Generating a Protocol to Model Organic Photovoltaic...
Transcript of Generating a Protocol to Model Organic Photovoltaic...
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Generating a Protocol to Model Organic
Photovoltaic Devices (OPVs) from Material
Properties to their Quantum Efficiencies Vikram Singh1,Samarendra P Singh2
Electronics and Electrical Department, Shiv Nadar University
Village Chithera,Greater Noida, India. 1
Abstract— The demand for developing a design for better harvesting the natural and renewable resources for power is
increasing. This paper aims to develop a protocol to model
organic photovoltaic cells with modifications in models for
inorganic counterparts.
Keywords— Organic photovoltaic cells, modelling, matlab, organic semiconductors, green technologies, solar cells.
I . INTRODUCTION
A. Prologue
With growing demand of power and non-renewable sources
reaching to their limit there is need to develop more efficient and
inexpensive renewable energy sources. Market of photovoltaic
sources is on expansion with new devices achieving more and more
efficiency and getting less expensive. The greatest challenge that
organic PV cells face against their inorganic counterpart is their
less payback for their whole life time as their production cost is
more than they produce in their lifetime. Thus inorganic solar cells
were mostly in use, organic solar cells remained mostly functional
only in laboratories.
In recent times with development of new polymers and
techniques 1, efficiency up-to 8.5% has been achieved. These
devices are slowly coming into the market in various
applications. Organic Light Emitting Diode (OLEDs)
televisions and mobile screens are one of the notorious
examples, but this is just the beginning.
Organic semiconductors form a very flexible devices which
boost their uses in various activities. Moreover Si and other
inorganic semiconductors though being abundant in nature
are limited resources and very costly.
B. Materials & Device Structures
Organic polymers having delocalized π electron can absorb
sunlight and create bounded charge carriers called excitons.
Since because of higher dielectric constant (Ɛr~4) have high
binding energy as:
Fbinding= 𝑒2
4𝜋ɛ0ɛ𝑟
where e is electronic charge ɛ0 and is the permittivity of
the free space.
On account of this high binding energy excitons do not
dissociate easily into a hole and an electron. The hole and
the electron tend to recombine causing geminate pair
recombination. Thus extra offset and electric field is
required in order to dissociate them into free charge carriers
for conduction. The excitons have to reach to the Donor-
Acceptor interface within their life time, thus an interface
should be available for an exciton within its diffusion length
(i.e. ~10-20nm). Thus different device structures is used to
provide a large interface area for the device to achieve high
quantum efficiencies. The dissociation energy is provided by
the energy offset between HOMO (highest occupied
molecular orbit) level of the donor materials (usually P3HT,
MDMO/PPV etc.) and LUMO ( lowest occupied molecular
orbit) level of the acceptor materials(PCMB, C60 etc.). After
dissociation these carriers are to be transported to their
respective contact terminals, avoiding bimolecular
recombination.
Proper modeling of these devices is very difficult after
fabrications as changes in one parameter could affect
another, causing an unexpected response. There are no
proper equations to study their performances on real basis.
Though they are studied by relating them with their
inorganic equivalents.
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Figure 1: Equivalent PV cell model
LiF
Figure 3: OPV device structure for which the simulation will be performed.
Figure 2: IV characteristics
This paper aims to develop a protocol and endorse effects of
parameters of the organic devices in previously inorganic
device models for to create an accurate prototype of organic
photovoltaic cells. This paper is divided into several part,
first collecting the factors then to apply them to develop and
accurate digital prototype and then calculate the
approximate effect of various parameters and processes on
the behavior of the device. Then those observed behaviors
will be applied for modification of the current PV cells so as
to maximize efficiency for the limited resource available.
MATLAB and Simulink software is used for simulation and
verification of the theory.
II. PV MODULE
Generally a solar cell is modelled using a diode model as
particularized below:
Which can be illustrated as
I = -Id+IR- Ip eq.0
I = Is [exp(eV
ἡkT)-1]+ IRp -Ip
Here Id is the diode current, V is the voltage, ἡ is the diode
ideality factor, Is is the saturation current of the diode, k is
the Boltzmann constant and T is the temperature in degree
Kelvin. This equation is further modified to model the
organic photovoltaic cell as:
I = Is[exp(e (V−IRs)
nkt-1)]+
V−IRs
Rp-Ip eq.1
Ip can be estimated with
Ip = Isc G(1+αT)
1000
G is the irradiation in W/m2, α is the temperature coefficient
of the Isc and Isc is the short circuit current or the current at
cell voltage=0.
Further Is is calculated with
Is = 𝐼𝑝
exp(𝑉𝑜𝑐+𝛽𝑇
𝑘𝑇)−1
Where Voc is the open circuit voltage i.e. where current=0, β
is the temperature coefficient of the Voc. With these few
approximation and experimentally finding the value of the
other constants of PV model can be used to simulate up to a
fair estimate.
