⇦Chinese Physics Letters, 2020, Vol. 37, No. 12, Article code 127101 HfX$_{2}$ (X = Cl, Br, I) Monolayer and Type II Heterostructures with Promising Photovoltaic Characteristics Xingyong Huang (黄兴勇)1,2,3, Liujiang Zhou (周柳江)3*, Luo Yan (燕罗)3, You Wang (王浟)1, Wei Zhang (张伟)1, Xiumin Xie (谢修敏)1, Qiang Xu (徐强)1, and Hai-Zhi Song (宋海智)1,3* Affiliations 1Southwest Institute of Technical Physics, Chengdu 610041, China 2Faculty of Science, Yibin University, Yibin 644007, China 3Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China Received 10 September 2020; accepted 26 October 2020; published online 8 December 2020 Supported by the National Key Research and Development Program of China (Grant No. 2017YFB0405302).
*Corresponding authors. Email: liujiang86@gmail.com; hzsong1296@163.com; Citation Text: Huang X Y, Zhou L J, Yan L, Wang Y, and Zhang W et al. 2020 Chin. Phys. Lett. 37 127101    Abstract Two-dimensional (2D) materials and their corresponding van der Waals (vdW) heterostructures are considered as promising candidates for highly efficient solar cell applications. A series of 2D HfX$_{2}$ (X = Cl, Br, I) monolayers are proposed, via first-principle calculations. The vibrational phonon spectra and molecular dynamics simulation results indicate that HfX$_{2}$ monolayers possess dynamical and thermodynamical stability. Moreover, their electronic structure shows that their Heyd–Scuseria–Ernzerhof(HSE06)-based band values (1.033–1.475 eV) are suitable as donor systems for excitonic solar cells (XSCs). The material's significant visible-light absorbing capability (${\sim}10^{5}$ cm$^{-1}$) and superior power conversion efficiency (${\sim}$20%) are demonstrated by establishing a reasonable type II vdW heterostructure. This suggests the significant potential of HfX$_{2}$ monolayers as a candidate material for XSCs. DOI:10.1088/0256-307X/37/12/127101 PACS:71.15.Mb, 71.20.-b, 88.40.H- © 2020 Chinese Physics Society Article Text Solar cells, which convert solar energy into electricity, are an environmentally friendly energy conversion device, contributing to sustainable development in terms of global technology.[1] Employed in conventional commercial photovoltaic devices, silicon-based solar cells have a theoretical limit, in terms of energy conversion efficiency, of 29.1%.[2] In the search to improve upon this level of efficiency, the investigation of alternative energy materials to replace silicon has become a hot topic. With this aim in view, two-dimensional (2D) type II vdW heterostructures, with their extraordinary electronic, optical, and mechanical properties,[3,4] and specifically the ultra-high specific surface area of a monolayer, with its effective electron-hole separation, are anticipated to replace silicon-based solar cells in the next generation of high-efficiency solar cells. Although 2D type II vdW heterostructures have been designed for photovoltaic devices, their energy conversion efficiency is as yet unsatisfactory.[5] In this regard, the 2D IVB–VIIA-group transition-metal halides (IVGTMHs), a new family of 2D semiconductors, have exhibited many novel properties, such as the quantum spin Hall effect, and large nontrivial band gaps.[6] In this work, we focus on a heterojunction composed of HfX$_{2}$ (X = Cl, Br, I) monolayers, a material belonging to the 2D IVGTMH group, which serves as a kind of layered compound for photovoltaic applications. Based on first-principles calculations, we evaluate the stability of HfX$_{2}$ monolayers, predict 2D type II vdW heterostructures, and calculate their power conversion efficiency (PCE) for excitonic solar cells (XSCs). The Vienna ab initio simulation package (VASP) is used to implement our density functional theory (DFT) calculations.[7,8] The frozen-core projector-augmented wave (PAW) method[7,8] is also applied. The Perdew–Burke–Ernzerhof (PBE) function within the generalized gradient approximation (GGA)[9] is used to describe the exchange-correlation interaction of electrons. To take into account the vdW interaction between different monolayers in the heterostructures, the OptB88vdW method[10] is adopted. With regard to calculations for monolayers, inter-monolayer interactions are considered negligible, given that the vacuum thickness is set to more than 15 Å from the border in the $Z$ direction. The energy cut-off for the planewave basis is set at 420 eV. The convergence criteria of total energy and force are 10$^{-6}$ eV and 0.001 eV/Å, respectively. The canonical ensemble, with a Nose–Hoover thermostat[11] at 300 K for 10 ps, is performed via molecular dynamics simulations, so as to evaluate thermodynamic stability. The Phonopy code[12] is used to calculate phonon dispersion, in order to assess the material's dynamical stability. More accurate band edge characteristics are obtained using Heyd–Scuseria–Ernzerhof (HSE06) hybrid functions.[13]
cpl-37-12-127101-fig1.png
Fig. 1. Top (a) and side [(b), (c)] view of the crystal structure of the HfX$_{2}$ monolayer, together with the top (d) and side (f) view of the crystal structure of the designed 2D vdW heterostructures. (e) First Brillouin zone of HfX$_{2}$ monolayers, with their points of high symmetry.
