Implications of the Negative Capacitance Observed at Forward Bias in

NANO LETTERS

Implications of the Negative Capacitance Observed at Forward Bias in Nanocomposite and Polycrystalline Solar Cells

2006 Vol. 6, No. 4 640-650

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 Si monocrystalline solar cells has impelled the research and development of thin-film solar cells based on highly absorbing inorganic semiconductors and on nanocomposite concepts such as the DSSC1,2 and the eta-solar cells.3-5 One of the most intensively studied types of thin-film devices is the polycrystalline cell based on CdS/CdTe heterojunction, with a record efficiency of 16.5%.6 Such devices are among the best candidates for terrestrial applica* Corresponding authors. E-mail: [email protected]; [email protected]. † Now at NPAC, Northumbria University, Ellison Building, Ellison Place, Newcastle upon Tyne, NE1 8ST. 10.1021/nl052295q CCC: $33.50 Published on Web 02/23/2006

© 2006 American Chemical Society

tions because of the relatively high efficiency, long-term stability in the performance, and potential for low-cost production. Because of the high absorption coefficient of CdTe (>104 cm-1), a layer of this material with a thickness of only about 2 µm is sufficient to absorb most of the useful part of the solar spectrum.7,8 However, other types of solar cells such as DSSC and etasolar cells, based on alternative concepts, have also been investigated thoroughly with the aim to decrease the production cost significantly. The attractive side of such devices is a very thin absorber, a monolayer of dye for DSSC, or a semiconductor absorber layer with thickness of tenths of

nanometers for eta-solar devices. In these devices, the absorber layer is situated in a nanometric or micrometric matrix allowing for a significant improvement in the light absorption because of the large effective area of the matrix. In these cells, the photogenerated carriers are transferred into two different media. This fact allows one to relax the highquality requirements of single-crystal p-n junction devices, enabling low-cost fabrication processes to be employed. In the conventional DSSC, the dye molecules are regenerated by a redox couple dissolved in an electrolyte. The use of an electrolyte causes problems in the process of its encapsulation and in the long-term stable performance. One of the options intended to avoid this problem is substituting this liquid electrolyte with a transparent hole semiconductor, such as Spiro-OMeTAD (2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenilamine)-9,9′-spirobifluorene).9 However, these solidstate devices present a lower efficiency (∼4.5%) than those with a liquid electrolyte DSSC (∼10%). Those effects have been attributed to higher recombination dynamics.10 The DSSC configuration has also inspired an alternative all-solid device, the eta-solar cell with a semiconducting extremely thin absorber sandwiched between two transparent, highly interpenetrated semiconductors of different kinds.3-5 The highest efficiency demonstrated to date for this type of cell is 2.3% at 1/3 sun, obtained for an eta-solar cell of columnar structure ZnO/CdSe/CuSCN,11 which is one of the types of cells studied in this work. Additionally, an eta-solar cell made with microporous TiO2/In(OH)xSy/PbS/PEDOT (∼1% efficiency) has also been studied, presenting the interests of the use of an organic polymer as a hole conductor and the system of In(OH)xSy/PbS to improve the contact selectivity. The potentialities of these four types of solar cells (in the presented and related configurations) stimulate an interest in the study of their ac impedance behavior, which can provide diverse information on device properties and performance. Impedance spectroscopy (IS) is a well-known ac technique used for the study of electrochemical and solidstate systems and has been employed extensively in the characterization of DSSC devices.12-16 However, the utilization of this technique in the characterization of solid-state solar cells is not regular, although a few examples are shown in the literature.17,18 In principle, impedance spectroscopy measurements taken over a broad frequency range (millihertz to megahertz) may provide information on any system that is composed of a combination of interfacial and bulk transport processes, particularly on transport coefficients, recombination parameters, and interfacial states in solar cells. It is this that makes the technique especially valuable for the characterization of the devices mentioned above, with a broader aim to find the ways to improve their performance and/or stability. In solar cells, ac impedance measurements are normally used in reverse conditions to obtain information on interfacial characteristics (admittance spectroscopy). In this work we have systematically analyzed by IS data over a wide range of biasing potential, both under reverse and forward bias, using dark and light conditions, for samples of four different Nano Lett., Vol. 6, No. 4, 2006

