Introduction

Because of its rapid increment in the power conversion efficiencies as well as its potential applications of high-performance photovoltaic devices, the hybrid lead trihalide perovskite attracted world attention widely. A race has started on both the development of new synthesis approaches and the research on fascinating properties of these materials1,2,3,4,5,6,7. With the former active research, the usage of halide perovskites has expanded not only in photovoltaic devices but also in other equally important applications such as photodetectors7, lasers8, and light emitting diodes (LEDs)9. Furthermore, many excellent experimental works have been done to research CH3NH3PbX3 as photovoltaic material, where X = I, Br, and Cl. And most important experimental results were obtained in the preliminary phase of study for CH3NH3PbX3 as photovoltaic material5,10,11,12,13,14. Prior to that, the search for CH3NH3PbX3 bulk materials includes nuclear magnetic resonance (NMR) spectroscopy15, X-ray diffraction16, ptical characterization techniques17,18, dielectric and millimetre wave measurements19, calorimetry20, which is a series of quite a few fundamental problems. Recently, many more advanced experimental methods have emerged, such as thermally stimulated current (TSC) measurements which is used to study point-defect and trap in CH3NH3PbI321. On the other hand, the former researchers have fabricated hybrid perovskites as single crystals,, thin films, or nanocrystals (NCs), which have not noly novel optical properties but also excellent electrical properties. At the nanoscale, especially, they are advanced and superior in exhibit technology because of its higher photoluminescence quantum yield (PLQY)22 and quantum confinement effect. Up to now, much work has been done to fabricate CH3NH3PbX3 at the nanoscale successfully. For instance, Vybornyi et al.23 have verified cubic shapes for CH3NH3PbI3 nanocrystals (NCs) and nanoplatelets for CH3NH3PbBr3. And Shamsi et al.24 have reported that halide perovskites employing N-methyl formamide of methylammonium (MA). The cubic structure for MAPbCl3 and MAPbI3 NCs as well as the tetragonal phase for the MAPbI3 NCs was confirmed by XRD patterns of the different NC samples.

A great deal of operating light emitting devices that was established upon MAPbX3 have indeed been demonstrated9,25,26,27,28,29, and the recent development of organic-inorganic halide perovskite materials including MAPbI3, the light harvesters in solid-state sensitized solar cells, has accomplished with a significant efficiency values exceeding 20%30. In addition, the structural properties of these hybrid lead trihalide perovskites, which are arranged in parallel, have also been studied31. However there is not enough study on their electrical transport properties and its current-voltage characteristic. Moreover, their potential application in the logic circuit such as diodes has not been reported so far. We also suppose the electronic behavior of MAPbX3 would change with carbon nanotube or silicon carbide nanotube encapsulated. How do these perovskite devices exhibit unidirectional penetrability in current-voltage characteristics? Can large influence occur in the current-voltage characteristics of these hybrid lead trihalide perovskite devices with carbon nanotube and silicon carbide nanotube? All the questions above, which are critical for perovskite electronics, need to be further throughly studied. The goal of this work is to solve these two issues.

To this end, we present a first-principles DFT study of MAPbX3 (X = I, Br) and their encapsulation in silicon carbide/carbon nanotube as a function of composition. By adopting computation in this way, we demonstrate sensitivity to electronic properties information on the microscopic scale, hence, it can connect microscopic scale structure to novel electronic properties determined by this work, informing new design for novel efficient and stable diodes which can be employed in confidential-needing aspect.

Results

Our calculations assess the current sensitivity to halide identity and the influence of the encapsulation of nanotubes. Figure 1 exhibits the atomic structures of CH3NH3PbI3 and CH3NH3PbBr3 designed by Feng and Xiao32. Analogous to CH3NH3PbI3, perovskite CH3NH3PbBr3 has the same lattice structure, in which Br and I have the same position. Although peroviskites possess several advantages, they are not stable in presence of moisture and heat. In consideration of the rapid moisture-induced degradation of the system, the encapsulation sealing will be important for perovskites33. It has been reported that nanotube in solar cells based on perovskites is better in electron transport and recombination behaviors than traditional films34. And the single-walled carbon nanotube is found to create an additional barrier to degradation35. All these results suggest the encapsulation plays a key role in determining the stability. Many experiments of carbon nanotubes have been done36,37,38, which make the encapulation of nanotubes possible. Inspired by the above studies, we here insert the molecules CH3NH3PbI3 and CH3NH3PbBr3 into the silicon carbide nanotube and carbon nanotube to explore their electronic properties and potential applications in electronic circuits, as shown in Fig. 2.