cpl-37-12-127101-fig2.png
Fig. 2. Phonon spectra of (a) HfCl$_{2}$, (b) HfBr$_{2}$, and (c) HfI$_{2}$. $\varGamma$, $X$, $S$, and $Y$ correspond to the (0.0, 0.0, 0.0), (0.5, 0.0, 0.0), (0.5, 0.5, 0.0), and (0.0, 0.5, 0.0) $k$-points in the first Brillouin zone, respectively.
Figures 1(a)–1(c) and 1(d) depict the crystal structures of the HfX$_{2}$ monolayer, and the design of the vdW heterojunctions. The HfX$_{2}$ monolayer hosts a rectangular lattice, where the Hf is enclosed in an HfX$_{6}$ octahedron. The HfX$_{2}$ monolayer possesses a 1T'-MoS$_{2}$ structure, such that the Hf is not positioned centrally in the HfX$_{6}$ octahedron. Figure 1(e) shows the corresponding high symmetry points in the first Brillouin zone. The 2D structure in Figs. 1(d) and 1(f) is a vertical vdW heterostructure, and with the upper and lower layers being composed of different HfX$_{2}$ monolayers. The lattice parameters of the fully optimized HfX$_{2}$ monolayer are shown as follows: $a=6.144$ and $b=3.2686$.144 Å for HfCl$_{2}$; $a=6.416$ and $b=3.429$ Å for HfBr$_{2}$; $a=6.814$ and $b=3.707$ Å for HfI$_{2}$. Note that a larger atomic radius corresponds to a larger lattice parameter. Vibrational phonon spectra are employed to assess dynamical stability. Having been fully optimized, the phonon spectra of the HfX$_{2}$ monolayers along the high-symmetry points are then calculated (see Fig. 2). The absence of imaginary frequencies in the phonon spectra indicates that HfX$_{2}$ monolayers are dynamically stable. The highest frequency of the HfX$_{2}$ monolayer phonon spectrum is ${\sim}10$ THz (${\sim}350$ cm$^{-1}$), which is comparable to MoS$_{2}$ (${\sim}350$ cm$^{-1}$)[14] and smaller than silicene (${\sim}580$ cm$^{-1}$),[15] suggesting that the bond strength of Hf–X is lower than that of Si–Si. In order to further evaluate the stability of the HfX$_{2}$ monolayer, the thermodynamic stability (molecular dynamic) criterion was adopted. The results of a molecular dynamics simulation at 300 K (see Fig. 3) depict the total energy and fluctuations as a function of simulation time. Ignoring thermal fluctuations, it is evident that the HfX$_{2}$ monolayer shows no obvious structural deterioration after 10 ps, indicating that the HfX$_{2}$ monolayer is thermally stable at room temperature.
cpl-37-12-127101-fig3.png
Fig. 3. Evolution of potential energy with respect to simulation time at 300 K for the HfX$_{2}$ monolayer. Final snapshots for HfCl$_{2}$, HfBr$_{2}$ and HfI$_{2}$ are shown in (a), (b) and (c), respectively.
