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Abstract
Linear photogalvanic effects in monolayer WSe2 with defects are investigated by non-equilibrium Green’s function technique combined with density functional theory. Monolayer WSe2 generates photoresponse in the absence of external bias voltage, showing potential applications in low-power consumption photoelectronic devices. Our results show that the photocurrent changes in perfect sine form with the polarization angle. The maximum photoresponse Rmax produced in the monoatomic S substituted defect material is 28 times that of the perfect material when the photon energy is 3.1 eV irradiated, which is the most outstanding among all the defects. Monoatomic Ga substitution extinction ratio (ER) is the largest, and its ER value is more than 157 times that of the pure condition at 2.7 eV. As the defects concentration increases, the photoresponse is changed. The concentrations of Ga substituted defects have little effect on the photocurrent. The concentrations of Se/W vacancy and S/Te substituted defect have a great influence on the photocurrent increase. Our numerical results also show that monolayer WSe2 is a candidate material for solar cells in the visible light range and a promising polarization detector material.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Due to their unique electronic properties and atom-thin geometry, two dimensional transition metal dichalcogenides (TMD) and graphene-like structural materials have attracted great interest in various electronic and optoelectronic devices’ applications. These unique two-dimensional layered materials can be stripped into a few or single atomic layers. The band structure of TMD material will change from indirect to direct one when it is stripped into single-layer structure. Among TMD crystals, WSe2 is one of the most widely studied materials due to both the easy synthesis and tunable doping techniques. The bulk WSe2 has an indirect band gap (∼ 1.2 eV), and changes into a direct one (∼ 1.6 eV) in monolayers [1,2]. Therefore, this material has attracted much attention in applications of functional electronics and optoelectronics.
By absorbing photons, electrons in materials without spatial inversion symmetry are excited from the valence bands to the conduction bands, and then flow out of the semiconductor to the left or right lead. This is the photogalvanic effect (PGE). Recently, the PGEs has been studied in several new materials. For example, topological insulators [3,4], Weyl semimetals [5], and two dimensional TMD [6–10]. However, only a few studies focused on the PGE of WSe2 monolayer. The study of monolayer WSe2 is mainly focused on the adsorption and sensing performances [11,12], single-photon emitters [13,14], and photocatalysts [15].
In the present paper, we theoretically predicted the PGE in WSe2 taking intrinsic defects, which are common in experiments and affect the material’s electronic structure, optical properties, as well as magnetism, into consideration. Monolayer WSe2 is a hexagonal warped structure with covalent bonds between atoms with lattice parameter a = b = 3.327 Å. The bond lengths of W-Se, Se-Se and W-W are 2.553Å, 3.362 Å and 3.327 Å, respectively. In order to calculate the photocurrent flowing through this material under polarized light, a front-back double probes (leads) device is constructed as shown in Fig. 1, in which (a) and (b) are respectively the top and side views. The left and right leads individually extend to ${\pm} \infty$ along the transmission direction x, and the whole system periodically extends in the x-y plane. The central region which has 39 atoms is irradiated vertically by linearly polarized light in the z axis, as shown in Fig. 1(b), and the photocurrent flows along the x direction. Six configurations of the central region are discussed here, namely pure WSe2, W-vacancy (c), Se-vacancy (d), Ga-substituted (e), and S/Te-substituted (f) as shown in Fig. 1. All the defects are in the middle of the central region. The blue, orange, purple and red spheres represent the W atoms, the Se atoms, the Ga atoms and the S/Te atoms, respectively. The C3h symmetry of the pristine WSe2 monolayer is reduced to C2v/Cs due to the introduction of holes, which breaks the spatial inversion symmetry.
Fig. 1. The top (a) and side (b) views of the monolayer WSe2 photodetector. The polarization angle $\theta$ of the linearly polarized light is formed with respect to the x-direction. The blue, orange, purple and red spheres represent the W atoms, the Se atoms, the Ga atoms and the S/Te atoms, individually. The defective supercells are (c) W-vacancy, (d) Se-vacancy, (e) Ga-substituted and (f) S-substituted (or Te-substituted). All the monoatomic defects are in the middle of the central region.
