First principles study on the electronic and optical behavior of atomically thin MXene/MC (M = Si, Ge) heterostructures

Following the discovery of graphene, research on two-dimensional (2D) materials has surged. To enhance the performance and broaden the applications of these materials, heterostructures are formed by stacking two different layered materials through van der Waals (vdW) interactions. This study, based on first-principles calculations, explores the intriguing properties of heterostructures made from Zr₂CO₂, SiC, and GeC monolayers. The results indicate that the Zr₂CO₂/SiC and Zr₂CO₂/GeC vdW heterostructures retain their original band structure and exhibit robust thermal stability at 300 K. Additionally, the Zr₂CO₂/MC heterostructure, with an I-type band alignment, shows promise as a light-emitting device material. Charge transfer between Zr₂CO₂ and SiC (or GeC) monolayers are obtained as 0.1459 |e| and 0.0425 |e|, respectively. The potential drop across the interface for Zr₂CO₂/SiC and Zr₂CO₂/GeC is 6.457 eV and 3.712 eV, respectively. Besides, the Zr₂CO₂/SiC vdW heterostructure presents excellent carrier mobility along the transport direction (about 3656 cm² V⁻¹·s^–1). These heterostructures exhibit remarkable optical absorption, further demonstrating the potential of Zr₂CO₂/MC for optoelectronic applications. This study provides valuable theoretical insights for designing photocatalytic and photovoltaic devices using heterostructures.

Introduction

Since graphene was isolated via mechanical exfoliation in 2004 by Novoselov and Geim, its exceptional physical and chemical features have sparked extensive interest in the broader family of 2D materials [1–3]. Many of these exhibit outstanding properties of their own [4, 5]. For instance, black phosphorene, a puckered-layered structure, demonstrates high carrier mobility reaching 1000 cm²/V·s at a thickness of 10 nm and shows great potential for transistors under ambient conditions [6]. The bandgap of arsenene can be tuned through applied strain, even transforming into a direct bandgap semiconductor with just 1% strain [7]. Transition metal dichalcogenides (TMDs), another important 2D family, exhibit desirable optical, thermal, and electronic characteristics [8]. MoS₂, for example, offers excellent photodetection capabilities with high responsivity and thermal resilience [9]. Furthermore, Janus-type TMDs break structural symmetry, greatly enhancing carrier mobility and separation efficiency for photogenerated charge carriers, enabling efficient redox processes under light illumination [10–13].

To achieve more complex or application-specific functionalities, researchers often engineer heterostructures by stacking different 2D layers using weak vdW interactions [14–16]. These heterostructures exhibit novel interfacial, optical, and electronic behaviors [17]. For example, SiC-based vdW heterostructures serve as efficient photocatalysts for water splitting [18], and PbSe/CdSe systems exhibit near-infrared emission due to type-I band alignment [19]. In the PbI₂/WS₂ heterostructure, comparable interlayer diffusion rates of electrons and holes were observed [20]. Such type-I systems hold significant promise in solar energy harvesting, photocatalysis, and optoelectronics [21]. Recently, exfoliated MAX phase derivatives known as MXenes have attracted attention for their diverse properties, ranging from electrical conductivity to chemical stability [22]. Though many MXenes are metallic, some—like Zr₂CO₂—exhibit semiconducting behavior with advantageous bandgaps. Cr₂TiC₂, for instance, acts as a bipolar antiferromagnetic semiconductor and may be applied in spintronic devices [23–25]. features high carrier mobility (∼1531.48 cm²/V·s) and promising thermoelectric behavior, making it ideal for photocatalysis and nanoelectronics. Its properties are further tunable via external strain, and its sensitivity to gases like NH₃ enables substantial conductivity changes [26]. Similarly, MC monolayers (M = Si, Ge) have recently shown desirable mechanical, optical, and electronic traits, making them candidates for optoelectronic integration [27–29]. Meanwhile, ultrathin SiC is being explored for UV LEDs and laser diodes, while GeC has been synthesized using encapsulated epitaxial techniques and considered for applications in heterojunctions and photocatalysis [30, 31]. Although some heterostructures involving Zr₂CO₂ or MC have been examined—such as Zr₂CO₂/WS₂, Zr₂CO₂/blue phosphorene, and MoS₂/MC—there remains a lack of research on heterostructures combining Zr₂CO₂ with MC directly. Given their complementary and tunable properties, forming Zr₂CO₂/MC heterostructures is a logical step toward realizing advanced multifunctional 2D materials.