Figure 1
figure 1

Atomic structures of (a) CH3NH3PbI3, (b) CH3NH3PbBr3. Key: grey-Pb, purple-I, red-Br, blue-N, black-C, and pink-H.

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Figure 2
figure 2

Schematics of CH3NH3PbX3 (X = I, Br) encapsulated in silicon carbide/carbon nanotube.

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Figure 3 depicts the current−voltage characteristics of the six models studied in this work. I–V characteristics have been measured by Sarswat et al.39 and Tang et al.40 showing the memory effect and negative differential resistance (NDR) effect. And these curves they obtained have two characteristics. One is a local current maximum (when V = Vmax), and then the NDR effect appear. Another is the dual states when V < Vmax, where the on state is the situation when the first time the device reach the Vmax. Before quickly returning to zero, restore the off state by accessing a voltage that exceeds the NDR region. Although the NDR effect is also appear in our study, there are some differences. It is not performed voltage sweep like Sarswat et al.39 and Tang et al.40. And no memory effect display. The only I–V characteristic of one model is calculated based on the corresponding transmission spectra at different bias voltages one by one. Here, for simplicity, we regard the region when no current appears (I = 0A) as off state and the region when current has value (I ≠ 0A) as on state. We can see from Fig. 3(a) that MAPbI3 model has unidirection continuity of the diode, showing on-state in the negative bias and off-state in the positive range. The reverse recovery (RR) phenomenon occurs when a negative voltage is applied to a certain value across the MAPbI3 device. When the stage of the reverse current starts to build up, the current would reaches its peak value and then drop back to the beginning state (off state). What is noteworthy is that it is not conducting under a certain negative bias range from −0.5 to 0, but a turn-on operation in other negative states. That is to say, as for MAPbI3, −0.5 bias is a threshold value and the current can be conducted only beyond this threshold. Thus, based on this property, threshold voltage can be set for security under the application of some electronic security locks. As shown in Fig. 3(b), MAPbBr3 device has similar diode character like MAPbI3, which has on-state in a certain negative bias and off-state in the whole positive range. But at the on-state region, with the increase of the negative bias, the current of the MAPbBr3 device increases continuously and the strong NDR effect would disappear.

Figure 3
figure 3

I–V characteristic curves of CH3NH3PbI3 and CH3NH3PbBr3 and their encapsulation with silicon carbide/carbon nanotube.

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When MAPbI3 and MAPbBr3 are inserted into the silicon carbide nanotube, the value of the threshold voltage shifts a bit to the right, meaning that silicon carbide nanotube probably regulate the diode activity of MAPbX3 (X = I, Br), as shown in Fig. 3(c). The grey line represents MAPbI3 encapsulated in silicon carbide nanotube while the orange line represents the MAPbBr3 encapsulated in silicon carbide nanotube. It can be obviously seen that these two composite structures hold on-state in a certain negative bias and off-state in the whole positive range as exhibited by the individual MAPbX3 (X = I, Br) device. Importantly, NDR effect appears on the operating region of this MAPbI3-SiCNT device whose maximum peak-valley ratio (PVR) is 3.03 (28.8/9.5) and on-off ratio is 720 (28.8/0.04). These two parameters manifest that the diode performance of MAPbI3 becomes advanced when encapsulated in the silicon carbide nanotube.

There is another important observation after we further encapsulate MAPbI3 into carbon nanotube (CNT), as illustrated in Fig. 3(d). Some novel and interesting things have come up that it emerges current throughout positive voltage range different from MAPbX3 and MAPbX3-SiCNT. And MAPbI3-CNT sustains open-up feature in negative bias, which begins operating beyond −1.4 V. Nevertheless, MAPbBr3-CNT displays transmission characteristic of traditional electronic devices. What counts is that it arises two platforms on [−1 V, 0 V] and [0.5 V, 1 V] respectively.

