Elimination of interlayer Schottky barrier in borophene/C₄N₄ vdW heterojunctions via Li-ion adsorption for tunneling photodiodes

Abstract

The nonzero interlayer Schottky barrier leads to a compromise between photodetectivity and photoresponsivity in photodiodes based on vdW heterojunctions. Seeking for the appropriate vdW heterojunction with Ohmic contact and a high tunneling barrier is of great significance to realize high-performance photodiodes. We built borophene/C₄N₄ (B/C₄N₄) vdW heterojunctions with a reduced interlayer Schottky barrier, by combining density functional theory and non-equilibrium Green's function. The adsorption of Li-ions can further tune its Schottky contact into n-type Ohmic contact. The electronic properties of the Li-ion-adsorbed B/C₄N₄ vdW heterojunction, including the separation of hole–electron pairs, the work function, as well as the effective mass of carrier, can be modulated by changing the adsorption site of Li-ions. B/C₄N₄/Li shows the most excellent absorbing capability of the infrared illumination and the strongest negative rectification, due to the highest interlayer tunneling barrier. The bottom surface of the C₄N₄ sublayer is the optimal adsorption site of Li-ions, for the potential application of B/C₄N₄ vdW heterojunctions in tunneling photodiodes. Our work unveils the great significance of Li-ion adsorption in modulating the interlayer Schottky and tunneling barriers in vdW heterojunctions, thus improving their device performance.

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1. Introduction

Semiconductor-based photodiodes, as a photoelectric sensing component to convert optical signals into photocurrent, has been widely studied and applied in many areas, such as image sensing, environmental monitoring, surveillance and spectroscopy.^1–4 Schottky barrier photodiodes are considered superior to p-i-n photodiodes, metal-semiconductor–metal photodiodes, and so on, in terms of their low power consumption, large current, and ultrahigh response speed.^5–8 Recently, van der Waals (vdW) heterostructures, which are formed by stacking different two-dimensional (2D) semiconductors vertically through vdW forces, have attracted the interest of a growing number of researchers. vdW heterojunctions have a large specific surface area, and their bandgap can be adjusted, while suppressing the recombination rate of the photogenerated carriers, which is greatly beneficial to the photoelectric process.⁹ Unfortunately, the interlayer Fermi level pinning effect in vdW heterojunctions often leads to Schottky barriers at the interface and thus probably results in undesirable large contact resistance.¹⁰ As a result, an inevitable compromise between photodetectivity and photoresponsivity often emerges in Schottky barrier photodiodes based on vdW heterojunctions.¹¹ In 2017, Zhai's group demonstrated the main positive contribution of high tunneling barrier to the high photocurrent, on the basis of which a highly sensitive WSe₂/SnS₂ photodiode was fabricated, exhibiting both ultrahigh photodetectivity of 1.29 × 10¹³ Jones (I_ph/I_dark ratio of ≈10⁶) and photoresponsivity of 244 A W⁻¹ at a reverse bias under the illumination of 550 nm light (3.77 mW cm⁻²).¹² Hence, seeking for the appropriate vdW heterojunction with Ohmic contact and a high tunneling barrier is of great significance to construct high-performance photodiodes.

Monolayer C₄N₄, as a novel p-type semiconductor, is competitive in the construction of vdW heterojunctions for applications in nanoscale electronics and optoelectronics, since it is reported that the Ohmic contact between C₄N₄ and graphyne could improve the conductivity of Li–S battery electrodes.¹³ Moreover, monolayer C₄N₄ is predicted to display a strong infrared response, opening the possibilities of C₄N₄-based vdW heterojunctions for tunneling photodiodes.¹⁴ Yang et al. reported the fabrication of C₃N by polymerization of 2,3-diaminophenazine (DAP), in which both N and C atoms are distributed homogeneously.¹⁵ They provided a feasible way to control the distribution of N atoms for improving the experimental methods of C₄N₄ synthesis. By comparing the cohesive energy per atom and the n-layer exfoliation energy per unit area, the C₄N₄ monolayer is more stable than many other carbonitride monolayers and can be easily prepared from its bulk forms using a similar experimental mechanical exfoliation method to that of graphene.^16–18 It is possible to prepare C₄N₄ monolayers by experiments successfully, even though they have not been achieved hitherto. To eliminate the Schottky barrier, theoretical assessments suggest that monolayer borophene can be used as a substitute for the traditional noble metal for contact with monolayer C₄N₄.¹⁹ For building tunneling photodiodes based on vdW heterojunctions, doping control is critical to further reduce the interlayer Schottky barrier. Considerable time and effort have been expended to develop effective doping strategies, such as thickness engineering,^20,21 surface modifications,^22–24 atomic substitutions,^25–27 and mechanical strain,^28,29 however these are not applicable to vdW heterojunctions, due to their peculiar structures. Experimentally, ionic intercalations have been developed to complementarily dope vdW materials for diode devices, providing a potential method to realize tunneling photodiodes based on borophene/C₄N₄ (B/C₄N₄) vdW heterojunctions.³⁰

In this study, based on density functional theory (DFT), we built B/C₄N₄ vdW heterojunctions by stacking monolayer borophene and C₄N₄ vertically and further decorating them with Li-ions. The electronic properties of free-standing borophene and C₄N₄ monolayers, including the separation of hole–electron pairs (Δρ), work function (ΔΦ), and effective mass of carriers (Δm*), are rationally modulated by the combination of vertical stacking and Li-ion adsorption. Most significantly, the interlayer Schottky contact in B/C₄N₄ vdW heterojunctions has been transformed into an Ohmic contact via the adsorption of Li-ions. By modulating Li-ions from the top to bottom site on B/C₄N₄ vdW heterojunctions, the increasing tunneling barrier will not only enhance the optical absorption in the entire infrared region, but also improve the negative rectification behavior. This work shows the great significance of Li-ion adsorption on modulating the interlayer energy barrier in vdW heterojunctions, paving the way towards applications in high-performance tunneling photodiodes.