types of solar cells: CdS/CdTe thin-film solar cells, microporous TiO2/In(OH)xSy/PbS/PEDOT, columnar ZnO/ CdSe/CuSCN eta-solar cells, and a solid-state DSSC with doped and undoped Spiro-OMeTAD as the transparent hole conductor. In all cases, a strong negative capacitance has been observed at low frequencies for high forward bias conditions. Such behavior is compared with the (positive) capacitance of a high performance silicon solar cell, and the implications of the negative capacitance effect as well as possible interpretations are discussed. 2. General Model for Solar Cell Ac Impedance and Capacitance. As a preliminary step toward the discussion of negative capacitance, we summarize in this section a basic but quite general model for a solar cell that incorporates the fundamental photovoltaic principles2 and the corresponding behavior under measurement of ac impedance, extending a previous model of frequency response of solar cells.19 The key point of the efficient solar-cell energy conversion is the combination of carrier generation by light absorption and charge separation.2 The simple model of Figure 1a contains the basic elements of the conversion process common to all solar cells.2 The model is a simple two-level general system formed by an absorber material (which can be a single molecule, a semiconductor crystal network, or an organic polymer), where carriers can be promoted from the valence band to the conduction band by light excitation. The solar cell is completed with selective contacts to electrons and holes, which consist of n- and p-type materials, respectively, both in contact with the light absorber. Although the diagram is one-dimensional for the sake of clarity, the spatial structure of the solar may have any form, but it is obviously required that the n- and p-type materials be separated spatially in order to avoid internal short-circuit. The selective contacts have the function of converting the carriers from a state of nonequilibrium Fermi level in the absorber to a material (normally a metal) in which the carrier is at the equilibrium Fermi level.20 Selective contacts may require some combination of materials, such as nanostructured TiO2 plus conducting glass in DSSC. Efficient charge separation requires that each selective contact equilibrates its Fermi level to only one kind of carrier.21 With ideal, reversible selective contacts, the quasi-Fermi level is continuous at the interfaces between both n- and p-type materials and the absorber, as shown in Figure 1a so that there are no irreversible losses associated with the extraction process. The only irreversible process necessarily present in this ideal model of a solar cell is the radiative recombination of excess carriers in the absorber, which is unavoidable because of the microscopic reversibility of the excitation process.22 The excitation by light produces excess electrons and holes in the carrier bands, which causes the separation of the quasiFermi levels, EFn and EFp, of the two states in the absorber.23 To simplify the number of variables in the model, we assume, without loss of generality, that the increase of density of holes can be neglected (by initial p-doping of the absorber), so that EFp ) EF0, the equilibrium Fermi level. It is also assumed in this simple model that the mobilities of both electrons and holes are infinite. There are, therefore, no limitations 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 extended; hence, the Fermi levels are homogeneous, and the voltage measured at outer contacts is given by V ) -(EFn - EF0)/e

(1)

where e is the positive elementary charge. The concentration of electrons with density n under generation by incident light at a rate G is governed by the conservation equation dn ) -Ic + G - U dt

(2)

where Ic is the volume density of electrons extracted per unit 642

time through the electron-selective contact, and U is the recombination rate, which we assume of the simplest type

U)

n - n0 τ

(3)

where n0 is the equilibrium concentration and τ is the lifetime for first-order recombination. Equation 2 states the variation of the number of electrons in the conduction band in a volume element by the three processes indicated by arrows in Figure 1a: extraction, generation, and recombination. Note 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 G ) 0. Nano Lett., Vol. 6, No. 4, 2006

If the electrons obey Boltzmann statistics, then n ) n0e(EFn - EF0)/kBT

(4)

where kB is Boltzmann’s constant and T the temperature. At steady state (dn/dt ) 0) a certain concentration of electrons, nj, is established by equilibrium between injection, generation, and recombination at a fixed rate. From eqs 2-4 the steadystate relationship between the number of extracted carriers per unit time and applied voltage can be written Ic ) G -

n0 -eV/kBT - 1) (e τ

(5)

This is the ideal diode equation, which is seen to arise from a simple conservation equation. The characteristic exponential law in eq 5 is produced by the combination of Boltzmann statistics and first-order recombination kinetics. Note in eq 5 that the forward bias is obtained at negative voltage, as is conventional in semiconductor device literature, while the opposite convention is often used in the solar cell literature. The thermal generation current, n0/τ, gives the constant current at reverse bias in the diode equation. Equation 5 also relies on the assumption that the electron Fermi level, EFn, is determined by the voltage applied at the outer contacts, through eq 1, independent of the photogeneration rate, G.24 Let us derive the ac impedance model corresponding to the fundamental, idealized model of the solar cell that we have presented. In IS the solar cell is set at a certain steady state of illumination, G h , and applied potential, V h , with the corresponding current hIc given in eq 5. A small timedependent perturbation of potential is applied, so that V ) V h + φ(t), with the associated change of current, Ic ) hIc + ic(t). The photogeneration rate, G, cannot be affected by the potentiostat. But the modulation of potential does change the electron Fermi level, EFn ) E h Fn - eφ, and hence the electron concentration. Expanding eq 4 to first order it is found that

