Solar Cell Characterization - Electronics & Communication Engineering Video Lecture - Electronics and Communication Engineering (ECE)

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so I'm going to describe the basic
classification of solar cell
characterization methods and then I'll
describe some of the characterization
tools that are used to measure JSC
losses and other tools that are used to
measure vo C and fill factor losses
right so getting a sense of the lay of
the land let me ask you how would you
characterize how would you create a
taxonomy of solar cell characterization
techniques those of you who might have a
little bit more experience might
actually have used a few
characterization techniques in your
laboratories what taxonomy would you use
how would you slice the pie of all of
these characterization techniques go
what are what are ways to divide the
characterization universe into distinct
groupings how about we start overhead
yeah yeah okay so we can describe based
on the economic variables right like
efficiency and then with an efficiency
JSC vo C fill factor mechanical yield
reliability right these are all
parameters that can lump into a cost
model and ultimately impact the the cost
dollars per watt let's say if a PV panel
excellent so we can describe it based on
performance if we dive into performance
a little more what are some of the
properties that affect performance we
have electrical properties optical
properties mechanical right thermal and
so forth so we can break up
characterization techniques space in the
properties that they probe and we can
also character right where you can
create a taxonomy of characterization
techniques based on how fast they are
whether it's something that you have to
sit around and twiddle your thumbs for a
half hour two hours to get done or
whether it's something that gets done in
ten milliseconds of which there are
several characterization techniques what
would the 10 millisecond variety enable
you to do in a manufacturing environment
yeah sort them test them measure them
every single cell coming through so you
might have a barcode like one of those
fancy two-dimensional barcodes laser
marked on each single wafer going
through your line so you can trace it
back in your mes system all the way back
to the crystal that will
groan or from the thin film growth
chamber where it was deposited so yes
you have in line and shall we say say
the the in line characterization
techniques and what are called off line
characterization techniques which tend
to be lower throughput you can think of
the in line characterization techniques
as as being in the line of the
manufacturing environment and the off
line is being those techniques that are
sitting in your laboratory right waiting
to be used in in the R&D lab which might
be next door to the to the manufacturing
line device performance metric affected
that addresses the efficiency point up
here and then buy property tests at
electrical structural optical mechanical
so if you talk to somebody who works in
a PV company she will likely give you a
breakdown based on number three right
here okay these are the techniques that
we have in our inspection system and
those are the techniques that I have
over there in the R&D lab if you talk to
somebody who is giving a fundamental
course of material science they're
likely to pick part number one way up
there and give you the breakdown based
on the properties that are probed I'm
going to opt for number two today in
lecture not because it's any better or
worse than all the others but just
because that's the metric that we care
about right now is we're trying to probe
dollars per watt
that's relates to our quiz and our
homework but also relates to the
ultimate economic driver solar so we
have will keep this in mind that we
might need to ferret out references for
the different techniques in different
textbooks or different papers based on
whether they're probing electrical
structural optical mechanical properties
of our solar cells but we're going to be
focused on efficiency short circuit
current open circuit voltage fill factor
so let's go ahead and dive into that we
are going to first start with techniques
to measure JSC or short-circuit current
losses and some of these slides are
going to be repeats and the reason
they're repeats is because the first
time you saw it okay you sort of kind of
got it you went into the lab made your
devices tested them and now all of a
sudden you have a much I would say much
stronger background with which to
understand we're going to start by
discussing the optical components just
very briefly
in spectral response minority carrier
diffusion length revisiting some of
these concepts that we already seen but
now with the benefit of having all of
our background knowledge
spectrophotometer majors specular and
diffuse reflectance and transmission
alright let's let's break that down
specular reflectance spec your mirror
Latin right so specular reflectance
means light comes in and out pretty much
at the same angle relative to the
surface normal so if you come in from
here it's going to bounce out like there
right the same angle relative to the
surface normal diffuse reflectance means
that if you shine light in a certain
angle it's going to reflect back not
necessarily at that angle I could have a
distribution limbering scatterer might
qualify and reflecting some transmission
okay we talked about the different
optical losses of a solar cell material
reflectance means that light comes back
off the surface transmission means that
light did not get absorbed so it went
through the material and didn't get
absorbed that is an optical loss as well
so the spectrophotometer is useful for
measuring these different loss
mechanisms and it can tease apart the
specular from the diffuse reflectance
giving you some indication some idea of
how the surface is behaving and what you
might do to improve it so the
spectrophotometer is useful in that
regard in terms of increasing absorption
we talked about various methods to
increase absorption those who attended
the Eloi a bloody bitches talk heard
about many more the goal here is
essentially to increase the optical path
length by texturing your surface for
instance the physical thickness can
remain very low and again just to
refresh ourselves if we decrease the
thickness of our devices but managed to
have very good light trapping what
happens to our excess carrier density it
goes up right because now we have more
carriers being generated in a smaller
volume so the carrier density increases
and as the carrier density goes up that
means the separation of the quasi Fermi
energies increases which means the
maximum voltage extractable from our
device increases as well so there's a
strong push right now in the field to go
to thinner and thinner devices that also
has the added benefit economically of
using
material so we want to decrease the
thickness by improving our optical
trapping our light trapping the another
benefit is that allows carriers to be
absorbed closer to the junction which
increases their probability of
collection and we talked about this
