Free Access
Issue
Eur. Phys. J. Appl. Phys.
Volume 89, Number 1, January 2020
Article Number 10103
Number of page(s) 8
Section Semiconductors and Devices
DOI https://doi.org/10.1051/epjap/2020190325
Published online 27 March 2020

© EDP Sciences, 2020

1 Introduction

With the rapid development of materials science, 2D heterostructures are expected to be used in the next generation electron devices and have attracted extensive studies. A simplified and efficient method to utilize the different kinds of low-dimensional materials in nanoelectronic and optoelectronic devices is the persistent pursuit of people [1,2]. Many forms of 2D structured composites have been studied in detail experimentally and theoretically, such as graphene(g)-BN [3], g-MoS2/WS2 [4], BN/transition-metal dichalcogenides (TMDs) [5], g-phosphorene, and phosphorene-TMDs [6]. These 2D vdW heterostructures often exhibit many unique properties superior to freestanding components in some applications for their excellent physical and chemical properties. Experimentally, a majority of 2D materials can be obtained by exfoliating corresponding bulk structure, such as graphene could be extracted from graphite by ordinary adhesive tapeis, or fabricated by chemical method as the synthesis of TMDs [7,8].

Recently, black phosphorus with few layers that similar to graphene has been successfully prepared by exfoliating of the bulk phosphorus [9,10]. This kind of layer structured black phosphorus attracts enormous interests for it possesses much more advantages than that of metallic graphene in many electronic applications. More recently, as the successful fabrication of BP through epitaxial growth method, it quickly caught people's attention. BP is an allotrope of black phosphorus and has the same stability at room temperature [11,12]. BP displays hexagonal structure with a larger bandgap of ∼2 eV than black phosphorus. Theoretically, molecular dynamics predicted a phase transformation from black phosphorus to BP while it still needs to be confirmed experimentally [13]. Many computation studies concluded that BP should be an ideal substrate to composite with other 2D materials for it has many particular electronic properties and can preserve intrinsic electronic properties in heterogeneous structure.

For a nanomaterial, its certain property relies heavily on the band alignment around interface. Therefore, it would be quite promising for designing new versatile materials if bands of a semiconductor are adjustable. So for now, the band alignments of freestanding conventional materials have been studied extensively [14]. When it comes to the practical application of the heterostructures, Alamri et al. [15] fabricated graphene-WS2 nanodiscs heterostructure through a layer-by-layer transfer-free chemical vapor deposition method. The lateral dimension of nanodiscs is about 200–400 nm with 4–7 layers. They achieved localized surface plasmonic resonance on this WS2-graphene vdW heterostructures, which can greatly improve the light absorption compared with the freestanding continuous WS2 layer. The measuring data indicated that the photoresponsivity of WS2(NDs)-graphene photodetectors is 6.4 A/W which significantly better than WS2-graphene (0.91 A/W) at a 550 nm light intensity of 10 µW/cm2. Besides, this WS2(NDs)-graphene photodetector also sensitive to lower lights. They considered that this heterostructure is promising for scalable high-performance optoelectronics applications. Basu et al. [16] synthesized CuS nanostructures decorated ZnO nanotubes with type-II heterojunction via wet-chemical method at low temperature. This heterojunction exhibited enhanced photocatalytic efficiency of visible light for the degradation of methylene blue. They believed the enhanced photocatalytic activity was originated from the formation of type-II heterojunction formalization, which could lead an efficient photoinduced carriers' separation. Tien et al. [17] synthesized α-In2S3/In2O3 heterostructure via a controlled sulfurization synthesis process. Optical detections exhibited an obviously decreased visible light emission and an enhanced visible light absorption inversely for an efficient photo-induced carriers' separation compared with pristine In2O3. X-ray photoemission spectroscopy characterization provided the band alignment of this α-In2S3/In2O3 heterostructure. It exhibited a well-defined type-II alignment at the interface, implying a certain promising potential in photo-conversion applications. In brief, the band alignments and the corresponding possible applications of related materials have been widely studied; while BP based heterostructures have not yet been adequately explored until now.