(

n ) nj 1 -

eφ kBT

)

(6)

Introducing eq 6 into eq 2, and removing the timeindependent terms that cancel out by eq 5, we find the following result eic )

nje2 dφ nje2 + φ kBT dt kBTτ

(7)

We express this result as j ) Cµ

dφ φ + dt Rrec

(8)

The term in the left of eq 8 is j ) -eic, the electrical current extracted per unit volume. The first term in the right Nano Lett., Vol. 6, No. 4, 2006

side can be recognized as a capacitive current of the type j ) C(dV/dt). The capacitance per unit volume is the chemical capacitance, Cµ, given by Cµ )

nje2 kBT

(9)

Equation 9 is a particular instance, for the Boltzmann statistics, of the general definition19 C µ ) e2

∂n ∂EFn

(10)

Chemical capacitance is an equilibrium property that relates a variation of carrier density to a displacement of the Fermi level. As an equilibrium property it is always a positive quantity. The second term on the right of eq 8, φn/Rrec, defines the recombination resistance Rrec )

kBTτ nje2

(11)

More exactly, the steady-state value φss ) 0 is taken as the baseline for potentials φ, so that the small perturbation 19 value of the recombination current is irec ) R-1 rec (φ - φnss). In the measurement of impedance spectroscopy, the time variation of the small perturbation signals is sinusoidal. This case is obtained by the Laplace transform of eq 8, with the substitution d/dt f iω, being ω the angular frequency. Hence j ) iωCµφ +

φ Rrec

(12)

Because the impedance of the capacitor is Z ) 1/iωCµ, eq 12 indicates that the current to the outer circuit is composed of two branches in parallel at the common voltage φ so that the model can be represented as the equivalent circuit of Figure 1b. Although IS does not consider explicitly the light generation term as a circuit element, the equivalent circuit model of Figure 1b contains the fundamental elements of photovoltaic conversion.19 Excess carriers in the conduction band create a Voltage (Fermi level) by virtue of the chemical capacitor. The carriers have two ways to escape: either through the recombination resistor or the external pathway and will take that of less resistance. Therefore, the recombination resistance is the element that keeps the carriers contained in the capacitor and facilitates their extraction. For efficient conversion, Rrec must be large. Traditionally, equivalent circuits used in solar cell descriptions are for dc characteristics and include a diode and no capacitor. In the ac model of Figure 1b the diode is represented by the voltage dependence of the recombination resistance, indicated in eq 11 through dependence on nj. In fact Rrec is equivalent to the reciprocal derivative of eq 5. 643

Figure 2. Representation of the impedance in the complex plane plot and real part of the capacitance vs frequency for solar cell impedances. (a and b) RC-RC circuit representing recombination resistance Rrec ) 103 Ω/cm2 and chemical capacitance Cµ ) 5 × 10 - 6 F/cm2 in parallel, and the effect of nonideal selective contact with parameters Rc1 ) 5 × 102 Ω/cm2 and Cc1 ) 10 - 8 F/cm2. 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 2 frequency ωτ ) τ-1 n ) 1/RrecCµ, and the characteristic frequency of the contact (3.2 × 10 Hz), related to the angular frequency ωc1 ) 1/Rc1Cc1. (c) Complex plane plot of the impedance model R + RC(R + L) circuit representing recombination resistance Rrec1 ) Rrec ) 103 Ω/cm2 and chemical capacitance Cµ ) 5 × 10 - 4 F/cm2 in parallel, and the inductive effect by an inductor L ) 1 × 105 H/cm2 in series with a resistor Rrec2 ) 3 × 103 Ω/cm2 (f)0.75). CL ) 0.011 F/cm2, CN0 ) 0.010 F/cm2. 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 ) -3 Hz), related to the angular frequency ω τ-1 RL ) Rrec2/L. (d n ) 1/RrecCµ, and a characteristic frequency of the inductive loop (0.47 × 10 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 contact, it must be a material (or combination of materials) different than the absorber in order to block the holes. The process of electron transfer through the interface introduces a drop of the Fermi level between the absorber and the n material, as indicated in Figure 1c. In the equivalent circuit the electron-selective contact is associated with resistance and capacitance as indicated in Figure 1d. The contact resistance, Rc1, reduces the extracted current, therefore Rc1 is required to be low for efficient solar cell operation. For representation, the impedance is separated in real and imaginary parts as Z ) Z′ + iZ′′. Figure 2a shows the complex plane plot of the impedance of the model of Figure 1c, consisting of two semicircles that corrrespond to the two RC circuits in series. Another possible representation of the impedance response, useful in many cases, is the complex capacitance, defined from the impedance, as C ) 1/(iωZ). The complex capacitance is written as C ) C′ + iC′′ where C′ ) Re(C). Figure 2b shows the real part of the capacitance for the model of Figure 1d. 644