2. Calculations and methods
When the central region is illuminated by linearly polarized light, the photocurrent can be generated from the two leads. Based on linear response approximation [16], the photocurrent in the left lead (marked as L), $J_\textrm{L}^{(ph)}$ can be written as [17,18]
Here, $G_{1,2,3}^{ > / < (ph)}$ is the greater (lesser) Green functions with photon-electron interaction. $G_0^{r/a}$ and $G_0^{ > / < }$ corresponds to the retarded/advanced and greater/lesser Green’s functions without photons. ${e_{1/2x,y,z}}$ means the Cartesian component of the unit vector ${e_{1(2)}}$ determined by the light polarization and ${p_{x,y,z}}$ the Cartesian component of the electron momentum. The polarization vector of the linearly polarized light can be written as $\hat{e} = \cos \theta {\hat{e}_1} + \sin \theta {\hat{e}_2}$, where $\theta$ represents the angle between the polarization direction and the vector ${\hat{e}_1}$, which represents the transport direction (x-axis) in our calculation. In Eq. (2), C0 can be expressed as ${C_0} = \frac{{{e^2}\hbar \sqrt {{\mu _r}{\varepsilon _r}} }}{{2Nm_0^2\omega \varepsilon C}}{I_\omega }$, where ${\mu _r}$ the relative magnetic susceptibility, ${\varepsilon _r}$ the relative dielectric constant, and $\varepsilon$ the dielectric constant, N the number of photons, ${m_0}$ the bare electron mass, $\omega$ the photon frequency, C the speed of light, ${I_\omega }$ the photon flux determined by the number of photons per unit area per unit time. The photoresponse function can be expressed as $R = J_\textrm{L}^{(ph)}/e{I_\omega }$. Here R in the unit of $a_0^2/\textrm{phonon}$ has the dimension of the area, where $a_0^{}$ is the Bohr radius.
The above theoretical formalism, in which density functional theory is implemented in the framework of nonequilibrium green’s function formalism, has been realized in the first-principle quantum transport packet NanoDcal [19–21]. In subsequent numerical calculations, double Zeta polarization atomic orbital bases are used to expand all physical quantities. Local density approximation is used to deal with interchange and correlation. Under the framework of local density approximation, the problems of exchange and correlation are discussed. Besides, we employ the standard norm that preserves the nonlocal pseudopotentials to define the nucleus. The k-point mesh of 6 × 11 is employed in the band structure calculation and 20 × 1 is employed in the calculation of photocurrent transport from the front probe to the back probe.
3. Results and discussions
Figure 2 shows that the WSe2 monolayer is a direct semiconductor with a band gap of 1.532 eV, which is consistent with previous first-principles calculation results [1,2]. Both the pure and the defective WSe2 monolayers induce PGEs and generate photocurrent under vertical irradiation of linearly polarized light, as is seen from Figs. 3(a)-(f). As mentioned above, the pristine and the defected WSe2 monolayers have no spatial inversion symmetry, and vertical irradiation with linearly polarized light induces PGE resulting in photocurrent generation. This result is in excellent agreement with the PGE phenomenological theory under the D3h, Cs and C2v symmetry [22–25]. Photon energies of 2.6 eV (black line), 2.8 eV (red line) and 3.0 eV (blue line), are selected as special points to study the law of the variation of photoresponse R with the polarization angle $\theta$. It is shows that the photocurrent is related to the angle of polarization $\theta$ in the form of sin(2$\theta$). The maximum photoresponse Rmax appears at the polarization angle of 45° or 135°. For pure WSe2 monolayer in Fig. 3(a), ${R_{\max }} ={\pm} 0.09$ emerge at photon energies of 3.0 eV. In Fig. 3(b), there is one W atom vacancy in the center primary cell, ${R_{\max }} ={\pm} 0.60$ for photon energies of 2.6 eV. Figure 3(c) is the case that there is only one Se atom vacancy in the same primary cell, ${R_{\max }} ={\pm} 0.64$ for photon energies of 2.8 eV. Figure 3(d) shows the defects of only one W atom substituted by Ga atoms in the center primary cell, in which ${R_{\max }} ={\pm} 0.29$ for photon energies of 2.6 eV. In Fig. 3(e), one Se atom is substituted by S atoms in the same primary cell, ${R_{\max }} ={\pm} 0.46$ for photon energies of 2.6 eV. When the same Se atom is substituted by Te atoms, ${R_{\max }} ={\pm} 1.08$ for photon energies of 3.0 eV as shown in Fig. 3(f). Comparing Fig. 3(e) with Fig. 3(f), it can be seen that different doped atoms can bring different effects under the same symmetry. In these cases, Te substitution is more beneficial to photocurrent’s enhancement. Compared with Fig. 3(f), Rmax in Fig. 3(c) and 3(e) are greatly reduced because the symmetry of the structure is optimized. The introduction of defects enhances the photoresponses not only in the positive direction, but also in the opposite direction.