during the very beginning of class how
you might texture your surface but now
we actually saw it in producing
ourselves so this is an example an SEM
image of textured silicon in that
particular case this was an alkali edge
on a single crystalline sample probably
of 1 0-0 orientation so that these edges
of the pyramids are 1 1 1 planes you
could also achieve a similar although
not identically looking result if you
performed an acidic etch which would be
an isotropic in nature so the light
comes in for the textured surface some
of it goes in to the device
notice that Snell's laws in effect so
the light bent or was refracted and some
of the light is reflected off the
surface now because of the texturization
you get that second chance absorption so
the light has to bounces before leaving
which means that the probability of the
light getting absorbed is 1 minus our
quantity squared right and so you get an
enhanced absorption and for those who
looked at the samples before and after
texturization you could visibly see that
they looked darker the reflectivity had
gone down I see some smiles over here
there were probably some initial itching
processes that didn't quite work out but
eventually the process was controlled in
and worked out fine so we have as well
other mechanisms to trap the light
besides just texturing our front surface
these we didn't get to in to do an
actual cell fab but we could envision
putting a reflective or diffuse scatter
on the back and a reflective layer so
that the light that goes all the way
through the material once gets bounced
back in perhaps at an angle right to
increase the light trapping in the back
and that I think is represented on the
previous slide it is indeed so we have a
textured back surface and we also have
this layer probably in this case it
would most likely be a dielectric
material
with a refractive index that is
significantly different than the
absorber itself so if your absorber
material is inorganic you might have a
refractive index somewhere between 1.5
and 2 maybe on the high end and if you
have an inorganic material you could
have refractive indices as high as 3 3
and 1/2 and the material you put on the
back would probably be as close as you
could possibly get to air right to get a
large reflection off the back as
possible in the case of silicon devices
oftentimes you have a dielectric
material with a refractive index
somewhere between 1.5 and 2 and that
serves also to passivate the surface to
prevent carriers from recombining on
that back side so collection probability
we talked about this earlier now that
we've performed quantum efficiency and
we've tested our own devices we want to
walk through it again it's an important
concept to really grasp I want to make
sure that everybody got it we have here
a PN Junction here's our p-type material
here's our n-type material shown at the
blue little dots those are our holes
free holes mobile holes able to move
around the material and then the n-type
side we have here the red dots those are
also free to move around the materials
or electrons negative charge carriers
omitted from this diagram omitted from
this diagram is the fixed charge
associated with each connectivity type
we have for example fixed negative
charge from the ionized acceptors from
the p-type and fixed positive charge
from the ionized donors in the n-type
but we've emitted it for clarity we note
that an electric field builds up here at
the junction between and that sweeps
carriers into one side or another so
that if light comes in and generates a
pair of charges due to charge neutrality
it generates a pair positive in a
negative the 1 1 charge carrier type
will be swept across the junction and
the other will remain inside of the
material and so to be more precise about
the exact motion that occurs with the
carriers we have at first a diffusion
process until the electric field starts
becoming large and then finally drift
across that Junction
that's what generates the current inside
of the solar cell device so collection
probability means that light alike
generated a photo generated minority
carrier can readily recombine but if the
carrier reaches the edge of this of the
space charge region the minority carrier
it can be swept across and collected so
the probability of collection means for
every electron hole pair that I generate
at a certain depth what is a probability
that the minority carrier will make it
across a junction and this is what we're
probing in spectral response yes
okay so great question the exit on in
silicon has a binding energy less than
KT which means at room temperature the
exit on readily dissociates so we so the
exit on diffusion length can only be
measured at lower temperatures the at
room temperature you essentially just
discussed minority carriers and the
minority carrier diffusion length let's
let's revert it in terms of lifetime and
then do the translation to diffusion
length in terms of lifetimes one
typically has a range between a
microsecond to a millisecond millisecond
being in the high end it can go as high
as five milliseconds even and so if you
revert that into a diffusion length one
microsecond lifetime would correspond to
a 50 micron diffusion length and then
you can do the rest of the conversion
from there just taking the square root
sign into account so it can be rather
long on the order of the thickness of
these solar cell devices now that's
those length scales which we're talking
about hundreds of microns maybe even a
thousand microns compare that now to ten
nanometer diffusion length say for an
exit on in a polymer blend material then
you have to reconsider your device
architecture how you're going to
actually collect them so this is a very
generic picture which could easily be
substituted instead of n type P type it
can be easily substituted by say polymer
1 and polymer 2 that just have the right
band alignment two separate charge then
it gets a little more complicated as
well here we're assuming that the
carriers that are swept across the
junction can move easily away from the
junction in a polymer not always so you
might have charge accumulation right at
the edge of the space charge region
which creates his own field which
counteracts the built-in field here and
also inhibits current flow so things get
a lot more complicated as you venture
away from the simple case of say a well
behaved
what I call what is called in this case
a homo Junction meaning a PN Junction
created from the same material on both
sides silicon just doped N and p-type if
you have a hetero Junction comprised of
two different materials you may have
even I say additional effects occurring
but it's always helpful to think about
the motion of carriers from the
perspective of drift and diffusion and
if you're ever in doubt you can begin
thinking about
in terms of Delta T's small increments
of time where you imagine light coming
in generating an electron hole pair
imagining what happens is that carrier
moves across the general moves to the
junction then moves across the junction
and then what happens does it
immediately get collected does it stay
there what is the what what happens next
is there a potential