This work utilizes density functional theory to evaluate the structural and electronic features of Zr₂CO₂/MC (M = Si, Ge) heterostructures. We assess their stability via binding energy and ab initio molecular dynamics (AIMD) simulations. Additionally, we characterize their band alignment, charge redistribution, interfacial potential shifts, and light absorption properties, aiming to understand their suitability for optoelectronic applications.

Methods

The calculations in this study are grounded in density functional theory (DFT), carried out using the Vienna Ab initio Simulation Package (VASP) [32, 33]. Exchange–correlation effects were treated within the generalized gradient approximation (GGA) framework, utilizing the Perdew–Burke–Ernzerhof (PBE) functional [34–36]. To achieve more accurate predictions of electronic bandgaps, we employed the hybrid Heyd–Scuseria–Ernzerhof (HSE06) functional [37]. To incorporate van der Waals interactions, the DFT-D3 correction scheme developed by Grimme was applied [38], along with dipole corrections to address long-range dispersion forces. The plane-wave energy cutoff was set at 500 eV following convergence testing. For Brillouin zone sampling, a Monkhorst–Pack k-point mesh of 7 × 7 × 1 was used during structure optimization, whereas denser grids (11 × 11 × 1) were employed for static and optical calculations. A vacuum spacing of 25 Å was introduced along the z-axis to eliminate interlayer interactions arising from periodic boundary conditions. The total energy convergence criterion was set as 10⁻¹ eV, and ionic relaxation was halted when the maximum Hellmann–Feynman force on any atom fell below 0.01 eV Å^–1.

Results and discussion

We initially carried out geometry optimizations for monolayered Zr₂CO₂, SiC, and GeC. Their respective top and side atomic views, along with the calculated band structures, are shown in Figures 1a–c. The optimized lattice constants were determined to be 3.363 Å for Zr₂CO₂, 3.235 Å for SiC, and 3.096 Å for GeC, agreeing with the previous research [26, 39, 40]. The bond lengths shown as Table 1 include 2.369 Å for Zr–C, 2.132 Å for Zr–O, 1.805 Å for Si–C, and 1.895 Å for Ge–C. Electronic structure calculations using the HSE06 functional confirmed semiconducting behavior for all three monolayers, with corresponding bandgaps of 1.820 eV (Zr₂CO₂), 4.042 eV (SiC), and 3.354 eV (GeC), which also consistent with previous investigations [41–43]. In the Zr₂CO₂ monolayer, the conduction band minimum (CBM) lies at the M point, while the valence band maximum (VBM) appears at the Γ point. For SiC and GeC, the CBM and VBM are located at Γ and K points, respectively. These findings are consistent with previous computational results.

Figure 1

Figure 1. The structure and the HSE06 calculated band structure of the (a) Zr₂CO₂, (b) SiC and (c) GeC monolayers. The grey, black, red, pink, green balls represent the Zr, C, O, Si and Ge atoms, respectively and the Fermi energy level is 0 shown by gray dashed.

Table 1

Table 1. The equilibrium lattice constant (a, Å), bond distance (B, Å), binding strength (E_b, meV/Å^–2), interfacial separation (H, Å), and electronic bandgap (E_g, eV) for Zr₂CO₂, SiC, GeC monolayers, as well as for Zr₂CO₂/SiC and Zr₂CO₂/GeC heterostructures.