Fig. 3. The photoresponse R of the six different central regions varies with the polarization angle θ at the photon energies of 2.6 eV, 2.8 eV and 3.0 eV respectively. (a) pure WSe2; (b) W-vacancy; (c) Se-vacancy; (d) Ga-substituted; (e) S-substituted; (f) Te-substituted.
To verify the reliability of the above results, the curve of Rmax varies with the continuous change of photon energy, which covers the near-infrared and visible ranges, is presented in Fig. 4. When the photon energy is lower than 1.5 eV, all the defects have almost no effect on the photoresponse. The Rmax in pure WSe2 monolayer (black line) is 0.06 whereas it is 1.67 in material with S-substituted defect (green line) at photon energy 3.1 eV, which is 28 times greater than that in perfect material. For the W-vacancy (red line) and the Se-vacancy (blue line) cases, the peaks are Rmax = 1.37 and Rmax = 0.95 at photon energy 2.7 eV and 3.2 eV, respectively. The Rmax in Ga-substituted (magenta line) has a peak of 0.45 at photon energy of 2.7 eV. For the Te-substituted (orange line) cases, the peaks are Rmax = 1.49 at photon energy 3.2 eV. From the above figures, one can see that S atom substituted is more efficient for PGE as compared to other defects in WSe2. It was found that the introduction of such defect is an effective method to enhance the photocurrent. In contrast, WSe2-MoS2 lateral heterojunction can generate stronger photocurrents, which can reach 23 in Ref. [7]. Although the current of the device in our paper is small, it has the advantage of easy material synthesis. Reference [6] provides an explanation on the behavior of photoresponse, which is achieved using a combination of analysis on the band structure and joint density of states. They find that there exist zero points in the photocurrent for both linear photogalvanic effect (LPGE) and circular photogalvanic effect (CPGE), but the underlying mechanisms are different as their paper illustrates. Different from this paper, our paper focuses on the effect of intrinsic defects (vacancies and substitutions) on photocurrent, mainly because they are unavoidable in experiments and also affect the energy band of the material, thus enhancing PGE. Shao et. al. [8] studied the photogalvanic Effect in chromium-doped monolayer MoS2, by changing the photon energy in the long-wavelength visible light, the type of polarized light (linearly and circularly polarized light), polarization angle (θ), and the helicity angle (φ) to control the photocurrent in 2D photovoltaic devices. Here, we focus on the near-infrared and visible ranges linearly polarized visible light.
Fig. 4. The maximum photoresponse Rmax varies with the photon energy in six different central regions, which is pure WSe2 (black line), W-vacancy (red line), Se-vacancy (blue line), Ga-substituted (magenta line), S-substituted (green line) and Te-substituted (orange line).
