Self-doped p–n junctions in two-dimensional In2X3 van der Waals materials

Rui Penga, Yandong Ma*a, Shuai Zhanga, Baibiao Huanga, Liangzhi Koub and Ying Dai*a
aSchool of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Street 27, Jinan 250100, China. E-mail:;
bSchool of Chemistry, Physics and Mechanical Engineering Faculty, Queensland University of Technology, Garden Point Campus, QLD 4001, Brisbane, Australia

Received 17th July 2019 , Accepted 1st October 2019

First published on 1st October 2019

With the advent of two-dimensional materials, it is now possible to realize p–n junctions at the ultimate thickness limit. However, the performance of p–n junctions significantly degrades as their thicknesses approach the nanoscale and the conventional fabrication processes, such as implantation and doping, become invalid. Here, using first-principles calculations, we report a novel strategy to realize self-doped p–n junctions in two-dimensional materials. By stacking triple-layer In2X3 (X = S, Se), an atomically thin p–n junction forms naturally without any additional modulation involved, which is attributed to the asymmetric structure-induced self-doping. In addition, such self-doped p–n junctions are also obtained when sandwiching single-layer and double-layer In2S3 in-between graphene layers. More interestingly, the outmost layers in all these systems become metallic due to the self-doping, achieving natural low-resistance contact. This work illustrates a straightforward method for developing more effective electronic and optoelectronic nanodevices.

New concepts

Challenges faced by atomically thin p–n junctions largely impede their development. On one hand, conventional processes to realize p- and n-type regions in three-dimensional crystals, such as implantation and doping, become invalid for two-dimensional crystals. On the other hand, the quality of the electrical contacts between two-dimensional semiconductors and metal electrodes is often masked by the high Schottky barrier at the hybrid interface. There is thus a pressing need to search for effective strategies to obtain p–n junctions and realize their low-resistive contacts with metal electrodes. We present here a novel strategy to realize p–n junctions in two-dimensional materials via self-doping. By stacking triple-layer In2X3 (X = S, Se), or sandwiching single-layer and double-layer In2S3 in-between graphene layers, atomically thin p–n junctions form naturally via self-doping without any additional modulation involved, which is attributed to the asymmetric structure-induced dipole field. More interestingly, the outmost layers in all these systems become metallic due to the self-doping, achieving natural low-resistance contact. These extraordinary features would largely simplify the device fabrication process and optimize the performances of two-dimensional electronic devices.

1. Introduction

A p–n junction is the fundamental functional element of modern semiconductor devices, which mainly include diodes, light-emitting diodes, photodetectors, and bipolar transistors.1–4 The recent emergence of two-dimensional (2D) semiconductors offers a promising opportunity for their miniaturization. To this end, extensive efforts have been devoted to fabricating p–n junctions based on atomically thin building blocks. To realize p- and n-type regions in 2D crystals, the most common approaches are atomic doping,5–8 surface modification9–11 and heterojunctions.12–22 However, all these approaches have their own side effects, therefore limiting their applications. For example, atomic doping is challenging for 2D crystals due to the spatial confinement and can turn the channel metallic easily as it cannot be strictly limited to the local regions, thus degrading the performance of p–n junctions.5–8 Surface modification can achieve significant local doping by surface charge transfer, but typically suffers from poor chemical and thermal stability.9–11 Heterojunctions constructed using transition-metal dichalcogenides and black phosphorus12–22 have recently been developed by stacking 2D layers with dissimilar charge-carrier types; however, the inevitable contaminants and bubbles induced during the dry transfer process unambiguously prohibit their high-performance applications. This shows the great necessity and urgency to find or design new schemes for realizing p–n junctions in 2D crystals.

