Ultra-fast hot-carrier relaxation via electron-phonon (e-ph) coupling fundamentally limits efficiency in optoelectronic devices. This ab initio study employs density functional theory (DFT) and many-body perturbation theory to probe these dynamics in the fully fluorinated GeC (F-GeC-F) monolayer, a wide-gap 2D semiconductor with exceptional stability. Our calculations show that optical phonons dominate electron-phonon scattering, with the LO2 mode governing the VBM and the LO3 mode dominating the CBM, where scattering is significantly stronger, making LO3 the primary channel overall. This strong coupling drives ultra-fast thermalization 100 fs across 0 - 400 K, matching unfluorinated GeC despite fluorination’s dramatic bandgap expansion. Pronounced anisotropy emerges in linewidths along high-symmetry k-paths, with coupling strength varying dramatically by crystallographic direction and temperature. These mode-resolved, temperature-dependent insights, nearly impossible to isolate experimentally, offer a microscopic blueprint for engineering carrier lifetimes in next-generation 2D nanoelectronics and photodetectors.
References
[1]
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., etal. (2004) Electric Field Effect in Atomically Thin Carbon Films. Science, 306, 666-669. https://doi.org/10.1126/science.1102896
[2]
Aufray, B., Kara, A., Vizzini, S., Oughaddou, H., Léandri, C., Ealet, B., et al. (2010) Graphene-Like Silicon Nanoribbons on Ag(110): A Possible Formation of Silicene. Applied Physics Letters, 96, Article 183102. https://doi.org/10.1063/1.3419932
[3]
Bianco, E., Butler, S., Jiang, S., Restrepo, O.D., Windl, W. and Goldberger, J.E. (2013) Stability and Exfoliation of Germanane: A Germanium Graphane Analogue. ACS Nano, 7, 4414-4421. https://doi.org/10.1021/nn4009406
[4]
Drissi, L.B., Sadki, S. and Sadki, K. (2018) Phosphorene under Strain: Electronic, Mechanical and Piezoelectric Responses. Journal of Physics and Chemistry of Solids, 112, 137-142. https://doi.org/10.1016/j.jpcs.2017.09.017
[5]
Zhu, F., Chen, W., Xu, Y., Gao, C., Guan, D., Liu, C., et al. (2015) Epitaxial Growth of Two-Dimensional Stanene. Nature Materials, 14, 1020-1025. https://doi.org/10.1038/nmat4384
[6]
Ding, T., Jiang, X., Quan, J., Wang, R., Li, M., Lan, C., et al. (2025) Recent Progress in Two-Dimensional Van Der Waals Heterojunctions for Flexible Energy Storage Applications. Advanced Composites and Hybrid Materials, 8, Article No. 324. https://doi.org/10.1007/s42114-025-01410-1
[7]
Ni, Z., Liu, Q., Tang, K., Zheng, J., Zhou, J., Qin, R., et al. (2012) Tunable Bandgap in Silicene and Germanene. Nano Letters, 12, 113-118. https://doi.org/10.1021/nl203065e
[8]
Kanga, N.B.J., Insad, S. and Drissi, L.B. (2018) Electron-Phonon Investigation in Stanene. Computational Materials Science, 155, 63-68. https://doi.org/10.1016/j.commatsci.2018.08.038
[9]
Gao, N., Li, J.C. and Jiang, Q. (2014) Bandgap Opening in Silicene: Effect of Substrates. ChemicalPhysicsLetters, 592, 222-226. https://doi.org/10.1016/j.cplett.2013.12.036
[10]
Ouarrad, H., Drissi, L.B., Assad, R. and Fritzsche, W. (2024) Photoluminescence Mechanism and Optoelectronic Responses of Janus Pyrene and Janus Coronene QDs for OLEDs & Nanomedical Applications. Journal of Physics and Chemistry of Solids, 184, Article 111675. https://doi.org/10.1016/j.jpcs.2023.111675
[11]
Drissi, L.B., Saidi, E.H., Bousmina, M. and Fassi-Fehri, O. (2012) DFT Investigations of the Hydrogenation Effect on Silicene/Graphene Hybrids. Journal of Physics: Condensed Matter, 24, Article 485502. https://doi.org/10.1088/0953-8984/24/48/485502
[12]
Zhang, J., Ren, J., Fu, H., Ding, Z., Li, H. and Meng, S. (2015) Two-Dimensional Silicon-Carbon Hybrids with a Honeycomb Lattice: New Family for Two-Dimensional Photovoltaic Materials. Science China Physics, Mechanics & Astronomy, 58, Article 106801. https://doi.org/10.1007/s11433-015-5703-6
[13]
Drissi, L.B., Ramadan, F.Z., Ferhati, H., Djeffal, F. and Kanga, N.B. (2019) New Highly Efficient 2D SiC UV-Absorbing Material with Plasmonic Light Trapping. Journal of Physics: Condensed Matter, 32, Article 025701. https://doi.org/10.1088/1361-648x/ab3ab6