It should be recognized that the model presented in Figure 1c and the equivalent circuit in Figure 1d is in many ways a first approximation to the ac response of solar cells and does not aim to be universal. In particular, the impedance response of selective contacts may be more complex, and recombination and extraction are not necessarily serial processes. Elements of the contacts may appear connected in parallel with the basic circuit RrecCµ, and the selective contact itself may display a significant chemical capacitance, as in TiO2 DSSC.25 However, in reasonably efficient solar cells we do expect to observe at forward bias a predominance of the RrecCµ subcircuit so that the model should be generally appropriate. In contrast, at reverse bias the absorber will be depleted of carriers and the impedance will be controlled by the response of the selective contacts that will exhibit their blocking nature. 3. General Characteristics of the Negative Capacitance in Electronic and Electrochemical Devices. Although most systems investigated by IS can be described with (positive) resistors and capacitors, with Z′ > 0 and C′ > 0, respectively, Nano Lett., Vol. 6, No. 4, 2006

the appearance of negative capacitance (or inductive behavior) is not uncommon. For an electronic device that is close to equilibrium, that is, at low dc current, negative capacitance or resistance are not allowed because such elements would upset the principles of thermodynamics. However, far from equilibrium, under strong steady-state bias, negative capacitance and resistance is not prevented by thermodynamics. Negative capacitance (or inductive behavior) has been observed in a variety of electronic devices such as Schottky diodes,26,27 short based p-n junctions,28-30 polymer lightemitting diodes,31-33 and DSSC.34 The inductive feature of the ac impedance is also found in electrochemical measurements of electrocatalysis, electrodeposition, and electrodissolution.35-43 Recently, inductive behavior at high frequency was found in the nanostructured TiO2 permeated with ionic liquid.44 There are two main types of interpretations suggested for the negative capacitance. In the short-base p-n junction, the minority carrier depopulation at high forward bias induces a change of sign of the capacitance.28-30 The mechanism, associated to spatial distribution of the carriers, has been modeled regarding the series resistance corresponding to the neutral diode regions in addition to the diffusion (minority carrier) capacitance.29 In another more general class of mechanism, the inductive behavior takes place when the current between two electronic reservoirs (such as oxidized and reduced ionic species in solution or two bulk semiconductors connected by a quantum well) is governed by the occupation of an intermediate state, which decreases when the applied potential increases. An example is the electrocatalytic reaction A T C controlled by an intermediate absorbed species B. Such electrocatalytic reactions display an inductive feature when the concentration of the adsorbed species decreases while the potential increases, contrary to the equilibrium isotherm, as a result 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 Fermi level.27 In double-barrier resonant tunneling diodes (RTD), the quantum capacitance, defined as the change of the charge stored in the quantum well with respect to a change of the potential in the RTD46 (in close correspondence to the chemical capacitance discussed above), becomes 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 4. Impedance Model for Solar Cells with Inductive Behavior. Examples of devices such as RTD and polymer LEDs indicate that the existence of extended transport layers, as in the minority carrier injection model,28-30 is not required for the occurrence of inductive behavior. Inductive behavior occurs even when charge is injected in layers of small or ultrasmall dimensions, that is, a range of a few nanometers. The main necessary (but of course not sufficient) condition is that the layer can be subjected to a strong difference of Fermi levels at the two sides with approprite contacting structures. This condition is realized in the solar cells discussed in this work, which contain absorber layers in the Nano Lett., Vol. 6, No. 4, 2006