Another key challenge in this field is the quality of the electrical contacts. This problem does not occur in modern silicon-based microelectronics, where the low-resistive contact is realized by employing ion implantation.23 Applying this scheme in the 2D limit is not straightforward because ion bombardment not only implants but also knocks out atoms from the channel.24 Often, the electrodes in 2D semiconductor devices are bulk metals, but the direct contact with bulk metals typically leads to strong hybridization at the interfaces, resulting in the nasty Fermi level pinning effect.25–28 One solution that has been deployed is to insert an insulating layer, such as a BN layer, at the interfaces,29–31 which suppresses the formation of mid-gap states and the Fermi level pinning effect, but the vertical tunnel barriers are also considerably widened, thus degrading their transport properties. Although some special 2D materials such as multiphase TMDs32–34 can be alternatively utilized to reduce the contact resistance, they are too limited and lack generality. Practical strategies to solve the contact problems remain to be discovered and are highly needed.

In this work, we propose intriguing atomically thin p–n junctions constructed by triple-layer (TL) In2X3 (X = S, Se), on the basis of density functional theory calculations. Remarkably, distinct from the previously reported p–n junctions in the 2D limit, the p- and n-type regions in TL In2X3 form naturally by self-doping due to their asymmetric structures, which does not need any additional tuning. Besides, upon sandwiching single-layer (SL) and double-layer (DL) In2S3 in-between graphene layers, such self-doped p–n junctions can be also obtained. Meanwhile, the level of p- and n-doping can even be modulated by tuning the layer thickness of the sandwiched In2S3 in-between the two-graphene layers. More excitingly, the outmost layers in all these stacked systems become metallic resulting from self-doping, acting as electrodes and thus achieving natural low-resistance contact. Our work provides not only extraordinary candidates but also a compelling scheme for designing high-performance atomically thin p–n junctions.

2. Methods

All calculations are performed using the Vienna ab initio simulation package (VASP)35 based on density functional theory.36 The projected augmented wave (PAW)37 method is used to describe the electron–ion interactions. The generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof (PBE) functional38 is applied to treat the exchange–correlation interaction. The cut-off energy is set to 450 eV. The convergence criteria for energy and force are set to 1 × 10−5 eV and 0.01 eV Å−1, respectively. The van der Waals (vdW) interaction between layers is described by the DFT-D2 method.39 We also optimize the DL and TL structures based on optPBE-vdW40,41 and strongly constrained appropriately normed (SCAN) meta-GGA,42 and the results are summarized in Table S1 (ESI). We can see that the obtained structures are similar to that based on the DFT-D2 method, suggesting the robustness of our results. All structures are optimized based on the PBE functional, while all electronic structures are calculated using the HSE0643 functional unless otherwise specified. The mixing parameter for the Hartree–Fock potential is set to 0.25. The valence configurations of In, S, and Se atoms taken into account in the calculations are 4d105s25p1, 3s23p4, and 4s23d104p4, respectively. For 2D In2X3, a Monkhorst–Pack (MP)44 grid of 7 × 7 × 1 is used to sample the Brillouin zone. The vacuum space along the z direction is set to 15 Å to separate periodic images. Dipole correction is adopted to meet the convergent criterion.45 Ab initio molecular dynamics (AIMD) simulations are performed at 300 K for 5 ps with a time step of 1 fs.

3. Results and discussion

Bulk In2X3 (X = S, Se) has been known to us for a long time.46–50 It exhibits a layered crystal structure with the space group of R3m, in which the layers are stacked by van der Waals interactions. Recently, 2D ultrathin In2X3 has been obtained in the experiment by mechanical exfoliation51–53 and has attracted intensive interest owing to its particular structure and properties.52–61 Fig. 1(a) depicts the crystal structure of SL In2X3, which consists of five triangular atomic planes stacked in the sequence of X–In–X–In–X. The optimized lattice constants for SL In2S3 and In2Se3 are 3.94 and 4.11 Å. To estimate its chemical stability under ambient conditions, the AIMD simulations are carried out at 300 K for SL In2X3 and O2. As shown in Fig. S1 (ESI), after 5 ps, SL In2X3 remains intact and the oxygen molecules move away from the SL without dissociating into oxygen atoms, and the free energy fluctuates slightly during annealing, showing antioxidant properties at room temperature. This unique stability is attributed to the exposed X layers, similar to the cases of transition metal dichalcogenides.
image file: c9mh01109a-f1.tif
Fig. 1 (a) Top and side views of the crystal structure of SL In2X3. The orientation of the intrinsic dipole is represented by a green arrow. Band structures of (b) SL In2S3 and (c) SL In2Se3. The Fermi level is set to 0 eV.