But this structure mostly fails to be applied to an organic PV
model, since an OPV has many different parameters whose
negligence causes unexpected results.
Thus it is required to include all what the design of an OPV
demands for an accurate results. In this section various
parameters will be approximated to a good accuracy from
experimental or theoretical relations of organic devices .
Results will be obtained for P3HT: PCBM solar cells and will
be verified with experimental values. Values of few
parameters like n (charge current density), μ (mobility at zero
electric field), Ɛr (dielectric constant) etc. has been taken
directly (experimental values) for better results.
A. Calculating Vfb & Voc
Flat band voltage regime is obtained by the equation -
Vfb = Δϕ= W𝐼𝑇𝑂−W𝐴𝐿
e in eVs.
Vfb = WITO- WAL in Volts. eq.2
Aluminum
Active Layer (P3HT: PCBM)
PEDOT: PSS
ITO
Glass
- +
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where WITO is the work function of the ITO layer whereas the
WAL is the work function of the aluminum contact.
At Voc the resulting current density is zero. A supplementary
voltage is applied to obtain the drift current (let VA). Voltage
VA is automatically equal to the required potential to generate
drift current. Since
J=JDrift + JDiff
J=enμE+ Dn 𝜕𝑛
𝜕𝑥 =0
which implies that drift and diffusion current will be equal
and thus enμE= -Dn 𝜕𝑛
𝜕𝑥.
Dn 𝜕𝑛
𝜕𝑥 = -enμ
𝜕(VA)
𝜕𝑥
Thus the open circuit voltage is given by
Voc= Vfb + VA. eq.3
If we assume Fermi level pinning in device
WITO ~ ELUMO acceptor and WAL ~ EHOMO donor.
Thus using eq.2 in eq.3, we get
Voc= (EHOMO donor -ELUMO acceptor) - 0.3. eq.4.1
For P3HT: PCBM material:
Voc= (5.2-4.3)-0.3=0.7 Volts
That is also can be related from the formula :
Voc = Eg – ϕn- ϕp eq.4.2
Where Eg is the effective band-gap (EHOMO donor -ELUMO acceptor)
and ϕn and ϕp are electron and hole injection barrier. These
two sum up to around 0.3eV thus matches to eq.4.1.
We must use this formula in our program model to obtain the
value of Voc from the LUMO level of acceptor and HOMO
level of the donor, in order to match the simulated IV curve
to the real characteristic curve.
B. Computing Mobility
The mobility of the hole is less than the electron mobility.
According to the Pool-Frenkel effect the mobility is directly
proportional to the electric field as and is also dependent on
the temperature as:
μ = μ 0 exp[e
32⁄
2kT(
E
πɛ0Ɛr)
12⁄
] eq.5
where k is the Boltzmann constant, T is the temperature, Ɛ𝑟
is the dielectric constant of the material, e is the electronic
charge, E is the applied electric field, Ɛ0 is the permittivity of
the free space. If we know the mobility at zero electric field
we can add this equation as offset for increasing electric field
and obtain the value of the mobility.
C. Obtaining Isc
Concerning the case of ideal contacts, Isc can be determined
from the product of the charge current density (n), mobility
at the particular temperature (μ), electronic charge (e) and
applied electric field (E) as:
Isc = neμE eq.6
We can observe that electric field increases the mobility by
many fold (refer to fig.4), which causes Isc to increase.
Electric field also directly affects Isc, but it is encouraged to
apply a reasonable electric field as we aim to extract more
power and there will be no sense in applying voltage more
than we receive. After certain point mobility increase goes to
saturation and thus there is not much increase in power on
account of increase of applied electric field.
Thus on feeding the values of E as 3x106 V/m and observing
the value of mobility at the corresponding electric field from
eq5 and fig.4 as 2x10-4. The value of charge current density
for fully illuminated device is when taken as 1x1015, which
gives the value of the short circuit current as 10.6 mA.
D. Series Resistance
Initial value of series resistance Rs0 is obtained from the slope
of the IV curve in dark at the voltage =Voc.
Thus Rs0 = 𝑑𝑉
𝑑𝐽 at V=Voc.
Since during absence of light there is no photovoltaic current
(i.e Ip=0), and assuming that parallel resistance is high that
ignoring IRp, the eq.0 (I=IRp+Id-Ip) reduces to:
I=Id
Figure 4: Manual plot of mobility on Electric Field, showing how mobility changes with the electric field. Hole mobility at
zero electric field is taken to be 1x10-4 cm2V-1s-1 @ Ɛ𝑟 =4 and
T=300k for P3HT: PCBM device.
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Figure 6: Plot of 𝑑𝑉
𝑑𝐽 from the original dark characteristics.
