Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

Paul
Dalla Valle
* and
Nicolas
Cavassilas

Aix Marseille Université, CNRS, Université de Toulon, IM2NP UMR 7334, 13397, Marseille, France. E-mail: paul.dalla-valle@im2np.fr

Received
24th March 2022
, Accepted 29th April 2022

First published on 14th May 2022

Solar water splitting (SWS) has been widely studied as a promising technology for generating carbon-free hydrogen. In this article, we propose an unassisted SWS system based on van der Waals heterojunctions using monolayers of transition metal dichalcogenides as active core materials. This architecture, with its small band gap materials and high surface/volume ratio, has an intrinsic type-II band alignment that offers many advantages, such as direct Z-scheme configuration and wide absorption. To estimate the solar-to-hydrogen (STH) efficiency of the system, we developed a multiphysics model. While electronic and optical properties are computed with ab initio calculations, we implemented the detailed balance method and the Butler–Volmer kinetics to simulate the photoelectrochemical behaviour. Under realistic operating conditions, the system achieves a STH efficiency greater than 15%, which is higher than the critical 10% efficiency required to make SWS economically viable. Since our system is wireless and requires simple manufacturing processes (exfoliation), this result is remarkable.

To improve the electrochemical reactions in the overall water splitting process, the generation of electron–hole pairs must occur as close to the surface as possible. Thanks to their large surface/volume ratio, two-dimensional (2D) materials, such as transition metal dichalcogenide (TMDC) seem perfectly suited for this purpose. As reviewed by Das et al., TMDC and their van der Waals heterojunctions (vdWH) are attractive for photovoltaic applications^{7} thanks, in particular, to their remarkable optical properties^{8–12} and Z-scheme architectures based on TMDC vdWH have already been proposed.^{13–16} Also, 2D TMDC present appealing catalytic properties.^{17,18} Yin et al. reviewed applications such as the electrocatalytic hydrogen evolution reaction and photocatalysis^{19} while Wu et al. demonstrated the catalytic performance of MoS_{2} in oxygen evolution reaction, which is comparable to the benchmark IrO_{2}.^{18} Interestingly, these photocatalytic properties can be enhanced by chalcogen vacancy of the TMDC monolayer.^{20} Moreover, the production of 2D TMDC is low-cost thanks to the exfoliation process.^{17,21,22} Consequently, the use of these vdWH is increasingly considered as a credible alternative for the overall SWS, as evidenced by theoretical papers showing high efficiencies.^{20,23} In this paper, we present a direct Z-scheme system based on a MoS_{2}/WSe_{2} vdWH. We go beyond the presentation of the potential performances of the heterojunction as we propose a complete design of the photoelectrochemical cell. The active core of the cell contains the vdWH and an insulating layer to prevent unwanted recombinations. This active core is embedded in transparent insulating layers which are porous to enable the circulation of water and gases. To investigate our system, we calculate the electronic properties of the heterojunctions with density functional theory (DFT). Based on these results, we implement a photoelectrochemical model using the detailed balance method and the Butler–Volmer kinetics to compute the solar-to-hydrogen (STH) efficiency under realistic conditions. In the following section, we describe the system operation. We then detail the developed photoelectrochemical model. We finally present and discuss the calculated STH efficiency of the system.

One must encapsulate the ultra-thin active core to protect and support it without avoinding the circulation of water and gases. To this end, mesoporous transparent oxides^{28} appear as good option. Also, high-quality optical absorption in the TMDCs is essential as their ultimate thinness remains limiting. Many works have been interested in improving optical absorption in 2D materials, as presented in the review by Li et al.^{29} The mesoporous oxides can serve as a support for absorption enhancement systems, such as photonic crystals, resonant cavities, nanoparticles.

V_{PEC}(J) = V_{MoS2}(J) + V_{WSe2}(J) − V_{MoS2/WSe2}(−J) − V_{cat,a/c}(J) ≥ E_{rxn} | (1) |

The voltage V_{PEC} must be greater than or equal to the electrochemical reaction potential for the reaction to take place. For water electrolysis, this potential is E_{rxn} = 1.23 V.