As shown in Fig. 1(a), the asymmetric positions of X atoms in the middle layer lead to different coordination environments of In atoms and thus break the centrosymmetry of the 2D plane, giving rise to an intrinsic dipole pointing from the top to bottom surfaces along the z direction. The dipole moment per unit cell for SL In2S3 (In2Se3) is 0.53 (0.46) Debye. The electrostatic potential difference in SL In2S3 (In2Se3) is found to be 1.54 (1.20) eV. SL In2X3 are indirect gap semiconductors with CBM locating at the Γ point and VBM locating at the A point along ΓM line; see Fig. 1(b) and (c). The indirect band gap based on the HSE06 level for SL In2S3 (In2Se3) is 1.89 (1.42) eV. These results are listed in Table 1, and agree well with the previous studies.60 The band structures of SL In2X3 with and without spin–orbital coupling (SOC) are shown in Fig. S2 (ESI), from which we can see that SOC has little effect on the band structures. Moreover, 2D In2X3 shows a high carrier mobility as large as ∼2.6 × 103 cm2 V−1 s−1.60

Table 1 The lattice constants (a), dipole moments (μ), differences of electrostatic potential (ΔV), and indirect band gaps (Eg) of 2D In2X3
  a (Å) μ (Debye) ΔV (eV) Eg (eV)
SL In2S3 3.94 0.53 1.54 1.89
SL In2Se3 4.11 0.46 1.20 1.42
DL In2S3 3.85 0.89 2.61 0.25
DL In2Se3 4.00 0.74 1.97 0.24
TL In2S3 3.85 0.91 2.98 0
TL In2Se3 4.00 0.77 2.29 0
Bulk In2S3 3.85 0 0 1.96
Bulk In2Se3 4.00 0 0 1.21

After estimating the electronic properties of SL systems, we then investigate their device potentials when forming few-layer (FL) systems. We first study DL In2X3. DL In2X3 stacked in AB stacking mode is constructed according to bulk In2X3,46–50 which is shown in Fig. S3(a) (ESI). When forming DL systems, the dipole moment in In2S3 (In2Se3) increases to 0.89 (0.74) Debye, almost two times that in SL In2S3 (In2Se3). As listed in Table 1, the electrostatic potential difference also increases significantly for DL In2X3. The fat band structures, density of states (DOS), and partial charge density of DL In2X3 are shown in Fig. 2(a) and Fig. S4(a) (ESI). Obviously, DL In2S3 (In2Se3) is still an indirect gap semiconductor, however, the band gap significantly decreases to 0.25 (0.24) eV. The band dispersions for each individual layer in DL In2X3 remain almost unchanged with respect to SL In2X3, suggesting the weak hybridization between the layers in DL In2X3. Due to the intrinsic dipole, the contributions of two individual layers in DL In2X3 are separated largely, namely, 1.69 and 1.25 eV respectively for In2S3 and In2Se3. Such separations result in the CBM of DL In2X3 coming from the top layer, while the VBM is contributed by the bottom layer, which can also be clearly observed in DOS and partial charge density. Therefore, the typical type-II band edge alignment forms in DL In2X3. This also well explains why the band gap of DL In2X3 is so small compared with that of SL In2X3.

image file: c9mh01109a-f2.tif
Fig. 2 Fat band structures, DOS, and partial charge density of CBM and VBM for (a) DL In2S3 and (b) TL In2S3. The Fermi level is set to 0 eV. Red (blue) regions in the right panels represent the band decomposed charge density for the CBM (VBM). The isosurface value is set to 0.04 e Å−3.

