NANO LETTERS

2006 Implications of the Negative Vol. 6, No. 4 Observed at Forward Bias 640-650 in Nanocomposite and Polycrystalline Solar Cells

Iva´n Mora-Sero´ ,* Juan Bisquert,* Francisco Fabregat-Santiago, and Germa` Garcia-Belmonte

Departament de Cie`ncies Experimentals, UniVersitat Jaume I, E-12080 Castello´, Spain

Guillaume Zoppi,† Ken Durose, and Yuri Proskuryakov Departament of Physics, UniVersity of Durham, South Road, Durham DH1 3LE, U.K.

Ilona Oja, Abdelhak Belaidi, and Thomas Dittrich Hahn-Meitner-Institut, Glienicker Str. 100, D-14109 Berlin, Germany

Ramo´ n Tena-Zaera, Abou Katty, and Claude Le´vy-Cle´ment LCMTR, Institut des Sciences Chimiques Seine Amont, CNRS, 2/8 rue Henri Dunant, 94320 Thiais, France

Vincent Barrioz and Stuart J. C. Irvine Department of Chemistry, UniVersity of Wales, Bangor, Gwynedd, LL57 2UW, U.K.

Received November 21, 2005; Revised Manuscript Received January 28, 2006

ABSTRACT Four different types of solar cells prepared in different laboratories have been characterized by impedance spectroscopy (IS): thin-film CdS/ CdTe devices, an extremely thin absorber (eta) solar cell made with microporous TiO2/In(OH)xSy/PbS/PEDOT, an eta-solar cell of nanowire ZnO/CdSe/CuSCN, and a solid-state dye-sensitized solar cell (DSSC) with Spiro-OMeTAD as the transparent hole conductor. A negative capacitance behavior has been observed in all of them at high forward bias, independent of material type (organic and inorganic), configuration, and geometry of the cells studied. The experiments suggest a universality of the underlying phenomenon giving rise to this effect in a broad range of solar cell devices. An equivalent circuit model is suggested to explain the impedance and capacitance spectra, with an inductive recombination pathway that is activated at forward bias. The deleterious effect of negative capacitance on the device performance is discussed, by comparison of the results obtained for a conventional monocrystalline Si solar cell showing the positive chemical capacitance expected in the ideal IS model of a solar cell.

1. Introduction. The relatively high cost of the conventional tions because of the relatively high efficiency, long-term Si monocrystalline solar cells has impelled the research and stability in the performance, and potential for low-cost development of thin-film solar cells based on highly absorb- production. Because of the high absorption coefficient of ing inorganic and on nanocomposite concepts CdTe (>104 cm-1), a layer of this material with a thickness such as the DSSC1,2 and the eta-solar cells.3-5 of only about 2 µm is sufficient to absorb most of the useful One of the most intensively studied types of thin-film part of the solar spectrum.7,8 devices is the polycrystalline cell based on CdS/CdTe However, other types of solar cells such as DSSC and eta- heterojunction, with a record efficiency of 16.5%.6 Such solar cells, based on alternative concepts, have also been devices are among the best candidates for terrestrial applica- investigated thoroughly with the aim to decrease the produc- tion cost significantly. The attractive side of such devices is * Corresponding authors. E-mail: [email protected]; [email protected]. † Now at NPAC, Northumbria University, Ellison Building, Ellison Place, a very thin absorber, a monolayer of dye for DSSC, or a Newcastle upon Tyne, NE1 8ST. absorber layer with thickness of tenths of

