Issue 
EPJ Photovolt.
Volume 8, 2017
Topical Issue: Theory and modelling



Article Number  85501  
Number of page(s)  6  
Section  Theory and Modelling  
DOI  https://doi.org/10.1051/epjpv/2017001  
Published online  24 March 2017 
https://doi.org/10.1051/epjpv/2017001
Influence of Schottky contact on the CV and JV characteristics of HTMfree perovskite solar cells
^{1} UMR FOTON CNRS 6082, INSA, 35708 Rennes, France
^{2} Institute of Chemistry, Casali Center for Applied Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 91904 Jerusalem, Israel
^{a}
email: jacky.even@insarennes.fr
Received: 30 September 2016
Accepted: 3 January 2017
Published online: 24 March 2017
The influence of the Schottky contact is studied for hole transport material (HTM) free CH_{3}NH_{3}PbI_{3} perovskite solar cells (PSCs), by using driftdiffusion and small signal models. The basic currentvoltage and capacitancevoltage characteristics are simulated in reasonable agreement with experimental data. The build in potential of the finite CH_{3}NH_{3}PbI_{3} layer is extracted from a MottSchottky capacitance analysis. Furthermore, hole collector conductors with workfunctions of more than 5.5 eV are proposed as solutions for high efficiency HTMfree CH_{3}NH_{3}PbI_{3} PSCs.
© Y. Huang et al., published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
Due to their potential for photoinduced carrier separation [1], various HeteroJunction Solar Cells (HJSCs) have been experimentally [2, 3] and theoretically [4, 5] investigated Selected doped functional materials are added on each side of the Light Harvesting Material (LHM) to select photoinduced carriers. The electron transport material (ETM) is used to extract photoinduced electrons and block holes, while the hole transport material (HTM) has a complementary function. HJSCs based on lowcost, easy processed [6, 7, 8] and highly absorbing [9, 10] semiconductor [11] halide perovskites have indeed led to high Photontoelectron Conversion Efficiency (PCE) rising from 3.8% (2009) up to 22.1% (2016). Nowadays, these values are very close to the record value of silicon based solar cells (25.6%) [12].
As predicted from the detailed balance principle [13], if no defectassisted recombination occurs in LHM and if the cell open circuit voltage (V_{OC}) equals to LHM’s energy band gap (E_{g}) divided by elemental electron charge (q) the silicon based and the Perovskite based Solar Cells (PSC) should achieve maximum PCE of 44% and 37%, respectively. However, due to limited Internal PL quantum yield (iQY) and nonzero entropy, the maximum V_{OC}[14] is smaller than E_{g}: (1)where T is the absolute temperature and k_{B} is the Boltzmann constant. If optical losses are weak and the contacts are almost ideal, an open circuit voltage (V_{OC}) of about 1.2 V is expected for CH_{3}NH_{3}PbI_{3}[15]. In pace with the enhancement of stability [16, 17], the influence of defects was weakened down to an acceptable level [18, 19], while the band offsets between the LHM and ETM or HTM remain major factors impeding PCE [15, 20, 21, 22, 23]. ZnO nanorods [24] or PCBM [25], ETM [26] are able to minimize the band offset at the conduction band minimum (CBM) and allow building almost ideal contact at ETM/LHM interface. However HTM very often present large band offsets at valence band maximum (VBM) and low carrier mobility [23, 27, 28, 29]. Alternatively, PSC without HTM layer was proposed as a solution towards high efficiency. After Etgar and coworkers early directly deposited gold on CH_{3}NH_{3}PbI_{3} and demonstrated that the CH_{3}NH_{3}PbI_{3} material can be simultaneously considered as a light harvester and a hole conductor, leading to PCE of 8% [30]. Then porous carbon film was used as contact for fully printable HTMfree PSCs with efficiency of 12.8% [17]. And PSCs with singlewalled carbon nanotubes as hole collector achieved efficiency of 15% [31, 32]. In such case, solar cells benefit from fewer interfaces, and the optical and electrical losses in the HTM layer are eliminated as well. In Figure 1, the architecture of the HTMfree CH_{3}NH_{3}PbI_{3} PSC is schematic represented by comparison to that of classical PSC Gold for example, is directly connected with CH_{3}NH_{3}PbI_{3} as the hole collection electrode and a Schottky contact is formed [33].