Compared with DL In2X3, more interesting behaviors are observed in TL In2X3. According to bulk In2X3,46–50 TL In2X3 with ABC stacking mode is constructed; see Fig. S3(b) (ESI). Table 1 summarizes the calculated dipole moments and electrostatic potential differences for TL In2X3, which are slightly larger than those of DL In2X3. The fat band structures, DOS and partial charge density of TL In2X3 are plotted in Fig. 2(b) and Fig. S4(b) (ESI). It can be seen that, like the DL case, the band dispersions for each individual layer in TL In2X3 are roughly similar to those of SL In2X3, which also characterizes the weak hybridization among the layers in TL In2X3. The projected band structures on the top and middle layers in TL In2X3 form a type-II band edge alignment, and so do those on the middle and bottom layers. In other words, intriguingly, a three-step-stair-like band edge alignment is obtained in TL In2X3; see Fig. 3(a). This three-step-stair-like feature originates from the effect of intrinsic dipole field pointing from top to bottom. As a result, the CBM of TL In2X3 is from the top layer, the VBM is contributed by the bottom layer, but the middle layer has no contributions to the band edges. More importantly, as shown in Fig. 2(b) and Fig. S4(b) (ESI), the VBM from the bottom layer and the CBM from the top layer both slightly cross the Fermi level, resulting in spatial charge transfer between these two outmost layers. Accordingly, the bottom and top layers in TL In2X3 are p- and n-doped, respectively, while the middle layer remains semiconducting. That is to say, TL In2X3 forms a long-desired natural p–n junction: the bottom and top layers are the p- and n-type regions, and the middle layer is the semiconducting channel. We wish to emphasize that different from all the previously reported atomically thin p–n junctions,5–22 the p–n junction identified here arises from the compelling self-doping. Also, it holds high experimental feasibility because TL In2X3 can readily be exfoliated from their bulks.46–50 Such a self-doped p–n junction doesn’t require complicated device structures, nor does it need any further external tuning. Meanwhile, the metallic outmost layers in TL In2X3 could act as electrodes, thereby leading to natural electrical contact with low-resistance. These extraordinary features would largely simplify the device fabrication process and optimize the performances of 2D electronic devices based on TL In2X3.

image file: c9mh01109a-f3.tif
Fig. 3 (a) Schematic diagram of band alignments of the individual layers in TL In2X3. (b) The evaluations of band gap and electrostatic potential difference of In2X3 as a function of the number of layers.

We then investigate the corresponding properties of FL In2X3. The electrostatic potential difference and band gap of FL In2X3 as a function of the number of layers (N = 1–5) are summarized in Fig. 3(b). As we can see, the band gap of FL In2X3 decreases dramatically from SL to DL, and vanishes when N ≥ 3. Therefore, the electron transfer between the two outmost layers occurs when N ≥ 3. Upon transferring electrons from the bottom to top layer, as shown in Fig. 3(a), a compensated electric field is introduced, with an opposite orientation to the intrinsic one. This compensated electric field would neutralize the intrinsic electric field and restrict the increase of electrostatic potential difference as well as the dipole moment. Accordingly, the electrostatic potential difference shown in Fig. 3(b) exhibits a nonlinear increase with the increase of N, and becomes saturated when N > 3. With these results in hand, it is also easy to understand why the dipole moment and electrostatic potential difference for TL In2X3 are only slightly larger than those of DL In2X3. However, the properties of bulk In2X3 are totally different from FL systems. The lattice constants of bulk In2X3 are listed in Table 1, and the bond lengths and angles are listed in Table S2 (ESI). They are comparable to that of DL and TL systems but smaller than those of SL systems due to the interlayer vdW interaction. The crystal structures and band structures of bulk In2X3 are shown in Fig. S5 (ESI). We can see that their band gaps are 1.96 and 1.21 eV, respectively. Due to their periodicity, there are no dipole moments in bulk In2X3. Therefore, the separation of bands from different layers is absent. As a result, the bulk systems exhibit band gaps comparable to that of SL systems due to the weak vdW interlayer interaction.