10.1021/nl052295q CCC: $33.50 © 2006 American Chemical Society Published on Web 02/23/2006 nanometers for eta-solar devices. In these devices, the types of solar cells: CdS/CdTe thin-film solar cells, mi- absorber layer is situated in a nanometric or micrometric croporous TiO2/In(OH)xSy/PbS/PEDOT, columnar ZnO/ matrix allowing for a significant improvement in the light CdSe/CuSCN eta-solar cells, and a solid-state DSSC with absorption because of the large effective area of the matrix. doped and undoped Spiro-OMeTAD as the transparent hole In these cells, the photogenerated carriers are transferred into conductor. In all cases, a strong negative capacitance has two different media. This fact allows one to relax the high- been observed at low frequencies for high forward bias quality requirements of single-crystal p-n junction devices, conditions. Such behavior is compared with the (positive) enabling low-cost fabrication processes to be employed. capacitance of a high performance silicon solar cell, and the In the conventional DSSC, the dye molecules are regener- implications of the negative capacitance effect as well as ated by a redox couple dissolved in an electrolyte. The use possible interpretations are discussed. of an electrolyte causes problems in the process of its 2. General Model for Solar Cell Ac Impedance and encapsulation and in the long-term stable performance. One Capacitance. As a preliminary step toward the discussion of the options intended to avoid this problem is substituting of negative capacitance, we summarize in this section a basic this liquid electrolyte with a transparent hole semiconductor, but quite general model for a solar cell that incorporates the such as Spiro-OMeTAD (2,2′,7,7′-tetrakis(N,N-di-p-meth- fundamental photovoltaic principles2 and the corresponding oxyphenilamine)-9,9′-spirobifluorene).9 However, these solid- behavior under measurement of ac impedance, extending a state devices present a lower efficiency (∼4.5%) than those previous model of frequency response of solar cells.19 with a liquid electrolyte DSSC (∼10%). Those effects have The key point of the efficient solar-cell energy conversion been attributed to higher recombination dynamics.10 is the combination of carrier generation by light absorption The DSSC configuration has also inspired an alternative and charge separation.2 The simple model of Figure 1a all-solid device, the eta-solar cell with a semiconducting contains the basic elements of the conversion process extremely thin absorber sandwiched between two transparent, common to all solar cells.2 The model is a simple two-level highly interpenetrated semiconductors of different kinds.3-5 general system formed by an absorber material (which can The highest efficiency demonstrated to date for this type of be a single molecule, a semiconductor crystal network, or cell is 2.3% at 1/3 sun, obtained for an eta-solar cell of an organic polymer), where carriers can be promoted from columnar structure ZnO/CdSe/CuSCN,11 which is one of the the valence band to the conduction band by light excitation. types of cells studied in this work. Additionally, an eta-solar The solar cell is completed with selective contacts to cell made with microporous TiO2/In(OH)xSy/PbS/PEDOT electrons and holes, which consist of n- and p-type materials, (∼1% efficiency) has also been studied, presenting the respectively, both in contact with the light absorber. Although interests of the use of an organic polymer as a hole conductor the diagram is one-dimensional for the sake of clarity, the and the system of In(OH)xSy/PbS to improve the contact spatial structure of the solar may have any form, but it is selectivity. obviously required that the n- and p-type materials be The potentialities of these four types of solar cells (in the separated spatially in order to avoid internal short-circuit. presented and related configurations) stimulate an interest The selective contacts have the function of converting the in the study of their ac impedance behavior, which can carriers from a state of nonequilibrium in the provide diverse information on device properties and per- absorber to a material (normally a metal) in which the carrier formance. Impedance spectroscopy (IS) is a well-known ac is at the equilibrium Fermi level.20 Selective contacts may technique used for the study of electrochemical and solid- require some combination of materials, such as nanostruc- state systems and has been employed extensively in the tured TiO2 plus conducting glass in DSSC. Efficient charge characterization of DSSC devices.12-16 However, the utiliza- separation requires that each selective contact equilibrates tion of this technique in the characterization of solid-state its Fermi level to only one kind of carrier.21 With ideal, solar cells is not regular, although a few examples are shown reversible selective contacts, the quasi-Fermi level is con- in the literature.17,18 In principle, impedance spectroscopy tinuous at the interfaces between both n- and p-type materials measurements taken over a broad frequency range (millihertz and the absorber, as shown in Figure 1a so that there are no to megahertz) may provide information on any system that irreversible losses associated with the extraction process. The is composed of a combination of interfacial and bulk only irreversible process necessarily present in this ideal transport processes, particularly on transport coefficients, model of a solar cell is the radiative recombination of excess recombination parameters, and interfacial states in solar cells. carriers in the absorber, which is unavoidable because of It is this that makes the technique especially valuable for the microscopic reversibility of the excitation process.22 the characterization of the devices mentioned above, with a The excitation by light produces excess electrons and holes broader aim to find the ways to improve their performance in the carrier bands, which causes the separation of the quasi- 23 and/or stability. Fermi levels, EFn and EFp, of the two states in the absorber. In solar cells, ac impedance measurements are normally To simplify the number of variables in the model, we assume, used in reverse conditions to obtain information on interfacial without loss of generality, that the increase of density of holes characteristics (admittance spectroscopy). In this work we can be neglected (by initial p-doping of the absorber), so have systematically analyzed by IS data over a wide range that EFp ) EF0, the equilibrium Fermi level. It is also assumed of biasing potential, both under reverse and forward bias, in this simple model that the mobilities of both electrons using dark and light conditions, for samples of four different and holes are infinite. There are, therefore, no limitations

