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PROFESSOR: All right,
so let's get started.

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00:00:26,530 --> 00:00:31,780
So today-- our last lecture we
talked about different device

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parameters, mainly
our series resistance

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00:00:35,410 --> 00:00:39,037
and shunt resistance, and how
that affects our efficiencies.

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Today we're going to talk a
lot about different material

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properties and how they affect
certain device characteristics,

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00:00:46,310 --> 00:00:48,760
and mainly just affect
our output efficiency.

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00:00:48,760 --> 00:00:53,700
So we've been talking a
lot about the fundamentals.

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00:00:53,700 --> 00:00:56,154
I'm sure you guys are
loving this right now.

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00:00:56,154 --> 00:00:58,570
So we're going to complete
this in probably the next three

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00:00:58,570 --> 00:01:00,722
lectures and then
move on to a lot

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00:01:00,722 --> 00:01:02,180
of the kind of
cross cutting themes

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00:01:02,180 --> 00:01:05,715
in PV-- some advanced concepts,
different device architectures,

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00:01:05,715 --> 00:01:08,090
and that kind of thing.

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00:01:08,090 --> 00:01:10,050
And so that is
coming in the future,

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00:01:10,050 --> 00:01:13,950
but we're still doing
fundamentals today.

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And so I know you're probably
all aware of this equation.

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00:01:19,830 --> 00:01:22,650
And again, this is kind
the progress we've made,

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00:01:22,650 --> 00:01:27,360
so we're almost all the way
through explaining basic device

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00:01:27,360 --> 00:01:29,660
physics and basic
semiconductor physics so you

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00:01:29,660 --> 00:01:32,600
can understand simple devices.

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00:01:32,600 --> 00:01:36,460
And it's always important to
remember that your device is

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00:01:36,460 --> 00:01:38,897
like a leaky bucket, and
you're limited by the largest

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00:01:38,897 --> 00:01:39,730
hole in that bucket.

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00:01:39,730 --> 00:01:42,710
So the weakest aspect
of your solar cell

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00:01:42,710 --> 00:01:47,806
is really what's going to
limit your device performance,

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00:01:47,806 --> 00:01:49,180
and especially if
any of you here

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00:01:49,180 --> 00:01:52,840
are trying to make devices,
it's really important

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00:01:52,840 --> 00:01:55,510
to think about all of these
things when building it.

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00:01:55,510 --> 00:01:57,475
And this is very
difficult to do.

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00:01:57,475 --> 00:01:58,725
I can certainly tell you that.

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00:02:02,442 --> 00:02:03,650
So I kind of like this slide.

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00:02:03,650 --> 00:02:05,740
What this is saying
what's the thing we care

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00:02:05,740 --> 00:02:07,000
about most in our solar cells?

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00:02:07,000 --> 00:02:10,000
Well, as scientists, other
than dollars per watt,

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00:02:10,000 --> 00:02:13,884
we want to maximize our
efficiency for a certain price.

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00:02:13,884 --> 00:02:15,800
And our efficiency,
there's several parameters

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00:02:15,800 --> 00:02:16,466
that go into it.

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00:02:16,466 --> 00:02:19,220
Again, we talked about our
GSC, our short circuit current,

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00:02:19,220 --> 00:02:21,830
our open circuit voltage,
and our fill factor.

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And that gives our output
energy, or output power,

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00:02:24,207 --> 00:02:25,790
and we divide that
by the input power,

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00:02:25,790 --> 00:02:27,470
which is the solar insulation.

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00:02:27,470 --> 00:02:29,470
Now we can split up that
again into open circuit

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00:02:29,470 --> 00:02:33,150
voltage, short circuit
current, and fill factor.

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00:02:33,150 --> 00:02:36,140
We talked a little bit last
lecture about fill factor

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and how that's influenced
by different resistive

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losses in our solar cell.

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00:02:40,909 --> 00:02:43,200
Today we're going to mainly
be focused on short circuit

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current and things like internal
quantum efficiency, which

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are highly affected by
our diffusion length.

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And the diffusion
length is often

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limited by certain
defects in our materials,

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and we're going to
get into why that is.

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And to a certain extent,
we'll talk about open circuit

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voltage, because your GSC
really has a large effect

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on your open circuit voltage.

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So what we're going
to learn today

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is what is minority
carrier diffusion length.

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It was in the homework.

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Hopefully you guys have
some idea coming to lecture,

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but today we're going
to talk about it

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a little more in depth,
and why it's important,

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and how it's affected.

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What are the parameters
of determinants?

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So mainly diffusivity
and lifetime.

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We're going to describe
how it's actually

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measured in a solar
cell, which is actually

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a really cool measurement,
and we actually

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have the capabilities
in our lab.

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And possibly some of you,
when you're making cells,

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will be able to do
that measurement.

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We're also going to look
at some of the things that

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limit lifetime, some of the
basic recombination mechanisms.

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Also look at how your excess
carrier concentration changes

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as a function of lifetime
and generationally.

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And then also talk about
the last material parameter,

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which is mobility,
which discusses

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of how well these excited
charges can move around

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in your material.

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00:04:00,230 --> 00:04:02,600
So without further ado,
here are minority curve,

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diffusion length.

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00:04:03,310 --> 00:04:05,010
The definition is really simple.

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If you generate--
let's say, a photon

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00:04:07,020 --> 00:04:10,540
comes in and hits a silicon atom
and generates an electron pair

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00:04:10,540 --> 00:04:11,550
over here.

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How far or how much
volume can it explore?

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00:04:14,920 --> 00:04:19,290
And that volume
it can explore is

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00:04:19,290 --> 00:04:21,170
described by some
characteristic radius,

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00:04:21,170 --> 00:04:24,550
and that radius is known
as the diffusion length.

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00:04:24,550 --> 00:04:27,230
And it's really
important to solar cells,

99
00:04:27,230 --> 00:04:29,790
because when you think
about these carriers

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00:04:29,790 --> 00:04:30,990
that you're generating.

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If they can only explore
a very short area,

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00:04:33,132 --> 00:04:34,340
they're not going to make it.

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00:04:34,340 --> 00:04:36,300
This is a very good solar
cell, so the diffusion length

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00:04:36,300 --> 00:04:38,020
is really long, and
all these carriers

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00:04:38,020 --> 00:04:39,436
that are just
generated there will

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00:04:39,436 --> 00:04:42,660
be able to make our junction.

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00:04:42,660 --> 00:04:45,600
So again, just so we're
familiar, this is our base.

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00:04:45,600 --> 00:04:47,990
In the top, we have our emitter.

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00:04:47,990 --> 00:04:51,100
So the junction would be at this
line right here on that plane.

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00:04:53,660 --> 00:04:55,730
If we have a really
bad solar cell--

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00:04:55,730 --> 00:04:57,940
so let's say a lot
of defects present,

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00:04:57,940 --> 00:05:01,701
a lot of areas for these excited
carriers to recombine-- they

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00:05:01,701 --> 00:05:02,950
won't make it to the junction.

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00:05:02,950 --> 00:05:06,140
They'll have a very
short diffusion length,

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00:05:06,140 --> 00:05:08,870
and as a result, your short
circuit current and your VOC

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00:05:08,870 --> 00:05:10,410
will suffer dramatically.

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00:05:10,410 --> 00:05:13,450
So it's really important
to get good crystal quality

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00:05:13,450 --> 00:05:15,960
and good material quality,
but up to a certain point.

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00:05:15,960 --> 00:05:19,602
There's kind of
diminishing returns

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00:05:19,602 --> 00:05:21,310
as you go to higher
and higher qualities,

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00:05:21,310 --> 00:05:22,851
so we'll talk about
that in a second.

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00:05:25,890 --> 00:05:32,220
So if we assume--
what this is showing

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00:05:32,220 --> 00:05:35,540
is how our short circuit current
scales with our diffusion

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00:05:35,540 --> 00:05:36,490
length.

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So we have something
called the generation rate,

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00:05:39,330 --> 00:05:41,780
and this is often
proportional to the photon

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00:05:41,780 --> 00:05:42,970
flux on your material.

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00:05:42,970 --> 00:05:45,290
So the number of photons
hitting your solar cell.

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00:05:45,290 --> 00:05:47,547
And this generation
rate is something--

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00:05:47,547 --> 00:05:49,880
the number of carriers produced
per second in some given

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00:05:49,880 --> 00:05:51,320
volume.

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00:05:51,320 --> 00:05:53,130
So it's a volumetric term.

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And if we assume that
everything within one diffusion

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00:05:55,420 --> 00:05:57,820
length of our junction
gets collected,

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00:05:57,820 --> 00:06:00,820
that'll all be counted
as short circuit current.

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So basically your
JSC has this kind

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00:06:02,820 --> 00:06:05,680
of linear dependence on
your diffusion length,

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00:06:05,680 --> 00:06:07,940
but that's only true
up to a certain point.

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00:06:07,940 --> 00:06:09,940
So for example, if we
have a diffusion length

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00:06:09,940 --> 00:06:11,925
that is much longer than
the device thickness.

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00:06:11,925 --> 00:06:13,800
It's really not going
to be-- you get, again,

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00:06:13,800 --> 00:06:15,940
diminishing returns as you go
to longer and longer diffusion

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00:06:15,940 --> 00:06:16,730
lengths.

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00:06:16,730 --> 00:06:19,510
So this is a calculation I
did using a 1D simulation

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00:06:19,510 --> 00:06:22,550
program called PC1D, which if
you want to play around with,

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00:06:22,550 --> 00:06:23,590
it's free.

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00:06:23,590 --> 00:06:25,410
It's a lot of fun
to use, actually,

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00:06:25,410 --> 00:06:29,390
and you can put in
things like lifetimes--

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00:06:29,390 --> 00:06:31,310
and very basically,
the lifetime, which

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00:06:31,310 --> 00:06:33,080
we'll get to in a second--
how that changes the diffusion

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00:06:33,080 --> 00:06:33,800
length.

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00:06:33,800 --> 00:06:36,133
And you can see that there
actually is a linear relation

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00:06:36,133 --> 00:06:39,170
until the diffusion length
is about on the order of 300

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00:06:39,170 --> 00:06:41,071
microns, which is
the device thickness.

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00:06:41,071 --> 00:06:42,820
So you can see this
kind of trailing often

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00:06:42,820 --> 00:06:45,473
and become sub linear
in its response.

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00:06:45,473 --> 00:06:48,311
Yeah?

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00:06:48,311 --> 00:06:51,839
AUDIENCE: Can you clarify
why when the minority carrier

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00:06:51,839 --> 00:06:53,630
flux at the edge of
the space charge region

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00:06:53,630 --> 00:06:55,920
matters, because
I'm thinking about

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00:06:55,920 --> 00:06:58,290
there's the back contact
and the front contact,

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00:06:58,290 --> 00:07:02,025
and there's a junction right
near the front project.

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00:07:02,025 --> 00:07:04,350
They're not
[INAUDIBLE] connecting.

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00:07:04,350 --> 00:07:07,100
PROFESSOR: So let's think
about it one step back.

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00:07:07,100 --> 00:07:09,570
Why do we care about
minority carriers?

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00:07:09,570 --> 00:07:12,450
AUDIENCE: Because those are
the ones that are actually

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00:07:12,450 --> 00:07:13,890
generating the current.

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00:07:13,890 --> 00:07:15,514
PROFESSOR: Right, so
if, let's say, you

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00:07:15,514 --> 00:07:18,940
generate an electron hole
pair and n-type material,

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00:07:18,940 --> 00:07:21,900
the hole wants to move
to the p-type side.

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00:07:21,900 --> 00:07:25,170
And the electric field will
actually repel and keep

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00:07:25,170 --> 00:07:31,512
the electron on the n-type side.

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00:07:31,512 --> 00:07:33,220
So it's your minority
carriers the matter

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00:07:33,220 --> 00:07:34,761
in terms of the
separation, and we'll

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00:07:34,761 --> 00:07:38,060
talk about that again if that's
still fuzzy in people's heads.

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00:07:38,060 --> 00:07:40,600
And so what matters
in terms of-- you're

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00:07:40,600 --> 00:07:43,272
talking about deriving
the ideal diode equation?

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00:07:43,272 --> 00:07:45,677
AUDIENCE: Well, no. [INAUDIBLE].

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00:07:45,677 --> 00:07:49,350
So it seems like the important
thing is that some carrier gets

180
00:07:49,350 --> 00:07:50,792
to the metallization?

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00:07:50,792 --> 00:07:52,250
PROFESSOR: Well,
yeah, but in order

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00:07:52,250 --> 00:07:55,810
to be separated, which is the
first part that we care about,

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00:07:55,810 --> 00:07:59,277
it matters that it's
reached the junction.

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00:07:59,277 --> 00:08:01,860
And so it's that concentration
at the junction that determines

185
00:08:01,860 --> 00:08:04,265
the flux across the junction.

186
00:08:04,265 --> 00:08:05,140
Does that make sense?

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00:08:05,140 --> 00:08:05,765
AUDIENCE: Yeah.

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00:08:09,844 --> 00:08:12,260
PROFESSOR: And so there's also
this other loose dependence

189
00:08:12,260 --> 00:08:15,290
on VOC on your diffusion length.

190
00:08:15,290 --> 00:08:17,660
And so if you recall
from a few lectures ago,

191
00:08:17,660 --> 00:08:20,350
this is your equation for VOC.

192
00:08:20,350 --> 00:08:23,910
It's dependent on your short
circuit current, temperature,

193
00:08:23,910 --> 00:08:27,253
and your saturation current,
which you can often think also

194
00:08:27,253 --> 00:08:30,010
think of as your
reverse bias current.

195
00:08:30,010 --> 00:08:35,080
And your saturation current
is dependent on your diffusion

196
00:08:35,080 --> 00:08:35,750
length.

197
00:08:35,750 --> 00:08:38,770
JSC, if you recall, was
linearly proportional

198
00:08:38,770 --> 00:08:40,919
to the diffusion length,
so the VOC actually

199
00:08:40,919 --> 00:08:43,381
scales with the natural log
of the square of the diffusion

200
00:08:43,381 --> 00:08:43,880
length.

201
00:08:43,880 --> 00:08:46,660
And if you pull
out that exponent,

202
00:08:46,660 --> 00:08:50,190
it just squares with the natural
log of your diffusion length.

203
00:08:52,750 --> 00:08:55,810
And again, very,
very simple analogy--

204
00:08:55,810 --> 00:08:59,100
we're assuming, again, that fill
factor is not really affected

205
00:08:59,100 --> 00:09:02,830
by your diffusion length
and that your efficiency is

206
00:09:02,830 --> 00:09:07,110
proportional to the product
of your JSC and your VOC,

207
00:09:07,110 --> 00:09:10,390
so your short circuit current
and your open circuit voltage.

208
00:09:10,390 --> 00:09:13,290
And you can see as go to
longer diffusion lengths,

209
00:09:13,290 --> 00:09:15,490
there's this area of
diminishing return.

210
00:09:15,490 --> 00:09:19,050
And again, there's two
different regimes here.