nanometer range that can be strongly forward-biased. Furthermore, such solar cells display a rather irregular distribution of electrical fields in the complex morphological structure, and in addition, minority carriers do not exist as such because electrons and holes are transported in separate materials. We propose that injection in recombination layers of nanostructured solar cells may also lead to inductive behavior. We have argued above that at high forward bias the solar cell impedance is generally controlled by recombination resistance and chemical capacitance. Therefore, we extend such a model as indicated in the equivalent circuit Figure 1e. In addition to the recombination resistance, Rrec1, that is in parallel with the chemical capacitance, as in the ideal model, in Figure 1e an additional recombination pathway is included, consisting of the combination of a resistance, Rrec2, and an inductor with impedance Z ) iωL. In the absence of sufficient knowledge about the specific mechanisms that may lead to the inductive behavior in the different solar cells discussed below, the model is proposed at the level of equivalent circuits. The impedance and capacitance response of the inductive solar cell model are shown in Figure 2c-e. In the complex plot, Figure 2c, we observe the inductive loop at low frequency that reduces the dc value of the recombination resistance. If we denote Rrec1 ) Rrec and Rrec2 ) f/(1 - f)Rrec, where 0 < f < 1, then, because of the fact that the inductor is shunted at zero frequency, we obtain that the dc value of the total recombination resistance, Rrec, is decreased with respect to the inductor-free model as Rrec0 ) f Rrec. The admittance, Y ) Z-1, of the three-branched circuit is given by Y(ω) )

1 1 + + iωCµ Rrec1 Rrec2 + iωL

(13)

The low-frequency limit of eq 13 is Y(ω) )

1 - iωCN0 Rrec0

(14)

where CN0 ) CL - Cµ

(15)

CL ) L/R2rec2

(16)

According to eq 14 at very low frequency (ω < 1/(Rrec0CN0)), the impedance of the solar cell is a parallel connection of the dc value of recombination resistance, and a constant negative capacitance, of magnitude CN0, provided that CL > Cµ. Then the impedance traces a low-frequency arc, toward decreasing resistance, in the fourth quadrant. Otherwise, if CL < Cµ, the impedance remains in the first quadrant. The intercept of Z with the real axis (i.e., the transition of C′(ω) to negative values) is at the frequency 645

ωNC )

[(

1 1 1 L Cµ CL

)]

1/2

(17)

In the capacitance versus frequency representation, Figure 2d, the presence of the inductor appears as a negative capacitance that becomes more negative toward lower frequencies. The shape of the capacitance over several orders of magnitude of variation of C′ is better appreciated in the plot of the absolute value of capacitance versus frequency, Figure 2e. At large frequencies the capacitance plot is governed by a plateau corresponding to the chemical capacitance, Cµ, and at lower frequencies the circuit capacitance begins to decrease because of the inductive effect. It shows a dip at the transition from positive to negative values, at ωNC, and then the absolute value increases toward lower frequencies, until it saturates at the value CN0. Note in Figure 2d and e that the presence of a series resistance (or additional elements) in the equivalent circuit, indicated by a line, modifies strongly the shape of the capacitance spectra. In the experiments described below it is found that CL is much larger than Cµ; hence, one can use the approximations CN0 ) CL and ωNC ≈ (LCµ)-1/2

(18)

Comparing the solar cell equivalent circuit models with and without inductor, the inductive effect produces a decrease of charge accumulation ability of the solar cell and reduces the steady-state performance as well as the effective lifetime of the carriers. 5. Experimental Section. The four solar cells analyzed have been manufactured in four different laboratories. The CdS/CdTe solar cells were grown on 4 × 4 cm2 transparent conductive oxide (8 Ω/0) on glass by metal-organic chemical vapor deposition (MOCVD)48 at the University of Wales, Bangor. The 120-nm CdS window layers were deposited at a substrate temperature of 300 °C using the organometallics dimethylcadmium (DMCd) and ditertiarybutylsulfide (DTBS) in the ratio 1:2. The 4-µm CdTe absorber layers were grown at 350 °C using DMCd and di-isopropyltelluride (DIPTe) in the ratio 1:1. The structures were activated using the wellknown cadmium chloride (CdCl2) treatment at Durham University using a 40-nm-thick chloride layer followed by annealing in nitrogen in a tube furnace at 420 °C for 18 min. The surfaces were etched using a solution of nitric and phosphoric acids (1% HNO3, 70% H3PO4, 29% H2O). Finally, gold contacts (∼2.5-mm-diameter dots) were evaporated onto the CdTe layer as back contacts, and In-Ga amalgam was applied to the front contact for electrical connection. Each device comprised four gold dots on a ∼1 cm2 area; the areas around the dot contacts were not scribed to further define the region of charge collection. The efficiency of the analyzed cell is 3.5%. The microporous TiO2/In(OH)xSy/PbS/PEDOT:PSS etasolar cells were produced in the Hahn-Meitner-Institute at Berlin. Compact and microporous layers of TiO2 were 646

