Femtosecond laser induced ultrafast interface dynamics between single layer graphene and quartz substrate: A theoretical study

Graphene is one of the most promising quantum material for the next generation electrical and optoelectronic devices due to the excellent conductivity,^1–6 mechanical strength, chemical stability,^7–11 and other fascinating physical properties including the strain induced pseudomagnetic field,^12,13 magic angle superconductivity, and higher harmonics.^14–20 As an atomic thick material, substrates are crucial for modulating graphene devices and improving their performance, in which SiO₂ is the most widely used dielectric substrate thanks to accessible fabrication technologies and feasible surface chemical modifications. Therefore, investigating the interface interaction and dynamics mechanism between graphene and SiO₂ is significant.

In the past several years, density functional theory (DFT) was used as an effective tool to study interface interactions and electrical properties of the graphene–SiO₂ system in ground states without external field excitations. For example, Fan et al. built SiO₂ substrates based on alpha quartz and cristobalite quartz structures, respectively.²¹ They observed that graphene is mainly stabilized on the SiO₂ surface through physical adsorption, and oxygen defects lead to hole doping in graphene. Ao et al. studied the types and strengths of graphene–SiO₂ interface interactions on oxygen terminated SiO₂ surfaces, indicating that van der Waals (vdW) forces are mainly dominant.²² Gao et al. found that the SiO₂ surface hydroxylation and water molecule adsorption can reduce the interface adhesion energy.²³ Li et al. investigated the strong chemical covalent interaction between Si terminated β-quartz and graphene.²⁴ They found that the formed C–Si covalent bonds significantly alter the band structure of graphene and lead to electron doping. Kang et al. revealed the influence of surface polarity of SiO₂ substrate on graphene through charge transfer, where graphene is p-type doped on oxygen polar surfaces but n-type doped on silicon polar surfaces.²⁵ 

However, when applying intense ultrafast optical fields, e.g., femtosecond laser pulse, to a graphene-SiO₂ interface, the internal electron and lattice systems will be excited, which cannot be handled by using the ground-state DFT method. At present, there is an urgent need to theoretically study the ultrafast optical excitation dynamics at the graphene-SiO₂ interface beyond DFT.

In fact, in recent years, the real-time time-dependent density functional theory (rt-TDDFT) method was developed rapidly that provides an effective way to handle the photoexcitation problem by involving external fields in Hamiltonian.²⁶ For example, Wang et al. studied the microscopic force driving the structural transition of IrTe₂ between the high-temperature phase and low-temperature phase arising from photoinduced electron modulation by using the PWmat code.^27,28 You et al. analyzed the atomic-scale pathways of photogenerated charge carrier transport and photoinduced water dissociation at the prototypical water–rutile TiO₂ (110) interface by using the TDAP code in order to elucidate the mechanism of photoinduced water splitting.²⁹ He et al. used the ABACUS code to investigate the photoisomerization of azobenzene and showed that the photon-excited electrons play essential roles in the isomerization processes, where the laser wavelength has a significant influence.³⁰ Duchateau et al. studied the femtosecond laser induced excitation dynamics of electrons in bulk α-quartz by using the SALMON code and evaluated the effect of pulse-to-pulse delay on the laser energy deposition into this material.³¹ The recent developments of rt-TDDFT and available codes were detailedly introduced in the following review article.³² 

In this work, the rt-TDDFT method was used to study the ultrafast interface dynamics in a graphene–quartz system triggered by a femtosecond laser pulse with a commercial PWmat code. The dissociation of Si–O bonds and the detachment of graphene off the quartz were observed, and the redistributions and dynamics of excited electrons were analyzed. This work is valuable to uncover the graphene–substrate interactions under the ultrafast photoexcitation.