an attractive potential between the
carriers on either side of that Junction
so asking those sorts of questions can
help you walk through and troubleshoot
what exactly is going wrong with your
device collection probability so we take
this this diagram that we just saw on
the previous slide this one right here
and we say hmm if light were to come in
and generate an electron hole pair right
here then I would expect very high
probability of collection meaning the
one what the minority carrier be swept
across the majority care would stay on
this side and presuming that they can
get from here to the contacts big
assumption but assuming that they can
then the probability of collection of
those carriers will be very very high
but if my light comes in deep within the
device and generates an electron hole
pair the minority carrier will have to
cruise through it can think about it
maybe a nice tasty chicken in the
Everglades National Park trying to make
its way over from that side all the way
over to the junction in across the
minority carriers at risk of recombining
and many of them don't make it so we
have the following graph the collection
probability versus distance into the
device where this yellow region
represents the space charge region where
the probability of collection is very
high and as you move away from the space
charge region the probability of
collection decreases and you can see it
decreases exponentially as a function of
distance from the space charge region
the reason you have almost not exactly
symmetric these are two different decay
constants but they're both exponential
functions on either side is because over
here on the what ostensibly would be the
what did we call it the p-type side the
electrons would be the minority carriers
and over on the n-type side the holes of
the minority carriers and each one is
trying to get to the other side so the
collection probability is actually the
collection probability of minority
carriers the precise definition of which
is chain
from one side of the junction to the
other I on one side of the junction the
electrons and minority carriers on the
other side of the holes in the minority
carriers all right so by probing at
different wavelengths of light
we essentially change the optical
absorption coefficient of the material
which means that the light will get
absorbed at different depths so we might
have a very short wavelength light that
probes up here and then say light is
coming in from this side right so short
wavelength light is absorbed near the
front surface and then longer longer
longer and longer and longer and longer
wavelengths until we're deep within the
material and we can flesh out exactly
what the current collection probability
would be as a function of depth then we
essentially take that data
knowing the generation rate and the
collection probability we can tease out
the minority carrier diffusion length
using the spectrophotometer so let me
show you examples of good and bad cells
this would be a bad solar cell and a
good solar cell device right over here
the good solar cell has a high internal
quantum efficiency out to longer
wavelengths and as we know from the very
second lecture of our class the longer
wavelengths get absorbed deeper into the
device further from the junction and so
you can see this tail off occurring
actually the tail off somewhere in this
region right here for this device is
occurring within the bulk at some point
the device just isn't thick enough to
absorb all the light so there is an
inevitable drop toward longer
wavelengths but the bad cell doesn't
even pour a job of collecting these
longer wavelengths and thus in part
because the minority carrier diffusion
length of that particular cell was much
lower or say the minority carrier
diffusion length of the material which
comprised the cell is much lower than
the good cell so if you come in with a
longer wavelength of light let's say oh
maybe 933 nanometers in silicon that
would give an absorption depth of around
100 microns that's pretty far from the
the junction now you you would have a
much lower probability in the bad cell
of collecting than the good cell and
that's precisely because the diffusion
length is lower
so integrated over all of the
wavelengths one obtains the
short-circuit current and the method of
measurement was the spectrophotometer
now I understand most of you opted to
choose Suns vo C for your one
characterization tool to apply to
yourself did anybody choose the
spectrophotometer show of hands anybody
it was broken yeah so the filter wheel
was down okay that was that was it so
let's see the filter wheel the filter
wheel let's go fixing this here it is so
the filter wheel was it was broken so
essentially the the polychromatic light
source was shining through a filter
wheel which is selecting one wavelength
of light the monochromator of course was
helping as well and and eventually onto
the solar cell sample which was shown in
front of the light so that's the way in
principle inspect response works and one
variant of spectral response that's for
the full device you typically have an
illuminated area of a few millimeters
squared or maybe even a few centimeters
squared but let's say you that wasn't
good enough for you you knew you had an
in homogeneous material and you wanted
to probe the in homogeneity across your
device you got a large device maybe
about that big a few a few tens of
centimeters squared and you wanted to
probe the distribution of minority
carrier diffusion lengths across your
device how would you do that well in one
incarnation you would use a much more
finely focused beam instead of having
something in order of a millimeter you
might shrink the beam spot size down to
the range of single microns and then use
an XY stepper motor to scan across your
device and that's precisely what this
does right here this white piece is the
XY stage and this black head right here
is essentially comprised of several
lasers that will shine onto the sample
now you need a few different wavelengths
of light to really flesh out this curve
to determine the minority carrier
diffusion length from this curve and so
the laser light is typically chosen at
very auspicious wavelengths to maximize
utility in this particular type of
evaluation
and so we have usually four you know
minimum three you can always fit a line
through two data points so minimum three
laser wavelengths and usually about four
or more to process the quantum
efficiency as a function of position and
so we the XY stage moves a sample around
and the laser head is or moves the laser
head around while the sample stays fixed
and you map out the current response at
each point on the device obtaining a map
that looks much like this right here
where this is on the y scale or the Z
scale sorry you have from 0 to 120
micron diffusion length on that
particular solar cell device and points
3-1 and to represent regions in which
the minority carrier diffusion length
was calculated using the method that we
have discussed in the previous lectures
the bazoer Paul bezoar method so we have
a map of minority carrier diffusion
length across our device some regions