In this case, we conduct a detailed band alignment study of BP-GeX (X = C/H/Se) heterostructures and explore the interlayer coupling response when the strain applied. The band alignment of a heterojunction could be significantly affected by the external strain, and thus we expect that BP- GeX heterojunctions may also sensitive to the applied strain. Calculations proved that the band alignment at the heterostructures can be effectively regulated, indicating these materials are promising for novel applications. Next, we will present the details of the computational methodology, the effect of the different BP-GeX geometries and electronic structures of composites are discussed. Finally, band re-alignments of different systems are plotted and some concluding remarks have been drawn based on the present theoretical calculations.

2 Computational methods

Figure 1a–c presents different twisted BP-GeX (X = C/H/Se) heterostructure configurations. In this work, the mismatch between BP and GeX should be strictly controlled at a low level when under 2D periodic structure precondition [18]. Here, the BP and GeX layer rotated between each other. Look down on the BP-GeC heterostructure, a half of P atoms are completely covered by Ge atoms while the remaining half situates the hexagonal center of GeC. For this configuration, the rotation is defined as 0° and the corresponding lattice mismatch is calculated to be 0.37%. For the other 19°, 16° and 28° twisted configurations, the calculated mismatches are 4.63%, 3.11% and 2.13%, respectively. Therefore, the first 0° twisted heterostructure has the minimum mismatch and is applied in the subsequent computations. Similarly, the 160° twisted BP-GeH and 19° twisted BP-GeSe heterostructures show the lowest mismatches of 1.95% and 1.14% in their respective configurations. In the 2D structured heterostructure, strong bonding coupling between two layers is inexistence while weak vdW interactions are expected to play a dominating role [19]. Because the standard PBE functional cannot properly handle this weak interaction, we employ a correction proposed by Grimme with DFT-D3(BJ), in which force field parameters are calculated from the PBE functional [20]. Therefore, the total energy of a specific heterostructure is composed by two parts: Kohn–Sham DFT energy and the corresponding dispersion correction energy [21,22]. A dipole correction should also be considered to eliminate the artificial electrostatic influence between two periodic supercells. Besides, an additional 15 Å vacuum layer is placed between two adjacent layers along c axis to isolate the calculated lattice for a further elimination of the possible interaction effects [23]. In structural optimization process, the cell parameters are fixed while ionic positions are fully relaxed with k-point mesh of 5 × 5 × 1 generated based on Monkhorst and Pack scheme and 10−5 eV energy convergence criteria. The optimized parameters including bond angles and atomic distances for stand-along BP/GeX meet well with previous results, ensuring the credibility of the above approach [2427]. The above structures are further optimized until the forces on each atom are less than 0.01 eV/Å. The vacuum level is set as the reference point for the comparison of edge alignments. A 500 eV cutoff energy for the plane-wave basis set is employed in all calculations, which is an enough precise parameter to reach convergence.

thumbnail Fig. 1

(a)–(c) Top schematic views of BP-GeC, BP-GeH and BP-GeSe with various rotated angles. The legends under figure are the twisted angle and the corresponding mismatch between two layers. The right figures are the relevant side view.

3 Results and discussion

The schematic diagram of binding energies versus distance (d0 ) is plotted in right Figure 2. It clearly reveals the corresponding heterogeneous constructions. The most stable interlayer spacings of three structures are exhibited. The binding energy is defined as: E(binding) = E(BP-GeX) − E(BP) − E(GeX), where E(BP-GeX), E(BP), and E(GeX) signifies the calculated energy of BP-GeX composites, freestanding BP and GeX, respectively [28]. The negative binding energy implies the corresponding heterostructure is stable. The lowest binding energies of BP-GeC, BP-GeH and BP-GeSe are calculated to be −0.80, −0.62 and −1.87 eV, that implies these interfaces are theoretically stable [29]. The associated optimal initial spacings are 3.29, 2.57 and 3.01 Å for three heterostructures, respectively. It should be noted that these configurations are initial structures and a further subtle relaxation will be performed for the following calculation.