The HSE06-based electronic structural properties of the HfX$_{2}$ monolayer are shown in Figs. 4(a)–4(c). The bandgap values of HfCl$_{2}$, HfBr$_{2}$, and HfI$_{2}$ are 1.475, 1.337, and 1.033 eV, respectively. Evidently, halogens with larger atomic sizes would reduce the bandgap. This is understandable, given that the increment of the bond lengths of the HfX$_{2}$ (Cl $\to$ Br $\to$ I) monolayer reduces the repulsive effect, similarly to the behavior of bulk semiconductors.[16] In particular, the valence and conduction bands are primarily contributed by Hf atoms. The Hf-$d$ ($xy$, $x^{2}$–$y^{2}$) orbit dominates the conduction band minimum (CBM) and valence band maximum (VBM), and halogens primarily affect the deep energy levels. Figures 5(a)–5(c) illustrate the band structure of the heterojunction, depicting the valence and conduction band edges referenced to vacuum level, and indicating three possible designs for type II vdW heterojunction structures (HfI$_{2}$/HfCl$_{2}$, HfI$_{2}$/HfBr$_{2}$, and HfBr$_{2}$/HfCl$_{2}$). The square of dipole moment transition matrix elements was calculated to evaluate the electronic transition between valence and conduction bands. As shown in Figs. 4(d)–4(f), the dominant transition probability is concentrated to the in-plane states of the Hf atoms, where the maximum transition probability occurs in the 2$^{\rm nd}$ to 3$^{\rm rd}$ band for region I, and the 1$^{\rm st}$ to 3$^{\rm rd}$ band for region II. Moreover, the halogens enable the tuning of the transition probability competitiveness of regions I and II.
cpl-37-12-127101-fig4.png
Fig. 4. HSE06-based band structure, with the corresponding transition dipole moment for [(a), (d)] HfCl$_{2}$, [(b), (e)] HfBr$_{2}$, and [(c), (f)] HfI$_{2}$ monolayers. Regions I and II, corresponding to the pale green shaded areas, are utilized to mark the main dipole moment transition process. The 2$^{\rm nd}$ band is the highest occupied valence band. The Fermi level is set to zero.
cpl-37-12-127101-fig5.png
Fig. 5. Band structure of HfI$_{2}$/HfCl$_{2}$ (a), HfI$_{2}$/HfBr$_{2}$ (b), and HfBr$_{2}$/HfCl$_{2}$ (c) heterostructures. The solid lines in red and green represent the highest occupied and the lowest non-occupied state of HfCl$_{2}$ (HfBr$_{2}$ and HfI$_{2}$). (d) PCE contour as a function of $E_{\rm g}^{\rm d}$ and $\Delta E_{\rm c}$. The PCE limits of HfI$_{2}$/HfCl$_{2}$, HfI$_{2}$/HfBr$_{2}$, and HfBr$_{2}$/HfCl$_{2}$ heterostructures are indicated by a pink triangle, a blue circle, and a black square, respectively.
Clearly, vdW (vertical) heterostructures can be applied effectively to XSCs.[17–19] Here, the adopted vdW (vertical) heterostructure configuration has been optimized by searching for that with the lowest energy, which is the most stable stacking method. For the type II vdW heterojunction XSCs, the PCE was calculated following Scharber's method.[20] The upper limit of PCE can be calculated in the limit of 100% external quantum efficiency, which can be expressed as[20] $$ \eta =\frac{0.65(E_{\rm g}^{\rm d}-\Delta E_{\rm c}-0.3)\int_{E_{\rm g}^{\rm d}}^{\infty} {\frac{P(\hbar \omega)}{\hbar \omega }d(\hbar \omega)} }{\int_{E_{\rm g}^{\rm d}}^{\infty} {P(\hbar \omega)d(\hbar \omega)} }, $$ where 0.65 is a band-filling factor deduced from the Shockley–Queisser limit, and $P\left( \hbar \omega \right)$ denotes the AM1.5 solar energy flux at the photon energy, $\hbar \omega$. The parameter 0.3 eV is used to explain the energy conversion kinetics. Including the band gap of the donor ($E_{\rm g}^{\rm d}$), and the conduction band offset ($\Delta E_{\rm c}$), taken from the HSE06 calculations. Figure 5(d) shows the PCE contour plots for all type-II heterostructures. Clearly, small $\Delta E_{\rm c}$ and suitable $E_{\rm g}^{\rm d}$ (${\sim}1.3$ eV) would result in satisfactory PCEs. The PCEs for HfI$_{2}$/HfCl$_{2}$, HfI$_{2}$/HfBr$_{2}$, and HfBr$_{2}$/HfCl$_{2}$ are 17.150%, 21.438%, and 20.439%, respectively. These values are comparable with the PCE of polycrystalline CdTe thin films (21.5%)[20,21] and perovskite (22.1%)[20,22] solar cells, and higher than dye-sensitive (${\sim}12$%)[20,21] and organic (${\sim} 12$%)[20,23,24] solar cells. Moreover, the efficiency of XSCs is dependent on their sunlight absorption capacity. The HSE06-calculated optical absorption spectra are given in Fig. 6, with the incident AM1.5 G solar spectrum shown for comparison. The results reflect an excellent sunlight absorption performance, as compared with that previously reported for intrinsic silicon.[25] Since the HfX$_{2}$ monolayer is anisotropic, all heterojunctions appear to absorb near-ultraviolet light in the $x$ direction, and visible light in the $y$ direction. In addition, the heterojunction structure results in a peak characteristic at ${\sim}900$ nm [Fig. 6(b)] and the harvesting of visible light in the $y$ direction. The visible light harvesting capacity of the heterojunctions reaches as much as 10$^{5}$ cm$^{-1}$ in the $y$ direction, which is comparable to, or even higher than, intrinsic silicon and organic perovskite materials (10$^{4}$–$10^{5}$ cm$^{-1}$),[26] and is higher than the absorption coefficient reported for other 2D materials in visible light, such as phosphaalkene[27] and MnPSe$_{3}$ monolayers.[28] The optical absorption spectra suggest that the heterostructures considered here can efficiently utilize solar energy.