underperforming other regions performing
rather well and we can see that in
general these lower cost materials tend
to be fairly in homogeneous in terms of
their performance response right and if
you really want to get fancy and say my
goodness if I spend all this time
mapping my device I'm not going to get
through many devices during my PhD I'm
going to have to make do with very poor
statistics how do i speed this up some
very clever people have figured out that
if you fire your laser diode
simultaneously but with different
frequencies each of them with its own
frequency you can D convolute the
current response of your device using a
Fourier transform to pick out the
current response at each portion of the
frequency space and in other words
decouple the different wavelengths of
light so it's a little clever method
involving Fourier transforms and lock-in
method to speed up the measurement a
little bit small aside small footnote
there okay important minority carrier
diffusion length that's that's a most
important so we can relate the diffusion
length directly back to our IV curve via
the saturation current by the J naught I
naught depending on whether you're
looking at density or
Sulaiman let's shift gears a bit I want
to talk about the vo C measurements and
fill factor loss measurements so how do
you determine losses in vo C and fill
factor before I jump into this does
anybody have any questions about DSC
loss mechanisms so sad that the
spectrophotometer wasn't up and running
sniff that's a it should be fixed
relatively soon right Joe it's fixed now
all right so we have I think David Barry
Needleman is back on board right hey
over the route back as well yeah so if
we have folks who still want to measure
their devices using spectrophotometer
measurement we can probably make
arrangements for say what 10 10 cells to
be measured something that means okay
okay yeah let's let's let's fitmin the
three people who wanted to do them and
we'll have our full data set good so
let's describe fill factor in vo C
losses and this is essentially generate
venturing into operating conditions
under short circuit conditions how much
power is running through the solar cell
device power defined as current voltage
product zero why is that no voltage
right so you're not testing your solar
cell under ideal operating conditions
it's a sense an artificial operating
condition simply to probe a bulk
property characteristics right to
minimize the effect of the junction now
if you really want to see how is the
junction behaving how is that charge
separation going you might want to
venture into forward bias conditions and
eventually into open circuit voltage
conditions to really test what the
junction quality is instead of just
probing bulk properties so let's talk
about some of the measurement techniques
to really get the heart of how a solar
cell is performing it's helpful to do
the JSC measurements helps you predict
what might be some of the lost
mechanisms later on but but this really
gets at the meat of it IV curve
measurements check we we study that we
did that in the laboratory and I think
we have a pretty good sense of what's
going on there now series resistance
losses we talked earlier in the class
about contact and sheet resistance
losses now we'll go back to it again
just to revisit so we have the materials
necessary to write up the report here on
this project shunt resistance
specifically in shunt resistance will
talk about lock-in thermography and
electroluminescence and finally we'll
have a small slide on Sun's vo C and
talk about that as well since I know the
majority of you selected that as your
measurement tool all right
so open circuit voltage so reading
straight off of the slide here if the
collected light generated carriers are
not extracted in the solar cell but
instead remain that then a charge
separation exists across meaning there's
a buildup of charge
and the charge separation reduces the
electric field in the depletion region
which reduces the barrier to diffusion
current and causes the diffusion current
to flow in other words if you have light
coming into your device but you're not
able to extract the charges from either
side to make sure that the chemical
potential is equal on both sides the
chemical potential will change on either
side you'll have a buildup of one charge
type on one side of the junction and
buildup of the opposite charge type on
the other side of the junction so that
will shift the the quasi shift the the
Fermi energy on either side of the
junction result in a bias of your device
and eventually counteract the built-in
electric field to the point where the
diffusion current is now enabled to flow
all the sound familiar to folks might be
a little rusty but it's all there
so the idea now is to begin probing that
that Junction condition we talked about
the ideal diode equation and now we're
going to piece through it once again
this is your current density here and I
believe if you really want to be precise
about this you should use straight
current and not current density reason
being if you look at current resistance
product that gives you voltage but
current density resistance product gives
you essentially a voltage density which
is not a unit that we typically use so
just keep that in mind as small little
asterisks this equation is often used in
PV that little unit conversion issues
generally ignored but but you might want
to flag it for your own benefit so we
have the current output of our device as
a function of voltage and this is a
rather complicated expression going well
beyond the ideal diode equation the
ideal diode equation which would consist
of the J sub L the illumination current
this is the light coming in creating the
carriers that are then swept across the
junction the J sub L is going to be the
integral current under a spectral
response curve right at each wavelength
waited for the wavelength of the
incoming light are the intensity at that
particular bandwidth of the incoming
light think of it this way
you're measuring the spectral response
at each particular wavelength what the
collection probability is then if you
multiplied by the total number photons
in that wavelength range you're
determining the total number of carriers
generated within that frequency range of
light and if you add up all of the
little bins you get all of the carriers
generated by all of the light right and
you can adjust depending what spectral
conditions you have say a 1.5 spectrum
so the J sub L here this one is our
short circuit current effectively and
what is derived from a spectral response
measurement the rest of these terms here
are are of interest so that J let's
break it on two pieces here this term
over here is essentially to take into
account shunt resistance losses if we
have shunts in our device we're going to
be reducing the total power output these
two components what are usually called
diffusion current and recombination
current this one you have to take me for
my word at it right now this is the
recombination within the space charge
region and this over here is a
recombination within the bulk of the
solar cell here's a good way to think