All the calculations and modeling were implemented with the commercial PWmat code. A single layer graphene is placed on the surface of a Si-terminated α-quartz (001) substrate with a symmetry group P3121. The initial model is composed of a 4 × 4 graphene supercell and a 2 × 2 quartz supercell, including 32 carbon atoms, 16 silicon atoms, and 24 oxygen atoms. The initial vacuum layer thickness between graphene and quartz is set to 4 Å. Several ground layers of quartz substrate were fixed, including eight silicon atoms and eight oxygen atoms. The bottom of the substrate is passivated by eight hydrogen atoms. The calculations applied the Perdew–Burke–Ernzerhof (PBE) functional in the generalized gradient approximation (GGA) to describe electron exchange correlations. The SG15 pseudopotential was used. Structure optimization was performed on the initial model before the optical excitation, and the optimized distance between graphene and quartz was reduced to 3.48 Å. Then, rt-TDDFT calculations were performed to simulate the ultrafast optical excitation process under femtosecond laser irradiation. The simulations were carried out based on norm-conserving pseudo-potentials and the PBE functional with a plane wave nonlocal pseudo-potential Hamiltonian. The plane wave cutoff energy is 680 eV and the k-point sampling is 1 × 1 × 1. The photon energy of the laser pulse is 2.37 eV and the optical excitation period is 40 fs. The following structure relaxation time is 100 fs.

The initial atomic model contains a single layer graphene and a Si-terminated α-quartz substrate [Figs. 1(a) and 1(b)], where the substrate was passivated by hydrogen atoms. The structure optimization was implemented by using the PWmat code, and the optimized structures are shown in Figs. 1(c) and 1(d).

As shown in Fig. 2(a), the laser pulse was described by a Gaussian wave packet of electric field $Et=E⁡cosωtexp−t−to22σ2$ that was also used in previous rt-TDDFT literature.³³ The corresponding laser power density is estimated to be 5.9 × 10¹⁶ W/cm² based on the equation $I=12ε0E2C$⁠, where ε₀ is the vacuum dielectric constant, E is the electric field intensity of laser pulse, and C is the velocity of light.³⁴ As shown in the inset of Fig. 2(b), the total energy of the graphene–quartz system increases stimulated by the laser pulse and then remains constant after the laser pulse is switched off, which was in accord with the energy conservation. The band structure of graphene–quartz was calculated, and the topology of conical intersections was successfully predicted (Fig. S1), proving again the effectiveness of the time dependent density functional theory (TDDFT) methodology.

The time-dependent crystal structure evolution stimulated by the laser pulse is shown in Fig. 3. Two important phenomena can be found. First, Si–O bonds (marked by the black dashed circles) underneath the graphene layer rapidly elongate in the calculation and finally dissociate. Second, the distance between the graphene and the bottom hydrogen atoms gradually increases from 9.90 Å at the initial moment to 10.59 Å at 140 fs. The blue dashed line shown in Fig. 3(f) represents the initial position of the graphene. In addition, distortion of graphene occurs in its travel up process. The above-mentioned rt-TDDFT calculation displays the complete nonequilibrium ultrafast process at the graphene–quartz interface triggered by a transient optical excitation, which cannot be described with the ground-state DFT method or classical Molecular Dynamics  (MD) simulation.

In order to understand the reasons for the dissociation of Si–O bonds and the displacement of graphene, the laser-induced dynamic mechanisms were analyzed.

Figure 4(a) shows the time-dependent length change of two Si–O bonds near the graphene layer. It can be found that the Si–O bonds begin to elongate at about 30 fs within the laser pulse and then rapidly dissociate during the following relaxation process. The differential charge density distributions near the Si–O bonds were calculated at two moments, i.e., 30 fs [Fig. 4(b)] and 32 fs [Fig. 4(c)], which reflect the variations of spatial electron distribution from the initial time to the selected moments. In Figs. 4(b) and 4(c), the big gray balls refer to the Si atoms and the small white balls refer to the O atoms. As shown in Fig. 4(b), induced by the laser pulse, more electrons appear outside the Si–O bonds at 30 fs. At the same time, the transient forces acting on the Si atoms and O atoms at 30 fs were analyzed and labeled with orange arrows shown in Fig. 4(b), respectively, indicating repulsive interactions within the Si–O bonds, which is well in agreement with the differential charge density distributions. In addition, similar differential charge density distributions and atomic forces were observed at 32 fs [Fig. 4(c)]. Therefore, the elongation of Si–O bonds was resulted from the ultrafast laser induced electron excitation and spatial redistribution. In addition, the lengths of Si–O bonds located farther from the graphene layer have no significant changes [Fig. S2(a)] due to confinement from the surrounding atoms, indicating a relatively stable internal structure in quartz. In addition, an oscillation characteristic of C–C bond lengths in graphene was observed under femtosecond laser irradiation [Fig. S2(b)].

