Chapter 2 Charge Transport and Recombination in Organic Solar Cells (OSCs)

Transcription

1 Chapter Charge Trasport ad Recombiatio i Orgaic Solar Cells (OSCs) Najia Zhou ad Atoio Facchetti. Basic Cocepts of Charge Trasport i Orgaic Semicoductors Orgaic compouds are maily hydrocarbo compouds with a backboe of carbo atoms. The strog bods that form the molecular backboe are a result of overlap of sp hybridized atomic orbitals of adjacet carbo atoms, yieldig a bodig σ ad a atibodig σ* orbitals. The remaiig uhybridized p orbitals overlap ad form π ad π*orbitals. The eergies of π orbitals are higher tha those of σ orbitals, whereas eergies of π* orbitals are lower tha those of σ orbitals. Based o Pauli exclusio priciple ad Hud s rule, the eergies of π ad π* orbitals are defied as highest occupied molecular orbital (HOMO), ad lowest uoccupied molecular orbitals (LUMO), respectively. For charge trasport to take place i orgaic solids, there must be a charge o the molecular uit. This may either be a additioal electro that is accommodated i a atibodig orbital, or oe that is removed from bodig orbital. The molecule is the o loger i the groud state but rather i a charged excited state. There are a umber of factors that ca ifluece charge carrier mobilities, icludig molecular packig, disorder, temperature, impurities, electric field, ad pressure []. N. Zhou ( ) Departmet of Materials Sciece ad Egieerig, Northwester Uiversity, campus Drive, Evasto, IL 68, USA ajiazhou@u.orthwester.edu A. Facchetti Departmet of Chemistry, Northwester Uiversity, 45 Sherida Road, Evasto, IL 68, USA a-facchetti@orthwester.edu Spriger Iteratioal Publishig Switzerlad 4 H. Huag, J. Huag (eds.), Orgaic ad Hybrid Solar Cells, DOI.7/ _ 9

2 N. Zhou ad A. Facchetti.. Geeral Approach to Charge Trasfer Mechaisms For iorgaic semicoductors such as silico (Si) ad germaium (Ge), which ivolve covalet bods with high-bodig eergy, charge carriers move as highly delocalized plae waves ad carrier mobilities are ofte far larger tha cm /Vs. I these systems, as a result of carrier scatterig, icreasig temperature reduces the carrier mobilities. O the other had, i the case for orgaic semicoductors, they cosist of π-cojugated uits ad they are kept together maily by weak va der Waals forces with weak bodig eergies o the same order as molecular vibratioal eergies at room temperature. I additio, the separatios betwee molecules are sufficietly large for molecular orbitals to overlap. Therefore, charge trasport i orgaic semicoductors takes place i the form of hoppig mechaism. I cotrast to iorgaic semicoductors, elevated temperature icreases the charge carrier mobilities for orgaic semicoductors. Uderstadig the fudametal charge trasport mechaisms at both molecular ad device levels are of special importace to orgaic semicoductors. There are several excellet review articles to cover this topic. For example, iterested readers ca fid these recet reviews regardig charge trasport i orgaic semicoductors [, ]. Typically, it is believed that semicoductors with carrier mobilities higher tha cm /Vs ivolve carrier trasport via delocalized plae waves, whereas carrier mobilities less tha. cm /Vs are suggestive of hoppig coductio betwee localized states across differet molecules. For hoppig trasport, the relatioship betwee carrier mobility ad temperature follows Eq. (.). µ = µ α T T α exp, is betwee ad 4. (.) The exact charge trasport mechaisms i orgaic semicoductors are still uder debate. The most commoly used model is the Holstei s small-polaro model [3]. I covalet π-cojugated orgaic systems, the distributio of electroic cloud i molecules is highly delocalized. Self-trappig occurs via the creatio of localized states i the gap betwee coductio bad ad valece bad, which results i the formatio of polaros. The Holstei model simplifies the charge trasport as a D, oe-electro model. The total eergy i the system cosists of three elemets: (i) lattice eergy E L which is a sum of N umber of harmoic oscillator at a sigle frequecy, ω, i the form of: N EL = + Mω u = M i u (.) where u is the displacemet of th molecule from its equilibrium positio ad M is the reduced mass of each molecular site; (ii) the eergy dispersio of the electro which ca be writte i the form of: Ek = E J cos( ka) (.3)