We compute the current–voltage characteristics of the isolated MoS_{2}, the isolated WSe_{2} and the MoS_{2}/WSe_{2} heterojunction to calculate V_{MoS2}(J) and V_{WSe2}(J) and V_{MoS2/WSe2}(J) respectively. To this end, we use a detailed balance model based on the balance between the generation and the recombination rates of the electron/hole pairs. The carrier generation rate G_{TMDC} is the number of electron–hole pairs photogenerated in the TMDC per unit of volume and time. Here, “TMDC” refers to either MoS_{2}, WSe_{2} or the MoS_{2}/WSe_{2} heterojunction. G_{TMDC} depends on the number of incident photons and the absorption of these photons. In this paper, we use the AM1.5 G solar spectrum. The generation rate is given by the expression

(2) |

The absorbance A_{TMDC}(E) is a function of the absorption coefficient of the materials and the geometry of the active core. We use DFT to compute the ab initio absorption coefficients of MoS_{2}, WSe_{2} and the MoS_{2}/WSe_{2} heterojunction. The complete expression of A_{TMDC}(E) is presented in ESI 1.†

The carrier recombination rate R_{TMDC} is the number of recombination of electron–hole pairs in each TMDC per unit of volume and time. We use generalized Planck's law to describe spontaneous radiative recombination. To take into account the non-radiative recombination, we introduce an external radiative efficiency coefficient (ERE)^{31} in the calculation of R_{TMDC}. The latter is given by

(3) |

As the recombination rate R_{TMDC} depends on V_{TMDC}, we can define the current–voltage characteristic of a TMDC of thickness L_{TMDC} as:

J(V_{TMDC}) = −q(G_{TMDC} − R_{TMDC}(V_{TMDC}))L_{TMDC} | (4) |

We now introduce the parameter γ which represents the fraction of the MoS_{2}/hBN/WSe_{2} heterojunction in the active core. The proportion 1 − γ is thus the fraction of the region without hBN. In the region with the hBN, eqn (4) thus becomes

J(V_{TMDC}) = −q × γ(G_{TMDC} − R_{TMDC}(V_{TMDC}))L_{TMDC} | (5) |

J(V_{HJ}) = −q × (1 − γ)(G_{HJ} − R_{HJ}(V_{HJ}))L_{HJ} | (6) |

We numerically invert eqn (5) to get the relations V_{MoS2}(J) and V_{WSe2}(J), and we invert eqn (6) to get V_{MoS2/WSe2}(J).

To determine the current dependence of the catalytic overpotentials we use an inverse formulation of the Butler–Volmer kinetics and we assume that the charge transfer coefficients at the anode and the cathode are equal (α_{a} = α_{c} = α).^{32} We implement the overpotentials of the anode and the cathode V_{cat,a/c}(J) with the following expression,

(7) |

Once eqn (1) is implemented, we calculate the STH efficiency of the device. To do so, we first compute the optimal current density J_{op}, which is the maximum current density that satisfies the condition V_{PEC}(J_{op}) ≥ 1.23 V. We get η_{PEC}, the STH efficiency, thanks to the following equation:

(8) |

(9) |

Before presenting the results of the model, we focus on its important parameters. We classify them into two categories: intrinsic parameters and parameters related to the design of the device. The first category accounts for the non-ideality of the materials and their heterojunctions and includes the external radiative efficiency (ERE) and the anodic and cathodic catalytic exchange current density (J_{0,a} and J_{0,c} respectively). These intrinsic parameters are specific to the materials and their manufacture and a priori unknown for our system. Inspired by the work of Fountaine et al.,^{30} we distinguish three cases, summarised in Table 1, to study the STH efficiency of the device. Case no. 1 corresponds to the ideal limit case where each recombination is radiative (ERE = 1) and the overpotentials are zero (which corresponds mathematically to infinite catalytic exchange current densities). Case no. 2 is a realistic case with high radiative and electrochemical performances. Finally, case no. 3 accounts for average radiative and electrochemical quality. We assume that the external radiative efficiencies are equal for the isolated TMDCs and the heterojunction. We discuss the validity and the consequences of this assumption in ESI 2.†