2. Computational details

A vertical interface consisting of borophene and C₄N₄ monolayers, i.e. a B/C₄N₄ van der Waals (vdW) heterojunction, was built by matching the two crystals. For comparison, bilayer borophene and bilayer C₄N₄ were modeled as vdW homojunctions.^31–33 In the Atomistix-toolkit Virtual-nano-lab (ATK-VNL) package, the linear combination of atomic orbitals (LCAO) techniques was utilized to optimize the geometry of the stacking superlattice and to calculate its electronic properties.^34,35 A vacuum layer of about 25 Å was introduced to minimize the spurious interaction between neighboring layers. A specialized Grimme's approach (DFT-D3) was adopted to correct interfacial dispersion, taking van der Waals interactions into account.³⁶ The scalar-relativistic (SG15) optimized norm-conserving Vanderbilt (ONCV) pseudopotentials were employed with an energy cutoff of 100 Hartree, combined with the plane-wave basis set.³⁷ The k-point mesh of 10 × 1 × 10 was selected in the Brillouin zone during geometric optimization. The position of the upper layer relative to the bottom layer was optimized until the energy and stress error were less than 1.0 × 10⁻³ eV Å⁻¹ and 5.0 × 10⁻³ GPa, respectively. A much denser k-point mesh (15 × 1 × 15) was applied in the band structure and density of states (DOS) calculation. The electron–electron interactions were treated using the DFT-1/2 method considering the electron spin within Perdew–Burke–Ernzerhoff (PBE) parameterization, which has been widely applied to calculate the bandgap with more accuracy in a feasible time.^38,39

Furthermore, the ballistic transport behavior of the two-probe B/C₄N₄ vdW heterojunction was systematically analyzed, by using DFT combined with the non-equilibrium Green's function (NEGF) method. Monolayer borophene with a length of 20.74 Å was used as the left electrode, whereas monolayer C₄N₄ with the same length was used as the right electrode. In the central region, monolayer borophene and C₄N₄ were stacked with each other with a length of 20.74 Å, which was further relaxed until the force on each atom was less than 0.5 eV. The wave functions and other physical operators are expanded with a double zeta polarized (DZP) LCAO basis and the fineness of the real space grid is determined by an equivalent plane wave cut-off of 100 Hartree. The current and transmission spectra were calculated by using the NEGF-implemented ATK-VNL package. The current was obtained by integrating the transmission within the bias window:^40,41

where f is the Fermi function, E^L_F is the Fermi energy, T_L and T_R are the electron temperatures of the left and right electrodes and set as 300 K in this work, and V_L and V_R are the bias voltages applied to the left and right electrodes, respectively. T(E) is the transmission coefficient around the Fermi level, describing the probability of an electron with a given energy (E) that transfers from the left electrode through the central region and into the right electrode.

3. Results and discussion

Among all possible allotropes in borophene, the free-standing β₁₂ phase derived from the α-sheet structure is thermodynamically, mechanically, and dynamically the most stable.^42–44 In the following discussion, β₁₂ borophene is chosen as the material to build a van der Waals heterojunction with C₄N₄ monolayers. As shown in Fig. 1a–e, monolayer borophene has a planar structure with anisotropic corrugation. The optimized constant lattices in monolayer C₄N₄ are a = 6.08 Å and c = 3.58 Å, with a buckling height of ≈ 0.35 Å. During the formation of the B/C₄N₄ vdW heterojunction, we adapt the borophene supercell to vertically stack with 1 × 3 C₄N₄, in which the corresponding mismatch of the lattice constants is less than 2%. There is an angle of 29.0° between the arrangement of vacancies and the z-direction in the monolayer borophene supercell. In the formed B/C₄N₄ vdW heterojunction, the relative position of borophene is freely relaxed, while the C₄N₄ sublayer remains frozen. After geometric optimization, the vertical distance between borophene and C₄N₄ is d_y = 3.26 Å. Compared with bilayer borophene (B/B) and bilayer C₄N₄ (C₄N₄/C₄N₄) as van der Waals (vdW) homojunctions (d_y = 3.15 and 2.93 Å, respectively), the above B/C₄N₄ vdW heterojunction possesses the widest interlayer distance. The binding energy (E_b) of the bilayer system is defined as:

E_b = (E_upper+bottom − E_upper − E_bottom)/(N_B + N_C + N_N), (2)

where E_upper+bottom, E_upper, and E_bottom are the relaxed energies of the bilayer system, and the isolated upper and bottom layers, respectively. N_B, N_C, and N_N are the number of boron atoms in the borophene supercell, and carbon and nitrogen atoms in the C₄N₄ supercell. The relevant results are listed in Table 1. It is indicated from the negative E_b (−0.10 eV per atom) that the B/C₄N₄ vdW heterojunction is energetically feasible and can be obtained easily, even though it is weaker than those in bilayer borophene and C₄N₄. The wider interlayer distance and smaller E_b value of the B/C₄N₄ vdW heterojunction than the corresponding homojunctions might be ascribed to the lower number of unpaired electrons.⁴⁵

Fig. 1 Top and side views of free-standing (a) borophene and (b) C₄N₄ monolayers. Optimized configurations of (c) bilayer borophene (B/B), (d) bilayer C₄N₄ (C₄N₄/C₄N₄) as vdW homojunctions, and (e) B/C₄N₄ vdW heterojunctions. The lowest energy structures for Li-ion-decorated B/C₄N₄ vdW heterojunctions with (f) top, (g) sandwiched, and (h) bottom adsorption sites, respectively.