Figure 5: IV characteristics in dark
The equation can be more evaluated as:
I= Is [exp(eV
ἡkT)-1] eq.7
which is nothing but the diode current depending on the
diode’s ideality factor ἡ.
Plotting the IV characteristics graph for dark current is the
diode characteristic plot modelled for the concerned organic
device with the diode ideality factor.
As discussed we must now calculate 𝑑𝑉
𝑑𝐽 from the graph
using gradient function and on plot it.
The above relation gives the value of Rs0 was approximately
0.01 ohms.
Total series resistance can now be calculated as given by the
relation:
Rs = Rs0 - 1
Is e
ἡ𝑘𝑇exp(
𝑒𝑉𝑜𝑐
ἡ𝑘𝑇) eq.8
where Is the saturation current given by the relation as:
Is = 𝐼𝑝
𝑒𝑥𝑝 (𝑒𝑉𝑜𝑐
ἡ𝑘𝑇−1)
Ip can be calculated as:
Ip =Isc 𝐺
1000
where G is the irradiation in W/m2.
III. CONSTRUCTION OF THE MODEL
Using Newton’s method to finally sum up the results, that
approximates behavior of the device up to fairly accurate
results.
I = I - 𝐼𝑠𝑐−𝐼−𝐼𝑠(𝑒𝑥𝑝
(𝑉+𝐼𝑅𝑠
ἡ𝑘𝑇)
−1)
−1−𝐼𝑠(𝑒𝑅𝑠
ἡ𝑘𝑇)𝑒𝑥𝑝
(𝑉+𝐼𝑅𝑠
ἡ𝑘𝑇)
eq.9
where V is the voltage that has to generated by sweeping from
zero to at least Voc for measuring the current at all those
values of voltages for the IV plot. The equation is put it in a
loop for repetition for at least 5-10 times, so as to get more
accurate values. Other parameters are as described before.
A. Traditional Model
The above model’s circuits can also be simulated using
Simulink by the following arrangement (fig.7), for easy and
quick response.
The below shown arrangement gives very limited and
inaccurate values for the organic PV device. Thus we will
stick to the model which we have developed through the
paper, in order to completely exploit the behavior of an OPV
device.
Figure 7.1: General Model of the solar cell.
Figure 7.2: IV curve opted from the above model (fig.7.1).
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B. Calculating Efficiency
We are now in condition to be able to calculate the efficiency
from the available data. We can calculate the fill factor (FF)
and efficiencies using following two methods :
1) Using the following equations:
FF = Vn−ln (Vn+.72)
Vn +1 eq.10
where Vn is the normalized Voc and is calculated as:
Vn = eVoc
ἡkT
The eq.10 is standardized to work at room temperature. We
already have calculated Isc and Voc from the previous
equations and can be put to use to calculate the power
conversion efficiency (PCE) from the relation:
PCE = Isc Voc FF
Pi eq.11
where Pi is the incident power and the equation is
standardized to give power conversion efficiencies accurately
at irradiance of G=1000 w/m2 or 100mW/cm2.
2) From the IV characteristics
We can obviously calculate the fill factor from the IV plot
obtained from the model response.
The voltage and the current value at the maximum power
point from the IV characteristics corresponds to the Vmp and
Imp. The fill can be calculated as
FF= ImpVmp
IscVoc eq.12
where Isc and the Voc are short circuit current and the open
circuit voltage respectively. The power conversion efficiency
can be obtained from the eq.2.
C. Developing Protocol
We now have obtained most of the variables, constants and
equations required to exploit the behavior of an OPV device.
It is now required to assemble all the calculations into one
protocol to create a digital prototype for the simulation of the
device.
IV. SIMULATION OF THE CREATED MODEL
The protocol can now be put into the Matlab, as a simple
program. The material properties and other conditions are fed
as input to generate the characteristics of the particular
device.
Here is the result of the simulation for a P3HT: PCBM
device, in our developed program.
Figure 8: Obtaining Vmp and Imp points from the IV characteristics
Figure 9: The protocol developed for modelling the OPV device.
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(a) (b)
A. Effect of difference between HOMO level of donor material
and LUMO level of the acceptor material
An enough offset is required to provide energy for the
dissociation of the exciton generated. This offset provides
energy at the interface of the material for the process of
dissociation.
The low level of ΔELUMO (fig.11) suppresses the quantum
efficiency due to increase in geminate pair recombination,
whereas higher level of which results in loss of power. For
consideration of the material these two facts must be kept in
mind. We can observe the effect of the increasing ΔELUMO on
decreasing the LUMO level of the acceptor material, through
the simulation on our model.
This simulation is valid in this particular case only as it may
affect other factors for the device, causing a slight change in
the response curve.
B. Effect of mobility on the behavior of the device
The mobility can be a factor to the performance of the device.