Electron transmission spectrum (TS) as a function of energy is shown in Fig. 5, which is the cause of the peaks in photoresponse. For the pure material in Fig.5a (black line), there are large TS peaks at about -1.50 eV and 1.80 eV (A, A' in Fig. 5(a)) respectively. By radiating photons with energy of 3.3 eV, the energy difference between the two peaks generates a larger photocurrent because of the greater probability of transition amplitude. This is consistent with the peak of the black line in Fig. 4. For the Ga-substituted case, the peak value of TS locates at photon energy of -1.35 eV and 1.35 eV (B, B' in Fig. 5(a)). For the Se-vacancy case, the peak value of TS is located at -1.71 eV and 1.49 eV (C, C' in Fig. 5(b)). The electron transition probability is the greatest between these peaks, and then a large photoresponse appears at 3.2 eV, which is consistent with the blue line in Fig. 4. Similarly, the TS peaks at -1.43 eV and 1.87 eV (D, D' in Fig. 5(b)) result in the Rmax at the photon energy of 3.3 eV for the W-vacancy center region. The TS peak at -1.84 eV and 1.26 eV (E, E' in Fig. 5(c)) leads to the Rmax at the photon energy of 3.1 eV for the S-substituted center region. The TS peak at -1.53 eV and 1.27 eV (F, F' in Fig. 5(c)) leads to Rmax at the photon energy of 2.8 eV for the Te-substituted center region. The results show that the existence of defects can adjust the maximum photoresponse at different wavelengths because the impurities and intrinsic defect alter the absorption properties of WSe2. Frindt examined absorption bands produced in WSe2 crystals in an electron microscope [26]. Because of spin-orbit interaction, valence bands split, resulting in different transitions. The strong absorption bands are attributable to the formation of exciton states.
Fig. 5. The electron transition spectrum for the pure WSe2 and Ga-substituted (a), W- and Se-vacancy (b), S- and Te-substituted (c) center regions, respectively. The electron transitions between valence bands and conduction bands are indicated by dotted lines with arrows. “A, A', B, B', C, C', D, D', E, E', F, F'” denotes TS peaks.
According to the results in Fig. 3, the photoresponse depends on the polarization angle of incident light in the form of sin(2$\theta$), so a polarized photodetector can be developed and its sensitivity can be evaluated by ER, which can be written as ${R_{/{/}}}/{R_ \bot }$ (black line) or ${R_ \bot }/{R_{/{/}}}$ (red line), where R// and ${R_ \bot }$ are individually the magnitudes of the photoresponse in the transport direction when the polarization angle is 0°and 90°.
Figure 6 shows the variation of ER with photon energy for light detectors in six different central regions. In Fig. 6(a), there is a maximum ER value of 23.97 when the photon energy is 2.5 eV for the pure material. For the photodetectors with Se-vacancy (Fig. 6(b)), W-vacancy (Fig. 6(c)), Ga-substituted (Fig. 6(d)), Te-substituted (Fig. 6(e)) and S-substituted (Fig. 6(f)), the maximum ERs are 75.43 at 3.2 eV, 21.42 at 1.9 eV, 108.38 at 2.7 eV, 21.59 at 2.7 eV and 29.79 at 2.1 eV, respectively. Among them, the Ga substitution is the most prominent case, and the ER value is more than 157 times of that for the pure case at 2.7 eV. These results suggest that appropriate Ga-substituted defects can significantly enhance ER. Introduction of defects is a promising method to improve the polarization sensitivity of PGE-driven photodetectors.
Fig. 6. The variation of ER of the photoresponse with photon energy for six different central regions. (a) pure WSe2; (b) Se-vacancy; (c) W-vacancy; (d) Ga-substituted; (e) Te-substituted; (f) S-substituted. ${R_{/{/}}}/{R_ \bot }$ (black line) and ${R_ \bot }/{R_{/{/}}}$ (red line).