3 Charge Trasport ad Recombiatio i Orgaic Solar Cells (OSCs) where J is the electro trasfer eergy ad a is the lattice costat; (iii) the electrolattice couplig i the form of ε = Au, where A is a costat. Aother importat parameter to cosider is the polaro-bidig eergy, E b, which is described as the eergy gai of a ifiitely slow carrier due to polarizatio ad deformatio. It ca be described as: E = A / ( Mω ) b (.4) Whe electroic badwidth, J, is smaller tha E b, the small-polaro model faces its limit. I such coditio, the electroic term of the total Hamiltoia ca be treated as a small perturbatio, ad the mobility of the small polaro ca be described as a time-depedet Schrödiger equatio. At high temperature (T > Θ, Θ is the Debye temperature), mobility is obtaied through: 3 π ea J Eb µ = ( kt ) exp E kt b (.5) ea where has the dimesio of a carrier mobility, ad is close to cm /Vs for most orgaic crystals. It is also worth otig that at high field (> 5 V/cm), the carrier trasport i orgaic materials is field-depedet. This is because the exteral field ca alter the columbic potetials ear localized-eergy levels, thus icreasig the electro tuel trasfer rate betwee sites. This pheomeo is described as Poole Frakel mechaism. The field-depedet mobility, µ( F), ca be described as: q µ ( F) = µ ()exp β F kt (.6) Where µ() is the mobility at zero field, ad β is the Poole Frakel costat, which ca be obtaied from: e β = πεε (.7) Where ε is the dielectric costat ad ε is the vacuum dielectric costat [3]. The multiple trappig ad release (MTR) model is most widely used i describig charge trasport i amorphous silico. MTR model assumes that: (i) the probability of carrier arrivig at a trap site ad beig trapped is close to uity; (ii) the release of trapped carrier is a thermally activated process. The relatioship betwee drift mobility, µ D ad the mobility i the delocalized bad, µ, ca be described as: Et µ D = µα exp kt (.8)

4 N. Zhou ad A. Facchetti Where E t is the eergy differece betwee trap ad bad edge of delocalized bad, ad α is the ratio betwee the effective desity of states at delocalized bad bad edge to the cocetratio of traps. Various other models have bee employed for describig charge trasport i orgaic semicoductors [4 6]. For example, Borseberger et al. [4] described the charge trasport i disordered molecular solids i the form of hoppig trasport betwee the Gaussia DOS of hoppig sites. Meijer et al. [6] i the studies of petacee ad α-hexathiophee, discovered that the carrier trasport follows Meyer Neldel rule (MNR), i which the carrier trasport mobility ca be described as: = X X exp Ea kt B E MN (.9) Where E MN is the Meyer Neldel eergy, ad E a is the activatio eergy.. Operatio of Orgaic Photovoltaic (OPV) I this sectio, some basics of OPV are outlied. First, the fudametals of photovoltaic effect kow from covetioal semicoductor models are outlied. The, equivalet circuit models widely used for describig differet solar cell systems are preseted. Next, we outlie the uique processes occurred i OPVs ad the origis of V OC, J SC, ad fill factor (FF) are described. Last, we focus o the two types of recombiatio dyamics, gemiate ad ogemiate recombiatio, which are the two domiatig loss mechaisms limitig the performace of OPVs... Photovoltaic Effect... Photo Absorptio The basic relatioship betwee photo wavelegth, λ, ad eergy is: λ C hc.4 = = = ( m ) ν hν hν µ (.) where C is the speed of light i vacuum, ν is the frequecy of light, h is Plack s costat. Whe a semicoductor iteracts with icidet light, photos ca be absorbed uder these circumstaces: (i) whe hν = Eg electros are activated from the valece bad to the coductio bad; (ii) whe hν > Eg, i additio to the formatio of electro-hole pair, the excess eergy hν Eg is released i the form of heat; (iii) whe hν < Eg, the photos ca be absorbed oly if there exist deep level states as a result of chemical impurities or physical defects.

5 Charge Trasport ad Recombiatio i Orgaic Solar Cells (OSCs) 3 Fig.. Equivalet circuit of a practical solar cell... Semicoductor Photovoltaic Effect ad Charge Trasport Equatios The trasport of electros ad holes i iorgaic semicoductors ca be described usig field curret ad diffusio curret. The oe-dimesioal drift-diffusio equatio follows: Ec J = q µ e + qd (.) x x E J = qµ p qd x v p h p p x (.) Where J e,h, is the electro/hole curret desity, µ e,h is the electro/hole mobilities, ad D e,h is the electro/hole diffusio coefficiets. Assumig a electric field E = gradφ ad uiform distributio of electros ad holes, the total charge, j Q, ca be writte as: σe σe jq = gradηe gradηe e e (.3) For covetioal p-juctio solar cells, the space charge forms a stable electric field i the directio of -type toward p-type, with the diffusio voltage beig: N N ψ = ψ ψ = V l d a p T i (.4) Where N a is the majority carrier cocetratio, N d is the door impurity cocetratio, i is the itrisic carrier cocetratio, ad V T is the thermoelectric field... Solar Cell Equivalet Circuit Model For a ideal solar cell, the I V characteristics ca be described usig equivalet circuit (Fig..):

