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PROFESSOR: Why don't we
go ahead and get started.

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What we're going
to be talking about

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today, is what happens after
that photon gets absorbed.

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So we spent a great deal of
time in our last lecture talking

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about light absorption, the
interaction between light

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and the semiconductor.

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Now we're going to
talk about what happens

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once that light is absorbed.

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So we're in the
fundamental section.

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We're right here.

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Later on, we'll get
into the technologies

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and the cross cutting themes.

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As we go through
the fundamentals,

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I'm going to attempt to
relate those fundamentals

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to real solar cell technology.

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So you're not left
kind of floating,

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00:00:55,895 --> 00:00:58,020
wondering why it is that
we're studying this stuff,

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00:00:58,020 --> 00:00:59,645
but you're really
seeing the connection

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00:00:59,645 --> 00:01:01,660
to solar cell devices.

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00:01:01,660 --> 00:01:05,857
So first if we remind everyone
of the broader picture

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that the conversion efficiency,
the ultimate performance

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00:01:08,190 --> 00:01:11,880
of the device, is defined as the
output energy versus the input

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energy.

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00:01:12,850 --> 00:01:14,890
And for most solar
cells, this breaks down

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into the inputs and the outputs.

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The input being
the solar spectrum

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and the output being the
collection of charge.

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00:01:21,100 --> 00:01:24,440
And there are multiple processes
that occur here in the middle.

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00:01:24,440 --> 00:01:26,370
Light absorption, we
talked about last time.

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We're going to be talking about
charge excitation in charge

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00:01:29,180 --> 00:01:32,157
transport today, mostly
charge excitation.

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So we're right here.

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00:01:32,990 --> 00:01:34,070
We're going to be
marching steadily

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00:01:34,070 --> 00:01:36,260
down toward the right over
the next few lectures.

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00:01:36,260 --> 00:01:38,080
And let me remind
you, everybody,

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that the efficiency
of the device

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00:01:39,960 --> 00:01:42,370
is the product of each
individual efficiency

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of each different step.

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00:01:43,610 --> 00:01:45,980
So if anything is
going wrong here,

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00:01:45,980 --> 00:01:47,680
it will be limiting
device performance.

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00:01:47,680 --> 00:01:49,888
And the image you should
definitely have in your mind

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is of that bucket, with
each plank representing

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a different component
of the device, perhaps

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a different physical
process or perhaps

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00:01:57,980 --> 00:02:00,920
a different physical component
of the device itself.

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00:02:00,920 --> 00:02:03,180
And whatever is the
poorest, is going

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to be limiting
overall performance.

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Your efficiency is going to be
flowing out from that low plank

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and you will have a
low efficiency device.

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So the art of making a
high efficiency solar cell

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is really understanding
everything

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that goes into the
physical processes,

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but also the devices.

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And that's why we break
it down like this.

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We have the physical
processes, and finally we

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get into some of the
devices in the architectures

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of manufacturing methods.

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So learning objectives today.

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Oops.

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That was a little bit of a typo.

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It's not the solar resource.

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We're talking about
charge excitation today.

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We will be talking phenomena
logically how this thing called

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a band gap forms.

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It's a very important
physical concept.

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We'll lead off the
lecture with it,

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and then very quickly
go into applications

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that you see why it's
important, returning back

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to the fundamentals,
how it actually forms,

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going back and
forth until we have

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a pretty solid understanding.

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From the background surveys,
I understand that about 50%

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of you understand
what a band gap is.

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So 50% of you may be a little
bored, or a little entertained,

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at my hand wave explanations
during the first part of class.

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I encourage you to
think about the band gap

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from the perspective of
the solar cell device,

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because this is probably not
something you've done before.

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You've probably
understood band gap

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from the perspective of
a semiconductor device as

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packaged in the dark, perhaps
in a little gadget like this.

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But not something
that's exposed to light

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with the addition of
a generation current.

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Or at least not in detail.

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So I welcome you
to think about that

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as we go through
the explanations

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in the beginning of class.

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Then we'll describe how optical
absorption in semiconductors

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represents the transitions
of charge in an energy band

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diagram.

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In other words, if
we imagine a given

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space of the
semiconductor divisive,

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00:03:41,740 --> 00:03:44,280
say a surrounding
of a given atom,

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and we imagine that different
orbitals, different electron

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orbitals will have different
energies associated with them.

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We are going to be talking
about how light gets absorbed

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in transitions electrons
between those different energy

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orbitals.

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That's important
because then we'll

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be able to calculate
the fraction of photons

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lost, not absorbed, by a
given semiconductor material.

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We'll be able to calculate
the fraction of incident

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solar energy that is lost
as well, due to a phenomenon

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called thermalization.

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And finally, we're
going to be able to plot

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efficiency versus
band gap, and denote

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00:04:15,310 --> 00:04:16,570
specific materials on it.

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In other words, we are going to
be doing our first higher level

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efficiency calculations
for a solar cell device

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00:04:21,760 --> 00:04:23,750
by the end of today's lecture.

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And the idea is to expose a
little bit on the technology

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side as well, so that you have
an appreciation for what's

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up and coming in the field,
what are some of the ways

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to enhance the performance
of social devices.

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So band gap.

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Very, very basic description.

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If you've never been
exposed to band gaps before,

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the reason it's important
is because the band gap

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is going to define
what color, what

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portion of the solar
spectrum that material

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absorbs light most efficiently.

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How a band gap forms is related
to the atomic structure.

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00:05:00,140 --> 00:05:04,270
Think of bonds as essentially
why stuff is tough.

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If the mechanical
engineers in the room,

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if you remember
linear elasticity,

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00:05:08,750 --> 00:05:10,360
those bonds are
what are essentially

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forming those springs
between the atoms that

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are keeping them, the
material, from flying apart.

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There is also a very
interesting property here,

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that if you have
a bound electron,

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00:05:18,920 --> 00:05:21,360
it's usually not moving
very far that atom.

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It's usually in a very
localized electronic state

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00:05:24,450 --> 00:05:26,120
close to that atom.

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00:05:26,120 --> 00:05:30,500
So if you were to apply a
resistance meter, an Ohm meter,

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00:05:30,500 --> 00:05:33,630
to your device to measure
the resistance across it,

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and you had just
bound electrons,

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you would measure a very,
very low current passing

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00:05:38,810 --> 00:05:39,870
through that material.

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Because there would be very few
free charge carriers to move

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00:05:43,070 --> 00:05:45,609
in that applied field, when
you apply the two probes

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00:05:45,609 --> 00:05:47,650
and there's a little
battery in here that applies

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00:05:47,650 --> 00:05:49,930
a field across the
material, you wouldn't

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00:05:49,930 --> 00:05:51,644
be able to measure
much current flow,

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00:05:51,644 --> 00:05:54,060
because there wouldn't be too
many free electrons to carry

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that current.

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So the bound
electrons essentially

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enhance the strength
of the material.

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But it doesn't help us from a
semiconductor point of view.

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What we need are
excited electrons.

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And excited electrons are
why materials conduct.

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So let's imagine we have a bond.

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For example, in
this material right

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here, these gray lines
are really two electrons

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that are covalently bonded.

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Essentially two
electrons-- one electron

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from each little black circle
representing a carbon atom.

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And each electron associated
with that carbon atom

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is shared with the other,
in a covalent bond.

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And for the chemists
in the room, more

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precisely, you have
sp3 hybridized orbitals

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in this diamond cubic
crystal structure.

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For everyone else, these
are shared electrons

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in a covalent bonding
configuration.

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Now if light comes in
with enough energy,

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it can excite an electron
from that covalently bonded

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state into an excited state,
where it can then roam freely

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throughout the lattice.

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And that's the nature
of charge excitations.

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So the big question
that we have to ask

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ourselves is, what
color of light

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will this material
absorb most effectively?

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Will those electrons
in the covalent bonds

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00:06:56,560 --> 00:06:58,722
absorb light and be
excited into a state

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00:06:58,722 --> 00:07:00,680
where they can roam freely
around the material,

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00:07:00,680 --> 00:07:03,500
and ultimately
conduct electricity?

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00:07:03,500 --> 00:07:04,000
OK.

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00:07:04,000 --> 00:07:08,230
So the answer to that
question is not simple.

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Understanding how
a band gap forms

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can be an entire semester
of quantum physics.

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But what we're going to do is
do it in a three step approach.

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Simple, very, very
simple explanations

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00:07:19,990 --> 00:07:22,830
that hopefully
everyone will get.

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00:07:22,830 --> 00:07:24,730
The next most
simple explanation,

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00:07:24,730 --> 00:07:28,100
which hopefully 80% of
you will get, and then

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perhaps a more detailed
explanation that only a few

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of you will get.

193
00:07:32,540 --> 00:07:34,560
But the idea is
to really progress

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in levels of explanation.

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00:07:38,120 --> 00:07:40,411
So let me go back one step.

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Yeah.

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The band gap energy can
be most simply understood

198
00:07:43,502 --> 00:07:44,960
as a finite amount
of energy needed

199
00:07:44,960 --> 00:07:47,170
to excite a highly
localized electron

200
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into a de-localized excited
state in the semiconductor

201
00:07:49,720 --> 00:07:52,920
where it can move
around the crystal.

202
00:07:52,920 --> 00:07:53,670
OK.

203
00:07:53,670 --> 00:07:56,620
So this is the description
of the band gap,

204
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how a band gap forms that
you'll see in many chemistry

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textbooks.

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00:07:59,625 --> 00:08:02,000
And I like it, because it's
something that you can really

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00:08:02,000 --> 00:08:04,654
grasp and understand.

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00:08:04,654 --> 00:08:06,320
We have to start with
the simple premise

209
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that electrons are a type of
particle called a fermion.

210
00:08:10,330 --> 00:08:11,350
What is a fermion?

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00:08:11,350 --> 00:08:14,240
Let's refresh our
basic physics here.

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00:08:14,240 --> 00:08:16,870
What means a fermion?

213
00:08:16,870 --> 00:08:18,010
Spin one half.

214
00:08:18,010 --> 00:08:21,430
And it also means-- can two
fermions occupy the same state?

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00:08:21,430 --> 00:08:22,100
No, they can't.

216
00:08:22,100 --> 00:08:23,300
Bosons can.

217
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But fermions cannot.

218
00:08:24,680 --> 00:08:27,200
And so what happens when you
put two fermions together

219
00:08:27,200 --> 00:08:28,540
in a system?

220
00:08:28,540 --> 00:08:32,340
And say we have
discretized quantum states.

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We begin filling up from
the bottom up, right?

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00:08:34,320 --> 00:08:35,190
Typically.

223
00:08:35,190 --> 00:08:37,900
So the lowest energy
states get occupied first.

224
00:08:37,900 --> 00:08:40,735
You have, for example, spin up,
spin down in your s orbital.

225
00:08:40,735 --> 00:08:43,110
And then they begin populating
the next electron orbital.

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00:08:43,110 --> 00:08:46,060
Once that's filled, you go to
the next one, and the next one.

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So if we have one
atom in isolation,

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the easiest example
is that hydrogen atom,

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00:08:50,490 --> 00:08:52,620
for those who took quantum
mechanics, who actually

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00:08:52,620 --> 00:08:55,520
calculated the energy
of the bound electron

231
00:08:55,520 --> 00:08:59,410
there in the ground state of the
hydrogen atom, around 13.6 eV.

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So imagine now you take a
silicon atom, or carbon atom,

233
00:09:03,870 --> 00:09:05,930
or something else,
a little bit bigger,

234
00:09:05,930 --> 00:09:08,160
more electrons in its structure.

235
00:09:08,160 --> 00:09:11,660
So you have the core,
the 1s orbital filled.

236
00:09:11,660 --> 00:09:14,440
And then you start
progressing outward.

237
00:09:14,440 --> 00:09:15,840
2s2p and so forth.

238
00:09:15,840 --> 00:09:17,834
And so you begin
filling up the orbitals.

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Let's see atomic separation.

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So imagine that we have our
atoms infinitely separated.

241
00:09:21,830 --> 00:09:23,780
So we have just one
atom in the middle

242
00:09:23,780 --> 00:09:26,170
of an infinite lonely space.

243
00:09:26,170 --> 00:09:27,160
One atom.

244
00:09:27,160 --> 00:09:30,160
And we would have discrete
energy levels corresponding

245
00:09:30,160 --> 00:09:33,080
to the different orbitals,
the different orbitals

246
00:09:33,080 --> 00:09:35,330
around the nucleus.

247
00:09:35,330 --> 00:09:37,190
Now imagine the atom
is no longer lonely.

248
00:09:37,190 --> 00:09:38,374
It now has a partner.

249
00:09:38,374 --> 00:09:40,790
And you bring those two atoms
closer and closer and closer

250
00:09:40,790 --> 00:09:41,590
together.

251
00:09:41,590 --> 00:09:43,870
That's this d getting
closer and closer together.

252
00:09:43,870 --> 00:09:44,650
What happens?

253
00:09:44,650 --> 00:09:46,990
Well, electrons are fermions.

254
00:09:46,990 --> 00:09:50,610
They don't like occupying
the same electronic state.

255
00:09:50,610 --> 00:09:53,236
So first, the first
shell that's going

256
00:09:53,236 --> 00:09:54,610
to quote, unquote
see each other,

257
00:09:54,610 --> 00:09:56,776
the first electron shell
that will interact is what?

258
00:09:56,776 --> 00:09:59,090
Is it the outermost,
or the innermost?

259
00:09:59,090 --> 00:09:59,650
Outermost.

260
00:09:59,650 --> 00:10:00,200
Right?

261
00:10:00,200 --> 00:10:02,140
Because they're the
closest together.

262
00:10:02,140 --> 00:10:04,098
So you're moving the two
atoms closer together,

263
00:10:04,098 --> 00:10:06,890
that outermost shell will
begin to quote, unquote see

264
00:10:06,890 --> 00:10:08,060
the other atom.

265
00:10:08,060 --> 00:10:10,610
And those electrons will say,
hey, you're occupying my state.

266
00:10:10,610 --> 00:10:12,610
And what will happen is
they'll begin splitting,

267
00:10:12,610 --> 00:10:15,800
in energy level, and that's
what you see right here.

268
00:10:15,800 --> 00:10:18,840
What this is representing is not
just two atoms coming together,

269
00:10:18,840 --> 00:10:21,199
but a multitude of
atoms coming together.

270
00:10:21,199 --> 00:10:22,990
And we have to really
imagine, for example,

271
00:10:22,990 --> 00:10:25,920
and in most matter, we have
something in the order of 10

272
00:10:25,920 --> 00:10:31,620
to the 22, 10 to the 23
atoms per cubic centimeter.

273
00:10:31,620 --> 00:10:34,020
So atoms per cubic centimeter.

274
00:10:34,020 --> 00:10:36,090
Fun math, just total aside.

275
00:10:36,090 --> 00:10:38,990
If anybody talks about
teletransporttion,

276
00:10:38,990 --> 00:10:41,020
think about the number
of atoms in your body.

277
00:10:41,020 --> 00:10:43,140
And assign an
xyz-coordinate to them,

278
00:10:43,140 --> 00:10:47,276
and then calculate the
amount of data in terabytes.

279
00:10:47,276 --> 00:10:48,900
And then calculate
our Ethernet speeds,

280
00:10:48,900 --> 00:10:50,750
and try to figure out how
long it would take to transmit

281
00:10:50,750 --> 00:10:52,330
that data to the other side.

282
00:10:52,330 --> 00:10:53,230
Anyway.

283
00:10:53,230 --> 00:10:54,730
So this is to give
you an impression

284
00:10:54,730 --> 00:10:57,590
of the density of atoms
within the cubic centimeter.

285
00:10:57,590 --> 00:10:59,450
So you have a lot of
atoms coming together,

286
00:10:59,450 --> 00:11:02,280
even though the electron
wave function can

287
00:11:02,280 --> 00:11:05,450
be highly localized, they still
interfere with each other.

288
00:11:05,450 --> 00:11:07,440
There's still enough
atoms coming together

289
00:11:07,440 --> 00:11:08,850
that you have this interference.

290
00:11:08,850 --> 00:11:12,130
And it's not just two electron
states, but many of them

291
00:11:12,130 --> 00:11:16,290
that are splitting, that
are forming a band of states

292
00:11:16,290 --> 00:11:18,640
because no two electrons
can occupy the same energy

293
00:11:18,640 --> 00:11:20,710
level as these atoms
are coming together.

294
00:11:20,710 --> 00:11:23,130
Now, as they become closer
and closer and closer,

295
00:11:23,130 --> 00:11:25,750
it's not only that outer
shell that begins interacting.

296
00:11:25,750 --> 00:11:28,130
It's the next most outer shell.

297
00:11:28,130 --> 00:11:29,890
This one, here, that
begins interacting.

298
00:11:29,890 --> 00:11:33,900
And finally another
shell, and another shell.

299
00:11:33,900 --> 00:11:36,660
And so at some
equilibrium distance,

300
00:11:36,660 --> 00:11:38,330
the equilibrium
distance here defined

301
00:11:38,330 --> 00:11:40,810
as the attractive
potential between atoms.

302
00:11:40,810 --> 00:11:44,030
There's an energy gain
by forming that bond.

303
00:11:44,030 --> 00:11:46,530
And the repulsive
force of the nuclei,

304
00:11:46,530 --> 00:11:48,567
their large concentration
of positive charge

305
00:11:48,567 --> 00:11:50,650
in the nucleus, that if
you tried pushing them too

306
00:11:50,650 --> 00:11:52,990
close together, they'll repel.