Case | ERE |
J
_{0,a} (mA cm^{−2}) |
J
_{0,c} (mA cm^{−2}) |
---|---|---|---|

No. 1 | 1 | +∞ | +∞ |

No. 2 | 10^{−2} |
10^{−3} |
1 |

No. 3 | 10^{−6} |
10^{−5} |
1 |

The second category of parameters groups two design parameters: γ, the proportion of region with hBN and N, the absorption quality. We introduced γ during the presentation of the model in eqn (5) and (6). N represents the number of light passages through the device. It models, in a simplified manner, the absorption quality, which can be enlarged by considering for instance a photonic crystal, a resonant cavity and/or by considering several layers of the active core. We describe the influence of N on the active core absorption in ESI 1.†

We first present the ab initio band structure calculated with DFT. The band structures of the isolated materials are shown in ESI 4† and are in good agreement with the literature. From these band structures, we deduce χ_{O2} and χ_{H2} from the redox potentials E_{H2O/O2} and E_{H+/H2} respectively. These redox potentials have a bearing on the pH of water and are calculated with the following expression,^{23}

E_{H2O/O2} = −4.44 eV + pH × 0.059 eV | (10) |

E_{H+/H2} = −5.67 eV + pH × 0.059 eV | (11) |

Fig. 3 shows the projected band structure of the MoS_{2}/WSe_{2} heterojunction. The red (blue) dots represent electronic states around the nuclei of MoS_{2} (WSe_{2}). We first note that the band structure shows a direct band gap of 0.58 eV at the K point of the first Brillouin zone. We identify the band edge electronic states mainly localised around MoS_{2} or WSe_{2} and thus find a type II (tandem) heterojunction. The band structure shows that the band gap of the MoS_{2} is 1.46 eV and that of the WSe_{2} is 1.88 eV. We note that these values are different from the gaps obtained for the isolated materials (ESI 4†) due to the stress induced by the heterojunction.^{33} Finally, the most important point to note in this band structure is the state hybridisation in the valence band. Close to the VBM, the electronic states are localised around both MoS_{2} and WSe_{2}. This hybridisation enables direct recombination of electrons and holes in MoS_{2}. Hence, we expect radiative recombination with emission of photons of energy E_{g} = 0.58 eV. This hybridization is confirmed by experimental results which show the existence of an interlayer exciton in this heterojunction.^{27} Regarding both the band alignment and the type II configuration, the MoS_{2}/WSe_{2} heterojunction fulfils the basic requirements of the overall water splitting.

Fig. 4 displays the ab initio absorption coefficients of the isolated MoS_{2} and WSe_{2} and their heterojunction. The absorption coefficient of the isolated monolayers, Fig. 4(a), shows that MoS_{2} and WSe_{2} have analogous behaviours around the band edges. This could be a problem in the case of a 3D heterojunction where the top material would absorb all the incident light. Due to their extreme thinness, the single-pass absorption of 2D TMDCs is less than 10%.^{34} In a 2D vdWH, the top TMDC will absorb less than 10% of the incident light. The remaining more than 90% will be available for the bottom TMDC, which will in turn absorb 10%. Having two absorbers in the same energy range is therefore not a problem for the operation of the device. However, we will see below that we must enhance the total absorption to improve the efficiency of the system, i.e. we need more than a single-pass. Fig. 4(b), which represents the absorption coefficient of the MoS_{2}/WSe_{2} heterojunction, shows that the absorption is non-zero for energy larger than 0.4 eV. Corresponding radiative recombination is thus expected.