Nano Lett., Vol. 6, No. 4, 2006 641 Figure 1. (a) Basic scheme of a solar cell. It consists of a light absorber in which photon absorption can excite electronic charge carriers from a low energy EV to a high energy Ec state (process 1). Excitation causes a separation of the quasi-Fermi levels of electrons EFn and holes EFp that is limited by recombination of the carriers (process 2). Reversible selective contacts to each kind of carrier allows their extraction (process 3) (b) The ac equivalent circuit with recombination resistance Rrec and chemical capacitance Cµ describing the ac impedance response of the system. (c) The scheme shows the elements in part a and in addition a nonideal electron-selective contact indicated by a drop of the quasi-Fermi level (process 4). (d) The ac equivalent circuit of scheme c including a resistance Rc1 and capacitance Cc1 at the selective contact. (e) The ac equivalent circuit of scheme c also includes an inductive response that is in series with a recombination resistance. by transport in our model, even if the solar cell is spatially time through the electron-selective contact, and U is the extended; hence, the Fermi levels are homogeneous, and the recombination rate, which we assume of the simplest type voltage measured at outer contacts is given by n - n V )-(E - E )/e (1) U ) 0 (3) Fn F0 τ where e is the positive elementary charge. The concentration of electrons with density n under where n0 is the equilibrium concentration and τ is the lifetime generation by incident light at a rate G is governed by the for first-order recombination. Equation 2 states the variation conservation equation of the number of electrons in the conduction band in a volume element by the three processes indicated by arrows dn )- + - in Figure 1a: extraction, generation, and recombination. Note Ic G U (2) dt that n0/τ in eq 3, when inserted in eq 2, is the rate of thermal generation that occurs if there is no incident light, when where Ic is the volume density of electrons extracted per unit G ) 0.

642 Nano Lett., Vol. 6, No. 4, 2006 If the electrons obey Boltzmann statistics, then side can be recognized as a capacitive current of the type j ) C(dV/dt). The capacitance per unit volume is the - ) (EFn EF0)/kBT chemical capacitance, Cµ, given by n n0e (4)

j 2 where kB is Boltzmann’s constant and T the temperature. At ) ne ) Cµ (9) steady state (dn/dt 0) a certain concentration of electrons, kBT nj, is established by equilibrium between injection, generation, and recombination at a fixed rate. From eqs 2-4 the steady- Equation 9 is a particular instance, for the Boltzmann state relationship between the number of extracted carriers statistics, of the general definition19 per unit time and applied voltage can be written

2 ∂n n0 - C ) e (10) I ) G - (e eV/kBT - 1) (5) µ ∂E c τ Fn

This is the ideal diode equation, which is seen to arise Chemical capacitance is an equilibrium property that from a simple conservation equation. The characteristic relates a variation of carrier density to a displacement of the exponential law in eq 5 is produced by the combination of Fermi level. As an equilibrium property it is always a positive Boltzmann statistics and first-order recombination kinetics. quantity.

Note in eq 5 that the forward bias is obtained at negative The second term on the right of eq 8, æn/Rrec, defines the voltage, as is conventional in semiconductor device literature, recombination resistance while the opposite convention is often used in the solar cell literature. The thermal generation current, n0/τ, gives the kBTτ constant current at reverse bias in the diode equation. R ) (11) rec j 2 Equation 5 also relies on the assumption that the electron ne Fermi level, EFn, is determined by the voltage applied at the outer contacts, through eq 1, independent of the photoge- More exactly, the steady-state value æss ) 0 is taken as neration rate, G.24 the baseline for potentials æ, so that the small perturbation ) -1 - 19 Let us derive the ac impedance model corresponding to value of the recombination current is irec Rrec(æ ænss). the fundamental, idealized model of the solar cell that we In the measurement of impedance spectroscopy, the time have presented. In IS the solar cell is set at a certain steady variation of the small perturbation signals is sinusoidal. This state of illumination, Gh , and applied potential, Vh, with the case is obtained by the Laplace transform of eq 8, with the corresponding current hIc given in eq 5. A small time- substitution d/dt f iω, being ω the angular frequency. Hence dependent perturbation of potential is applied, so that V ) h+ ) h + V æ(t), with the associated change of current, Ic Ic æ j ) iωC æ + (12) ic(t). The photogeneration rate, G, cannot be affected by the µ R potentiostat. But the modulation of potential does change rec the electron Fermi level, EFn ) EhFn - eæ, and hence the electron concentration. Expanding eq 4 to first order it is Because the impedance of the is Z ) 1/iωCµ, found that eq 12 indicates that the current to the outer circuit is composed of two branches in parallel at the common voltage æ so that the model can be represented as the equivalent ) j - eæ n n(1 ) (6) circuit of Figure 1b. Although IS does not consider explicitly kBT the light generation term as a circuit element, the equivalent Introducing eq 6 into eq 2, and removing the time- circuit model of Figure 1b contains the fundamental elements 19 independent terms that cancel out by eq 5, we find the of photovoltaic conversion. Excess carriers in the conduc- V following result tion band create a oltage (Fermi level) by virtue of the chemical capacitor. The carriers have two ways to escape: j 2 j 2 either through the recombination resistor or the external ) ne dæ + ne eic æ (7) pathway and will take that of less resistance. Therefore, the kBT dt kBTτ recombination resistance is the element that keeps the carriers contained in the capacitor and facilitates their extraction. For We express this result as efficient conversion, Rrec must be large. Traditionally, equivalent circuits used in solar cell descrip- ) dæ + æ tions are for dc characteristics and include a diode and no j Cµ (8) dt Rrec capacitor. In the ac model of Figure 1b the diode is represented by the voltage dependence of the recombination The term in the left of eq 8 is j )-eic, the electrical resistance, indicated in eq 11 through dependence on nj.In current extracted per unit volume. The first term in the right fact Rrec is equivalent to the reciprocal derivative of eq 5.