307
00:11:52,990 --> 00:11:55,840
This balance of forces,
the attractive potential

308
00:11:55,840 --> 00:11:58,840
due to that bond formation, the
repulsive force to the nucleic,

309
00:11:58,840 --> 00:12:01,220
results in an equilibrium
bond distance,

310
00:12:01,220 --> 00:12:03,390
d, shown here as
this dotted line.

311
00:12:03,390 --> 00:12:06,390
And at that equilibrium bond
distance, some of the orbitals

312
00:12:06,390 --> 00:12:09,050
will be forming bands and
other orbitals will still

313
00:12:09,050 --> 00:12:11,130
be discrete, namely
the core orbitals

314
00:12:11,130 --> 00:12:12,200
will still be discrete.

315
00:12:12,200 --> 00:12:15,500
The outermost orbitals
here will be forming bands.

316
00:12:15,500 --> 00:12:19,770
Now an interesting thing
happens when it just so occurs,

317
00:12:19,770 --> 00:12:21,650
and say, for example,
in the system right

318
00:12:21,650 --> 00:12:23,980
here, this shell is filled.

319
00:12:23,980 --> 00:12:25,430
This shell is filled.

320
00:12:25,430 --> 00:12:28,470
This shell is completely filled.

321
00:12:28,470 --> 00:12:30,330
And let's imagine that
this orbital exists,

322
00:12:30,330 --> 00:12:32,040
but it's unpopulated.

323
00:12:32,040 --> 00:12:33,090
You ran out of electrons.

324
00:12:33,090 --> 00:12:34,930
And you started
filling in the orbitals

325
00:12:34,930 --> 00:12:35,900
of this atom over here.

326
00:12:35,900 --> 00:12:37,800
You had enough for this orbital,
that orbital, that orbital,

327
00:12:37,800 --> 00:12:38,850
but then you ran
out of electrons.

328
00:12:38,850 --> 00:12:40,140
You didn't have anything more.

329
00:12:40,140 --> 00:12:42,370
And this band of
states was empty.

330
00:12:42,370 --> 00:12:45,740
So the band of allowed
states exists up there,

331
00:12:45,740 --> 00:12:46,660
but it's empty.

332
00:12:46,660 --> 00:12:49,200
And this band right here
exists, and it's filled.

333
00:12:49,200 --> 00:12:51,750
These core states exist,
and they're filled as well.

334
00:12:51,750 --> 00:12:53,930
So the action is really
happening right here.

335
00:12:53,930 --> 00:12:58,370
If light comes in, if
visible light comes in,

336
00:12:58,370 --> 00:13:01,170
it's probably going to excite an
electron from this filled band

337
00:13:01,170 --> 00:13:04,970
right here to somewhere in
this unoccupied band up there.

338
00:13:04,970 --> 00:13:08,870
And this gap, right here,
is an interesting thing.

339
00:13:08,870 --> 00:13:13,300
There is no stable
electron orbital.

340
00:13:13,300 --> 00:13:16,770
If you were somehow to take
an electron with that given

341
00:13:16,770 --> 00:13:19,406
energy, this energy
here, from the vacuum

342
00:13:19,406 --> 00:13:21,030
and stick it inside
of the system here,

343
00:13:21,030 --> 00:13:24,840
it would quickly decay
into a stable orbital.

344
00:13:24,840 --> 00:13:27,480
So this is a prohibited
band of states.

345
00:13:27,480 --> 00:13:29,710
There is no stable
orbital for that electron

346
00:13:29,710 --> 00:13:31,030
to exist at that energy.

347
00:13:31,030 --> 00:13:34,800
And hence we call it a band gap.

348
00:13:34,800 --> 00:13:36,490
The reason band gaps
are interesting,

349
00:13:36,490 --> 00:13:38,890
is because different materials
have different, or can

350
00:13:38,890 --> 00:13:40,181
have different, size band gaps.

351
00:13:40,181 --> 00:13:42,200
Some don't have a
band gap at all.

352
00:13:42,200 --> 00:13:45,600
Most of those that don't
have a band gap, because you

353
00:13:45,600 --> 00:13:49,109
have a band of states like
this one that's partially full.

354
00:13:49,109 --> 00:13:50,650
Let's imagine we
have three electrons

355
00:13:50,650 --> 00:13:51,649
in this band right here.

356
00:13:51,649 --> 00:13:52,650
One, two, three.

357
00:13:52,650 --> 00:13:55,840
And then we have these other
four empty states about it.

358
00:13:55,840 --> 00:13:58,010
In fact, you have a
partially filled band.

359
00:13:58,010 --> 00:13:59,740
And let's imagine,
instead of just having

360
00:13:59,740 --> 00:14:02,210
seven states within that band,
we had a multitude of states

361
00:14:02,210 --> 00:14:03,570
within that band.

362
00:14:03,570 --> 00:14:04,910
Almost too many to count.

363
00:14:04,910 --> 00:14:08,410
And now, with even the
slightest of energy,

364
00:14:08,410 --> 00:14:10,950
we could excite an
electron from this state

365
00:14:10,950 --> 00:14:14,470
into that state
plus little delta.

366
00:14:14,470 --> 00:14:16,600
That would be a metal.

367
00:14:16,600 --> 00:14:18,830
Now if we had a
really big band gap,

368
00:14:18,830 --> 00:14:20,929
we wouldn't be able
to absorb much light.

369
00:14:20,929 --> 00:14:22,720
Because you'd need a
large amount of energy

370
00:14:22,720 --> 00:14:25,430
to excite across that band gap.

371
00:14:25,430 --> 00:14:27,600
And that would be an
example of, say, glass.

372
00:14:27,600 --> 00:14:28,987
Where light would come in.

373
00:14:28,987 --> 00:14:31,320
Most of our visible spectrum
makes it through the glass,

374
00:14:31,320 --> 00:14:34,500
and that's why we see
through the other side.

375
00:14:34,500 --> 00:14:36,750
And diamonds as well.

376
00:14:36,750 --> 00:14:37,420
OK.

377
00:14:37,420 --> 00:14:39,410
So let's review.

378
00:14:39,410 --> 00:14:41,980
An atom in isolation has
discrete electron energy

379
00:14:41,980 --> 00:14:42,510
levels.

380
00:14:42,510 --> 00:14:44,210
And on this diagram
right here, it's

381
00:14:44,210 --> 00:14:47,040
represented with this d,
the atomic separation being

382
00:14:47,040 --> 00:14:47,610
way out here.

383
00:14:47,610 --> 00:14:49,740
We have discrete energy levels.

384
00:14:49,740 --> 00:14:52,410
And that we can remember from
our basic physics, especially

385
00:14:52,410 --> 00:14:54,020
the hydrogen atom.

386
00:14:54,020 --> 00:14:55,970
And as atoms move
closer together,

387
00:14:55,970 --> 00:14:58,510
as in a crystal, where you
have a regularly repeating

388
00:14:58,510 --> 00:15:02,010
arrangements of atoms, the
electron wave functions begin

389
00:15:02,010 --> 00:15:05,000
overlapping, and since
electrons are fermions,

390
00:15:05,000 --> 00:15:09,250
meaning that the two electrons
can't occupy the same state,

391
00:15:09,250 --> 00:15:13,969
you have a splitting of those
energy levels forming bands.

392
00:15:13,969 --> 00:15:16,510
And you can see the splitting
as you move from right to left,

393
00:15:16,510 --> 00:15:18,860
as you move from
further to closer,

394
00:15:18,860 --> 00:15:20,847
on these diagrams right here.

395
00:15:20,847 --> 00:15:22,930
First starting with the
outermost states, the most

396
00:15:22,930 --> 00:15:25,550
valence of electron orbitals,
and then slowly moving

397
00:15:25,550 --> 00:15:27,950
into the core states as well.

398
00:15:27,950 --> 00:15:30,450
And the gap between
bands denoting an energy

399
00:15:30,450 --> 00:15:33,800
range in which no stable orbital
exists is called a band gap.

400
00:15:33,800 --> 00:15:35,800
Sometimes you'll see it
all written as one word.

401
00:15:35,800 --> 00:15:39,105
Sometimes there will be a space
between the band and the gap.

402
00:15:39,105 --> 00:15:39,980
Any questions so far?

403
00:15:42,820 --> 00:15:44,930
OK.

404
00:15:44,930 --> 00:15:48,780
So now this explanation should
be relatively straightforward.

405
00:15:48,780 --> 00:15:50,780
What I want you to
log into your ram,

406
00:15:50,780 --> 00:15:52,375
because we're going into some
more detailed explanations,

407
00:15:52,375 --> 00:15:54,360
and I want to set a
marker, a flag, so we

408
00:15:54,360 --> 00:15:55,736
can come back here afterward.

409
00:15:55,736 --> 00:15:58,110
And even if you're lost with
the subsequent explanations,

410
00:15:58,110 --> 00:15:59,090
you still get this one.

411
00:15:59,090 --> 00:15:59,650
Right?

412
00:15:59,650 --> 00:16:01,286
So remember these three points.

413
00:16:01,286 --> 00:16:03,410
If you make a note of them
in your notes, and we're

414
00:16:03,410 --> 00:16:07,230
going to move on to a few
more explanations here.

415
00:16:07,230 --> 00:16:12,660
OK, so another way of looking
at this which really builds

416
00:16:12,660 --> 00:16:15,320
on the folks who have had a more
advanced physics backgrounds,

417
00:16:15,320 --> 00:16:19,400
is that the wave function
of an electron, inside

418
00:16:19,400 --> 00:16:22,520
of a crystal-- if
you recall the wave

419
00:16:22,520 --> 00:16:25,510
function of an electron in
free space, we have what

420
00:16:25,510 --> 00:16:27,980
is called the plane wave
equation for the electron.

421
00:16:27,980 --> 00:16:31,720
It's this regular repeating,
nice stable function.

422
00:16:31,720 --> 00:16:35,660
Now if we introduce that
electron into a crystal,

423
00:16:35,660 --> 00:16:40,620
it's almost like an infinitely
repeating system of atoms.

424
00:16:40,620 --> 00:16:42,640
And so you could
envision that you

425
00:16:42,640 --> 00:16:45,410
could describe the wave
function of that electron

426
00:16:45,410 --> 00:16:47,860
as a combination
of a plane wave,

427
00:16:47,860 --> 00:16:50,450
but perturbed by that
locally repeating potential

428
00:16:50,450 --> 00:16:52,450
from the atomic nuclei.

429
00:16:52,450 --> 00:16:54,320
And let me be more
specific about

430
00:16:54,320 --> 00:16:55,720
regular repeating potential.

431
00:16:55,720 --> 00:16:59,310
What I mean is that you have
a series of nuclei here,

432
00:16:59,310 --> 00:17:02,360
and if you imagine the electron
potential around these nuclei,

433
00:17:02,360 --> 00:17:04,530
there is a propensity
for the election

434
00:17:04,530 --> 00:17:07,109
to be bound by the atom.

435
00:17:07,109 --> 00:17:10,190
And so as it's moving along,
instead of just a free plane

436
00:17:10,190 --> 00:17:13,359
wave, now it's almost like
driving along a bumpy road,

437
00:17:13,359 --> 00:17:15,780
bump, bump, bump.

438
00:17:15,780 --> 00:17:18,550
And so the wave
function of the electron

439
00:17:18,550 --> 00:17:20,780
can be described as this
combination or product

440
00:17:20,780 --> 00:17:23,619
of the wave function
of a plane wave,

441
00:17:23,619 --> 00:17:27,369
envelope function describing
the electron localization.

442
00:17:27,369 --> 00:17:29,670
So you have this
localized function here

443
00:17:29,670 --> 00:17:34,480
and the delocalized function
describing the plane wave

444
00:17:34,480 --> 00:17:36,930
behavior of the electron as
it moves through space inside

445
00:17:36,930 --> 00:17:38,350
of the crystal.

446
00:17:38,350 --> 00:17:42,270
Now what we have as an
easy way to describe this

447
00:17:42,270 --> 00:17:45,050
mathematically, is we
make an approximation.

448
00:17:45,050 --> 00:17:50,410
Instead of describing
this potential in detail,

449
00:17:50,410 --> 00:17:54,280
the easiest way to do this is
to describe this square well

450
00:17:54,280 --> 00:17:55,450
potential.

451
00:17:55,450 --> 00:17:57,659
We have a so-called
Kronig-Penney idealization

452
00:17:57,659 --> 00:17:59,200
of the repeating
Coulombic potential.

453
00:17:59,200 --> 00:18:01,050
It's easier to
solve numerically.

454
00:18:01,050 --> 00:18:03,250
And then essentially
what we do is

455
00:18:03,250 --> 00:18:07,350
we solve Schrodinger's equation
for two possible solutions.

456
00:18:07,350 --> 00:18:09,550
One is for the electron
wave function centered

457
00:18:09,550 --> 00:18:11,040
on the atoms themselves.

458
00:18:11,040 --> 00:18:13,320
So that would be
the bound state.

459
00:18:13,320 --> 00:18:17,840
And the other is we solve the
equation for electron function

460
00:18:17,840 --> 00:18:19,410
centered between the atoms.

461
00:18:19,410 --> 00:18:23,420
So essentially in the
unbound state, right here.

462
00:18:23,420 --> 00:18:27,032
Which do you think will have
the higher energy level?

463
00:18:27,032 --> 00:18:28,240
In between the states, right?

464
00:18:28,240 --> 00:18:31,620
Because if the electron wave
function is centered over here,

465
00:18:31,620 --> 00:18:34,980
it's further away from the
positive charge of the nuclei.

466
00:18:34,980 --> 00:18:37,290
You need more energy to
put it into that position.

467
00:18:37,290 --> 00:18:40,870
It's an unbound state, but it's
also at a higher excited energy

468
00:18:40,870 --> 00:18:41,510
level.

469
00:18:41,510 --> 00:18:44,000
Whereas if it's bound
around the atoms themselves,

470
00:18:44,000 --> 00:18:47,860
you would have a
lower energy state.

471
00:18:47,860 --> 00:18:50,890
In this delta of energy
levels between the bound

472
00:18:50,890 --> 00:18:53,730
and the excited states
represents the band gap

473
00:18:53,730 --> 00:18:57,100
of the semiconductor in
this simple approximation

474
00:18:57,100 --> 00:18:58,190
right here.

475
00:18:58,190 --> 00:19:01,290
Now you can take that one step
further and say, well, gee,

476
00:19:01,290 --> 00:19:03,030
if I could solve
that in one dimension

477
00:19:03,030 --> 00:19:04,780
in a very simple
case, why don't I

478
00:19:04,780 --> 00:19:07,830
put a three dimensional
structure in place,

479
00:19:07,830 --> 00:19:11,729
such as a real crystal, and then
solve the Schrodinger equation?

480
00:19:11,729 --> 00:19:12,770
And sure you can do that.

481
00:19:12,770 --> 00:19:13,895
You can definitely do that.

482
00:19:13,895 --> 00:19:18,210
It becomes much more complicated
solution numerically,

483
00:19:18,210 --> 00:19:21,230
but the general principle
stays roughly the same.

484
00:19:21,230 --> 00:19:23,870
You can add several more
tricks, and bells, and whistles.

485
00:19:23,870 --> 00:19:26,906
And of course, I would
probably emphasize

486
00:19:26,906 --> 00:19:28,280
that the solution
could either be

487
00:19:28,280 --> 00:19:31,180
done numerically or you
could use the symmetry

488
00:19:31,180 --> 00:19:33,430
relations of the
crystal to develop

489
00:19:33,430 --> 00:19:37,940
a very simple expression
of the crystal,

490
00:19:37,940 --> 00:19:41,830
minimizing the
redundant directions

491
00:19:41,830 --> 00:19:43,660
inside of the crystal,
collapsing it down

492
00:19:43,660 --> 00:19:46,420
into the bare essential
to describe that crystal

493
00:19:46,420 --> 00:19:47,350
structure.

494
00:19:47,350 --> 00:19:53,690
And we would have some uniform
energy space that looks,

495
00:19:53,690 --> 00:19:56,150
for example, represented by
this yellowish surface, where

496
00:19:56,150 --> 00:19:58,191
you'd have an isopotential
inside of your crystal

497
00:19:58,191 --> 00:20:00,110
structure.

498
00:20:00,110 --> 00:20:03,970
So these are different ways of
looking at the band gap inside

499
00:20:03,970 --> 00:20:05,465
of a semiconductor crystal.

500
00:20:05,465 --> 00:20:07,840
If you're really interested,
and for the advance reading,

501
00:20:07,840 --> 00:20:09,673
I would definitely
suggest this book called,

502
00:20:09,673 --> 00:20:12,750
Fundamentals of Semiconductors,
by Professor Peter Yu,

503
00:20:12,750 --> 00:20:15,200
now retired at UC Berkeley.

504
00:20:15,200 --> 00:20:17,280
Very nice explanation.

505
00:20:17,280 --> 00:20:20,160
Uses an elegant
application of group theory

506
00:20:20,160 --> 00:20:26,210
to derive the band structure
of a semiconductor in detail.

507
00:20:26,210 --> 00:20:29,523
So let's hop back to this one,
real quick-- actually, yeah?

508
00:20:29,523 --> 00:20:30,898
AUDIENCE: I'm just
curious if you

509
00:20:30,898 --> 00:20:32,906
could tell us the name
of the equation that

510
00:20:32,906 --> 00:20:34,670
was at the top of--

511
00:20:34,670 --> 00:20:37,330
PROFESSOR: Sure.

512
00:20:37,330 --> 00:20:37,980
Absolutely.

