research article numerical procedure for optimizing...

Research ArticleNumerical Procedure for Optimizing Dye-Sensitized Solar Cells

Mihai Razvan Mitroi1 Laurentiu Fara12 and Magdalena Lidia Ciurea23

1 University Politehnica of Bucharest 313 Splaiul Independentei 060042 Bucharest Romania2 Academy of Romanian Scientists 54 Splaiul Independentei 050094 Bucharest Romania3 National Institute of Materials Physics 105 bis Atomistilor Street PO Box MG-7 077125 Magurele Romania

Correspondence should be addressed to Magdalena Lidia Ciurea ciureainfimro

Received 23 July 2013 Revised 13 November 2013 Accepted 29 November 2013 Published 5 January 2014

Academic Editor Hyeong-Ho Park

Copyright copy 2014 Mihai Razvan Mitroi et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

We propose a numerical procedure consisting of a simplified physical model and a numerical method with the aim of optimizingthe performance parameters of dye-sensitized solar cells (DSSCs) We calculate the real rate of absorbed photons (in the dyespectral range) 119866real(119909) by introducing a factor 120573 lt 1 in order to simplify the light absorption and reflection on TCO electrode Weconsider the electrical transport to be purely diffusive and the recombination process only to occur between electrons from the TiO

2

conduction band and anions from the electrolyte The used numerical method permits solving the system of differential equationsresulting from the physical model We apply the proposed numerical procedure on a classical DSSC based on Ruthenium dye inorder to validate it For this we simulate the J-V characteristics and calculate the main parameters short-circuit current density 119869scopen circuit voltage 119881oc fill factor FF and power conversion efficiency 120578 We analyze the influence of the nature of semiconductor(TiO2) and dye and also the influence of different technological parameters on the performance parameters of DSSCsThe obtained

results show that the proposed numerical procedure is suitable for developing a numerical simulation platform for improving theDSSCs performance by choosing the optimal parameters

1 Introduction

The technology and materials used for the third generationsolar cells give the opportunity to obtain cells with highefficiency [1ndash5]The solar cells based on dye-sensitized nano-structure with mesoporous metal oxides (DSSCs) haveattracted considerable attention since the work of OrsquoReganand Gratzel [6] their manufacturing being environment-friendly and energy-efficient [1 7] Up to now certified effi-ciencies over 10 under standard conditions or even higher(124) at the laboratory scale were reported [7ndash10] Basedon the low cost of materials and the simplicity of fabricationprocess DSSC can have lower fabrication costs than con-ventional silicon-based solar cells Taking into account thisadvantage the improvement of DSSC parameters for makingthem widely used appears as a strong necessity

Further optimization of the DSSC parameters requires abetter correlation between interrelated processes of transportand accumulation of electrons in themesoporous oxide phase

and recombination of electrons with electron acceptors [11]In order to understand the different processes governingthe DSSCrsquos mode of operation and to enhance the DSSCsperformance modeling of processes and numerical simu-lation of the cells were carried out [12ndash23] The thicknessmorphology (particle diameter and porosity) for the TiO

2

layer electronmobility and recombination rate (electron life-time) absorption spectrumof the dye thickness andmaterialquality of transparent conductive oxide (TCO) layers andthe used electrolyte determine the 119869-119881 characteristics [1718 20ndash22 24] Consequently the extracted parameters fromsimulation the short-circuit current density 119869sc the opencircuit voltage119881oc the fill factor FF and the power conversionefficiency 120578 were analyzed

In the present paper we propose a numerical procedurefor optimizing the DSSCs consisting of a simplified physicalmodel and a numerical method capable of solving the systemof differential equations resulted from the physical modelWe applied this proposed procedure on a DSSC with Ru dye

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2014 Article ID 378981 6 pageshttpdxdoiorg1011552014378981

2 Journal of Nanomaterials

in order to show its validity For this the current density-voltage (119869-119881) characteristics were simulated and the mainparameters 119869sc 119881oc FF and 120578 were obtained and discussedThe influence of the thickness of TiO

2film and electron

lifetime on the cell performance parameters was analyzedaiming to be used in the cell manufacturing

2 Physical Model and Numerical Method

We use a classical DSSC which is presented in Figure 1This device contains two electrodes made of TCO glasscommonly used being fluorine-doped tin oxide (FTO) Theilluminated electrode is coated with a nanoporous TiO

