Fig. 1. Schematic illustrations of structural models of germanenes grown on Al (111) along with the configuration of the Al (111) itself. Only two top layers of substrate are shown. Black rhombuses are periodic units used in calculations. Grey, blue, and green spheres represent Al atoms in substrate, Ge atoms in basal plane of the 2D sheet, and Ge atoms protruded upward which can be seen in STM image of the 2D sheet, respectively.

Fig. 1. Doping configurations of a single Al atom in 2D germanene models supported on Al (111) corresponding to (a) HL, (b) KL, (c) TRP-1T, (d) BHS-2T, (e) BHS-1H, (f) SRT19-3T, and (g) SRT7-1T structures. Grey, blue, green, and red spheres denote Al atoms in substrate, Ge atoms in basal plane of the 2D sheet, Ge atoms protruded upward which can be seen in STM image of the 2D sheet, and Al atoms doped in basal plane of the 2D sheet, respectively.

Fig. 2. Ground state configurations of two Al atoms doped in 2D germanenes supported on Al (111) corresponding to (a) HL, (b) KL, (c) TRP-1T, (d) BHS-2T, (e) SRT19-3T, and (f) SRT7-1T structures. Grey, blue, green, and red spheres denote Al atoms in substrate, Ge atoms in basal plane of the 2D sheet, Ge atoms protruded upward which can be seen in STM image of the 2D sheet, and Al atoms doped in basal plane of the 2D sheet, respectively.

Fig. 2. Plots of relative energy release ΔEeralloy, step wise formation energy E_swf, and the second-order finite difference of the total energy Δ₂versus doping concentration, with solid green down triangle, empty blue square, empty red circle, and solid black square denoting the alloying of BHS-2T, TRP-1T, SRT7-1T, and SRT19-3T germanenes supported on Al (111), respectively.

Fig. 3. Alloy configurations with negative formation energy E_swf corresponding to (a) SRT19-3T, (b) SRT7-1T, (c) TRP-1T, and (d) BHS-2T germananes supported on Al (111). Number ratio of Al and Ge atoms in unit Al:Ge is also provided. Black rhombuses represent periodic units used in calculations, and grey, blue, purple, green, and red spheres denote Al atoms in substrate, Ge atoms in basal plane of the 2D sheet, Al atoms protruded upward in the 2D sheet, protruded Ge atoms in the 2D sheet, and Al atoms doped in the basal plane of the 2D sheet, respectively.

Fig. 3. Alloy configurations with positive formation energy E_swf corresponding to (a) SRT19-3T, (b) SRT7-1T, (c) TRP-1T, and (d) BHS-2T germananes supported on Al (111). The Al:Ge ratio of numbers of Al and Ge atoms in unit is also provided. The black rhombuses are the periodic units used in calculation. Grey, blue, green, and red sphere denote Al atom in substrate, Ge atom in the basal plane of the 2D sheet, Ge atom protruded upward which can be seen in STM image of the 2D sheet, and Al atoms doped in basal plane of the 2D sheet, respectively.

Fig. 4. STM images simulated at +1.3-V bias of pure germanenes TRP-1T, BHS-2T, SRT19-3T, and SRT7-1T and the corresponding stable alloy species Al₃Ge₅ TRP-2T, Al₃Ge₅ BHS-2T, Al₉Ge₉ SRT19-1T, and Al₃Ge₃ SRT7-1T supported on Al (111), with yellow rhombuses representing periodic units used in calculation.

Fig. 4. Alloy configurations with negative formation energy E_swf corresponding to (a) SRT7-(3 × 3)-9H, (b) TRP-1T, and (c) BHS-2T germananes supported on Al₂Ge. Number ratio of Al and Ge atoms in unit Al:Ge is also provided. Black rhombuses represent the periodic units used in the calculations. The grey, blue, purple, green, and red spheres denote Al atoms in Al₂Ge substrate, Ge atoms in basal plane of the 2D sheet, Al atoms protruded upward in the 2D sheet, protruded Ge atoms in the 2D sheet, and Al atoms doped in the basal plane of the 2D sheet, respectively.