Table 1 The lattice constants along the x (a) and z (c) directions, binding energy (E_b), and the interlayer distance (d_y) in B/B, C₄N₄/C₄N₄, and B/C₄N₄ bilayer systems before and after the adsorption of Li-ions, respectively. The nearest length of the Li–X bond in Li-adsorbed B/C₄N₄ vdW heterojunctions

Superlattice	a (Å)	c (Å)	E b (eV per atom)	d y (Å)	L Li–X (Å)
a Before Li-ions adsorption: Eb = (Eupper+bottom − Eupper − Ebottom)/(NB + NC + NN), where Eupper+bottom, Eupper, and Ebottom are the relaxed energies of the bilayer systems, the isolated upper and bottom layers, respectively, and NB, NC, and NN are the numbers of B atoms in the borophene supercell, and C and N atoms in the C4N4 supercell. b After Li-ion adsorption: Eb = (ELi+B+C4N4 − NLiELi − EB − EC4N4)/(NB + NC + NN + NLi), where ELi+B+C4N4 denotes the total energy of Li-adsorbed B/C4N4 vdW heterojunctions, whereas ELi, EB, and EC4N4 represent the total energies of isolated Li-ion, monolayer borophene and C4N4 supercells, respectively. NLi, NB, NC, and NN are the numbers of Li-ions, and B, C, and N atoms in a unit supercell of the adsorption system.
B/B	5.86	10.13	−0.045^a	3.15	—
C4N4/C4N4	6.08	10.77	−0.036^a	2.93	—
B/C4N4	6.08	10.77	−0.010^a	3.26	—
Li/B/C4N4	6.08	10.77	−0.22^b	3.26	2.25 (Li–B)
B/Li/C4N4	6.08	10.77	−0.24^b	3.50	2.30 (Li–B)
					2.21 (Li–N)
B/C4N4/Li	6.08	10.77	−0.13^b	3.18	1.99 (Li–N)

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We further decorate Li-ions on the top, sandwiched, and bottom sites of the B/C₄N₄ vdW heterojunction, respectively. Li-ions are inclined to be adsorbed on the hollow site of the vacancies. By comparing Fig. 1f–h and Fig. S1 (ESI†), when Li-ions are adsorbed on the top and bottom sites of the B/C₄N₄ vdW heterojunctions (which are called Li/B/C₄N₄ and B/C4N4/Li for short, respectively), the lengths of the Li–B bond and Li–N bond are 2.25 and 1.99 Å, respectively, irrespective of the formation of B/C₄N₄ vdW heterojunctions. Meanwhile, the interlayer distance in B/C₄N₄ vdW heterojunctions is also insensitive to the adsorption of Li-ions. However, the insertion of Li-ions between borophene and C₄N₄ has expanded the interlayer distance by 7.36% from 3.26 Å to 3.50 Å. It is commonly believed that such an expanded bilayer, considered as an ideal structure for Li-ion batteries, can provide pathways for rapid electron transfer and further enhance the gravimetric and areal capacities.^46,47

The stability of Li-ion adsorption on B/C₄N₄ vdW heterojunctions is evaluated by the binding energy (E_b) of each Li-ion according to the following formula:^48,49

E_b = (E_Li+B+C4N4 − N_LiE_Li − E_B − E_C4N4)/(N_Li + N_B + N_C + N_N), (3)

where E_Li+B+C4N4 denotes the total energy of B/C₄N₄ vdW heterojunctions with Li-ion adsorption, whereas E_Li, E_B, and E_C4N4 represent the total energies of isolated Li-ion, monolayer borophene and C₄N₄ supercells, respectively. N_Li, N_B, N_C, and N_N are the number of Li-ions, and B, C, and N atoms in a unit supercell of the adsorption system. Obviously, the adsorption of Li-ions on B/C₄N₄ is much stronger than the weak vdW interaction between borophene and C₄N₄, as a strong ionic binding is brought about between the Li-ion and substrate. Bonding characteristics of B/C₄N₄ vdW heterojunctions can be revealed by analyzing the commonly used electron localization function (ELF), whose corresponding isosurfaces are shown in Fig. 2. In general, a large ELF value (>0.5) manifests a covalent bond, whereas the ionic bond is denoted by a smaller ELF value (<0.5).⁵⁰Fig. 2a and b show the electron localization around B atoms in borophene and that around N atoms in a C₄N₄ monolayer. It could be found that in borophene, the B–B bonds far away from the vacancies are covalent, while those near the vacancies are ionic. There also exists a similar bonding characteristic in the C₄N₄ monolayer. Such coexistence of covalent and ionic bonds has resulted in their good structural stabilities. Fig. 2c–e demonstrate that the weak vdW forces play a key role in bilayer systems, as no strong bonds could be observed in the interface between borophene and C₄N₄. Furthermore, the adsorption of Li-ions on B/C₄N₄ vdW heterojunctions causes the formation of Li–B bonds on the top adsorption site and Li–N bonds on the bottom site with high ionization degree, similar to those in monolayer borophene and C₄N₄ in Fig. S2 (ESI†). Meanwhile, the interaction between borophene and C₄N₄ keeps control of the vdW forces. Different from the above two kinds of adsorption sites, the sandwiched Li–B and Li–N ionic bonds in B/Li/C₄N₄ vdW heterojunctions have effectively strengthened the interaction between borophene and C₄N₄.

Fig. 2 Top views of ELF isosurfaces for (a) borophene and (b) C₄N₄ monolayers. Side views of ELF maps for (c) B/B, (d) C₄N₄/C₄N₄ vdW homojunctions, and (e–h) B/C₄N₄ vdW heterojunctions before and after Li-ion adsorption at the top, sandwiched, and bottom sites, respectively.