2layer

which is also coated with amonolayer of the Ru-complex dyeOn the counter electrode of TCO glass a thin layer of Pt(sim5 nm) which acts as a catalyst for the redox reaction isdeposited [25] The space between the two electrodes isfilled with an electrolyte (propyl methyl imidazolium iodide)containing an iodidetriiodide (119868minus119868minus

3) redox couple

In a DSSC under visible light an electron from the dyemolecule is excited then injected into the conduction band ofTiO2nanostructured semiconductor and finally collected by

the TCO glass electrode and transported in the external loadThe positive charge (dye cations) is reduced by receiving anelectron from the iodide ion (119868

minus) which will be subsequently

regenerated by reducing triiodide ions (119868minus3) at the platinized

counter electrodeBy using the nanostructured TiO

2 the depletion process

is less pronounced so that under reverse bias the electricfield is negligible [14 26] The origin of the photovoltage isexplained by a built-in potential barrier between TiO

2semi-

conductor and the TCO electrode andor by changing theposition of Fermi level due to the electron injection [26] Themost probable recombination process takes place betweenelectrons from TiO

2and 119868minus

3ions [18 19]

In the ideal case the rate of the absorbed photons in thevolume unit can be written as

119866ideal (119909) = int

1205822

1205821

120572 (120582) 120601ideal (120582) exp [minus120572 (120582) sdot 119909] 119889120582 (1)

where 119909 isin [0 119889] describes the position inside the TiO2film

(including the dye) with a thickness 119889 120582 is the wavelength ofthe radiation limits 120582

1and 120582

2are imposed by the absorption

characteristics of the dye through the absorption coefficient120572(120582) and 120601ideal(120582) is the spectral incident photon flux density

In the real case the rate of the absorbed photons119866ideal(119909)in the volume unit is reduced to 119866real(119909) due to the lightabsorption in TCO glass electrodes and to the reflection onto[16] We describe the contributions of these processes by afactor 120573 lt 1 aiming to propose a simplified model to be usedfor designing and optimizing any type of DSSCs Therefore119866real(119909) is given by

119866real (119909) = 120573 sdot 119866ideal (119909) (2)

The rate of electron injection 119866inj(119909) should take intoaccount the injection efficiency 120578inj [11] so that

119866inj (119909) = 120578inj sdot 119866real (119909) (3)

Counterelectrode (TCO)

Spacer

FTO

ElectrolytePlatinized

NanoporousFTO

Illuminatedelectrode (TCO)

(+)

TiO2 with dye

(minus)

Figure 1 Sketch of a classical DSSC Nanoporous TiO2with dye has

119889 thickness

In our simplified model we consider the electrical trans-port to be purely diffusive and therefore it is described by adiffusive transport equation for the electrical current density119869 [17 19] We neglect the internal electric field generated byunbalanced local charge because of its very low value [12 17]The electron density 119899(119909) in the conduction band of theTiO2layer is described by the continuity equation in quasi-

stationary regime In this case the system of equations hasthe following form

minus1

119890

119889119869 (119909)

119889119909= 119866inj (119909) minus 119877 (119909) (4)

119869 (119909) = 119890119863119889119899 (119909)

119889119909 (5)

where 119890 is the elementary charge 119909 describes the positioninside the TiO

2film119909 isin [0 119889]119877(119909) is the recombination rate

and119863 is the electron diffusion coefficientWe neglect the trappingdetrapping processes so that in

the continuity equation (see (4)) the corresponding termsdo not appear [15] Also we assume that the recombinationprocess takes place only between electrons from conductionband of TiO

2layer and anions present in the electrolyte

[18] Consequently the recombination rate is proportional to119899(119909) minus 119899

0 so that

119877 (119909) =119899 (119909) minus 119899

0

120591 (6)

where 1198990is the electron density at equilibrium (in the dark)

and 120591 is the electron lifetime

The boundary conditions are the following

(1) Assuming that electrons are extracted by applicationof an external voltage 119881 the boundary condition at119909 = 0 is

119899 (119909)|119909=0 = 119873119888exp(minus

119864 minus 119890119881

119896119861119879

) (7)

Journal of Nanomaterials 3

where 119873119888is the density of states in the conduction

band of TiO2semiconductor given by the formula

119873119888= 2 (

2120587119898lowast

119890119896119861119879

ℎ2)

32

(8)

where 119898lowast

119890is the effective mass of the electron 119896

119861is

Boltzmann constant ℎ is Planck constant119879 is the celltemperature and 119864 = 119864