211
00:09:19,050 --> 00:09:21,360
One is when your diffusion
length is, again, much less

212
00:09:21,360 --> 00:09:22,150
than your device thickness.

213
00:09:22,150 --> 00:09:24,680
You can see that there's a
huge increase in efficiency,

214
00:09:24,680 --> 00:09:26,580
but as your diffusion
length gets well,

215
00:09:26,580 --> 00:09:28,405
well above your
device thickness,

216
00:09:28,405 --> 00:09:29,990
it becomes less
and less important.

217
00:09:40,100 --> 00:09:42,300
So how do you deal with this?

218
00:09:42,300 --> 00:09:44,030
So if you have,
let's say-- suppose

219
00:09:44,030 --> 00:09:45,950
you want to make a
really cheap solar cell,

220
00:09:45,950 --> 00:09:48,240
and you have a
very dirty material

221
00:09:48,240 --> 00:09:50,010
with very short
lifetime shown here.

222
00:09:50,010 --> 00:09:53,440
There's several ideas
of what you can do.

223
00:09:53,440 --> 00:09:57,710
You can have a very,
very thin device.

224
00:09:57,710 --> 00:10:00,220
Now, that's a problem if you
can't absorb it very well.

225
00:10:00,220 --> 00:10:02,160
So you can have
some optical tricks.

226
00:10:02,160 --> 00:10:03,580
You can do surface texturing.

227
00:10:03,580 --> 00:10:06,680
There's all sorts of other
ideas for basically having

228
00:10:06,680 --> 00:10:08,940
the carriers coming
in at angles or having

229
00:10:08,940 --> 00:10:11,830
a good reflector on the back.

230
00:10:11,830 --> 00:10:15,920
So that's ways you can work
with very low diffusion length

231
00:10:15,920 --> 00:10:22,390
materials and still get a device
efficiency that's not too bad.

232
00:10:22,390 --> 00:10:25,846
Now we're going to talk quickly
about how our minority carrier

233
00:10:25,846 --> 00:10:27,720
diffusion length is
measured, and again, this

234
00:10:27,720 --> 00:10:30,120
is something we're
able to do in our lab.

235
00:10:30,120 --> 00:10:34,430
And one of the important
things to say is defined

236
00:10:34,430 --> 00:10:35,770
is collection probability.

237
00:10:35,770 --> 00:10:38,210
So for example, if
this is our junction

238
00:10:38,210 --> 00:10:41,820
right here-- so our
space charge region--

239
00:10:41,820 --> 00:10:44,300
if you generate a carrier,
let's say very, very close

240
00:10:44,300 --> 00:10:47,440
to the junction, it's going
to have a high or near unity

241
00:10:47,440 --> 00:10:50,930
probability of making it to the
junction and being collected.

242
00:10:50,930 --> 00:10:53,090
If it's generated very,
very, very far away,

243
00:10:53,090 --> 00:10:54,720
it's going to have
a lower probability.

244
00:10:54,720 --> 00:10:55,660
And that's what
this graph is trying

245
00:10:55,660 --> 00:10:58,201
to show-- is that right near
the junction you have near unity

246
00:10:58,201 --> 00:11:01,490
collection probability, and
as you go way, it comes down.

247
00:11:01,490 --> 00:11:03,290
And the different
colored lines are

248
00:11:03,290 --> 00:11:08,940
showing different ways of
increasing that diffusion

249
00:11:08,940 --> 00:11:09,440
length.

250
00:11:09,440 --> 00:11:10,890
Service passivation
is important.

251
00:11:10,890 --> 00:11:12,387
We'll talk about
what that is soon.

252
00:11:12,387 --> 00:11:13,970
And also diffusion
lengths-- if you're

253
00:11:13,970 --> 00:11:15,860
limited by diffusion
length, you can see

254
00:11:15,860 --> 00:11:20,105
this very, very sharp drop off.

255
00:11:20,105 --> 00:11:22,101
AUDIENCE: Just a follow up.

256
00:11:22,101 --> 00:11:27,550
So is collection meaning
collected by the front contact

257
00:11:27,550 --> 00:11:31,580
to be used in your
external circuit?

258
00:11:31,580 --> 00:11:33,612
PROFESSOR: Mm-hm.

259
00:11:33,612 --> 00:11:35,070
Right here it's
technically defined

260
00:11:35,070 --> 00:11:37,360
as reaching the junction
and being separated,

261
00:11:37,360 --> 00:11:39,858
which, in essence, will
hopefully be the same thing.

262
00:11:39,858 --> 00:11:44,340
AUDIENCE: So is surface
passivation [INAUDIBLE]

263
00:11:44,340 --> 00:11:46,830
sort of like diffusion?

264
00:11:46,830 --> 00:11:49,010
PROFESSOR: It can affect
the diffusion length,

265
00:11:49,010 --> 00:11:51,360
and we'll-- or the affect
of diffusion length.

266
00:11:51,360 --> 00:11:53,056
We'll to that in a second.

267
00:11:53,056 --> 00:11:53,930
It'll be a bit later.

268
00:11:53,930 --> 00:11:55,270
This is kind of just
showing that there's

269
00:11:55,270 --> 00:11:56,790
a lot of different
material parameters--

270
00:11:56,790 --> 00:11:58,880
not just your diffusion
length-- that can really

271
00:11:58,880 --> 00:12:00,510
affect your device performance
and your collection

272
00:12:00,510 --> 00:12:01,010
probability.

273
00:12:04,760 --> 00:12:06,317
So if you recall
a few slides back,

274
00:12:06,317 --> 00:12:07,900
we said that our
short circuit current

275
00:12:07,900 --> 00:12:10,172
is directly proportional
to our diffusion length.

276
00:12:10,172 --> 00:12:12,380
And the reason is that, if
you're generating carriers

277
00:12:12,380 --> 00:12:14,130
within the diffusion
length, you generally

278
00:12:14,130 --> 00:12:16,296
think of that as the region
of which you're actually

279
00:12:16,296 --> 00:12:17,450
collecting those carriers.

280
00:12:17,450 --> 00:12:19,783
And if you go back to the
next slide, that kind of makes

281
00:12:19,783 --> 00:12:21,980
sense.

282
00:12:21,980 --> 00:12:23,202
So this is highlighted.

283
00:12:23,202 --> 00:12:24,410
So this is our junction here.

284
00:12:24,410 --> 00:12:28,760
We have our n-type material
on top, our p-type below.

285
00:12:28,760 --> 00:12:31,470
And within a diffusion length
of your minority carrier--

286
00:12:31,470 --> 00:12:34,095
so on your p-type type side you
care about the diffusion length

287
00:12:34,095 --> 00:12:34,889
of your electrons.

288
00:12:34,889 --> 00:12:37,180
On the n-type side, you care
about the diffusion length

289
00:12:37,180 --> 00:12:39,750
of your holes, and that's the
region where you're really

290
00:12:39,750 --> 00:12:40,870
collecting carriers.

291
00:12:40,870 --> 00:12:43,289
Of course, there's a tail
off, but the first order

292
00:12:43,289 --> 00:12:45,330
approximation-- this is
actually a very good one.

293
00:12:48,400 --> 00:12:50,540
And so now putting
those all together.

294
00:12:50,540 --> 00:12:54,460
If we know how our
carriers are generated

295
00:12:54,460 --> 00:12:57,800
as a function of x, and we what
the collection probability is

296
00:12:57,800 --> 00:13:00,300
as a function of x based on
diffusion length, surface

297
00:13:00,300 --> 00:13:02,270
passivation, and
other parameters,

298
00:13:02,270 --> 00:13:04,800
we can multiply them
and then integrate

299
00:13:04,800 --> 00:13:07,940
to actually get what our
illuminated current will be.

300
00:13:07,940 --> 00:13:08,440
Yeah?

301
00:13:08,440 --> 00:13:10,314
AUDIENCE: [INAUDIBLE]
have like three regimes

302
00:13:10,314 --> 00:13:13,390
because the diffusivities are
different at each [INAUDIBLE].

303
00:13:16,382 --> 00:13:17,340
PROFESSOR: The emitter?

304
00:13:17,340 --> 00:13:19,915
AUDIENCE: [INAUDIBLE]
the junction afterwards?

305
00:13:19,915 --> 00:13:21,237
PROFESSOR: Mm-hm.

306
00:13:21,237 --> 00:13:22,820
For most models you
pretty much assume

307
00:13:22,820 --> 00:13:24,610
that anything
absorbed-- first of all,

308
00:13:24,610 --> 00:13:27,960
the space charge region
is very, very narrow.

309
00:13:27,960 --> 00:13:30,980
It's almost assumed just
to be negligibly thin.

310
00:13:30,980 --> 00:13:34,900
And the emitter is
generally very, very short,

311
00:13:34,900 --> 00:13:37,910
and the diffusion lengths are so
poor in the emitter for reasons

312
00:13:37,910 --> 00:13:41,170
we'll get to soon that
it's almost a dead layer.

313
00:13:41,170 --> 00:13:43,130
Your response, the
very short wavelengths,

314
00:13:43,130 --> 00:13:45,527
where you're absorbing most
of your light and emitter

315
00:13:45,527 --> 00:13:47,610
generally don't add to
your short circuit current,

316
00:13:47,610 --> 00:13:49,110
and we'll talk about that soon.

317
00:13:49,110 --> 00:13:50,160
So excellent question.

318
00:13:50,160 --> 00:13:50,962
Yeah?

319
00:13:50,962 --> 00:13:52,230
AUDIENCE: Is that first
region right there--

320
00:13:52,230 --> 00:13:52,520
PROFESSOR: Wait, sorry.

321
00:13:52,520 --> 00:13:53,030
Say that again.

322
00:13:53,030 --> 00:13:53,530
I couldn't--

323
00:13:53,530 --> 00:13:55,640
AUDIENCE: People just
approximate the first region

324
00:13:55,640 --> 00:13:58,082
there and not care about
[INAUDIBLE] afterwards?

325
00:13:58,082 --> 00:14:00,040
PROFESSOR: So for certain
wavelengths of light,

326
00:14:00,040 --> 00:14:03,640
let's say, that
are-- this curve,

327
00:14:03,640 --> 00:14:06,850
this is kind of representing
Beer Lambert's law.

328
00:14:06,850 --> 00:14:10,920
If it attenuates
less drastically,

329
00:14:10,920 --> 00:14:12,690
that characteristic
absorption length,

330
00:14:12,690 --> 00:14:15,600
if it's a lot longer than
this length here, then yes.

331
00:14:15,600 --> 00:14:18,710
You can assume that this emitter
region is negligibly thin,

332
00:14:18,710 --> 00:14:20,835
and that's a little bit
what the homework goes over

333
00:14:20,835 --> 00:14:21,980
as well in problem three.

334
00:14:21,980 --> 00:14:24,590
Excellent question.

335
00:14:24,590 --> 00:14:29,270
And so what we care about
is the spectral response

336
00:14:29,270 --> 00:14:30,850
of our short circuit current.

337
00:14:30,850 --> 00:14:33,330
So what this is is this a
quantum efficiency tool.

338
00:14:33,330 --> 00:14:35,280
This is something
we have in our lab.

339
00:14:35,280 --> 00:14:38,750
It's a really fun tool
to play around with.

340
00:14:38,750 --> 00:14:42,610
How it works is you
basically have--

341
00:14:42,610 --> 00:14:45,740
we have a light source
that's white light,

342
00:14:45,740 --> 00:14:47,470
and it goes through
a series of filters.

343
00:14:47,470 --> 00:14:51,620
There's a monochromator,
which basically-- it

344
00:14:51,620 --> 00:14:53,250
diffracts the light,
so it spatially

345
00:14:53,250 --> 00:14:56,050
separates the light,
kind of like a rainbow.

346
00:14:56,050 --> 00:14:59,900
And then you can focus
that onto your solar cell

347
00:14:59,900 --> 00:15:03,210
and measure the current output
under short circuit conditions.

348
00:15:03,210 --> 00:15:07,320
And that will tell you-- because
you know the carrier generation

349
00:15:07,320 --> 00:15:09,950
profile for different
wavelengths of light,

350
00:15:09,950 --> 00:15:12,497
because you know what
alpha is for silicon,

351
00:15:12,497 --> 00:15:14,080
you can actually
pretty well calculate

352
00:15:14,080 --> 00:15:18,142
what your diffusion
length is, and we'll

353
00:15:18,142 --> 00:15:19,350
talk about on the next slide.

354
00:15:19,350 --> 00:15:22,760
So this is kind of what
your quantum efficiency will

355
00:15:22,760 --> 00:15:23,260
look like.

356
00:15:23,260 --> 00:15:25,284
This is, I think--
I actually don't

357
00:15:25,284 --> 00:15:26,700
know if this
internal or external,

358
00:15:26,700 --> 00:15:31,280
but they're just related
by a factor of 1 over r.

359
00:15:31,280 --> 00:15:34,171
So here you're blue
response-- so everything

360
00:15:34,171 --> 00:15:36,170
that's absorbed right in
the near surface region

361
00:15:36,170 --> 00:15:38,470
in your emitter generally
doesn't get collected,

362
00:15:38,470 --> 00:15:40,260
and this is due to
really bad diffusion

363
00:15:40,260 --> 00:15:43,240
lengths in the emitter region.

364
00:15:43,240 --> 00:15:47,820
As you go to longer wavelengths,
the absorption length

365
00:15:47,820 --> 00:15:49,706
is much, much deeper.

366
00:15:49,706 --> 00:15:52,080
You're collecting a lot of
it, and then what do you think

367
00:15:52,080 --> 00:15:53,030
is happening here?

368
00:15:57,070 --> 00:15:59,420
Generally these longer
wavelengths-- your alpha

369
00:15:59,420 --> 00:16:01,340
is so low that
you're not actually

370
00:16:01,340 --> 00:16:03,150
absorbing much of
this light, which

371
00:16:03,150 --> 00:16:04,820
is part of the reason that
you're not collecting it,

372
00:16:04,820 --> 00:16:07,195
or that you're absorbing it
so far away from the junction

373
00:16:07,195 --> 00:16:09,450
that it's not being
able to diffuse there.

374
00:16:09,450 --> 00:16:13,534
And so that's kind
of how you can

375
00:16:13,534 --> 00:16:15,200
look at these quantum
efficiency curves,

376
00:16:15,200 --> 00:16:16,800
and it's this region
here that's really

377
00:16:16,800 --> 00:16:17,966
limited by diffusion length.

378
00:16:17,966 --> 00:16:19,756
And again, you have
a homework problem

379
00:16:19,756 --> 00:16:20,880
discussing how that's done.

380
00:16:23,750 --> 00:16:26,840
Some of the cool other tools--
the lab can kind of do this,

381
00:16:26,840 --> 00:16:30,360
but it requires a little
more-- I don't know--

382
00:16:30,360 --> 00:16:31,920
hand work on the operator.