prepared by several dippings in a solution containing titanium 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 (successive ion layer adsorption reaction) technique from 0.01 M InCl3, 0.005 M Pb(AcO)2, and 0.01 M Na2S (pH ) 7-8) precursor salt solutions and annealing in air at 200 and 120 °C, respectively. During the SILAR process, the samples were rinsed in water after each dipping step while the water was exchanged after each five dips. PEDOT:PSS layers were spin coated. The contact areas were defined by carbon ink back contacts. More details about TiO2/In(OH)xSy/ PbS/PEDOT:PSS eta-solar can be obtained in ref 49. The columnar ZnO/CdSe/CuSCN eta-solar cells were produced in the LCMTR at Thiais. A ZnO nanowire array was electrodeposited on conducting glass substrates, which were previously covered with a continuous ZnO sprayed layer. As a second step, a very thin CdSe coating was electrodeposited on ZnO nanowires, giving a ZnO/CdSe core-shell nanowire array. The empty space of the nanostructure was filled with chemically deposited CuSCN. To finish the eta-solar cell, a gold contact was vacuum evaporated on the CuSCN. More details about deposition processes 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 CuSCN deposition. The solid-state DSSC with doped and undoped SpiroOMeTAD as the transparent hole conductor were made at the Imperial College of London. Details about the preparation method of the undoped samples are described in ref 10. Doped samples were obtained by adding Sb to the OMeTAD solution prior to spin coating the sample. To discuss the effect of the negative capacitance, we compared the IS results obtained for the above cells with those obtained for a Si monocrystalline solar cell supplied by BP-Solar Spain. From the original cell with a size of 12.5 × 12.5 cm2 a smaller piece of 0.49 cm2 was cut in order to obtain a near homogeneous illumination on the entire cell surface. Impedance measurements for all of the cells, except for the CdS/CdTe solar cells, were carried out at Universitat Jaume I, Castello´, with an Autolab PGSTAT-30 apparatus, equipped with a frequency analyzer module. These measurements were made in the dark and under different illumination intensities employing a halogen lamp. Bias potentials in both reverse and forward ranges were applied, while 10 mV ac perturbation was used in impedance measurements with a frequency range from 1 MHz to 0.01 Hz. All of the experiments were performed inside a Faraday cage or screened box. IS of CdS/CdTe solar cells was measured at the University of Durham using a Solartron 1260 frequency response analyzer and a 1296 dielectric interface. The amplitude of the ac signal was 40 mV for frequencies ranging from 3 MHz to 0.3 Hz at 20 values per decade. Similarly, experiments were repeated for different bias conditions. Light measurements were done under AM1.5 light spectrum at various intensities using a commercial ORIEL 300 W solar simulator. 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 the parallel association of the chemical capacitance, Cµ,19 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)

where VD is the potential difference in the parallel association of Rrec and Ctot and η is the diode factor. For reverse bias the space charge region of the p-n junction (which constitutes the selective contact to the absorber) enlarges while Cµ diminishes so that Ctot ≈ Cdl. The value Cdl can be expressed as C-2 dl ) B(V0 - VD) where V0 is the built-in potential and B is a constant.50 In Figure 3, Ctot is plotted as function of VD for different light illumination intensities. The behavior of Ctot is divided in two regions. For high forward bias, VD < -0.4 V, the capacitance increases exponentially with the absolute VD value as predicted in eq 19. This is the chemical capacitance (usually known in semiconductor device literature as the diffusion capacitance) of the whole silicon absorber material, which is a layer of several hundred micrometers. Fitting the data in this region, we have obtained the diode factor η ) 1.18, which is close to the ideal value η ) 1, as can be expected from a high-performance solar cell. It should be Nano Lett., Vol. 6, No. 4, 2006

Figure 4. Impedance spectra for a CdS/CdTe solar cell. (a-c) Complex plane plot of the impedance at two different forward bias in dark conditions. The frequency range employed in the measurement was 1 MHz to 0.1 Hz. (d) Absolute value of capacitance vs frequency at forward bias, same data as in Figure 6 but with series resistance subtracted.