119888minus 119864119865is the energy between

the conduction band edge 119864119888and the Fermi quasi-

level 119864119865

(2) Assuming that all the electrons are collected at 119909 = 119889

(there is no recombination process inside TiO2film

meaning that TiO2film has a good quality from the

technological point of view) the boundary conditionat 119909 = 119889 is

119889119899 (119909)

119889119909

10038161003816100381610038161003816100381610038161003816119909=119889

= 0 (9)

The open circuit voltage119881oc is derived from the condition119869 = 0 and is given by the expression

119881oc =119896119861119879 ln ((120591 sdot 119866inj (0) + 119899

0) 119873119888) + 119864

119890 (10)

where 119866inj(0) is the rate of electron injection at 119909 = 0 whilethe short-circuit current density 119869sc is obtained for thecondition 119881 = 0

The system of differential equations (4) and (5) togetherwith boundary conditions (see (7) and (9)) has no enoughconditions at 119909 = 0 but has the boundary condition at 119909 =

119889 (see (9)) This problem is known as ldquothe boundary valueproblemrdquo being defined by differential equations in whichsome conditions are specified at the initial point while theothers are specified at the end point In order to solve thissystem we used a numerical method based on the ldquoshootingmethodrdquo [27] which generates different values for the initialcondition at 119909 = 0 until the final condition at 119909 = 119889 issatisfied We used this method in a program developed inMathcad

Consequently the numerical procedure we propose fordesigning and optimizing any type of DSSCs considers theessential processes which occur in a real DSSC and its tech-nological parameters and simplifies the others for examplethe contribution of the light absorption and reflection on theTCO electrodes by introducing 120573 lt 1 for obtaining 119866real(119909)

3 Results and Discussion

In order to validate our numerical procedure (simplifiedmodel and numerical method) we apply it on a DSSC basedon Ru dye and simulate the 119869-119881 characteristics For this wetook into account the absorption coefficient 120572(120582) of the Rudye between the spectral limits 120582

1= 300 nm and 120582

2=

800 nm where its absorption is very good (sim103Mminus1 cmminus1)[28] The numerical procedure can be applied on a DSSCbased on a different dye by changing the spectral limits and

Table 1 The constants and parameters used in simulation

Parameters Value119898lowast

11989056119898119890(119898119890= electron mass)

T 300K1198990

1017 cmminus3

119864 = 119864119888minus 119864119865

09 eV120578inj 095D 5 sdot 10

minus5 cm2s

0

5

10

15

0 02 04 06 08Voltage (V)

Curr

ent d

ensit

y (m

Ac

m2)

Figure 2 119869-119881 characteristics obtained for 120578inj = 095 119863 = 5 sdot

10minus5 cm2s 120573 = 09 and 119889 = 20 120583m and for different values of the

electron lifetime 120591◼ 120591 = 2ms o 120591 = 10ms ∙120591 = 20ms998779120591 = 50ms

Table 2 The values of 119869sc 119881oc FF and 120578 obtained for different 120573

120573 119869sc (mAcm2) 119881oc (mV) FF 120578 ()08 11170 819 0828 757209 12470 822 0828 8482095 13120 823 0827 89371 13770 824 0827 9392

the absorption coefficient For the incident flux density weconsidered the AM15G spectrum [29] The other constantsand parameters used in the simulation were taken from theliterature [11 12 21] and are presented in Table 1

Figure 2 shows the simulated 119869-119881characteristics obtainedfor 119889 = 20 120583m and 120573 = 09 and different values for theelectron lifetime 120591 in the conduction band

Thevalues obtained for 119869sc119881oc FF and 120578using the param-eters 120591 = 20ms and 119889 = 20 120583m and different values for 120573 arelisted in Table 2 One can see that an increase of 120573 with 20(by using suitable TCO electrodes) produces an increase ofboth 119869sc and 120578 with about 24 while 119881oc and FF remainpractically constant

The simulated values for 119869sc 119881oc FF and 120578 as a functionof the TiO

2film thickness using 120591 = 20ms are presented in

Table 3 According to this Figures 3(a) and 3(b) present the


6

8

10

12

14

0 10 20 30 40 50

J sc

(mA

cm2)

d (120583m)

(a)

4

5

6

7

8

9

0 10 20 30 40 50d (120583m)

120578(

)

(b)

Figure 3 The thickness dependence of 119869sc (a) and 120578 (b) calculated for 120578inj = 095119863 = 5 sdot 10minus5 cm2s 120573 = 09 and 120591 = 20ms