To create heterostructures between Zr₂CO₂ and MC (M = Si, Ge), six distinct stacking configurations were explored, as illustrated in Figures 2a–f. The binding energy (E_b) for each configuration was calculated using the Equation 1 [44]:

$E_{\mathrm{b}}=E_{\text{Zr}2\text{CO}2/\text{MC}}–E_{\text{Zr}2\text{CO}2}–E_{\text{MC}}(1)$

where E_Zr2CO2/MC, E_Zr2CO2 and E_MC show the total energy of the Zr₂CO₂/MC heterostructure, monolayered Zr₂CO₂ and MC, respectively. The smaller binding energy means the more stable structure for the heterostructure. Among the six configurations shwoing as Figures 2a–f, the ZM-1 stacking arrangement exhibited the lowest binding energy, indicating it as the most energetically favorable. For the most stable configuration, the binding energies of the Zr₂CO₂/SiC and Zr₂CO₂/GeC heterostructures were found to be −55.69 meV/Ų and –51.33 meV/Ų, respectively, which is smaller than that in graphites about −18 meV/Å⁻², suggesting van der Waals (vdW) interactions between the interface of the Zr₂CO₂/MC heterostructure [45]. Besides, all the obtained binding energy of the Zr₂CO₂/SiC and Zr₂CO₂/GeC heterostructure with different stacking configurations are demonstrated as Supplementary Table S1. As expected, the interfacial bonding does not drastically alter the original intra-layer bond lengths, confirming the weak yet stable coupling. The calculated interface separations are 1.895 Å for Zr₂CO₂/SiC and 2.254 Å for Zr₂CO₂/GeC. Henceforth, discussions will focus on these energetically preferred heterostructures.

Figure 2

Figure 2. Top and side views of the (a) ZM-1, (b) ZM-2, (c) ZM-3, (d) ZM-4, (e) ZM-5 and (f) ZM-6 stacking configurations of the Hf₂CO₂/MC heterostructure.

To assess the thermal robustness of the Zr₂CO₂/MC heterostructures, we performed ab initio molecular dynamics (AIMD) simulations using the Nosé–Hoover thermostat approach [46]. Supercells of size 6 × 6 × 1 were constructed for both Zr₂CO₂/SiC and Zr₂CO₂/GeC systems, encompassing a total of 252 atoms. These simulations were carried out at a constant temperature of 300 K for a duration of 10 picoseconds. Post-simulation snapshots of the atomic configurations are displayed in Figures 3a,c, illustrating that both heterostructures maintain structural integrity throughout the simulation. This outcome indicates excellent thermal stability under ambient conditions. Additionally, Figures 3b,d show the fluctuations in total energy as a function of time. The minor oscillations and consistent convergence confirm that the systems reach thermal equilibrium, further validating the reliability of the simulations.

Figure 3

Figure 3. The AIMD simulation results at 300 K over 10 ps, including structural snapshots of (a) Zr₂CO₂/SiC and (c) Zr₂CO₂/GeC vdWs heterostructures, along with corresponding energy and temperature profiles shown in (b,d), respectively.

The projected band structures for the Zr₂CO₂/SiC and Zr₂CO₂/GeC heterostructures are presented in Figures 4a,c, respectively. These results reveal indirect bandgaps of 2.056 eV for the SiC-based system and 1.902 eV for the GeC-based counterpart. In each case, the colored bands denote the individual contributions from the Zr₂CO₂ and MC layers, with red and gray representing the MXene and MC monolayers, respectively. Both the conduction band minimum (CBM) and valence band maximum (VBM) are predominantly contributed by the Zr₂CO₂ layer, indicating a type-I band alignment. This conclusion is further supported by the projected density of states (PDOS) shown in Figures 4b,d, which clearly display dominant contributions from the MXene near the Fermi level. These findings suggest that Zr₂CO₂/MC heterostructures retain the desirable features of the constituent layers while exhibiting new interfacial properties favorable for light-emitting and optoelectronic devices. Furthermore, the band structures of the Zr₂CO₂/SiC and Zr₂CO₂/GeC vdW heterostructures by all six different stacking configurations are obtained in Supplementary Figures S1, S2, respectively, in the Supplementary Material.

Figure 4

Figure 4. The computed projected band structures for (a) Zr₂CO₂/SiC and (c) Zr₂CO₂/GeC van der Waals heterostructures. Corresponding projected density of states are illustrated in (b,d), respectively. The Fermi energy level is set to zero.