It is generally accepted that the performance of a certain semiconductor material could be strongly influenced by the specific electronic structure. This is because a suitable configured band alignment can be favorable to a better use of the corresponding materials [30,31]. In order to study the modified electronic structure of BP-GeX heterostructures, we here firstly analyze the electronic structure of pristine structures. The valence band maximum (VBM) is set to zero as the reference and the Fermi level (Ef ). Figure 3a shows that the projected bandstructure and partial density of states (DOS) of freestanding BP. Generally, it is known that the in-planer and out-of-plane p states are originated from the sp2 hybridization of C atoms in graphene. In this work, the extra valence electrons of phosphorus can lead to the sp3 hybridization, which further arouse the buckled geometric construction of 2D phosphorus. Phosphorus has a most common allotrope of the bulk black phosphorus which has a direct bandgap ∼0.3 eV. Besides, the BP is another stable allotrope of phosphorus with buckled layer and hexagonal lattice crystal [32]. It has been concluded that the above two phosphorus allotropes are equally stable since the binding energies of the two structures are very near to each other [33]. It is reported that the monolayer BP is a semiconductor and has a ∼2.0 eV indirect gap [34]. After fully optimization, the lattice constants of hexagonal BP are a = b = 3.28 Å, which accords well with previous results [35].

Figure 3a shows that VBM and conduction band minimum (CBM) of the BP is predominantly composed of P-pz states, including some hybridization with P-py states in CBM. A further calculation implies that the bandgap of freestanding BP is ∼1.95 eV. This theoretic value is very close to the recent reported experimental value of 1.93 eV and further guarantees the reliability of subsequent calculations [24]. Figure 3b demonstrates the electronic structure of GeC, it has some differences in the overall characteristic. Its CBM is primarily comes from Ge-s state, while VBM is from C-2p states. The calculated bandgap of pristine GeC is 2.2 eV which is wider than that of the BP. This is a relatively large bandgap that limits its wide application. Next, we will further survey what happens if the above two structures compound together. Figure 3c shows the electronic structure of GeH. Its CBM is mainly contributed by Ge-s states, while VBM is originated from Ge-p states with a direct bandgap of about 0.96 eV. The H atoms states are mainly localized in a lower energy around −3 eV. As for freestanding orthorhombic GeSe, the CBM and VBM are mainly contributed by Ge-p and Se-p states, respectively. The calculated bandgap of pristine GeSe is 1.36 eV, which is wider than that of the GeH.

Figure 4a displays the decomposited bandstructure of the BP-GeC heterostructure. The composite's electronic structure exhibits quite different properties versus freestanding structures. The bandgap of the BP-GeC composite decreases to 1.82 eV and is narrower than those of pristine BP/GeC. The well-arranged stagger band edges formalization is responsible for the narrowed bandgap. Further observation on the band structure reveals that the VBM is located in K point while the CBM is situated in G point. BP-GeC heterostructure has indirect bandgaps with CBM mainly originated from BP and VBM from GeC. As for BP-GeH heterostructure shown in Figure 4b, the VBM is mainly originated from GeH while CBM is mainly from BP. The corresponding bandgap decreases to 0.75 eV that smaller than pristine BP and GeH. This situation is also applied to the last BP-GeSe heterostructure shown in Figure 4c that the CBM is mainly contributed by GeSe. The above three band alignments are all well-defined type-II heterostructures. As shown in Figure 4d, the CBM/VBM of BP are higher than that of GeX. Under light irradiation, both BP and GeX can absorb photons of energy larger than bandgap. This process will further excite electrons to the CB while leave holes filled in VB. As for heterostructure, the photoinduced electrons of BP will transfer to the CB of GeX while the holes converge on the VB of BP for the straddled band alignment of the BP-GeX composite. Therefore, the carriers' recombination could be effectively restrained. Besides, the built-in electric field caused by the redistribution of charge density can further facilitate the separation of photo-induced carriers. This unique carriers' separation mechanism would be of great benefit for the photocatalysis or photovoltaic cell utilization.