Table 3 The values of 119869sc 119881oc FF and 120578 obtained for different TiO2thicknesses

d (120583m) 119869sc (mAcm2) 119881oc (mV) FF 120578 ()2 6160 822 0842 42625 10564 822 0838 727610 12498 822 0833 855315 12601 822 0830 858920 12470 822 0828 848230 12320 822 0827 836950 12275 822 0826 8336

thickness dependence of the short-circuit current density 119869scand the power conversion efficiency 120578 the TiO

2film thick-

ness being an important technological parameter for design-ing and optimizing the cell One can see that both 119869sc and120578 increase with the film thickness up to maximum values of119869sc = 12601mAcm2 and 120578 = 8589 respectively reachedfor 119889 = 15 120583m By further increasing the film thicknessup to 50 120583m they insignificantly decrease (2-3) Conse-quently a thicker layer will not bring any improvement to119869sc or 120578 (helpful information for design and technologicalprocesses) Also one can observe that the increase of filmthickness from 2 to 10 120583m does not influence the open circuitvoltage119881oc (remains constant) and the fill factor FF (decreaseswith about 2)

In Table 4 the values for 119869sc 119881oc FF and 120578 calculated fordifferent values of the lifetime 120591 using 119889 = 20 120583m are givenFigures 4(a) and 4(b) present the corresponding curves thatis the lifetime dependence of the short-circuit current 119869sc andthe power conversion efficiency 120578 They show that both 119869scand 120578 significantly increasewhen 120591 increases up to 50msThismeans that if other materials instead of TiO

2(120591 takes values

Table 4 The values of 119869sc 119881oc FF and 120578 obtained for differentelectron lifetimes 120591

120591 (ms) 119869sc (mAcm2) 119881oc (mV) FF 120578 ()2 9349 766 0833 59685 10267 787 0825 667410 11274 804 0831 753220 12470 822 0828 848230 13210 832 0824 905350 14107 845 0818 9737100 15123 863 0823 10742200 15840 881 0827 11544

up to 50ms) are used the performance parameters of DSSCcan be controlled and consequently optimized

The values for all parameters we obtained from simula-tion are in good agreement with those reported in the litera-ture for this type of DSSC [14 19 21 25 30ndash32] which demon-strate that our proposed numerical procedure is valid andversatileTherefore it can be used for designing and optimiz-ing DSSCs

4 Conclusions

In this paper we propose a numerical procedure for opti-mizing the parameters of any type of DSSC consisting of asimplified physical model and a numerical method capableof solving the system of differential equations resulted fromthe model

We applied this procedure on a classical DSSC based onRu dye by simulating the 119869-119881 characteristic and calculating allmain parameters 119869sc 119881oc FF and 120578 and the obtained resultsare in good agreement with those reported in the literaturewhich validate our proposed procedure


8

10

12

14

16

0 50 100 150 200

J sc

(mA

cm2)

120591 (ms)

(a)

5

6

7

8

9

10

11

12

0 40 80 120 160 200120591 (ms)

120578(

)

(b)

Figure 4 The lifetime dependence of 119869sc (a) and 120578 (b) using 120578inj = 095119863 = 5 sdot 10minus5 cm2s 120573 = 09 and 119889 = 20 120583m

For this we analyzed the influence of the nature of semi-conductor and dye and also the influence of different techno-logical parameters on the performance parameters of DSSCsThus for obtaining the real rate of the absorbed photons119866real(119909) we simplified the light absorption and reflection ofTCO by introducing the factor 120573 and we considered thenature of dye by using the specific absorption coefficient120572(120582) We analyzed the influence of TiO

2semiconductor

thickness and electron lifetime in the conduction band on themain cell parameters We showed that the increase of TiO

2

semiconductor thickness over the optimal thickness of 15 120583mdoes not influence the 119869sc and 120578 values (119869sc = 12601mAcm2and 120578 = 8589)We obtained a similar result for the electronlifetime higher than 40ndash50ms The obtained results in goodagreement with the literature validate our numerical proce-dureThe analysis made on this classical DSSC based on TiO

2

with Ru dye can be extended to any other DSSCsThe proposed numerical procedure allows a comprehen-

sive analysis of the performance parameters of DSSCs andpermits the development of a numerical simulation platformfor designing and optimizing any type of DSSCs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was partially supported by the Romanian NationalAuthority for Scientific Research through the CNCS-UEFISCDI under Contract no PN II-PT-PCCA-92012