Fig. 1 Schematic representations of perovskite solar cells with (a) a heterojunction or (b) a Schottky contact at hole collector side, respectively. 
To get an insight into the HTMfree PSC operation, direct current and small signal simulation analyses [5, 34, 35, 36, 37] were performed including basic semiconductor models: the Poisson equation, the current continuity equation and a driftdiffusion model. The critical transport and recombination processes in solar cells can thus be quantitatively analyzed. Nevertheless, few numerical analyses were dedicated up to now to HTMfree PSCs. In our work, the basic currentvoltage (JV) and capacitancevoltage (CV) characteristics of HTMfree CH_{3}NH_{3}PbI_{3} based PSCs are studied with driftdiffusion and small signal models [38], which are integrated in Silvaco Atlas simulator [39].
2 Numerical modeling
The physical model is numerically simulated in Atlas by solving a set of coupled equations including Poisson’s equation (2), continuity (3a) and (3b) and transport equations (4a) and (4b) for electrons and holes densities. These equations link together the electrostatic potential profile and the charge distributions, and describe the evolution of electron and hole densities under external bias and light illumination, including carrier transport, generation, and recombination processes. The bimolecular recombination model corresponds to the formula (5). The trapassisted recombination model is described in formula (6), (7a) and (7b), while the photoinduced carrier generation processes are introduced through complex refractive index of materials. Simulations were carried out under equilibrium and small AC conditions, with and without AM1.5 sun illumination, in order to obtain JV and CV characteristics of HTMfree CH_{3}NH_{3}PbI_{3} PSCs (2)where ψ is the potential, ρ is the charge density and ε is the dielectric constant. where n(p) is the electron (hole) density, t is the time, J_{n} (J_{p}) is the electron (hole) current density, G and R are the generation and recombination rates respectively. The footnote n(p) is related to electron (hole). where μ is mobility and ϕ is the quasiFermi level (5)where k_{bi} is the bimolecular recombination coefficient and n_{i} the intrinsic electron density (6)The ShockleyReadHall (SRH) recombination mechanism is described by equation (6) τ is the charge carrier lifetime for trapassisted process. The relationship between τ and trap density (N_{t}) (Eq. (7)) depends on the traps capture cross section (SIG) and the thermal velocity (v). ΔE is the absolute energy difference between the trap level and the intrinsic Fermi level (E_{i}) in the bulk. E_{i} is approximately located in the middle of energy band gap. If ΔE = 0, the maximum of SRH recombination rate is obtained. In other words, the deep trap centers lead to the highest recombination rates and are harmful for photoinduced carrier extraction. We set τ_{n} = τ_{p}, μ_{n} = μ_{p} to reduce the number of parameters in the present work.
3 Basic properties of HTMfree PSC
A basic modeling of HTMfree Perovskite Solar Cells (PSCs) studied experimentally by Etgar’s group [40], relies on TiO_{2}/CH_{3}NH_{3}PbI_{3}/Au architecture with a computed static band alignment shown in Figure 2. Heavily ntype doped ETM anatase (TiO_{2})[41, 42, 43] and hole collector gold are added on each sides of lightly n or pdoped CH_{3}NH_{3}PbI_{3}[1, 44, 45]. Under thermal equilibrium and short circuit condition, the Fermilevel (E_{f}) remains constant as reference through the device, and the band offsets at each interface yield two potential barriers. It is clear that the major potential drop Δψ is located in the CH_{3}NH_{3}PbI_{3} layer. Therefore, the major part of the electrical current originates from carrier drifting rather than carrier diffusion. The main properties of the materials used for the simulation are summarized in Table 1, including χ, E_{g}, the doping level (N), the effective masses of electron and hole (& and the relative dielectric constant (ε_{r}). The thickness of TiO_{2} and CH_{3}NH_{3}PbI_{3} layers are both equal to 300 nm. The work function (WF) of gold is 5.1 eV [33, 46]. An Ohmic contact is considered at the bottom of the TiO_{2} layer on the other side. The bimolecular recombination coefficient k_{bi} of CH_{3}NH_{3}PbI_{3} is 10^{9}cm^{3}/s [47]. Due to lack of precise trap characterization, ΔE is set to zero and N_{t} is 10^{10}cm^{3}, while τ and μ are tuned to match the experimental data.