Using these absorption coefficients and our multiphysics model, we calculate the system efficiency. Fig. 5 presents the STH efficiency η_{STH} according to the design parameters for the three cases previously described in Table 1. Fig. 5(a) shows a strong dependence of the efficiency with N. Without optical absorption enhancement (i.e. N = 1), the STH efficiency is less than 0.5% whatever the case. Hence, the development of high-performance absorption enhancement system is mandatory to get valuable efficiencies. At high absorption quality (N > 1000), the efficiency saturates because all the photons are absorbed. The efficiency is 17.2% in cases no. 1 and no. 2 and 13.8% in case no. 3. The absorption quality is then a key factor in the device performance. Indeed, for a constant incident power, better absorption generate more carriers and thus a larger current, which increases the STH efficiency (eqn (8)). Even if the parameter N is a simplified way of describing the absorption, we use it to state that to reach 10% efficiency in case no. 3, the active core must absorb 71% of the photons with an energy higher than the band gap energy. In case no. 2, it has to absorb 56% of the incident light in the same energy range to reach the 10% efficiency. We present the detail of these statements in ESI 5.†

Fig. 5(b) depicts the STH efficiency versus the proportion of region with hBN. The result shows that γ must be larger than 0.9 whatever the case. Indeed, increasing the proportion of the MoS_{2}/hBN/WSe_{2} heterojunction increases the surface of the device dedicated to photon absorption and electrochemical reactions. Moreover, the recombination in the region without hBN is sufficiently efficient to be non-limiting. However, if γ is too close to 1, the efficiency drops to zero because there is not enough recombination of the excess carriers. This result is advantageous for the design of the device since one can imagine to randomly stack exfoliated flakes of MoS_{2} then hBN and finally, WSe_{2} to produce the active core. This non-ideal stacking will inevitably create some regions without hBN which will naturally enable the recombination of the carriers.

In both graphs of Fig. 5(a) and (b), we note that the curves representing cases no. 1 and no. 2 (i.e. the ideal case and the case of high-performance materials) are identical. To understand this result, we study the STH efficiency versus the intrinsic parameters. Fig. 6 shows η_{STH}versus the external radiative efficiency ERE and versus the catalytic exchange current density at the anode j_{0,c}.‡ The efficiency is zero if the intrinsic parameters are too poor. Indeed, poor radiative efficiency (i.e. ERE ≪ 1) leads to a low voltage generated by TMDCs and a poor catalytic behaviour (i.e. weak j_{0,a/c}) requires applying a larger overpotential to maintain a given current density. We refer the reader to ESI 6 and 7† for more details on the influence of radiative efficiency and the exchange current density respectively. The combination of these two phenomena leads to a voltage available for the electrochemical reaction too low to enable the electrolysis of water (we have V_{PEC}(J) < 1.23 V regardless of the current density), which gives a zero efficiency. This is the case for example if ERE = 10^{−7} and J_{0,a} = 10^{−8} mA cm^{−2} where the maximum voltage that the system can deliver is 1.16 V. Conversely, beyond a certain quality of the materials, better intrinsic parameters do not improve the performance. The latter presents constant 16.4% efficiency (Fig. 6) which is reached when the following condition is observed: J_{op} = min(J_{SC,MoS2}; J_{SC,WSe2}) where J_{SC,MoS2} and J_{SC,WSe2} are the short-circuit current densities of MoS_{2} and of WSe_{2} respectively. Once the efficiency reaches this limit, it is no longer useful to increase the voltages delivered by the cells or to decrease the losses.

It is, however, important to note that the DFT calculations involve systematic errors, in particular in the computation of the band gap energies of the system.^{36} These numerical results will have to be compared with experimental results of the optical properties of the 2D TMDCs (isolated and in heterojunction). These measurements will be the subject of future work. If the DFT calculations have underestimated the band gap energies too much, it will be possible to adjust the model with the new values. It is also conceivable to consider other TMDCs exhibiting photoelectrochemical properties similar to or better than those of this paper. We also note that in our study, the calculated band gaps of MoS_{2} and WSe_{2} are almost identical. This is not a necessary condition for the correct operation of the device. After selecting the active materials, it will be possible to carry out more in-depth and realistic modelling of the light management system. This point is crucial since the absorption quality is essential to obtain significant STH efficiency.

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## Footnotes |

† Electronic supplementary information (ESI) available: Absorbance formula, justification of the external radiative efficiency hypothesis, ab initio methods, TMDC band structures, modelling of the absorption enhancement system, influence of the intrinsic parameters. See https://doi.org/10.1039/d2na00178k |

‡ The cathodic exchange current density difference between standard and high-quality materials is negligible. It is not the case of the anodic exchange current density. |

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