References

[1] H S Jung and J K Lee ldquoDye sensitized solar cells for eco-nomically viable photovoltaic systemsrdquo The Journal of PhysicalChemistry Letters vol 4 no 10 pp 1682ndash1693 2013

[2] G Conibeer M Green R Corkish et al ldquoSilicon nanostruc-tures for third generation photovoltaic solar cellsrdquo Thin SolidFilms vol 511 pp 654ndash662 2006

[3] R R King D C Law K M Edmondson et al ldquo40 efficientmetamorphic GaInPGaInAsGe multijunction solar cellsrdquoApplied Physics Letters vol 90 no 18 Article ID 183516 2007

[4] J G J Adams B C Browne I M Ballard et al ldquoRecentresults for single-junction and tandemquantumwell solar cellsrdquoProgress in Photovoltaics vol 19 no 7 pp 865ndash877 2011

[5] V Iancu M R Mitroi A-M Lepadatu I Stavarache andM L Ciurea ldquoCalculation of the quantum efficiency for theabsorption on confinement levels in quantum dotsrdquo Journal ofNanoparticle Research vol 13 no 4 pp 1605ndash1612 2011

[6] B OrsquoRegan and M Gratzel ldquoA low-cost high-efficiency solarcell based on dye-sensitized colloidal TiO

2filmsrdquo Nature vol

353 no 6346 pp 737ndash740 1991[7] A Yella H-W Lee H N Tsao et al ldquoPorphyrin-sensitized

solar cells with cobalt (IIIII)-based redox electrolyte exceed 12percent efficiencyrdquo Science vol 334 no 6056 pp 629ndash634 2011

[8] M Gratzel ldquoDye-sensitized solar cellsrdquo Journal of Photochem-istry and Photobiology C vol 4 no 2 pp 145ndash153 2003

[9] L Han A Islam H Chen et al ldquoHigh-efficiency dye-sensitizedsolar cell with a novel co-adsorbentrdquo Energy and EnvironmentalScience vol 5 no 3 pp 6057ndash6060 2012

[10] X YangMYanagida andL YHan ldquoReliable evaluation of dye-sensitized solar cellsrdquo Energy and Environmental Science vol 6no 1 pp 54ndash66 2013

[11] T Oda S Tanaka and S Hayase ldquoDifferences in characteristicsof dye-sensitized solar cells containing acetonitrile and ionicliquid-based electrolytes studied using a novel modelrdquo Solar


Energy Materials and Solar Cells vol 90 no 16 pp 2696ndash27092006

[12] J Ferber R Stangl and J Luther ldquoElectrical model of the dye-sensitized solar cellrdquo Solar Energy Materials and Solar Cells vol53 no 1-2 pp 29ndash54 1998

[13] L Peter ldquoTransport trapping and interfacial transfer of elec-trons in dye-sensitized nanocrystalline solar cellsrdquo Journal ofElectroanalytical Chemistry vol 599 no 2 pp 233ndash240 2007

[14] M Berginc M Filipic U O Krasovec et al ldquoOptical andelectricalmodelling and characterization of dye-sensitized solarcellsrdquo Current Applied Physics vol 10 no 3 pp S425ndashS4302010

[15] J Bisquert and I Mora-Sero ldquoSimulation of steady-state char-acteristics of dye-sensitized solar cells and the interpretation ofthe diffusion lengthrdquo Journal of Physical Chemistry Letters vol1 no 1 pp 450ndash456 2010

[16] J Halme P Vahermaa K Miettunen and P Lund ldquoDevicephysics of dye solar cellsrdquoAdvancedMaterials vol 22 no 35 ppE210ndashE234 2010

[17] M Onodera K Ogiya A Suzuki et al ldquoModeling of dye-sensitized solar cells based on TiO

2electrode structure modelrdquo

Japanese Journal of Applied Physics vol 49 no 4 Article ID04DP10 2010

[18] L Andrade J Sousa H Aguilar Ribeiro and A Mendes ldquoPhe-nomenological modeling of dye-sensitized solar cells undertransient conditionsrdquo Solar Energy vol 85 no 5 pp 781ndash7932011

[19] S Wenger M Schmid G Rothenberger A Gentsch MGratzel and J O Schumacher ldquoCoupled optical and electronicmodeling of dye-sensitized solar cells for steady-state parameterextractionrdquo Journal of Physical Chemistry C vol 115 no 20 pp10218ndash10229 2011

[20] D Gentilini A Gagliardi and A D Carlo ldquoDye solar cellsefficiencymaps a parametric studyrdquoOptical andQuantumElec-tronics vol 44 no 3ndash5 pp 155ndash160 2012

