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Abstract
The Raman peaks observed in the ultrafast-laser induced chalcogen-hyperdoped Si are assigned to different configurations of defects formed in crystal Si. The disappearance of the Raman peaks of the chalcogen-hyperdoped Si after thermal annealing is attributed to the formation of polymers, which cannot display any Raman peaks except the strong peak of crystal Si. The imaginary parts of the dielectric functions indicate that sub-bandgap absorptions are also reduced when the chalcogen atoms combine to form a polymer. The reductions of the sub-bandgap absorptions are different for S- and Se-hyperdoped Si, which can give a good explanation for their different variations of infrared absorptance at the same annealing conditions.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past years, chalcogen-hyperdoped silicon has attracted considerable attention owing to its unique optical and electrical properties, such as strong near-infrared absorption and responsivity [1–5]. The reason for this is that hyperdoping chalcogen (S, Se, Te) in silicon can introduce an impurity band in the silicon bandgap and then lead to the sub-bandgap absorption [6–9]. The properties of the chalcogen-hyperdoped silicon would make it a promising intermediate-band (IB) solar cells [10, 11] and infrared photodetectors. The hyperdoped materials are mainly prepared by pulsed laser (nanosecond, picosecond, and femtosecond) irradiation so far, e.g., ion implantation followed by pulsed laser melting, pulsed laser irradiation in a gas atmosphere, etc [3, 12, 13]. The hyperdoped process is a highly non-equilibrium process and the configurations of dopants would be metastable in silicon [6]. In this case, formation energy would not be the chief factor in determining the dopant configurations in Si.
From the theoretical researches, some metastable configurations of chalcogen atoms can produce impurity band in the bandgap and induce strong sub-bandgap absorption [6, 9, 14]. After annealing the chalcogen-hyperdoped Si materials, the sub-bandgap absorption is reduced to different extent for different chalcogen elements [15]. Especially for the S-hyperdoped one, the sub-bandgap absorption almost disappeared after thermal annealing [15]. Concerning with this phenomenon, Tull et al. proposed a diffusion mechanism, which indicates that the deactivation of the sub-bandgap absorption may be caused by the precipitation of dopants [16]. While Shao et al. contended that the reduction of the sub-bandgap absorption is due to the structural transformations: from the higher energy ones to the lower ones [6, 14]. Anyway, the atomic condition of the dopant in Si is significant for the properties of hyperdoped materials. Therefore, exploring the main dopant configurations in Si and investigating their transformations after thermal annealing is the keys to understand the mechanisms of the sub-bandgap absorption of the materials, and then get the optimization schemes of their photoelectric transformation efficiency.
In this work, we explore in-depth the dopant configurations in the chalcogen-hyperdoped Si by first-principles calculations of their Raman spectra. We try to determine the dominant configurations and their transformations after thermal annealing by comparing the calculational Raman spectra and optical properties with experimental ones. Different from the previous viewpoint which assigned the Raman peaks of the chalcogen-hyperdoped Si to the polymorphic of Si [17], we assign the emerging Raman peaks of the material to different configurations of defects formed by pulsed laser irradiation. Based on this standpoint, we can get the main configurations of defects in silicon and give a reasonable interpretation for the variation of the Raman spectra and the sub-bandgap absorption of the material before and after thermal annealing.
2. Computational methods
All of the hyperdoped configurations are constructed in the 2 × 2 × 2 supercell of the conventional Si8 cubic unit cell. The calculations are performed by the density function theory (DFT) method in the CASTEP code of Materials Studio [18–20]. The CA-PZ functional in the framework of local-density approximation (LDA) is used to take into account the exchange-correlation potentials [21, 22], which can obtain more accurate results of Raman spectra compared with the generalized gradient approximation (GGA) method. The norm-conserving pseudo-potential calculations are used to represent the core electrons [23]. The cut-off energy of the plane-wave expansion is 650 eV for the configurations of S, and 400 eV for the configurations of Se, and 350 eV for pure Si. The geometry optimizations are performed by the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) algorithm [24]. The convergence condition to optimize the electronic structure is set at a maximum total energy change value of 1 × 10−6 eV/atom. The configurations are converged by setting the value of the total energy equal to 1 × 10−5 eV/atom, the maximum force equal to 0.03 eV/Å, the maximum stress equal to 0.05 GPa, and the displacement equal to 0.001 Å. All bands/EDFT method of the electronic minimization is used for the SCF calculation.
