160 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 N3/TiO2 لحسابات النظرية لثابت االنتقال االليكتروني عبر سطح ا والصبغة المستضاءه للخلية الشمسية ، جابر شاكر حميد الخاقاني هادي جبار مجبل العكيلي جامعة بغداد ¡ابن الهيثم–كلية التربية قسم الفيزياء ، الجامعة المستنصرية قسم الفيزياء، كلية التربية، 2011تشرين االول 18قبل البحث في 2011حزيران 21لبحث في استلم ا الخالصة النواع من المذيبات حسبت دالة لطاقة TiO2معدل االنتقال االلكتروني من الصبغة المستضاءة الى شبة الموصل وصل .إعادة االلتحام والطاقة الحرة للفعالة وحجم شبه الموصل وثابت التوهين ثابت الشبيكه لشبه الم االعتماد القوي لثابت معدل االنتقال االليكتروني على طاقة إعادة الترتيب والطاقة الحرة الفعالة. نتائج الحسابات تدل على المستضاءه في الخلية الشمسية اظهرت نتائج حساباتنا تطابقا N3متاح لالستعمال مع الصبغة 2TiOان شبه الموصل جيدا مع النتائج العملية. ،طاقة اعادة االلتحام. TiO2 ،شبه الموصلN3:معدل االنتقال االلكتروني،الصبغة المستضاءة ات المفتاحيةالكلم Theoretical Calculations of Rate Constant of Electron Transfer Across N3/TiO2 Sensitized Dye Interface Solar Cell H.J.M, Al-agealy, J. S. H. Al-Hakany Department of Physics,College of Education –Ibn Al-Haitham , University of Baghdad Department of Physics –College of Education, University of Al-Mustansirua Received in: 21 June 2011, Accepted in: 18 October 2011 161 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Abstract The rate of electron transfer from N3 sensitized by dye to TiO2 semiconductor in variety solvent have been calculated as a function of reorientation energy effective free energy , volume of semiconductor , attenuation and lattice constant of semiconductor . A very strong dependence of the electron transfer rate constant on the reorientation and effective free energy .Results of calculation indicate that TiO2 is available to use with N3 dye .Our calculation results show that a good agreement with experimental result. Key world :The rate of electron transfer, N3dye sensitized, TiO2 semiconductor, reorientation energy. Introduction The increase of the world's population combined with the growth per capita of energy consumption are expected to bring an explosive rise in energy consumption . To solve these problems , one need to save energy , increase the efficiency of equipment's transforming energy and develop the use of new sources of energy – solar energy is attracting a great deal of attention because it is a clean energy source and will not be depleted[1] . For more than 16 years dye sensitized solar cells (DSSC) have been under extensive research since the (DSSC) are especially attractive building integrated photovoltaic cell .The cell concept is believed to reduce the production costs and energy pay back time significantly compared to standard silicon cells or other thin film cells [2]. The modern dye technological advancement is almost entirely dependent on the semiconductor devices .The application of the semiconductor devices fabrication commonly requires that defect would be introduced in the semiconductor lattice intentionally during processing stage [3]. The first silicon solar cell with practical energy conversion efficiency appeared in1950 until to 1990s produced cell with efficiency 24%[4]. Electron transfer processes play a key role in dye sensitized semiconductor solar cells devices work .In this paper we studied these electron transfer process through the calculation of rate constant of ET processes depending on a quantum theory. In contrast, the transfer across molecular/ bulk interfaces has gained attention only recently and is poorly understood. These interfaces play a key role in many emerging fields, creating a need for a better theoretical treatment of the interfacial electron transfer [5]. Photo induced ET at molecular/bulk interfaces is the primary step in many solar energy–conversion devices because it creates free-charge carriers on the absorption of a photon. Increased concerns with energy sources have prompted researchers to propose and test a great variety of these novel photovoltaic designs. Examples include dye-sensitized semiconductor solar cells [6]. 