In this work, the Ef of BP, GeC, GeH and GeSe are calculated to be −6.22, −4.97, −4.57 and −4.69 eV w.r.t. the vacuum layer, respectively. The formation of heterostructure with different components and different Ef will naturally induce a redistribution of charges. In this case, BP will be negatively charged while GeX be positively charged after contact near the interface. We calculated the charge density difference of three nanocomposites. As demonstrated in Figure 5a-1–c-1, the charge density difference figures were obtained by subtracting the individual BP/GeX charges from BP-GeX composites. The green signifies charge depletion regions while red are accumulation regions for the computed structures. Clearly, the transfer occurs mainly between the top atoms of BP and GeX, which may result in an effective separation of the photoinduced carriers under this polarized field. Figure 5 further indicates that the charge transfer directions are always from GeC to BP, implying the built-in electric fields always point from GeX to BP. Figure 5a-2 to c-2 presents the plane-averaged charge density difference. The plane-averaged potential V̅(z) across the interface is given by in which S denotes the unit cell area parallel to xy plane. As can be seen in figures, charge transfer mainly focuses on facing area between BP and GeX. As mentioned above, the interaction of two individual parts should be rather weak for these 2D structures have no dangling bonds, and thus the charge transfer induced features would play an important role. Figure 5a-2 to c-2 plots the charge density difference in black and the corresponding integral curve in blue around the interface. Clearly, the charge transfer directions are all from GeX to BP.

Generally, the main purpose of doping is to narrow the corresponding active materials' bandgap [36]. However, the foreign atoms often introduce impurity levels that serve as the recombination center and markedly reduce the photoinduced carriers [37]. Hence, the heterostructure seems to be a better choice. After a semiconductor irritated by the light, the excited electrons will transfer to the CB while left holes in the VB. A portion of carriers then rapidly migrate to the external space and react with the surrounding ions. While another part of the carriers will spontaneously recombine and no longer participate in the following reactions. The latter process will dominate in the pristine BP/GeX as analyzed above and should be restrained. The calculated results of BP-GeX heterostructures with well-defined type-II staggered band alignments show higher BP states than that of GeX. Therefore, the three kinds of heterostructures can lead to an enhancement of solar energy utilization under certain circumstances.

As reported that electrical coupling between graphene and TMDs can make a rapid electron transfer from electrode to active TMDs. This process can further form an electron-rich environment and facilitate the overall chemical reaction. [38,39] In this case, a suitable bandgap value and the appropriate charge transfer direction also holds great promise for these applications. The bandgap of BP/GeX is still too large, a tentative exploration to solve this problem is through construction of heterostructure and bandgap engineering by applying strain. The panorama of the CBM/VBM for three heterostructures with various strains along a-axis, b-axis and biax are shown in Figure 6, providing important guidance for tuning the bandgap and CBM/VBM re-alignment of heterostructures to maximize the efficiency for solar energy. In the strain related calculations, the lattice constants along strain-imposed direction are fixed while relax the others. Through this method, it enables us to better study the strain induced effects. Figure 6 clearly demonstrates that three heterostructures all exhibit the adjustable bandgap with the variation of external strain along difference axis. For BP-GeC when strain applied along a-axis shown in Figure 6a-1, bandgap decreases notably with increase of the applied external strain along a-axis from 0% to 12% or from −6% to 0%. When the external strain along a-axis varies from 12% to 15%, there occurs an interesting phenomenon that the band alignment reversed. The VBM of BP acts as the VBM of heterostructure while CBM of GeC acts as the CBM of heterostructure. As for BP-GeC strain along b-axis shown in Figure 6a-2, the bandgap of heterostructure decreases monotonously when the strain imposed. When biax strain is applied, the type-II scope clearly narrows down. It should be noted that for the strain imposed along a-axis and b-axis structures, BP-GeC heterostructure reaches its maximum bandgap of 1.32 and 1.38 eV, respectively, while this value is 1.52 eV for biax strain-imposed structure. In brief, Figure 6a-4 shows that the type-II band alignment scope of a-axis, b-axis and biax strain-imposed structure are 20.07%, 19.39% and 11.45%, respectively. The adjustable range for uniaxial strain-imposed condition is significantly greater than the biax. As for BP-GeH shown in Figure 6b, the bandgap goes through a monotonic change when strain applied till transition from type-II to type-I. Figure 6a-4 shows that the type-II band alignment scope of a-axis, b-axis and biax strain-imposed structure are 10.08%, 10.75% and 8.03%, respectively. The adjustable range for uniaxial strain-imposed condition is also greater than the biax. For the final BP-GeSe heterostructure, the type-II band alignment scope can exist in a wide range, 22.4%, 20.4% and 14.59% for a-axis, b-axis and biax strain-imposed structures respectively. In conclusion, strain does have a marked impact on the electronic properties of BP-GeX heterostructure [40]. Up to now, we have presented a detailed discussion on how strain can influence the band edges and gaps. The re-alignment of band edges for BP-GeX heterostructures all reveal tunable electronic structure, and the type-II scope can exist in a relatively wide range and exhibit adjustability of its bandgap when the strain is imposed.