Main properties of the materials.
Fig. 2 Static band diagram of (a) ndoped and (b) pdoped CH_{3}NH_{3}PbI_{3} based HTMfree PSCs. 
3.1 Capacitance characteristics
In order to obtain efficient energy conversion in solar cells with low mobility LHM, a high build in potential (V_{bi}) is necessary to prevent significant losses due to carrier recombination processes competing with charge extraction processes [52]. In our case, a Schottky contact [53] is formed at interface CH_{3}NH_{3}PbI_{3}/Au. Therefore, V_{bi} can be extracted from a MottSchottky capacitance analysis. The device architecture in our work is shown together with the circuit in Figure 3. The capacitance expression is given by: (8)where C is the junction capacitance, A is the junction area, ε is the vacuum permittivity, N is the activated dopant density in semiconductor and ε_{r} is the relative permittivity. In our work, a small signal analysis [38] is used to simulate CV characteristics of HTMfree CH_{3}NH_{3}PbI_{3} PSC. The signal frequency is set at 1 kHz for simulation, as in practical measurement. The theoretical characteristics is presented in Figure 4 and compared to available experimental data [40]. In order to fit the experimental data, an effective interfacial layer (IF) was introduced into the architecture for each type of CH_{3}NH_{3}PbI_{3}. For ndoped CH_{3}NH_{3}PbI_{3}, the IF of 8.5 nm is heavily ndoped and located between Au and CH_{3}NH_{3}PbI_{3}. For pdoped CH_{3}NH_{3}PbI_{3}, the IF of 3.4 nm is heavily pdoped and located between TiO_{2} and CH_{3}NH_{3}PbI_{3}. The doping level of each IF is equal to 2e19 cm^{3}. The influence of IF is further discussed at the end of the section.
Fig. 3 Circuit used for MottSchottky capacitance analysis. 
Fig. 4 The computed and experimental (solid line) CV characteristics in dark of HTMfree PSC. Ndoped HOIP with (without) an ndoped interfacial layer (IF) at Au/HOIP interface is indicated as dash dot (dash) line. Pdoped HOIP with (without) a pdoped IF at TiO_{2}/HOIP interface is indicated as short dash dot (short dash) line. The V_{bi} values extracted from the IS1 and IS2 intersections are equal to 0.6 and 0.9 V, respectively. 
As the bias reversely increases, the extension of the depletion region starts at the CH_{3}NH_{3}PbI_{3}/Au interface, then goes through the CH_{3}NH_{3}PbI_{3} and finally into the TiO_{2} Because of the different N and ε_{r} values in both CH_{3}NH_{3}PbI_{3} and TiO_{2}, CV curves under reverse bias are bent into two stages. Similar phenomena were observed for IIIV semiconductors [54, 55]. The roughly constant capacitance at stage II is due to the heavy doping level in TiO_{2}, in comparison with the smaller slope related to the small doping level in CH_{3}NH_{3}PbI_{3}. The point A in Figure 4 corresponds to the transition point of the depletion region from stage I to stage II. According to expression (8), the V_{bi} of a finite CH_{3}NH_{3}PbI_{3} layer is extracted from the intersection (IS) as pointed out in Figure 4. The fluctuations of experimental data at stage II can be explained by nonuninform doping in the TiO_{2} layer. Because of the huge effective surface area of nanoporous TiO_{2}[56, 57, 58] and the rough surface of CH_{3}NH_{3}PbI_{3} layer [58], it is risky to extract N, ε_{r} or thickness (d) of CH_{3}NH_{3}PbI_{3} from the expression (8) and classic parallel plate capacitance expression (9), directly. In the model the effective area of capacitance interface (A_{eff}) is around two times as large as the active area of practical gold electrode (9)If more uniform growth of material layers for HTMfree PSCs is achieved in the future, it will be possible to extract more quantitative information from CV measurements, related to N, ε_{r} and the thickness of the CH_{3}NH_{3}PbI_{3} layer.