For the detachment of graphene from the quartz substrate shown in Fig. 5, we analyzed the average height, average velocity, and the force applied to the graphene. The black line in Fig. 5(a) shows the average height variation of the graphene from 0 to 140 fs. It can be found that distance between graphene and the bottom hydrogen atoms increases from 9.90 to 10.59 Å. The upward average velocity of graphene [red line in Fig. 5(a)] constantly increases, indicating an accelerated detachment process off the quartz substrate. In addition, the interlayer distance between graphene and SiO₂ also increases over time [Fig. S2(c)]. Herein, the interface forces between graphene and the silicon atoms were analyzed to investigate the detachment dynamics of graphene. As shown in Fig. 5(b), for the moment of 80 fs, there is an upward force F₁ = 4.05 eV/Å acting on graphene labeled by the black arrow. At the same time, there are downward forces F₂ = 1.32 eV/Å and F₃ = 1.75 eV/Å acting on the two Si atoms underneath the graphene. Therefore, the detachment of graphene off the quartz substrate was attributed to the repulsive force from the underneath Si atoms. According to the monotonically increasing velocity curve of graphene shown in Fig. 5(a), the upward repulsive force caused by the Si atoms always existed before 140 fs. In this case, the graphene layer will be peeled off from the quartz substrate. Based on the above-mentioned analysis, the ultrafast optical excitation of the graphene–quartz system stimulated by the femtosecond laser pulse includes the following interface dynamics processes. The optical excited electrons tend to be located in both sides of Si–O bonds on the quartz surface, which rapidly dissociate the Si–O bonds. The dissociated Si atoms hit the upper graphene layer and made it fleetly peel off from the substrate.

In addition, a variation in bandgap was preliminarily observed (Fig. S3) in the laser irradiation process, which may be caused by complex electron and lattice dynamics. The authors will detailedly investigate this issue in future studies.

A further discussion about the comparison between the calculations and experimental counterparts is necessary. For actual graphene-SiO₂ devices, the SiO₂ substrate might process multiple crystal or amorphous structures with various element dopings that maybe different from the ideal quartz substrate we used. In addition, the initial local stress, lattice defects, and molecular adsorptions always appear unavoidably in graphene in experiments. In addition, a laser pulse actually contains multidimensional parameters such as the pulse width, wavelength, polarization, and energy density that all affect the transient interface dynamics. Thus, the real interaction between an ultrafast laser pulse and a graphene–SiO₂ system is fairly complicated. This work only presents the interface interaction with a defect-free graphene–quartz system and typical laser parameters. Even so, this work reveals the underlying time-dependent electron dynamics and the coupled nuclear dynamics for graphene–quartz interface under ultrafast optical excitation by using the powerful rt-TDDFT method beyond the classical molecular dynamics simulations and ground-state DFT frameworks. Actually, the rt-TDDFT method used here is capable to study a more complicated graphene–SiO₂ system, which benefits for mechanism analysis and device designs.

In conclusion, the rt-TDDFT method was used to calculate the time-dependent evolution of electrons and nucleus in a graphene–quartz interface system under femtosecond laser irradiation. The Si–O bonds beneath the single layer graphene were dissociated due to the strong repelling effect of redistributed electrons, which also leads to the rapid detachment of graphene from the quartz substrate. The current investigation on an idealized defect-free model can help experimentalists capture the fundamental and crucial physical mechanism and thus design specific device structures to achieve proper photoexcitation dynamics. In fact, the rt-TDDFT method is also capable of involving more complicated conditions such as a graphene layer with defects, doping, and wrinkles, as well as an amorphous SiO₂ substrate. In the future, the effect of material defects and complex light field on the photoexcitation should be further investigated, which will largely contribute to the graphene-based device design.