Compared with freestanding structures, three heterostructures all exhibit much more effective band alignment variability. When it comes to solar cells, the heterojunction-based material also has great potential for it is long been considered as a low-cost photovoltaic technology. In this case, we further explore the correlated characteristic and find something interesting by chance. Generally, the quality of a heterojunction based solar cell can be evaluated by calculating power conversion efficiency (PCE) [41]:

the factor of 0.65 is the band-fill factor, P(ℏϖ) represents photon energy (ℏω) versus the solar energy flux (W/m−2/eV−1) under AM1.5 condition, Eg and ΔEc denote the bandgap of the donor and the conduction band offset (CBO), respectively. The (Eg − ΔEc − 0.3) is an estimated value of the maximum open circuit voltage (Voc in eV). From the above we can know that the PCE heavily depends on the band alignment between donor and acceptor of a heterojunction. The calculated results shown in Figure 7, it is found that the PCE of the BP-GeH can be as high as 11.8%. This value is very close to the reported heterostructures when used in solar cells, such as PCBM/CBN (10–20%) [41], and g-SiC/GaN (12–20%) [42]. Although the proposed solar-cell application of BP-GeH is two-layer thin, thicker multilayers by stacking could be a feasible way to increase the interface area. It also reveals that the PCE of BP-GeSe and BP-GeC all significantly lower than that of BP-GeH. However, this situation will be improved when the external strain applied. Based on the interface band alignment shown in Figure 6, we here present the change direction of three heterostructures and marked in green arrows. As shown in Figure 6(a)-1, when the tensile strain is imposed between 0% and 12% along a axis, the band gap of donor and the corresponding CBO all clearly decrease. The direct effect of this trend is reflected in Figure 7. The green arrow of BP-GeC denotes the moving direction of PCE when two factors are all decrease. Obviously, the imposed tensile strain between 0% and 12% can significantly promote the PCE of BP-GeC along an axis. This situation also exists in the imposed tensile strain along b axis and biaxial. The only difference is the scope of the imposed strain. When it comes to BP-GeH, the green arrow corresponds to the tensile strain scope between 0% and 3%. As for the final BP-GeSe, even though it PCE could be improved when the tensile strain applied between 0% and 6%, it initial PCE is too low to reach an ideal value after the strain imposed. In brief, the above calculated results prove that the strain is an effective method to modify the PCE of heterostructures. In the scope of solar cell application, BP-GeH is an ideal choice for it is an intrinsic type-II heterostructure with suitable PCE value that can be further improved by the applied external strain.

thumbnail Fig. 2

(a) Binding energy Eb as a function of the separation d0 between BP and GeX.

thumbnail Fig. 3

(a)–(d) The projected bandstructures and partial density of states of pristine BP, GeC, GeH and GeSe, respectively.

thumbnail Fig. 4

(a)–(c) The projected bandstructures BP-GeC, BP-GeH and BP-GeSe heterostructures, respectively. (d) The ideal schematic illustration of carriers' separation for BP-GeX vdW heterostructure.

thumbnail Fig. 5

(a)–(c)-1 Charge difference density for three BP-GeX heterostructures. The planes passing through (110) planes perpendicular to the atomic layers. Red and green regions correspond to ρ > 0 and ρ < 0, respectively. (a)–(c)-2 Black curves stand for plane averaged charge difference Δρ. The blue denotes the amount of transferred charge ΔQ(z) along the normal direction.

thumbnail Fig. 6

(a)–(c)-1 Band edge evolutions for BP-GeX as a function of imposed strain along a-axis. (a)–(c)-2 Band edge evolutions for BP-GeX as a function of imposed strain along a-axis. (a)–(c)-3 Band edge evolutions for BP-GeX as a function of imposed strain along a-axis. (a)–(c)-4 The strain scope of type-II band alignment and the corresponding bandgap of BP-GeX heterostructures.

thumbnail Fig. 7

The calculated PCE contour as a function of the bandgap of donor and CBO ΔEc. The level curves are plotted up to 20%. The red dots represent the PCE of three BP-GeX heterostructures. Green arrows represent the PCE variation trends of the three heterostructures with type-II alignment after the external strain applied.