162 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 A dye coupled to semiconductor is an excellent model for processes that occur in the above fields. This system represents one of the best-studied photovoltaic devices, the dye-sensitized semiconductor solar cell, or organic dye molecules that are adsorbed to a nanocrystalline TiO2 (7). Visible light excites the dye-sensitize molecules from the ground state, which is located energetically in the semiconductor band gap, to an excited state resonant with theTiO2 conduction band (CB) . The electron is then transferred to the semiconductor on an ultrafast timescale. It travels through the semiconductor to one of the electrodes, carries a load while makingits way to the other electrode, and then enters an electrolyte that brings it back to the chromospheres ground state[8].In this paper we can studies the electron transfer in N3 sensitized dye - TiO2 semiconductor solar cell system. The chemical structure of N3dye sensitized is shown in figure(1)[9]. Theory For the system Dye – sensitized semiconductor solar cell setting is that introducing the donor state vector l and acceptor state vector l on solution side perturbs the energy between the electrode of semiconductor and molecule in solution and electron can tunnel to the acceptor state . Model Hamiltonians is used to describe the interfacial electron transfer dynamics is given by. …………………….(1) Where describes the sum of Hamiltonians for the molecules of dye state , and the Hamiltonian for the semiconductor state that is given by . The rate constant for electron transfer of the molecule dye acceptor relation to the semiconductor donor in solar cells can then be further written as [10] = ………….. (2) For dye sensitized semiconductor solar cells devices where several electron transfer processes play a key role in dye sensitized solar cell ,and it can be outlined as follows [11]. The adsorbed sensitized molecules (S) are brought into their excited state by photon absorption |(semiconductor )+ h | semiconductor (photo excited )..(3) Electron injection dynamics from the electronically excited state of dye in conduction band of semiconductor with rate constant |(semiconductor ) |semiconductor + e-CB (semiconductor ) ..(4) The excited sensitized ( ) is relaxation to the ground state . |(semiconductor ) S | semiconductor + h ………(5) The oxidized sensitized in its ground state is rapidly reduced by ions solution (regeneration) 163 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 |(semiconductor )+ S | semiconductor + Regeneration ..(6) the probability reduced to the Boltzmann's equation where a change transfer from dye molecule sensitized ( donor state ) to acceptor semiconductor state , one need to integrate over all occupied state for [12] = …… (7) The free energy of reaction is related to by [13]. = - …………………..(8) And substituting = - )[13],in Eq(8),results. = ( - ) – = ( - ) - ……………. (9) Inserting Eq (9) in (7) we gate = Where[15]. The coupling by coefficient matrix element is estimated by using [10]. =- ………………………(12) Where is the decay constant , is the lattice constant , is the factor multiplying and is the energy of state k Solving integral integrate equation to get . [ +2( ) + ] ……………………(13) Simplified to = (0) Such that (0)= [ +2( ) + ]… …………..(15) Where V is the volume of semiconductor attenuation parameter, a is the lattice parameter ,ħ is the Planck constant, is the Boltzmann's constant and is the temperature ,λ the reorientation energy and ,the effective free energy(driving force) given by [16]. 164 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Where , is Planck constant, is the frequency, c is the velocity of light and is the reorientation energy. The reorientation energy arises from the reorientation of the charge in the medium .Its magnitude is dependent on the radius of the molecular donor and acceptor site, on its distance (d) from the semiconductor , and on the dielectric properties of the molecule dye, the semiconductor , and the medium solvent .For electron transfer between reactant molecule dye and semiconductor , the medium reorientation energy is [17]. = [ ( )- ( - )] (17) Where = the difference in energy in donor and acceptor ,R is the radius of molecule dye, d is the distance between dye and semiconductor , , are the optical and statistical dielectric constant and and are the optical and statistical dielectric constant for semiconductor. Results The theoretical calculation reported here where performed on using quantum model,and first order perturbations theory .The electron transfer rate was calculated for interface from a photo excited state molecular N3 sensitized dye to conduction band of TiO2 semiconductor depending on estimated the reorientation energy,driving force(free energy), hight barer,coupling overlap between TiO2 state and excited state molecular N3 sensitized dye. One can be used the expression in Eq(17) to calculate the reorientation energy for TiO2/N3 system with nine variety solvent .Inserting the values of optical ,and static dielectric constant for solvent from table [1], and =2.488 , =86 [13] for TiO2semiconductor . R N3=6.5 [22],and d=. R N3+1A o,results are summarized in table(2). Next we are using Eq.