remarked that once the bias potential is established the capacitance is independent of illumination intensity. This observation indicates that the forward voltage applied at the contacts really fixes the Fermi level throughout the absorber silicon layer, as discussed above in the ideal model. For reverse bias, the behavior of Ctot with VD has a much smaller gradient, and in this region Ctot ≈ Cdl so that the capacitance is governed by the junction and follows a MottSchottky plot. For a conventional DSSC with electrolyte an analogous behavior to that shown in Figure 1 has been observed, although with a higher value of η.12,14,15 For the four types of nanostructured and polycrystalline solar cells studied in this work, a negative capacitance has 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 monocrystalline 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. The behavior of the capacitance as a function of frequency is observed in Figure 6 for the four kinds of analyzed solar cells in the dark. The doped OMeTAD sample produced the same effect, but it is not plotted for the sake of clarity. In all of the cases shown in Figure 6 the general features of the capacitance behavior correspond to the model system presented before in Figure 2e. For high frequency the real part of the capacitance of the device increases as the frequency is decreased, which is the effect of the series resistance, until a quasi-plateau region is attained, corresponding to the chemical capacitance at forward bias. The value of the real part of the capacitance in this plateau region increases progressively as the forward bias is increased. 648

Figure 6. Absolute value of the real part of the capacitance for the solar cells analyzed under dark conditions. The minimum observed at intermediate frequencies indicates the transition frequency between positive (high frequency) and negative capacitance (low frequency).

Toward low frequencies, the capacitance turns into negative values, and for the CdS/CdTe solar cells, it is observed that the negative capacitance wing bends toward a constant value at the lowest frequencies, as in Figure 2e. In the rest of the solar cells, only the range of frequencies with increasing negative capacitance is observed. The frequency of transition between positive and negative capacitance, ωNC, is displaced to higher values as the forward bias increases. 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) MottSchottky plot of the capacitance. (c) Inductor and inductive negative capacitance. (d) Recombination resistances.

As remarked before in Figure 2e, the series resistance modifies strongly the apparent values of capacitances in the C′ versus frequency representation. In Figure 4d the capacitance is represented with the series resistance subtracted for the CdS/CdTe solar cell. Here, in contrast to Figure 6, the high frequency plateau shows the chemical capacitance in isolation, and the capacitance is clearly seen to increase at forward bias. In addition, in this representation both this plateau and the transition to negative capacitance at low frequencies take the true values corresponding to the equivalent circuit elements. The negative values of capacitance are observed only at forward bias, either in dark or illumination conditions, which is expected, as discussed above, because at reverse bias the solar cell only displays the blocking nature of the selective contacts, and injection effects are suppressed. An exception is the microporous TiO2/In(OH)xSy/PbS/PEDOT eta-solar cells. Under illumination a negative capacitance is also observed for the reverse bias, presumably because of the particularities of structure of this cell. Our results show that for all of the types of cells studied here, the negative capacitance behavior is enhanced under illumination in the same manner as for TiO2/InS/PbS/PEDOT eta-solar cell described above. This observation indicates that the Fermi level is not fixed by the voltage applied in the contact, in contrast with the Si cell discussed above. A reduction in the capacitance of CdS/CdTe solar cells has also been observed by Friesen et al.,51 and to explain this effect they employed a model52 in which the CdS/CdTe/ Au contact behaves as a back-to-back diode. However, while that model can explain a reduction of the device capacitance for high forward bias, it is not capable to explain the negative capacitance observed in the present work. Although the equivalent circuit model proposed in Figure 1e is quite simplified, not taking into consideration the spatial Nano Lett., Vol. 6, No. 4, 2006

extension of the solar cells and the associated diffusion effects, we have used the model to fit the data of the ZnO/ CdSe/CuSCN solar cell in order to obtain an impression of the behavior of the parameters in the model, which are shown in Figure 7. First we remark that the model effectively realizes the distinction between the positive chemical capacitance and the negative contribution of the inductor, while both contributions are mixed in the representation of low frequency measured capacitance of Figure 5. Indeed Figure 7a shows that the capacitance in the model is positive in all bias conditions and increases at forward bias, as physically expected. However, the exponential increase expected in the chemical capacitance, eq 9, is not observed. In reverse voltage (positiVe potentials) the capacitance can be attributed to depletion layer in ZnO nanowires, as seen in the MottSchottky plot in Figure 7b. Then at negatiVe potentials the capacitance increases faster, but at around -0.5 V the increase is detained. This can be attributed to the activation of the inductor recombination pathway because at -0.5 V the inductor is first detected (Figure 1c) as well as the associated recombination resistance, Rrec2, Figure 1d. We conclude that in the voltage range around -0.5 V the inductive effect prevents the Fermi level from increasing at augmenting forward bias. It should also be remarked that the inductor decreases toward forward bias by 4 orders of magnitude in a small potential window, while the capacitance increases only modestly. This explains the observed shift of the frequency of negative capacitance to higher values with increasing forward bias, eq 18. Summarizing, the negative capacitance observed in the solar cells investigated here indicates a failure in the operation of these devices, due to some dynamic effect that prevents the accumulation of charge and reduces the solar cell performance. In crystalline silicon solar cells the dominant pathway of recombination is a surface recombina649