4 Conclusion

In summary, this work studied the construction of the different BP-GeX (X = C/H/Se) heterostructures and calculated the corresponding electronic properties with various applied external strain via first-principles computation. For three freestanding heterostructures, all present a well-defined type-II alignment. The photoinduced electrons will transfer to CB from BP to GeX while holes to VB from GeX to BP. The charge redistribution around interface further facilitates the carriers' separation. This separation induced built-in electric field can effectively restrain the recombination of electron–hole pairs, which should be beneficial to an efficient use of light energy. After the strain applied, the electronic properties can be flexibly manipulated by varying the imposed strain. It is found that the adjustable range for uniaxial strain-imposed condition is greater than the biax for three heterostructures. The predicted PCE for monolayer BP-GeH bilayer can be as high as ∼12% and is expected to be a promising candidate in optoelectronic devices. This work implies the composite processing and strain involvement could provide a feasible approach and a valuable reference to obtain a better light use of heterostructure in the future.

Acknowledgments

The authors acknowledge financial support by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201800501), the Program for Leading Talents in Science and Technology Innovation of Chongqing City (No. cstc2014kjcxljrc0023), Chongqing Normal University Fund Project (Grant No. 17XLB012), the National Natural Science Foundation of China (Grant No. 11904041, 11947105) and the Science and Technology Research Project of Chongqing Education Committee (Grant No. KJQN201900542).

Author contribution statement

H.L. Li performed the calculations, Y.T. Cui conceived and designed the computations, H.J. Luo analyzed the data, W.J. Li wrote the paper. All authors have reviewed the manuscript.

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Cite this article as: Honglin Li, Yuting Cui, Haijun Luo, Wanjun Li, The strain induced type-II band re-alignment of blue phosphorus-GeX (X = C/H/Se) heterostructures, Eur. Phys. J. Appl. Phys. 89, 10103 (2020)

All Figures

thumbnail Fig. 1

(a)–(c) Top schematic views of BP-GeC, BP-GeH and BP-GeSe with various rotated angles. The legends under figure are the twisted angle and the corresponding mismatch between two layers. The right figures are the relevant side view.

In the text
thumbnail Fig. 2

(a) Binding energy Eb as a function of the separation d0 between BP and GeX.

In the text
thumbnail Fig. 3

(a)–(d) The projected bandstructures and partial density of states of pristine BP, GeC, GeH and GeSe, respectively.

In the text
thumbnail Fig. 4

(a)–(c) The projected bandstructures BP-GeC, BP-GeH and BP-GeSe heterostructures, respectively. (d) The ideal schematic illustration of carriers' separation for BP-GeX vdW heterostructure.

In the text
thumbnail Fig. 5

(a)–(c)-1 Charge difference density for three BP-GeX heterostructures. The planes passing through (110) planes perpendicular to the atomic layers. Red and green regions correspond to ρ > 0 and ρ < 0, respectively. (a)–(c)-2 Black curves stand for plane averaged charge difference Δρ. The blue denotes the amount of transferred charge ΔQ(z) along the normal direction.

In the text
thumbnail Fig. 6

(a)–(c)-1 Band edge evolutions for BP-GeX as a function of imposed strain along a-axis. (a)–(c)-2 Band edge evolutions for BP-GeX as a function of imposed strain along a-axis. (a)–(c)-3 Band edge evolutions for BP-GeX as a function of imposed strain along a-axis. (a)–(c)-4 The strain scope of type-II band alignment and the corresponding bandgap of BP-GeX heterostructures.

In the text
thumbnail Fig. 7

The calculated PCE contour as a function of the bandgap of donor and CBO ΔEc. The level curves are plotted up to 20%. The red dots represent the PCE of three BP-GeX heterostructures. Green arrows represent the PCE variation trends of the three heterostructures with type-II alignment after the external strain applied.

In the text

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