513
00:20:37,980 --> 00:20:42,503
So what we're describing here
is essentially the e to the ikx,

514
00:20:42,503 --> 00:20:45,440
or e to the ikr,
essentially describing

515
00:20:45,440 --> 00:20:46,790
that periodic potential.

516
00:20:46,790 --> 00:20:50,450
And then in essentially
an envelope function.

517
00:20:50,450 --> 00:20:52,599
So, yeah, that would
be the wave function

518
00:20:52,599 --> 00:20:54,890
that would be introduced into
the Schrodinger equation.

519
00:20:58,810 --> 00:21:00,850
So let's go back to
here really quickly,

520
00:21:00,850 --> 00:21:03,590
because I don't want to
get us lost in the weeds.

521
00:21:03,590 --> 00:21:06,930
I want us to focus on the
main concepts at hand.

522
00:21:06,930 --> 00:21:09,740
Let's, from an engineering
point of view--

523
00:21:09,740 --> 00:21:14,470
given this formation of bands
inside of real materials,

524
00:21:14,470 --> 00:21:17,300
since the atoms are coming
together and forming crystals,

525
00:21:17,300 --> 00:21:20,830
we can envision a few
different scenarios.

526
00:21:20,830 --> 00:21:22,520
Let's focus on the
this band here,

527
00:21:22,520 --> 00:21:25,200
and that band here, and the
space in between them, the band

528
00:21:25,200 --> 00:21:25,740
gap.

529
00:21:25,740 --> 00:21:27,880
And let's assume that
we have this band

530
00:21:27,880 --> 00:21:30,300
here either completely
filled or partially filled,

531
00:21:30,300 --> 00:21:32,530
and talk about what
happens in three

532
00:21:32,530 --> 00:21:35,170
different extreme scenarios.

533
00:21:35,170 --> 00:21:38,300
In one case, when we have
the band partially filled,

534
00:21:38,300 --> 00:21:40,850
we have what is
known as a metal.

535
00:21:40,850 --> 00:21:42,640
And the reason this
case is interesting

536
00:21:42,640 --> 00:21:45,130
is because a very
small amount of energy

537
00:21:45,130 --> 00:21:48,530
is all that it would take
to excite an electron

538
00:21:48,530 --> 00:21:50,480
and make it to move
around the crystal.

539
00:21:50,480 --> 00:21:52,105
As a matter of fact,
a metal has what's

540
00:21:52,105 --> 00:21:56,040
called electron c, that
serves to conduct electricity

541
00:21:56,040 --> 00:21:59,100
at room temperature and
even at very, very, very

542
00:21:59,100 --> 00:22:00,900
low temperatures.

543
00:22:00,900 --> 00:22:02,670
Semiconductor, on
the other hand.

544
00:22:02,670 --> 00:22:04,964
Now semiconductor has
a finite band gap,

545
00:22:04,964 --> 00:22:06,380
and we'll get to
this in a minute.

546
00:22:06,380 --> 00:22:08,296
Let's start with the
insulator, because that's

547
00:22:08,296 --> 00:22:10,680
a more easy to understand case.

548
00:22:10,680 --> 00:22:14,240
If the band gap is
very, very, very big,

549
00:22:14,240 --> 00:22:16,730
then a large amount
of energy is required

550
00:22:16,730 --> 00:22:19,780
to excite an electron
into an unbound state,

551
00:22:19,780 --> 00:22:21,780
so it can move freely
across the crystal.

552
00:22:21,780 --> 00:22:23,560
And as a result,
you're not going

553
00:22:23,560 --> 00:22:26,220
to have a very large population
of electrons up here.

554
00:22:26,220 --> 00:22:28,380
The photo excited
carrier population,

555
00:22:28,380 --> 00:22:32,930
meaning the population of
charge carriers, electrons,

556
00:22:32,930 --> 00:22:35,960
that are excited into here
from light, is very small.

557
00:22:35,960 --> 00:22:37,990
And the thermally excited
carrier concentration,

558
00:22:37,990 --> 00:22:39,490
just some background
thermal energy,

559
00:22:39,490 --> 00:22:42,520
kt, Boltzmann's constant
times temperature,

560
00:22:42,520 --> 00:22:45,450
that energy is also going to be
insufficient to drive electrons

561
00:22:45,450 --> 00:22:46,520
across this band gap.

562
00:22:46,520 --> 00:22:49,370
And as a result, you will have
a very, very small population

563
00:22:49,370 --> 00:22:52,780
of carriers up here.

564
00:22:52,780 --> 00:22:55,760
And this will be an
insulator, because you

565
00:22:55,760 --> 00:22:59,540
will have very few charges
to transport current.

566
00:22:59,540 --> 00:23:02,170
If you apply a potential
across an insulator,

567
00:23:02,170 --> 00:23:04,380
you will not have very
much current flow.

568
00:23:04,380 --> 00:23:06,790
And that's the principle
of insulating materials

569
00:23:06,790 --> 00:23:08,260
around wires.

570
00:23:08,260 --> 00:23:10,020
Actually this is in
the semiconductor.

571
00:23:10,020 --> 00:23:11,290
This is a polymer.

572
00:23:11,290 --> 00:23:14,360
But if we had, for
example, glass or diamond,

573
00:23:14,360 --> 00:23:18,330
that would serve as a
nice insulator as well.

574
00:23:18,330 --> 00:23:20,960
Now a semiconductor material
is somewhere between a metal

575
00:23:20,960 --> 00:23:22,180
and an insulator here.

576
00:23:22,180 --> 00:23:24,610
And that the band
gap is now shrinking.

577
00:23:24,610 --> 00:23:27,280
The band gap is small enough
to interact with lights,

578
00:23:27,280 --> 00:23:28,211
typically.

579
00:23:28,211 --> 00:23:29,960
For example, this
little piece of silicon,

580
00:23:29,960 --> 00:23:31,900
which I'll show in
detail in a minute,

581
00:23:31,900 --> 00:23:33,330
towards the end of class.

582
00:23:33,330 --> 00:23:35,500
It doesn't look clear,
like glass does.

583
00:23:35,500 --> 00:23:37,310
It looks opaque.

584
00:23:37,310 --> 00:23:39,090
And that's because
it's absorbing photons

585
00:23:39,090 --> 00:23:41,220
in the visible spectrum.

586
00:23:41,220 --> 00:23:43,720
But it's letting some of the
infrared photons go through it.

587
00:23:43,720 --> 00:23:45,178
Some of the very
low energy photons

588
00:23:45,178 --> 00:23:47,280
can go through the material,
because those photons

589
00:23:47,280 --> 00:23:49,470
have insufficient energy
to excite carriers

590
00:23:49,470 --> 00:23:51,830
across that band gap.

591
00:23:51,830 --> 00:23:55,220
So we have a semiconductor
material, defined here

592
00:23:55,220 --> 00:23:57,130
as having a band gap.

593
00:23:57,130 --> 00:24:00,100
That band gap defines the
energy of the light that

594
00:24:00,100 --> 00:24:01,700
is most efficiently absorbed.

595
00:24:01,700 --> 00:24:04,814
And any photon with energy
in excess of the band gap

596
00:24:04,814 --> 00:24:06,605
can also be absorbed
by that semiconductor.

597
00:24:09,610 --> 00:24:12,612
Any questions so far?

598
00:24:12,612 --> 00:24:15,027
AUDIENCE: Are there
any natural materials

599
00:24:15,027 --> 00:24:17,721
where the spacing
of the bands is such

600
00:24:17,721 --> 00:24:20,179
that three bands are active,
or is it always just two bands

601
00:24:20,179 --> 00:24:20,840
which are active?

602
00:24:20,840 --> 00:24:21,798
PROFESSOR: Interesting.

603
00:24:21,798 --> 00:24:24,250
So the question is, are
there more bands above here

604
00:24:24,250 --> 00:24:26,300
that you could excite into?

605
00:24:26,300 --> 00:24:28,090
Absolutely.

606
00:24:28,090 --> 00:24:32,740
So as you can envision,
back here for instance,

607
00:24:32,740 --> 00:24:35,710
you could continue drawing
more and more and more bands.

608
00:24:35,710 --> 00:24:37,750
They're unoccupied,
but they exist.

609
00:24:37,750 --> 00:24:40,280
And as the atoms come
closer and closer together,

610
00:24:40,280 --> 00:24:42,120
those begin interacting as well.

611
00:24:42,120 --> 00:24:44,610
And so in a few
lectures we'll look

612
00:24:44,610 --> 00:24:46,600
at a band diagram
of a semiconductor,

613
00:24:46,600 --> 00:24:48,310
and we'll see all
the occupied bands,

614
00:24:48,310 --> 00:24:49,886
and all the unoccupied bands.

615
00:24:49,886 --> 00:24:51,510
And you can excite
into any one of them

616
00:24:51,510 --> 00:24:55,000
if you have the right
excitation condition.

617
00:24:55,000 --> 00:24:57,750
Let's put it that way.

618
00:24:57,750 --> 00:24:59,400
Any other questions?

619
00:24:59,400 --> 00:25:00,059
Yeah.

620
00:25:00,059 --> 00:25:02,100
AUDIENCE: I'm having
trouble seeing the chemist's

621
00:25:02,100 --> 00:25:04,237
description along
with the physicist's

622
00:25:04,237 --> 00:25:07,688
description along with
this slide all together.

623
00:25:07,688 --> 00:25:10,646
How does, once it's in
the crystal structure

624
00:25:10,646 --> 00:25:13,111
and it's in its
lattices and everything,

625
00:25:13,111 --> 00:25:15,320
how does that look
in this picture?

626
00:25:15,320 --> 00:25:16,570
Where is that in this picture.

627
00:25:16,570 --> 00:25:17,236
PROFESSOR: Sure.

628
00:25:17,236 --> 00:25:19,680
So this one here, let
me describe the axes,

629
00:25:19,680 --> 00:25:22,300
because that might make things
a little easier to understand.

630
00:25:22,300 --> 00:25:25,480
In the vertical axis
here, we have energy.

631
00:25:25,480 --> 00:25:29,000
And that's the same axis as
we have right here, energy.

632
00:25:29,000 --> 00:25:31,389
In this axis right here, we
had inter atomic separation.

633
00:25:31,389 --> 00:25:32,930
So this was meant
to demonstrate what

634
00:25:32,930 --> 00:25:35,730
happens when we bring atoms
closer and close together.

635
00:25:35,730 --> 00:25:37,550
In this description
right here, this

636
00:25:37,550 --> 00:25:41,850
is an unlabeled axis that could
be x real space, for instance.

637
00:25:41,850 --> 00:25:45,707
Why do we plot an
x in the x-axis?

638
00:25:45,707 --> 00:25:46,790
Why do we plot real space?

639
00:25:46,790 --> 00:25:49,262
Well sometimes, when we talk
about solar cell devices,

640
00:25:49,262 --> 00:25:50,720
we're talking about
bringing charge

641
00:25:50,720 --> 00:25:52,970
from deep within the device
to the front surface where

642
00:25:52,970 --> 00:25:54,070
the contact is.

643
00:25:54,070 --> 00:25:57,240
And so we want to talk about the
flow of charge in real space.

644
00:25:57,240 --> 00:26:00,010
So that's oftentimes why
you see in these band

645
00:26:00,010 --> 00:26:02,060
diagrams for solar
cells, you'll see

646
00:26:02,060 --> 00:26:05,350
e versus x, versus real space.

647
00:26:05,350 --> 00:26:08,330
Now let me show you what these
two levels here represent.

648
00:26:08,330 --> 00:26:11,040
This is the top
of the filled band

649
00:26:11,040 --> 00:26:13,150
and the bottom of
the empty band.

650
00:26:13,150 --> 00:26:15,010
And those correspond over here.

651
00:26:15,010 --> 00:26:16,830
I'm going to use the
mouse now, because I'm

652
00:26:16,830 --> 00:26:17,930
going to be stretching.

653
00:26:17,930 --> 00:26:22,730
Let's imagine that this
level on down was filled.

654
00:26:22,730 --> 00:26:24,840
And that this level
up here is empty.

655
00:26:24,840 --> 00:26:28,980
So if I may, these
are all filled.

656
00:26:28,980 --> 00:26:29,890
All filled.

657
00:26:29,890 --> 00:26:33,620
And this one here is empty.

658
00:26:33,620 --> 00:26:35,070
Gonna take a little bit.

659
00:26:35,070 --> 00:26:35,720
Here we go.

660
00:26:35,720 --> 00:26:36,220
All right.

661
00:26:36,220 --> 00:26:40,030
So now this band is going to
be filled, because we're really

662
00:26:40,030 --> 00:26:43,820
looking at the equilibrium inter
atomic separation in a crystal.

663
00:26:43,820 --> 00:26:45,990
We're looking right here this d.

664
00:26:45,990 --> 00:26:48,182
That's the spacing right
now of those atoms inside

665
00:26:48,182 --> 00:26:50,140
of that piece of
semiconductor material, inside

666
00:26:50,140 --> 00:26:51,210
of that silicon.

667
00:26:51,210 --> 00:26:56,960
So what we care about
is this right here.

668
00:26:56,960 --> 00:27:00,320
And this would be the
top of the filled band,

669
00:27:00,320 --> 00:27:03,170
and this would be the
bottom of the empty band,

670
00:27:03,170 --> 00:27:08,310
corresponding to the top of
the filled band right here

671
00:27:08,310 --> 00:27:11,830
and the bottom of the
empty band right there.

672
00:27:11,830 --> 00:27:13,940
So that's how it
all fits together.

673
00:27:13,940 --> 00:27:16,700
This diagram here can
get kind of confusing

674
00:27:16,700 --> 00:27:19,740
when you're looking in
the abscissa, essentially

675
00:27:19,740 --> 00:27:20,780
the x-axis.

676
00:27:20,780 --> 00:27:22,892
Because you're thinking
in terms of real space.

677
00:27:22,892 --> 00:27:25,350
Well, it is real space, but
you're bringing atoms together.

678
00:27:25,350 --> 00:27:27,433
So it's really meant to
be a phenomenological tool

679
00:27:27,433 --> 00:27:29,610
to describe how band gaps form.

680
00:27:29,610 --> 00:27:32,267
This diagram over
here, we're now

681
00:27:32,267 --> 00:27:34,350
starting to get into the
engineering diagrams that

682
00:27:34,350 --> 00:27:36,930
can help explain how
solar cells work.

683
00:27:36,930 --> 00:27:41,550
And from here on out, we'll
be abandoning that chemists

684
00:27:41,550 --> 00:27:43,960
diagram and simply
using this one

685
00:27:43,960 --> 00:27:46,950
because we assume that we're not
applying a significant strain

686
00:27:46,950 --> 00:27:50,360
to our semiconductor
material to get

687
00:27:50,360 --> 00:27:51,530
significant deviations here.

688
00:27:51,530 --> 00:27:54,520
We'd have to apply strains
of several percent,

689
00:27:54,520 --> 00:27:56,830
and probably result in
fracture of our semiconductor

690
00:27:56,830 --> 00:28:01,850
before we ended up changing
that inter-atomic distance.

691
00:28:01,850 --> 00:28:03,629
We could also heat it up.

692
00:28:03,629 --> 00:28:05,920
It's another way of introducing
strain, thermal strain,

693
00:28:05,920 --> 00:28:09,470
but not mechanical.

694
00:28:09,470 --> 00:28:09,970
OK.

695
00:28:09,970 --> 00:28:12,850
So did that help
answer the question?

696
00:28:12,850 --> 00:28:13,350
OK.

697
00:28:16,160 --> 00:28:18,390
So the second
point here, we want

698
00:28:18,390 --> 00:28:20,630
to first off describe
phenomenological band gap

699
00:28:20,630 --> 00:28:22,950
and understand how that works.

700
00:28:22,950 --> 00:28:25,180
Secondly, we want to
describe optical transitions

701
00:28:25,180 --> 00:28:28,490
in the semiconductor and
understand how charge carriers,

702
00:28:28,490 --> 00:28:31,430
in other words, how electrons
on an energy band diagram

703
00:28:31,430 --> 00:28:32,540
are moving around.

704
00:28:32,540 --> 00:28:35,280
Why do we call electrons
charge carriers once again?

705
00:28:35,280 --> 00:28:36,780
Remind me, from
this diagram here.

706
00:28:42,080 --> 00:28:44,020
Exactly.

707
00:28:44,020 --> 00:28:44,767
It's brilliant.

708
00:28:44,767 --> 00:28:46,850
I just want to make sure
that those two things are

709
00:28:46,850 --> 00:28:48,600
synonymous in people's
minds, that we're not getting

710
00:28:48,600 --> 00:28:50,080
caught up on the language.

711
00:28:50,080 --> 00:28:50,770
Thank you.

712
00:28:50,770 --> 00:28:53,040
So again, charge
carriers, electrons,

713
00:28:53,040 --> 00:28:56,130
being free electrons, unbound
electrons, not any electron,

714
00:28:56,130 --> 00:28:58,740
not the ones down here, but
the ones that are excited.

715
00:28:58,740 --> 00:29:04,340
OK, so let's go back to lecture
number two, I think it was,

716
00:29:04,340 --> 00:29:07,480
where we talk about
the duality of light.

717
00:29:07,480 --> 00:29:09,764
It's a wave and a particle.

718
00:29:09,764 --> 00:29:12,180
Well it can be thought of, can
be described mathematically

719
00:29:12,180 --> 00:29:13,138
as waves and particles.

720
00:29:13,138 --> 00:29:14,910
We've, in last
lecture, when we talked

721
00:29:14,910 --> 00:29:17,990
about lights and the interaction
with lights with materials,

722
00:29:17,990 --> 00:29:20,480
we referred to light
mostly as a wave.