The above bilayer systems before and after Li-ion adsorption can be classified into two types of adsorption systems, according to the type of substrate. Specifically, the borophene-substrate-systems consist of Li/B monolayer, B/B vdW homojunction, and B/C₄N₄, B/Li/C₄N₄, and B/C₄N₄/Li vdW heterojunctions, in which Li-ions, borophene, C₄N₄, Li top-site-adsorbed C₄N₄ (Li/C₄N₄), and Li bottom-site-adsorbed C₄N₄ (C₄N₄/Li) monolayers are considered as the surface adsorbates. The cases of C₄N₄-substrate-systems are similar to the borophene-substrate-adsorption systems. Through this classification strategy, we explored the doping effect of various adsorbates on the electronic properties of borophene and C₄N₄ monolayers.

Mulliken charge densities in the above adsorption systems were calculated in Fig. 3a, to investigate the effect of vertical stacking and Li-ion adsorption on the interfacial separation of hole–electron pairs of bilayer structures. The electron density difference (Δρ) is defined as follows:^51,52

in which ρ_{adsorbate+substrate}(x,y,z), ρ_adsorbate(x,y,z), and ρ_substrate(x,y,z) denote the electron densities of the adsorption system, the isolated adsorbate and substrate at the (x, y, z) point, respectively, and N_substrate is the number of atoms in the substrate. All the adsorption systems are electrically neutral, as no external electric field is applied vertically. In Fig. 3a, a negative Δρ(y) indicates not only the electron accumulation on thte substrate but also the electron depletion on surface adsorbate, thus generating the separation of hole–electron pairs. In contrast, a positive Δρ(y) represents an opposite separation direction of hole–electron pairs. Conceptually, the amount of Δρ(y) can be employed to quantify the separation of hole–electron pairs.⁵³ In a unit supercell, each atom in C₄N₄ can draw 0.12 electrons from the adsorbed 3 Li atoms, leading to their ionization, which is much larger than that (0.093 e per atom) in Li-adsorbed borophene monolayers. The stronger electron-drawing capability of the C₄N₄ monolayer can also be reflected by the fact that each B atom in borophene has donated 0.032 electrons into C₄N₄ in the B/C₄N₄ vdW heterojunctions. This remarkable separation of hole–electron pairs is probably attributed to both the electron-deficient property of B atoms in upper borophene and the electron-rich property of N atoms in bottom C₄N₄. In contrast, due to the nonexistence of interfacial charge transfer, it is difficult for hole–electron pairs to separate in B/B and C₄N₄/C₄N₄ vdW homojunctions, leading to their inapplicability in optoelectronics, which will be validated in the following optical absorption analysis. By changing the adsorption site of Li-ions on B/C₄N₄ vdW heterojunctions, it is observed that the amount of charge transfer between B/Li and C₄N₄ (−0.074 e per atom) is more than twice that between Li/B and C₄N₄ (−0.029 e per atom), indicating that the separation of hole–electron pairs between borophene and C₄N₄ can be enhanced by the sandwiched-site adsorption of Li-ions. Moreover, the adsorption of Li-ions on the bottom site can even reverse the separation direction of hole–electron pairs from −0.074 e per atom in B/Li/C₄N₄ to 0.024 e per atom in B/C₄N₄/Li. This is because the electron-drawing capability of C₄N₄ is so strong that it can accept not only the electrons from Li-ions but also those in borophene. Therefore, the carrier type and concentration on each sublayer of the B/C₄N₄ vdW heterojunctions can be modified by changing the adsorption site of Li-ions.

Fig. 3 (a) Mulliken charge transfer (Δρ) between surface adsorbates and borophene (C₄N₄) substrates, (b) change of work function (ΔΦ), and (c and d) changes of electron effective mass (Δm_e) and hole effective mass (Δm_h) on borophene (C₄N₄) substrates at the GGA-1/2 level.

The variation of work function before and after surface adsorption will provide guidelines on how to tune the carrier concentration on borophene and C₄N₄ monolayers by the choice of surface adsorbate. The electrostatic potential calculations are performed to probe changes of the work function (ΔΦ = Φ_{adsorbate+substrate} − Φ_substrate) for borophene and C₄N₄ monolayers with different surface modifications.⁵⁴ The local density approximation (LDA) method predicted that the Φ values of isolated borophene, C₄N₄, and Li-ions are ca. 5.59, 7.12, and 2.29 eV, respectively. As shown in Fig. 3b, the formation of B/C₄N₄ vdW heterojunctions can decrease the work function of bottom C₄N₄ by 0.46 eV, meanwhile increasing that of upper borophene by 1.74 eV. As a result, n-type doping of C₄N₄ and p-type doping of borophene are effectively achieved. Conversely, the formation of B/B and C₄N₄/C₄N₄ vdW homojunctions has a negligible effect on the work function, owing to the minimum separation of hole–electron pairs. The adsorption of Li-ions may further change the work function in B/C₄N₄ vdW heterojunctions. For upper borophene, the adsorption of Li/C₄N₄ will increase its work function by 1.24 eV, whereas C₄N₄/Li can decrease its work function by 3.27 eV, showing an opposite doping effect. This is because the direct B–Li ionic bonds in B/Li/C₄N₄ are so strong that numerous electrons are donated from Li-ions to borophene, whereas electrons are accumulated on the C₄N₄ sublayer in B/C₄N₄/Li, because of the strong electron-donating capabilities of borophene and Li-ions. As for the C₄N₄ substrate, the adsorption of Li/B effectively decreases the work function by 3.96 eV, showing a stronger n-type doping effect than B/Li (−2.27 eV), due to the fact that borophene in B/Li/C₄N₄ shares a proportion of electrons injected from the inserted Li-ions.