The band structures of orthorhombic MAPbX3 (X = I, Br) calculated by the PBE/GGA functional are shown in Fig. 4(a,b). Our results are successfully match the previous theoretical value with the same function employed31. It can be seen that MAPbI3 and MAPbBr3 have the similar band structure because they have the same lattice constants. This phenomenon also appears in the research by Mosconi et al.41. There are obvious band gap between the VBM and CBM, showing a typical semiconductor nature for both MAPbI3 and MAPbBr3. This also make it rational for their semiconductive current-voltage characteristic curves. We also calculate the band structures when MAPbX3 (X = I, Br) encapsulated in CNT as shown in Fig. 4(c,d). The band gap vanishes and only one subband for MAPbI3-CNT and for MAPbBr3-CNT passes through the Ef, respectively, showing a metal characteristic. These also correspond to their I-V curves which have both forward current and reverse current, distinguishing from that of MAPbX3 which has semiconductor diode rectifying.

Figure 4
figure 4

The band structure of (a) orthorhombic CH3NH3PbI3 and (b) CH3NH3PbBr3 crystals along the high-symmetry lines in the first Brillouin zone. The band structure of (c) CH3NH3PbI3 and (d) CH3NH3PbBr3 encapsulated in CNT. Γ and Z in the band structures correspond to the (0, 0, 0) and (0, 0, 0.5) k-points, respectively, in the Brillouin-zone.

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By moving to analyze the electronic structures of these devices, we show the density of states (DOS) and projected density of states (PDOS) as well as the band structure (BS) in Fig. 5. The PDOS is the DOS projected onto the Pb and halide atoms. After encapsulated in a SiC nanotube, bands of MAPbI3 move down and up leading to semiconductor behavior with a very narrowed gap of 16 meV. And MAPbBr3 has further narrowing gap after encapsulated in the SiC nanotube like MAPbI3. The Bloch states at the highest occupied valence band maximum (HOVBM) and the Bloch states at the lowest unoccupied conductance band minimum (LUCBM) of device MAPbI3-SiCNT are shown in Fig. 5(a,b). Both the HOVBM and LUCBM are located at the Γ point in the Brillouin zone, illustrating it has the feature of a semiconductor with direct band gap. As shown in Fig. 5(a–d), both the HOVBM and LUCBM of the MAPbX3-SiCNT corresponds to the bottom of MAPbX3 part localized at N atoms mainly. And the LUCBM of the MAPbI3-SiCNT is also localized at SiCNT partially while the HOVBM is hardly localized at SiCNT. These two corresponding Bloch states at the Γ point indicate that only the conductance band is induced by the hybridization of SiCNT and the valence band actually results from the states of the N atoms of CH3NH3+ cations. This result is against the result from Wang et al.31 who pointed out that organic CH3NH3+ cations made little contribution to the bands of CH3NH3PbI3 around the Fermi energy level. The SiCNT is a main factor contributing to these two results. However, the MAPbBr3-SiCNT has the opposite case that only the HOVBM localized at SiCNT as shown in Fig. 5(c,d), indicating its valence band is induced by the hybridization of SiCNT and the conductance band results from both the states of the N atoms of CH3NH3+ cations and the hybridization of SiCNT. The BS, TDOS and PDOS for MAPbX3-SiC are manifested in Fig. 5(e,f). The PDOS shows that the DOS originates mainly from the contribution of halide atoms rather than Pb atoms, more precisely, it results from their unsaturated p orbitals. That is to say, the chemistry modification of I/Br atoms can tune the electronic phenomenon of MAPbX3-SiCNT. Furthermore, we can see that PDOS peaks for Pb and X (X = I, Br) atoms can align very well, which indicates that a orbital hybridization and a strong bonding have been established among these atoms. Interestingly, the PDOS peaks of I atoms in the bottom conductance bands are stronger and sharper than those of Br atoms in the top valence bands. The PDOS images of I and Br atoms support the argument that these two kinds of halide atoms are chemically non-equivalent though MAPbI3-SiCNT and MAPbBr3-SiCNT have the same lattice structure. The different PDOS images of I and Br atoms indicate a stronger bonding between Pb and I atoms in MAPbI3-SiCNT than that between Pb and Br atoms in MAPbBr3-SiCNT. This result is different from that of MAPbX3 without SiCNT41.

Figure 5
figure 5

The electronic properties for MAPbX3-SiCNT devices. (a,b) The Bloch sates at the HOVBM and LUCBM of MAPbI3-SiCNT, respectively. (c,d) The Bloch sates at the HOVBM and LUCBM of MAPbBr3-SiCNT, respectively. (e,f) The band structure (BS), total density of states (DOS), and projected density of states (PDOS) for MAPbI3-SiCNT and MAPbBr3-SiCNT, respectively. Γ and Z in the band structures correspond to the (0, 0, 0) and (0, 0, 0.5) k-points, respectively, in the Brillouin-zone. (g,h) The local density of states (LDOS) for MAPbI3-SiCNT and MAPbBr3-SiCNT, respectively. The colors represent the phase. The isovalue is 0.1.

