1. Introduction

With a moderate, direct bandgap ^[1], two-dimensional silicon carbide (2d-SiC) has recently drawn great attention in both theoretical investigation and practical applications ^[1-5], including a work of significant importance where the growth of the material was successfully demonstrated experimentally ^[6]. Lin et al. have shown that the optoelectronic properties of 2d-SiC are highly dependent on its geometric configuration and thickness ^[4]. Unlike the bulk zinc blende or wurtzite structures ^[7], 2d-SiC with the honeycomb structure possesses a direct bandgap of 2.5 eV ^{[2, 8, 9]}, which can be tuned through in-plane strain, number of layers and doping ^[4]. Similar to semiconducting transition metal dichalcogenides with layered structures such as MoS₂, a gradual transition from indirect to direct bandgap can be observed from bulk to monolayer ^[10]. A caveat is that a controllable direct bandgap in even multilayer 2d-SiC can still be realized via interlayer orientational misalignment and the direct-bandgap character can be actually maintained for a wide range of rotation angles ^[11]. On the other hand, compared to silicene and other graphene-like two-dimensional (2d) semiconductors (GaN, black phosphorus, AlN etc), monolayer 2d-SiC has greater in-plane stiffness ^[12]. Taking the advantage that the bulk SiC has long been used in p-n junction devices and the method to dope SiC is highly mature ^[13-15], 2d-SiC, with its novel properties as a 2D material, is a promising candidate for next generation electronics, in particular, for devices requiring p-n junctions, in contrast to the gapless graphene ^[16-19] and the insulating hexagonal boron nitride ^[20-24]. p-n junction is a fundamental building block for electronic devices, including in diodes, transistors, photodetectors, solar cells, light emitting diodes, etc. Although recently huge efforts have been put into designing p-n junctions with 2D materials ^[25-28], the potential of 2d-SiC has not been well explored in spite of its features.

In this paper, p-n junctions based on 2d-SiC are theoretically investigated by first principles calculations. We partially replace carbon with nitrogen and boron atoms in 2d-SiC along the zigzag or armchair direction to form p-type and n-type doping regions, following the recent work by Wu et al. ^[2] and Kamiyama et al. ^[29]. Our results on transport properties of such p-n junctions show negative differential resistance (NDR) effect and a diode-like behavior. In particular, the p-n junction along the zigzag direction is found to have optimized rectification performance with lower doping density.

2. Methods

We design three different 2d-SiC-based p-n junctions along the zigzag or armchair direction; see Fig. 1. We denote the p-n junction along the armchair direction with low doping density as PN-A_low [Fig. 1(b)], and the p-n junctions along the zigzag direction with low and high doping density as PN-Z_low [Fig. 1(a)] and PN-Z_high [Fig. 1(c)], respectively. The low doping density is 6×10¹⁴ cm^-2, and the high is 1.8× 10¹⁵ cm^-2. The transport properties of the p-n junctions are simulated by using the two-probe model and calculated employing density functional theory, as implemented in the SIESTA code ^[30] and the TranSIESTA package ^[31] with local density approximation (LDA) ^[32]. Troullier-Martin type norm-conserving pseudo-potentials and double $\zeta$ polarized numerical atomic basis sets are used. We set a large interlayer spacing of 15 Å along the out-of-plane direction, to simulate the monolayer SiC. Atomic positions are relaxed and determined by the balance of bonding and elastic energy with a force tolerance of 0.01 eV/Å. With these relatively high doping concentrations, the structure is stable after optimization. We would like to mention that this is a theoretical work and the stability of the designed systems needs to be tested in experiments. A k-grid-Monkhorst-Pack mesh of 300×1×300 for electrodes (the light-yellow shadow region in Fig. 1) and 300×1×1 for scattering region (the region between two electrodes in Fig. 1) is set. Finally, a 300 Ry energy cutoff is used to ensure convergent results. A higher cutoff energy and larger k-point sampling than normal values are probably due to the large concentration of doping in this case.

3. Results and discussions

Fig. 2 shows the transport properties of the three 2d-SiC-based p-n junctions we model in this work. The I-V curves are asymmetric to the zero point in all three structures; see Fig. 2(a). It is worth noticing that when they are biased with a suitable negative voltage, all the p-n junctions exhibit negative differential resistance (NDR). For PN-Z_low, the I-V curve shows NDR at $-0.7$ to $-0.25$ V bias range, with 5.096 μA absolute peak current at $-0.25$ V and 1.435× 10⁴ μA minimum current at $-0.7$ V. This gives a large peak-to-valley ratio (PVR) of 3.6×10⁴. For PN-Z_high and PN-A_low, NDR is observed at different bias ranges (see Fig. 2(a)), with 5.2×10⁴ and 4.2×10⁴ PVR, respectively. Though different, PVRs of all three types of p-n junctions are of the same order of magnitude. All the junctions show very high PVR, at least one order of magnitude higher than those of other semiconductor materials, as summarized in Table 1. In the positively biased region, the current through all the p-n junctions increases with the bias voltage. The shift rates for the junctions along the zigzag direction are significantly higher than those along the armchair direction; see Fig. 2(a)-that is, a higher resistance along the armchair direction than along the zigzag direction. It is the same case for the p-doped 2d-SiC-based resistors as shown in the inset of Fig. 2(a). The pristine 2d-SiC has a normal symmetric I-V relation to the zero point, similar to the p-doped shown in the inset. Fig. 2(b) shows the rectification ratio RR $= | I(V)/I(-V)|$ as a function of bias, also asymmetric, of these 2d-Si based junctions. A high RR indicates better rectification, while a value of 1 is no rectification. In most of the investigated bias range, the RR is above 10⁴ for all the p-n junctions as shown in Fig. 2(b), implying an excellent diode behavior. Among the three p-n junctions in Fig. 2(b), the PN-Z_low has the highest rectification ratio and the widest working area. In Table 1, we would like to point out that the PVR and RR in the tunnel diode made of 2d-SiC p-n junction is relatively large, compared to others, indicating their huge potential in electronics.

