:16:29,500
PROFESSOR: So the current
that the material's

1828
01:16:29,500 --> 01:16:30,940
able to pass through
is increasing

1829
01:16:30,940 --> 01:16:34,310
as a result of the increasing
temperature, because you're

1830
01:16:34,310 --> 01:16:36,650
exciting more carriers
into the conduction band,

1831
01:16:36,650 --> 01:16:38,450
leaving more holes
in the valence band,

1832
01:16:38,450 --> 01:16:40,750
and these are free charge
carriers are able to conduct

1833
01:16:40,750 --> 01:16:43,140
charge through the material.

1834
01:16:43,140 --> 01:16:44,290
Cool, OK.

1835
01:16:44,290 --> 01:16:48,500
So with that, I will leave
you, and I will return Tuesday.

1836
01:16:48,500 --> 01:16:51,880
And Joe give a fantastic
lecture on device physics

1837
01:16:51,880 --> 01:16:53,920
as well since I
will be at a kickoff

1838
01:16:53,920 --> 01:16:58,390
meeting for a big NSF-related
center in Phoenix, Arizona.

1839
01:16:58,390 --> 01:16:59,710
But it will be great lecture.

1840
01:16:59,710 --> 01:17:02,370
You won't want to miss
it, and look forward

1841
01:17:02,370 --> 01:17:04,490
to seeing you on Tuesday.