Fig. 5. Schematic illustrations of structural models of germanenes grown on Al₂Ge surface alloy along with the configuration of Al₂Ge itself. Only two top layers of substrate are shown. Black rhombuses are periodic units used in calculation. Grey, blue, green, and yellow spheres are Al atom in substrate, Ge atom in basal plane of the 2D sheet, Ge atom protruded upward which can be seen in STM image of the 2D sheet, and Ge atoms doped in Al₂Ge surface alloy, respectively.

Fig. 5. Isosurfaces at 0.015 e/ų for charge accumulation colored in cyan in the left panel and the charge depletion colored in orange in the right one indicating (a) HL, (b) KL, (c) BHS-1H, (d) BHS-2T, (e) TRP-1T, (f) SRT19-3T, and (g) SRT7-1T pure germanane structures supported on Al (111), respectively relatively stable alloy species (h) Al₃Ge₅ BHS-2T, (i) Al₃Ge₅ TRP-2T, (j) Al₃Ge₃ SRT7-1T, (k) SRT7-1T, and (k) Al₉Ge₉ SRT19-1T structures, respectively.

Fig. 6. Calculated PDOSs of Ge atom in Al₉Ge₄₅ SRT7-(3 × 3) sheet. The green line is for protruded Ge atom that can be seen in the simulated STM image, and grey line is for protruded Ge atom that could not be seen in the simulated STM image.

Fig. 6. Plots of relative energy release ΔEeralloy, step wise formation energy E_swf, and second order finite difference of total energy Δ₂versus doping concentration, with empty yellow up triangle, solid green down triangle, empty blue square, and empty red circle denoting alloying of the BHS-1H, BHS-2T, TRP-1T, and SRT7-1T germanenes supported on Al₂Ge, respectively.

Fig. 7. Alloy configurations with positive formation energy E_swf corresponding to (a) TRP-1T, (b) SRT7-(3×3)-9H, (c) BHS-2T, and (d) BHS-1H germananes supported on Al₂Ge. The Al:Ge ratio between the numbers of Al and Ge atoms in the unit is also provided. Black rhombuses represent periodic units used in calculation. Grey, blue, green, yellow, and red sphere denote Al atom in substrate, Ge atom in basal plane of the 2D sheet, Ge atom protruded upward which can be seen in STM image of the 2D sheet, Ge atoms doped in the Al₂Ge surface alloy, and Al atoms doped in basal plane of the 2D sheet, respectively.

Fig. 7. Isosurfaces at 0.015 e/ų for charge accumulation colored in cyan in the left panel and the charge depletion colored in orange in the right one indicating (a) HL, (b) KL, (c) BHS-1H, (d) BHS-2T, (e) TRP-1T, and (f) SRT7-(3 × 3)-9H pure germanane structures supported on Al₂Ge, respectively relatively stable alloy species (g) Al₄Ge₄ BHS-1T, (h) Al₃Ge₅ TRP-2T, and (i) Al₂₇Ge₂₇ SRT7-(3 × 3)-9T structures, respectively.

Fig. 8. STM images simulating +1.3-V bias for Ge₈ TRP-1T and its alloy sheet Al₃Ge₅ TRP-2T, Ge₈ BHS-2T, and Al₄Ge₄ BHS-1T, Ge₈ BHS-1H and Al₂Ge₆ BHS-1H, and Ge₅₄ SRT7-(3 × 3)-9H, and Al₂₇Ge₂₇ SRT7-(3 × 3)-9T supported on Al₂Ge. In image of Al₂₇Ge₂₇ SRT7-(3 × 3)-9T, red rhombus corresponds to the smallest repeated unit of the bright-spot pattern. The yellow rhombuses denote periodic units used in calculation.

Fig. 9. Isosurfaces at 0.015 e/ų for charge accumulation (cyan) in left panel and the charge depletion (orange) in right panel. Panels (a) and (b) are for pure germanane structure HL and stable Al₃Ge₅ BHS-2T supported on Al (111). Panels (c) and (d) are for pure germanene structure BHS-1H and the stable Al₄Ge₄ BHS-1T supported on Al₂Ge surface alloy.

Table 1. Calculated adhesive energy (in units of meV/Ų) between 2D sheet and substrate with Ge_n and Al_mGe_n corresponding to unit of pure and alloyed 2D sheet, respectively.