The effective mass of carriers (m*) is another critical factor to describe the influence of surface modification on the interfacial carrier transport in adsorption systems. m* in the adsorption system is assessed by fitting parabolic functions to the conduction band bottom (valence band top) as follows:⁵⁵

where k is the wave vector, and E_k is the energy corresponding to the wave vector k. The smaller effective masses of electrons (m_e)/holes (m_h) usually indicate the higher electron/hole mobility. Using the above method, m_e and m_h in the borophene monolayer are calculated to be 0.023m₀ and 0.046m₀, respectively, where m₀ stands for the mass of free-electrons. Such extremely high carrier mobility leads to the metallic property of pristine borophene. In the C₄N₄ monolayer, m_e is 0.84m₀, much larger than m_h = 0.52m₀, exhibiting a p-type characteristic. Fig. 3c and d depict the change of effective mass of electron (Δm_e) and hole (Δm_h) in borophene and C₄N₄ substrate with various surface adsorbates. In B/C₄C₄/Li vdW heterojunctions, m_e and m_h on the borophene sublayer have reached 1.04m₀ and 0.72m₀, respectively, which are nearly 21.65 and 30.43 times larger than those in pristine borophene, showing the largest extent of reduction of the carrier mobility. It is speculated that in the meantime of carrier injection from C₄N₄/Li, a large number of scattering centers are also introduced into borophene, consequently impeding the carrier transport. The negligible interfacial separation of hole–electron pairs in B/B vdW homojunctions can reduce such carrier scattering, thus resulting in nearly zero Δm_e. However, the formation of C₄N₄/C₄N₄ vdW homojunctions has increased m_e and m_h by 0.19m₀ and 0.36m₀, respectively. It is attributed to the fact that the interlayer vacuum has blocked the carrier mobility between the upper and bottom C₄N₄ monolayers. In contrast, the remarkable separation of hole–electron pairs in B/C₄N₄ vdW heterojunctions has overwhelmed the blocking effect of interlayer vacuum. Hence, vertical stacking with borophene has a positive influence to improve the electron mobility of the C₄N₄ monolayer. In addition, the negative Δm_e and Δm_h in Li/B/C₄N₄ is nearly twice those in B/Li/C₄N₄, revealing that the adsorption of Li/B has promoted the carrier transport efficiency on the C₄N₄ substrate more dramatically.

Fig. 4a and b show the band structures of pristine borophene and C₄N₄ monolayer before and after Li-ion adsorption. The bands projected to borophene, C₄N₄ and Li-ions are indicated by red, blue, and yellow colors, respectively. Obviously, the electron-donating capability of Li-ions is so strong that their adsorption can effectively enhance the metallic property of borophene and even tune the C₄N₄ monolayer from p-type into metallic. The domination of interlayer vdW interaction in bilayer systems is quite different from the above ionic interaction in modulating the band structure. Fig. 4c demonstrates that the original band structures of pristine borophene and C₄N₄ monolayers are well preserved in B/B and C₄N₄/C₄N₄ vdW homojunctions, owing to the negligible separation of hole–electron pairs. In contrast, the strong separation of hole–electron pairs has enhanced the interlayer coupling effect and thus opened the bandgap of borophene to 0.18 eV. As a result, the band hybridization in the B/C₄N₄ vdW heterojunction is much stronger than those in the corresponding vdW homojunctions.

Fig. 4 Band structures for pristine borophene and C₄N₄ monolayers (a) before and (b) after Li-ion adsorption, (c) bilayer systems consisting of borophene and C₄N₄, and (d) B/C₄N₄ vdW heterojunctions with Li-ions at the top, sandwiched, and bottom sites, respectively. Red line: borophene; blue line: C₄N₄; yellow line: adsorbed Li-ions. The Fermi level is set at zero energy and denoted by the dashed line.

A large Schottky barrier height (SBH) impedes the interlayer electronic transport and degrades the performance of a photodiode based on the p–n junction. The homogeneous stacking of materials in the bottom and upper sublayers makes B/B and C₄N₄/C₄N₄ vdW homojunctions inappropriate to build p–n junctions, from the point of view of photodiode application. When using borophene and C₄N₄ monolayers as the left and right electrodes, it will be very important to explore the interfacial Schottky barrier height (Φ_S) in B/C₄N₄ vdW heterojunctions before and after Li-ions adsorption. Φ_S is defined by the difference between the CBM/VBM of the C₄N₄ sublayer and the Fermi level (E_F) of the borophene sublayer and can be attained from the band structures of B/C₄N₄ vdW heterojunctions.⁴⁵ The vertical electron SBH (Φ^e_S) in B/C₄N₄ vdW heterojunctions is 0.013 eV, whereas the vertical hole SBH (Φ^h_S) is 1.06 eV, forming an n-type Schottky contact. As shown in the enlarged band structure near E_F in Fig. 4d, the adsorption of Li-ions at the top site has decreased the vertical Φ^e_S to zero, since the CBM of C₄N₄ has shifted downward to lower than E_F, while keeping Φ^h_S unchanged. By changing the adsorption of Li-ions from the top to the sandwiched site, the vertical Φ^h_S has been dramatically reduced to 0.05 eV. Furthermore, in the B/C₄N₄/Li vdW heterojunction, both the CBM and VBM projected on C₄N₄ are shifted across E_F, thus resulting in zero Schottky barrier. Therefore, the Schottky contact between C₄N₄ and borophene can be effectively tuned into Ohmic contact, via optimizing the adsorption site of Li-ions. By comparing the band structures of B/C₄N₄ vdW heterojunctions with Li-ions on different adsorption sites, it is observed that CBM across E_F in B/C₄N₄/Li is mainly contributed by C₄N₄, whereas that in Li/B/C₄N₄ is dominated by borophene. This is largely due to the stronger charge transfer between Li-ions and the sublayer in direct contact. The projected density of states (PDOS) in Fig. 5 indicates that the bottom C₄N₄ sublayer becomes more metallized, by moving down the adsorption site of Li-ions in the B/C₄N₄ vdW heterojunctions. Accordingly, the Fermi level is dominated by C₄N₄, which further validates the leading role of C₄N₄ in the n-type Ohmic contact between borophene and C₄N₄ in B/C₄N₄/Li. Such n-type Ohmic contact is highly desirable to the application of vdW heterojunctions in high-performance electronic and optoelectronic devices, because it can promote the electronic transport efficiency.^56,57