[21] K Nithyanandam and R Pitchumani ldquoAnalysis and design ofdye-sensitized solar cellrdquo Solar Energy vol 86 no 1 pp 351ndash368 2012

[22] P H Joshi D P Korfiatis S F Potamianou and K A ThThoma ldquoOptimum oxide thickness for dye-sensitized solarcells-effect of porosity and porous size a numerical approachrdquoIonics vol 19 no 3 pp 571ndash576 2013

[23] M R Mitroi and L Fara ldquoOrganic solar cells modelingand simulationrdquo in Advanced Solar Cell Materials TechnologyModeling and Simulation L Fara and M Yamaguchi Eds pp120ndash137 IGI Global 2013

[24] D M B P Ariyasinghe H M N Bandara R M G RajapakseK Murakami and M Shimomura ldquoImproved performanceof dye-sensitized solar cells using a diethyldithiocarbamate-modified TiO

2surfacerdquo Journal of Nanomaterials vol 2013

Article ID 258581 6 pages 2013[25] J S Agnaldo J C Cressoni and G M Viswanathan ldquoUni-

versal aspects of photocurrent-voltage characteristics in dye-sensitized nanocrystalline TiO

2photoelectrochemical cellsrdquo

Physical Review B vol 79 no 3 Article ID 035308 2009[26] M Gratzel ldquoPhotoelectrochemical cellsrdquo Nature vol 414 no

6861 pp 338ndash334 2001[27] ldquoSolving Boundary Value Problems in MathCadrdquo 2013

httpwwwchemmtuedu simtbcocm3450bvppdf [28] F Gao Y Wang D Shi et al ldquoEnhance the optical absorp-

tivity of nanocrystalline TiO2film with high molar extinction

coefficient ruthenium sensitizers for high performance dye-sensitized solar cellsrdquo Journal of the American Chemical Societyvol 130 no 32 pp 10720ndash10728 2008

[29] ldquoASTM G173-03 Reference Spectra Derived from SMARTSv 2 9 2rdquo 2012 httprredcnrelgovsolarspectraam15ASTMG173ASTMG173html

[30] B E Hardin E T Hoke P B Armstrong et al ldquoIncreased lightharvesting in dye-sensitized solar cells with energy relay dyesrdquoNature Photonics vol 3 no 7 pp 406ndash411 2009

[31] C-H Lee K-Y Liu S-H Chang et al ldquoGelation of ionic liquidwith exfoliated montmorillonite nanoplatelets and its applica-tion for quasi-solid-state dye-sensitized solar cellsrdquo Journal ofColloid and Interface Science vol 363 no 2 pp 635ndash639 2011

[32] TDittrichAOfir S Tirosh LGrinis andA Zaban ldquoInfluenceof the porosity on diffusion and lifetime in porous TiO2 layersrdquoApplied Physics Letters vol 88 no 18 Article ID 182110 2006

Submit your manuscripts athttpwwwhindawicom

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MaterialsJournal of


Nano

materials


Journal ofNanomaterials


in order to show its validity For this the current density-voltage (119869-119881) characteristics were simulated and the mainparameters 119869sc 119881oc FF and 120578 were obtained and discussedThe influence of the thickness of TiO

2film and electron

lifetime on the cell performance parameters was analyzedaiming to be used in the cell manufacturing

2 Physical Model and Numerical Method

We use a classical DSSC which is presented in Figure 1This device contains two electrodes made of TCO glasscommonly used being fluorine-doped tin oxide (FTO) Theilluminated electrode is coated with a nanoporous TiO

2layer

which is also coated with amonolayer of the Ru-complex dyeOn the counter electrode of TCO glass a thin layer of Pt(sim5 nm) which acts as a catalyst for the redox reaction isdeposited [25] The space between the two electrodes isfilled with an electrolyte (propyl methyl imidazolium iodide)containing an iodidetriiodide (119868minus119868minus

3) redox couple

In a DSSC under visible light an electron from the dyemolecule is excited then injected into the conduction band ofTiO2nanostructured semiconductor and finally collected by

the TCO glass electrode and transported in the external loadThe positive charge (dye cations) is reduced by receiving anelectron from the iodide ion (119868

minus) which will be subsequently

regenerated by reducing triiodide ions (119868minus3) at the platinized

counter electrodeBy using the nanostructured TiO

2 the depletion process

is less pronounced so that under reverse bias the electricfield is negligible [14 26] The origin of the photovoltage isexplained by a built-in potential barrier between TiO