The optical properties of the configurations are investigated from the imaginary parts of the dielectric functions, which can be obtained from the momentum matrix elements between the occupied and unoccupied wave functions with selection rules [25,26]. The formation energies of the dopants in Si are obtained by using the Eq.
where Et(Compound) is the total energy of the configuration, E(Si) and E(D) are the chemical potentials of one Si and one dopant in their corresponding supercell, respectively, n and m are numbers of Si and dopant in the hyperdoped supercells. For the S-hyperdoped configurations, E(D) is derived from the orthorhombic (α) phase of S, which is the most stable phase for the element: E(D) = E(S128)/128 [8]; while for the Se-hyperdoped configurations, E(D) is derived from the trigonal (γ) phase of Se, which is also the stable phase at normal conditions: E(D) = E(Se3)/3 [8,27].3. Results and discussion
We construct several probable configurations of defects formed in Si, such as vacancy, self-interstitial Si atoms, substitutional dopant atoms, interstitial dopant atoms, quasi-substitutional dopant atoms (combination of the self-interstitial Si and the substitutional dopant), et al. For the interstitial configurations, we first construct several typical sites for the dopants, such as bond-center, hexagonal, and tetrahedral sites. Nevertheless, we find that the hexagonal and tetrahedral configurations for the chalcogen atoms are not stable in Si and would be easily transformed into the bond-center one, which is the most stable configurations in Si besides the substitutional one [6]. Therefore, we mainly consider the bond-center interstitial configurations in this work. Some probable configurations of defects in the S-hyperdoped Si material are constructed and optimized, as shown in Fig. 1. Figure 1(a) shows the self-interstitial configuration of Si, which contains interstitial Si atom at the bond-center site of two nearest Si atoms. Figure 1(b) shows a vacancy (white ball), which is constructed by deleting a Si atoms. Figure 1(c) shows a quasi-substitutional configuration of S, which contains a self-interstitial Si atom and a substitutional S atom. Figures 1(d) and 1(e) show the bond-center interstitial and substitutional configurations of S, respectively. The configurations of Se are similar to those of S, except some differences in bond-lengths and bond-angles. To get a better comparison between the calculational and experimental Raman spectra, we provide the experimental Raman spectra of the sulfur-hyperdoped Si and pure Si in Fig. 1(f), which have been reported in our previous work [28]. To comprehensively investigate the Raman spectra of the material, the experimental Raman spectra from 100 to 200 cm−1 are also given in this work, which are not provided in our previous report [28].
Fig. 1 Configurations of defects in Si after geometry optimization: (a) self-interstitial Si defect; (b) vacancy; (c) quasi-substitutional configuration of chalcogen in Si; (d) bond-center interstitial configuration of chalcogen in Si; (e) substitutional configuration of chalcogen in Si. (f) Experimental Raman spectra of the sulfur-hyperdoped Si (dash-dot) and pure Si (solid) [28]. Blue, yellow, and white balls represent the Si, chalcogen (sulfur), and vacancy, respectively.
From our previous experimental studies, the Raman peaks of the S-hyperdoped Si appear at around 356, 388, 401, 448 cm−1 [28], as well as the peak of the diamond cubic phase of Si at 519 cm−1 [17]. These Raman peaks of the laser-induced S-hyperdoped Si were also reported by Smith et al., although there are some tiny shifts in the wavenumbers of the peaks [17]. The Se-hyperdoped Si exhibits the similar Raman spectrum to the S-hyperdoped one [17]. These Raman peaks are previously assigned to the polymorphic crystal structures formed in Si, which are induced by the collision of pressure waves from multiple valleys [17, 28]. Nevertheless, we think that the origin of the Raman peaks needs more discussions, because the NF3-prepared (N-hyperdoped) silicon under the same laser conditions does not display any Raman peaks, although the microstructures are similar to those of the SF6-prepared (S-hyperdoped) ones [28]. Based on our present calculational work, the emerging Raman peaks should be assigned to the defects formed by pulsed laser irradition, because the positions of these Raman peaks are matched well with the calculational results of different configurations of defects in Si and we can give a reasonable interpretation for the variations of the Raman spectra and sub-bandgap absorptions before and after thermal annealing based on the perspective.
Figure 2 shows the calculational Raman spectra of the intrinsic defects of Si, such as vacancy and self-interstitial Si. For calibration, the Raman spectrum of the perfect diamond cubic structure is also shown in the figure. The perfect crystal structure of Si shows a strong Raman peak at 524 cm−1, which agrees well with the experimental result. For the self-interstitial Si defect, besides the strong Raman Peak of the diamond crystal structure at 515 cm−1, other small peaks appear at 435, 397, 371 cm−1, which shift to low-frequencies compared with the experimental results (448, 401, 388 cm−1). For the vacancy in Si, a strong Raman peak is observed at 354 cm−1, which matches well with the experimental value (356 cm−1). Besides these peaks which are matched well with the experimental results, there are also some peaks appear from 50 to 300 cm−1 for the two types of defects and the other dopant defects. It should be that the combination of the Raman peaks in this range of wavenumbers forms the broad Raman bands which are assigned to amorphous Si in experiment [17].