The photoresponse is also affected by the concentration of defects, which is the percentage of defect (vacancy or substitution) atoms in the number of atoms of the same kind. Uniform doping is selected as the research object here. For clear contrast, the pure case, i.e., defect concentrations of 0%, are depicted in black line. In addition, when the defect concentration is 7.7% (red line), 15.4% (blue line), 30.8% (magenta line) and 46.2% (green line). The continuous curve of Rmax with photon energy is also displayed in Fig. 7. For Se vacancy defects, the maximum photocurrent occurs when the photon energy is 2.1 eV and the defect concentration is 15.4%, with Rmax =2.23 (blue line in Fig. 7(a)). For W vacancy defects, the maximum photocurrent occurs when the photon energy is 2.7 eV and the defect concentration is 7.7%, Rmax =1.37 (red line in Fig. 7(b)). Figure 7(c) is the case that Ga substituted defects. When defect concentration is 30.8% and photon energy is 2.5 eV, Rmax is 0.55 as shown in the magenta line. Compared with the single Ga substituted in Fig. 3, the change of the Rmax is not obvious, indicating that the Ga substituted defect concentration does not have a great influence on the photocurrent. Figure 7(d) shows the S Substituted defects, in which Rmax is 5.46 in the blue line for photon energies of 3.1 eV with the concentration of the defect is 15.4%. For Te substituted defects, Rmax is 3.15 for photon energies of 3.3 eV with the concentrations of the defect is 7.7% as red line in Fig. 7(e). Obviously, S Substituted defect contribute more to the enhancement of photocurrent. Compared with the single atom defects in Fig. 3, Rmax of Se/W vacancy and S/Te substituted defects changes significantly, indicating that the Se/W vacancy and S/Te substituted defects concentration has a great influence on the photocurrent. By comparing Fig. 7(a) to Fig. 7(e), it can be seen that different concentration of defects can bring different effects under the same photo energy. There is no linear regularity between the defects concentration and Rmax. The defects concentration will change the material symmetry and thus affect the photoresponse. In these cases, S-substituted is more beneficial to photocurrent enhancement. Compared with Fig. 7(d), Rmax in Fig. 7(c) is greatly reduced because the symmetry of the structure is optimized.
Fig. 7. The photoresponse for defects at different concentrations. 0% (black line), 7.7% (red line), 15.4% (blue line), 30.8% (magenta line) and 46.2% (green line). (a) Se-vacancy; (b) W-vacancy; (c) Ga-substituted; (d) S-substituted; (e) Te-substituted.
In summary, the LPGE optical response was investigated by using a quantum transport simulation method in the WSe2 monolayer with six different central regions, which are Se-vacancy, W-vacancy, Ga-substituted, Te-substituted, S-substituted and pure WSe2. The results show that the photoresponse is related to the polarization angle in the form of sine function, and this is consistent with the previous finding [27]. In addition, appropriate vacancy defects and substitution defects can significantly enhance the photoresponse and ER. As compared to other defects, one S substituted has the largest photocurrent (1.67), but one Ga substituted has the largest ER value (180.38). As the defects concentration increases, the photoresponse is changed. For Se vacancy defects, Rmax = 2.23 when the photon energy is 2.1 eV and the defect concentration is 15.4%. For W vacancy defects, Rmax =1.37 when the photon energy is 2.7 eV and the defect concentration is 7.7%. For S substituted defects, Rmax = 5.46 for photon energies of 3.1 eV with the concentration of the defect is 15.4%. For Te substituted defects, Rmax = 3.15 for photon energies of 3.3 eV with the concentration of the defect is 7.7%. The Ga substituted defect concentration does not have a great influence on the photocurrent. Se/W vacancy and S/Te substituted defect concentration has a great influence on the photocurrent. Our results suggest an effective method to enhance the photoresponse by introducing vacancy defects and substitution defects, and prove that WSe2 monolayer is promising in photodetection.
Funding
National Natural Science Foundation of China (12264037); Natural Science Foundation of Inner Mongolia (2021MS03036); Fundamental Research Funds for Inner Mongolia University of Science & Technology.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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