1

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

vikram-ece15@snu.edu.in 2

samarendra.singh@snu.edu.in

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.

2

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

- +

3

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.

4

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).

5

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.

6

(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.

7

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.

8

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%