Fig. 2 Calculational Raman spectra of self-interstitial Si (short-dash), vacancy (dash-dot), and diamond crystal structure of Si (solid) in the 2 × 2 × 2 supercell.
Then, the Raman spectra displayed by the dopant defects are shown in Fig. 3. Figure 3(a) shows the Raman spectra of three types configurations of S. Among them, the substitutional configuration of S which has the lowest formation energy displays several Raman peaks at 327, 400, and 458 cm−1, as well as the diamond crystal Raman peak at 518 cm−1. The Raman peak at 400 cm−1 is especially strong and is comparatively consistent with the experiment result (401 cm−1) [28]. For the quasi-substitutional configuration of S, two strong Raman peaks are observed at 396 and 514 cm−1. The bond-center interstitial configuration of S shows one strong peak assigned to diamond crystal Si at 516 cm−1 and one weak peak at 451 cm−1. The Raman spectra of the Se defects are same to those of S defects with the same configurations, as shown in Fig. 3(b). The calculational results are in good agreement with the experimental measurements that the S- and Se hyperdoped Si exhibit same Raman spectra [17]. By contrast with the experimental results, it seems that the Raman peak at around 401 cm−1 is mainly contributed by the substitutional and quasi-substitutional configuration. Nevertheless, according to Shao et al.'s fist-principles calculational studies, the substitutional chalcogen atoms should not be the dominant configuration in Si and they are not likely to be the origin of the sub-bandgap absorption of the material, although they can lead to the sub-bandgap absorption [6]. The reason is that the substitutional site is the most stable configuration in Si, but the sub-gap absorption of the material can still be significantly affected by thermal annealing. Our calculational results also support this opinion, because the experimental Raman peak intensity at 401 cm−1 is not especially strong compared with other peaks (it is weaker than the peak at 356 cm−1 and comparable to the peak at 448 cm−1), and the substitutional configuration can also exhibit a strong Raman peak at around 325 cm−1 which cannot be observed in experiment. Consequently, we believe that the Raman peak at 401 cm−1 should be mainly assigned to the quasi-substitutional configuration. It is easy to understand: the intense interaction between pulsed-laser and silicon would generate a mixture of various defects, such as the combination of the substitutional chalcogen and self-interstitial Si which is called quasi-substitutional configuration [6]. Therefore, the simple self-interstitial Si without the substitutional chalcogen is also considered to be inexistent. The Raman peak at 448 cm−1 should be assigned to the bond-center interstitial configuration.
Fig. 3 (a) Calculational Raman spectra of quasi-substitutional (solid), bond-center interstitial (dash), and substitutional (dash-dot) configurations of S in Si. (b) Calculational Raman spectra of quasi-substitutional (solid), bond-center interstitial (dash), and substitutional (dash-dot) configurations of Se in Si.
In addition, the experimental researches show that the Raman peaks disappear after thermal annealing [17]. Besides, the annealing-induced reductions of the sub-bandgap absorptions are different for the S- and Se-hyperdoped Si [15]. Tull and Shao have provided two possible explanations for the annealing-induced reduction mechanism of the material as mentioned above [6, 16]. From Fig. 3, we can speculate that the bond-center interstitial site of chalcogen should not be the final configuration after thermal annealing even if it is the most stable configuration besides the substitutional one, because the Raman peak at 458 cm-1, which is assigned to this configuration disappears after thermal annealing. Considering the diffusion of chalcogen in Si, we calculate the Raman spectra of the polymers (dimers and trimers) of the chalcogen atoms in this work, and the results are shown in Fig. 4. For the dimers of chalcogen, we mainly consider two types of configurations: substitutional-interstitial (S-BI) and interstitial-interstitial (BI-BI) dimers. In addition, two types of trimers (S-BI-S and BI-BI-S) are constructed in this work. As with the single chalcogen-doped configurations, the S and Se polymers exhibit almost the same Raman spectra for the same configuration. The calculational Raman spectra indicate that the S-BI dimer and the S-BI-S-trimer cannot show any Raman peaks except the strong peak of crystal Si, which is consistent with the experimental results of the annealed chalcogen-hyperdoped Si [17]. But for the BI-BI-dimer and BI-BI-S-trimer, some small peaks can be observed besides the peak of crystal Si.
Fig. 4 (a) Four polymer configurations of chalcogen (sulfur) in Si after geometry optimization, blue and yellow balls represent the Si and chalcogen (sulfur), respectively. (b) Calculational Raman spectra of the polymer configurations of S and (c) Se.