383
00:16:31,920 --> 00:16:35,650
But if you can take
different EQE or I IQE

384
00:16:35,650 --> 00:16:39,002
curves at different
points on your solar cell

385
00:16:39,002 --> 00:16:40,460
and you get those
spectrums, you'll

386
00:16:40,460 --> 00:16:42,168
get a whole bunch of
different spectrums.

387
00:16:42,168 --> 00:16:45,347
You'll scan with
your light beam.

388
00:16:45,347 --> 00:16:46,930
You can actually get
diffusion lengths

389
00:16:46,930 --> 00:16:49,260
as a function of
position and get

390
00:16:49,260 --> 00:16:51,520
a spatial map of your
different diffusion lengths.

391
00:16:51,520 --> 00:16:52,930
And it's really
helpful if you're

392
00:16:52,930 --> 00:16:55,440
trying to fine spatial
inhomogeneities in your cell.

393
00:16:55,440 --> 00:16:58,690
So I believe that this is
some multi-crystalline cell,

394
00:16:58,690 --> 00:17:00,770
and see all sorts
of grain boundaries.

395
00:17:00,770 --> 00:17:03,390
And those are areas of very
short diffusion length,

396
00:17:03,390 --> 00:17:07,530
and we'll talk about why
that's the case, actually,

397
00:17:07,530 --> 00:17:08,740
on the next couple slides.

398
00:17:08,740 --> 00:17:09,030
Question?

399
00:17:09,030 --> 00:17:09,240
Yeah?

400
00:17:09,240 --> 00:17:11,240
AUDIENCE: Could you just
clarify the difference

401
00:17:11,240 --> 00:17:15,490
between diffusion length,
absorption length, and band

402
00:17:15,490 --> 00:17:16,240
depth energy?

403
00:17:16,240 --> 00:17:19,240
Because I thought that the
middle weight ones were more

404
00:17:19,240 --> 00:17:21,240
absorbed because they were bent?

405
00:17:21,240 --> 00:17:26,080
Their higher weight [INAUDIBLE]
for bigger-- to cross

406
00:17:26,080 --> 00:17:28,530
bigger band depth energies.

407
00:17:28,530 --> 00:17:32,780
I didn't think it was because
of the absorption [INAUDIBLE].

408
00:17:32,780 --> 00:17:36,540
PROFESSOR: So alpha is what
tells you is your absorption

409
00:17:36,540 --> 00:17:40,860
coefficient, and it's often in
units of one over centimeters,

410
00:17:40,860 --> 00:17:42,350
so inverse centimeters.

411
00:17:42,350 --> 00:17:45,410
And so if you plot
what that looks like,

412
00:17:45,410 --> 00:17:50,880
it's an exponential
function with x.

413
00:17:50,880 --> 00:17:52,760
And the point to
which it is attenuated

414
00:17:52,760 --> 00:17:57,410
by a factor of one over e,
that point is 1 over alpha.

415
00:17:57,410 --> 00:18:03,070
And that's often called
the absorption depth

416
00:18:03,070 --> 00:18:05,690
or-- what am I thinking of?

417
00:18:05,690 --> 00:18:08,070
Absorption length
of that wavelength.

418
00:18:08,070 --> 00:18:10,250
And alpha will vary as a
function of wavelength.

419
00:18:10,250 --> 00:18:16,695
If you recall that, if you
look at lambda, for silicon,

420
00:18:16,695 --> 00:18:20,030
it's something that continues to
go down at longer wavelengths.

421
00:18:20,030 --> 00:18:22,480
So the short wavelengths
are absorbed very strongly,

422
00:18:22,480 --> 00:18:26,180
and so most of the light is
absorbed very, very close

423
00:18:26,180 --> 00:18:31,649
to the surface, where the longer
wavelengths-- most of the light

424
00:18:31,649 --> 00:18:33,690
is actually absorbed rather
far from the surface.

425
00:18:33,690 --> 00:18:35,350
Does that make sense?

426
00:18:35,350 --> 00:18:38,130
And so there's a difference
between your absorption length

427
00:18:38,130 --> 00:18:40,040
and your diffusion
length, and that ratio

428
00:18:40,040 --> 00:18:41,260
is what's really important.

429
00:18:41,260 --> 00:18:45,620
If you're absorbing really
far away from the junction,

430
00:18:45,620 --> 00:18:47,250
but you have a long
diffusion length,

431
00:18:47,250 --> 00:18:49,490
there's a greater chance
of it making there.

432
00:18:49,490 --> 00:18:51,830
And it's that ratio that's
really, really important.

433
00:18:51,830 --> 00:18:52,440
Does that answer your question?

434
00:18:52,440 --> 00:18:52,930
AUDIENCE: Yeah.

435
00:18:52,930 --> 00:18:53,513
PROFESSOR: OK.

436
00:18:56,890 --> 00:18:59,204
So what limits this minority
carrier diffusion length?

437
00:18:59,204 --> 00:19:00,620
We're going to get
to the equation

438
00:19:00,620 --> 00:19:03,030
in a second for the minority
carrier diffusion length,

439
00:19:03,030 --> 00:19:05,900
but basically when you
excite an electron hole pair,

440
00:19:05,900 --> 00:19:09,610
you have this mobile electron,
and it's in this excited state.

441
00:19:09,610 --> 00:19:11,360
You've given it this
energy from a photon,

442
00:19:11,360 --> 00:19:13,152
and now it can move
around, and it can only

443
00:19:13,152 --> 00:19:14,568
exist for a certain
amount of time

444
00:19:14,568 --> 00:19:16,660
before it finds another
whole and recombines.

445
00:19:16,660 --> 00:19:20,320
And that event, again,
is called recombination.

446
00:19:20,320 --> 00:19:24,580
And a lot of this is actually
determined by the size

447
00:19:24,580 --> 00:19:25,750
of grains in your material.

448
00:19:25,750 --> 00:19:28,419
If you've seen-- I
think on the cell

449
00:19:28,419 --> 00:19:30,210
that [INAUDIBLE] brought
in earlier-- sorry

450
00:19:30,210 --> 00:19:33,620
I don't have a good
example-- it didn't just look

451
00:19:33,620 --> 00:19:34,910
like one kind of flat plane.

452
00:19:34,910 --> 00:19:37,720
You could see different
grain orientations,

453
00:19:37,720 --> 00:19:40,470
and the edges of those grains
are called grain boundaries,

454
00:19:40,470 --> 00:19:43,590
and those can act as
recombination centers

455
00:19:43,590 --> 00:19:45,980
and actually reduce
your-- it's called

456
00:19:45,980 --> 00:19:48,970
your lifetime, which we're
going to get to on this slide.

457
00:19:52,920 --> 00:19:58,360
So this slide has a
lot of stuff going on.

458
00:19:58,360 --> 00:20:00,900
What it's saying is that
your diffusion length

459
00:20:00,900 --> 00:20:05,350
is characteristic
of the diffusivity--

460
00:20:05,350 --> 00:20:07,520
the square root of the
product of your diffusivity

461
00:20:07,520 --> 00:20:10,180
in your lifetime.

462
00:20:10,180 --> 00:20:12,000
The way I like to
think of diffusivity

463
00:20:12,000 --> 00:20:17,120
is that it goes up
with temperature,

464
00:20:17,120 --> 00:20:19,000
and it's also affected
by your mobility.

465
00:20:19,000 --> 00:20:21,300
The mobility is saying
that, if you apply,

466
00:20:21,300 --> 00:20:24,090
let's say, an external
field, and electric field,

467
00:20:24,090 --> 00:20:27,190
how well can those
electrons move around?

468
00:20:27,190 --> 00:20:30,590
So a really high mobility
means that those electrons can

469
00:20:30,590 --> 00:20:33,174
move really easily, and you'll
accelerate them really quickly,

470
00:20:33,174 --> 00:20:34,715
where very low
mobility means they're

471
00:20:34,715 --> 00:20:36,390
going to continue
to hit into things,

472
00:20:36,390 --> 00:20:40,240
and bump around, and not
move around too well.

473
00:20:40,240 --> 00:20:43,880
And your diffusion is this
kind of thermal process.

474
00:20:43,880 --> 00:20:46,730
If you think of, let's
say, gases in a room,

475
00:20:46,730 --> 00:20:49,860
and you have a hot gas, that's
going to diffuse a lot faster.

476
00:20:49,860 --> 00:20:51,870
So it's the product
of these two things.

477
00:20:51,870 --> 00:20:53,840
It's how well it can
move around times

478
00:20:53,840 --> 00:20:57,530
it's thermal energy that
it has to move around,

479
00:20:57,530 --> 00:20:59,220
the energy it has for moving.

480
00:20:59,220 --> 00:21:03,300
And so that's kind of what
the diffusivity means to me.

481
00:21:03,300 --> 00:21:05,360
The lifetime, again,
is what I mentioned

482
00:21:05,360 --> 00:21:07,570
earlier-- is that when
you create this excited

483
00:21:07,570 --> 00:21:13,180
electron that's now free to
move, this mobile electron,

484
00:21:13,180 --> 00:21:16,580
it can move around and explore
a certain area, that area.

485
00:21:16,580 --> 00:21:19,480
Volume is defined by
the diffusion length.

486
00:21:19,480 --> 00:21:23,160
And it exists in that excited
state for some amount of time,

487
00:21:23,160 --> 00:21:26,889
tau, and that tau is not--
not every carrier that

488
00:21:26,889 --> 00:21:28,680
is generated necessarily
has that lifetime,

489
00:21:28,680 --> 00:21:34,080
but it's a characteristic
lifetime that it could have.

490
00:21:34,080 --> 00:21:36,080
And then they're pointed
out here what they are.

491
00:21:40,350 --> 00:21:42,850
So that's what affects
our diffusion length.

492
00:21:42,850 --> 00:21:44,580
So in the next bunch
of slides, we're

493
00:21:44,580 --> 00:21:48,280
going to talk about mainly
how we can affect tau.

494
00:21:48,280 --> 00:21:52,470
So tau is mainly affected by
recombination centers-- so

495
00:21:52,470 --> 00:21:56,260
defects, and semiconductors,
and a few other things

496
00:21:56,260 --> 00:21:57,580
that we're going to talk about.

497
00:21:57,580 --> 00:22:00,590
And then this is almost
limited depending

498
00:22:00,590 --> 00:22:03,630
on what kind of materials
you're using, the mobility,

499
00:22:03,630 --> 00:22:06,060
and so we'll talk
about that, as well.

500
00:22:06,060 --> 00:22:08,250
So what affects lifetime?

501
00:22:08,250 --> 00:22:11,322
We're going to go over,
again, basic recombination

502
00:22:11,322 --> 00:22:12,530
mechanisms in semiconductors.

503
00:22:12,530 --> 00:22:13,880
There's a lot of them.

504
00:22:13,880 --> 00:22:21,250
A lot of them have some rather
complex equations behind them.

505
00:22:21,250 --> 00:22:24,207
We're not going to delve too
deeply into how to derive them.

506
00:22:24,207 --> 00:22:25,290
You're welcome to do that.

507
00:22:25,290 --> 00:22:27,890
It was actually kind
of fun to do on my own

508
00:22:27,890 --> 00:22:30,340
and refresh myself, so
it was really useful--

509
00:22:30,340 --> 00:22:32,340
and also be able to
calculate our excess carrier

510
00:22:32,340 --> 00:22:34,387
concentration, which
we're going to do

511
00:22:34,387 --> 00:22:35,470
in the next couple slides.

512
00:22:35,470 --> 00:22:43,700
So n-- let's say
for n-type material,

513
00:22:43,700 --> 00:22:47,820
the number of mobile electrons
you have is defined as n.

514
00:22:47,820 --> 00:22:52,984
n0 is very frequently
your doping density--

515
00:22:52,984 --> 00:22:54,150
these come up one at a time.

516
00:22:54,150 --> 00:22:54,850
Sorry.

517
00:22:54,850 --> 00:22:58,714
Wrong direction-- are generally
the doping concentration.

518
00:22:58,714 --> 00:23:00,380
So if you're putting
in phosphorus atoms

519
00:23:00,380 --> 00:23:02,380
into your silicon, it
would be the concentration

520
00:23:02,380 --> 00:23:03,680
of phosphorus atoms.

521
00:23:03,680 --> 00:23:06,470
Your delta n is how
many extra electrons

522
00:23:06,470 --> 00:23:08,420
are you adding,
mobile electrons,

523
00:23:08,420 --> 00:23:10,780
due to the photo
excitation of light.

524
00:23:10,780 --> 00:23:12,670
And so that's what
this is saying--

525
00:23:12,670 --> 00:23:14,810
is that you have
some-- your delta n is

526
00:23:14,810 --> 00:23:16,150
equal to your generation rate.

527
00:23:16,150 --> 00:23:17,670
So your generation
rate is generally

528
00:23:17,670 --> 00:23:20,950
in units of carriers
per volume per second--

529
00:23:20,950 --> 00:23:24,580
so how many carries you're
generating in a certain volume.

530
00:23:24,580 --> 00:23:28,980
And because delta n
is actually a density,

531
00:23:28,980 --> 00:23:31,190
you need to say, OK, how
long do those carriers last

532
00:23:31,190 --> 00:23:32,200
once they're excited?

533
00:23:32,200 --> 00:23:35,056
And so it's the g tau product
is what gives you your delta n.

534
00:23:38,322 --> 00:23:40,530
Now, when working with
silicon, it's really important

535
00:23:40,530 --> 00:23:42,670
to understand what the
different ratios are

536
00:23:42,670 --> 00:23:46,004
of n, n0, delta n, the
doping concentrations.

537
00:23:46,004 --> 00:23:47,920
So getting these relative
numbers in your head

538
00:23:47,920 --> 00:23:50,140
is an important step
in moving forward.

539
00:23:50,140 --> 00:23:54,840
So let's say we subject a piece
of silicon to AM1.5 spectra.

540
00:23:58,810 --> 00:24:03,460
So your G-- sorry.

541
00:24:03,460 --> 00:24:05,750
This is a little off.

542
00:24:05,750 --> 00:24:07,800
There we go.

543
00:24:07,800 --> 00:24:08,590
Sorry about that.

544
00:24:08,590 --> 00:24:13,270
When I added some equations--
so your generation rate is

545
00:24:13,270 --> 00:24:16,300
on the order of 10 to the 16th.

546
00:24:16,300 --> 00:24:19,080
A care lifetime for silicon--
this is not a great lifetime,

547
00:24:19,080 --> 00:24:21,340
but an OK one-- is
about 10 microseconds.

548
00:24:21,340 --> 00:24:23,540
And so as a result of
that, you'll get about 10

549
00:24:23,540 --> 00:24:30,300
to the 11th excess carriers
per centimeter cubed.

550
00:24:32,910 --> 00:24:37,379
And if we compare that-- so for
every excess electron we make,

551
00:24:37,379 --> 00:24:38,920
remember we also
leave behind a hole.

552
00:24:38,920 --> 00:24:43,230
So we have delta n is
generally equal to delta p.

553
00:24:43,230 --> 00:24:45,630
And that's about 10 to the 11th.