about it if our solar cell is not
forward biased if it's very very
slightly forward by it's just a little
bit there's going to be a large barrier
for care effort for majority carriers on
one side of the junction to overcome to
drive a drift current right side
diffusion current very large barrier to
overcome and hence the recombination is
most likely to occur within the space
charge region the carriers aren't likely
to overcome that barrier get into the
bulk and recombine there whereas if
we're under large forward bias
conditions now the carrier's can very
easily go over that barrier and
recombine in the bulk so this term right
here dominates under low forward bias
conditions and this term over here
dominates under larger forward bias
conditions and that's why you see when
you plot your IV curve on log linear
scale you see essentially two flat
points on your IV curve let me for that
to the next slide right here here we go
so this is log of current versus linear
voltage and you see one flat portion
right here and another flat portion
right here before the series resistance
begins to dominate at two high voltage
and your shunt resistance dominates at
two low-voltage this flat portion right
there is being driven by three common
within the space charge region why well
the forward bias voltage isn't enough to
really lower that barrier enough to
allow the carrier's deep within the bulk
to recombine so the carriers are
recombining in the space charge region
whereas here they're recombining within
the bulk all right
so this is a more complicated expression
for the IV characteristics of a solar
cell device not always are these precise
mechanisms at work if you have a new
material system that you're working with
there might be different recombination
mechanisms at work there might be charge
accumulation effects at work but they
can all be encapsulated in some form of
current voltage expression think of the
IV characteristics of the solar cell
similar to say the constitutive
relations of a complex of viscoelastic
material where you have say a nice
linear elastic component a dashpot
component right so you have a very
complex expression describing the
stress-strain relationship in material a
similar thing goes on here with the
solar cell where you're describing the
current voltage relationship if you
understand all of the mechanisms driving
carry recombination in your material and
charge separation you can come up with
an expression that describes very
precisely the IV characteristics but if
you change material systems you may not
necessarily be able to transition the
same models over it's helpful to start
with them but sooner or later you might
decide well gee I have to I have to make
some modifications all right
okay series resistance we already
studied this before but just a quick
refresher we have the series resistance
of the bulk we have the series
resistance of the emitter and then we
have the series resistance of our of the
contacts as we contact the device and in
the series resistance within the contact
itself so at least four different
components of series resistance in our
device that are all lumped together when
we take these when we express our IV
curve in this manner we all lump them
together and that R sub s yeah question
to
ah yeah so um simple explanation if you
would like is mostly where the Fermi
energy is sitting relative to the
conduction or valence band in the space
charge region the quasi neutral region
is closer to mid gap as opposed to
closer to bandage hand-wavy
if you really want to get into it I
spent about three months studying this
as a graduate student the the one in the
to the ideology factor which is to show
more precisely it's the number that
comes before the KT right for each of
these that's called the ideology factor
it's typically expressed as n sub 1 or n
sub 2 in this case I just substituted it
straight out for a 1 and a 2 those
numbers aren't always 1 and 2 as a
matter of fact especially the G naught 1
the bulk recombination current depending
on where the defect levels lie it can be
somewhere between say a 1.1 and a 1.4
typically and beautiful thesis work done
by fellow in in Australia hold on Keith
McIntosh and the title of the thesis is
called humps bumps and lumps it's all
about non idealities within an IV curve
so if you really curious about that
humps bumps and lumps bye-bye McIntosh I
believe was the name okay so we talked
about series resistance already hold
that put that in your RAM that's our R
sub s right over here that's our R sub s
and our our shunt you want to hold this
other component near ram so that's the
picture to have our series this is our
shunt this is an IV sorry a pn-junction
this is your n plus region and this is
your p and this is looking at the
electron energy in 3d so we typically
take a slice out like that right just
like this and we draw the electron
energy as a function of position in a
nice little wavy form that we typically
do to create describe the PN Junction
what's being described right here is
adding a leaner dimension a spatial
dimension in what's shown as the
abscissa and this plot and showing what
is a weakness in the PN Junction it
could be a localized defect this could
be a
art of metal that happened to lie on the
wrong place in your device and poke and
fire through essentially when you did
the firing step to adhere the metal to
create the contact it could have gone
straight through the pn-junction contact
to the other side it could be a charge
dislocation it could be a structural
defect and so forth but a local
reduction in the barrier height now
where the SI electron going to go if you
have a diffusion current it's going to
be crowding through that little
localized reduction in the energy
barrier and you're going to have a
higher current flowing through the
specific region so how to measure that
well if I measure my full IV curve like
this might manifest itself as some
reduced shunt resistance so you have a
larger current flowing through it at
lower bias voltages but but how do I
know what's going on without some
spatial a spatially resolved measurement
tool I'm in the dark no pun intended
so I have to figure out how to measure
the current flow as a function of
position now somebody thought about this
a while they said huh well let me get
this straight if I apply a known bias
voltage to my device I'm going to get
some current flowing through it and that
current what I read out of the whole
device macroscopically has some spatial
distribution to it let me think about
this
okay so current times voltage is power
right and power generates Heat so if I
have a current crowding at some portion
of my device I'm going to be generating
a large amount of heat as the carriers
flow through that specific region so if
I have some method of measuring the heat
heat distribution across my device is
very very sensitive I might be able to
divide that heat measurement if
calibrated properly to determine total
power I might be able to divide that
heat measurement by current sorry by
voltage by voltage so I know the applied
bias voltage to my device I take my
power divided by the voltage and I get