In the Zr₂CO₂/MC heterostructures, the narrower bandgap of the Zr₂CO₂ layer compared to that of SiC or GeC positions both its CBM and VBM within the wider gap of the MC layers, as illustrated schematically in Figures 5a, b. This energy alignment confirms the presence of a type-I band structure. Under external excitation, electrons in the MC layers are promoted to their CBM, and corresponding holes form at the VBM. Owing to the conduction band offset (CBO) and valence band offset (VBO), these photoexcited carriers migrate from the MC layer to the Zr₂CO₂ layer. For the Zr₂CO₂/SiC heterostructure, the CBO and VBO are calculated as 2.458 eV and 1.779 eV, respectively. In the case of Zr₂CO₂/GeC, these values are 0.447 eV and 0.336 eV. Because the Zr₂CO₂ layer has a lower potential energy at both band edges, it acts as a well that confines the carriers, thus minimizing their leakage back into the MC layers. This characteristic is advantageous for light-emitting applications, as it facilitates efficient radiative recombination by concentrating electrons and holes in the same material region.

Figure 5

Figure 5. Illustration of charge carrier migration across the interface within the type-I band alignment of the Zr₂CO₂/MC van der Waals heterostructure with the mechanism of (a) circulation and (b) non connectivity.

Carrier mobility plays a crucial role in developing efficient light-emitting applications. In this work, the electron and hole mobilities of Zr₂CO₂/MC van der Waals heterostructures are investigated. First, the effective masses (m^*) of the electron and hole are decided by fitting the parabolic functions, which can be represented by Equation 2:

$m^{*}=\pm {\mathrm{\hslash }}^2{\left(\frac{{\mathrm{d}}^2{E}_k}{\mathrm{d}{k}^2}\right)}^{-1}(2)$

where k, E_k are the wave vector and the corresponding electronic energy, respectively. The calculations of carrier mobility (μ) are performed using the Bardeen–Shockley model as Equation 3:

${\mu }_{2\mathrm{D}}=\frac{e{\mathrm{\hslash }}^3{C}_{2\mathrm{D}}}{k_{\mathrm{B}}T{m}_{\mathrm{e}}^{*}{m}_{\mathrm{d}}{\left(E_1^i\right)}^2}(3)$

where e, $\mathrm{\hslash }$, k_B, T, m_d, and m_t denote the elementary charge, Planck’s constant, Boltzmann constant, temperature, transport-direction effective mass, and the average effective mass, respectively. Here, m_d is determined based on the effective mass tensor. The deformation potential constant, E₁, is obtained from the relation involving ΔV_i, which represents the energy shift between the conduction band minimum and valence band maximum under applied uniaxial strain. The elastic modulus for the considered two-dimensional structure (C_2D) is derived using the formula involving ΔE, l, and S₀, where ΔE is the total energy difference under strain, l is the applied strain magnitude, and S₀ is the equilibrium lattice area. The carrier transport directions in the Zr₂CO₂/SiC (or Zr₂CO₂/GeC) vdW heterostructures are illustrated in Figure 6a, corresponding to the armchair and zigzag orientations, respectively. The elastic modulus is derived from the variation in total energy (ΔE) under applied uniaxial strain. The strain responses along the transport directions for both heterostructures are shown in Figures 6b,d. Meanwhile, Figures 6c,e depict the modulation of the band edge positions under such strain conditions. The calculated carrier mobilities for the Zr₂CO₂/MC vdW heterostructures are presented in Table 2. Specifically, for electron transport along the armchair direction, mobilities of 275 cm² V⁻¹·s^–1 (Zr₂CO₂/SiC) and 388 cm² V⁻¹·s^–1 (Zr₂CO₂/GeC) are obtained, while in the zigzag direction, the respective values are 278 cm² V⁻¹·s^–1 and 574 cm² V⁻¹·s^–1. Regarding hole transport, mobilities reach 3479 cm² V⁻¹·s^–1 and 283 cm² V⁻¹·s^–1 along the armchair axis, and 3656 cm² V⁻¹·s^–1 and 337 cm² V⁻¹·s^–1 in the zigzag direction for Zr₂CO₂/SiC and Zr₂CO₂/GeC, respectively. The notably high hole mobility in Zr₂CO₂/SiC can be attributed to the minimal strain dependence of its valence band maximum (VBM). In contrast, the relatively low mobility in Zr₂CO₂/GeC is mainly due to its large hole effective mass, although it still surpasses that of several known 2D popular materials, such as monolayer MoS₂ [47], WS₂ [48], and BlueP [49].