554
00:24:45,630 --> 00:24:47,760
If we look at our intrinsic
carrier concentration--

555
00:24:47,760 --> 00:24:51,830
so if we had no dopants,
how many carriers

556
00:24:51,830 --> 00:24:53,637
would we have just for
thermal excitation?

557
00:24:53,637 --> 00:24:54,970
And that's about 10 to the 10th.

558
00:24:54,970 --> 00:24:58,220
And so you can see that
delta n is actually

559
00:24:58,220 --> 00:25:00,030
larger than your
intrinsic carrier

560
00:25:00,030 --> 00:25:04,285
concentration for silicon under
normal illumination conditions.

561
00:25:04,285 --> 00:25:05,410
Now, let's take an example.

562
00:25:05,410 --> 00:25:08,730
Suppose we add phosphorus at
the order about 10 to the 16th,

563
00:25:08,730 --> 00:25:13,294
and so that's generally
about what a base doping

564
00:25:13,294 --> 00:25:14,960
concentration should
be-- in that realm.

565
00:25:14,960 --> 00:25:16,376
It might be a
little high, but you

566
00:25:16,376 --> 00:25:21,220
can see that your delta p
is much greater than p0.

567
00:25:21,220 --> 00:25:24,300
So p0 would be how
many holes do you have,

568
00:25:24,300 --> 00:25:27,069
which is a ratio of your
intrinsic carrier squared

569
00:25:27,069 --> 00:25:28,110
over your doping density.

570
00:25:28,110 --> 00:25:30,370
And that's about 10 to the
fourth, so it's way, way

571
00:25:30,370 --> 00:25:35,680
less than what was there
without excitation.

572
00:25:35,680 --> 00:25:39,890
So the number of holes without
any light shining on it is p0.

573
00:25:39,890 --> 00:25:42,280
You generate a bunch
of holes, delta p,

574
00:25:42,280 --> 00:25:43,990
by shining light
on it, and you can

575
00:25:43,990 --> 00:25:47,874
see that these numbers
are drastically different.

576
00:25:47,874 --> 00:25:49,290
And of course,
your doping density

577
00:25:49,290 --> 00:25:54,000
is actually much, much
larger than your delta n.

578
00:25:54,000 --> 00:25:56,300
Your majority carriers
don't change very much,

579
00:25:56,300 --> 00:25:58,675
but your minority carriers
change very, very drastically.

580
00:25:58,675 --> 00:26:00,049
That's really what
this is trying

581
00:26:00,049 --> 00:26:01,315
to say here under excitation.

582
00:26:05,850 --> 00:26:07,760
What is lifetime?

583
00:26:07,760 --> 00:26:09,720
So that bubble
shouldn't be up yet.

584
00:26:13,140 --> 00:26:17,460
So we measure tau by creating
some excess carrier population

585
00:26:17,460 --> 00:26:20,330
and then watch them decay.

586
00:26:20,330 --> 00:26:24,060
And they decay at some
rate, recombination rate,

587
00:26:24,060 --> 00:26:26,630
and under steady
state conditions--

588
00:26:26,630 --> 00:26:28,350
so under constant
illumination, we're

589
00:26:28,350 --> 00:26:32,650
not looking at transients-- your
recombination rate is actually

590
00:26:32,650 --> 00:26:34,005
equal to your generation rate.

591
00:26:34,005 --> 00:26:35,510
So if you compare
the two equations

592
00:26:35,510 --> 00:26:38,390
on the previous slide, they're
true under steady state

593
00:26:38,390 --> 00:26:38,890
conditions.

594
00:26:42,644 --> 00:26:43,810
[INAUDIBLE] going to pop up.

595
00:26:46,500 --> 00:26:49,630
And so your lifetimes add
up like parallel resistors.

596
00:26:49,630 --> 00:26:52,360
So we have tau
bulk, which is kind

597
00:26:52,360 --> 00:26:54,935
of the effective lifetime of
these photo excited carriers.

598
00:26:58,910 --> 00:27:01,120
1 over tau bulk is equal
to 1 over tau radiative,

599
00:27:01,120 --> 00:27:03,370
so this is radiative
recombination.

600
00:27:03,370 --> 00:27:05,500
And this has to do
with-- basically if you

601
00:27:05,500 --> 00:27:08,610
read the Shockley-Queisser
efficiency limit paper,

602
00:27:08,610 --> 00:27:11,270
this is the lifetime that
they assume was limiting.

603
00:27:11,270 --> 00:27:13,480
And for silicon, this is absurd.

604
00:27:13,480 --> 00:27:15,200
This is never ever
the limiting factor.

605
00:27:15,200 --> 00:27:17,240
And a lot of direct band gap
materials-- for those of you

606
00:27:17,240 --> 00:27:19,323
who don't know what that
is, don't worry about it.

607
00:27:19,323 --> 00:27:22,140
That's often the
limiting factor,

608
00:27:22,140 --> 00:27:24,440
and it has to do with
the absorption is always

609
00:27:24,440 --> 00:27:27,230
equal to the emissivity
in a material.

610
00:27:27,230 --> 00:27:28,930
AUDIENCE: [INAUDIBLE]?

611
00:27:28,930 --> 00:27:30,680
PROFESSOR: For a direct
band gap material,

612
00:27:30,680 --> 00:27:33,190
radiative recombination
can be an issue,

613
00:27:33,190 --> 00:27:36,720
and I'll talk about
that in a second.

614
00:27:36,720 --> 00:27:39,160
And there's also
another combination

615
00:27:39,160 --> 00:27:41,410
called Auger recombination.

616
00:27:41,410 --> 00:27:43,870
It's not "Oger" like I thought
when I first came here.

617
00:27:43,870 --> 00:27:47,720
It's "O-jay," kind of like--
I don't know-- OJ Simpson,

618
00:27:47,720 --> 00:27:48,462
I guess.

619
00:27:48,462 --> 00:27:50,190
[LAUGHTER]

620
00:27:50,190 --> 00:27:53,650
And it's dominant only under
very high injection conditions

621
00:27:53,650 --> 00:27:54,950
or very high doping density.

622
00:27:54,950 --> 00:27:57,397
So in your emitter layer where
there's really, really high

623
00:27:57,397 --> 00:27:58,980
doping densities,
you're going to have

624
00:27:58,980 --> 00:28:00,800
a lot of Auger recombination.

625
00:28:00,800 --> 00:28:03,381
And the last one is
Shockley-Read-Hall

626
00:28:03,381 --> 00:28:04,380
So these are three guys.

627
00:28:04,380 --> 00:28:10,450
They came up with this kind of
a model for how recombination

628
00:28:10,450 --> 00:28:14,790
happens in defective
materials-- so materials

629
00:28:14,790 --> 00:28:18,740
with levels, electronic
levels, in the mid-gap.

630
00:28:18,740 --> 00:28:20,690
And again, these add
like parallel resistors,

631
00:28:20,690 --> 00:28:22,910
so you're always-- so
if you remember back

632
00:28:22,910 --> 00:28:26,770
to the leaky bucket, these your
leaky buckets for diffusion

633
00:28:26,770 --> 00:28:27,510
length.

634
00:28:27,510 --> 00:28:30,360
You're always limited by your
shortest diffusion length--

635
00:28:30,360 --> 00:28:32,740
or, sorry, your
shortest lifetime.

636
00:28:32,740 --> 00:28:35,955
And this is often your
limiting lifetime--

637
00:28:35,955 --> 00:28:38,284
is your Shockley--Read--Hall
recombination.

638
00:28:38,284 --> 00:28:41,210
AUDIENCE: Is it for silicon
and for [INAUDIBLE]?

639
00:28:41,210 --> 00:28:42,210
PROFESSOR: For silicon--

640
00:28:42,210 --> 00:28:43,132
AUDIENCE: [INAUDIBLE].

641
00:28:43,132 --> 00:28:46,907
The Shockley-Read-Hall
is the [INAUDIBLE].

642
00:28:46,907 --> 00:28:48,490
PROFESSOR: So radiative
recombination.

643
00:28:48,490 --> 00:28:50,560
So you can probably
guess from the name

644
00:28:50,560 --> 00:28:54,110
that radiative recombination
involves a photon.

645
00:28:54,110 --> 00:28:55,940
The ability to
absorb photons also

646
00:28:55,940 --> 00:28:57,870
means you have the
ability to emit them,

647
00:28:57,870 --> 00:29:00,820
and so silicon, or
many semiconductors,

648
00:29:00,820 --> 00:29:05,010
will emit photons when
you get a recombination

649
00:29:05,010 --> 00:29:06,640
event across the band.

650
00:29:06,640 --> 00:29:12,170
And when that happens, you emit
a photon under equilibrium.

651
00:29:12,170 --> 00:29:14,454
So equilibrium means
no outside excitation.

652
00:29:14,454 --> 00:29:16,620
It doesn't mean steady
state, so this is, let's say,

653
00:29:16,620 --> 00:29:18,640
in the dark.

654
00:29:18,640 --> 00:29:22,292
You get your recombination rate
is equal to your generation

655
00:29:22,292 --> 00:29:24,000
rate, because it's in
thermal equilibrium

656
00:29:24,000 --> 00:29:25,070
with the area around it.

657
00:29:25,070 --> 00:29:28,900
So it's absorbing protons and
emitting them at the same rate.

658
00:29:28,900 --> 00:29:33,470
And this is equal to B.
So some material parameter

659
00:29:33,470 --> 00:29:38,174
times your hole in a
electron concentration.

660
00:29:38,174 --> 00:29:39,840
And again, under
equilibrium conditions,

661
00:29:39,840 --> 00:29:42,070
that's equal to your intrinsic
carrier concentration.

662
00:29:42,070 --> 00:29:43,690
np product is equal
to ni squared.

663
00:29:47,490 --> 00:29:51,210
Now, when you shine
light on it, your n,

664
00:29:51,210 --> 00:29:57,410
which is to n0 plus delta n--
so this is you excited carriers,

665
00:29:57,410 --> 00:29:58,960
your excess carriers.

666
00:29:58,960 --> 00:30:01,710
So your n now increases and
is greater than n sub i,

667
00:30:01,710 --> 00:30:06,541
and your net recombination rate
is determined by this equation

668
00:30:06,541 --> 00:30:07,040
right here.

669
00:30:07,040 --> 00:30:10,200
So B np minus B ni
squared-- so the difference

670
00:30:10,200 --> 00:30:13,670
between your equilibrium
and your now excited carrier

671
00:30:13,670 --> 00:30:15,414
concentrations.

672
00:30:15,414 --> 00:30:17,342
AUDIENCE: I'm not
sure if I missed this.

673
00:30:17,342 --> 00:30:19,149
Is B just a proportionality?

674
00:30:19,149 --> 00:30:20,940
PROFESSOR: It's a
material parameter, yeah.

675
00:30:20,940 --> 00:30:23,070
It depends on-- for
silicon, I forget.

676
00:30:23,070 --> 00:30:24,130
It was on the next slide.

677
00:30:24,130 --> 00:30:26,550
It's 10 to the minus 15th.

678
00:30:26,550 --> 00:30:28,400
I don't know for
other materials,

679
00:30:28,400 --> 00:30:32,270
but I presume that that
would change-- probably

680
00:30:32,270 --> 00:30:35,700
be a lot higher for
other materials.

681
00:30:35,700 --> 00:30:39,320
And it turns out your radiative
recombination lifetimes,

682
00:30:39,320 --> 00:30:43,029
when you plug these numbers in
and you make some assumptions

683
00:30:43,029 --> 00:30:45,070
about what's really small
compared to each other,

684
00:30:45,070 --> 00:30:47,740
you get these equations here.

685
00:30:47,740 --> 00:30:51,940
And again, this is tau is
equal to delta n over R.

686
00:30:51,940 --> 00:30:53,360
And so you get that.

687
00:30:53,360 --> 00:30:58,510
And now if you look
at for silicon,

688
00:30:58,510 --> 00:31:01,780
you get B is about 2 times
10 to the minus 15th.

689
00:31:01,780 --> 00:31:06,130
Your delta n I
put-- n I determined

690
00:31:06,130 --> 00:31:09,490
just was 10 to the 16th--
some doping concentration.

691
00:31:09,490 --> 00:31:12,160
And your radiative lifetime is
incredibly, incredibly long--

692
00:31:12,160 --> 00:31:14,200
about 50 milliseconds.

693
00:31:14,200 --> 00:31:16,110
And if you remember
from before when

694
00:31:16,110 --> 00:31:18,440
I was calculating a
generation rate for silicon,

695
00:31:18,440 --> 00:31:20,540
we used about 10 microseconds.

696
00:31:20,540 --> 00:31:22,600
So this is really, really long.

697
00:31:22,600 --> 00:31:25,400
And so radiative recombination
is very, very slow,

698
00:31:25,400 --> 00:31:27,600
and it's rarely ever
the limiting lifetime

699
00:31:27,600 --> 00:31:30,680
in silicon solar cells.

700
00:31:30,680 --> 00:31:32,370
However, as you
mentioned earlier,

701
00:31:32,370 --> 00:31:35,870
it's actually a big problem
in direct band gap materials.

702
00:31:35,870 --> 00:31:38,010
And if you think of
there's some materials

703
00:31:38,010 --> 00:31:41,760
we actually want a very short
radiative recombination time.

704
00:31:41,760 --> 00:31:44,010
So for example, if you're
trying to make an LED,

705
00:31:44,010 --> 00:31:46,010
you inject carriers
using a voltage

706
00:31:46,010 --> 00:31:48,162
that recombination
emits photons,

707
00:31:48,162 --> 00:31:49,120
and then you get light.

708
00:31:49,120 --> 00:31:51,105
And that's basically
how an LED works.

709
00:31:57,385 --> 00:31:59,510
So now we'll talk a little
about Shockley-Read-Hall

710
00:31:59,510 --> 00:32:00,180
recombinations.

711
00:32:00,180 --> 00:32:02,840
So this is something
that our lab works,

712
00:32:02,840 --> 00:32:05,060
I think, very, very well in.

713
00:32:05,060 --> 00:32:09,940
We do a lot of defects in
semiconductors, specifically

714
00:32:09,940 --> 00:32:10,730
iron.

715
00:32:10,730 --> 00:32:12,740
And so iron is one of
these really, really awful

716
00:32:12,740 --> 00:32:14,180
contaminants in solar cells.

717
00:32:14,180 --> 00:32:16,230
Just a little bit of iron,
I think-- [INAUDIBLE],

718
00:32:16,230 --> 00:32:17,230
correct me if I'm wrong.

719
00:32:17,230 --> 00:32:19,188
I don't remember what
year production this was.

720
00:32:19,188 --> 00:32:22,334
Maybe it was 2009,
but two grams of iron

721
00:32:22,334 --> 00:32:24,000
could contaminate the
entire year supply

722
00:32:24,000 --> 00:32:26,090
of silicon detrimentally.

723
00:32:26,090 --> 00:32:27,016
So that's a lot.

724
00:32:27,016 --> 00:32:28,682
AUDIENCE: I think you
actually calculate

725
00:32:28,682 --> 00:32:29,723
this in your [INAUDIBLE].