tion at the contacts, while bulk recombination is slower by orders of magnitude. It is likely that in the cells investigated here the additional recombination pathway that results in negative capacitance arises because the forward bias also enhances recombination at the contacts of n and p-type materials to the absorber. The phenomenon appears to be fairly general, and we call for further investigation to determine the mechanistic origin of the negative capacitance in the polycrystalline and nanocomposite solar cells. 7. Conclusions. A negative capacitance behavior has been observed in high forward bias and low frequency in four different types of solar cells: of thin-film CdS/CdTe devices, microporous TiO2/In(OH)xSy/PbS/PEDOT and columnar ZnO/CdSe/CuSCN eta-solar cells, and a solid-state DSSC with Spiro-OMeTAD as the transparent hole conductor. In all cases the photogenerated carriers due to device illumination enhance this effect. The negative capacitance is associated with an additional recombination pathway that opens up at forward bias and decreases the charge accumulation ability of the solar cell, reducing its performance. Acknowledgment. The work was supported by Ministerio de Educacio´n y Ciencia of Spain under project MAT200405168. We acknowledge BP Spain for providing the Si monocrystalline solar cell. References (1) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737. (2) Bisquert, J.; Cahen, D.; Ru¨hle, S.; Hodes, G.; Zaban, A. J. Phys. Chem. B 2004, 108, 8106. (3) Ernst, K.; Belaidi, A.; Ko¨nenkamp, R. Semicond. Sci. Technol. 2003, 18, 63. (4) Ernst, K.; Lux-Steiner, M. C.; Ko¨nenkamp, R. Eur. PhotoVoltaic Sol. Energy Conf., Proc. Int. Conf., 16th 2000, 63. (5) Le´vy-Cle´ment, C.; Katty, A.; Bastide, S.; Zenia, F.; Mora, I.; MunozSanjose, V. Physica E 2002, 14, 229. (6) Wu, X.; Kane, J. C.; Dhere, R. G.; DeHart, C.; Albin, D. S.; Duda, A.; Gessert, T. A.; Asher, S.; Levi, D. H.; Sheldon, P. 17th European Photovoltaic Solar Energy Conference and Exhibition, Munich, 2002. (7) Romeo, A.; Terheggen, M.; Abou-Ras, D.; Ba¨tzner, D. L.; Haug, F.-J.; Ka¨lin, M.; Rudmann, D.; Tiwari, A. N. Prog. PhotoVoltaics 2004, 12, 93-111. (8) Durose, K.; Edwards, P. R.; Halliday, D. P. J. Cryst. Growth 1999, 197, 733. (9) Kru¨ger, J.; Plass, R.; Cevey, L.; Piccirelli, M.; Gra¨tzel, M.; Bach, U. Appl. Phys. Lett. 2001, 79, 2085. (10) Fabregat-Santiago, F.; Bisquert, J.; Palomares, E.; Durrant, J. R., in preparation, 2005. (11) Le´vy-Cle´ment, C.; Tena-Zaera, R.; Ryan, M. A.; Katty, A.; Hodes, G. AdV. Mater. 2005, 17, 1512. (12) Kern, R.; Sastrawan, R.; Ferber, J.; Stangl, R.; Luther, J. Electrochim. Acta 2002, 47, 4213. (13) Fabregat-Santiago, F.; Garcı´a-Can˜adas, J.; Palomares, E.; Clifford, J. N.; Haque, S. A.; Durrant, J. R.; Garcia-Belmonte, G.; Bisquert, J. J. Appl. Phys. 2004, 96, 6903. (14) Fabregat-Santiago, F.; Bisquert, J.; Garcia-Belmonte, G.; Boschloo, G.; Hagfeldt, A. Sol. Energy Mater. Sol. Cells 2005, 87, 117.

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