Figure 6

Figure 6. Atomic configurations of the armchair and zigzag terminations in monolayer (a) Zr₂CO₂/MC vdWs heterostructures. Panels (b,d) illustrate the variation in total energy (ΔE) for orthorhombic Zr₂CO₂/SiC and Zr₂CO₂/GeC systems, respectively, under uniaxial strain applied along both armchair and zigzag directions. (c,e) display the evolution of band edge positions for these heterostructures subjected to strain along the same orientations.

Table 2

Table 2. Effective mass (m*), elastic modulus (C), deformation potential constant (E_i), and carrier mobility (μ) of the carriers (electron and hole) along the transport directions for the monolayered MoSSe/XN (X = Ga, Al) vdW heterostructure calculated by PBE functional at 300K.

To gain insight into the interfacial electronic interactions, we analyzed the charge redistribution in the Zr₂CO₂/MC heterostructures. The differential charge density (Δρ) was calculated using the following Equation 4:

$\Delta \rho ={\rho }_{\text{MXene}/\text{MC}}–{\rho }_{\text{MXene}}–{\rho }_{\text{MC}}(4)$

where ρ_MXene/MC, ρ_MXene and ρ_MC show the total charge density of the Zr₂CO₂/SiC (or Zr₂CO₂/GeC) vdW heterostructure, monolayered Zr₂CO₂ and SiC (or GeC), respectively. Figures 7a, 6b illustrate the charge distribution at the interfaces of Zr₂CO₂/SiC and Zr₂CO₂/GeC. It is evident that both SiC and GeC layers serve as electron donors upon contact, transferring charge to the Zr₂CO₂ layer. This electron movement leads to the emergence of regions enriched and depleted in charge, forming distinct dipole layers at the interface. Quantitatively, Bader charge analysis reveals that 0.1459 |e| and 0.0425 |e| electrons are transferred from SiC and GeC to the Zr₂CO₂ layer, respectively. Furthermore, the charge transfer between the Zr₂CO₂/SiC and Zr₂CO₂/GeC heterostructures with other stacking structures have been calculated as Supplementary Table S2, one can see that the ZM-1 configuration still results maximum charge transfer. This charge redistribution also induces a potential drop (ΔV) across the interface, calculated to be 6.457 eV for Zr₂CO₂/SiC and 3.712 eV for Zr₂CO₂/GeC. Such interfacial potential differences serve as an internal driving force, enhancing carrier transport across the heterostructure.

Figure 7

Figure 7. The electrostatic potential profiles at the interface of (a) Zr₂CO₂/SiC and (b) Zr₂CO₂/GeC van der Waals heterostructures are illustrated. Yellow regions indicate electron accumulation, while cyan regions represent electron depletion. An isosurface value of 0.0001 |e| has been selected for visualization.

The optical characteristics of the Zr₂CO₂/MC heterostructures were evaluated through absorption spectrum analysis derived from the complex dielectric function. The absorption coefficient α(ω) was obtained using the Equation 5:

$\alpha \left(\omega \right)=\frac{\sqrt{2}\omega }{c}{\left\{{\left[{\epsilon }_1^2\left(\omega \right)+{\epsilon }_2^2\left(\omega \right)\right]}^{1/2}-{\epsilon }_1\left(\omega \right)\right\}}^{1/2}(5)$

where ω is the angular frequency, c denotes the speed of light, and ε₁, ε₂ are the real and imaginary parts of the dielectric function, respectively. Furthermore, ε₂ (ω) can be calculated by Equation 6 [50]:

${\epsilon }_2\left(q\to O_{\widehat{u}},\mathrm{\hslash }\omega \right)=\frac{2e^2\pi }{\mathrm{\Omega }{\epsilon }_0}{\displaystyle \sum _{k,v,c}}\mid 〈\left.{\mathrm{\Psi }}_k^c\right|{\left.\widehat{u}·r\left|{\mathrm{\Psi }}_k^v\right.〉\right|}^2\times \delta \left(E_k^c-E_k^v-E\right)(6)$

where the wave function, energy, and unit vector of the incident light electric field are denoted by ${\mathrm{\Psi }}_k$, $E_k$ and $\widehat{u}$, respectively. The conduction and valence bands are indicated by the superscripts (v and c) in the ${\mathrm{\Psi }}_k$, $E_k$ and $\widehat{u}$, labels, respectively. The complex dielectric function is given by ε (ω) = ε₁ (ω) + iε₂ (ω), where the real part ε₁ can be derived from ε₂ using the Kramers–Kronig relation. As shown in Figure 8, both Zr₂CO₂/SiC and Zr₂CO₂/GeC heterostructures demonstrate broad absorption across the visible and near-infrared (NIR) spectral regions. This response is more substantial than that of the individual SiC, GeC, or Zr₂CO₂ monolayers. Specifically, in the visible range, the maximum absorption peaks reach 3.568 × 10⁵ cm^–1 for Zr₂CO₂/SiC and 3.698 × 10⁵ cm^–1 for Zr₂CO₂/GeC. Additionally, secondary peaks of 1.125 × 10⁵ cm^–1 and 0.879 × 10⁵ cm^–1 appear near wavelengths of 441 nm and 425 nm, respectively. These are significantly stronger than the 0.853 × 10⁵ cm^–1 peak found in pristine Zr₂CO₂. It is worth noting that the obtained light absorption capacity of the Zr₂CO₂/SiC or Zr₂CO₂/GeC heterostructure is also higher than that of reported 2D heterostructure, such as CdO/Arsenene (8.47 × 10⁴ cm^–1) [51], PtS₂/MoTe₂ (2.57 × 10⁵ cm^–1) [52] and AlN/Zr₂CO₂ (3.97 × 10⁵ cm^–1) [53] etc.

Figure 8

Figure 8. The HSE06 functional obtained optical absorption spectrum for the Zr₂CO₂, SiC, GeC monolayers and Zr₂CO₂/SiC, Zr₂CO₂/GeC vdW heterostructures.

Conclusion

In this work, the structural, electronic, and optical characteristics of monolayer Zr₂CO₂, SiC, and GeC—as well as their corresponding van der Waals heterostructures—have been comprehensively explored using first-principles calculations. The constructed Zr₂CO₂/SiC and Zr₂CO₂/GeC heterostructures demonstrate high thermal resilience, retaining their integrity at 300 K based on ab initio molecular dynamics simulations. These heterostructures exhibit type-I band alignment, with indirect bandgaps of 2.056 eV and 1.902 eV, respectively. The band edges are mainly derived from the Zr₂CO₂ layer, positioning these systems as promising candidates for light-emitting applications. Interlayer charge transfer was observed, with calculated electron donation from the MC layers of 0.1459 |e| (SiC) and 0.0425 |e| (GeC), inducing interfacial potential drops of 6.457 eV and 3.712 eV. These potential differences facilitate efficient carrier transport across the interface. Additionally, both heterostructures display significantly improved optical absorption, particularly across visible and near-infrared wavelengths, outperforming their monolayer counterparts. These optical features support the use of Zr₂CO₂/MC systems in energy-related optoelectronic technologies.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.

Author contributions

BT: Validation, Writing – review and editing, Writing – original draft, Visualization, Data curation, Resources. ZZ: Writing – review and editing, Resources, Data curation, Validation. JL: Software, Investigation, Funding acquisition, Writing – review and editing, Supervision.

Funding

The author(s) declare that financial support was received for the research and/or publication of this article. All authors thank the Anhui Province Higher Education Science Research Project Funding (2022AH052432), the research Projects of Department of Education of Guangdong Province (2024ZDZX3081) and Shenzhen Polytechnic Research Fund (6023310003K).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declare that no Generative AI was used in the creation of this manuscript.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphy.2025.1655987/full#supplementary-material

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