723
00:29:20,480 --> 00:29:24,510
This was very easy for us
to describe interference.

724
00:29:24,510 --> 00:29:27,380
It made it convenient to
do the homework problems,

725
00:29:27,380 --> 00:29:30,170
especially for the graduate
students, the last problem.

726
00:29:30,170 --> 00:29:31,350
That was a lot of fun

727
00:29:31,350 --> 00:29:33,460
But now we will be
talking about life

728
00:29:33,460 --> 00:29:36,050
in terms of discrete
quanta of energy,

729
00:29:36,050 --> 00:29:37,870
because one photon
is going to be

730
00:29:37,870 --> 00:29:40,060
absorbed by an electron,
an excited electron,

731
00:29:40,060 --> 00:29:41,560
into another state.

732
00:29:41,560 --> 00:29:45,340
So now we think of the photon
as having a certain energy,

733
00:29:45,340 --> 00:29:48,140
defined by the
wavelength of light,

734
00:29:48,140 --> 00:29:51,900
and that energy is going to be
given to the electron, which

735
00:29:51,900 --> 00:29:55,254
will then be excited inside
of our semiconductor crystal.

736
00:29:55,254 --> 00:29:55,920
So what happens?

737
00:29:55,920 --> 00:29:57,316
Well we have our sun.

738
00:29:57,316 --> 00:29:58,940
Here we have our
semiconductor crystal.

739
00:29:58,940 --> 00:30:02,780
Again, I'm representing
it in terms of e versus x.

740
00:30:02,780 --> 00:30:05,630
I'm saying that these
states here are filled.

741
00:30:05,630 --> 00:30:07,970
And these states here
are mostly empty.

742
00:30:07,970 --> 00:30:09,200
And these are mostly filled.

743
00:30:09,200 --> 00:30:11,050
Mostly empty.

744
00:30:11,050 --> 00:30:13,230
And this is my band
gap right here.

745
00:30:13,230 --> 00:30:17,410
I'm plotting e in the
ordinate and x real space

746
00:30:17,410 --> 00:30:18,520
in the abscissa.

747
00:30:18,520 --> 00:30:20,589
And again, x because,
ultimately, we'll

748
00:30:20,589 --> 00:30:22,630
be looking at the cross
section of the solar cell

749
00:30:22,630 --> 00:30:25,570
in x, in describing how charge
gets extracted from the device.

750
00:30:25,570 --> 00:30:28,210
So that's why we're going
to be using x on this axis.

751
00:30:28,210 --> 00:30:30,510
Now we have sunlight here,
outside of our device.

752
00:30:30,510 --> 00:30:32,050
And it's going to
be shining light

753
00:30:32,050 --> 00:30:34,400
onto the semiconductor crystal.

754
00:30:34,400 --> 00:30:35,280
So what happens?

755
00:30:35,280 --> 00:30:36,859
Well, we know
intuitively that charge

756
00:30:36,859 --> 00:30:38,400
should be excited
from a bound states

757
00:30:38,400 --> 00:30:41,750
to an unbound state, where it
can move around the material.

758
00:30:41,750 --> 00:30:44,870
But not all light
serves this function.

759
00:30:44,870 --> 00:30:48,970
If we have a photon that has
an energy above the band gap

760
00:30:48,970 --> 00:30:53,110
energy, so e photon, meaning the
energy of the incident photon

761
00:30:53,110 --> 00:30:56,040
is greater than e gap, the
energy band gap, then we'll

762
00:30:56,040 --> 00:30:57,350
have an excitation of charge.

763
00:30:57,350 --> 00:31:00,670
We'll have an electron taken
from somewhere here, brought up

764
00:31:00,670 --> 00:31:03,060
to a higher excited
states, and it

765
00:31:03,060 --> 00:31:06,690
might come to settle down at the
bottom of that band of states

766
00:31:06,690 --> 00:31:07,730
that is allowed.

767
00:31:07,730 --> 00:31:10,510
A settling, if you will.

768
00:31:10,510 --> 00:31:14,270
But if our photon energy
is less than our band gap,

769
00:31:14,270 --> 00:31:15,730
we won't have this
process occur.

770
00:31:15,730 --> 00:31:19,450
Instead we'll have the light
going straight through it.

771
00:31:19,450 --> 00:31:21,720
And this is
brilliant, because you

772
00:31:21,720 --> 00:31:24,400
can begin to understand
the behavior of many solids

773
00:31:24,400 --> 00:31:25,370
in this way.

774
00:31:25,370 --> 00:31:26,811
Let's take a glass,
for instance.

775
00:31:26,811 --> 00:31:29,060
How many you have noticed
that you never get sunburned

776
00:31:29,060 --> 00:31:30,810
when the windows are up?

777
00:31:30,810 --> 00:31:33,990
But you get sunburned when you
forget to put the windows up,

778
00:31:33,990 --> 00:31:36,820
when you're driving around
and your arm's sticking out,

779
00:31:36,820 --> 00:31:38,850
you get that nice truckers tan.

780
00:31:38,850 --> 00:31:42,270
That's because the ultraviolet
photons have enough energy

781
00:31:42,270 --> 00:31:45,360
in glass to excite electrons
across the band gap.

782
00:31:45,360 --> 00:31:47,730
So the ultraviolet photons
gets absorbed by the glass,

783
00:31:47,730 --> 00:31:51,250
but the visible photons instead
are coming straight through,

784
00:31:51,250 --> 00:31:53,080
much like this.

785
00:31:53,080 --> 00:31:55,710
Now glass has a
very large band gap.

786
00:31:55,710 --> 00:31:58,610
Now silicon, much
smaller band gap.

787
00:31:58,610 --> 00:32:01,940
And in that case, in
the case of silicon,

788
00:32:01,940 --> 00:32:03,190
even the visible gets blocked.

789
00:32:03,190 --> 00:32:05,600
So silicon would make
a really crummy window.

790
00:32:05,600 --> 00:32:08,310
But it makes a really
great infrared window.

791
00:32:08,310 --> 00:32:10,050
So if you're detecting
infrared light,

792
00:32:10,050 --> 00:32:11,650
and want to block
out all the visible,

793
00:32:11,650 --> 00:32:15,310
you might consider sticking
up a filter made of silicon.

794
00:32:15,310 --> 00:32:18,064
And that's regularly
done in laboratories.

795
00:32:18,064 --> 00:32:19,480
So you can begin
to understand how

796
00:32:19,480 --> 00:32:22,350
light interacts with
matter, with solids,

797
00:32:22,350 --> 00:32:24,280
using this energy band diagram.

798
00:32:24,280 --> 00:32:27,810
And ultimately how these
optical absorption spectra

799
00:32:27,810 --> 00:32:29,360
come into being.

800
00:32:29,360 --> 00:32:31,580
So we studied these
optical absorption spectra

801
00:32:31,580 --> 00:32:32,330
in our last class.

802
00:32:32,330 --> 00:32:34,390
We just took them as a given.

803
00:32:34,390 --> 00:32:37,410
We didn't question
where they came from.

804
00:32:37,410 --> 00:32:40,890
Now we're going to be focusing
on this so-called turn

805
00:32:40,890 --> 00:32:43,030
on energy, or turn
on wave length.

806
00:32:43,030 --> 00:32:45,750
Remember wavelength and
energy are interchangeable.

807
00:32:45,750 --> 00:32:48,440
I've written down below here
the energy corresponding

808
00:32:48,440 --> 00:32:50,770
to a given wavelength,
around 2000 nanometers.

809
00:32:50,770 --> 00:32:53,160
We have an energy
of around 0.62 eV.

810
00:32:53,160 --> 00:32:58,480
At around 200 nanometers,
we have an energy of 6.2 eV.

811
00:32:58,480 --> 00:33:02,540
Since one is the reciprocal
of the other, related by hc,

812
00:33:02,540 --> 00:33:04,200
it's only natural
that if we change one

813
00:33:04,200 --> 00:33:05,750
by an order of magnitude,
we're changing the other

814
00:33:05,750 --> 00:33:07,874
by an order of magnitude
in the opposite direction.

815
00:33:07,874 --> 00:33:10,520
So we're wrapping our minds
around this interchangeability

816
00:33:10,520 --> 00:33:11,884
of wavelength and energy.

817
00:33:11,884 --> 00:33:13,300
That's important,
because we'll be

818
00:33:13,300 --> 00:33:17,440
referring to them very
naturally as a photon

819
00:33:17,440 --> 00:33:20,030
either having a certain
wavelength or a certain energy.

820
00:33:20,030 --> 00:33:22,550
You notice that there are
certain turn on energies.

821
00:33:22,550 --> 00:33:24,610
So energy is increasing
in that direction there.

822
00:33:24,610 --> 00:33:28,040
So as we go from
infrared to ultraviolet,

823
00:33:28,040 --> 00:33:30,800
the energy of the incoming
light is increasing.

824
00:33:30,800 --> 00:33:33,390
And if the energy is too low,
the semiconductor crystal

825
00:33:33,390 --> 00:33:34,360
just won't absorb.

826
00:33:34,360 --> 00:33:36,570
The absorptance is 0,
or very, very small.

827
00:33:36,570 --> 00:33:39,500
It doesn't even appear
on the log plot here.

828
00:33:39,500 --> 00:33:41,270
And as we begin
increasing the energy,

829
00:33:41,270 --> 00:33:42,770
suddenly there's like a turn on.

830
00:33:42,770 --> 00:33:45,500
The semiconductor begins
to absorb that light,

831
00:33:45,500 --> 00:33:49,450
and you begin to have this
process occur right here.

832
00:33:49,450 --> 00:33:52,662
You begin to go from
that red light that

833
00:33:52,662 --> 00:33:54,120
went straight
through the material,

834
00:33:54,120 --> 00:33:58,742
to this blue light example here
where we have absorption event.

835
00:33:58,742 --> 00:33:59,822
Yeah?

836
00:33:59,822 --> 00:34:02,280
AUDIENCE: This is probably a
minor question, but where does

837
00:34:02,280 --> 00:34:04,488
the energy go-- that it's
released when your electron

838
00:34:04,488 --> 00:34:06,527
settles back down?

839
00:34:06,527 --> 00:34:08,110
PROFESSOR: We're
going to get to that.

840
00:34:08,110 --> 00:34:09,510
We're taking it step by step.

841
00:34:09,510 --> 00:34:10,909
That's a really good question.

842
00:34:10,909 --> 00:34:13,139
You're one step ahead of me.

843
00:34:13,139 --> 00:34:16,060
We're going to be describing the
actual shape and character up

844
00:34:16,060 --> 00:34:18,210
here, because this
is really equally

845
00:34:18,210 --> 00:34:20,770
important for the functioning
of a solar cell device,

846
00:34:20,770 --> 00:34:22,166
over the next few lectures.

847
00:34:22,166 --> 00:34:23,540
But that gets
really complicated.

848
00:34:23,540 --> 00:34:26,326
So for now, we're going to just
focus on this turn on energy.

849
00:34:26,326 --> 00:34:28,409
And we're going to make
some assumptions from here

850
00:34:28,409 --> 00:34:30,500
on out that the
semiconductor doesn't absorb,

851
00:34:30,500 --> 00:34:35,250
and all of a sudden it absorbs,
and the absorption goes high.

852
00:34:35,250 --> 00:34:37,612
It begins absorbing
all of our light,

853
00:34:37,612 --> 00:34:39,320
for purposes of our
homework assignments.

854
00:34:39,320 --> 00:34:43,730
So again, just to put this
all into one big picture,

855
00:34:43,730 --> 00:34:48,121
so far we have the case out
here where very little light is

856
00:34:48,121 --> 00:34:49,370
absorbed by our semiconductor.

857
00:34:49,370 --> 00:34:52,100
We have the case of glass, light
coming straight through it,

858
00:34:52,100 --> 00:34:53,350
visible light rather.

859
00:34:53,350 --> 00:34:55,219
Because the incident
photon energy

860
00:34:55,219 --> 00:34:57,600
is less than the band gap,
there is insufficient energy

861
00:34:57,600 --> 00:34:59,360
to excite into the
conduction band.

862
00:34:59,360 --> 00:35:03,660
Now as we transition
from a photon energy

863
00:35:03,660 --> 00:35:06,160
less than the band gap to photon
energy larger than the band

864
00:35:06,160 --> 00:35:09,060
gap, we can begin exciting
electrons or charges

865
00:35:09,060 --> 00:35:10,690
across the band
gap, and that's why

866
00:35:10,690 --> 00:35:16,080
we get absorption inside of
our semiconductor materials.

867
00:35:16,080 --> 00:35:17,200
Any questions so far?

868
00:35:20,460 --> 00:35:21,760
OK.

869
00:35:21,760 --> 00:35:22,260
Good.

870
00:35:22,260 --> 00:35:25,120
Everybody's still with me.

871
00:35:25,120 --> 00:35:28,440
We're going to now calculate
the fraction of photons lost,

872
00:35:28,440 --> 00:35:30,200
not absorbed by a
semiconductor material

873
00:35:30,200 --> 00:35:33,230
with a given band gap,
thickness, and reflectivity.

874
00:35:33,230 --> 00:35:36,620
And this gets to Ashley's
question right here.

875
00:35:36,620 --> 00:35:39,480
So again, we ran through a
thickness estimate in class

876
00:35:39,480 --> 00:35:40,540
the last time.

877
00:35:40,540 --> 00:35:42,325
And we assumed for
a semiconductor,

878
00:35:42,325 --> 00:35:44,320
I think it was around
800 nanometers.

879
00:35:44,320 --> 00:35:46,800
For gallium,
arsenide, and silicon.

880
00:35:46,800 --> 00:35:49,510
Or maybe it was a little
less, somewhere around 550.

881
00:35:49,510 --> 00:35:53,090
What was the thickness necessary
to absorb say 90% of the light

882
00:35:53,090 --> 00:35:54,490
at a given wavelength?

883
00:35:54,490 --> 00:35:56,170
And we, in the
back of our minds,

884
00:35:56,170 --> 00:36:00,110
have the solar spectrum
here as a reference point

885
00:36:00,110 --> 00:36:02,860
to begin visualizing
the number of photons

886
00:36:02,860 --> 00:36:06,050
that occur within each of these
delta wavelengths down here.

887
00:36:06,050 --> 00:36:08,420
Essentially what portions of
the spectrum really matter?

888
00:36:08,420 --> 00:36:10,670
Obviously you're not going
to optimize your solar cell

889
00:36:10,670 --> 00:36:13,450
to absorb light way out here,
because there's really not

890
00:36:13,450 --> 00:36:15,340
too much of the solar
spectrum way out there.

891
00:36:15,340 --> 00:36:16,480
You're probably
going to optimize it

892
00:36:16,480 --> 00:36:18,790
somewhere around the peak
of the solar spectrum,

893
00:36:18,790 --> 00:36:20,200
somewhere near there.

894
00:36:20,200 --> 00:36:22,450
So we walked through
that in the last class.

895
00:36:22,450 --> 00:36:25,590
I want to have that in your
ram as we move forward.

896
00:36:25,590 --> 00:36:27,920
We want to calculate
the fraction

897
00:36:27,920 --> 00:36:30,860
of incident solar energy
lost to this thing called

898
00:36:30,860 --> 00:36:33,240
thermalization that Ashley
was mentioning before.

899
00:36:33,240 --> 00:36:36,140
We have, in this simplified
diagram right here,

900
00:36:36,140 --> 00:36:38,750
an electron popping up
to a higher energy level

901
00:36:38,750 --> 00:36:42,967
and then settling down to the
bottom of this conduction band,

902
00:36:42,967 --> 00:36:44,800
we call it, this band
of states that's empty

903
00:36:44,800 --> 00:36:46,410
right here, or largely empty.

904
00:36:46,410 --> 00:36:48,530
And this settling
down to the bottom

905
00:36:48,530 --> 00:36:51,780
of what is this mostly
empty band of states

906
00:36:51,780 --> 00:36:54,450
is a process called
thermalization.

907
00:36:54,450 --> 00:36:57,000
And it occurs,
well, because there

908
00:36:57,000 --> 00:36:59,580
are a series of states the
electron can very easily move

909
00:36:59,580 --> 00:37:02,830
between them by emitting
phonons, or lattice vibrations,

910
00:37:02,830 --> 00:37:03,900
or heat.

911
00:37:03,900 --> 00:37:06,200
And very quickly that
electron will settle down

912
00:37:06,200 --> 00:37:09,030
into what is called or referred
to as the conduction band

913
00:37:09,030 --> 00:37:12,190
minimum, the minimum energy
level within the conduction

914
00:37:12,190 --> 00:37:13,390
band.

915
00:37:13,390 --> 00:37:15,510
And this little arrow
shown in red right

916
00:37:15,510 --> 00:37:19,820
here has a component in the
y-axis, in e space here,

917
00:37:19,820 --> 00:37:21,850
which is a finite energy.

918
00:37:21,850 --> 00:37:23,480
We can quantify that.

919
00:37:23,480 --> 00:37:25,260
That thermalization
loss right there

920
00:37:25,260 --> 00:37:27,620
is the difference
between this energy level

921
00:37:27,620 --> 00:37:30,160
and that energy level
of the electron.

922
00:37:30,160 --> 00:37:34,210
And so that's the
thermalization loss.

923
00:37:34,210 --> 00:37:37,070
That is another type of loss
of a semiconductor crystal.

924
00:37:37,070 --> 00:37:38,590
So we've discussed two so far.