With low mobility the recombination increases manifold and
damps the efficiency of the device heavily. This is actually
one of the measure problems in organic PV devices and one
of the main parameters responsible for the low efficiency of
the organic PV devices.
Figure 11: D- A Interface for the P3HT: PCBM device.
Figure 10.3 The data obtained for the whole range of
operating points (v & I) which can be stored as an excel file for further investigation and study. One may have to adjust a thing or two to get precise results.
Figure 10.2: Results obtained from the program by the methods for finding the fill factor (FF) and power
conversion efficiency (PCE), as discussed in the section 3.2
Figure 10.1: Characteristic plot for the device. Data is obtained for simulation at the light intensity of 1000 W/m 2 and 27o Celsius temperature.
Figure 12 (a) Effect of increase of ΔELUMO between the donor
and acceptor material. (b) Effect on the efficiency of the device, calculated through the model.
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Figure 14.1 IV curve for different irradiance.
(a)
(b) (c)
The behavior of a device with increasing mobility (1Times,
1.5Times and 2Times of the original) has been simulated on
the protocol developed earlier.
Figure 13.1 IV characteristics for changing mobility
Mobility Fill Factor PCE
1 Times (1x) 0.7076 5.25%
1.5x 0.6447 7.17%
2x 0.5944 8.44%
Tab1.
Data was obtained for default irradiance and temperature
values i.e. 1000 W/m2 and 27o Celsius respectively. It was
observed that due to expanded/stretched graph (Isc increasing
manifold), FF factor may have seemed to have reduced but
overall power conversion was increased.
C. Irradiance Effect
It is expected that the amount of light that is being received
by the device directly affects the performance of the device.
Here is the response from the model which we have
developed through this paper.
The curve gets amplified and device performance is
increased.
Tab2.
The efficiency table can be prepared from the data from our
model’s simulation.
D. Other factors
Other factor which play an important role in the functioning
of an OPV device can one way or the other included in the
model. For example, we have calculated Rs from the dark
current curve, but for obtaining a better operating point , the
effect of series resistance can be analyzed by bypassing
different values of series resistance.
Irradiance Fill Factor PCE
1000 W/m2 .7076 5.25%
1500 W/m2 1.0324 7.66%
2000 W/m2 1.3270 9.84%
Figure 13.2 Power with increase in the mobility.
Figure 15: IV curve and Power curve obtained for
(a) Rs= 0.007 ohms, (b) 3 times Rs, (c) 5 times Rs . Simulated at irradiance of 1000W/m2.
Figure 14.2: The power curve for the different light intensity.
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Figure 16.1: IV characteristics for different temperature
Figure 16.2: Effect of increasing temperature on output power
Tab3.
It can observed that increasing resistance distorts the curve
and damp the efficiency of the device, thus extra care must
be taken for Rs during the device modelling.
Temperature of device operation is through an outer
parameter also determines the working efficiency of the
device. Until now we have been operating our device at a
constant room temperature. On working our device at
different temperature and other parameters at constant but
plausible values we can clearly observe the effect of
temperature.
‘
.
Tab4.
Important: We can calculate responses for change in most of
the parameters following the prototype model developed, but
it is your device’s specifications comprised of values for all
the parameters that will generate an appropriate curve for
your device.
V. CONCLUSION
Thus with a proper protocol involving all the parameters for
the organic devices, simulation can be done up to a high
accuracy, including most of the parameters . Real device
modelling of organic devices are very hefty and costly thus a
proper simulation model can be followed for the device
before finalizing the model. In this way the structure of the
model can be more closely moderated to achieve high
efficiency within the cost and limited resources available.
REFERENCES
[1] Serap Guner et al. , “Conjugated Polymer-Based Organic
Solar Cells,”, 2006 © American Chemical Society. doi:
[10.1021/cr050149z]
[2] Jonathan D. Servaits et al., “Organic Solar Cells: A new
look at traditional models,” Energy Environ. Sci., 2011, ©
The Royal Society of Chemistry. doi: [10.1039/c1ee01663f]
[3] R. A. Marsh et al., “A microscopic model for the behavior
of nanostructured organic photovoltaic devices, ” 2007 ©
American Institute of Physics. doi: [10.1063/1.2718865]
[4] Andre Moliton and Jean-Michel Nunzi, “How to model
the behavior of organic photovoltaic cells,” 2005 © Society
of Chemical Industry. doi: [10.1002/pi.2038]
[5] Miguel Pareja Aparicio, “PV Cell simulation with
QUCS,” July 2013.
[6] Shamica Green, “A Circuit Model for Polymer Solar
Cells,” unpublished.
Rs Fill Factor PCE
Original (1x) 0.7076 5.25%
3x 0.5541 4.11%
5x 0.4248 3.15%
Temperature Fill Factor PCE
30o C 0.7004 5.19%
50o C 0.6591 4.83%
70o C 0.6033 4.47%