To get more insight into the role of the intrinsic dipole in forming the natural p–n junctions, we construct a virtual DL configuration stacked in A′B mode (A′B-DL In2X3) and a virtual TL configuration stacked in A′BC mode (A′BC-TL In2X3) in comparison to the configurations in AB and ABC modes, respectively. Their crystal structures are shown in Fig. S3(c and d) (ESI). In A′B-DL In2X3, the dipole directions of the bottom and top layers are opposite, while in A′BC-TL In2X3, the dipole direction of the bottom layer is opposite to the other two layers. Obviously, for A′B-DL In2X3, the intrinsic electric fields for the bottom and top layers are neutralized by each other, which can be confirmed by charge density differences and band structures. As shown in Fig. S6(b) (ESI), the charge density differences of A′B-DL In2X3 with respect to the individual layers are symmetric, showing no charge transfer tendency at the interface. This is in sharp contrast with that of DL In2X3 in AB mode in Fig. S6(a) (ESI). The band structures of A′B-DL In2X3 are plotted in Fig. S7(a) (ESI). It can be seen that A′B-DL In2X3 has a larger band gap compared with DL In2X3 in AB mode. The reason is, for A′B-DL In2X3, the contributions of the two individual layers to the bands are identical, and their separation is zero. Therefore, with offsetting the dipoles, the properties of A′B-DL In2X3 are totally different from those of DL In2X3 in AB mode. And it is not hard to imagine that similar results would also be obtained in A′BC-TL In2X3. As shown in Fig. S6(c and d) (ESI), the charge transfer does not occur in A′BC-TL In2X3, which is different from the abundant charge transfer for TL In2X3 in ABC mode. Every individual layer in A′BC-TL In2X3 remains semiconducting, and the desired self-doping as well as the p–n junction are deformed; see Fig. S7(b) (ESI). We thus conclude that the intrinsic dipole in 2D In2X3 plays an important role in forming the self-doped p–n junctions.

Considering the important role of the dipole in realizing self-doped p–n junctions in homostructures, one may wonder if it is possible to realize the self-doped p–n junctions by stacking SL In2X3 with other materials. Here, we select graphene as the stacking material because its semi-metallic character can facilitate charge transfer and avoid the dipole cancellation which is usually caused by bulk metals. Heterostructures of In2X3/G and G/In2X3, which are constructed by stacking graphene respectively on the top and bottom surfaces of SL In2X3, are first studied; see Note 1 and Fig. S8 (ESI). The work function of graphene, SL In2S3 and SL In2Se3 is calculated to be 4.57, 6.55 and 6.05 eV, respectively. To simulate In2X3/G and G/In2X3, the strain of 3.8% and 3.9% is induced on graphene (see Note 1 in the ESI), respectively, whose work function is slightly changed with respect to the free case. Therefore, the electrons would transfer from graphene to SL In2X3 when forming heterostructures between them. For both In2X3/G and G/In2X3, the band structure is a rough sum of the bands of each individual layer, which is attributed to their weak van der Waals interlayer interactions; see Fig. S9 and S10 (ESI). Due to the intrinsic dipole, the work functions at two surfaces of SL In2X3 are different, and hence In2X3/G and G/In2X3 exhibit different band alignments for the bands contributed by SL In2X3 and graphene. As shown in Fig. S9 and S10 (ESI), for In2S3/G (In2Se3/G), the Dirac point of graphene shifts above the Fermi level by 62.8 (51.5) meV, and the CBM of In2S3 (In2Se3) shifts below the Fermi level by 285 (607) meV, implying electron transfer from graphene to SL In2X3. Therefore, the band structure of In2X3/G exhibits an Ohmic contact between In2S3 (In2Se3) and graphene. While for G/In2S3 (G/In2Se3), the band structure harbors an n-type Schottky contact between SL In2S3 (In2Se3) and graphene, with a barrier of 0.87 (0.11) eV. This agrees well with the results based on charge density differences where electrons tend to deplete (accumulate) around graphene (SL In2X3). The different contact behaviors between In2X3/G and G/In2X3 are sought in the competition between the intrinsic dipole of SL In2X3 and interface dipole resulting from interfacing graphene and the outmost X layer. In In2X3/G (G/In2X3), the directions of these two dipoles are identical (opposite), thus facilitating (suppressing) the charge transfer.