726
00:32:29,723 --> 00:32:31,740
PROFESSOR: Yes, you
do for a single panel,

727
00:32:31,740 --> 00:32:35,430
and it shocked me.

728
00:32:35,430 --> 00:32:37,180
So basically what we're
trying to say here

729
00:32:37,180 --> 00:32:39,420
is that you have
iron atoms and it

730
00:32:39,420 --> 00:32:41,380
can sit in different
areas of your lattice,

731
00:32:41,380 --> 00:32:43,900
but you have these
defects that exist,

732
00:32:43,900 --> 00:32:46,390
and they introduce
different energy levels

733
00:32:46,390 --> 00:32:49,150
within the band gap.

734
00:32:49,150 --> 00:32:52,860
So the outer electrons of iron
can either sit at these sites--

735
00:32:52,860 --> 00:32:55,582
so these blue sites
where they're donors,

736
00:32:55,582 --> 00:32:58,040
or they can create acceptor
states kind of like boron does,

737
00:32:58,040 --> 00:33:00,430
but they're much
higher up into the gap.

738
00:33:00,430 --> 00:33:02,080
And these act as
recombination centers,

739
00:33:02,080 --> 00:33:04,060
and we'll talk about
why that is in a second.

740
00:33:07,400 --> 00:33:09,880
So these trap
levels can interact

741
00:33:09,880 --> 00:33:14,630
with mobile carriers in a
whole bunch of different ways.

742
00:33:14,630 --> 00:33:16,380
They can capture an electron.

743
00:33:16,380 --> 00:33:19,280
That electron can
then sit there.

744
00:33:19,280 --> 00:33:20,894
If there's enough
heat energy, it

745
00:33:20,894 --> 00:33:23,310
might actually get promoted
and jump out of that, and then

746
00:33:23,310 --> 00:33:26,800
which case it wouldn't
have actually decreased

747
00:33:26,800 --> 00:33:29,630
your excess carrier population.

748
00:33:29,630 --> 00:33:34,000
It can also capture holes,
and it can also emit holes.

749
00:33:34,000 --> 00:33:38,220
And there's a bunch of things
that go into these equations

750
00:33:38,220 --> 00:33:40,600
here.

751
00:33:40,600 --> 00:33:44,000
It depends on a lot of the
energy of this trap state.

752
00:33:44,000 --> 00:33:46,027
It depends on the
carrier excitation.

753
00:33:46,027 --> 00:33:47,860
We'll talk about that
in another few slides.

754
00:33:47,860 --> 00:33:52,000
And it also depends
on these-- what

755
00:33:52,000 --> 00:33:54,320
are effective-- I
forget the exact word,

756
00:33:54,320 --> 00:33:58,410
but the effective hole
in electron lifetimes.

757
00:33:58,410 --> 00:34:00,670
And those are limited
by your trap density.

758
00:34:00,670 --> 00:34:02,870
So these can be
thought of-- suppose

759
00:34:02,870 --> 00:34:05,300
they're each-- let's say
each iron atom is introducing

760
00:34:05,300 --> 00:34:06,424
one trap level.

761
00:34:06,424 --> 00:34:08,840
It would be the number of trap
levels, the density of trap

762
00:34:08,840 --> 00:34:13,969
levels within your system,
times some thermal energy,

763
00:34:13,969 --> 00:34:15,639
and then a capture
cross section,

764
00:34:15,639 --> 00:34:18,940
which is saying, OK, that trap
state exists in one location.

765
00:34:18,940 --> 00:34:23,040
How much area can it see in
terms of what effective area is

766
00:34:23,040 --> 00:34:25,940
it capturing electrons?

767
00:34:25,940 --> 00:34:29,449
And oftentimes under the
right conditions-- so

768
00:34:29,449 --> 00:34:32,510
with very, very deep
traps, so traps mid-gap

769
00:34:32,510 --> 00:34:34,741
under low injections,
your Shockley-Read-Hall

770
00:34:34,741 --> 00:34:36,949
recombination is actually
one of those two lifetimes,

771
00:34:36,949 --> 00:34:38,870
and it's a very simple equation.

772
00:34:38,870 --> 00:34:41,142
And under very, very high
injection conditions,

773
00:34:41,142 --> 00:34:42,850
it's actually summing
them up, and if you

774
00:34:42,850 --> 00:34:44,266
look in the previous
slide, if you

775
00:34:44,266 --> 00:34:45,989
go to delta n goes
to infinity, you

776
00:34:45,989 --> 00:34:48,150
can see that this becomes true.

777
00:34:48,150 --> 00:34:48,674
Joel?

778
00:34:48,674 --> 00:34:51,605
AUDIENCE: The energy,
the thermal energy type

779
00:34:51,605 --> 00:34:53,234
[INAUDIBLE]?

780
00:34:53,234 --> 00:34:54,650
PROFESSOR: That's
a good question.

781
00:34:54,650 --> 00:34:55,608
That would be my guess.

782
00:34:59,961 --> 00:35:01,752
Sorry, there's another
question back there?

783
00:35:01,752 --> 00:35:05,640
AUDIENCE: Yeah, so is iron
worse or is gold worse?

784
00:35:05,640 --> 00:35:06,825
PROFESSOR: I can't hear you.

785
00:35:06,825 --> 00:35:09,387
AUDIENCE: Is iron a
worse dopant, or is gold

786
00:35:09,387 --> 00:35:11,566
your worst dopant in
terms of [INAUDIBLE]?

787
00:35:11,566 --> 00:35:13,640
PROFESSOR: Oh, in terms
of capture cross section?

788
00:35:13,640 --> 00:35:14,790
AUDIENCE: Yeah.

789
00:35:14,790 --> 00:35:19,780
PROFESSOR: I know they're
both bad, really bad.

790
00:35:19,780 --> 00:35:23,340
[INAUDIBLE], do you know that
off the top of your head?

791
00:35:23,340 --> 00:35:26,990
AUDIENCE: Sure, so gold
has a larger lifetime

792
00:35:26,990 --> 00:35:30,294
impact at lower
concentrations than iron,

793
00:35:30,294 --> 00:35:32,390
but it's perhaps one
of worst, and that's

794
00:35:32,390 --> 00:35:36,110
why you're not allowed to wear
gold jewelry at the cleaners.

795
00:35:36,110 --> 00:35:39,460
They ask you to take off your
wedding bands and other jewelry

796
00:35:39,460 --> 00:35:42,863
before entering the
[INAUDIBLE] cleaners.

797
00:35:42,863 --> 00:35:44,446
PROFESSOR: So no
bling in the cleaner.

798
00:35:44,446 --> 00:35:46,930
There you go.

799
00:35:46,930 --> 00:35:50,180
And so for the material
scientists and physicists

800
00:35:50,180 --> 00:35:53,060
in the room, if that does not
apply to you, don't worry.

801
00:35:53,060 --> 00:35:56,250
This is just to explain
what is going on.

802
00:35:56,250 --> 00:35:57,870
Often when you
want recombination

803
00:35:57,870 --> 00:36:01,540
to happen-- so this is a
momentum, or k, versus energy--

804
00:36:01,540 --> 00:36:04,150
it requires not only the
emission of a photon,

805
00:36:04,150 --> 00:36:10,400
but also a phonon to
change its momentum.

806
00:36:10,400 --> 00:36:15,100
When you introduce a trap level,
or these localized impurities,

807
00:36:15,100 --> 00:36:16,670
because it's localized
in real space,

808
00:36:16,670 --> 00:36:18,590
it's delocalized
in k space, so you

809
00:36:18,590 --> 00:36:20,540
have this kind of
flat level in k,

810
00:36:20,540 --> 00:36:23,375
and you have these very,
very efficient pathways

811
00:36:23,375 --> 00:36:24,980
for recombination.

812
00:36:24,980 --> 00:36:26,620
If that doesn't
resonate with you,

813
00:36:26,620 --> 00:36:27,911
don't worry about it right now.

814
00:36:36,720 --> 00:36:38,850
So here we see that
really the impurities can

815
00:36:38,850 --> 00:36:41,640
have a very, very large effect.

816
00:36:41,640 --> 00:36:43,960
If you think of the doping
densities that we put in,

817
00:36:43,960 --> 00:36:45,560
we've been using
about 10 to the 15th,

818
00:36:45,560 --> 00:36:47,570
10 to the 16th for
our doping density.

819
00:36:47,570 --> 00:36:49,990
This is on the order
of like a million less,

820
00:36:49,990 --> 00:36:53,290
and it can have a huge
impact on lifetime.

821
00:36:53,290 --> 00:36:56,080
So one of the worst, again,
as we said, was iron,

822
00:36:56,080 --> 00:36:58,320
and these interstitial
irons are especially bad.

823
00:36:58,320 --> 00:37:01,870
And at 10 to the-- I
don't know-- looks like 10

824
00:37:01,870 --> 00:37:03,122
to the 11th.

825
00:37:03,122 --> 00:37:04,330
Very, very low concentration.

826
00:37:04,330 --> 00:37:06,460
That's one in 10 to the 12th.

827
00:37:06,460 --> 00:37:08,420
So that's one in
a trillion atoms

828
00:37:08,420 --> 00:37:12,140
are iron-- cane detrimentally
impact your solar cell.

829
00:37:12,140 --> 00:37:13,590
So that's really, really bad.

830
00:37:13,590 --> 00:37:17,290
So keeping fabs
clean-- so again,

831
00:37:17,290 --> 00:37:19,520
no jewelry and other
things can really--

832
00:37:19,520 --> 00:37:23,020
that can actually have a very
large effect on your device

833
00:37:23,020 --> 00:37:24,300
performance.

834
00:37:24,300 --> 00:37:28,690
And if you plot that versus
your dislocation density,

835
00:37:28,690 --> 00:37:31,100
you can see that
if you have-- it's

836
00:37:31,100 --> 00:37:35,115
especially bad for very,
very high lifetime silicon.

837
00:37:35,115 --> 00:37:37,240
Just a few dislocations
can actually really, really

838
00:37:37,240 --> 00:37:39,124
hurt it, but the
effect is mitigated

839
00:37:39,124 --> 00:37:41,540
if you're already starting
with very low lifetime silicon.

840
00:37:46,260 --> 00:37:51,170
And again, this is something our
lab works on quite extensively.

841
00:37:51,170 --> 00:37:52,795
It's not just the
number of iron atoms.

842
00:37:52,795 --> 00:37:54,211
So if you take a
piece of silicon,

843
00:37:54,211 --> 00:37:55,646
and you want to
know its lifetime

844
00:37:55,646 --> 00:37:57,020
or how iron impacts
its lifetime,

845
00:37:57,020 --> 00:37:59,320
it's not just the total
number of iron atoms in it.

846
00:37:59,320 --> 00:38:01,110
It's also how
they're distributed.

847
00:38:01,110 --> 00:38:04,090
So if you have, let's say,
clusters of iron atoms, that

848
00:38:04,090 --> 00:38:07,040
would count as one defect,
or effectively less

849
00:38:07,040 --> 00:38:08,430
than the number of atoms in it.

850
00:38:08,430 --> 00:38:12,820
And so clustering these things
can actually be really, really

851
00:38:12,820 --> 00:38:16,380
a good way of cleaning up
your solar cell material,

852
00:38:16,380 --> 00:38:18,350
and this is an effect
called gettering.

853
00:38:18,350 --> 00:38:20,370
And if you can getter
these impurity atoms

854
00:38:20,370 --> 00:38:22,790
into one location, they'll
have less of a detrimental

855
00:38:22,790 --> 00:38:24,120
impact on your material.

856
00:38:28,659 --> 00:38:30,450
So this is kind of a
tricky one to explain,

857
00:38:30,450 --> 00:38:32,760
but this is-- so
Shockley-Read-Hall

858
00:38:32,760 --> 00:38:35,930
recombination can also
show up in something

859
00:38:35,930 --> 00:38:37,680
called service recombination.

860
00:38:37,680 --> 00:38:40,550
So if you look at
your silicon lattice,

861
00:38:40,550 --> 00:38:43,650
each silicon atom has
four valence electrons,

862
00:38:43,650 --> 00:38:47,520
and it bonds to four
silicon atoms around it,

863
00:38:47,520 --> 00:38:49,510
and it has satisfied
covalent bonds.

864
00:38:49,510 --> 00:38:53,000
So this silicon atom has all its
satisfied, all its satisfied,

865
00:38:53,000 --> 00:38:54,410
until you get to the surface.

866
00:38:54,410 --> 00:38:57,260
And at the surface, you have
what are called dangling bonds.

867
00:38:57,260 --> 00:38:59,530
And these dealing
bonds can actually

868
00:38:59,530 --> 00:39:01,590
introduce traps
states, and so you

869
00:39:01,590 --> 00:39:05,370
can see that actually
introduces a whole ton of levels

870
00:39:05,370 --> 00:39:07,766
within the band gap
that can provide

871
00:39:07,766 --> 00:39:09,390
Shockley-Read-Hall
recall recombination

872
00:39:09,390 --> 00:39:11,280
pathways for your carriers.

873
00:39:11,280 --> 00:39:17,090
And so surfaces are incredibly
important, and the way

874
00:39:17,090 --> 00:39:19,350
we tend to think
of it-- and this

875
00:39:19,350 --> 00:39:22,040
is a concept that might be
difficult to grasp at first,

876
00:39:22,040 --> 00:39:23,570
but it scales with two things.

877
00:39:23,570 --> 00:39:26,140
There's two things going on.

878
00:39:26,140 --> 00:39:29,570
You can think of that this
is the width of your cell,

879
00:39:29,570 --> 00:39:31,970
and you have some service
recombination velocity,

880
00:39:31,970 --> 00:39:35,100
which is some kind of
characteristic of how well they

881
00:39:35,100 --> 00:39:37,800
can recombine at the surface.

882
00:39:37,800 --> 00:39:40,955
And at let's say infinite
surface recombination

883
00:39:40,955 --> 00:39:43,330
velocities, it means that any
carrier that comes and hits

884
00:39:43,330 --> 00:39:45,690
that surface will
most surely recombine.

885
00:39:45,690 --> 00:39:46,925
So this drops to zero.

886
00:39:46,925 --> 00:39:49,300
So then you're limited by,
OK, how well can they actually

887
00:39:49,300 --> 00:39:51,310
diffuse to your surface?

888
00:39:51,310 --> 00:39:55,720
So it's again some kind of
ratio of your self thickness

889
00:39:55,720 --> 00:39:58,450
squared over the diffusivity,
your carrier diffusivity,

890
00:39:58,450 --> 00:40:00,080
and that that gives
you an idea of what

891
00:40:00,080 --> 00:40:01,163
your limiting factors are.

892
00:40:01,163 --> 00:40:05,790
So under very low surface
recombination velocities,

893
00:40:05,790 --> 00:40:07,349
you're limited by
this term here,

894
00:40:07,349 --> 00:40:09,140
the first one, and then
the very high ones,

895
00:40:09,140 --> 00:40:11,146
you're limited by this term.