[14]
Drissi, L.B., Kanga, N.B., Lounis, S., Djeffal, F. and Haddad, S. (2019) Electron-Phonon Dynamics in 2D Carbon Based-Hybrids XC (X=Si, Ge, Sn). Journal of Physics: Condensed Matter, 31, Article 135702. https://doi.org/10.1088/1361-648x/aaff3b
[15]
Ha, C.V., Ha, L.T., Hue, D.T., Nguyen, D.K., Anh, D.T., Guerrero-Sanchez, J., et al. (2023) First-Principles Study of SiC and GeC Monolayers with Adsorbed Non-Metal Atoms. RSC Advances, 13, 14879-14886. https://doi.org/10.1039/d3ra01372c
[16]
Bentaibi, B., Drissi, L.B., Saidi, E.H. and Bousmina, M. (2022) New Room-Temperature 2D Hexagonal Topological Insulator OsC: First Principle Calculations. Materials Science in Semiconductor Processing, 151, Article 107009. https://doi.org/10.1016/j.mssp.2022.107009
[17]
Shafi, H.Z., Mahmood, A., Ali, Z. and Mehmood, M. (2010) Optical and Structural Analysis of GeC Thin Films Deposited by Reactive Pulsed Laser Ablation Technique. Key Engineering Materials, 442, 178-186. https://doi.org/10.4028/www.scientific.net/kem.442.178
[18]
Hu, C.Q., Zheng, W.T., Zheng, B., Li, J.J., et al. (2004) Chemical Bonding of A-Ge1-xCx: H Films Grown by RF Reactive Sputtering. Vacuum, 77, 63-68. https://doi.org/10.1016/j.vacuum.2004.08.004
[19]
Ji, Y., Dong, H., Hou, T. and Li, Y. (2018) Monolayer Graphitic Germanium Carbide (g-GeC): The Promising Cathode Catalyst for Fuel Cell and Lithium-Oxygen Battery Applications. Journal of Materials Chemistry A, 6, 2212-2218. https://doi.org/10.1039/c7ta10118j
[20]
Drissi, L.B. and Ramadan, F.Z. (2015) Excitonic Effects in GeC Hybrid: Many-Body Green’s Function Calculations. Physica E: Low-dimensional Systems and Nanostructures, 74, 377-381. https://doi.org/10.1016/j.physe.2015.07.030
[21]
Fan, X., Jiang, J., Li, R. and Mi, W. (2021) Half-Metallicity and Magnetic Anisotropy in Transition-Metal-Atom-Doped Graphitic Germanium Carbide (g-GeC) Monolayers. The Journal of Physical Chemistry C, 125, 13688-13695. https://doi.org/10.1021/acs.jpcc.1c04139
[22]
Taleb, A.A., Drissi, L.B., Kanga, N.B.J. and Lounis, S. (2024) Half-Metallic Ferromagnetism with High Critical Temperatures in Substitutionally Doped Rare-Earth 2D Germanene. Journal of Magnetism and Magnetic Materials, 606, Article 172392. https://doi.org/10.1016/j.jmmm.2024.172392
[23]
Li, J., Li, Z., Li, J., Hu, Z., Kang, M., Xiong, T., et al. (2024) GeC Monolayer: A Promising 2D Material for Reusable SO2 and NO2 Gas Sensor with High Sensitivity. Materials Today Communications, 40, Article 110085. https://doi.org/10.1016/j.mtcomm.2024.110085
[24]
Drissi, L.B., Kanga, N.B.J. and Ramadan, F.Z. (2018) Excitonic and Fluorination Effects on Optoelectronic Response of GeC Hybrid. Computational Condensed Matter, 14, 49-54. https://doi.org/10.1016/j.cocom.2017.12.003
[25]
Drissi, L.B., Ramadan, F.Z. and Kanga, N.B.J. (2016) Fluorination-Control of Electronic and Magnetic Properties in GeC-Hybrid. Chemical Physics Letters, 659, 148-153. https://doi.org/10.1016/j.cplett.2016.07.017
[26]
Karlický, F., Kumara Ramanatha Datta, K., Otyepka, M. and Zbořil, R. (2013) Halogenated Graphenes: Rapidly Growing Family of Graphene Derivatives. ACS Nano, 7, 6434-6464. https://doi.org/10.1021/nn4024027
[27]
Vu, T.V., Anh, N.T.T., Tran, D.P., Hoat, D.M., Binh, N.T.T., Tong, H.D., et al. (2020) Surface Functionalization of GeC Monolayer with F and Cl: Electronic and Optical Properties. Superlattices and Microstructures, 137, Article 106359. https://doi.org/10.1016/j.spmi.2019.106359
[28]
Giustino, F. (2017) Electron-Phonon Interactions from First Principles. Reviews of Modern Physics, 89, Article 015003. https://doi.org/10.1103/revmodphys.89.015003
[29]
Bardeen, J., Cooper, L.N. and Schrieffer, J.R. (1957) Theory of Superconductivity. Physical Review, 108, 1175-1204. https://doi.org/10.1103/physrev.108.1175
[30]
Kohn, W. (1959) Image of the Fermi Surface in the Vibration Spectrum of a Metal. PhysicalReviewLetters, 2, 393-394. https://doi.org/10.1103/physrevlett.2.393
[31]
Peierls, R.E. (1955) Quantum Theory of Solids. Oxford University Press.