2semi-

conductor and the TCO electrode andor by changing theposition of Fermi level due to the electron injection [26] Themost probable recombination process takes place betweenelectrons from TiO

2and 119868minus

3ions [18 19]

In the ideal case the rate of the absorbed photons in thevolume unit can be written as

119866ideal (119909) = int

1205822

1205821

120572 (120582) 120601ideal (120582) exp [minus120572 (120582) sdot 119909] 119889120582 (1)

where 119909 isin [0 119889] describes the position inside the TiO2film

(including the dye) with a thickness 119889 120582 is the wavelength ofthe radiation limits 120582

1and 120582

2are imposed by the absorption

characteristics of the dye through the absorption coefficient120572(120582) and 120601ideal(120582) is the spectral incident photon flux density

In the real case the rate of the absorbed photons119866ideal(119909)in the volume unit is reduced to 119866real(119909) due to the lightabsorption in TCO glass electrodes and to the reflection onto[16] We describe the contributions of these processes by afactor 120573 lt 1 aiming to propose a simplified model to be usedfor designing and optimizing any type of DSSCs Therefore119866real(119909) is given by

119866real (119909) = 120573 sdot 119866ideal (119909) (2)

The rate of electron injection 119866inj(119909) should take intoaccount the injection efficiency 120578inj [11] so that

119866inj (119909) = 120578inj sdot 119866real (119909) (3)

Counterelectrode (TCO)

Spacer

FTO

ElectrolytePlatinized

NanoporousFTO

Illuminatedelectrode (TCO)

(+)

TiO2 with dye

(minus)

Figure 1 Sketch of a classical DSSC Nanoporous TiO2with dye has

119889 thickness

In our simplified model we consider the electrical trans-port to be purely diffusive and therefore it is described by adiffusive transport equation for the electrical current density119869 [17 19] We neglect the internal electric field generated byunbalanced local charge because of its very low value [12 17]The electron density 119899(119909) in the conduction band of theTiO2layer is described by the continuity equation in quasi-

stationary regime In this case the system of equations hasthe following form

minus1

119890

119889119869 (119909)

119889119909= 119866inj (119909) minus 119877 (119909) (4)

119869 (119909) = 119890119863119889119899 (119909)

119889119909 (5)

where 119890 is the elementary charge 119909 describes the positioninside the TiO

2film119909 isin [0 119889]119877(119909) is the recombination rate

and119863 is the electron diffusion coefficientWe neglect the trappingdetrapping processes so that in

the continuity equation (see (4)) the corresponding termsdo not appear [15] Also we assume that the recombinationprocess takes place only between electrons from conductionband of TiO

2layer and anions present in the electrolyte

[18] Consequently the recombination rate is proportional to119899(119909) minus 119899

0 so that

119877 (119909) =119899 (119909) minus 119899

0

120591 (6)

where 1198990is the electron density at equilibrium (in the dark)

and 120591 is the electron lifetime

The boundary conditions are the following

(1) Assuming that electrons are extracted by applicationof an external voltage 119881 the boundary condition at119909 = 0 is

119899 (119909)|119909=0 = 119873119888exp(minus

119864 minus 119890119881

119896119861119879

) (7)




119873119888= 2 (

2120587119898lowast

119890119896119861119879

ℎ2)

32

(8)

where 119898lowast


119861is




level 119864119865





119889119899 (119909)

119889119909

10038161003816100381610038161003816100381610038161003816119909=119889

= 0 (9)


119881oc =119896119861119879 ln ((120591 sdot 119866inj (0) + 119899

0) 119873119888) + 119864

119890 (10)







1= 300 nm and 120582

2=




11989056119898119890(119898119890= electron mass)

T 300K1198990

1017 cmminus3

119864 = 119864119888minus 119864119865

09 eV120578inj 095D 5 sdot 10

minus5 cm2s

0

5

10

15

0 02 04 06 08Voltage (V)

Curr

ent d

ensit

y (m

Ac

m2)





120573 119869sc (mAcm2) 119881oc (mV) FF 120578 ()08 11170 819 0828 757209 12470 822 0828 8482095 13120 823 0827 89371 13770 824 0827 9392








6

8

10

12

14

0 10 20 30 40 50

J sc

(mA

cm2)

d (120583m)

(a)

4

5

6

7

8

9

0 10 20 30 40 50d (120583m)

120578(

)