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To explore origin of the above current-voltage characteristic, we further analyze the transmission spectra of MAPbI3-CNT, which is depicted in Fig. 6. The current through devices is inseparable from the transmission coefficients of devices since the current here is calculated by the Landauer-Büttiker formula. In this work, the average Fermi level, which is the average chemical potential of left and right electrodes, is set as zero. We define and discuss NDR effect follow a classical mode proposed by Shen et al.42 who employed the same simulation method and software as us. The colormap shows the current value, for example, red color stands for I = −16 μA and green color represents I = 6 μA. We select four typical points which are pointed by black circles to analyze their transmission spectra. The shaded area at every insert transmission spectra represents the energy interval of the chemical potential from the left to the right electrode. The transmission peaks within the bias window are important since they mainly contribute to the current. It is observed that values of all transmission peaks do not exceed 1, which illustrates all transmission spectra are contributed by single channel. In this work, when negative bias voltage rises to 2 V, the MAPbI3-CNT device has the maximum reverse current of almost 16 μA. At this moment, the bias window in transmission spectra at V = −2 V has four significant transmission peaks, elucidating the existence of transport. This result also identifies with conducting state of MAPbI3-CNT device. Furthermore, this device has non-conducting state in the region of [−1, 0]. To analyze this domain, we select the center dot at −0.5. From the corresponding transmission spectrum, we can see that there is no electronic transport regardless of whether at bias window nor in the whole range. When applied the positive voltage, the current increases at the beginning and then begins to decrease at V = 0.5 V and finally increases again continuously. We define the two inflection points (0.5 V, 1 V) as peak and valley respectively, which is not consistent with ohm’s law called NDR effect. It is obvious that the peaks in the 0.5 bias window are enhanced when compared to peaks in the 1 bias. Other MAPbX3 devices have the similar reasons.

Figure 6
figure 6

I–V curve of the MAPbI3-CNT device. The four typical points are labeled by circles. The inserts are transmission spectra under a bias of −2, −1.0, 0.5, and 1 V, respectively. The shaded area represents the bias window.

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Discussion

In conclusion, DFT calculations have provided a new idea that MAPbX3 (X = I, Br) can act well as diodes and its behavior can be modulated by encapsulation of the silicon carbide/carbon nanotube (SiCNT/CNT). It can be observed that MAPbX3 models display on-state in the negative bias and off-state in the positive range. And the diode activity of MAPbX3 changes after inserted into SiCNTs. It could be applied in some electronic security locks, based on the character that they only conduct in a certain bias. In addition, when MAPbX3 are inserted into CNTs, it emerges current throughout positive voltage range different from MAPbX3 and MAPbX3-SiCNT. Origin of their diode behavior is interpreted by their transmission spectra and density of states. The electronic structures are also discussed. This represents an important step in designing new diodes for high-efficiency electronic components.

Methods

In this work, we employ the first-principles density functional theory (DFT) in combination with the Non-equilibrium Green Function (NEGF) method as implemented in Atomistic ToolKit (ATK) software package to calculate transport properties. The device is divided into two parts, that is, the electrode and the channel. The source and drain electrodes are composed of graphene nanoribbons (GNRs), between which is the electron transfer channel (MAPbX3), as shown in Fig. 2. The mesh cutoff for the electrostatic potentials is 75 Ha. Double-zeta single polarized basis sets of local numerical orbitals and generalized gradient approximations (GGA) for exchange correlation potentials are used. K samples in the x, y, and z directions are 3, 3, and 50, respectively. The standard of convergence of the total energy is set to 10−5 eV.

The current I is calculated by Landauer formula when coherent transport of electrons occurs between left and right electrodes with Fermi levels μL and μR through the central scattering region43:

$$I=\frac{2e}{h}{\int }_{-\infty }^{\infty }dE({\rm{T}}({\rm{E}},{\rm{V}})({f}_{1}(E)-{f}_{2}(E)))$$

where T(E, V) is the transmission probability of electrons from left to right region, f1,2(E) is the Fermi-Dirac distribution function of the source and drain respectively, e and h are the electron charge and Planck constant, respectively.