3.2 Photovoltaic characteristics
Due probably to the different growth procedures employed by the experimental groups, some deviations are found for the absorption coefficients values of CH_{3}NH_{3}PbI_{3} in reference [59]. For that reason, the absorption coefficient curve used in our simulation was rather obtained by fitting the experimental IPCE spectrum data. In Figure 5, the simulated JV characteristics under 1 sun of 1.5 AM illumination are presented along with experimental data. A good matching to the experimental JV curve is achieved based on ntype CH_{3}NH_{3}PbI_{3} when its τ = 80ns and μ = 0.2cm^{2}/Vs. These empirical values are consistent with commonly measured values for the CH_{3}NH_{3}PbI_{3} material. The paper will only discuss ndoped CH_{3}NH_{3}PbI_{3} based PSCs in the following sections, because a better agreement with experimental CV and JV characteristics is obtained in this case
Fig. 5 JV characteristics under 1 sun illumination of ndoped CH_{3}NH_{3}PbI_{3} based HTMfree PSCs with (dash line) and without (dash dot line) interfacial layer (IF) The τ and μ of ndoped CH_{3}NH_{3}PbI_{3} are equals to 80 ns and 0.2 cm^{2}/Vs, respectively. And ptype CH_{3}NH_{3}PbI_{3} is pictured by dot line as example with τ of 18 ns and μ of 0.2 cm^{2}/Vs. 
From the comparison of the experimental and computed CV characteristics (Fig. 4), it is necessary to assume that a heavily ndoped IF exists at the CH_{3}NH_{3}PbI_{3}/Au contact. Alternative hypotheses with layers containing acceptors or surface states, were explored but without success. Indirect evidences of the existence of such an IF can be found in the report of Liu’s group [33]. Using ultraviolet photoemission spectroscopy (UPS), these authors indeed showed that during the deposition of the gold contact, the Fermi level undergoes a progressive shift. Noteworthy, the presence of metal nano particles [60] or charged ions [61, 62, 63] at the interface was discussed by other groups. This Fermi level shift is simulated in the present work by introducing an effective and heavily ndoped CH_{3}NH_{3}PbI_{3} IF. The high density of positive ionized charges in the IF leads to a reduction of the V_{bi} from 0.9 to 0.6 V, in good agreement with the experimental value (Fig. 4).
Fig. 6 (a) Static band alignment and (b) potential profile with and without interfacial layer (IF). 
The static band alignment and potential profile with and without IF are represented in Figures 6a and 6b, to have an insight into the device operation. Even though the band offset at the CH_{3}NH_{3}PbI_{3} surface is pinned by the gold contact, the effective potential drop across the CH_{3}NH_{3}PbI_{3} layer is lowered by the presence of the IF. As a consequence, the losses due to carrier recombination processes increase and the efficiency of PSC decreases from 11% to 8%, as shown in Figure 5. A thick IF has clearly a detrimental effect on the photovoltaic efficiency.
Fig. 7 (a) Open circuit voltage (V_{OC}), fill factor (FF) and efficiency (Eff) of HTMfree CH_{3}NH_{3}PbI_{3} PSC as a function of the workfunction (WF) of hole collector conductor. (b) Valence band variation as a function of WF. 