Fig. 5 Projected density of states (PDOS) of B/C₄N₄ vdW heterojunctions (a) before and (b–d) after Li-ion adsorption at the top, sandwiched, and bottom sites, respectively. The Fermi level is set at zero energy and denoted by the dashed line.

There also exists another type of vertical energy barrier in the above B/C₄N₄ vdW heterojunctions, namely, the tunneling barrier. Different from the Schottky barrier, electrons and holes can be effectively separated with less energy loss in the tunneling barrier, thus generating photoelectric conversion.^58–60 Generally, the tunneling barrier height is dependent on the asymmetry of the heterojunction and can be evaluated by the Hartree difference potential (δV_H).^61,62 Herein, δV_H is calculated from the electron difference density as:

with the electron difference density δn(r) being defined through the relation:where n_I(r) is the compensation charge of atom I and N_atoms is the number of atoms in the system. Fig. 6a demonstrates the change of δV_H in bilayer systems, by changing the type of material in the sublayer. δV_H in B/B and C₄N₄/C₄N₄ vdW homojunctions is nearly zero, revealing that the structure with high symmetry is not applicable in optoelectronic nanodevices. In contrast, δV_H in the B/C₄N₄ vdW heterojunction has reached 6.18 eV, owing to the strong interlayer separation of hole–electron pairs. Furthermore, its δV_H value can be modulated from 6.11 eV in Li/B/C₄N₄ to 7.48 eV in B/C₄N₄/Li, showing that the adsorption of Li-ions on the bottom site can improve the asymmetry of B/C₄N₄ vdW heterojunctions most significantly. In contrast, the adsorption of Li-ions on the sandwiched site decreases the δV_H value to 6.03 eV, which weakens the structure asymmetry. Thereupon, B/C₄N₄/Li possesses the highest tunneling barrier, making it the optimal unit for photodiode applications.

Fig. 6 The interlayer Hartree difference potentials for (a) bilayer systems consisting of borophene and C₄N₄ monolayers, and (b) B/C₄N₄ vdW heterojunctions with Li-ions at the top, sandwiched, and bottom adsorption sites, respectively.

We further calculated the optical absorption coefficients in various bilayer systems in comparison with isolated borophene and C₄N₄ monolayers. Normally, a wide direct bandgap can induce larger probabilities of electron migration under illumination. As shown in Fig. 7a and b, the adsorption of Li-ions on monolayer C₄N₄ severely suppresses its high absorption peak (>23.55 μm⁻¹) in a wide solar spectrum from the ultraviolet region (0.29 μm) to the mid-infrared (2.76 μm), due to the disappearance of the bandgap in Li/C₄N₄. In contrast, the optical absorption peak of pristine borophene in the range from 0.25 to 0.83 μm has been remarkably intensified nearly 5 times by the adsorption of Li-ions and extended from the near-infrared to mid-infrared region as far as >7.48 μm, since the adsorbed Li-ions on the borophene substrate provide states shallower than that in the Li/C₄N₄ system. As for the formation of a bilayer structure, the wide bandgap in C₄N₄/C₄N₄ vdW homojunctions results in its sharp optical absorption peak in the visual region, whereas the higher tunneling barrier in B/C₄N₄ vdW heterojunctions leads to its wider optical absorption peak in the entire infrared region (>1.46 μm). The integral area ratio of infrared light reaches nearly 50% in the solar radiation spectrum, much larger than those of ultraviolet and visual lights. The strong optical response under infrared illumination allows the B/C₄N₄ vdW heterojunctions to make the best use of sunlight. In view of the poor infrared-light capturing capabilities, B/B and C₄N₄/C₄N₄ vdW homojunctions will not be considered in the following electronic transport behavior study for photodiode applications. In B/C₄N₄ vdW heterojunctions with Li-ion adsorption, the optical absorption peak has been enhanced by approximately 14% without a remarkable shift, by changing the adsorption site from the top to the bottom, since the tunneling barrier becomes higher. Therefore, the adsorption of Li-ions on the bottom site provides a feasible method to enhance its optical absorption, which would be conducive to improving the performance of optoelectronic nanodevices based on B/C₄N₄ vdW heterojunctions.

Fig. 7 Optical absorption spectra for borophene and C₄N₄ monolayers (a) before and (b) after Li-ion adsorption, (c) bilayer systems consisting of borophene and C₄N₄, and (d) B/C₄N₄ vdW heterojunctions with Li-ions on various adsorption sites, respectively.

The effect of tunneling barrier on the device performance of a photodiode based on B/C₄N₄ vdW heterojunctions can also be reflected by the change of its quantum transport behavior via Li-ion adsorption. Fig. 8a displays the schematic diagram of a two-probe B/C₄N₄ vdW heterojunction system with Li-ion adsorption, in which the Li-ion adsorption can be manipulated between the top, sandwiched, and bottom sites. In the central region, the supercell of B/C₄N₄ vdW heterojunctions repeats twice along the z-direction, i.e. the direction of the electric field.