(17) to calculate the effective free energy (driving force),with taking the wave length of absorption light for N3 spectral(500- 1000)nm,and h=6.626×10-34 J.sec,c=3×108m/sec. The results obtained are summarized in table [3], parameters to calculate the rate of electron transfer is volume of TiO2 semiconductor that calculated using by V=a.b.c where a=b=4.570Ao,and c=2.989 Ao[13],for TiO2 semiconductor. Result of volume of unit cell for V TiO2 =6.26424×10 -29m3. For the dye/ semiconductorion , inserting of all these factors as data in a designed program to calculate the rate constant of electron transfer through the solution of the theoretical equation. These factors has been calculated with =0.9 [10],using a Mat lab program is writing to compute the all factors that’s guding to estimate the rate constant of electron transfer in TiO2/N3 sensitized solar cells system using Eq.(14-15),results are listed in table (4). 165 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Discussion Electron transfer upon excitation rate were determined by electronic coupling coefficients between the excited state of N3 sensitized dye molecule and conduction band of the TiO2 semiconductor, the driving force energy , the reorientation free energy , volume of semiconductor and attenuation parameters. The Electron transfer upon excitation in states of molecule N3 sensitized dye when absorption a wave length (500-1000)nm and has to be rapidly injectied into semiconductor before it can fall back to its ground state. The photo induce electron transfer from organic N3 dye molecule to TiO2 semiconductor is the first and most important reaction in solar cell system. The electron transfer dynamics are determined by solvent reorientation free energy for orienting the N3 dye molecule with respect to the semiconductor. Data of results for rate electron transfer table (4 ) indicates that electron transfer depend on properties of the dye and TiO2 semiconductor with polar solvents. As can be seen from table (2), the solvent controlled of reorientation energy for TiO2/ N3 system for nine solvents, the TiO2/ N3 system has large reorientation energy with most polar solvent than less polar solvent . Consequently, the rate of Electron transfer is expected to be most favorable in more polar solvent. From table (3) and table (4) we can find the rate is strongly depending on dielectric constant. This means increasing polarity Ds for solvent leads to increase the reorientation energy and results to increase in rate constant for TiO2/ N3 system and vice versa. But the shift in the reorientation energy and rate constant results in DMF and Formamide solvent,indicate because the high value of optical dielectric constant Dop ,and 1.445 for DMF and Formamide.The results of TiO2 force free energy for electron transfer between N3 senstized dye and TiO2 semiconductor is relative energy difference between the conduction band and oxidation.Results in table (4) show the rate constant of electron transfer is small ,where the driving force due to potential different between the conduction band and the radius of dye was not enough for electron transfer to occur. Observably ,a large value of would give rise a small Ket ,hover ,these values continue to be large with small value of . The activation energy(height barrier) leading to the small Ket.The barrier created between two materials N3 sensitized dye and TiO2semiconductor,and depending on characteristic of two materials .Near dye/semiconductor interface ,due to energy level difference the barrier is formed with properties of two dye ,semiconductors and caused impedance of charge transfer .Consequently the rate of electron transfer to be large when the barrier height is small and vice versa on the other hand ,we can find the rate of electron transfer is proportional with volume ofTiO2semiconducto ,and inversely proportional withβ. 