Nano Lett., Vol. 6, No. 4, 2006 643 Figure 2. Representation of the impedance in the complex plane plot and real part of the capacitance vs frequency for solar cell impedances. 3 2 - 6 2 (a and b) RC-RC circuit representing recombination resistance Rrec ) 10 Ω/cm and chemical capacitance Cµ ) 5 × 10 F/cm in 2 2 - 8 2 parallel, and the effect of nonideal selective contact with parameters Rc1 ) 5 × 10 Ω/cm and Cc1 ) 10 F/cm . Shown are the frequencies in Hertz at selected points, the characteristic frequency of the recombination-accumulation arc (0.32 Hz, square point), related to the angular ) -1 ) × 2 ) frequency ωτ τn 1/RrecCµ, and the characteristic frequency of the contact (3.2 10 Hz), related to the angular frequency ωc1 3 1/Rc1Cc1. (c) Complex plane plot of the impedance model R + RC(R + L) circuit representing recombination resistance Rrec1 ) Rrec ) 10 2 - 4 2 5 2 Ω/cm and chemical capacitance Cµ ) 5 × 10 F/cm in parallel, and the inductive effect by an inductor L ) 1 × 10 H/cm in series 3 2 2 2 with a resistor Rrec2 ) 3 × 10 Ω/cm (f)0.75). CL ) 0.011 F/cm , CN0 ) 0.010 F/cm . Shown are the frequencies in Hertz at selected points, the characteristic frequency of the recombination-accumulation arc (0.32 Hz, square point), related to the angular frequency ωτ ) -1 ) × -3 ) τn 1/RrecCµ, and a characteristic frequency of the inductive loop (0.47 10 Hz), related to the angular frequency ωRL Rrec2/L.(d and e) Points indicate real part of the capacitance vs frequency for (Z - Rc1) of the model in c, that is, with series resistance suppressed, while the lines represent Z for the same model.

Now considering the structure of the electron-selective It should be recognized that the model presented in Figure contact, it must be a material (or combination of materials) 1c and the equivalent circuit in Figure 1d is in many ways different than the absorber in order to block the holes. The a first approximation to the ac response of solar cells and process of electron transfer through the interface introduces does not aim to be universal. In particular, the impedance a drop of the Fermi level between the absorber and the n response of selective contacts may be more complex, and material, as indicated in Figure 1c. In the equivalent circuit recombination and extraction are not necessarily serial the electron-selective contact is associated with resistance processes. Elements of the contacts may appear connected and capacitance as indicated in Figure 1d. The contact in parallel with the basic circuit RrecCµ, and the selective resistance, Rc1, reduces the extracted current, therefore Rc1 contact itself may display a significant chemical capacitance, 25 is required to be low for efficient solar cell operation. as in TiO2 DSSC. However, in reasonably efficient solar For representation, the impedance is separated in real and cells we do expect to observe at forward bias a predominance imaginary parts as Z ) Z′ + iZ′′. Figure 2a shows the of the RrecCµ subcircuit so that the model should be generally complex plane plot of the impedance of the model of Figure appropriate. In contrast, at reverse bias the absorber will be 1c, consisting of two semicircles that corrrespond to the two depleted of carriers and the impedance will be controlled RC circuits in series. Another possible representation of the by the response of the selective contacts that will exhibit impedance response, useful in many cases, is the complex their blocking nature. capacitance, defined from the impedance, as C ) 1/(iωZ). 3. General Characteristics of the Negative Capacitance The complex capacitance is written as C ) C′ + iC′′ where in Electronic and Electrochemical Devices. Although most C′ ) Re(C). Figure 2b shows the real part of the capacitance systems investigated by IS can be described with (positive) for the model of Figure 1d. resistors and , with Z′ > 0 and C′ > 0, respectively,