925
00:37:38,590 --> 00:37:40,332
We've discussed
non-absorption of light.

926
00:37:40,332 --> 00:37:42,540
There are certain long
wavelengths, low energy light,

927
00:37:42,540 --> 00:37:43,950
that go straight to our
material and doesn't

928
00:37:43,950 --> 00:37:46,491
get absorbed, because the photon
energy is less than the band

929
00:37:46,491 --> 00:37:47,100
gap.

930
00:37:47,100 --> 00:37:49,180
And the second
major loss mechanism

931
00:37:49,180 --> 00:37:51,960
is when we have too much
energy of the incoming photon,

932
00:37:51,960 --> 00:37:54,340
we have an excitation
of a bound electron

933
00:37:54,340 --> 00:37:56,670
into a very highly
unbound state,

934
00:37:56,670 --> 00:38:00,890
and then a quick loss of that
excess energy due to a process

935
00:38:00,890 --> 00:38:03,490
called thermalization.

936
00:38:03,490 --> 00:38:05,791
Any questions so far?

937
00:38:05,791 --> 00:38:07,739
AUDIENCE: You said that
the thermalization can

938
00:38:07,739 --> 00:38:11,640
result in heat being
released or phonons--

939
00:38:11,640 --> 00:38:12,540
PROFESSOR: Mh-hmm.

940
00:38:12,540 --> 00:38:14,120
Yeah.

941
00:38:14,120 --> 00:38:20,210
So not the prime energy that
we extract from the solar cell

942
00:38:20,210 --> 00:38:22,150
of electricity.

943
00:38:22,150 --> 00:38:24,410
In principle, if you could
develop some clever way

944
00:38:24,410 --> 00:38:26,780
of extracting heat,
perhaps by slapping

945
00:38:26,780 --> 00:38:29,430
on a thermoelectric device in
the back of your solar cell,

946
00:38:29,430 --> 00:38:31,320
then you could extract
that energy as well.

947
00:38:31,320 --> 00:38:33,680
So there's a potential
to recover that heat.

948
00:38:33,680 --> 00:38:37,357
It's not total loss, but from
a mechanical engineering point

949
00:38:37,357 --> 00:38:39,690
of view, if you think about
the thermodynamic efficiency

950
00:38:39,690 --> 00:38:43,400
of a Carnot engine, where
your t high is this,

951
00:38:43,400 --> 00:38:45,320
and your t low is your
ambient temperature,

952
00:38:45,320 --> 00:38:47,511
that delta really
doesn't look that good.

953
00:38:47,511 --> 00:38:48,010
Yeah.

954
00:38:48,010 --> 00:38:48,807
It's really tiny.

955
00:38:48,807 --> 00:38:51,140
So you have to think of a
more clever mechanism, perhaps

956
00:38:51,140 --> 00:38:53,473
through a thermoelectric
device, or some other mechanism

957
00:38:53,473 --> 00:38:56,800
to extract that extra
thermalization loss.

958
00:38:56,800 --> 00:38:59,070
I wanted to-- so
what we're doing

959
00:38:59,070 --> 00:39:01,140
is we're taking the
simplest picture,

960
00:39:01,140 --> 00:39:02,920
and then adding
layers of complexity.

961
00:39:02,920 --> 00:39:05,030
And you'll hear me
stumbling over my language,

962
00:39:05,030 --> 00:39:07,520
as I sanitize it in
my head, to remove

963
00:39:07,520 --> 00:39:11,430
all of the complex techno lingo,
and reduce it to its essence.

964
00:39:11,430 --> 00:39:13,180
And so right now I'm
going to add one more

965
00:39:13,180 --> 00:39:14,720
layer of complexity,
and ultimately

966
00:39:14,720 --> 00:39:18,160
build up to the point where
I can feel conversant again.

967
00:39:18,160 --> 00:39:20,605
We have incoming light,
not exciting the electron

968
00:39:20,605 --> 00:39:22,980
all the way up to there from
the top of the valence band,

969
00:39:22,980 --> 00:39:25,280
but typically somewhere
within the valence band.

970
00:39:25,280 --> 00:39:28,500
Not really at the valence band
maximum or the maximum energy

971
00:39:28,500 --> 00:39:32,150
level within the valence band,
these being the filled states.

972
00:39:32,150 --> 00:39:34,850
So this is a more
realistic representation

973
00:39:34,850 --> 00:39:35,910
of charge excitation.

974
00:39:35,910 --> 00:39:38,680
We have an electron
being excited up.

975
00:39:38,680 --> 00:39:41,400
And this little h plus that's
right here, who did the reading

976
00:39:41,400 --> 00:39:43,840
and know what that
h plus represents?

977
00:39:43,840 --> 00:39:44,900
A hole.

978
00:39:44,900 --> 00:39:46,520
So what is a hole?

979
00:39:46,520 --> 00:39:47,990
It's just what it sounds like.

980
00:39:47,990 --> 00:39:49,879
It's the absence of an electron.

981
00:39:49,879 --> 00:39:51,170
There used to be electron here.

982
00:39:51,170 --> 00:39:51,940
Now it's up there.

983
00:39:51,940 --> 00:39:53,640
It left behind a hole.

984
00:39:53,640 --> 00:39:55,210
An easy way to
think about a hole

985
00:39:55,210 --> 00:39:59,970
is if you're in a big traffic
jam, bumper to bumper,

986
00:39:59,970 --> 00:40:04,510
something bad happened up ahead,
and backed up the traffic.

987
00:40:04,510 --> 00:40:08,520
Now imagine just removing
one car from that highway.

988
00:40:08,520 --> 00:40:10,100
You've created a hole.

989
00:40:10,100 --> 00:40:15,574
So the car that used to be
behind that hole moves forward.

990
00:40:15,574 --> 00:40:17,990
And the car that used to be
behind that one moves forward.

991
00:40:17,990 --> 00:40:20,406
And the car that used to be
behind that one moves forward.

992
00:40:20,406 --> 00:40:21,680
So three cars moved forward.

993
00:40:21,680 --> 00:40:25,420
And the hole moved
backward three places.

994
00:40:25,420 --> 00:40:25,920
Right.

995
00:40:25,920 --> 00:40:28,610
So you can either describe
the dynamics of the system

996
00:40:28,610 --> 00:40:30,870
as n number of
cars moving forward

997
00:40:30,870 --> 00:40:34,780
or one hole moving
backwards n places.

998
00:40:34,780 --> 00:40:38,130
It's much simpler from an
accountability point of view

999
00:40:38,130 --> 00:40:41,070
to be talking about one
quasi particle, a hole,

1000
00:40:41,070 --> 00:40:43,070
rather than talking about
n cars moving forward,

1001
00:40:43,070 --> 00:40:44,260
n electrons moving.

1002
00:40:44,260 --> 00:40:46,760
So when we talk about
this hole right here,

1003
00:40:46,760 --> 00:40:50,790
thermalization is going
to drive this electron

1004
00:40:50,790 --> 00:40:54,210
to the lowest energy level
within the conduction band.

1005
00:40:54,210 --> 00:40:56,690
And it's also going to drive
the electrons above the hole,

1006
00:40:56,690 --> 00:40:58,387
essentially to fall
down into the hole.

1007
00:40:58,387 --> 00:41:00,220
In other words, the
hole is going to move up

1008
00:41:00,220 --> 00:41:02,080
to the top of the valence band.

1009
00:41:02,080 --> 00:41:02,580
Yes.

1010
00:41:02,580 --> 00:41:03,520
Question.

1011
00:41:03,520 --> 00:41:05,478
AUDIENCE: Why isn't the
hole originally created

1012
00:41:05,478 --> 00:41:07,120
at the top of the band?

1013
00:41:07,120 --> 00:41:10,912
PROFESSOR: Well,
it really depends

1014
00:41:10,912 --> 00:41:13,120
on what's called the matrix
element of the absorption

1015
00:41:13,120 --> 00:41:13,659
process.

1016
00:41:13,659 --> 00:41:15,950
In other words, what electrons
have the largest capture

1017
00:41:15,950 --> 00:41:18,104
cross section for
that incident photon.

1018
00:41:18,104 --> 00:41:20,020
And it is a probability
distribution function.

1019
00:41:20,020 --> 00:41:23,980
So you will get some
electrons further down

1020
00:41:23,980 --> 00:41:27,281
from the top of the valence
band absorbing light, as well

1021
00:41:27,281 --> 00:41:28,780
as some of the
electrons right there

1022
00:41:28,780 --> 00:41:31,570
at the tippy top of the
valence band absorbing light.

1023
00:41:31,570 --> 00:41:34,440
So I'm representing, say
for example, a typical case,

1024
00:41:34,440 --> 00:41:36,500
where you have an
electron that's

1025
00:41:36,500 --> 00:41:39,880
not right at the top of the
valence band, and certainly not

1026
00:41:39,880 --> 00:41:42,410
deep in the core level,
but nearish enough

1027
00:41:42,410 --> 00:41:45,830
to the top of the valence band
absorbing that light being

1028
00:41:45,830 --> 00:41:47,380
excited across.

1029
00:41:47,380 --> 00:41:49,930
So in reality,
this is meant to be

1030
00:41:49,930 --> 00:41:52,320
an arbitrary scale here,
but more representative

1031
00:41:52,320 --> 00:41:54,110
of a whole process.

1032
00:41:54,110 --> 00:41:56,970
And to think about this in
a more realistic sense, what

1033
00:41:56,970 --> 00:42:01,514
you would do is you think,
OK, I've this incoming photon,

1034
00:42:01,514 --> 00:42:03,430
and there's a certain
probability distribution

1035
00:42:03,430 --> 00:42:06,710
function that represents the
probability of absorptance

1036
00:42:06,710 --> 00:42:08,650
by different electrons
in my system.

1037
00:42:08,650 --> 00:42:11,380
Which one is going to absorb
the light, let's roll the dice.

1038
00:42:11,380 --> 00:42:12,089
Do a Monte Carlo.

1039
00:42:12,089 --> 00:42:12,588
OK.

1040
00:42:12,588 --> 00:42:13,990
That one absorbed it this time.

1041
00:42:13,990 --> 00:42:15,270
That one got excited up.

1042
00:42:15,270 --> 00:42:15,460
OK.

1043
00:42:15,460 --> 00:42:17,418
Another photon with
identical energy coming in.

1044
00:42:17,418 --> 00:42:18,580
Which electron absorbs it?

1045
00:42:18,580 --> 00:42:20,060
That one.

1046
00:42:20,060 --> 00:42:22,730
So that's the way I would
say it really works.

1047
00:42:22,730 --> 00:42:27,590
This is a simple representation
on the lecture slide.

1048
00:42:27,590 --> 00:42:31,590
So we have the hole going up,
and the electron going down.

1049
00:42:31,590 --> 00:42:34,060
Both particles are relaxing.

1050
00:42:34,060 --> 00:42:34,560
Right.

1051
00:42:34,560 --> 00:42:37,010
So the electron is moving
to its lowest energy state

1052
00:42:37,010 --> 00:42:40,930
and the hole is also moving
to its lowest energy state.

1053
00:42:40,930 --> 00:42:44,160
So if you want to think about
the electron as a bowling ball,

1054
00:42:44,160 --> 00:42:47,140
and the hole as a balloon,
you're welcome to.

1055
00:42:47,140 --> 00:42:51,380
Whatever mechanism helps you
think through this process,

1056
00:42:51,380 --> 00:42:54,520
use that as a crutch right
now as we move forward.

1057
00:42:54,520 --> 00:42:56,080
Always remember
that in the system,

1058
00:42:56,080 --> 00:42:58,120
these are electrons essentially
moving down, and filling up

1059
00:42:58,120 --> 00:42:59,495
that hole, and
the hole is moving

1060
00:42:59,495 --> 00:43:03,040
in the opposite direction, much
like the vacancy in a traffic

1061
00:43:03,040 --> 00:43:05,230
jam.

1062
00:43:05,230 --> 00:43:07,890
So again, thermalization
losses can

1063
00:43:07,890 --> 00:43:10,700
be described by both electrons
and holes in our system,

1064
00:43:10,700 --> 00:43:17,040
by both the rattling around of
an electron in the conduction

1065
00:43:17,040 --> 00:43:19,370
band and the
settling of electrons

1066
00:43:19,370 --> 00:43:20,790
here in the valence
band as well,

1067
00:43:20,790 --> 00:43:23,840
or the rising of that hole
toward the valence band

1068
00:43:23,840 --> 00:43:26,500
maximum and the settling of that
electron toward the conduction

1069
00:43:26,500 --> 00:43:27,940
band minimum.

1070
00:43:27,940 --> 00:43:31,400
So a natural question is,
how fast is this process?

1071
00:43:31,400 --> 00:43:32,260
Can it be reversed?

1072
00:43:32,260 --> 00:43:34,510
If we're losing all this
energy due to thermalization,

1073
00:43:34,510 --> 00:43:38,790
can somehow we halt it and
stop it from happening?

1074
00:43:38,790 --> 00:43:40,820
There are people trying.

1075
00:43:40,820 --> 00:43:42,880
It is a valiant fight.

1076
00:43:42,880 --> 00:43:46,550
This plot right here
represents what's

1077
00:43:46,550 --> 00:43:49,665
called the density of states.

1078
00:43:49,665 --> 00:43:51,790
We're going to get to that
in another lecture here,

1079
00:43:51,790 --> 00:43:56,000
but I'm going to expose you
to the rough concept here.

1080
00:43:56,000 --> 00:43:57,310
Y-axis is energy.

1081
00:43:57,310 --> 00:43:59,820
So again, we have our
valence band maximum

1082
00:43:59,820 --> 00:44:02,050
and our conduction
band minimum up there.

1083
00:44:02,050 --> 00:44:04,600
X-axis here is
representing time.

1084
00:44:04,600 --> 00:44:07,420
So we're going from the
excitation event, which

1085
00:44:07,420 --> 00:44:09,720
occurs right at t equals zero.

1086
00:44:09,720 --> 00:44:13,230
Zero plus represents what this
is on the positive side, moving

1087
00:44:13,230 --> 00:44:15,230
time forward from
the excitation event,

1088
00:44:15,230 --> 00:44:18,090
so instantaneously after
the execution event.

1089
00:44:18,090 --> 00:44:22,350
We had to the equilibrium
population of holes

1090
00:44:22,350 --> 00:44:25,220
and of electrons inside of
our semiconductor system.

1091
00:44:25,220 --> 00:44:27,660
There weren't absolutely
zero electrons

1092
00:44:27,660 --> 00:44:29,366
in the conduction
band, because of heat.

1093
00:44:29,366 --> 00:44:31,240
There was enough thermal
energy in our system

1094
00:44:31,240 --> 00:44:33,210
to excite some of
those electrons across.

1095
00:44:33,210 --> 00:44:36,210
And that's why we had that small
population of electrons there

1096
00:44:36,210 --> 00:44:38,920
and holes down here, the
holes they left behind.

1097
00:44:38,920 --> 00:44:41,700
Now we had a photon coming
in, high energy photon,

1098
00:44:41,700 --> 00:44:45,190
that excited these
electrons down here up there

1099
00:44:45,190 --> 00:44:46,160
into the valence band.

1100
00:44:48,800 --> 00:44:51,770
Up into here, in
the valence band.

1101
00:44:51,770 --> 00:44:55,440
And over time, this
excited population

1102
00:44:55,440 --> 00:44:59,542
will decay down to the
conduction band minimum

1103
00:44:59,542 --> 00:45:01,750
and valence band maximum,
the electrons and the holes

1104
00:45:01,750 --> 00:45:02,880
respectively.

1105
00:45:02,880 --> 00:45:05,540
And over time, when
I say over time,

1106
00:45:05,540 --> 00:45:09,060
I'm referring to something in
the range of one picosecond, 10

1107
00:45:09,060 --> 00:45:11,090
to the minus 12 seconds.

1108
00:45:11,090 --> 00:45:13,540
That's like that, but faster.

1109
00:45:13,540 --> 00:45:16,605
So we have a quick decay of
these photoexcited carriers,

1110
00:45:16,605 --> 00:45:18,250
and so extraction
of that energy is

1111
00:45:18,250 --> 00:45:20,750
going to be nearly impossible,
unless we do something

1112
00:45:20,750 --> 00:45:22,737
very clever with our
crystal to prevent

1113
00:45:22,737 --> 00:45:23,820
that decay from happening.

1114
00:45:23,820 --> 00:45:26,230
Somehow we suppress
the phonons from being

1115
00:45:26,230 --> 00:45:30,070
emitted at that frequency,
at least, or at that energy.

1116
00:45:30,070 --> 00:45:32,260
So there are a lot of
people, clever people,

1117
00:45:32,260 --> 00:45:35,526
working on this problem and
trying to prevent the decay.

1118
00:45:35,526 --> 00:45:36,900
The next challenge,
of course, is

1119
00:45:36,900 --> 00:45:40,570
extracting those so-called hot
carriers, the excited carriers,

1120
00:45:40,570 --> 00:45:42,502
from your device and
keeping that energy when

1121
00:45:42,502 --> 00:45:43,710
they're going into the metal.

1122
00:45:43,710 --> 00:45:45,210
That's a whole
another can of worms.

1123
00:45:45,210 --> 00:45:49,200
So we have the time
scales of thermalization,

1124
00:45:49,200 --> 00:45:52,040
and this is why, at least
from the perspective

1125
00:45:52,040 --> 00:45:54,840
of your homework, we're going to
treat thermalization losses as

1126
00:45:54,840 --> 00:45:55,800
inevitable.