Then we sandwich SL In2S3 in-between two graphene layers, and the crystal structures are shown in Fig. S8 (ESI). Fig. 4(a) depicts the band structures and charge density differences. Interestingly, for G/In2S3/G, the Dirac point from the top (bottom) graphene layer shifts above (below) the Fermi level, forming a p(n)-doped graphene. These two Dirac points are separated by 220 meV. And for SL In2S3, it is still semiconducting. From the charge density difference, it can also clearly be seen that holes are distributed around the top graphene layer, while electrons are distributed around the bottom graphene layer. Accordingly, we design an abrupt p–n junction based on G/In2S3/G, which is plotted in Fig. 4(b). In this p–n junction, the two graphene layers are p- and n-type regions, and SL In2S3 is the semiconducting channel. Like the case of TL In2X3, the two graphene layers in G/In2S3/G also act as electrodes, and it can give rise to low-resistance electrical contacts. As we mentioned above, the dipole is critical for achieving such p–n junctions and as DL In2S3 exhibits larger dipoles, it is expected that p- and n-doping would become heavier for sandwiching DL In2S3 in-between the two graphene layers (G/DL-In2S3/G). As shown Fig. S12 (ESI), the separation between the two Dirac points in G/DL-In2S3/G indeed is enlarged to 522 meV. Therefore, we could modulate the level of p- and n-doping by tuning the layer thickness of the sandwiched In2S3. Different from G/In2S3/G, the device performance of G/In2Se3/G leaves much to be desired as SL In2Se3 in G/In2Se3/G becomes metallic. For more detail about G/In2Se3/G, please see Note 2 and Fig. S13 (ESI).

image file: c9mh01109a-f4.tif
Fig. 4 (a) Fat band structure and charge density difference of G/In2S3/G. The middle panel is the enlarged band structure of G/In2S3/G. The Fermi level is set to 0 eV. The Red and blue regions in the right panel indicate the accumulation and depletion of electrons, respectively. The isosurface value is set to 0.001 e Å−3. (b) Schematic diagram of the proposed p–n junction based on G/In2S3/G.

We wish to stress that such scheme for designing self-doping p–n junctions in In2X3 is also applicable for other 2D materials with an intrinsic dipole in the out-of-plane direction. But the critical layer number for achieving self-doping p–n junctions is largely dependent on the magnitude of the intrinsic dipole and the band gap of their SL structures.

4. Conclusions

In conclusion, we systematically investigate the electronic properties of FL In2X3 and their heterostructures with graphene to unveil the device potentials of 2D In2X3. We find that the long-sought natural p–n junctions can be achieved in TL In2X3, which results from the self-doping due to the intrinsic dipole. Importantly, TL In2X3 can readily be exfoliated in the experiment, indicating the high experimental feasibility of realizing such p–n junctions. This is different from the previously reported p–n junctions in the 2D limit whereby the p- and n-type regions are obtained by complicated additional fabrication processes and the device performance usually degrades. Besides TL In2X3, we also realize a self-doped p–n junction in G/In2S3/G and G/DL-In2S3/G, which is also attributed to the intrinsic dipole in In2S3. And the level of p–n doping can even be modulated by tuning the layer thickness of the sandwiched In2S3 in-between the two-graphene layers. And more excitingly, for all these studied systems, the outmost layers become metallic due to the self-doping, which can act as electrodes and thus realize the natural low-resistance contact. All these appealing properties not only make FL In2X3 and their heterostructures with graphene promising candidates for applications in electronic and optoelectronic nanodevices. We hope our results will motive experimental and theoretical efforts on developing more self-doped p–n junctions.

Conflicts of interest

The authors declare no competing financial interests.


This work was supported by the National Natural Science Foundation of China (No. 11804190), Shandong Provincial Natural Science Foundation of China (No. ZR2019QA011 and ZR2019MEM013), Qilu Young Scholar Program of Shandong University, and Taishan Scholar Program of Shandong Province, and Youth Science and Technology Talents Enrollment Project of Shandong Province.


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Electronic supplementary information (ESI) available: Stabilities, structures and electronic properties for 2D In2X3 and its heterostructures with graphene. See DOI: 10.1039/c9mh01109a

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