To analyze the transport properties of the three 2d-SiC p-n junctions, the transmission spectra and band structures of the left/right regions at zero bias voltage are calculated; see Fig. 3. It is worth noticing that 2d-SiC is a broad bandgap semiconductor ^{[1, 2]}, while N and B-doping can transform it to a degenerate semiconductor. In the band structures of the left and right electrode regions at zero bias, we see that the Fermi level is in the conduction band of the left electrode region and the valence band of the right electrode region. This leads to the resonant tunneling between the two electrode regions; see Fig. 3(d). As the result, a transmission peak emerges at zero bias. In Figs. 3(a) and 3(b), with the decrease of doping densities, the left and right electrode regions become less degenerated and thus induce less tunneling states at zero bias. This enhances the NDR effect and the rectification effect. In Figs. 3(a) and 3(c), the transmission peak of the device with low doping density along the armchair direction is lower than that along the zigzag direction.

From the band structures shown in Figs. 3(a) and 3(c), the effective mass of PN-Z_low and PN-A_low along k_x are calculated, to be 0.02 $m_0$ and 0.06 $m_0$ , respectively. According to $\mu=e\tau/m^*$ , a lower carrier mass results in a higher mobility. Therefore, the junction along the zigzag direction of a lower mass has a higher conductivity. Furthermore, compared with the effective masses of $m^*_\bot=0.42 m_0$ and $m^*_\|=0.42 m_0$ of bulk SiC ^[39], the monolayer SiC has much higher mobility owing to its much smaller effective masses.

To elucidate the underlying physical mechanism of the NDR effect and the diode-like behavior, the transmission spectra of PN-Z_low and the band structures of the left and right electrodes at various biases ( $V_{\mathrm{ds}})$ are calculated; see Fig. 4. According to the Landauer formalism $I(V)=\frac{2e}{h}\int_{\mu_{\rm L}}^{\mu_{\rm R}}\text{d} ET(E, V)[f(E, \mu_{\rm L})-f(E, \mu_{\rm R)}]$ , where E is the energy of the electron, $f(E, \mu_{\rm L/R})=1/[1+\text{e}^{(E-\mu_{\rm L/R})/k_{\rm B}T}]$ is the Fermi-Dirac distribution of the electrodes, and $\mu_{\rm L/R}=E_{\rm F}\pm V_{\rm ds}/2$ is the electrochemical potential of electrodes, we see that only the transmission within the bias window, i.e. [ $-V_{\mathrm{ds}}$ /2, $V_{\mathrm{ds}}$ /2], will contribute to the formation of the current. At zero bias, although we have a transmission peak around the Fermi levels of two electrodes, it does not contribute to the current and hence the output is zero. When a negative bias voltage is applied, the width of the bias window increases. Nevertheless, the transmission peak stays within the bias window only at small negative bias voltage, then rapidly decreases above a critical bias value ( $-$ 0.25 V for PN-Z_low, $-$ 0.55 V for PN-Z_high and $-$ 0.2 V for PN-A), and finally vanishes, due to the mismatch between the bands of the left and right electrode regions, see Figs. 4(c) and 4(d). Therefore, we have a maximum current output at the critical negative bias value, leading to the NDR effect. At positive bias voltage, the width of the bias window increases with the increasing bias voltage, accompanied by more resonant states of the left and right electrodes in the bias window, see Figs. 4(a) and 4(b). As the result, the current increases with the increasing positive bias voltage. Because of the distinct transport behaviors at the positive and negative biases, the 2d-SiC-based p-n junctions have excellent rectification performance.

To visualize some of the above points, we plot the electron density distribution of PN-Z_low at zero bias in Fig. 5(a). The induced external electron densities of PN-Z_low device at various biases are presented in Fig. 5(b) with the zero-bias density subtracted. In Fig. 5(a), we can see that the accumulation and depletion of the electrons only occur at the doping sites, indicating that the transmission channel results from the substitutional doping. Figure 5(b) shows that the electron density of the whole scattering region decreases at a small bias of $-0.25$ V, indicating a high probability of tunneling. At a larger bias of $-0.7$ V, electrons accumulate only at the left side of the scattering region. The rest has a trivial change under the uniform distribution of electric field. This implies that the wave-function changes only at the left side of the scattering region and decreases to zero after tunneling through the barrier, signifying the low probability of tunneling. This corresponds to the NDR phenomenon shown above. When a positive bias is applied, electrons accumulate at the whole scattering region due to the change of the wave-function at both sides of the junction, indicating a high probability of tunneling. Thus, the current increases sharply with increasing bias voltage, leading to a high rectification ratio.

4. Conclusion

Based on the first-principle calculations, we have investigated the electronic and transport properties of 2d-SiC based p-n junctions. In these junctions, the NDR phenomena with a PVR up to 10⁴ and a high rectification ratio above 10⁴ have been seen in a wide bias range >2 V. We also find that the rectification performance is optimized when the device is designed along the zigzag direction with lower doping density. These unique properties imply that 2d-SiC could be a very promising platform for differential negative resistance amplifier and other emerging applications in nanoelectronics.

Acknowledgements

The authors would like to thank Profs. X. Pi, Prof. W. Ji, Prof. H. Wong, Prof. J. Luo and Prof. B. Yu for helpful discussion and valuable comments. Y. Xu is supported by ZJU Cyber Scholarship, and Cyrus Tang Center for Sensor Materials and Applications, and a visiting fellowship of Churchill College, University of Cambridge.