(b)



d (120583m) 119869sc (mAcm2) 119881oc (mV) FF 120578 ()2 6160 822 0842 42625 10564 822 0838 727610 12498 822 0833 855315 12601 822 0830 858920 12470 822 0828 848230 12320 822 0827 836950 12275 822 0826 8336


2film thick-





120591 (ms) 119869sc (mAcm2) 119881oc (mV) FF 120578 ()2 9349 766 0833 59685 10267 787 0825 667410 11274 804 0831 753220 12470 822 0828 848230 13210 832 0824 905350 14107 845 0818 9737100 15123 863 0823 10742200 15840 881 0827 11544



4 Conclusions




8

10

12

14

16

0 50 100 150 200

J sc

(mA

cm2)

120591 (ms)

(a)

5

6

7

8

9

10

11

12

0 40 80 120 160 200120591 (ms)

120578(

)

(b)



2semiconductor


2


2





Acknowledgment


References



















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






119873119888= 2 (

2120587119898lowast

119890119896119861119879

ℎ2)

32

(8)

where 119898lowast


119861is




level 119864119865





119889119899 (119909)

119889119909

10038161003816100381610038161003816100381610038161003816119909=119889

= 0 (9)


119881oc =119896119861119879 ln ((120591 sdot 119866inj (0) + 119899

0) 119873119888) + 119864

119890 (10)







1= 300 nm and 120582

2=




11989056119898119890(119898119890= electron mass)

T 300K1198990

1017 cmminus3

119864 = 119864119888minus 119864119865

09 eV120578inj 095D 5 sdot 10

minus5 cm2s

0

5

10

15

0 02 04 06 08Voltage (V)

Curr

ent d

ensit

y (m

Ac

m2)





120573 119869sc (mAcm2) 119881oc (mV) FF 120578 ()08 11170 819 0828 757209 12470 822 0828 8482095 13120 823 0827 89371 13770 824 0827 9392








6

8

10

12

14

0 10 20 30 40 50

J sc

(mA

cm2)

d (120583m)

(a)

4

5

6

7

8

9

0 10 20 30 40 50d (120583m)

120578(

)

(b)



d (120583m) 119869sc (mAcm2) 119881oc (mV) FF 120578 ()2 6160 822 0842 42625 10564 822 0838 727610 12498 822 0833 855315 12601 822 0830 858920 12470 822 0828 848230 12320 822 0827 836950 12275 822 0826 8336


2film thick-





120591 (ms) 119869sc (mAcm2) 119881oc (mV) FF 120578 ()2 9349 766 0833 59685 10267 787 0825 667410 11274 804 0831 753220 12470 822 0828 848230 13210 832 0824 905350 14107 845 0818 9737100 15123 863 0823 10742200 15840 881 0827 11544



4 Conclusions




8

10

12

14

16

0 50 100 150 200

J sc

(mA

cm2)

120591 (ms)

(a)

5

6

7

8

9

10

11

12

0 40 80 120 160 200120591 (ms)

120578(

)

(b)



2semiconductor


2


2





Acknowledgment


References



















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




6

8

10

12

14

0 10 20 30 40 50

J sc

(mA

cm2)

d (120583m)

(a)

4

5

6

7

8

9

0 10 20 30 40 50d (120583m)

120578(

)

(b)



d (120583m) 119869sc (mAcm2) 119881oc (mV) FF 120578 ()2 6160 822 0842 42625 10564 822 0838 727610 12498 822 0833 855315 12601 822 0830 858920 12470 822 0828 848230 12320 822 0827 836950 12275 822 0826 8336


2film thick-





120591 (ms) 119869sc (mAcm2) 119881oc (mV) FF 120578 ()2 9349 766 0833 59685 10267 787 0825 667410 11274 804 0831 753220 12470 822 0828 848230 13210 832 0824 905350 14107 845 0818 9737100 15123 863 0823 10742200 15840 881 0827 11544



4 Conclusions




8

10

12

14

16

0 50 100 150 200

J sc

(mA

cm2)

120591 (ms)

(a)

5

6

7

8

9

10

11

12

0 40 80 120 160 200120591 (ms)

120578(

)

(b)



2semiconductor


2


2





Acknowledgment


References



















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




8

10

12

14

16

0 50 100 150 200

J sc

(mA

cm2)

120591 (ms)

(a)

5

6

7

8

9

10

11

12

0 40 80 120 160 200120591 (ms)

120578(

)

(b)



2semiconductor


2


2





Acknowledgment


References



















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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