644 Nano Lett., Vol. 6, No. 4, 2006 the appearance of negative capacitance (or inductive behav- nanometer range that can be strongly forward-biased. Fur- ior) is not uncommon. For an electronic device that is close thermore, such solar cells display a rather irregular distribu- to equilibrium, that is, at low dc current, negative capacitance tion of electrical fields in the complex morphological or resistance are not allowed because such elements would structure, and in addition, minority carriers do not exist as upset the principles of thermodynamics. However, far from such because electrons and holes are transported in separate equilibrium, under strong steady-state bias, negative capaci- materials. tance and resistance is not prevented by thermodynamics. We propose that injection in recombination layers of Negative capacitance (or inductive behavior) has been nanostructured solar cells may also lead to inductive observed in a variety of electronic devices such as Schottky behavior. We have argued above that at high forward bias diodes,26,27 short based p-n junctions,28-30 polymer light- the solar cell impedance is generally controlled by recom- emitting diodes,31-33 and DSSC.34 The inductive feature of bination resistance and chemical capacitance. Therefore, we the ac impedance is also found in electrochemical measure- extend such a model as indicated in the equivalent circuit ments of electrocatalysis, electrodeposition, and electro- Figure 1e. In addition to the recombination resistance, Rrec1, dissolution.35-43 Recently, inductive behavior at high fre- that is in parallel with the chemical capacitance, as in the quency was found in the nanostructured TiO2 permeated with ideal model, in Figure 1e an additional recombination ionic liquid.44 pathway is included, consisting of the combination of a There are two main types of interpretations suggested for resistance, Rrec2, and an inductor with impedance Z ) iωL. the negative capacitance. In the short-base p-n junction, the In the absence of sufficient knowledge about the specific minority carrier depopulation at high forward bias induces mechanisms that may lead to the inductive behavior in the a change of sign of the capacitance.28-30 The mechanism, different solar cells discussed below, the model is proposed associated to spatial distribution of the carriers, has been at the level of equivalent circuits. modeled regarding the series resistance corresponding to the The impedance and capacitance response of the inductive neutral diode regions in addition to the diffusion (minority solar cell model are shown in Figure 2c-e. In the complex carrier) capacitance.29 plot, Figure 2c, we observe the inductive loop at low In another more general class of mechanism, the inductive frequency that reduces the dc value of the recombination ) ) - behavior takes place when the current between two electronic resistance. If we denote Rrec1 Rrec and Rrec2 f/(1 f)Rrec, reservoirs (such as oxidized and reduced ionic species in where 0 < f < 1, then, because of the fact that the inductor solution or two bulk semiconductors connected by a quantum is shunted at zero frequency, we obtain that the dc value of well) is governed by the occupation of an intermediate state, the total recombination resistance, Rrec, is decreased with ) which decreases when the applied potential increases. An respect to the inductor-free model as Rrec0 fRrec. example is the electrocatalytic reaction A T C controlled The admittance, Y ) Z-1, of the three-branched circuit is by an intermediate absorbed species B. Such electrocatalytic given by reactions display an inductive feature when the concentration of the adsorbed species decreases while the potential ) 1 + 1 + increases, contrary to the equilibrium isotherm, as a result Y(ω) + iωCµ (13) Rrec1 Rrec2 iωL of a significant charge-transfer current.43,45 In the case of Schottky diodes the negative capacitance was interpreted in terms of the loss of interface charge at occupied states below The low-frequency limit of eq 13 is the Fermi level.27 In double-barrier resonant tunneling diodes (RTD), the quantum capacitance, defined as the change of ) 1 - Y(ω) iωCN0 (14) the charge stored in the quantum well with respect to a Rrec0 change of the potential in the RTD46 (in close correspondence to the chemical capacitance discussed above), becomes where negative in the region of negative differential resistance because of the decrease of electron charges in the quantum ) - well at increasing forward bias.46,47 CN0 CL Cµ (15) 4. Impedance Model for Solar Cells with Inductive C ) L/R2 (16) Behavior. Examples of devices such as RTD and polymer L rec2 LEDs indicate that the existence of extended transport layers, as in the minority carrier injection model,28-30 is not required According to eq 14 at very low frequency (ω < for the occurrence of inductive behavior. Inductive behavior 1/(Rrec0CN0)), the impedance of the solar cell is a parallel occurs even when charge is injected in layers of small or connection of the dc value of recombination resistance, and ultrasmall dimensions, that is, a range of a few nanometers. a constant negative capacitance, of magnitude CN0, provided The main necessary (but of course not sufficient) condition that CL > Cµ. Then the impedance traces a low-frequency is that the layer can be subjected to a strong difference of arc, toward decreasing resistance, in the fourth quadrant. Fermi levels at the two sides with approprite contacting Otherwise, if CL < Cµ, the impedance remains in the first structures. This condition is realized in the solar cells quadrant. The intercept of Z with the real axis (i.e., the discussed in this work, which contain absorber layers in the transition of C′(ω) to negative values) is at the frequency