the current as a function of X Y
position so I can map out my dark IV
curve at any arbitrary bias voltage
condition let's say I want to do the
measurement at point 4 volts for bias I
apply point 4 volts across my device and
I just measure the heat distribution and
in a calibrated measurement you can see
how the dark current is distributed
and how the diffusion current is
distributed and that's what lock-in
thermography is all about this is a say
a somewhat typical image not it's still
very noisy because it was a very fast
image but you have your solar cell
device you can barely make out the
contact grid right here and then the
fingers are moving down separated by
about this much on this particular image
you can see the fingers or the dark
shadow of the fingers right here and you
see bright spots 1 2 3 4 5 6 7 and so
forth across the device indicating
regions were more current is flowing aha
so I'm beginning to figure out that well
this dark IV curve that I have right
here this large amount of current
flowing through my device at lower bias
voltages that's not all uniformly
distributed but it's rather concentrated
in specific areas where I have
weaknesses in my PN Junction under low
forward bias voltages and at larger
forward bias voltages once this barrier
significantly reduced I may have more
carriers going through in regions of
smaller minority carrier diffusion
length why well because if a carrier
goes in and recombines quickly because
the diffusion length is very short that
means there's one less carrier in there
which means that now there's a greater
driving force for diffusion and another
carrier is going to come in and
recombine too and another carrier and
recombine too right so now you have a
larger diffusion current going into the
regions of lower minority carrier
diffusion length let's look at a few
lock-in thermography images and see how
this this this plays out so under low
bias conditions so I'm still still have
a very large barrier there in the in the
PN Junction region I'm typically going
to see isolated hot spots not always but
but typically isolated hot spots and
these most often are defects within the
PN Junction somebody might scratch the
junction or maybe drop their tweezer on
it or maybe a piece of metal during the
contact metallization fired through at
that particular region and so we have
what are typically these point shunts
sometimes you see shunts around the edge
as well if you didn't isolate the edge
well and it now as we forward bias
forward biased forward bias those
barriers become less
and now what's driving the current the
dark current in the device is a
recombination in the bulk so the regions
of higher recombination will be regions
of higher current flow they'll drive
more recombination current so this is a
higher bias voltage 560 millivolts or
0.5 6 volts as opposed to 0.36 volts we
can still see the shadow of the big 3
right here but they're they're much
diminished now instead what we see are
these wispier features right here now I
think gee if that really is if those
really are regions of lower minority
carrier diffusion life I just learned
about a method to measure might already
care diffusion length didn't I what was
that laser beam induced current method
right spatially resolved laser beam
discard so I have at least one method of
measuring minority carrier diffusion
length let's put one and one together
and see what we get so we'll take this
image right here and put it aside rotate
it and put it right beside the minority
carrier diffusion length and voila you
see how those wispier features are
corresponding to regions of lower
minority carrier diffusion length once
again the explanation if you have large
forward bias condition the barrier is
lower carriers can easily diffuse into
the bulk the carrier's diffusing into
the bulk will go a certain distance
before recombining if the diffusion
length is short the recombine quickly
which means now there's no more carrier
which means that the diffusion current
will push another carrier into that spot
right which means will recombine
recombine more current is flowing
through if the diffusion length is
shorter the alternative is a diffusion
length is long and one carrier makes it
over and then takes its time getting all
the way across before recombination
occurs so what you're seeing here is
essentially in effect the current the
the dark forward current meaning you're
measuring the IV curve in the dark
you're obtaining an IV curve here it is
you're obtaining an IV curve for your
device you're measuring in the dark
under larger forward bias conditions
somewhere out here where bulk
recombination is dominating and you're
able to visualize the current loss
mechanisms in your device so you say
well gee if I want in the dark if I want
this to be as small as possible so that
when I transpose this
delight and I shift everything into
negative into fourth quadrant territory
because I illuminate it now if I want
there to be a small dark forward current
as possible so as I maximize my fill
factor when I illuminate my device I
want all of these current loss
mechanisms to go away let me let me
repeat that one more time so people get
it if so what I'm doing right now is I'm
measuring this device in the dark and
this is my IV curve right here and I
have example of bad device good device
the bad device has so bad and good the
reason this is bad and good is because
when I transpose this curve under
illumination this is now under
illumination my good and bad right here
you'll see that the bad has a lower vo C
right so the intersection between these
illuminated curves this is now
illuminated and this is dark right over
here these are dark curves these here
are illuminated curves the intersection
between the illuminated curve and the
x-axis denotes the open circuit voltage
and you see that the larger this current
is in the dark the earlier you're going
to intersect with your x-axis the lower
the voltage output of your device will
be the lower the maximum power point
will be right so you want in in the dark
when you measure the IV curve you want
that current to be as small as possible
in the dark and obviously when you
illuminate it you want this jump to be
as large as possible and you want this
to almost look like a box that a large
fill factor so if we say okay we want
this to be small because we want a large
fill factor somehow we have to know
where the current loss mechanisms are
occurring and that's where we have our
lock-in thermography available to us we
can visualize it you say well you know
to do lock-in thermography well I'm
going to need in indium antimonide sorry
yeah
that would be it would be a in indium
antimonide camera sensitive to the 3 to
5 micron wavelength range that might
cost $70,000 to get a good one high
frame rate the locking systems so forth
that money I can go over and borrow
professor blown a cc system and use it
there or if my shunts are big enough I
can just use straight-out liquid crystal
thermionic sheets or thermochromic
sheets rather sorry so you can take
these liquid crystals and slap them
against your device and measure the heat