1127
00:45:55,800 --> 00:45:57,740
As Harvard and MIT
students, I would

1128
00:45:57,740 --> 00:46:00,750
urge you to never consider
anything is inevitable.

1129
00:46:00,750 --> 00:46:02,510
If we understand the
physics well enough,

1130
00:46:02,510 --> 00:46:04,550
we can probably
engineer a solution.

1131
00:46:04,550 --> 00:46:09,140
But for now, let's consider this
a reality, a loss mechanism.

1132
00:46:09,140 --> 00:46:11,530
So if we start putting
things together,

1133
00:46:11,530 --> 00:46:15,374
if we put non absorption, which
we talked about last lecture,

1134
00:46:15,374 --> 00:46:16,790
we actually ran
some calculations,

1135
00:46:16,790 --> 00:46:19,110
back of the envelope, and
we calculated the thickness

1136
00:46:19,110 --> 00:46:23,430
necessary to absorb 90% of the
photons at a given wavelength.

1137
00:46:23,430 --> 00:46:25,390
We also know how to
calculate reflectance off

1138
00:46:25,390 --> 00:46:27,470
of a front surface.

1139
00:46:27,470 --> 00:46:29,890
And so we get this
third point right here.

1140
00:46:29,890 --> 00:46:32,050
We actually got it last class.

1141
00:46:32,050 --> 00:46:35,740
And the fourth point right here,
we intuitively understand now

1142
00:46:35,740 --> 00:46:38,680
that if the photon comes in with
more energy than the band gap,

1143
00:46:38,680 --> 00:46:41,950
that excess energy is going to
be lost due to thermalization.

1144
00:46:41,950 --> 00:46:44,000
So now if we have
the solar spectrum,

1145
00:46:44,000 --> 00:46:46,130
and we know the band
gap of a semiconductor,

1146
00:46:46,130 --> 00:46:49,830
we should be able to do a very
cursory plot of the efficiency

1147
00:46:49,830 --> 00:46:54,550
versus band gap, versus energy.

1148
00:46:54,550 --> 00:46:56,580
So again, we have
thermalization losses.

1149
00:46:56,580 --> 00:46:58,150
The band gap is too small.

1150
00:46:58,150 --> 00:47:00,980
And non absorption losses,
if the band gap is too large.

1151
00:47:00,980 --> 00:47:04,640
And let's just do an
absurd thought experiment.

1152
00:47:04,640 --> 00:47:06,460
If we say, OK,
I'm really, really

1153
00:47:06,460 --> 00:47:08,220
scared of thermalization
losses, so I'm

1154
00:47:08,220 --> 00:47:10,679
going to make the biggest band
gap material I possibly can,

1155
00:47:10,679 --> 00:47:12,803
I'm going to have a very
low efficiency in my cell,

1156
00:47:12,803 --> 00:47:14,420
because I'm not
absorbing any light.

1157
00:47:14,420 --> 00:47:17,200
The solar cell will
be transparent.

1158
00:47:17,200 --> 00:47:19,920
If I'm scared of
non-absorption losses,

1159
00:47:19,920 --> 00:47:21,920
I say, OK, I'm going to
make my band gap really,

1160
00:47:21,920 --> 00:47:22,950
really, really tiny.

1161
00:47:22,950 --> 00:47:25,480
I'm going to be losing a
heck of a lot of energy

1162
00:47:25,480 --> 00:47:27,920
due to thermalization,
due to this loss mechanism

1163
00:47:27,920 --> 00:47:28,790
right up here.

1164
00:47:28,790 --> 00:47:30,750
And so there has to
be some happy optimum,

1165
00:47:30,750 --> 00:47:32,360
somewhere between
the two, where we

1166
00:47:32,360 --> 00:47:35,560
have the maximum potential
efficiency of a solar cell

1167
00:47:35,560 --> 00:47:38,680
device, given our
solar spectrum.

1168
00:47:38,680 --> 00:47:41,000
We're going to walk
through that right now.

1169
00:47:41,000 --> 00:47:45,480
So approximating non-absorption
losses, very first step.

1170
00:47:45,480 --> 00:47:49,070
What we're going to do, for
our non-absorption losses,

1171
00:47:49,070 --> 00:47:51,220
is run a very
quick approximation

1172
00:47:51,220 --> 00:47:56,550
that any photon
with photon energy

1173
00:47:56,550 --> 00:48:00,340
corresponding to the band gap
energy is going to be absorbed.

1174
00:48:00,340 --> 00:48:05,396
So if our photon has a larger
energy than the band bap,

1175
00:48:05,396 --> 00:48:06,480
it will be absorbed.

1176
00:48:06,480 --> 00:48:08,380
If it has an energy
less than the band gap,

1177
00:48:08,380 --> 00:48:09,670
it will not be absorbed.

1178
00:48:09,670 --> 00:48:11,878
And that's what this plot
right here is representing.

1179
00:48:11,878 --> 00:48:14,620
We have wavelength right
here, longer wavelength,

1180
00:48:14,620 --> 00:48:15,920
lower energy.

1181
00:48:15,920 --> 00:48:17,750
Smaller wavelength,
larger energy.

1182
00:48:17,750 --> 00:48:19,600
And at some point,
we have the turn

1183
00:48:19,600 --> 00:48:22,720
on of absorption of
our device, because we

1184
00:48:22,720 --> 00:48:26,710
have band gap at that energy.

1185
00:48:26,710 --> 00:48:30,720
And the y-axis here,
I've plotted EQE, which

1186
00:48:30,720 --> 00:48:32,902
is External Quantum Efficiency.

1187
00:48:32,902 --> 00:48:35,110
I've coined the term over
here on the left-hand side.

1188
00:48:35,110 --> 00:48:36,980
It's the efficiency
at which free charge

1189
00:48:36,980 --> 00:48:40,690
carriers are generated by an
incident photon on the device.

1190
00:48:40,690 --> 00:48:42,780
So one way to think
about it is if I

1191
00:48:42,780 --> 00:48:46,140
have a EQE of 100%, that means
that for each photon that I

1192
00:48:46,140 --> 00:48:50,040
throw at my solar cell device,
I'm generating and collecting

1193
00:48:50,040 --> 00:48:52,160
one free carrier
from that device.

1194
00:48:52,160 --> 00:48:56,050
One electron hole pair, if
you will, from that device.

1195
00:48:56,050 --> 00:48:58,160
So that's plotted right here.

1196
00:48:58,160 --> 00:48:59,800
That makes intuitive sense.

1197
00:48:59,800 --> 00:49:01,261
This is an approximation though.

1198
00:49:01,261 --> 00:49:03,260
And I wanted to take it
one step further, again,

1199
00:49:03,260 --> 00:49:04,390
planting the flag right here.

1200
00:49:04,390 --> 00:49:05,230
Because we're going
to come back to this,

1201
00:49:05,230 --> 00:49:06,235
we're going to use this.

1202
00:49:06,235 --> 00:49:08,360
But I wanted to go one
level deeper into the trees,

1203
00:49:08,360 --> 00:49:10,900
for everyone else who wants
some more advanced concepts.

1204
00:49:10,900 --> 00:49:14,260
This is the reality of how
quantum efficiency looks.

1205
00:49:14,260 --> 00:49:17,914
Yes, we have a turn on,
depending on the material

1206
00:49:17,914 --> 00:49:18,580
that's involved.

1207
00:49:18,580 --> 00:49:20,970
We have silicon, gallium
arsenide, copper indium gallium

1208
00:49:20,970 --> 00:49:25,362
diselenide, amorphous silicon,
dye sensitized solar cells,

1209
00:49:25,362 --> 00:49:27,820
organic solar cells, a variety
of different materials right

1210
00:49:27,820 --> 00:49:28,540
here.

1211
00:49:28,540 --> 00:49:31,670
And their different turn
on wavelengths right here.

1212
00:49:31,670 --> 00:49:33,630
So we have wavelengths,
different energies.

1213
00:49:33,630 --> 00:49:36,330
Some turn on at lower energies,
others at higher energies.

1214
00:49:36,330 --> 00:49:39,080
So this represents, more
or less, the band gap

1215
00:49:39,080 --> 00:49:40,790
turn on energy, more or less.

1216
00:49:40,790 --> 00:49:42,498
It also has to do with
the thickness, how

1217
00:49:42,498 --> 00:49:43,700
it absorbs light.

1218
00:49:43,700 --> 00:49:46,050
At the shorter
wavelengths though,

1219
00:49:46,050 --> 00:49:48,050
instead of just
having a QE of one,

1220
00:49:48,050 --> 00:49:50,930
going all the way out
to x-ray territory,

1221
00:49:50,930 --> 00:49:54,070
we have a turn
off at some point.

1222
00:49:54,070 --> 00:49:54,780
Why is that?

1223
00:49:58,330 --> 00:50:02,320
Why in a real device
would we-- Yeah.

1224
00:50:02,320 --> 00:50:04,260
We have glass absorbing,
on the front side,

1225
00:50:04,260 --> 00:50:06,130
that's one real big reason.

1226
00:50:06,130 --> 00:50:07,730
Do we have another idea?

1227
00:50:11,710 --> 00:50:12,210
Yep.

1228
00:50:12,210 --> 00:50:15,230
Glass absorption is
one real big one.

1229
00:50:15,230 --> 00:50:17,650
There are other dead layers
inside of a solar cell device

1230
00:50:17,650 --> 00:50:19,560
in the near surface
region that also absorb

1231
00:50:19,560 --> 00:50:22,370
the light in some architecture.

1232
00:50:22,370 --> 00:50:26,990
So it's not a perfect QE
spectrum that looks like that.

1233
00:50:26,990 --> 00:50:29,080
But why don't we care?

1234
00:50:29,080 --> 00:50:31,930
For the purposes of just
engineering approximation,

1235
00:50:31,930 --> 00:50:34,470
why aren't we bothered
by these photons

1236
00:50:34,470 --> 00:50:35,679
that we're losing down there?

1237
00:50:35,679 --> 00:50:38,136
AUDIENCE: Because the percentage
of the solar spectrum that

1238
00:50:38,136 --> 00:50:39,524
falls in that region is small.

1239
00:50:39,524 --> 00:50:40,440
PROFESSOR: Absolutely.

1240
00:50:40,440 --> 00:50:42,720
So what we're doing is an
engineering approximation

1241
00:50:42,720 --> 00:50:46,870
right here to get to a very
first cursory efficiency

1242
00:50:46,870 --> 00:50:50,630
calculation, neglecting
things at the extremes.

1243
00:50:50,630 --> 00:50:53,040
Two short wavelengths,
because there's just not

1244
00:50:53,040 --> 00:50:54,920
a whole lot of solar
flux down there.

1245
00:50:54,920 --> 00:50:56,880
And too long wavelengths,
because again,

1246
00:50:56,880 --> 00:50:58,880
not a whole lot of
solar flux right there.

1247
00:50:58,880 --> 00:51:06,010
So we're going to be using this
approximation in our homeworks

1248
00:51:06,010 --> 00:51:09,660
and that will get
us somewhat close.

1249
00:51:09,660 --> 00:51:14,210
If we really want it to be
true, instead of using a box

1250
00:51:14,210 --> 00:51:16,720
function like this, an
absorption box function,

1251
00:51:16,720 --> 00:51:19,200
we would use an
absorption spectrum that

1252
00:51:19,200 --> 00:51:24,000
looks something more like that.

1253
00:51:24,000 --> 00:51:27,180
We've used a two
absorption spectrum.

1254
00:51:27,180 --> 00:51:29,650
And then convolute that with
the thickness of the device

1255
00:51:29,650 --> 00:51:34,200
to calculate what fraction
of photons at each energy

1256
00:51:34,200 --> 00:51:36,430
is absorbed inside of my device.

1257
00:51:36,430 --> 00:51:38,629
And that would give
you a plot that

1258
00:51:38,629 --> 00:51:39,920
looks something more like this.

1259
00:51:39,920 --> 00:51:42,350
Instead of this
box plot up here,

1260
00:51:42,350 --> 00:51:45,550
it might give you plot that
looks something more like this.

1261
00:51:45,550 --> 00:51:48,790
So you'd have instead
of just a sharp turn on,

1262
00:51:48,790 --> 00:51:50,960
if you had a one micron
thick silicon wafer,

1263
00:51:50,960 --> 00:51:52,460
and we calculated
last class that we

1264
00:51:52,460 --> 00:51:54,418
need somewhere around 10
microns or 100 microns

1265
00:51:54,418 --> 00:51:56,170
to absorb light
well, if we reduce

1266
00:51:56,170 --> 00:51:58,140
the thickness of the
wafer to 1/10 or 1/100

1267
00:51:58,140 --> 00:51:59,910
of what's necessary
to absorb light well,

1268
00:51:59,910 --> 00:52:02,580
we don't see that sharp
turn on at the band gap.

1269
00:52:02,580 --> 00:52:05,067
We see rather a gradual
turn on of our silicon

1270
00:52:05,067 --> 00:52:07,150
as we move to shorter and
shorter wavelengths that

1271
00:52:07,150 --> 00:52:11,240
are absorbed more and more
efficiently by the device.

1272
00:52:11,240 --> 00:52:13,870
So again, just wrapping our
head around the basic concept

1273
00:52:13,870 --> 00:52:16,520
that we're going to use for the
purposes of our calculation,

1274
00:52:16,520 --> 00:52:18,980
but, again, some of the
more fine structure,

1275
00:52:18,980 --> 00:52:21,290
some of the more advanced
concepts that come into

1276
00:52:21,290 --> 00:52:24,790
play when we're doing more
detailed calculations.

1277
00:52:24,790 --> 00:52:27,370
Approximating
thermalization losses now.

1278
00:52:27,370 --> 00:52:29,480
We want to calculate
the amount of energy

1279
00:52:29,480 --> 00:52:32,650
lost of incident sunlight
lost due to thermalization,

1280
00:52:32,650 --> 00:52:33,624
due to heat.

1281
00:52:33,624 --> 00:52:36,290
And we're going to say here that
if the photon energy is greater

1282
00:52:36,290 --> 00:52:37,970
than the band gap,
than the photon

1283
00:52:37,970 --> 00:52:41,239
energy is approximately the
band gap plus thermalization.

1284
00:52:41,239 --> 00:52:43,280
Another way to put it
would be the thermalization

1285
00:52:43,280 --> 00:52:44,696
is approximately
the photon energy

1286
00:52:44,696 --> 00:52:47,357
minus the band gap energy.

1287
00:52:47,357 --> 00:52:49,190
I kind of wanted to
hide all this down here.

1288
00:52:49,190 --> 00:52:50,472
Forget this exists right now.

1289
00:52:50,472 --> 00:52:51,680
Let's focus on that top part.

1290
00:52:51,680 --> 00:52:54,184
So that's the easy way
of thinking about it.

1291
00:52:54,184 --> 00:52:55,725
We're going to be
thinking about this

1292
00:52:55,725 --> 00:52:58,360
in terms of just
any photon coming

1293
00:52:58,360 --> 00:52:59,950
into our device
with a larger energy

1294
00:52:59,950 --> 00:53:02,800
than the band gap is going to
generate one electron hole pair

1295
00:53:02,800 --> 00:53:06,850
and lose some energy
due to thermalization.

1296
00:53:06,850 --> 00:53:10,371
The reality is that for
very high energy photons,

1297
00:53:10,371 --> 00:53:12,870
say for example photons with
three times the band gap energy

1298
00:53:12,870 --> 00:53:16,180
or more, you could have
electron-electron interactions.

1299
00:53:16,180 --> 00:53:19,074
So if you excite one electron
to very highly excited state,

1300
00:53:19,074 --> 00:53:20,990
it can bounce around and
in the process excite

1301
00:53:20,990 --> 00:53:23,500
another electron
across the band gap.

1302
00:53:23,500 --> 00:53:26,900
That's the case when x-rays are
incident on a piece of silicon.

1303
00:53:26,900 --> 00:53:30,300
For instance, if you have
a 10 kilo-electron volt,

1304
00:53:30,300 --> 00:53:34,020
so a 10,000 eV x-ray incident
on a piece of silicon,

1305
00:53:34,020 --> 00:53:36,880
you will generate approximately
3,000 electron hole pairs

1306
00:53:36,880 --> 00:53:38,196
with that one x-ray.

1307
00:53:38,196 --> 00:53:40,320
Because that one x-ray is
going to take an electron

1308
00:53:40,320 --> 00:53:42,400
and excite it to very
highly excited state,

1309
00:53:42,400 --> 00:53:45,130
and that's going to
excite further electrons

1310
00:53:45,130 --> 00:53:49,300
across the band gap as that
excited carrier decays,

1311
00:53:49,300 --> 00:53:53,370
as it loses it's energy and
settles at the conduction band

1312
00:53:53,370 --> 00:53:54,580
minimum.

1313
00:53:54,580 --> 00:53:59,499
So we have what's called
multiple exciton generation.

1314
00:53:59,499 --> 00:54:01,540
Sometimes we've heard it
as multiple free carrier

1315
00:54:01,540 --> 00:54:02,450
generation.

1316
00:54:02,450 --> 00:54:04,260
In semiconductors,
it's a hot topic,

1317
00:54:04,260 --> 00:54:06,600
because folks would like to
take the ultraviolet portion

1318
00:54:06,600 --> 00:54:09,650
of the spectrum, the high
energy, short wavelength,

1319
00:54:09,650 --> 00:54:11,760
portion of the solar
spectrum, and use

1320
00:54:11,760 --> 00:54:13,580
it to excite multiple carriers.

1321
00:54:13,580 --> 00:54:16,940
One photon exciting multiple
carriers across the band gap.