Nano Lett., Vol. 6, No. 4, 2006 645 ) 1 1 - 1 1/2 prepared by several dippings in a solution containing titanium ωNC [ ( )] (17) L Cµ CL isopropoxide onto glass substrates coated with conductive SnO2:F and final firing at 500 °C for 30 min. The In(OH)xSy and PbS layers were deposited by the so-called SILAR In the capacitance versus frequency representation, Figure (successive ion layer adsorption reaction) technique from 2d, the presence of the inductor appears as a negative 0.01 M InCl , 0.005 M Pb(AcO) , and 0.01 M Na S (pH ) capacitance that becomes more negative toward lower 3 2 2 7-8) precursor salt solutions and annealing in air at 200 frequencies. The shape of the capacitance over several orders and 120 °C, respectively. During the SILAR process, the of magnitude of variation of C′ is better appreciated in the samples were rinsed in water after each dipping step while plot of the absolute value of capacitance versus frequency, the water was exchanged after each five dips. PEDOT:PSS Figure 2e. At large frequencies the capacitance plot is layers were spin coated. The contact areas were defined by governed by a plateau corresponding to the chemical carbon ink back contacts. More details about TiO /In(OH) S / capacitance, C , and at lower frequencies the circuit capaci- 2 x y µ PbS/PEDOT:PSS eta-solar can be obtained in ref 49. tance begins to decrease because of the inductive effect. It shows a dip at the transition from positive to negative values, The columnar ZnO/CdSe/CuSCN eta-solar cells were produced in the LCMTR at Thiais. A ZnO nanowire array at ωNC, and then the absolute value increases toward lower was electrodeposited on conducting glass substrates, which frequencies, until it saturates at the value CN0. Note in Figure 2d and e that the presence of a series were previously covered with a continuous ZnO sprayed resistance (or additional elements) in the equivalent circuit, layer. As a second step, a very thin CdSe coating was indicated by a line, modifies strongly the shape of the electrodeposited on ZnO nanowires, giving a ZnO/CdSe - capacitance spectra. core shell nanowire array. The empty space of the nano- structure was filled with chemically deposited CuSCN. To In the experiments described below it is found that C is L finish the eta-solar cell, a gold contact was vacuum evapo- much larger than C ; hence, one can use the approximations µ rated on the CuSCN. More details about deposition processes C ) C and N0 L are given in ref 11. The studied samples were annealed in air at temperatures in the range of 350-400 °C for 1 h before ≈ -1/2 ωNC (LCµ) (18) CuSCN deposition. The solid-state DSSC with doped and undoped Spiro- Comparing the solar cell equivalent circuit models with OMeTAD as the transparent hole conductor were made at and without inductor, the inductive effect produces a decrease the Imperial College of London. Details about the preparation of charge accumulation ability of the solar cell and reduces method of the undoped samples are described in ref 10. the steady-state performance as well as the effective lifetime Doped samples were obtained by adding Sb to the OMeTAD of the carriers. solution prior to spin coating the sample. 5. Experimental Section. The four solar cells analyzed To discuss the effect of the negative capacitance, we have been manufactured in four different laboratories. The compared the IS results obtained for the above cells with CdS/CdTe solar cells were grown on 4 × 4cm2 transparent those obtained for a Si monocrystalline solar cell supplied conductive oxide (8 Ω/0) on glass by metal-organic chemical by BP-Solar Spain. From the original cell with a size of vapor deposition (MOCVD)48 at the University of Wales, 12.5 × 12.5 cm2 a smaller piece of 0.49 cm2 was cut in Bangor. The 120-nm CdS window layers were deposited at order to obtain a near homogeneous illumination on the entire a substrate temperature of 300 °C using the organometallics cell surface. dimethylcadmium (DMCd) and ditertiarybutylsulfide (DTBS) Impedance measurements for all of the cells, except for in the ratio 1:2. The 4-µm CdTe absorber layers were grown the CdS/CdTe solar cells, were carried out at Universitat at 350 °C using DMCd and di-isopropyltelluride (DIPTe) Jaume I, Castello´, with an Autolab PGSTAT-30 apparatus, in the ratio 1:1. The structures were activated using the well- equipped with a frequency analyzer module. These measure- known cadmium chloride (CdCl2) treatment at Durham ments were made in the dark and under different illumination University using a 40-nm-thick chloride layer followed by intensities employing a halogen lamp. Bias potentials in both annealing in nitrogen in a tube furnace at 420 °C for 18 min. reverse and forward ranges were applied, while 10 mV ac The surfaces were etched using a solution of nitric and perturbation was used in impedance measurements with a phosphoric acids (1% HNO3, 70% H3PO4, 29% H2O). frequency range from 1 MHz to 0.01 Hz. All of the Finally, gold contacts (∼2.5-mm-diameter dots) were evapo- experiments were performed inside a Faraday cage or rated onto the CdTe layer as back contacts, and In-Ga screened box. IS of CdS/CdTe solar cells was measured at amalgam was applied to the front contact for electrical the University of Durham using a Solartron 1260 frequency connection. Each device comprised four gold dots on a response analyzer and a 1296 dielectric interface. The ∼1cm2 area; the areas around the dot contacts were not amplitude of the ac signal was 40 mV for frequencies ranging scribed to further define the region of charge collection. The from 3 MHz to 0.3 Hz at 20 values per decade. Similarly, efficiency of the analyzed cell is 3.5%. experiments were repeated for different bias conditions. Light The microporous TiO2/In(OH)xSy/PbS/PEDOT:PSS eta- measurements were done under AM1.5 light spectrum at solar cells were produced in the Hahn-Meitner-Institute at various intensities using a commercial ORIEL 300 W solar Berlin. Compact and microporous layers of TiO2 were simulator.

646 Nano Lett., Vol. 6, No. 4, 2006 Figure 3. BP Si monocrystalline solar cell, device capacitance Ctot as function of device potential, VD, for different light intensities, solid line represents the fit of Cµ in the potential region where it is dominant.