distribution straight up just by making
sure you have good thermal contact
between yourself and your thermochromic
sheets which cost about a hundred
dollars now the reason we use the
lock-in thermography and not these
thermochromic sheets is this curve right
here this is lock-in thermography
sensitivity versus integration time and
we're getting into the 10 micro Kelvin
range which is rattlesnake territory all
right that's how the rattlesnakes are
able to sense heat and reach out to you
is because they have those little organs
that look like a little black they're
kind of like integrating spheres to be
honest small little spot to open up
rattlesnake that's why the Sidewinder
missile anybody f-16s Hornets know okay
if you're into aviation
there's a special type of heat-seeking
missile developed I think in the 1950s
that uses a device not dissimilar from
the rattlesnakes heat sensing organs
regardless I digress we're looking at a
about a 10 micro Kelvin sensitivity in
this lock-in thermography technique
which is very sensitive can measure
under low forward bias conditions and
hence useful okay so that pretty much
sums up lock-in thermography it is a
difficult technique to wrap your brain
around right so for those of you who got
75% of it congratulations that was
really really well done for those who
got about 25 percent of my explanations
today don't worry you're not you're not
alone it just takes a lot of thinking it
through exactly okay whereas the current
flowing as a function bias condition
what does that do to my V curve and then
what is it doing this two dimensional
regime when i measuring heat output it's
a very complicated thing thankfully
there is an entire book on lock-in
thermography written by Othman baikin
Stein I gave to you today a paper one of
the papers that I distributed today
the one that has the PSS a written on it
this one that paper is by Othman
brightenstein
from the Max Planck Institute of
microstructure physics in Halle Germany
about two and a half hours south of
Berlin and this describes in more detail
that which I attempted to get across in
class today he with Martin Langenkamp
have also written the book on lock-in
thermography so if you're more
interested more information that's where
to go in your handout set today we also
have a classic paper on series
resistance effects of solar cell
measurements this one is from 63 yes
1963 classic paper worth the read if
you're in that regime making devices
that are series is series resistance
limited it's more optional reading for
folks and let's venture forward folks
who did these scanning albick techniques
for a while really found value in
measuring as a function of spatial
spatial resolve manner down to a micron
in spatial resolution the electric
electrical output of a solar cell device
and then they thought to themselves well
goodness if we measure with one micron
spot size it's going to take us a week
to get a measurement across the full
area solar cell device if not longer and
if we measure say with the 200 nano
meter spot size using some sort of x-ray
technique and we accumulated for say two
seconds of point it can take 10,000
years to map out a full sized solar cell
device literally do the math and they
said is there an easier way for us to
acquire information that does not rely
on scanning on point by point step by
step measurements and they thought about
it long and hard and they said well gee
these these new handheld digital cameras
coming out in the market are pretty cool
what technology do they rely on oh it's
a CCD charge couple display that
visualizes our images over a large area
the the output of a device and that's
exactly how the lock-in thermography
techniques were developed here with this
this imaging camera in that case an
indium antimonide CCD and they said well
what other wavelengths admit what in
what
the wavelength does a solar cell emit we
know that it emits heat right and heat
is typically in the three to five micron
wavelength regime maybe even as high as
10 microns depending on what temperature
and we know that as well we can have
band-to-band emission inside of a solar
cell that would emit around the bandgap
energy so let's set up a camera to image
the band to band recombination in
intensity or the band to band
illumination intensity and that's what
this paper is about
this is wavelength this is intensity
this is the emission spectrum of a solar
cell so if you were to measure what
colors what color light does a solar
cell emit after you pump current into it
this isn't more or less a spectrum so we
have the the thermal radiation shown
over here so this is longer wavelength
light that's the heat that it gives off
that's what indicates current flow
inside of the device there's the band to
band luminescence right here and we'll
neglect the other two for now those are
more advanced constants but the bantha
band luminescence is essentially just a
recombination of a carrier from the
conduction band to the valence band
right recombination current very
straightforward and the recombination
intensity is inversely proportional to
the minority carrier lifetime why is
that this was that that quote that I
remember who attended a light one of
itches talk he was saying it's
completely counterintuitive
do you remember specifically what he was
referring to in this me show you an
image here hmm
exactly yeah so so why is why what what
is going on here we have our towel 1
over tau effective R 1 over our lifetime
what we're measuring this is our
effective lifetime what we're measuring
and we have 1 over tau let's call it non
radiative so we have non radiative
recombination mechanisms this comprises
shockley-read-hall recombination no J
recombination a bunch of different
recombination mechanisms and then we
have 1 over tau radiative which is
essentially this recombination mechanism
shown right here which is just the band
to band recombination so if you have
defects around that will lower the
lifetime the non radiative lifetime if
you have tons and tons of defects the
carriers will most likely recombine
through the defects and not through the
bantha band they will only recombine
with band to band if there is nothing no
other recombination path left available
to them right it's a question of
probability so if this is really really
short non radiative recombination
lifetime is really really short because
the defect density is very very large so
the lifetime due to non radiative
recombination mechanisms very short then
the tau effective is also going to be
very short and very few carriers are
going to recombine radiatively
conversely if we have a very clean
material virtually defect free this non
radiative lifetime is then going to be
out the roof and now we're going to be
limited instead by the radiative
lifetime and so tau effective will be
more similar to rate is it now an
interesting thing happens when you have
a radiative recombination event as the
name would suggest it emits light and
that light can be detected by a CCD
camera nearby so what you Boopsie what
you have we go what you have right here
is a solar cell device that is being
biased so current is flowing into the