[32]
Coropceanu, V., Cornil, J., da Silva Filho, D.A., Olivier, Y., Silbey, R. and Brédas, J. (2007) Charge Transport in Organic Semiconductors. Chemical Reviews, 107, 926-952. https://doi.org/10.1021/cr050140x
[33]
Giustino, F., Cohen, M.L. and Louie, S.G. (2007) Electron-Phonon Interaction Using Wannier Functions. Physical Review B, 76, Article 165108. https://doi.org/10.1103/physrevb.76.165108
[34]
Hohenberg, P. and Kohn, W. (1964) Inhomogeneous Electron Gas. Physical Review, 136, B864-B871. https://doi.org/10.1103/physrev.136.b864
[35]
Baroni, S., Giannozzi, P. and Testa, A. (1987) Green’s-Function Approach to Linear Response in Solids. Physical Review Letters, 58, 1861-1864. https://doi.org/10.1103/physrevlett.58.1861
[36]
Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., et al. (2009) QUANTUM ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. Journal of Physics: Condensed Matter, 21, Article 395502. https://doi.org/10.1088/0953-8984/21/39/395502
[37]
Kohn, W. and Sham, L.J. (1965) Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review, 140, A1133-A1138. https://doi.org/10.1103/physrev.140.a1133
[38]
Perdew, J.P., Burke, K. and Ernzerhof, M. (1996) Generalized Gradient Approximation Made Simple. Physical Review Letters, 77, 3865-3868. https://doi.org/10.1103/physrevlett.77.3865
[39]
Hamann, D.R., Schlüter, M. and Chiang, C. (1979) Norm-Conserving Pseudopotentials. Physical Review Letters, 43, 1494-1497. https://doi.org/10.1103/physrevlett.43.1494
[40]
Noffsinger, J., Giustino, F., Malone, B.D., Park, C., Louie, S.G. and Cohen, M.L. (2010) EPW: A Program for Calculating the Electron-Phonon Coupling Using Maximally Localized Wannier Functions. Computer Physics Communications, 181, 2140-2148. https://doi.org/10.1016/j.cpc.2010.08.027
[41]
Tandon, N., Albrecht, J.D. and Ram-Mohan, L.R. (2015) Electron-Phonon Coupling and Associated Scattering Rates in Diamond. Diamond and Related Materials, 56, 1-5. https://doi.org/10.1016/j.diamond.2015.03.019
[42]
Shah, J. (2013) Phonon Dynamics, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures. Springer.
[43]
Bernardi, M., Vigil-Fowler, D., Lischner, J., Neaton, J.B. and Louie, S.G. (2014) Ab Initiostudy of Hot Carriers in the First Picosecond after Sunlight Absorption in Silicon. Physical Review Letters, 112, Article 257402. https://doi.org/10.1103/physrevlett.112.257402
[44]
Kanga, N.B.J., Taleb, A.A. and Drissi, L.B. (2024) Impact of Magnetism on (e-pH) Self-Energy and Thermalization of Hot Carriers in 2D Half-Functionalized GeC-Hybrid. Physica E: Low-Dimensional Systems and Nanostructures, 162, Article 116005. https://doi.org/10.1016/j.physe.2024.116005
[45]
Fischetti, M.V. and Vandenberghe, W.G. (2016) Mermin-Wagner Theorem, Flexural Modes, and Degraded Carrier Mobility in Two-Dimensional Crystals with Broken Horizontal Mirror Symmetry. PhysicalReviewB, 93, Article 155413. https://doi.org/10.1103/physrevb.93.155413