6. Results and Discussion. As a practical example for later reference, we first analyze a high-performance Si monocrystalline solar cell, which follows in many respects the ideal model exposed in Section 2. For the Si cell, the observed pattern of impedance in the complex plot consists of a semicircle (not shown). It can be described by means of a series resistance, Rs, connected in series with the parallel association of a resistance Rrec that should be identified with the recombination resistance and the total capacitance of the cell, Ctot. The later is given by Ctot ) Cµ + Cdl, and represents 19 the parallel association of the chemical capacitance, Cµ, which originates from the increase of the minority carrier density, and the capacitance, Cdl, due to the space charge region.17 When the cell is high forward-biased, its capacitance is determined mostly by the chemical capacitance, which increases exponentially with the potential as

∝ - Cµ exp( eVD/η kBT) (19) Figure 4. Impedance spectra for a CdS/CdTe solar cell. (a-c) Complex plane plot of the impedance at two different forward bias where VD is the potential difference in the parallel association in dark conditions. The frequency range employed in the measure- of Rrec and Ctot and η is the diode factor. For reverse bias ment was 1 MHz to 0.1 Hz. (d) Absolute value of capacitance vs the space charge region of the p-n junction (which frequency at forward bias, same data as in Figure 6 but with series constitutes the selective contact to the absorber) enlarges resistance subtracted. while Cµ diminishes so that Ctot ≈ Cdl. The value Cdl can be -2 ) - expressed as Cdl B(V0 VD) where V0 is the built-in remarked that once the bias potential is established the potential and B is a constant.50 capacitance is independent of illumination intensity. This In Figure 3, Ctot is plotted as function of VD for different observation indicates that the forward voltage applied at the light illumination intensities. The behavior of Ctot is divided contacts really fixes the Fermi level throughout the absorber in two regions. For high forward bias, VD <-0.4 V, the silicon layer, as discussed above in the ideal model. capacitance increases exponentially with the absolute VD For reverse bias, the behavior of Ctot with VD has a much value as predicted in eq 19. This is the chemical capacitance smaller gradient, and in this region Ctot ≈ Cdl so that the (usually known in semiconductor device literature as the capacitance is governed by the junction and follows a Mott- diffusion capacitance) of the whole silicon absorber material, Schottky plot. For a conventional DSSC with electrolyte an which is a layer of several hundred micrometers. Fitting the analogous behavior to that shown in Figure 1 has been data in this region, we have obtained the diode factor η ) observed, although with a higher value of η.12,14,15 1.18, which is close to the ideal value η ) 1, as can be For the four types of nanostructured and polycrystalline expected from a high-performance solar cell. It should be solar cells studied in this work, a negative capacitance has

Nano Lett., Vol. 6, No. 4, 2006 647 Figure 5. Real part of the capacitance for the solar cells analyzed under dark for a frequency of 10 Hz. The fit of Ctot for the Si monocrystalline solar cell under dark, Figure 4, is also included for comparison. been observed under dark conditions for high forward bias. An example of the IS results obtained for the CdS/CdTe solar cell is plotted in Figure 4a. In the low-frequency range the complex impedance plot exhibits an arc in the fourth quadrant at the lowest measurement frequencies, indicating that the real part of the capacitance adopts negative values in this frequency range, as shown before in Figure 2b. To obtain a broad view of the results obtained on the different types of solar cells described above, we compare in Figure 5 the bias dependence of the low frequency capacitance with that already described for the Si mono- crystalline solar cell. For the analyzed cells the device capacitance first increases with increasing negative bias, indicating the presence of the chemical capacitance. But in contrast to the Si solar cell, the exponential increase of the capacitance is suppressed at a certain point, and then the capacitance decreases a larger forward bias, taking negative values. We remark that in all of the solar cells considered the resistance is positiVe as it is observed by current-voltage experiments, showing that for all of the cells analyzed the current increases with the forward bias. Figure 6. Absolute value of the real part of the capacitance for The behavior of the capacitance as a function of frequency the solar cells analyzed under dark conditions. The minimum is observed in Figure 6 for the four kinds of analyzed solar observed at intermediate frequencies indicates the transition fre- cells in the dark. The doped OMeTAD sample produced the quency between positive (high frequency) and negative capacitance same effect, but it is not plotted for the sake of clarity. In (low frequency). all of the cases shown in Figure 6 the general features of the capacitance behavior correspond to the model system Toward low frequencies, the capacitance turns into negative presented before in Figure 2e. For high frequency the real values, and for the CdS/CdTe solar cells, it is observed that part of the capacitance of the device increases as the the negative capacitance wing bends toward a constant value frequency is decreased, which is the effect of the series at the lowest frequencies, as in Figure 2e. In the rest of the resistance, until a quasi-plateau region is attained, corre- solar cells, only the range of frequencies with increasing sponding to the chemical capacitance at forward bias. The negative capacitance is observed. The frequency of transition value of the real part of the capacitance in this plateau region between positive and negative capacitance, ωNC, is displaced increases progressively as the forward bias is increased. to higher values as the forward bias increases.