4 Influence of workfunction
The efficiencies of the PSC can be increased by improving the intrinsic properties of the perovskite (τ and μ). We propose in this work to explore an additional possibility for HTMfree PSC. It is indeed possible to enlarge V_{bi} by increasing the WF of the metal used for the Schottky contact. In Figure 7a, V_{OC}, fill factor and efficiency are presented as a function of WF. These parameters are improved until saturation is reached for a WF value of 5.6 eV, while the short circuit current (J_{SC}) is almost constant and equal to 19 mA/cm^{2}. The efficiency of HTMfree PSC can be enhanced up to 17% (Fig. 7a) by this way, and as stated before further enhancements could also be expected by improving the intrinsic properties of the perovskite.
Furthermore, as shown in Figure 7b, the change of VBM is very small except for the part close to the CH_{3}NH_{3}PbI_{3}/Au interface, as the WF of the metal increases up to 5.6 eV, larger than the VBM of CH_{3}NH_{3}PbI_{3} (5.5 eV). As a result, the overall V_{bi} in CH_{3}NH_{3}PbI_{3} layer becomes almost saturated. When the carrier recombination rate is small enough, the J_{SC} mainly depends on absorption properties and is almost independent of V_{bi}. Palladium [46, 64] or Selenium [65] are examples of hole collector conductors with WF larger than 5.5 eV.
5 Conclusion
In summary, a detailed investigation of CV and JV characteristics of HTMfree CH_{3}NH_{3}PbI_{3} PSC has been proposed, based on the driftdiffusion model and small signal analysis. The simulation results are in good agreement with experimental data. An effective heavily doped interfacial layer was introduced at the interface to fit the CV characteristics It is also shown in this work that, an increase of WF of the hole collector conductor, is expected to enhance the PSC efficiency.
Acknowledgments
The work at FOTON was supported by French ANR SupersansPlomb project.
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Cite this article as: Y. Huang, S. Aharon, A. Rolland, L. Pedesseau, O. Durand, L. Etgar, J. Even, Influence of Schottky contact on the CV and JV characteristics of HTMfree perovskite solar cells, EPJ Photovoltaics 8, 85501 (2017).
All Tables
All Figures
Fig. 1 Schematic representations of perovskite solar cells with (a) a heterojunction or (b) a Schottky contact at hole collector side, respectively. 

In the text 
Fig. 2 Static band diagram of (a) ndoped and (b) pdoped CH_{3}NH_{3}PbI_{3} based HTMfree PSCs. 

In the text 
Fig. 3 Circuit used for MottSchottky capacitance analysis. 

In the text 
Fig. 4 The computed and experimental (solid line) CV characteristics in dark of HTMfree PSC. Ndoped HOIP with (without) an ndoped interfacial layer (IF) at Au/HOIP interface is indicated as dash dot (dash) line. Pdoped HOIP with (without) a pdoped IF at TiO_{2}/HOIP interface is indicated as short dash dot (short dash) line. The V_{bi} values extracted from the IS1 and IS2 intersections are equal to 0.6 and 0.9 V, respectively. 

In the text 
Fig. 5 JV characteristics under 1 sun illumination of ndoped CH_{3}NH_{3}PbI_{3} based HTMfree PSCs with (dash line) and without (dash dot line) interfacial layer (IF) The τ and μ of ndoped CH_{3}NH_{3}PbI_{3} are equals to 80 ns and 0.2 cm^{2}/Vs, respectively. And ptype CH_{3}NH_{3}PbI_{3} is pictured by dot line as example with τ of 18 ns and μ of 0.2 cm^{2}/Vs. 

In the text 
Fig. 6 (a) Static band alignment and (b) potential profile with and without interfacial layer (IF). 

In the text 
Fig. 7 (a) Open circuit voltage (V_{OC}), fill factor (FF) and efficiency (Eff) of HTMfree CH_{3}NH_{3}PbI_{3} PSC as a function of the workfunction (WF) of hole collector conductor. (b) Valence band variation as a function of WF. 

In the text 
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