1322
00:54:16,940 --> 00:54:19,099
And so there's some
work, or was some work,

1323
00:54:19,099 --> 00:54:20,390
it was a hot topic for a while.

1324
00:54:20,390 --> 00:54:21,515
It's kind of decayed a bit.

1325
00:54:21,515 --> 00:54:22,450
It comes in waves.

1326
00:54:22,450 --> 00:54:24,690
It cycles, kind of
like a plane wave.

1327
00:54:24,690 --> 00:54:27,730
There is an interest, a
general interest in the field,

1328
00:54:27,730 --> 00:54:29,890
of how do you capture
these higher energy photons

1329
00:54:29,890 --> 00:54:31,429
and convert them
in some usable way,

1330
00:54:31,429 --> 00:54:33,220
instead of just having
thermalization loss,

1331
00:54:33,220 --> 00:54:35,360
instead of just having heat.

1332
00:54:35,360 --> 00:54:37,030
And then for really
high energy photons,

1333
00:54:37,030 --> 00:54:39,530
gosh, you can really get
into some neat physics.

1334
00:54:39,530 --> 00:54:42,730
I've given you a link
and cross section here.

1335
00:54:42,730 --> 00:54:46,510
This is the electron
cross section, or actually

1336
00:54:46,510 --> 00:54:50,280
really what it is is an
anatomic cross section,

1337
00:54:50,280 --> 00:54:53,020
because of the electrons in
the material versus photon

1338
00:54:53,020 --> 00:54:57,140
energy going through 10
eV out to 10 to eV 11.

1339
00:54:57,140 --> 00:54:59,080
A very high photon energy.

1340
00:54:59,080 --> 00:55:05,520
We're transiting from the
visible spectrum over here

1341
00:55:05,520 --> 00:55:07,890
deep into the infrared, and
then going into the x-ray,

1342
00:55:07,890 --> 00:55:09,390
and finally to the
gamma ray regime.

1343
00:55:09,390 --> 00:55:11,598
There you can have a number
of interesting phenomena.

1344
00:55:11,598 --> 00:55:14,370
You can even have an electron
hole, or electron-positron pair

1345
00:55:14,370 --> 00:55:18,180
generation with
gigaelectron-volt incident

1346
00:55:18,180 --> 00:55:18,977
radiation or above.

1347
00:55:18,977 --> 00:55:20,810
We're not gonna even
talk about this regime,

1348
00:55:20,810 --> 00:55:25,060
because the total amount of
solar flux in that regime

1349
00:55:25,060 --> 00:55:27,285
is really tiny
compared to visible.

1350
00:55:27,285 --> 00:55:29,410
But it's a lot of interesting,
fascinating physics.

1351
00:55:29,410 --> 00:55:32,890
So I put it on here anyway
just to keep our approximation

1352
00:55:32,890 --> 00:55:34,410
in focus.

1353
00:55:34,410 --> 00:55:38,120
So again, I'm kind of mixing
the forest in the trees

1354
00:55:38,120 --> 00:55:40,320
here to give you a
sense of the complexity.

1355
00:55:40,320 --> 00:55:42,860
But also to give you the
tools necessary to do

1356
00:55:42,860 --> 00:55:44,240
simple calculations.

1357
00:55:44,240 --> 00:55:48,250
We're going to combine this
simple approximation right here

1358
00:55:48,250 --> 00:55:50,010
of the non-absorption losses.

1359
00:55:50,010 --> 00:55:52,992
We're going to say that
any photon with energy

1360
00:55:52,992 --> 00:55:55,450
less than the band gap doesn't
get absorbed by our crystal.

1361
00:55:55,450 --> 00:55:57,552
It's gone to us.

1362
00:55:57,552 --> 00:55:59,260
And we're going to
make the approximation

1363
00:55:59,260 --> 00:56:01,770
that any photon with
energy above the band gap

1364
00:56:01,770 --> 00:56:05,510
will have that excess energy
loss due to thermalization.

1365
00:56:05,510 --> 00:56:07,180
And we put those
two things together.

1366
00:56:07,180 --> 00:56:10,460
And one very convenient
way of representing this

1367
00:56:10,460 --> 00:56:12,260
is shown in a paper in 1980.

1368
00:56:12,260 --> 00:56:13,710
Let me walk you through it.

1369
00:56:13,710 --> 00:56:17,860
So this curve right here,
this outermost curve,

1370
00:56:17,860 --> 00:56:22,020
represents the solar
spectrum, energy versus number

1371
00:56:22,020 --> 00:56:23,110
of photons.

1372
00:56:23,110 --> 00:56:28,230
So we have essentially
a photon density.

1373
00:56:28,230 --> 00:56:32,030
This is number of photons per
centimeter squared, per second.

1374
00:56:32,030 --> 00:56:35,350
So photon flux, if you will.

1375
00:56:35,350 --> 00:56:39,530
And over here we have the
energy of those photons.

1376
00:56:39,530 --> 00:56:41,820
And so what this is
meant to represent

1377
00:56:41,820 --> 00:56:43,760
is the cumulative
solar spectrum,

1378
00:56:43,760 --> 00:56:46,037
going from a high
energy here all the way

1379
00:56:46,037 --> 00:56:47,120
down to the lowest energy.

1380
00:56:47,120 --> 00:56:51,380
So we're essentially adding
the different components,

1381
00:56:51,380 --> 00:56:52,940
cumulation plot.

1382
00:56:52,940 --> 00:56:58,500
And if we have a photon energy
in excess of the band gap

1383
00:56:58,500 --> 00:57:01,270
energy, as would be the case,
say, for example three eV

1384
00:57:01,270 --> 00:57:06,830
photon, and let's say the band
gap is 1.35 eV, represented

1385
00:57:06,830 --> 00:57:08,660
by this straight
line right here,

1386
00:57:08,660 --> 00:57:11,146
this energy is going to be lost.

1387
00:57:11,146 --> 00:57:12,770
And so by drawing
this cumulation plot,

1388
00:57:12,770 --> 00:57:17,750
we're plotting the area here,
the energy area that is lost

1389
00:57:17,750 --> 00:57:20,710
to us due to thermalization.

1390
00:57:20,710 --> 00:57:24,390
We could also say that if
the photons have an energy

1391
00:57:24,390 --> 00:57:29,510
less than the band gap, that is
going to be lost to us as well.

1392
00:57:29,510 --> 00:57:32,750
And what we're left with is
a little box that represents

1393
00:57:32,750 --> 00:57:34,810
the total usable
photons, the usable

1394
00:57:34,810 --> 00:57:39,160
photons that we
can extract device.

1395
00:57:39,160 --> 00:57:41,120
This particular
plot is a little bit

1396
00:57:41,120 --> 00:57:43,970
complicated, because
it contains two curves.

1397
00:57:43,970 --> 00:57:45,640
One is this one right here.

1398
00:57:45,640 --> 00:57:47,930
The other one is
this one right here.

1399
00:57:47,930 --> 00:57:53,100
This second curve represents
another realistic loss

1400
00:57:53,100 --> 00:57:55,390
mechanism that we
didn't talk about yet.

1401
00:57:55,390 --> 00:58:00,560
And that is why the extractable
work, represented as w,

1402
00:58:00,560 --> 00:58:02,399
is going to be less
than the band gap energy

1403
00:58:02,399 --> 00:58:03,440
of our solar cell device.

1404
00:58:03,440 --> 00:58:07,650
So if the band gap is 1.35
eV, the total usable work

1405
00:58:07,650 --> 00:58:11,350
would be 0.9 eV, we'll get
to that in a lecture or two.

1406
00:58:11,350 --> 00:58:13,170
And that's why
the white box here

1407
00:58:13,170 --> 00:58:18,950
is going to be smaller than this
horizontal line box over there.

1408
00:58:18,950 --> 00:58:24,240
But it gives you a very first
approximation, a very easy way

1409
00:58:24,240 --> 00:58:28,020
to describe the different losses
that can occur in a solar cell,

1410
00:58:28,020 --> 00:58:31,990
and quickly visualize
them here, thermalization.

1411
00:58:31,990 --> 00:58:34,030
Over here, non-absorption.

1412
00:58:34,030 --> 00:58:38,990
And plot them out very
nicely as the total area

1413
00:58:38,990 --> 00:58:40,580
and representative
area fractions.

1414
00:58:40,580 --> 00:58:42,080
And that's why you
can see here that

1415
00:58:42,080 --> 00:58:46,970
the total usable
solar energy is going

1416
00:58:46,970 --> 00:58:50,110
to be somewhere around 30%.

1417
00:58:50,110 --> 00:58:52,860
This band gap right
here, around 1.35 eV

1418
00:58:52,860 --> 00:58:56,050
is actually pretty near
optimal for the solar spectrum.

1419
00:58:56,050 --> 00:58:59,800
You can imagine if we
increase the band gap energy,

1420
00:58:59,800 --> 00:59:01,930
we would be doing
something like this.

1421
00:59:01,930 --> 00:59:04,400
So we would draw another
box right around here.

1422
00:59:04,400 --> 00:59:07,230
This would be the new
band gap, instead of 1.35,

1423
00:59:07,230 --> 00:59:08,760
that would be out here.

1424
00:59:08,760 --> 00:59:10,260
If we increase the
band gap further,

1425
00:59:10,260 --> 00:59:12,400
we might have something
that looks like that.

1426
00:59:12,400 --> 00:59:13,990
And the area of this
little rectangle

1427
00:59:13,990 --> 00:59:17,441
would be much smaller than
the area of this rectangle.

1428
00:59:17,441 --> 00:59:19,940
Likewise, if we said, OK, we're
going to shrink our band gap

1429
00:59:19,940 --> 00:59:25,062
energy to avoid
non-absorption loss,

1430
00:59:25,062 --> 00:59:27,270
we're going to have an excess
of thermalization loss.

1431
00:59:27,270 --> 00:59:30,280
We'll have a very narrow
rectangle, right, like this,

1432
00:59:30,280 --> 00:59:32,522
and all of this would be loss.

1433
00:59:32,522 --> 00:59:34,480
The solar spectrum,
obviously, does not change.

1434
00:59:34,480 --> 00:59:39,680
This line right here this
is fixed, it's constant.

1435
00:59:39,680 --> 00:59:41,380
You folks kind of see it?

1436
00:59:41,380 --> 00:59:42,470
Beginning to grasp it?

1437
00:59:42,470 --> 00:59:46,860
This is a convenient way of
representing the total usable

1438
00:59:46,860 --> 00:59:50,560
portion of the solar spectrum
from a given semiconductor

1439
00:59:50,560 --> 00:59:52,520
material.

1440
00:59:52,520 --> 00:59:55,261
You can begin seeing the trade
offs between different material

1441
00:59:55,261 --> 00:59:55,760
systems.

1442
00:59:55,760 --> 00:59:57,843
You can say, what happens
if I change my band gap?

1443
00:59:57,843 --> 01:00:00,050
How would that change
the fraction of photons,

1444
01:00:00,050 --> 01:00:02,510
or fraction of photon
energy not absorbed?

1445
01:00:02,510 --> 01:00:05,920
Or fraction of photon energy
lost due to thermalization.

1446
01:00:05,920 --> 01:00:07,640
And you can also
see what happens

1447
01:00:07,640 --> 01:00:09,660
if you-- what would
be an easy way

1448
01:00:09,660 --> 01:00:12,390
to extract more
potential for the sun?

1449
01:00:12,390 --> 01:00:16,440
Instead of just using one
semiconductor material, you?

1450
01:00:16,440 --> 01:00:17,072
More than one.

1451
01:00:17,072 --> 01:00:17,655
More than one.

1452
01:00:17,655 --> 01:00:17,710
Right.

1453
01:00:17,710 --> 01:00:19,876
So now you're drawing
different boxes that represent

1454
01:00:19,876 --> 01:00:20,912
the different materials.

1455
01:00:20,912 --> 01:00:22,370
And if you stack
them right, you're

1456
01:00:22,370 --> 01:00:25,730
able to capture more of
this total area, more

1457
01:00:25,730 --> 01:00:29,310
of the total solar spectrum.

1458
01:00:29,310 --> 01:00:32,220
So this is a really cool plot.

1459
01:00:32,220 --> 01:00:35,927
A lot of good work back
in the 1970s, 1980s.

1460
01:00:35,927 --> 01:00:37,510
If you recall from
lecture number one,

1461
01:00:37,510 --> 01:00:41,500
this was the first wave of
real hardcore solar science,

1462
01:00:41,500 --> 01:00:43,620
after the initial
Bell Labs invention.

1463
01:00:43,620 --> 01:00:47,505
When we had the OPEC oil crises,
and there was a large rush

1464
01:00:47,505 --> 01:00:49,150
of funding into solar research.

1465
01:00:49,150 --> 01:00:51,525
So you had a lot of good work
coming out from those days.

1466
01:00:54,900 --> 01:00:56,730
This next plot that
I'm going to show you

1467
01:00:56,730 --> 01:01:04,650
represents the area of this box
relative to the solar spectrum,

1468
01:01:04,650 --> 01:01:08,270
the percentage of
light that is usable,

1469
01:01:08,270 --> 01:01:10,330
the balance between
non-absorption thermalization

1470
01:01:10,330 --> 01:01:12,146
losses as a function
of band gap energy.

1471
01:01:12,146 --> 01:01:14,020
So if the band gap is
too small, again, we're

1472
01:01:14,020 --> 01:01:15,420
losing a lot of energy
due to thermalization.

1473
01:01:15,420 --> 01:01:17,500
If the band gap's too
large, a lot of energy

1474
01:01:17,500 --> 01:01:19,350
we're losing to non-absorption.

1475
01:01:19,350 --> 01:01:22,010
And somewhere in the
middle is our happy medium.

1476
01:01:22,010 --> 01:01:24,550
These little symbols here
represent different materials.

1477
01:01:24,550 --> 01:01:26,008
Cadmium sulfide,
cadmium telluride,

1478
01:01:26,008 --> 01:01:28,330
gallium arsenide, indium
phosphide, silicon, germanium,

1479
01:01:28,330 --> 01:01:31,870
and so forth, and
calculated efficiencies.

1480
01:01:31,870 --> 01:01:34,140
So I'm going to go into
one advanced concept,

1481
01:01:34,140 --> 01:01:36,300
the multi-junction devices.

1482
01:01:36,300 --> 01:01:39,150
And we just talked
about this box here

1483
01:01:39,150 --> 01:01:43,100
representing the usable energy
from the solar spectrum.

1484
01:01:43,100 --> 01:01:47,160
Now if we go to an absurd
case of 36 band gaps.

1485
01:01:47,160 --> 01:01:51,170
If we imagine 36 materials
with graded band gaps,

1486
01:01:51,170 --> 01:01:53,890
starting from large band
gap at the top to small band

1487
01:01:53,890 --> 01:01:57,030
gap at the back, you
can envision almost

1488
01:01:57,030 --> 01:01:58,950
approximating the entire curve.

1489
01:01:58,950 --> 01:02:02,290
And you can estimate
what the upper efficiency

1490
01:02:02,290 --> 01:02:05,110
limit would be with many band
gaps inside of your material.

1491
01:02:05,110 --> 01:02:08,960
So for one band gap,
somewhere around 37,

1492
01:02:08,960 --> 01:02:10,930
we'll have an entire
lecture dedicated

1493
01:02:10,930 --> 01:02:12,850
to calculating that number.

1494
01:02:12,850 --> 01:02:14,460
For two band gaps
somewhere around 50.

1495
01:02:14,460 --> 01:02:16,330
For three band gaps, 56.

1496
01:02:16,330 --> 01:02:19,450
For 36 band gaps around 72.

1497
01:02:19,450 --> 01:02:22,500
So you can begin seeing how
the efficiency of solar energy

1498
01:02:22,500 --> 01:02:26,210
conversion changes as you
change or add materials,

1499
01:02:26,210 --> 01:02:28,130
you move materials
to your system.

1500
01:02:28,130 --> 01:02:31,300
So how do you practically
do that in a real device?

1501
01:02:31,300 --> 01:02:34,114
Well one method is to put one
material on top of another,

1502
01:02:34,114 --> 01:02:35,780
much like it's
demonstrated right there.

1503
01:02:35,780 --> 01:02:37,850
You have E versus x.

1504
01:02:37,850 --> 01:02:41,320
So I have my E versus x, and
I have multiple materials.

1505
01:02:41,320 --> 01:02:45,610
Another way to do it would be
to use optics to split our light

1506
01:02:45,610 --> 01:02:46,530
into different colors.

1507
01:02:46,530 --> 01:02:50,990
So if we have polychromatic
or multi-colored light coming

1508
01:02:50,990 --> 01:02:53,020
into our system, we
somehow have a set

1509
01:02:53,020 --> 01:02:56,172
of optics put up that
reflect one color, or one

1510
01:02:56,172 --> 01:02:57,880
band of the solar
spectrum, while letting

1511
01:02:57,880 --> 01:03:00,550
the other portion of the
solar spectrum through it.

1512
01:03:00,550 --> 01:03:03,490
And we have different solar
cells with different band gaps,

1513
01:03:03,490 --> 01:03:06,070
each matched to
the incident light.

1514
01:03:06,070 --> 01:03:09,190
Each matched to the
particular color of light.

1515
01:03:09,190 --> 01:03:13,370
Notice this paper, 1982,
this concept was out.

1516
01:03:13,370 --> 01:03:16,320
So again, during that first
wave of real photovoltaics

1517
01:03:16,320 --> 01:03:20,920
innovation in the late
1970s and early 1980s.

1518
01:03:20,920 --> 01:03:23,750
And this was coming right
out of Lincoln Laboratory.