Fig. 8 (a) Schematic diagram of two-probe B/C₄N₄ vdW heterojunction with Li-ion adsorption, in which the adsorption varies between the top and bottom sites. (b) The dependence of current and (c) the rectifying ratio on bias voltage in B/C₄N₄ vdW heterojunctions before and after Li-ion adsorption, respectively.

We plot the current–bias (I–V_b) dependence curves of B/C₄N₄ vdW heterojunctions with different Li-ions adsorption sites in Fig. 8b. In B/C₄N₄ vdW heterojunction without the adsorption of Li-ions, the reverse current (−1.0 to 0 V) decreases rapidly, which is much more remarkable than the forward one (1.0 to 0 V), by descending |V_b|. As a result, B/C₄N₄ shows an obvious negative rectification behavior. To quantitatively illustrate the rectifying behavior, we define the rectifying ratio (R) as R = |I(−V_b)/I(+V_b)|. R = 1 indicates no rectification effect, and R > 1 denotes a higher reverse current, i.e. a negative rectification, whereas R < 1 represents a higher forward current, known as a positive rectification.^63,64 The V_b–R curves in B/C₄N₄ vdW heterojunctions with various Li-ion adsorption sites are shown in Fig. 8c. The R value of B/C₄N₄ vdW heterojunctions reaches the maximum of 3.68 at |V_b| = 0.2 V and the minimum of 0.60 at |V_b| = 0.6 V. The reversed rectifying status in B/C₄N₄ reveals that the metallic-semiconductive asymmetry is tunable by changing the direction of the electric field. The R value in Li/B/C₄N₄ vdW heterojunctions shows the opposite tendency with rising |V_b|, in which the minimum is 0.46 at |V_b| = 0.2 V and the maximum is 2.40 at |V_b| = 0.6 V. It is indicated that the sandwiched-adsorption of Li-ions can reverse the metallic-semiconductive asymmetry.

An obvious negative differential resistance (NDR) effect under forward bias arises in B/Li/C₄N₄ and B/C₄N₄/Li vdW heterojunctions, making them competitive candidate structures for Esaki diodes, which are used as static random access memories, multivalued logic circuits, and so on.^65–68 Their peak and valley of the current are located at V_b = 0.4 V and 0.8–1.0 V, respectively, resulting in an increase of peak-to-valley ratio (PVR) from 1.76 to 2.60. In the meantime, the reverse current is apparently enhanced and also shows an NDR effect in B/C₄N₄/Li, when the reverse V_b rises to higher than −0.6 V. Its R value increases from 1.58 to 6.38 when |V_b| rises from 0.2 to 0.8 V and then decreases to 5.09 at |V_b| = 1.0 V, due to the emergence of NDR effect under reverse bias. The maximum R value in B/C₄N₄/Li is almost 2 times higher than those in B/C₄N₄ vdW heterojunctions with Li-ion adsorption on the other adsorption sites. The reason for this phenomenon might be that the injection of electrons from the adsorbed Li-ions to bottom C₄N₄ is so remarkable that the vdW heterojunction is transformed from metallic-semiconductor to metallic donor–acceptor. The separation of hole–electron pairs is much stronger than the former, consistent with the raised tunneling barrier as mentioned above. Such strong negative rectification in B/C₄N₄/Li vdW heterojunctions can be applied to improve the photosensitivity in the dark and under infrared illumination conditions in tunneling photodiodes.^69–71

In order to understand the tunable asymmetric transport behavior in B/C₄N₄ vdW heterojunctions via Li-ion adsorption, we explore the transport mechanism in two-probe Li-ion-adsorbed B/C₄N₄ systems. The transmission function T(E,V_b) is the sum of transmission probabilities of all channels available at energy E under external bias voltage V_b:

T(E,V_b) = Tr[Γ_L(V_b)G^R(E,V_b)Γ_R(V_b)G^A(E,V_b)], (8)

where G^R and G^A are the retarded and advanced Green's functions, respectively, and the coupling functions Γ_L and Γ_R are the imaginary parts of the left and right self-energies, which depend on the surface Green's functions of the electrode regions and come from the nearest-neighbor interaction between the extended central region and the electrodes.

Fig. 9 gives the contour maps of transmission spectra for all B/C₄N₄ vdW heterojunctions before and after Li-ion adsorption from −1.0 to 1.0 eV at V_b from −1.0 to 1.0 V. The region within the yellow dashed lines is the bias window, where the current depends on the integral of T(E,V_b). The blue color denotes a low transmission coefficient, whereas the red one represents a high transmission coefficient. Apparently, in B/C₄N₄ vdW heterojunctions, the transmission peak begins to appear in the bias window when |V_b| increases to higher than 0.5 V, revealing that the observable current starts to flow through the heterojunction only after |V_b| > 0.5 V. In addition, the integral area of T(E,V_b) in the reverse V_b region is much larger than that in the forward V_b region, thus leading to a negative rectification. It is most notable in B/C₄N₄/Li vdW heterojunctions that the peaks in the reverse V_b region move positively to higher energy levels and the corresponding integral of T(E,V_b) shows an increasing trend, by increasing |V_b|. Meanwhile, some peaks begin to emerge under a lower |V_b|. It is indicated that the increase of V_b can further strengthen the n-type doping effect of the adsorbed Li-ions on the C₄N₄ sublayer, which has modulated the C₄N₄ sublayer from hole-dominated semiconductive into electron-dominated metallic. A vast number of electrons are also withdrawn from the upper borophene to bottom C₄N₄. Eventually, the metallic donor–acceptor asymmetry in B/C₄N₄/Li shows improved negative rectification behavior, enabling its promising applications in high-performance photodiodes.