896
00:40:11,146 --> 00:40:15,736
And do there's two
effects going on there.

897
00:40:15,736 --> 00:40:17,110
And it's summarized
as well here.

898
00:40:19,740 --> 00:40:22,360
At very, very low surface
recombination velocities,

899
00:40:22,360 --> 00:40:27,610
your tau surface almost goes
to infinity-- very high.

900
00:40:27,610 --> 00:40:33,520
And you can passivate
these bonds using hydrogen.

901
00:40:33,520 --> 00:40:37,204
So for example, if you use
hydrofluoric acid, what it does

902
00:40:37,204 --> 00:40:39,620
is it etches away the silicon
oxide layer that sits there,

903
00:40:39,620 --> 00:40:42,590
and you have these hydrogen
atoms that now sit and satisfy

904
00:40:42,590 --> 00:40:43,832
these bonds.

905
00:40:43,832 --> 00:40:45,290
And if they're
perfectly satisfied,

906
00:40:45,290 --> 00:40:46,498
you'll have a mobile carrier.

907
00:40:46,498 --> 00:40:49,190
It'll actually elastically
scatter off, not

908
00:40:49,190 --> 00:40:52,220
lose any energy, and not
recombine through these trap

909
00:40:52,220 --> 00:40:52,946
states.

910
00:40:52,946 --> 00:40:54,314
AUDIENCE: I have a question.

911
00:40:54,314 --> 00:40:56,460
I thought [INAUDIBLE] is
a very good passivation

912
00:40:56,460 --> 00:40:57,440
barrier for silicon?

913
00:40:57,440 --> 00:40:58,620
PROFESSOR: What is?

914
00:40:58,620 --> 00:41:00,167
AUDIENCE: I thought
silicon dioxide

915
00:41:00,167 --> 00:41:03,127
is a really good passivation
barrier for silicon.

916
00:41:03,127 --> 00:41:05,210
PROFESSOR: I've seen some
diagrams of what silicon

917
00:41:05,210 --> 00:41:06,270
oxide looks like on silicon.

918
00:41:06,270 --> 00:41:07,650
It passivates many of the bonds.

919
00:41:07,650 --> 00:41:09,000
You're absolutely right.

920
00:41:09,000 --> 00:41:10,460
HF is actually
probably the best.

921
00:41:10,460 --> 00:41:12,610
The problem is that it etches
glass and other things that

922
00:41:12,610 --> 00:41:15,068
are in your source material,
and it's incredibly dangerous.

923
00:41:15,068 --> 00:41:18,480
It can kill you
rather dramatically.

924
00:41:18,480 --> 00:41:20,350
So it's only used in
laboratory settings.

925
00:41:20,350 --> 00:41:22,641
If you're trying to actually
take lifetime measurements

926
00:41:22,641 --> 00:41:28,250
and negate the effect of
surface recombination,

927
00:41:28,250 --> 00:41:29,770
silicon oxide can be a good one.

928
00:41:29,770 --> 00:41:30,920
If you actually look
at the structure,

929
00:41:30,920 --> 00:41:32,503
there's a few dangling
bonds in there,

930
00:41:32,503 --> 00:41:35,060
but it can passivate most of
them-- just not all of them.

931
00:41:35,060 --> 00:41:37,270
Another good
passivation technique

932
00:41:37,270 --> 00:41:39,550
is actually the silicon
nitride ARC coating.

933
00:41:39,550 --> 00:41:41,340
That passivates the
surface very well.

934
00:41:43,850 --> 00:41:45,507
So yeah, good question.

935
00:41:45,507 --> 00:41:48,090
There's other ways to mitigate
surface recombination, as well,

936
00:41:48,090 --> 00:41:50,390
and we'll talk about that, I
think, in either next lecture

937
00:41:50,390 --> 00:41:51,306
or the one after that.

938
00:41:57,187 --> 00:41:58,770
So yeah, this slide
is just telling us

939
00:41:58,770 --> 00:42:04,230
that, if we vary our
thickness of our silicon,

940
00:42:04,230 --> 00:42:08,770
we can actually measure our
surface recombination velocity,

941
00:42:08,770 --> 00:42:11,700
and we can fit it
so we can figure out

942
00:42:11,700 --> 00:42:14,290
our tau surface, which is
a really important material

943
00:42:14,290 --> 00:42:15,040
parameter.

944
00:42:15,040 --> 00:42:18,750
Generally, I think good surface
recombination velocities are

945
00:42:18,750 --> 00:42:23,150
anywhere from like 10 to maybe
in the 100ths for centimeters

946
00:42:23,150 --> 00:42:27,410
per second, and really bad
ones are much, much higher.

947
00:42:31,160 --> 00:42:34,660
And the last type of
recombination mechanism

948
00:42:34,660 --> 00:42:38,410
we're going to talk about
today is Auger recombination,

949
00:42:38,410 --> 00:42:40,680
and this looks like--
when I first saw this,

950
00:42:40,680 --> 00:42:43,670
I'm like, why on earth
would this ever happen?

951
00:42:43,670 --> 00:42:46,420
And the fact is it does
until you get to very, very

952
00:42:46,420 --> 00:42:48,880
high carrier concentration.

953
00:42:48,880 --> 00:42:51,620
So you can see that it
involves three particles.

954
00:42:51,620 --> 00:42:53,260
Let's say an n-type silicon.

955
00:42:53,260 --> 00:42:55,330
It needs two
electrons in the hole.

956
00:42:55,330 --> 00:42:59,855
What happens is that you get
the simultaneous relaxation

957
00:42:59,855 --> 00:43:00,820
and excitation.

958
00:43:00,820 --> 00:43:06,790
So you get this relaxation
of this excited electron

959
00:43:06,790 --> 00:43:11,130
into a hole, and then
you get this excitation

960
00:43:11,130 --> 00:43:13,860
of this other electron
into a higher energy state,

961
00:43:13,860 --> 00:43:17,120
and then it thermalizes
down and releases a phonon,

962
00:43:17,120 --> 00:43:17,867
releases heat.

963
00:43:17,867 --> 00:43:18,450
Yeah, Jessica?

964
00:43:18,450 --> 00:43:21,780
AUDIENCE: [INAUDIBLE]
terms of p-type here?

965
00:43:21,780 --> 00:43:24,970
PROFESSOR: So this is going
to be our n-type material.

966
00:43:24,970 --> 00:43:29,110
And again, because this
type of recombination event

967
00:43:29,110 --> 00:43:32,030
requires two particles,
it requires two electrons,

968
00:43:32,030 --> 00:43:33,570
so it's n squared in one hole.

969
00:43:33,570 --> 00:43:35,760
So the recombination
rate goes up

970
00:43:35,760 --> 00:43:39,200
with pn squared at high
enough concentrations.

971
00:43:39,200 --> 00:43:43,700
And so your tau goes out
with the 1 over n squared.

972
00:43:43,700 --> 00:43:47,185
And this is
particularly bad, again,

973
00:43:47,185 --> 00:43:48,560
only at very--
because it goes up

974
00:43:48,560 --> 00:43:50,950
with the square of the
carrier concentration,

975
00:43:50,950 --> 00:43:53,550
it's really bad at very
high carrier concentrations.

976
00:43:53,550 --> 00:43:56,240
So if we look at this plot, we
can see that our minority care

977
00:43:56,240 --> 00:43:58,820
lifetime drops well below
a microsecond around 10

978
00:43:58,820 --> 00:44:01,020
to the 18th, so
you generally want

979
00:44:01,020 --> 00:44:03,830
to stay out of that range
of doping concentrations

980
00:44:03,830 --> 00:44:07,542
in your base, because you'll
have very, very bad lifetimes.

981
00:44:07,542 --> 00:44:11,826
AUDIENCE: [INAUDIBLE]
are both sides--

982
00:44:11,826 --> 00:44:15,569
is that the top blue part and
the bottom blue part n-type?

983
00:44:15,569 --> 00:44:16,860
PROFESSOR: I didn't label this.

984
00:44:16,860 --> 00:44:17,401
You're right.

985
00:44:17,401 --> 00:44:18,680
This is the valence band.

986
00:44:18,680 --> 00:44:19,805
That's the conduction band.

987
00:44:26,330 --> 00:44:28,470
And so this is kind of
driving home, again,

988
00:44:28,470 --> 00:44:29,990
that leaky bucket
idea-- that is,

989
00:44:29,990 --> 00:44:32,730
you're really limited
by your worst lifetime.

990
00:44:32,730 --> 00:44:34,720
And so if you remember,
we're thinking

991
00:44:34,720 --> 00:44:36,520
about parallel circuits here.

992
00:44:36,520 --> 00:44:39,470
Your bulk, or your effective
lifetime of each carrier,

993
00:44:39,470 --> 00:44:42,580
is determined by these
three here-- your radiative.

994
00:44:42,580 --> 00:44:45,000
Sorry, that should
be tau band, which

995
00:44:45,000 --> 00:44:47,190
is the same as your
radiative recombination--

996
00:44:47,190 --> 00:44:49,200
Auger and Shockley-Read-Hall.

997
00:44:49,200 --> 00:44:51,460
And so at different excess
carrier densities-- so

998
00:44:51,460 --> 00:44:57,640
we're varying delta n by shining
various intensities of light.

999
00:44:57,640 --> 00:45:03,950
And we can kind of activate
different limiting lifetimes.

1000
00:45:03,950 --> 00:45:08,022
So at very low, you're
limited by Shockley-Read-Hall.

1001
00:45:08,022 --> 00:45:09,480
And Shockley-Read-Hall
can actually

1002
00:45:09,480 --> 00:45:14,136
go down with higher
illumination conditions.

1003
00:45:14,136 --> 00:45:16,260
And your Auger, remember
it gets really, really bad

1004
00:45:16,260 --> 00:45:18,930
around 10 to the 18th--
becomes your limiting.

1005
00:45:18,930 --> 00:45:22,770
So your tau bulk is
never doing better

1006
00:45:22,770 --> 00:45:23,858
than your worst lifetime.

1007
00:45:27,762 --> 00:45:30,446
AUDIENCE: So on
that graph is tau

1008
00:45:30,446 --> 00:45:32,160
and emitter also
the same thing as--

1009
00:45:32,160 --> 00:45:33,218
PROFESSOR: Tau Auger?

1010
00:45:33,218 --> 00:45:35,170
AUDIENCE: [INAUDIBLE]
tau [INAUDIBLE].

1011
00:45:35,170 --> 00:45:37,620
PROFESSOR: This came out of
Daniel McDonald's thesis.

1012
00:45:37,620 --> 00:45:40,420
Tau emitter-- it's
complicated because it

1013
00:45:40,420 --> 00:45:41,870
has other influences in it.

1014
00:45:41,870 --> 00:45:43,910
Auger, I always think
of recombination

1015
00:45:43,910 --> 00:45:45,900
in the emitter as
Auger, but you also

1016
00:45:45,900 --> 00:45:49,870
have other carriers coming
in due to injection currents.

1017
00:45:49,870 --> 00:45:51,670
And so your excess
carrier population

1018
00:45:51,670 --> 00:45:54,390
is also a function of
that, and so the equation

1019
00:45:54,390 --> 00:45:56,110
for it gets a little
more complicated,

1020
00:45:56,110 --> 00:45:59,940
but it would make sense that,
as you increase illumination,

1021
00:45:59,940 --> 00:46:02,980
you're increasing your
current into the emitter.

1022
00:46:02,980 --> 00:46:05,580
And you would get more
carriers, and it would decrease.

1023
00:46:05,580 --> 00:46:08,409
And it looks almost exactly like
Auger in his regime over here.

1024
00:46:08,409 --> 00:46:10,450
I'm not sure of the other
things that go into it,

1025
00:46:10,450 --> 00:46:11,980
but if you look up
his thesis, I think

1026
00:46:11,980 --> 00:46:13,438
it gives a pretty
good description.

1027
00:46:18,281 --> 00:46:20,280
So you're probably bored
of hearing me say this,

1028
00:46:20,280 --> 00:46:24,650
but again, we're always
limited by our weakest.

1029
00:46:24,650 --> 00:46:28,110
So in defect mitigated
recombination materials-- so

1030
00:46:28,110 --> 00:46:31,810
where your shortest
lifetime is due to some kind

1031
00:46:31,810 --> 00:46:33,310
of Shockley-Read-Hall
recombination.

1032
00:46:36,660 --> 00:46:38,160
Your lifetime for
Shockley-Read-Hall

1033
00:46:38,160 --> 00:46:40,970
is always going to
be much, much shorter

1034
00:46:40,970 --> 00:46:43,020
than your radiative
lifetimes, which

1035
00:46:43,020 --> 00:46:46,930
is a characteristic we
can exploit for measuring

1036
00:46:46,930 --> 00:46:48,630
the lifetimes of our materials.

1037
00:46:48,630 --> 00:46:51,180
So because very, very few
carriers will actually

1038
00:46:51,180 --> 00:46:54,590
radiatively recombine and emit
a photon, that, if more of them

1039
00:46:54,590 --> 00:46:56,160
are radiatively
recombining, then we

1040
00:46:56,160 --> 00:46:58,620
know that it's a very
high lifetime material.

1041
00:46:58,620 --> 00:47:00,349
If there's a lot
of defects and we

1042
00:47:00,349 --> 00:47:02,390
have very, very short
lifetimes, very few of them

1043
00:47:02,390 --> 00:47:04,150
will radiatively recombine.

1044
00:47:04,150 --> 00:47:10,050
And so this emission of photons
with energy at the band gap

1045
00:47:10,050 --> 00:47:12,590
can give us an idea of the
lifetime within our material,

1046
00:47:12,590 --> 00:47:13,900
and that's how we measure.

1047
00:47:13,900 --> 00:47:16,360
It's a technique called
photoluminescence,

1048
00:47:16,360 --> 00:47:19,160
and what you do is
you shine light on it,

1049
00:47:19,160 --> 00:47:20,304
generally with a laser.

1050
00:47:20,304 --> 00:47:21,970
We put a diffuser in
front of the lasers

1051
00:47:21,970 --> 00:47:26,142
so the laser beam spreads its
photons over a large area.

1052
00:47:26,142 --> 00:47:27,350
We excite all these carriers.

1053
00:47:27,350 --> 00:47:29,530
So this laser has very,
very short wavelengths,

1054
00:47:29,530 --> 00:47:31,380
and I think in our--
well, very short.

1055
00:47:31,380 --> 00:47:32,920
It's 900 nanometers.

1056
00:47:32,920 --> 00:47:36,170
Silicon's band gap corresponds
to about 1,108 nanometers.

1057
00:47:36,170 --> 00:47:38,830
And so 900 is easily
absorbed, not just right

1058
00:47:38,830 --> 00:47:42,850
near the emitter, but
also somewhat well deep

1059
00:47:42,850 --> 00:47:45,370
below the junction as well.

1060
00:47:45,370 --> 00:47:48,010
And then as you begin
to see recombination,

1061
00:47:48,010 --> 00:47:50,857
when radiative recombination
happens, we emit a photon.