1519
01:03:23,750 --> 01:03:26,990
This is about 35
minutes north of here.

1520
01:03:26,990 --> 01:03:32,280
And this group at the time, the
group number continues to exist

1521
01:03:32,280 --> 01:03:33,854
and is in operation
at Lincoln Labs.

1522
01:03:33,854 --> 01:03:35,770
So most of the people
have moved on obviously,

1523
01:03:35,770 --> 01:03:40,000
but several of the ideas
continue to this day.

1524
01:03:40,000 --> 01:03:41,550
There was a more
recent incarnation

1525
01:03:41,550 --> 01:03:45,390
in 2009 of a spectral splitter,
a very similar concept

1526
01:03:45,390 --> 01:03:47,270
as you can see,
optics to concentrate

1527
01:03:47,270 --> 01:03:50,400
the light, a dichroic
mirror, meaning

1528
01:03:50,400 --> 01:03:51,900
it reflects certain
wavelengths, let

1529
01:03:51,900 --> 01:03:53,750
another portion of
the spectrum past,

1530
01:03:53,750 --> 01:03:58,140
and solar cell devices down
below absorbing efficiently

1531
01:03:58,140 --> 01:04:00,700
in that region of the spectrum
and avoiding thermalization

1532
01:04:00,700 --> 01:04:04,030
losses, and avoiding
non-absorption losses.

1533
01:04:04,030 --> 01:04:07,380
This was a $50 million
DARPA project, in fact,

1534
01:04:07,380 --> 01:04:11,070
involving University of Delaware
and several other companies.

1535
01:04:11,070 --> 01:04:13,960
And they published
the results in 2009.

1536
01:04:13,960 --> 01:04:16,520
It was one of their wrap
up papers that described

1537
01:04:16,520 --> 01:04:18,090
the results of the project.

1538
01:04:18,090 --> 01:04:19,900
So concepts.

1539
01:04:19,900 --> 01:04:24,360
To this day, this
spectral splitter it's not

1540
01:04:24,360 --> 01:04:26,094
in commercial production.

1541
01:04:26,094 --> 01:04:28,760
What is in commercial production
are the multi-junction devices,

1542
01:04:28,760 --> 01:04:31,140
where you stack one
on top of another.

1543
01:04:31,140 --> 01:04:34,230
And we'll actually be having the
benefit of using some of them

1544
01:04:34,230 --> 01:04:35,210
in class.

1545
01:04:35,210 --> 01:04:38,490
Boeing spectral lab was kind
enough to donate a set of them

1546
01:04:38,490 --> 01:04:40,030
for our class purposes.

1547
01:04:40,030 --> 01:04:42,440
Yes, question.

1548
01:04:42,440 --> 01:04:44,274
AUDIENCE: This is
also basically what

1549
01:04:44,274 --> 01:04:48,170
plants do by having
multiple different pigment

1550
01:04:48,170 --> 01:04:51,092
molecules in leaves, right?

1551
01:04:51,092 --> 01:04:53,835
That would absorb the
different wavelengths?

1552
01:04:53,835 --> 01:04:56,240
PROFESSOR: Well, it's not
exactly separating light

1553
01:04:56,240 --> 01:04:57,560
by optics in that case.

1554
01:04:57,560 --> 01:04:58,490
So the question was--

1555
01:04:58,490 --> 01:04:59,990
AUDIENCE: No, I
mean multi-junction.

1556
01:04:59,990 --> 01:05:01,720
PROFESSOR: Oh, the
multi-junction idea.

1557
01:05:01,720 --> 01:05:05,190
Yes, if you consider
that there is a reaction

1558
01:05:05,190 --> 01:05:07,180
process occurring in series.

1559
01:05:07,180 --> 01:05:09,560
The important
distinguishing feature

1560
01:05:09,560 --> 01:05:12,360
of the multi-junction device
is that the same current

1561
01:05:12,360 --> 01:05:14,220
is flowing through
the entire device.

1562
01:05:14,220 --> 01:05:17,550
So each sub cell has to be
current matched to the others,

1563
01:05:17,550 --> 01:05:19,140
because the cumulative
current output

1564
01:05:19,140 --> 01:05:21,700
is a harmonic mean of each one.

1565
01:05:21,700 --> 01:05:25,850
So in other words, you're
limited by the worst resistor

1566
01:05:25,850 --> 01:05:27,920
in series, if you will.

1567
01:05:27,920 --> 01:05:30,172
So it's very tricky
to engineer properly

1568
01:05:30,172 --> 01:05:31,380
these multi-junction devices.

1569
01:05:31,380 --> 01:05:33,921
You have to be thinking about
the current output for each sub

1570
01:05:33,921 --> 01:05:35,499
cell and match the currents.

1571
01:05:35,499 --> 01:05:37,540
That means you match the
geometry, the thickness,

1572
01:05:37,540 --> 01:05:40,720
but also the resistivity
of each layer and so forth.

1573
01:05:40,720 --> 01:05:44,120
So similar to a
plant, but not quite.

1574
01:05:44,120 --> 01:05:46,460
There are some special
characteristics

1575
01:05:46,460 --> 01:05:49,250
of the inorganic system.

1576
01:05:49,250 --> 01:05:52,040
So we have a small
demonstration.

1577
01:05:52,040 --> 01:05:54,830
I'd like to welcome Joe
up to the front as well.

1578
01:05:54,830 --> 01:05:57,080
We have a small demonstration
of a few of the concepts

1579
01:05:57,080 --> 01:05:58,870
that we've covered
today in class.

1580
01:05:58,870 --> 01:06:01,710
We're going to be exciting
silicon with light,

1581
01:06:01,710 --> 01:06:04,920
and we're going to be monitoring
the current output using

1582
01:06:04,920 --> 01:06:09,320
this little resistance
measurement device right here.

1583
01:06:09,320 --> 01:06:11,560
So actually I think it's
set to a current readout.

1584
01:06:11,560 --> 01:06:12,434
Yes, current readout.

1585
01:06:12,434 --> 01:06:16,040
So it's in microamps right now,
probably going to milliamps.

1586
01:06:16,040 --> 01:06:16,760
Is that right?

1587
01:06:16,760 --> 01:06:18,470
OK, so milliamp current readout.

1588
01:06:18,470 --> 01:06:20,960
Let me explain to you
what we have right here.

1589
01:06:20,960 --> 01:06:25,530
We have a bare piece of
silicon, and two electric leads

1590
01:06:25,530 --> 01:06:26,370
on either side.

1591
01:06:26,370 --> 01:06:29,160
So a bare piece of
silicon, no device.

1592
01:06:29,160 --> 01:06:31,340
Just a piece of silicon.

1593
01:06:31,340 --> 01:06:33,810
And we have electrical leads
coming out of either side.

1594
01:06:33,810 --> 01:06:36,130
We have a very low resistance
contact on either end.

1595
01:06:36,130 --> 01:06:37,546
For those who are
curious, we used

1596
01:06:37,546 --> 01:06:39,880
a mixture of indium and
gallium, soldering iron,

1597
01:06:39,880 --> 01:06:42,690
scratch the surface, penetrated
the native surface oxide,

1598
01:06:42,690 --> 01:06:44,920
and put the electrical
leads on either side.

1599
01:06:44,920 --> 01:06:48,050
And we have this
connected in series here

1600
01:06:48,050 --> 01:06:51,730
to our current readout device.

1601
01:06:51,730 --> 01:06:56,830
So now what we're going to do is
we're going to illuminate this.

1602
01:06:56,830 --> 01:07:00,370
And again, bare silicon
leads on either side,

1603
01:07:00,370 --> 01:07:02,450
and we're going to be
passing the current

1604
01:07:02,450 --> 01:07:04,680
through the current
measurement system.

1605
01:07:04,680 --> 01:07:06,300
Before we turn it
on, we're going

1606
01:07:06,300 --> 01:07:09,550
to ask people, how
many people expect

1607
01:07:09,550 --> 01:07:12,550
there to be current
driving through the system?

1608
01:07:12,550 --> 01:07:14,600
We have light incident
on the material.

1609
01:07:14,600 --> 01:07:15,700
We're exciting charges.

1610
01:07:15,700 --> 01:07:18,720
Based on today's lecture, there
should be free charges moving

1611
01:07:18,720 --> 01:07:20,080
around that material now.

1612
01:07:20,080 --> 01:07:23,220
How many expect a
current to flow?

1613
01:07:23,220 --> 01:07:24,000
A few.

1614
01:07:24,000 --> 01:07:26,130
But a lot of people
shaking their heads.

1615
01:07:26,130 --> 01:07:30,357
Why do you think a
current won't flow?

1616
01:07:30,357 --> 01:07:31,440
There's no electric field.

1617
01:07:31,440 --> 01:07:32,315
There's no potential.

1618
01:07:32,315 --> 01:07:34,460
Why don't we give it a
shot, and why don't we see.

1619
01:07:34,460 --> 01:07:40,770
If we turn this on right
now, what do we see?

1620
01:07:40,770 --> 01:07:41,690
We see zero.

1621
01:07:41,690 --> 01:07:42,200
Right.

1622
01:07:42,200 --> 01:07:44,330
Can some of the folks right
here in the front see?

1623
01:07:44,330 --> 01:07:46,390
Says zero.

1624
01:07:46,390 --> 01:07:49,149
All right, so what this
is telling us again,

1625
01:07:49,149 --> 01:07:51,690
you're welcome to come up after
class and take a closer look.

1626
01:07:51,690 --> 01:07:55,300
What this is telling us here is
that yes, what we talked about

1627
01:07:55,300 --> 01:07:56,519
in class is important today.

1628
01:07:56,519 --> 01:07:58,060
Yes, it's all very
important and it's

1629
01:07:58,060 --> 01:08:01,070
the foundation of calculating
ultimate solar cell

1630
01:08:01,070 --> 01:08:03,410
efficiency, how the material
absorbs the light, how

1631
01:08:03,410 --> 01:08:04,740
charge is excited.

1632
01:08:04,740 --> 01:08:06,590
But we need something else too.

1633
01:08:06,590 --> 01:08:09,220
Once the charge is
excited, somehow we

1634
01:08:09,220 --> 01:08:11,840
have to give it an incentive
to leave the material.

1635
01:08:11,840 --> 01:08:14,229
We have to have a field.

1636
01:08:14,229 --> 01:08:16,520
In this case, we're going to
be using an applied field,

1637
01:08:16,520 --> 01:08:18,920
a couple of batteries.

1638
01:08:18,920 --> 01:08:21,250
So total voltage around
three volts, applied

1639
01:08:21,250 --> 01:08:25,310
across that small material.

1640
01:08:25,310 --> 01:08:27,600
But in a solar
cell device, we're

1641
01:08:27,600 --> 01:08:30,270
going to have a built
in electric field

1642
01:08:30,270 --> 01:08:32,757
that we'll engineer
into the device.

1643
01:08:32,757 --> 01:08:34,590
And we'll talk about
that over next lecture.

1644
01:08:34,590 --> 01:08:37,800
So just for purposes of sanity,
we have our batteries now

1645
01:08:37,800 --> 01:08:40,720
connected in series, and
is now applying a potential

1646
01:08:40,720 --> 01:08:42,000
across those two leads.

1647
01:08:42,000 --> 01:08:44,477
And now if we turn on the
light, what do we expect?

1648
01:08:44,477 --> 01:08:46,310
We expect to see some
current going through.

1649
01:08:50,750 --> 01:08:55,840
And voila, we have a
current running through it.

1650
01:08:55,840 --> 01:08:58,319
So now, what is the
nature of that current?

1651
01:08:58,319 --> 01:09:00,821
If we move the light closer,
we see the number go up.

1652
01:09:00,821 --> 01:09:02,279
What is the nature
of that current?

1653
01:09:02,279 --> 01:09:04,700
That current is photo excited.

1654
01:09:04,700 --> 01:09:06,700
That current is
exciting electrons

1655
01:09:06,700 --> 01:09:08,979
from the valence band,
from bound states,

1656
01:09:08,979 --> 01:09:11,370
into the conduction band,
it's unbound states,

1657
01:09:11,370 --> 01:09:13,450
where they can move freely
across the material.

1658
01:09:13,450 --> 01:09:15,450
And now, because we have
that potential applied

1659
01:09:15,450 --> 01:09:18,050
across the material, there's
an incentive for them

1660
01:09:18,050 --> 01:09:19,550
to drift in one direction.

1661
01:09:19,550 --> 01:09:23,260
The net flow of electrons
is in one direction.

1662
01:09:23,260 --> 01:09:27,029
We have a drift current in our
material, in our semiconductor,

1663
01:09:27,029 --> 01:09:29,010
and hence we have
the flow of charge

1664
01:09:29,010 --> 01:09:32,060
that is readable by this
current meter right here.

1665
01:09:32,060 --> 01:09:35,729
So without the light,
we have no current.

1666
01:09:35,729 --> 01:09:38,819
With the light, we have current
flowing through the material.

1667
01:09:38,819 --> 01:09:40,740
But current and
light-- actually light

1668
01:09:40,740 --> 01:09:44,189
is not the only thing necessary
to create that output current.

1669
01:09:44,189 --> 01:09:46,396
We also need the potential.

1670
01:09:46,396 --> 01:09:48,479
So next class we'll be
talking about the potential

1671
01:09:48,479 --> 01:09:51,370
and how that's created inside
of a solar cell device.

1672
01:09:51,370 --> 01:09:55,590
I've included a few slides
extra for people to see through.

1673
01:09:55,590 --> 01:09:58,250
I'm going to explain once
again the experiment.

1674
01:09:58,250 --> 01:10:00,780
We just had light coming in.

1675
01:10:00,780 --> 01:10:02,190
It was in the visible.

1676
01:10:02,190 --> 01:10:05,180
We were able to excite
carriers, but no current

1677
01:10:05,180 --> 01:10:07,350
was observe because we
didn't have a potential.

1678
01:10:07,350 --> 01:10:10,980
When we applied the battery,
or the potential across, now

1679
01:10:10,980 --> 01:10:12,570
when we shone light
of the sample,

1680
01:10:12,570 --> 01:10:15,310
we had a current
flowing through.

1681
01:10:15,310 --> 01:10:17,460
And we even have a
current, a very small one,

1682
01:10:17,460 --> 01:10:21,940
flowing through when we
have the battery applied

1683
01:10:21,940 --> 01:10:22,910
without the light on.

1684
01:10:22,910 --> 01:10:25,440
And you need microamp detection
I think to really see it.

1685
01:10:28,630 --> 01:10:29,320
Yeah.

1686
01:10:29,320 --> 01:10:30,480
Just from the battery.

1687
01:10:30,480 --> 01:10:34,340
These are a very small
population of excited carriers,

1688
01:10:34,340 --> 01:10:40,310
either thermally or donated to
the electron conduction band.

1689
01:10:40,310 --> 01:10:45,070
Any questions before
we close for the day?

1690
01:10:45,070 --> 01:10:45,750
Yes.

1691
01:10:45,750 --> 01:10:49,396
AUDIENCE: Yeah, so I guess--
I'm the devices person in here,

1692
01:10:49,396 --> 01:10:51,546
so also the notion of
the direct band gap,

1693
01:10:51,546 --> 01:10:54,312
versus an indirect band gap,
are we going to discuss that?

1694
01:10:54,312 --> 01:10:56,020
Or is that something
that's not relevant?

1695
01:10:56,020 --> 01:10:57,750
PROFESSOR: We will
definitely discuss

1696
01:10:57,750 --> 01:10:59,100
direct and indirect band gaps.

1697
01:10:59,100 --> 01:11:02,511
So this goes back to
describing the notion

1698
01:11:02,511 --> 01:11:04,010
of a direct and an
indirect band gap

1699
01:11:04,010 --> 01:11:08,680
is fundamental for
describing the reason

1700
01:11:08,680 --> 01:11:11,810
why these curves have
the shape they do.

1701
01:11:11,810 --> 01:11:13,760
For example, this
one right here,

1702
01:11:13,760 --> 01:11:19,307
if you plotted as alpha-- if
you plot it in a certain way,

1703
01:11:19,307 --> 01:11:21,390
you'll be able to see a
very characteristic shape,

1704
01:11:21,390 --> 01:11:24,520
indicative of direct transition
into a direct band gap.

1705
01:11:24,520 --> 01:11:27,030
The reason we aren't launching
into several of those terms

1706
01:11:27,030 --> 01:11:28,600
right now is because
several of your colleagues,

1707
01:11:28,600 --> 01:11:30,730
more than half, don't have
a semiconductor physics

1708
01:11:30,730 --> 01:11:31,660
background.

1709
01:11:31,660 --> 01:11:33,382
And the beauty of
this approach is

1710
01:11:33,382 --> 01:11:34,840
that you will be
able to understand

1711
01:11:34,840 --> 01:11:38,370
most things about a solar cell
without really diving deep

1712
01:11:38,370 --> 01:11:41,120
into the semiconductor
physics until it's necessary.

1713
01:11:41,120 --> 01:11:43,010
And hopefully we keep
everybody with us.

1714
01:11:43,010 --> 01:11:45,400
So for those who have a
strong semiconductor physics

1715
01:11:45,400 --> 01:11:48,860
background, I bid you, I
urge you to have patience,

1716
01:11:48,860 --> 01:11:51,310
because we will get to
the interesting stuff.

1717
01:11:51,310 --> 01:11:53,710
But we're working on that
fundamental background

1718
01:11:53,710 --> 01:11:54,760
right now.

1719
01:11:54,760 --> 01:11:56,310
Thanks.