Substitutional Doped GeSe: Tunable Oxidative States with Strain Engineering

Layered chalcogenide materials have a wealth of nanoelectronics applications like resistive switching and energy-harvesting such as photocatalyst owing to rich electronic, orbital, and lattice excitations. In this work, we explore monochalcogenide germanium selenide GeSe with respect to substitutional doping with 13 metallic cations by using first-principles calculations. Typical dopants including s-shell (alkali elements Li and Na), p-shell (Al, Pb and Bi), 3d (Fe, Cu, Co and Ni), 4d (Pd and Ag) and 5d (Au and Pt) elements are systematically examined. Amongst all the cationic dopants, Al with the highest oxidation states, implying a high mobility driven by electric field, and Al-doped GeSe may be a promising candidate for novel resistive switching devices. We show that there exist many localized induced states in the band gap of GeSe upon doping Fe, Co, or Ni, while for Cu, Ag, and Au cases there is no such states in the gap. The Ag and Cu are + 0.27 and + 0.35 charged respectively and the positive charges are beneficial for field-driven motion in GeSe. In contrast, Au is slightly negatively charged renders Au-doped GeSe a promising photocatalyst and enhanced surface plasmon. Moreover, we explore the coexistence of dopant and strain in GeSe and find dynamical adjustments of localized states in GeSe with levels successive shifting upward/downward with strain. This induces dynamic oxidative states of the dopants under strain which should be quite popular in composites where motion of metal adatoms causes significant deformation.


Introduction
The discovery of graphene and other two-dimensional (2D) layered crystal materials, such as black phosphorus (BP), stanene, transition metal dichalcogenides (TMDS), etc, has triggered great interests in various phenomena in atomically thin space [1][2][3][4][5][6][7][8] . These 2D materials bring about novel electronic and photonic performance different from their counterpart bulk materials due to their electrons, holes and phonons are confined in a small limited space [9][10][11] . As a result of unique physical properties, 2D 3 materials are promising for some innovative applications such as advanced catalyst and nanoelectronic devices 12,13 . Recently, layered group-Ⅳ monochalcogenides (GeS, GeSe, SnS and SnSe), a 2D family with isostructural and isoelectronic analogue of phosphorene have attracted great attentions. Due to their high stability and intriguing electronic properties, such chalcogenides compounds are potential candidates for resistive switching devices [14][15][16] and electrochemical memory cells 17,18 .
Germanium selenide (GeSe), which has highly in-plane anisotropic electronic and optical properties due to its unique "puckered" symmetry structure, has aroused extensively attention 19 for optoelectronics owing to its environmentally more friendly and biocompatible than other chalcogenides. Bulk GeSe has an intrinsically p-type conducting characteristics (similar to phosphorene) with a closely placed directindirect band gaps around 1.1 eV 20 . GeSe films have an excellent absorption under near infrared (NIR) excitation 21,22 , an optimal gap for a single junction solar cells [23][24][25] , efficient phototransistor 26,27 , and a highly sensitive to NIR light irradiation for photodetector [28][29][30] . 2D GeSe monolayer was successfully fabricated onto Si/SiO 2 substrates by using laser thinning, vapor transport and deposition techniques 30,31 . Anisotropic conductance inherent in GeSe is ideal platform for developing highefficiency plasmonic devices where the resonance frequency can be continuously tuned by light polarization direction 32,33 . GeSe monolayer has 4 also been proven to have giant piezoelectricity 34 and thermoelectrics 35 allowing energy harvesting. Twisted bilayer GeSe was reported to show intriguing Moiré patterns with the crossover from two to one dimension excitations 36 . More recently, GeSe has been found to be an ideal platform for laser 37 and novel nanoelectronic devices such as memristors 38,39 . Fewlayer GeSe sheets, together with proper ionic particles like Ag, are used as the ionic and electronic conductor, where high and low resistance with ratio up to 10 4 have been achieved for information storage 38 . An Ag/GeSe/TiN memristor for brain-inspired neuromorphic applications was fabricated and an electronic synapse was realized through controlling the electromigration and diffusion of Ag atoms within the GeSe flakes 40 . Therefore, understanding the behaviors metallic particles within the GeSe is highly important for such applications. The dopants can create significant distortion and strains 41 in the lattice while such effects are still unknown.
Understanding the oxidation states of the dopants under external stimuli is ultra-important. However, related information is still missing and unknown.
In this work, we investigate the coupling of the doping and strain effects on the electronic properties of GeSe by using first-principles calculations on the basis of density functional theory (DFT). We are particularly interested in the oxidative states of such dopants which are highly correlated with the chemical and novel electronic applications (i.e. resistive switching). We investigate the localized levels and charged states 5 of these dopants which are found to vary with lattice strain. This suggests a dynamic oxidative states of the dopants under strain which can provide useful hints in memory devices and energy applications.

Computational method and details
The structure optimization and electronic properties are performed using the Vienna ab initio simulation package (VASP) 42 , which is based on the framework of spin-polarized density functional theory. We adopt a supercell (5 × 4 × 1) of monolayer GeSe structure. The cutoff energy of 400 eV and k points of 3×3 grid are used. Furthermore, a vacuum layer with thickness of 15 Å is adopted to avoid spurious interaction of images under the periodic boundary condition. The structures are fully relaxed until the forces on atoms are smaller than 0.01 eV/Å. We also calculate the binding energy E b to evaluate the stability of X-GeSe system. The equation for E b of doping system is defined as: where X represents doped element, E X+GeSe denotes total energy of X doped GeSe monolayer, E X denotes energy of single atom X, E vacancy denotes the total energy of GeSe monolayer with one Ge atomic vacancy.