1062
00:47:50,857 --> 00:47:53,190
And that can happen in certain
areas better than others,

1063
00:47:53,190 --> 00:47:55,395
and a lot of it
depends on, like I

1064
00:47:55,395 --> 00:48:01,830
said, defect density and other
lifetime eliminating defects.

1065
00:48:01,830 --> 00:48:05,410
And it's a good way to
spatially locate where problems

1066
00:48:05,410 --> 00:48:07,690
are in your solar cell.

1067
00:48:07,690 --> 00:48:09,114
Any other questions?

1068
00:48:09,114 --> 00:48:09,614
Ben?

1069
00:48:09,614 --> 00:48:12,100
AUDIENCE: How good is spatial
resolution on [INAUDIBLE]?

1070
00:48:12,100 --> 00:48:13,641
PROFESSOR: It depends
on your camera.

1071
00:48:13,641 --> 00:48:17,680
So we use, I think, a germanium
camera to detect those photons,

1072
00:48:17,680 --> 00:48:20,110
because Silicon won't
have a very good response.

1073
00:48:20,110 --> 00:48:23,520
And it depends on the CCD
array within your camera.

1074
00:48:23,520 --> 00:48:25,260
It can be really good.

1075
00:48:25,260 --> 00:48:29,050
I do a similar technique
to measure shunts,

1076
00:48:29,050 --> 00:48:30,670
and we have microscope
objectively.

1077
00:48:30,670 --> 00:48:32,690
We just have to zoom
in really, really far,

1078
00:48:32,690 --> 00:48:34,340
and then we just
scan over an area.

1079
00:48:36,900 --> 00:48:42,230
And last little thing is
that, if you recall-- hold on.

1080
00:48:42,230 --> 00:48:46,840
Let me-- this slide.

1081
00:48:46,840 --> 00:48:48,765
Traps cannot only
trap an electron,

1082
00:48:48,765 --> 00:48:50,600
but you can also
emit an electron,

1083
00:48:50,600 --> 00:48:52,460
assuming it has
enough thermal energy,

1084
00:48:52,460 --> 00:48:56,510
and you can see
that on this plot.

1085
00:48:56,510 --> 00:48:57,960
And so this is an
Arrhenius plot.

1086
00:48:57,960 --> 00:49:00,590
So again, high temperatures
are in this direction.

1087
00:49:00,590 --> 00:49:02,230
Low temperatures are over here.

1088
00:49:02,230 --> 00:49:04,250
And you can see that
your lifetime actually

1089
00:49:04,250 --> 00:49:07,070
increases at higher
temperatures because electrons

1090
00:49:07,070 --> 00:49:09,640
that see that trap fall into
it, then can easily come back

1091
00:49:09,640 --> 00:49:11,681
out of it because they
have enough thermal energy

1092
00:49:11,681 --> 00:49:12,210
to escape.

1093
00:49:12,210 --> 00:49:14,180
And that's really what
this is depicting.

1094
00:49:14,180 --> 00:49:17,400
So one of the things I think
for researchers in the room who

1095
00:49:17,400 --> 00:49:19,840
are studying these types of
materials, varying temperature

1096
00:49:19,840 --> 00:49:21,590
is often a really,
really good way

1097
00:49:21,590 --> 00:49:24,920
of looking at electronic
structure materials.

1098
00:49:24,920 --> 00:49:27,280
And it can be very,
very powerful,

1099
00:49:27,280 --> 00:49:29,840
and this is one
example of a tool

1100
00:49:29,840 --> 00:49:36,350
to look at these types of traps.

1101
00:49:36,350 --> 00:49:36,850
Oh, good.

1102
00:49:36,850 --> 00:49:38,630
We have plenty of time.

1103
00:49:38,630 --> 00:49:41,240
We actually might end early.

1104
00:49:41,240 --> 00:49:43,090
So now we're going to
talk about mobility.

1105
00:49:43,090 --> 00:49:44,530
We've given a lot of-- sorry?

1106
00:49:44,530 --> 00:49:46,071
AUDIENCE: I was just
wondering, is it

1107
00:49:46,071 --> 00:49:49,440
possible to somehow introduce
defects that are at the energy

1108
00:49:49,440 --> 00:49:50,422
levels [INAUDIBLE]?

1109
00:49:53,614 --> 00:49:55,030
PROFESSOR: That's
a good question.

1110
00:49:55,030 --> 00:49:59,830
So phosphorus actually has, if
you draw it on an e versus x

1111
00:49:59,830 --> 00:50:09,242
diagram-- so if we have
our conduction band here,

1112
00:50:09,242 --> 00:50:12,790
our valence band here,
we said iron puts states

1113
00:50:12,790 --> 00:50:14,320
in the middle of the gap.

1114
00:50:14,320 --> 00:50:17,110
Phosphorus and boron actually
put states very, very, very

1115
00:50:17,110 --> 00:50:19,550
close to the valence
band and conduction band.

1116
00:50:19,550 --> 00:50:22,010
If you go to low enough
temperature-- so let's

1117
00:50:22,010 --> 00:50:25,010
say a below 100 Kelvin--
you can actually

1118
00:50:25,010 --> 00:50:28,320
freeze out those donor electrons
onto the phosphorus atoms.

1119
00:50:28,320 --> 00:50:31,750
And below certain concentrations
of phosphorus atoms,

1120
00:50:31,750 --> 00:50:36,530
for example-- so below like
10 to the 18th-- at 0 Kelvin,

1121
00:50:36,530 --> 00:50:38,720
you cannot conduct electricity.

1122
00:50:38,720 --> 00:50:40,355
It actually becomes
a total insulator.

1123
00:50:40,355 --> 00:50:41,563
That's an excellent question.

1124
00:50:41,563 --> 00:50:44,300
But at room temperature,
when kt is on the order--

1125
00:50:44,300 --> 00:50:47,530
so kt is your thermal energy,
and at room temperature,

1126
00:50:47,530 --> 00:50:49,630
if you put that
for electrons, it's

1127
00:50:49,630 --> 00:50:55,160
0.026 electron volts or
26 millielectron volts.

1128
00:50:55,160 --> 00:50:57,895
This is a good number to
have in mind, by the way.

1129
00:50:57,895 --> 00:50:59,960
When that number is on
the order of this binding

1130
00:50:59,960 --> 00:51:01,870
energy for phosphorus,
they're almost always

1131
00:51:01,870 --> 00:51:07,680
fully ionized and free, but
that's a very good question.

1132
00:51:07,680 --> 00:51:08,180
Anyone else?

1133
00:51:14,520 --> 00:51:17,280
So if we remember our
definition mobility

1134
00:51:17,280 --> 00:51:20,410
is related to or diffusivity,
and again, our mobility

1135
00:51:20,410 --> 00:51:24,209
is saying how well these
excited charges can move around.

1136
00:51:24,209 --> 00:51:26,000
And it's related to
how much thermal energy

1137
00:51:26,000 --> 00:51:30,660
these charges have, so that's
why we have this kbt factor.

1138
00:51:30,660 --> 00:51:33,480
And what's plotted
on the right is

1139
00:51:33,480 --> 00:51:37,940
the Shockley-Queisser efficiency
limit, which are the stars.

1140
00:51:37,940 --> 00:51:42,560
And then how if you-- let's say
you reduce your mobility by,

1141
00:51:42,560 --> 00:51:46,180
let's say, a factor
of 10 or 100.

1142
00:51:46,180 --> 00:51:48,280
What's the impact on
the overall efficiency?

1143
00:51:48,280 --> 00:51:51,010
And you can see that,
if you detrimentally

1144
00:51:51,010 --> 00:51:52,510
impact your mobility,
you can really

1145
00:51:52,510 --> 00:51:55,100
have a large effect on
your diffusion length,

1146
00:51:55,100 --> 00:51:57,710
and it can really hurt
your device performance.

1147
00:51:57,710 --> 00:51:59,870
So it's a really important
material parameter

1148
00:51:59,870 --> 00:52:00,560
to think about.

1149
00:52:04,070 --> 00:52:07,770
So there's lots of ways that
these mobile electrons can

1150
00:52:07,770 --> 00:52:08,980
do what's called scattering.

1151
00:52:08,980 --> 00:52:11,790
So if I'm a mobile
electron, I'm moving down

1152
00:52:11,790 --> 00:52:13,560
through the silicon lattice.

1153
00:52:13,560 --> 00:52:16,649
And let's say I see a
defect, and this defect,

1154
00:52:16,649 --> 00:52:18,190
because it has these
extra electrons,

1155
00:52:18,190 --> 00:52:21,420
it creates this kind
of area of charge.

1156
00:52:21,420 --> 00:52:24,290
It can see that it can scatter
off of it and lose its energy,

1157
00:52:24,290 --> 00:52:27,555
and so that's called
a scattering event.

1158
00:52:27,555 --> 00:52:28,710
Not really lose its energy.

1159
00:52:28,710 --> 00:52:29,210
Sorry.

1160
00:52:29,210 --> 00:52:30,680
It'll change direction.

1161
00:52:30,680 --> 00:52:34,420
It kind of impacts the
movement of that carrier.

1162
00:52:34,420 --> 00:52:40,280
And there's all sorts of other
defects scattering mechanisms.

1163
00:52:40,280 --> 00:52:45,170
You can also scatter with an
oscillating atom or a phonon.

1164
00:52:45,170 --> 00:52:48,410
There's another type of
scattering mechanism,

1165
00:52:48,410 --> 00:52:51,825
and it's heavily
dependent on what

1166
00:52:51,825 --> 00:52:53,790
you put into your
material, and we'll

1167
00:52:53,790 --> 00:52:55,350
talk about that in a second.

1168
00:52:55,350 --> 00:52:56,850
And for a lot of
materials that are,

1169
00:52:56,850 --> 00:53:02,020
let's say, porous or amorphous
in some way, or even a lot of,

1170
00:53:02,020 --> 00:53:04,470
let's say, organic
semiconductors,

1171
00:53:04,470 --> 00:53:07,530
having a good percolation
network is really important

1172
00:53:07,530 --> 00:53:08,660
to transport these charges.

1173
00:53:08,660 --> 00:53:10,670
And often it's a very
limiting factor in,

1174
00:53:10,670 --> 00:53:12,253
let's say, like
organic photovoltaics.

1175
00:53:15,004 --> 00:53:18,270
And so this is a relatively
simple scattering mechanism.

1176
00:53:18,270 --> 00:53:21,132
What time-- oh, we
have plenty time.

1177
00:53:21,132 --> 00:53:22,590
What's going on
here is that we can

1178
00:53:22,590 --> 00:53:26,660
see that, as we add carriers--
so this is n is 10 to 14th.

1179
00:53:26,660 --> 00:53:28,550
Very, very low
concentration of dopants--

1180
00:53:28,550 --> 00:53:30,530
as we increase the
number carriers,

1181
00:53:30,530 --> 00:53:32,860
are scattering off of
those ionized impurities.

1182
00:53:32,860 --> 00:53:34,610
So every time you add
a phosphorus atom,

1183
00:53:34,610 --> 00:53:38,160
lets say, you introduce
a static positive charge

1184
00:53:38,160 --> 00:53:41,060
and a mobile negative charge
when that electron leaves.

1185
00:53:41,060 --> 00:53:42,860
And so you now have
all of these scattering

1186
00:53:42,860 --> 00:53:44,834
centers of positive charge.

1187
00:53:44,834 --> 00:53:46,750
And so as you increase
the number of dopants--

1188
00:53:46,750 --> 00:53:54,340
this for silicon-- you decrease
the mobility of your material,

1189
00:53:54,340 --> 00:53:57,010
and it's also greatly a
function of temperature.

1190
00:53:57,010 --> 00:54:02,995
I think that's mostly due to
either phonon scattering--

1191
00:54:02,995 --> 00:54:03,930
is that right?

1192
00:54:03,930 --> 00:54:07,006
Is there any other mechanism
I'm missing, [INAUDIBLE],

1193
00:54:07,006 --> 00:54:09,690
if you're still there?

1194
00:54:09,690 --> 00:54:11,520
AUDIENCE: Sorry, I was on mute.

1195
00:54:11,520 --> 00:54:13,200
Yes, I think you're good so far.

1196
00:54:13,200 --> 00:54:16,050
We'll keep it simple, and
use the simplest case first.

1197
00:54:16,050 --> 00:54:18,860
I think that makes [INAUDIBLE].

1198
00:54:18,860 --> 00:54:21,630
PROFESSOR: But importantly is
that higher temperatures, you

1199
00:54:21,630 --> 00:54:26,140
generally get a much
lower, lower mobility.

1200
00:54:26,140 --> 00:54:27,580
And again, hitting
home for-- this

1201
00:54:27,580 --> 00:54:29,690
is not true necessarily
for silicon,

1202
00:54:29,690 --> 00:54:38,171
but for a lot of these
heterojunction devices--

1203
00:54:38,171 --> 00:54:40,420
so for example, organics
have very, very low diffusion

1204
00:54:40,420 --> 00:54:42,600
lengths, and a lot of
it's limited by mobility.

1205
00:54:42,600 --> 00:54:48,695
And so what you do is you make
these Interdigitated-- what

1206
00:54:48,695 --> 00:54:49,570
I would call p and n.

1207
00:54:49,570 --> 00:54:53,139
I forget the organic
analogy, but p and n layers

1208
00:54:53,139 --> 00:54:54,680
that interdigitated
so that they only

1209
00:54:54,680 --> 00:54:57,190
have to diffuse not the
width of the device,

1210
00:54:57,190 --> 00:54:58,980
but the length of those fingers.

1211
00:54:58,980 --> 00:55:01,335
So you effectively need a
much shorter diffusion length.

1212
00:55:01,335 --> 00:55:02,710
And so this is
talking about some

1213
00:55:02,710 --> 00:55:05,248
of those other
different ideas, and--

1214
00:55:05,248 --> 00:55:08,039
AUDIENCE: I'm sorry, that was
a heterojunction? [INAUDIBLE].

1215
00:55:08,039 --> 00:55:10,330
PROFESSOR: A heterojunction
is two different materials.

1216
00:55:10,330 --> 00:55:12,274
AUDIENCE: OK, what was
the thing you were just

1217
00:55:12,274 --> 00:55:13,250
describing with the--

1218
00:55:13,250 --> 00:55:17,586
PROFESSOR: That's an
interdigitated pn structure.

1219
00:55:26,156 --> 00:55:28,030
Yeah, so what we're
going to be talking about

1220
00:55:28,030 --> 00:55:33,320
is the product of n and mu.

1221
00:55:33,320 --> 00:55:37,280
And if you recall that your
conductivity-- so hold on.

1222
00:55:37,280 --> 00:55:40,010
Let's go back.

1223
00:55:40,010 --> 00:55:41,940
What we have here
is that we have

1224
00:55:41,940 --> 00:55:47,680
a highly doped semiconductor.

1225
00:55:47,680 --> 00:55:50,050
So this is about 10 to
the 16th, and then we

1226
00:55:50,050 --> 00:55:51,260
have our intrinsic silicon.