6 4 N. Zhou ad A. Facchetti Whe igorig the effect of series resistace ( R s ) ad shut resistace ( R sh ) ( R s = ad R sh = ) for ideal solar cell, curret ca be represeted by the differece betwee short circuit photocurret, I L, ad the forward curret of p-juctio, or dark curret, ID = V VT e (.5) I = IL ID = IL + I e V VT (.6) where I is the saturatio curret. Therefore, the voltage o p-juctio is give by: IL I V = V l (.7) T + I Uder short-circuit coditio ( V = ), the curret output is the short-circuit curret: I = IL = Isc Whereas uder ope-circuit coditio ( I = ), the ope-circuit voltage is give by: V oc I L = VT l +. I (.8) Based o the equivalet circuit diagram of solar cell, the solar cell output power is give simply by: V VT P = IV = ( I ) (.9) L I D V = I LV + IV e To further iclude the discussio of R s ad R sh for practical solar cells, the I V characteristics are modified from ideal solar cell coditio: ( ) e V IRs V IRs I = IL + I VT Rsh (.) The power coversio efficiecy (PCE) is represeted by the ratio betwee solar cell maximum power output, P m, ad iput power from icidet light, P i : Pm η = % P i (.) Here, accordig to Eq..9, P m ca be further represeted as:

7 Charge Trasport ad Recombiatio i Orgaic Solar Cells (OSCs) 5 Fig.. Compariso of the typical eergy diagrams of a a iorgaic solar cell ad b a orgaic solar cells. a I iorgaic p- juctio solar cells, absorptio of photo eergy leads to thermalizatio of the holes ad electros ear the top of the valece ad coductio bads ( step ), followed by the diffusio of miority carriers to the juctio ( step ) ad they are evetually swept away ad accumulate o the other side of the juctio where they become the majority carriers ( step 3). V oc of p- juctio solar cells is determied by the differece betwee the quasi-fermi level eergies of -ad p-type semicoductors (deoted as ε ad Fe ε, respectively). b I orgaic solar Fh cells, absorptio of photos ( step ) lead to the formatio of a boud electro-hole pair, excito, ( step ) which diffuse to the door/acceptor iterface ( step 3). As a result of eergy differece betwee electro affiity of the door ad the acceptor materials, excitos ca dissociate ad form free-charge carriers ( step 4). I this process, the maximum V oc is determied betwee ioizatio potetial of door ( IP(D)) ad electro affiity of acceptor ( EQ(A)). Reproduced from ref [7] VmP I L I Pm = VmPImP = + VmP + VT IL (.) where V mp ad I mp are the voltage ad curret at the maximum power poit per uit area. It is obvious that high solar cell efficiecy requires high I sc ad V oc. Aother importat factor, FF also cotributes to the solar cell efficiecy. FF is defied VmPImp as the ratio betwee P m ad the product of V oc ad Isc : FF =. Fially, accordig to Eq.., the PCE is therefore defied VocIsc as: Voc Isc FF η = P i..3 Orgaic Photovoltaic Cells I the simple picture of a eergy diagram, a p-type semicoductor ad a type semicoductor is placed adjacet to each other, formig a abrupt iterface. (Fig..) Differet from traditioal p- juctio type solar cells, i OPV operatio, the absorptio of a photo does ot directly lead to a free electro ad a free hole.

8 6 N. Zhou ad A. Facchetti This etity i which electro ad hole are still boud to each other by Coulomb forces is called a excito, ad it requires a relatively large drivig force to be separated []. The basic light absorptio process i OPV ca be simply summarized as followig: charge pairs are geerated throughout the device with the geeratio rate proportio to the optical absorptio profile Q( x), calculated as [8] Qx ( ) = cεα Ex ( ) (.3) where c is vacuum speed of light, ε is the vacuum permittivity, is the refractive idex, α is the absorptio coefficiet. Charge-pair separatio efficiecy is the determied via the Osager Brau formula that depeds o the local stregth of the iteral electrical field (see more further). Aother importat property of OPV active layer is that they are macroscopically homogeeous mixtures ad caot differetiate charge trasport directio without selective cotacts. Usually, a combiatio of a low-work fuctio ad a high-work fuctio electrode, as well as commo -type ad p-type iterfacial layers are used to differetiate electro ad hole trasport. A stadard model for charge collectio i bulk heterojuctio (BHJ) OPV is illustrated i a recet review by Bisquert et al. [9]. I priciple, the trasport of separated charges to the electrodes ca be modeled via drift-diffusio equatios as described previously with the additioal possibility of the trappig ad detrappig of electros from deep trap states. I the followig sectios, the excito dissociatio ad charge collectio processes ivolvig two key recombiatio mechaisms: gemiate recombiatio ad ogemiate recombiatio will be discussed i more details...4 Basic Charge Trasport Expressios i Orgaic Solar Cells Similar to iorgaic-type solar cells described previously, the fudametal relatioship betwee charge ad electric field ca be described by Poisso s equatio: de ρ q ( px ( ) x ( ) N D N A) dx = ε = ε + (.4) At ay give positio x i solar cell photoactive layer, the excito-geeratio rate (the umber of excito geerated) ca be represeted as: Qx ( ) Qx ( ) λ Gx ( ) = = = Qx ( ) E hν hc e (.5) hc where Ee = is the excito eergy, λ where E is the electric field, ρ is the charge desity ad ε is the material permittivity. The electro ad hole cotiuity equatios are:

9 Charge Trasport ad Recombiatio i Orgaic Solar Cells (OSCs) 7 dj ( x) + Gx ( ) Rx ( ) = q dx dj p ( x) + Gx ( ) Rx ( ) = q dx (.6) (.7) At ay give positio x i solar cell photoactive layer, the short-circuit curret desity J( x) is the differece betwee carrier geeratio rate ad recombiatio rate...5 Origi of V oc, J sc, ad FF..5. V oc V oc of OPV is a result of splittig electro ad hole quasi-fermi eergy levels triggered by illumiatio. Voc = ( EF EFp ) q (.8) Where E F ad E Fp are the electro ad hole quasi-fermi eergies, respectively. Scharber et al. [] summarized a series of OPV active layers ad propose the empirical relatioship betwee the HOMO of the door materials ad LUMO of the acceptors, proposed by Scharber et al., Voc = ( EHOMO, D ELUMO, A.3 V ) q (.9) It should be oted that the V oc loss of.3 ev is empirical, ad the loss could be greater or smaller. There are a umber of factors that ca adversely affect the V oc of OPV devices. Cosideratio o disorder-iduced V oc loss ad carrier recombiatio iduced V oc loss, V oc ca be expressed: [] σ NAND oc = DA B kbt p qv E k Tl (.3) I Eq..3, the first term is the effective badgap, EDA, the secod term is the disorder-iduced V oc loss, ad the third term represets carrier recombiatio iduced V oc loss. Experimetally, the depedece of V oc o temperature ad light itesity has profoud effect o idetifyig basic OPV properties. By liearly fit V oc with respect to temperature, it was foud that V OC = E DA whe T approaches K [, 3]. However, this liear depedece is oly valid at low temperature. V oc was rather

10 8 N. Zhou ad A. Facchetti foud to saturate at elevated temperatures ad started to decrease at certai temperature. This effect ca be easily simulated accordig to Eq..3 []. Therefore, by measurig V oc saturatio experimetally, oe ca estimate the degree of disorder i OPVs. The steady-state light itesity depedece of V oc is widely used to fit to a logarithmic relatioship: V = Sl( I / I ), oc (.3) where I is the light itesity uder su coditio [4 6]. Here the slope, S, ca be compared to kt/q, where is the ideality factor. For p- juctio-based iorgaic solar cells, is ofte observed to be close to sice bimolecular recombiatio is the predomiat loss mechaism. Whereas >.5 is ofte foud i several OPV systems [7, 7], idicatig the presece of possible other recombiatio mechaisms, i.e., trap-assisted recombiatio...5. J sc J sc is directly related to the spectral respose, ad it ca be simply calculated by itegratig the exteral-quatum efficiecy, η EQE, agaist the AM.5G spectrum. (where N ph ( λ ) is the photo flux desity at wavelegth ( λ )) Jsc = eηeqe ( λ) Nph ( λ) dλ (.3) AM.5 Where E is the photo eergy, q is the elemetary charge [7]. Similar to V oc, light itesity depedet J sc measuremet is also good idicator of recombiatio orders [8] FF Ulike V oc ad J sc which ca be estimated relatively easily through material-eergetic aligmet of D ad A, i.e., lowerig optical badgap to maximize J sc, while lowerig the HOMO eergies of door materials to icrease V oc. Note, however, that HOMO lowerig will also icrease the badgap, uderscorig the problematic tradeoff betwee V oc ad J sc. Realizig high FFs has prove elusive, although there is evidece that carrier mobility, active-layer microstructure, ad also iterfacial ad bulk charge recombiatio play a role [9, ]. After solvig equivalet circuit model, a commo expressio for ideal FF (o resistace cosidered) ca be writte as: v oc l( v oc +.7 V) FF = v + oc (.33)

11