cpl-37-12-127101-fig6.png
Fig. 6. Optical absorption spectra in the $x$ (a) and $y$ (b) directions, calculated via the HSE06 method. The colored region indicates the visible light spectrum.
In summary, we have investigated the geometry, stability, and electronic structures of the HfX$_{2}$ monolayer, and related type II vdW heterostructures. The results suggest that the HfX$_{2}$ monolayer is dynamically and thermodynamically stable. A PCE of over 20% corresponds to $E_{\rm g}^{\rm d}$ between ${\sim}0.9$ and ${\sim}1.7$ eV, suggesting bandgap values (1.033–1.475 eV) favorable to the donor system as XSCs. Furthermore, the valence band and conduction band around the Fermi level are primarily determined by the Hf-$d$ orbit. More importantly, significant visible light absorbing capability (${\sim}10^{5}$ cm$^{-1}$) and impressive PCE (17.150%, 21.438% and 20.439%) can be obtained by establishing type II vdW heterostructures for XSCs, demonstrating great potential for future solar energy conversion applications. The authors wish to thank Qiang Zhou, Guangwei Deng and Lei Hu for useful discussions. References Absorption Enhancement of Silicon Solar Cell in a Positive-Intrinsic-Negative JunctionRaising the one-sun conversion efficiency of III–V/Si solar cells to 32.8% for two junctions and 35.9% for three junctions2D lateral heterostructures of group-III monochalcogenide: Potential photovoltaic applicationsRecent advances in low‐dimensional semiconductor nanomaterials and their applications in high‐performance photodetectorsSolar-energy conversion and light emission in an atomic monolayer p–n diodeNew Family of Quantum Spin Hall Insulators in Two-dimensional Transition-Metal Halide with Large Nontrivial Band GapsEfficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis setEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setGeneralized Gradient Approximation Made SimpleChemical accuracy for the van der Waals density functionalA unified formulation of the constant temperature molecular dynamics methodsAIP Conference ProceedingsInfluence of the exchange screening parameter on the performance of screened hybrid functionalsPhonons in single-layer and few-layer MoS 2 and WS 2 Two- and One-Dimensional Honeycomb Structures of Silicon and GermaniumTuning the indirect–direct band gap transition of SiC, GeC and SnC monolayer in a graphene-like honeycomb structure by strain engineering: a quasiparticle GW studyAI 3 (A = As, Sb) Single Layers and Their vdW Heterostructure for Photocatalysis and Solar Cell ApplicationsSiC 2 Siligraphene and Nanotubes: Novel Donor Materials in Excitonic Solar CellsMonolayer, Bilayer, and Heterostructures of Green Phosphorene for Water Splitting and PhotovoltaicsDesign Rules for Donors in Bulk-Heterojunction Solar Cells—Towards 10 % Energy-Conversion EfficiencySolar cell efficiency tables (Version 45)Solar cell efficiency tables (version 49)Efficient organic solar cells processed from hydrocarbon solventsBilayer Phosphorene: Effect of Stacking Order on Bandgap and Its Potential Applications in Thin-Film Solar CellsTunable Magnetism and Extraordinary Sunlight Absorbance in Indium Triphosphide MonolayerFirst-principles insight into the photoelectronic properties of Ge-based perovskitesFirst-principles prediction of two atomic-thin phosphorene allotropes with potentials for sun-light-driven water splittingMnPSe 3 Monolayer: A Promising 2D Visible‐Light Photohydrolytic Catalyst with High Carrier Mobility
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