1227
00:55:51,260 --> 00:55:54,720
So this has no dopants
in it whatsoever.

1228
00:55:54,720 --> 00:55:57,170
And now, you remember
from last lecture

1229
00:55:57,170 --> 00:55:59,560
when we applied a voltage
across the terminals,

1230
00:55:59,560 --> 00:56:01,900
a current started to flow,
and when we heated it up,

1231
00:56:01,900 --> 00:56:02,955
what had happened?

1232
00:56:02,955 --> 00:56:04,964
Who remembers?

1233
00:56:04,964 --> 00:56:06,130
AUDIENCE: Current increased.

1234
00:56:06,130 --> 00:56:07,796
PROFESSOR: Current
increased, and that's

1235
00:56:07,796 --> 00:56:10,990
due to more thermally
excited carriers.

1236
00:56:10,990 --> 00:56:14,800
And so your intrinsic carrier
concentration goes up.

1237
00:56:14,800 --> 00:56:18,800
And so what was-- for
room temperature, what's

1238
00:56:18,800 --> 00:56:20,300
the intrinsic carrier
concentration?

1239
00:56:20,300 --> 00:56:24,570
It's about 10 to the
10th-- in that range.

1240
00:56:24,570 --> 00:56:30,450
And so in increase-- so a
small increase in temperature

1241
00:56:30,450 --> 00:56:32,200
can greatly increase
the intrinsic carrier

1242
00:56:32,200 --> 00:56:34,410
concentration-- maybe
something like 10 to the 12th.

1243
00:56:34,410 --> 00:56:36,910
Now in a doped
semiconductor, is that

1244
00:56:36,910 --> 00:56:38,492
going to affect it as much?

1245
00:56:38,492 --> 00:56:40,700
How about you guys think
about that for a little bit.

1246
00:56:40,700 --> 00:56:42,080
Mute and talk to your neighbor.

1247
00:56:42,080 --> 00:56:43,830
And so I'm going to
heat both of these up,

1248
00:56:43,830 --> 00:56:45,540
one with a high
dopant concentration,

1249
00:56:45,540 --> 00:56:46,425
and one with a low.

1250
00:56:46,425 --> 00:56:47,800
And which one you
think will have

1251
00:56:47,800 --> 00:56:50,133
the highest relative change
in connectivity and in which

1252
00:56:50,133 --> 00:56:52,439
direction?

1253
00:56:52,439 --> 00:56:53,730
So I'll give you three minutes.

1254
00:57:01,810 --> 00:57:04,552
So we're now going to subject.

1255
00:57:04,552 --> 00:57:05,760
You've seen this demo before.

1256
00:57:05,760 --> 00:57:09,250
We're now going to subject our
intrinsic carrier to my hair

1257
00:57:09,250 --> 00:57:11,920
dryer.

1258
00:57:11,920 --> 00:57:14,460
And right now we're
getting-- let's see.

1259
00:57:14,460 --> 00:57:16,560
It's about 10 microamps.

1260
00:57:16,560 --> 00:57:25,990
And if we heat this guy
up-- did I mix these two up?

1261
00:57:25,990 --> 00:57:27,790
Ah, there we go.

1262
00:57:27,790 --> 00:57:31,870
So you can see we get a rather
large increase in current.

1263
00:57:31,870 --> 00:57:35,227
That was up to 100
microamps, so a factor of 10.

1264
00:57:35,227 --> 00:57:36,310
So quite a large increase.

1265
00:57:38,840 --> 00:57:43,170
So let's see a show of hands.

1266
00:57:43,170 --> 00:57:46,146
So right now we're
getting-- maybe

1267
00:57:46,146 --> 00:57:49,240
we need to put
this on milliamps.

1268
00:57:49,240 --> 00:57:51,530
So we're getting about
58 milliamps of current

1269
00:57:51,530 --> 00:57:52,952
through the semiconductor.

1270
00:57:52,952 --> 00:57:55,160
Who thinks that the current
is going to increase when

1271
00:57:55,160 --> 00:57:56,480
we add more thermal carriers?

1272
00:57:59,224 --> 00:58:00,390
This is where the doped one.

1273
00:58:00,390 --> 00:58:01,473
We just saw the intrinsic.

1274
00:58:05,660 --> 00:58:08,262
Do you think it'll go
up, the connectivity?

1275
00:58:08,262 --> 00:58:09,720
So this is the
doped semiconductor.

1276
00:58:09,720 --> 00:58:13,300
Now who think it's
going to stay the same?

1277
00:58:13,300 --> 00:58:15,684
Who thinks it's
going to go down?

1278
00:58:15,684 --> 00:58:16,850
All right, so this is split.

1279
00:58:16,850 --> 00:58:18,160
Wow.

1280
00:58:18,160 --> 00:58:24,380
So right now we're getting about
57 milliamps, and let's heat

1281
00:58:24,380 --> 00:58:27,026
this guy up and
see what happens.

1282
00:58:27,026 --> 00:58:28,900
And so you can see, it's
actually going down.

1283
00:58:28,900 --> 00:58:31,165
It's now 52, 50, 49.

1284
00:58:34,360 --> 00:58:37,770
So what's important is that
we're measuring conductivity.

1285
00:58:37,770 --> 00:58:39,460
It's not only how
many carriers we have,

1286
00:58:39,460 --> 00:58:41,330
but also how well
they can move around.

1287
00:58:41,330 --> 00:58:43,650
And it's, again, that
product of number

1288
00:58:43,650 --> 00:58:45,156
of carriers times the mobility.

1289
00:58:45,156 --> 00:58:46,530
And again, each
of those carriers

1290
00:58:46,530 --> 00:58:47,530
carries an electric charge.

1291
00:58:47,530 --> 00:58:50,071
So you put the electric charge
of an electron in front of it.

1292
00:58:52,037 --> 00:58:54,370
This is what I was supposed
to have up in the background

1293
00:58:54,370 --> 00:58:55,430
while that was happening.

1294
00:58:55,430 --> 00:58:57,580
AUDIENCE: The intrinsic still
had to go change, right?

1295
00:58:57,580 --> 00:58:58,080
[INAUDIBLE].

1296
00:58:58,080 --> 00:59:00,110
PROFESSOR: Yeah,
so again, remember

1297
00:59:00,110 --> 00:59:02,220
there was huge changes.

1298
00:59:02,220 --> 00:59:03,500
One was measuring milliamps.

1299
00:59:03,500 --> 00:59:05,296
One was measuring microamps.

1300
00:59:05,296 --> 00:59:07,420
So if we look at room
temperature, we have about 10

1301
00:59:07,420 --> 00:59:09,440
to the 10th intrinsic carriers.

1302
00:59:09,440 --> 00:59:12,000
So this is for intrinsic silicon
with no dopants whatsoever.

1303
00:59:12,000 --> 00:59:14,910
As we increase the
heat, I don't think

1304
00:59:14,910 --> 00:59:17,450
we're going to 500 degrees,
but let's say we get the 400.

1305
00:59:17,450 --> 00:59:22,900
We're only going up by a factor
of 100, which is substantial,

1306
00:59:22,900 --> 00:59:25,850
but if we had 10 to
the 16th carriers

1307
00:59:25,850 --> 00:59:28,274
originally from our
dopants, these added number

1308
00:59:28,274 --> 00:59:29,690
of intrinsic
carriers aren't going

1309
00:59:29,690 --> 00:59:31,630
to have really much
of an effect at all

1310
00:59:31,630 --> 00:59:33,060
in terms of the connectivity.

1311
00:59:33,060 --> 00:59:34,870
So what's really
affecting the dope case

1312
00:59:34,870 --> 00:59:36,540
is that our mobility
actually goes down

1313
00:59:36,540 --> 00:59:38,123
with temperature due
to the scattering

1314
00:59:38,123 --> 00:59:40,050
events with temperature.

1315
00:59:40,050 --> 00:59:42,590
And for intrinsic silicon,
you get a little bit better

1316
00:59:42,590 --> 00:59:44,510
mobility, so it's a
little bit higher,

1317
00:59:44,510 --> 00:59:46,218
but they both have
the same general trend

1318
00:59:46,218 --> 00:59:49,150
of lower mobility, but
only by, let's say,

1319
00:59:49,150 --> 00:59:51,260
this is about a
factor of 10, where

1320
00:59:51,260 --> 00:59:57,260
it was about a factor of 100
for the intrinsic carrier.

1321
00:59:57,260 --> 00:59:59,770
So again, our carriers
in the intrinsic case

1322
00:59:59,770 --> 01:00:00,890
go up by a factor of 100.

1323
01:00:00,890 --> 01:00:02,640
Our mobility goes up
by a factor of 10,

1324
01:00:02,640 --> 01:00:06,220
so the conductivity then has
to increase by a factor of 10.

1325
01:00:06,220 --> 01:00:08,810
And for our doped
semiconductor, really the heat

1326
01:00:08,810 --> 01:00:11,062
is just hurting our
conductivity because

1327
01:00:11,062 --> 01:00:13,270
of the decrease in mobility,
and the thermal carriers

1328
01:00:13,270 --> 01:00:16,410
don't really add--
they're washed out

1329
01:00:16,410 --> 01:00:18,370
by the sea of dopant
atoms that are really

1330
01:00:18,370 --> 01:00:19,556
adding all the carriers.

1331
01:00:19,556 --> 01:00:20,056
Yeah?

1332
01:00:20,056 --> 01:00:23,840
AUDIENCE: So if you were
to obviously heat up

1333
01:00:23,840 --> 01:00:26,230
[INAUDIBLE] more--
[INAUDIBLE] the doped more,

1334
01:00:26,230 --> 01:00:29,098
it would probably eventually
get to the intrinsic case

1335
01:00:29,098 --> 01:00:31,120
where there are
constant increases,

1336
01:00:31,120 --> 01:00:35,259
but would you ever want
your solar cell that hot?

1337
01:00:35,259 --> 01:00:37,550
PROFESSOR: Would you ever
you your solar cell that hot?

1338
01:00:37,550 --> 01:00:38,902
That's a good question.

1339
01:00:38,902 --> 01:00:40,485
AUDIENCE: Yeah, I don't know
how [INAUDIBLE] would it

1340
01:00:40,485 --> 01:00:40,790
melt [INAUDIBLE].

1341
01:00:40,790 --> 01:00:43,320
PROFESSOR: So let's go--
there's an equation for that,

1342
01:00:43,320 --> 01:00:45,255
and we'll talk about
that later, too.

1343
01:00:49,170 --> 01:00:51,930
So if you look at our VOC,
if we have a large saturation

1344
01:00:51,930 --> 01:00:59,010
current, that means that we're
going to have a very low VOC.

1345
01:00:59,010 --> 01:01:00,520
We have this reverse
current that's

1346
01:01:00,520 --> 01:01:02,050
going in the opposite
direction of our illumination

1347
01:01:02,050 --> 01:01:04,210
current that's opposing
that illumination current.

1348
01:01:04,210 --> 01:01:08,960
And so if it's large,
then it'll hurt our VOC.

1349
01:01:08,960 --> 01:01:13,530
And you can see that it scales
with d, which scales with kt,

1350
01:01:13,530 --> 01:01:16,170
and so we get this
increase in temperature

1351
01:01:16,170 --> 01:01:19,270
is increasing this J0.

1352
01:01:19,270 --> 01:01:23,581
And so for most
types of cells, heat

1353
01:01:23,581 --> 01:01:25,830
is very, very bad, especially
for crystalline silicon.

1354
01:01:25,830 --> 01:01:27,150
For amorphous silicon,
it's different.

1355
01:01:27,150 --> 01:01:28,941
Well, I'm not going to
get into that today,

1356
01:01:28,941 --> 01:01:32,570
but for crystalline
silicon, heat is generally

1357
01:01:32,570 --> 01:01:35,770
very bad for the performance.

1358
01:01:35,770 --> 01:01:38,950
And when you do
testingg-- so for example,

1359
01:01:38,950 --> 01:01:44,390
when NREL does testing, they'll
rate all your cells at AM1.5G,

1360
01:01:44,390 --> 01:01:49,090
some calibrated solar
simulator that's illuminating

1361
01:01:49,090 --> 01:01:49,592
your sample.

1362
01:01:49,592 --> 01:01:51,300
And they're kept at
constant temperature,

1363
01:01:51,300 --> 01:01:52,883
so the temperature
is always reported,

1364
01:01:52,883 --> 01:01:54,440
and it's generally
kept at the 25 C.

1365
01:01:54,440 --> 01:01:56,690
So the temperature is a very
important characteristic.

1366
01:01:59,050 --> 01:02:03,430
But to answer your
question, if, again, we

1367
01:02:03,430 --> 01:02:06,590
looked at an Arrhenius
plot-- so this is 1/kt.

1368
01:02:06,590 --> 01:02:08,580
So this is high
temperatures over here,

1369
01:02:08,580 --> 01:02:09,720
low temperatures over here.

1370
01:02:12,708 --> 01:02:15,520
And this is carrier
concentration.

1371
01:02:15,520 --> 01:02:22,419
At very, very high temperatures,
when your thermal carrier--

1372
01:02:22,419 --> 01:02:24,460
so if you extend this out
to higher temperatures,

1373
01:02:24,460 --> 01:02:25,918
you can see that
this will actually

1374
01:02:25,918 --> 01:02:29,702
surpassed the number
of dopant atoms,

1375
01:02:29,702 --> 01:02:30,910
and you'll actually increase.

1376
01:02:30,910 --> 01:02:32,493
So this is high
temperature over here.

1377
01:02:37,184 --> 01:02:38,850
Your carrier concentration
will actually

1378
01:02:38,850 --> 01:02:42,940
increase at much, much
higher temperatures,

1379
01:02:42,940 --> 01:02:46,260
and this is what's
the extrinsic region.

1380
01:02:46,260 --> 01:02:49,070
So your donor concentration
is pretty much only determined

1381
01:02:49,070 --> 01:02:52,009
by your dopant
density, so this is ND.

1382
01:02:52,009 --> 01:02:53,550
And then at low
enough temperatures--

1383
01:02:53,550 --> 01:02:55,508
so this is very low
temperatures-- you actually

1384
01:02:55,508 --> 01:02:58,120
start freezing out
you're donor electrons

1385
01:02:58,120 --> 01:02:59,940
into these donor states.

1386
01:03:02,910 --> 01:03:05,330
So that actually sums it up.

1387
01:03:05,330 --> 01:03:07,220
If you guys have
other questions,

1388
01:03:07,220 --> 01:03:08,980
feel free to ask
them, but we actually

1389
01:03:08,980 --> 01:03:10,670
can end a little bit early.

1390
01:03:10,670 --> 01:03:14,200
I do have your homework, so if
you want those, come up here.

1391
01:03:14,200 --> 01:03:18,410
And I think [INAUDIBLE]
posted the projects online

1392
01:03:18,410 --> 01:03:22,800
so you can finish
homework number three.

1393
01:03:22,800 --> 01:03:24,580
That's it.