device and now the the map what you're
seeing is indicative of radiative
recombination why because nearby the
cell it's essentially very similar
mechanism or similar setup to what we
saw right here where we had bias voltage
across the
and imaging not with an infrared camera
but now with a camera matched to the
bandgap energy this could be in indium
gallium arsenide camera or say a silicon
camera depending on the precise bang gap
and your imaging the radiative
recombination as a function of XY
position across your wafer so these
darker regions here on the bottom and on
the right sorry left the other right
they indicate regions of lower minority
carrier diffusion length why because
there's less radiative recombination
because this term in those regions is
very very small so that there's not much
radiative recombination going on whereas
these other regions here that if you're
brighter have a lot more radiative
recombination going on any questions
about that yeah
getting hot days
sure so the question pertains to photon
recycling and how many photons that are
radiatively emitted get reabsorbed by
the material that would depend on the
optical path length inside of the
material of carriers being generated in
the material and you can assume that
carrier generation is fairly isotropic
in nature that there's not any preferred
direction unless you have a dye molecule
that's designed in a certain way to emit
light in a certain orientation so you
can assume that the carrier mission in
most materials is isotropic in nature
and then it's just a question of ray
tracing to figure out what the optical
path length is compare that to the
optical absorption coefficients in the
material and you'll get your answer what
fraction of light gets reabsorbed all
right
I can sense where we're reaching
threshold here in terms of new
information gathered I'm just going to
briefly go over the sun's vo see at the
very end and the sun's vo see technique
is useful as we saw during class because
as this paper right here by Ron Sinton
and dice Cuevas this one I know you
definitely have this one this paper
essentially describes the functioning of
the technique on page number two on the
upper left-hand side so figure two we
essentially have the figure that was
determined on the screen during the
measurements so for those of you are
close enough to the mana to actually
watch the the measurement being taken
the sun's BOC you saw the light
intensity decaying exponentially right
so the light intensity was a flash ball
poof and decay exponentially the open
circuit voltage measured by the device
so you had this solar cell device
sitting on the platen with a little
probe coming in and a 50 mega ohm
resistor connected in series very little
current flowing through that external
circuit right but it's measuring the
voltage so it's essentially maintaining
the solar cell in open circuit voltage
conditions while the flash is decaying
and it's measuring the open circuit
voltage across that device at each
illumination intensity as the pulse
decays so you can see the timescale here
as an eye order of a few tens of
Ekans so very fast measurement the
electronics response time has to be very
fast that tells you what the RC time
constant of the circuit is and the you
can notice that the voltage the open
circuit voltage decays linearly when the
illumination intensity decays
exponentially why is that there's a
natural log yes this is what we what Joe
showed to you yesterday or on Thursday
in class is how the voltage output of a
solar cell varies by illumination
intensity so there's a logarithmic
dependence there so that's why you take
the log of the exponentially decaying
light intensity and you obtain a linear
relation that's the open circuit voltage
decline as a function of time okay so we
can derive an IV characteristic by
translating that open circuit voltage
into an implied bias voltage and knowing
the short-circuit current density up
front essentially by measuring it using
an a by measuring the solar cell device
in a solar simulator we can obtain the
short-circuit current density we pin
both curves up here at the measured
short-circuit current density and then
we plot both curves out the IV curve and
the sun's v OC curve now the sun's V OC
curve is Union is similar to the IV
curve with only one difference there's
no current or very very little current
flowing through the external circuit
which means there isn't any real power
flowing through the external circuit
which means if we go back to our
expression right here if we have no
current flowing through that J is equal
to zero and now that R sub s term
disappears so we've come up with a
clever way to drop all of our R sub
asses out of that expression and the
only thing that matters essentially is
is well some degree shunt but this is
essentially the highest IV curve that
one could possibly obtain in the absence
of series resistance and that's what you
see right here that's this Delta in
between your illuminated IV curve what
is measured using the solar simulator
and your son's V OC curve which is
measured in the absence of series
now this works well with most materials
if you have a very high capacitance in
your device you'll want to look very
carefully at this at this decay right at
the light intensity decay if your
capacitance in your device is very large
it might actually flatten out the
voltage response so you want to make
sure that the time RC time constant of
your devices is matched to the the
flashbulb decay time that's just one
word of warning for those working on
high-voltage or organic materials any
questions on the Sun vo C measurement
this is gives you what's called an
implied IV curve and that is as a would
say in in the best case scenario what
you would get from the solar cell in the
absence of any series resistance losses
No
yeah it is important it would be a
different in essence it would be a
different current response right if you
didn't have the same exact solar
spectrum now that's a very important
point if you're venturing outside of say
silicon based devices and you're more
sensitive to the infrared or the UV you
really want to make sure that you
measure the intensity as a function of
wavelength output of that bulb otherwise
your you might be higher or lower
during the sun's boc measurement for a
silicon-based device majority falls
within the specified regime down here
actually right here sorry on this
diagram that little spot right there
that is a small calibration solar cell
of known short-circuit current an open
circuit voltage so that's used to
calibrate for other silicon devices if
you're moving away from silicon that
becomes an issue
correctible you can measure the spectral
response of that light source and
compare it to the solar simulator and do
the normalization accordingly here's
what I recommend
with the last 15 minutes of class I
wanted to catch each of the teams and
talk about your class projects to make
sure that things were rolling along
I have feelers out to some of the
mentors who haven't responded yet and so
I just wanted to touch base with each of
you for about three minutes just to make
sure everything is rolling along
you