Fig. 9 The transmission coefficient contours as a function of energy and bias voltage in (a) B/C₄N₄, (b) Li/B/C₄N₄, (c) B/Li/C₄N₄, and (d) B/C₄N₄/Li vdW heterojunctions, respectively. The region within the yellow dashed lines is the bias window.

To further analyze why B/C₄N₄/Li vdW heterojunctions have superior negative rectification behavior, its transport probability at V_b = −1.0 V is compared with that at V_b = 1.0 V. The projected local density of states (PLDOS) and spectral current of B/C₄N₄/Li vdW heterojunctions at V_b = −1.0 and 1.0 V are displayed in Fig. 10. In PLDOS, the bright block stands for the existence of DOS, whereas the dark one indicates the energy gap without DOS distribution. Borophene and C₄N₄/Li monolayers are separated by B/C₄N₄/Li vdW heterojunctions, as indicated by the green vertical line. It is worth noting that the current in B/C₄N₄/Li is mainly attributed to the transport behavior in the energy region higher than 0 eV, whether at −1.0 V or at 1.0 V. Nevertheless, the transport processes at V_b = −1.0 V and V_b = 1.0 V are quite different. V_b = −1.0 V implies a higher potential of the right C₄N₄/Li electrode, whereas V_b = 1.0 V means a higher potential of the left borophene electrode. At V_b = −1.0 V, CBM and VBM of the right C₄N₄/Li electrode are shifted upward relative to E_F and CBM of the left borophene electrode. The higher energy levels on the right C₄N₄/Li with respect to the left borophene provide enough channels for electrons to transport through B/C₄N₄/Li, as the current under negative bias starts to flow only after VBM of the right electrode reaches CBM of the left one.⁷² The n-type Ohmic contact in the central B/C₄N₄/Li vdW heterojunction has no blocking effect on the transport efficiency. Numerous electrons are injected from the adsorbed Li-ions to the C₄N₄ monolayer, which plays the role of the majority carriers and promotes the interband tunneling from VBM of C₄N₄/Li to CBM of borophene, thereby resulting in a large reverse current at V_b = −1.0 V. The electron-withdrawing capability of bottom C₄N₄ in B/C₄N₄/Li is so strong that it can not only accept electrons from Li-ions but also from upper borophene. As a result, VBM of borophene is occupied by holes, which play as the majority carriers under the forward bias. At V_b = 1.0 V, the higher potential of the left borophene electrode has significantly shifted the CBM and VBM of borophene upward to higher than the E_F and CBM of the right C₄N₄/Li. Consequently, the holes on VBM of the left borophene move to CBM of the right C₄N₄/Li with relatively low energy, bringing about the forward current. In comparison with the high electron concentration in C₄N₄/Li, the lower hole concentration in borophene has suppressed the forward current. Therefore, the large difference in carrier concentrations on the upper borophene and bottom C₄N₄/Li layers of B/C₄N₄/Li vdW heterojunctions is the origin of its high interlayer tunneling barrier, on which superior negative rectification behavior is generated. This will be of great importance to the application of B/C₄N₄/Li vdW heterojunctions in high-performance optoelectronic devices, such as photodetectors and photodiodes.

Fig. 10 Spatially resolved local density of states (LDOS) (left side) and the corresponding spectral current (right side) in B/C₄N₄/Li vdW heterojunctions at (a) V_b = −1.0 V and (b) V_b = 1.0 V, respectively.

4. Conclusions

In conclusion, we have developed a new strategy to eliminate the interlayer Schottky barrier in B/C₄N₄ vdW heterojunctions and finally realized the Ohmic contact between borophene and C₄N₄, through the combination of vertical stacking and Li-ion adsorption. The remarkable separation of hole–electron pairs in B/C₄N₄ vdW heterojunctions makes it superior to B/B and C₄N₄/C₄N₄ vdW heterojunctions as the candidate structure for photodiode application. The adsorption of Li-ions on B/C₄N₄ vdW heterojunctions can not only eliminate the Schottky barrier but also increase the tunneling barrier by modulating the adsorption site from top to bottom, achieving an n-type Ohmic contact, which is largely attributed to the enhanced electron injection into the C₄N₄ sublayer. B/C₄N₄/Li exhibits the most excellent absorbing capability of the infrared illumination and the strongest negative rectification, among a series of Li-adsorbed B/C₄N₄ vdW heterojunctions, showing great potential in tunneling photodiode applications. Both the transmission spectra and PLDOS demonstrate that the largest difference in carrier concentrations on the left and right electrodes is the origin of the highest tunneling barrier in the two-probe B/C₄N₄/Li system at reverse and forward bias, thus resulting in the largest rectifying ratio. Our study is expected to encourage experimental realization of the tunneling photodiode based on vdW heterojunction with Ohmic contact.

Author contributions

Cancan Zheng, Man Shi, Haiyan Li, Nianxi Dou, and Zhihao Ma: Data curation; Cong Zhou: Validation; FeiFei Xia: Visualization; Yuanyuan He: Conceptualization, investigation, and writing original draft; Jianwei Zhao: Methodology, software, and supervision.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51802121, and 51861145202), Jiaxing Science and Technology Project (Grant No. 2020AY10008, and 2020AD10017), the Student Research Training Program of Jiaxing University (CD8517203297), and the Open Project Program of Key Laboratory of Yarn Materials Forming and Composite Processing Technology, Zhejiang Province, Jiaxing University (MTC2020-17).

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Footnote

† Electronic supplementary information (ESI) available: Optimized geometries and electronic properties of Li-ion-adsorbed borophene and C₄N₄ monolayers. See DOI: 10.1039/d0tc05943a

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