166 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Conclusion In summary it can be concluded that rate of electron transfer is large in high polar solvent and small in the less polar solvent .This indicates that electron transfer was expected to be favorable in most polar solvents. In order to study the oxidation and conduction band as a function of for electron transfer ,the effective free energy it take for an electron to be recombined and can be determined from absorption of light for dye/semiconductor system .The rate Ket shift to minimum for large height barrier and small reorientation energy. Based on this work ,we concluded the useTiO2semiconducto with N3dye in polar solvent is good matching system ,because of flow of electron from dye to semiconductor is large compared with less polar solvents.Also we can see the use of TiO2semiconducto with N3dye is attractive because it is wide band gab semiconductor with better carrier mobility, the TiO2/N3 a good system. Refrences 1. Carol , C.;Bruce, S. 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Viscosity (cc)[18,20] Optical Dielectric Constant Dielectric constant [18- 19] Chemical Formula[18- 19] Solvent 2.57 1.397[20] 17.84 C4H10O 1-Butanol 1.3788[21] 18.8 C4H8O Methanol Ethyl Ketene 0.30 1.3563[21] 21.O1 C3H6O Acetone 168 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Table( 1): A common properties of solvent Table (2): The reorientation energies of electron transfer in TiO2/ N3 sensitized solar cell Tabl e (3): Resu lt of calc ulation of the effective free energy for electron transfer in TiO2/ N3 sensitized solar cell 1.94 1.359[21] 25.3 C2H2O Ethanol 0.55 1.329[20] 33.0 CH4O Methanol 0.34 1.3441[20] 37.5 C2H3N Acetone tril 1.370[21] 51.1 CH2O2 Formic Acid 1.987 1.4305[21] 38.25 C3H7NO DMF 3.3 1.445[20] 109 CH2NO2 Formamide Semiconduct or Dielectric constant Optical Dielectric Constant Energy gab (eV) Lattice constant (nm) Crystal structure TiO2[13] 86 2.488 3.2 A=4.570c=2.989 Zinc blend Solvent λ(eV) for TiO2 1-Butanol 0.378832185 Me thyl 0.39113637969367 Ace ton 0.40901963694359 Ethanol 0.41616144754285 Me thanol 0.44280216813319 Ace tonitrile 0.43818565882596 DMF 0.39455563784532 Formicacid 0.43184397805475 Formamide 0.40641128112508 Effective Free Energy ΔGo (eV) Wave lengt h Solvent 1000nm 950nm 900nm 850nm 800nm 750nm 700nm 650nm 600nm 550nm 500nm 0.8246 0.9272 0.9998 1.0809 1.1721 1.2755 1.393 1.5301 1.6892 1.8772 2.1028 1-Bu tan ol 0.8496 0.9149 0.9875 1.0686 1.1598 1.2632 1.3814 1.5178 1.6769 1.8649 2.0905 Eth yl 0.8318 0.8971 0.9696 1.0507 1.1420 1.2454 1.3635 1.4999 1.6590 1.8470 2.0726 Ace ton e 0.8246 0.8899 0.9625 1.0436 1.1348 1.2382 1.3564 1.4927 1.6518 1.8398 2.0654 Eth an ol 0.7980 0.8633 0.9358 1.0169 1.1082 1.2116 1.3298 1.4661 1.6252 1.8132 2.0388 Me th an ol 0.8026 0.8679 0.9405 1.0216 1.1128 1.2162 1.3344 1.4707 1.6298 1.8178 2.0434 Ace ton i tri l e 169 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 2 العدد Ibn Al-Haitham Journal for Pure and Applied S cience No. 2 Vol. 25 Year 2012 Table (4): Rate constant of e lectron trans fe r (e V.m)3 /sec in N3/ SnO2 in s e nsitize d s olar ce ll s ys te m. Fig.(1): Chemical structure of (N3) RuL2 (NCS) 2, L=2, 2’-bipyridyl-4, 4’-dicarboxylic acid [10]. 0.8462 0.9115 0.9841 1.0652 1.1564 1.2598 1.3780 1.5144 1.6734 1.8614 2.0870 DMF 0.8089 0.8742 0.9468 1.0279 1.1191 1.2225 1.3407 1.4771 1.6361 1.8241 2.0498 Form i c aci d 0.8344 0.8997 0.9722 1.0533 1.1446 1.2480 1.3661 1.5025 1.6616 1.8496 2.0752 Form am i de Solvent Rate Constant of Electron Transfer (eV.m)3/sec 500nm 550nm 600nm 650nm 700nm 750nm 800nm 850nm 900nm 950nm 1000n m X10-47 X10-44 X10-40 X10-38 X10-35 X10-34 X10-32 X10-30 X10-29 X10-28 X10-27 1-But anol 0.0139 0.0889 0.0128 0.0586 0.0109 0.0988 0.0498 0.0155 0.0323 0.0479 0.0532 Et hyl 0.0222 0.1414 0.0202 0.0925 0.0171 0.1545 0.0775 0.0240 0.0497 0.0732 0.0806 Acet one 0.0437 0.2773 0.0395 0.1792 0.0329 0.2953 0.1470 0.0451 0.0925 0.1348 0.1468 Et hanol 0.0574 0.3627 0.0516 0.2333 0.0428 0.3822 0.1896 0.0580 0.1184 0.1718 0.1861 Met hanol 0.1574 0.9866 0.1391 0.6226 0.1130 0.9966 0.4880 0.1470 0.2953 0.4205 0.4462 Acet onetrile 0.1322 0.8297 0.1171 0.5253 0.0955 0.8445 0.4145 0.1252 0.2522 0.3604 0.3840 DMF 0.0253 0.1609 0.0230 0.1050 0.0194 0.1749 0.0876 0.0271 0.0560 0.0823 0.0904 Formic acid 0.1039 0.6539 0.0925 0.4160 0.0758 0.6724 0.3311 0.1004 0.2030 0.2915 0.3121 Formamid 0.0396 0.2514 0.0358 0.1627 0.0299 0.2687 0.1339 0.0411 0.0845 0.1233 0.1346