648 Nano Lett., Vol. 6, No. 4, 2006 Figure 7. Parameters resulting from fit of the ZnO/CdSe/CuSCN solar cell spectra to the model of Figure 1e. (a) Capacitance. (b) Mott- Schottky plot of the capacitance. (c) Inductor and inductive negative capacitance. (d) Recombination resistances. As remarked before in Figure 2e, the series resistance extension of the solar cells and the associated diffusion modifies strongly the apparent values of in the effects, we have used the model to fit the data of the ZnO/ C′ versus frequency representation. In Figure 4d the capaci- CdSe/CuSCN solar cell in order to obtain an impression of tance is represented with the series resistance subtracted for the behavior of the parameters in the model, which are shown the CdS/CdTe solar cell. Here, in contrast to Figure 6, the in Figure 7. First we remark that the model effectively high frequency plateau shows the chemical capacitance in realizes the distinction between the positive chemical ca- isolation, and the capacitance is clearly seen to increase at pacitance and the negative contribution of the inductor, while forward bias. In addition, in this representation both this both contributions are mixed in the representation of low plateau and the transition to negative capacitance at low frequency measured capacitance of Figure 5. Indeed Figure frequencies take the true values corresponding to the 7a shows that the capacitance in the model is positive in all equivalent circuit elements. bias conditions and increases at forward bias, as physically The negative values of capacitance are observed only at expected. However, the exponential increase expected in the forward bias, either in dark or illumination conditions, which chemical capacitance, eq 9, is not observed. In reverse is expected, as discussed above, because at reverse bias the voltage (positiVe potentials) the capacitance can be attributed solar cell only displays the blocking nature of the selective to depletion layer in ZnO nanowires, as seen in the Mott- contacts, and injection effects are suppressed. An exception Schottky plot in Figure 7b. Then at negatiVe potentials the is the microporous TiO2/In(OH)xSy/PbS/PEDOT eta-solar capacitance increases faster, but at around -0.5 V the cells. Under illumination a negative capacitance is also increase is detained. This can be attributed to the activation observed for the reverse bias, presumably because of the of the inductor recombination pathway because at -0.5 V particularities of structure of this cell. Our results show that the inductor is first detected (Figure 1c) as well as the for all of the types of cells studied here, the negative associated recombination resistance, Rrec2, Figure 1d. We capacitance behavior is enhanced under illumination in the conclude that in the voltage range around -0.5 V the same manner as for TiO2/InS/PbS/PEDOT eta-solar cell inductive effect prevents the Fermi level from increasing at described above. This observation indicates that the Fermi augmenting forward bias. It should also be remarked that level is not fixed by the voltage applied in the contact, in the inductor decreases toward forward bias by 4 orders of contrast with the Si cell discussed above. magnitude in a small potential window, while the capacitance A reduction in the capacitance of CdS/CdTe solar cells increases only modestly. This explains the observed shift of has also been observed by Friesen et al.,51 and to explain the frequency of negative capacitance to higher values with this effect they employed a model52 in which the CdS/CdTe/ increasing forward bias, eq 18. Au contact behaves as a back-to-back diode. However, while Summarizing, the negative capacitance observed in the that model can explain a reduction of the device capacitance solar cells investigated here indicates a failure in the for high forward bias, it is not capable to explain the negative operation of these devices, due to some dynamic effect that capacitance observed in the present work. prevents the accumulation of charge and reduces the solar Although the equivalent circuit model proposed in Figure cell performance. In crystalline silicon solar cells the 1e is quite simplified, not taking into consideration the spatial dominant pathway of recombination is a surface recombina-

Nano Lett., Vol. 6, No. 4, 2006 649 tion at the contacts, while bulk recombination is slower by (15) van de Lagemaat, J.; Park, N.-G.; Frank, A. J. J. Phys. Chem. B orders of magnitude. It is likely that in the cells investigated 2000, 104, 2044. (16) Zhang, Z.; Zakeeruddin, S. M.; O’Regan, B. C.; Humphry-Baker, here the additional recombination pathway that results in R.; Gra¨tzel, M. J. Phys. Chem. B 2005, 109, 21818. negative capacitance arises because the forward bias also (17) Bisquert, J.; Fabregat-Santiago, F.; Mora-Sero´, I.; Garcia-Belmonte, enhances recombination at the contacts of n and p-type G. 20th European Photovoltaic Solar Energy Conference and Exhibition, Barcelona, 2005. materials to the absorber. The phenomenon appears to be (18) Kumar, R. A.; Suresh, M. S.; Nagaraju, J. IEEE Trans. Electron fairly general, and we call for further investigation to DeVices 2001, 48, 2177. determine the mechanistic origin of the negative capacitance (19) Bisquert, J. Phys. Chem. 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650 Nano Lett., Vol. 6, No. 4, 2006