Results and discussion
In this work, typical cationic dopants, with following typical electronic 6 configurations: s-shell (alkali elements Li and Na), p-shell (Al, Pb and Bi), 3d (Fe, Cu, Co and Ni), 4d (Pd and Ag) and 5d (Au and Pt), are systematically studied by substituting one of the germanium atom (forming X Ge type of defect where X is the dopant) in the supercell. The doping concentration is ~3%. The new bond length, formation energy and magnetic properties are calculated and listed in Table 1    Electronic properties of pristine GeSe: GeSe sheet adopts a puckered structure similar to phosphorene with forming Ge-Se zigzag chains aligned 8 along the armchair direction (Fig. 1a). Our optimized lattice constants of unit cell of monolayer GeSe are a= 3.58 Å, b= 3.91 Å, consistent with previous studies 43,44 . The atomic configuration, density of states (DOS) and band structure of pristine GeSe (for a 5 × 4 supercell) are plotted in Fig. 1.
It is shown that GeSe monolayer has an indirect band gap (1.

Li, Na and Al doped GeSe monolayer:
We give an attention to doped monolayer GeSe with Li, Na and Al atoms that have no electrons in their d-orbitals (Fig. 2). Alkali species doped 2D materials have attracted a great deal of interests for electrochemical applications (i.e. hydrogen storage or lithium battery) because of its weak binding of alkali species on surface and high surface-volume ratio [49][50][51] . Table 1  It should be noted that although Li and Na almost donate all of its outer 1s electron to the GeSe, the Fermi level (E F ) of the hybrid Li/Na-GeSe system is still below the VBM of GeSe, indicating a p-type conduction for such type of substitutional doping. The reason is that the substitutional doping (Li Ge or Na Ge ) is essentially a composite defect (Li i +V Ge or Na i +V Ge ) consisting of interstitial Li or Na (Li i , Na i ) and Ge vacancy (V Ge ). The creation of a V Ge leaves two holes states and the Li or Na donates single electron which only partially compensates it, thus there still has one hole in each Li Ge or Na Ge . As shown in Fig. 2g, the donating electron from Li at the V Ge causes slight splitting of the bands and pushes up of the V Ge related bands (crossing E F ), while no such effect are found in the Na case which should be attributed to the more localized electrons in Li than in Na.

11
In the Al case, the Al atom forms Al-Se bonds with three adjacent selenium atoms and the band length ranges from 2.45-2.55 Å (Fig. 2c). The  In addition, as shown in the band structure ( Fig. 3g-

Strain-induced variation of band structure
Manipulating electronic and magnetic properties of two-dimensional (2D) materials with effective approach is vital to explore the applications of 2D materials in many fields. Strain effects are proved to be an effective approach of tuning electronic and other properties [55][56][57][58][59] . In addition, examining the deformation of the lattice on the electronic properties is critical as 2D materials are highly likely to be subjected to external mechanical deformation. In this section, we investigate the variation of  GeSe monolayer under -2%, 0, 2%, 4%, 6% and 8% bi-axial strains.
Strain engineering of pristine GeSe monolayer: Firstly, we investigate the strain engineering of pristine GeSe monolayer. As shown in Figure 7a- eV for 2%, 4%, 6%, and 8%, respectively. As shown in Fig. 7d, the bands become flattened with tensile strains due to the gradual localization of the electrons. For the valence bands, the distance from the VBM relative to E f 22 almost has no significant changes while the maximum point shifts from X point to the Г point starting from 6% and multiple band crossings occur. In contrast, the CBM shifts upwardly from zero to 4% strain and levels off afterwards. The position of CBM evolves from Y to X point from 2% onward. Therefore, from zero to 2% strain, the band structure occurs an indirect to direct transformation, and evolves back to indirect gap again at ~ 6% strain. Our results are in good agreement with previous studies [55][56][57][58][59] .

Modulated oxidative states of cationic dopants with strain:
Finally, we perform Bader charge analysis on the charged state of each dopants. As shown in Fig. 12a Figure 12.
Due to the much larger electronegativity that Ag and Cu 52 , they are less oxidized in GeSe. Nevertheless, they also possess an overall trend of increasing oxidation with strain. Differential charge density plot (Fig. 12c) for typical dopants i.e. Cu, Ag, Au and Pt shows that due to chemical hybridization significant amounts of charges from/to the dopants are transferred to/from the Se-p orbital.
For Ag and Cu which are normally adopted in resistive switch devices, the higher degree of charges carried by the dopants under larger tensile strains implies that stronger forces by electric field will be exerted on these moving particles in highly stretched films. Consider the higher degree for deformation at the frontier area of newborn filament, our result of higher charged dopants in more stretched region uncovers the acceleration mechanism of the moving particles and growth of the filament in these devices 38,40 . Our results also demonstrate that the moving particles seems

Conclusion
In summary, we investigate the substitutional metal doped GeSe monolayer by using first-principles calculations based on density functional theory.
The energetics and electronic properties of these doped GeSe monolayers with respect to the localized states are systematically explored in this paper.