The formation energies of the paired-configurations with nearest (dimer) and longest atomic distance are calculated by using Eq. (1) and the results are shown in Table 1. The results indicate that the S-BI-dimer is more stable than the BI-BI-dimer for both S- and Se-hyperdoped Si. Especially for the S-hyperdoped Si, the substitutional and interstitial atoms tend to gather together to form a dimer but the two interstitial ones tend to separate from each other in the equilibrium process. Based on the results, the S-BI-dimer would be most likely to be formed after thermal annealing. Combined with the formation energies and the calculational Raman spectra of these configurations, we conclude that the isolate dopants would diffuse and stick together to form polymers which cannot display any Raman peaks after annealing the material. Although the trimers are also constructed in this work, the presence of them and the larger polymers should be researched further, because the clusters have not been confirmed by experiment so far.
Table 1. Formation energies of the paired-configurations for the S- and Se-hyperdoped Si. The superscripts letters D and S represent the dimer and the configuration with separate dopants, respectively.
To further determine the situation of the defects in Si before and after thermal annealing and the mechanisms of the annealing-induced reductions of the sub-bandgap absorption for S- and Se-hyperdoped Si, the optical properties of these configurations are provided, as shown in Fig. 5. For the intrinsic defects, both the vacancy and self-interstitial Si can lead to the sub-bandgap absorption, and the vacancy displays a relatively high absorption. For the S-hyperdoped Si, as reported previously [6], the quasi-substitutional configuration can lead to the sub-bandgap absorption while the bond-center interstitial configuration cannot. The polymers of S in Si exhibit similar optical properties to the bond-center one, which make no contribution to the sub-bandgap absorption. The Se-hyperdoped Si shows similar optical properties for the single-Se-doped configurations. Nevertheless, different from the S-hyperdoped Si, the sub-bandgap absorptions produced by the Se polymers are stronger than that of the bond-center configuration, but weaker than that of quasi-substitutional one. Combined with the formation energies and the calculational Raman spectra of these configurations, we can give a reasonable interpretation for the variations of the Raman spectra and optical properties before and after thermal annealing. The calculational Raman spectra indicate that some defects such as vacancy, quasi-substitutional configuration, and bond-center interstitial configuration exist in the laser-induced chalcogen-hyperdoped Si. All of these defects except the bond-center dopant can lead to the sub-bandgap absorption. After annealing the material, the isolate dopants would diffuse in Si and stick together to form polymers, which cannot display any Raman peaks. Among the polymers, the S-BI-dimer would be the most likely configurations. For the S-hyperdoped Si, all the dimers and trimers cannot bring any sub-bandgap absorptions. Unlike the S-hyperdoped Si, the dimers and trimers of Se can bring sub-bandgap absorptions, although they are weaker than that of quasi-substitutional configuration and vacancy. That may be the reason that the sub-bandgap absorption of S-hyperdoped Si is reduced sharply while the Se-hyperdoped Si can also keep a good absorption after thermal annealing. In addition, the different diffusivity of chalcogen should be also one of the reasons for their different reductions of infrared absorption, as reported by Tull et al [16].
Fig. 5 Imaginary parts of the dielectric functions calculated for the pure Si, self-interstitial Si configuration, and vacancy (a); configurations of S-hyperdoped Si (b); configurations of Se-hyperdoped Si (c).
4. Conclusion
In this work, we propose a new perspective for the origin of the Raman peaks observed in the pulsed-laser-induced chalcogen-hyperdoped Si material. We assign these Raman peaks to different configurations of defects formed in Si, e.g., the peak appears at 356 cm−1 is assigned to the vacancies in Si; the peak at 401 cm−1 is assigned to the quasi-substitutional configuration of chalcogen (combination of self-interstitial Si and substitutional chalcogen); the peak at 448 cm−1 should be assigned to the bond-center interstitial configuration of chalcogen. As the isolate dopants combine together to form a polymer, the obvious Raman peaks disappear. Especially for the S-BI dimer and the S-BI-S trimer, their Raman spectra are consistent with the experimental results of the material after thermal annealing. In addition, the sub-bandgap absorption is also reduced when the chalcogen atoms combine to form a polymer, but the reductions are different for S- and Se-hyperdoped Si. Based on these calculational results, we conclude that the variations of the Raman spectra and optical absorptance after thermal annealing should be attributed to the reduction of vacancies and the formation of polymers. Our calculational work provides a deeper understanding of the pulsed-laser-induced chalcogen-hyperdoped Si material, and would give a theoretical guidance for the optimization of the photoelectric properties of the material.
Funding
National Natural Science Foundation of China (NSFC) (11747070, 11747078, 11747082); Key Scientific and Technological Program of Henan Province (182102210365); Youth Scientific Funds of Henan Normal University (2016QK05).
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