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We have studied the optical properties of Sc-hyperdoped crystalline silicon based on quantum calculations. We have designed several probable configurations and found that the interstitial atomic positions of Sc (ScI, ScSI, ScTI, ScHI) are stable in the silicon matrix and can largely extend the absorption range of silicon from visible to infrared. The sub-band gap light absorption is attributed to the change of band structures of silicon and its intensity depends on the atomic concentration of Sc in silicon. The special effect of Sc on the properties of silicon will extend the sensitivity of silicon-based photodetectors to near infrared wavelength range.
© 2016 Optical Society of America
1. Introduction
Silicon is the most widely used material in photovoltaic devices due to its good quality and low cost. However, silicon-based photodetectors cannot detect wavelengths longer than 1.1 μm due to the existence of the band gap (1.07 eV) of bulk silicon [1]. Some wavelengths, such as 1330 nm and 1550 nm, are very important telecommunications wavelengths [1]. Therefore, how to expand the detection range of silicon has aroused great interests in photovoltaic field [1–7].
In recent years, hyperdoped semiconductors have been proposed constantly. Mazur et al. have developed the chalcogen-hyperdoped silicon materials and found that the materials have strong absorptance from 250 nm to 2500 nm and can generate responsivity in the near infrared wavelength range [1,8–10]. Sánchez et al. have studied the Ti-hyperdoped silicon in detail through first-principles calculations and found that the interstitial configurations of Ti can introduce an intermediate band (IB) in silicon band gap and lead to the sub-band gap absorption [4]. Zhuang et al. have found that hyperdoping nitrogen in silicon can lead to a strong absorptance in the mid-infrared wavelength range of 2.5-17 μm [6,7]. The design principles for these hyperdoped silicon material are derived from the intermediate band solar cell (IBSC) theory which was proposed by Luque and Martí [11]. If the hyperdoped impurities can form an IB in silicon band gap, electrons can be promoted from valence band (VB) to conduction band (CB) in a two-step process by absorbing photons with energies below the silicon band gap [4,12,13]. Many experimental data and theoretical analysis indicate that the wavelength range and intensity of the sub-band gap absorption depend on the dopant type and concentration [3,6–10,14–18]. Therefore, theoretically, the response range of the silicon-based detectors could be modulated by choosing specific dopant and controlling the doping concentration.
In our present work, we try to explore other deep level impurities doped in silicon through first-principles calculations and found that the hyperdoped Sc can change the electronic band structures of bulk-silicon and expand its absorption from the visible to infrared. We have constructed different configurations, such as substitutional, bond-center interstitial, split interstitial, tetrahedral interstitial, and hexagonal interstitial compositions, and studied their formation energies, optical properties, and band structures in detail to confirm its potential application in silicon-based infrared photodetectors.
2. Method
The calculations are performed by Density-functional theory (DFT) within the generalized gradient approximation (GGA) with the Perdew, Burke, and Ernzerhof (PBE) parametrization in the Cambridge Sequential Total Egergy Package (CASTEP) module of Materials Studio (MS). By this calculation, the band gap width of pure silicon is 0.64 eV, which is underestimated compared to the experimental value, but it does not influence the conclusions of our research. Before the calculation of energy, geometry optimizations are carried out by the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) algorithm. After relaxation, the lattice parameter of the 1 × 1 × 1 bulk silicon is about 5.48 Å, slightly longer than the experimental value (5.43 Å), which agrees with the tendency of GGA calculations [4].
3. Results and discussion
We firstly constructed several typical atomic configurations of the Sc-doped bulk silicon in this work and the models are shown in Fig. 1. Among these configurations, the substitutional position is unique and is denoted as ScS. Four different interstitial positions for single Sc atom are constructed: at the plane that bisects Si-Si bond, denoted as ScI; at the split <110> position, denoted as ScSI; at the geometric center of a tetrahedron formed by four silicon atoms, denoted as ScTI; at the geometric center of a hexagonal ring formed by six silicon atoms, denoted as ScHI. The formation energies of these configurations are calculated by
where E[ScSin], E[Sin], and E[Sc2] represent the total energies of the compound, bulk silicon, and common hcp crystalline structure of Sc made up of two atoms, respectively.
Fig. 1 Four typical atomic configurations of Sc-doped bulk Si with a Sc atom situated at (a) substitutional position, (b) bond-center interstitial position,(c) split <110> position,(d) tetrahedral interstitial position, and (e) hexagonal interstitial position, respectively. These configurations are denoted as ScS, ScI, ScSI, ScTI, and ScHI, respectively.
Our calculations indicate that for an isolate Sc atom, the substitutional position has the highest formation energy among these configurations and the value is −0.035 eV. As for the four kinds of interstitial configurations, their formation energies are roughly the same and the value is −0.56 eV. The results indicate that the substitutional configuration are not stable in silicon lattice and can be discounted in the equilibrium state due to its higher energy compared with other configurations. Owing to the similar formation energy, the proportion of these interstitial structures should be similar. From previous reports, due to the presence of impurity atoms in silicon lattice, there may arise some more complex configurations, such as the quasi-substitutional configurations which contain a substitutional impurity atom and a self-interstitial Si atom [16]. We calculate the formation energies of these structures in 2 × 2 × 2 supercell by the same equation described above. The calculational results indicate that all of the quasi-substitutional configurations have the positive formation energy, which implies that these structures are not stable in silicon and can be discounted. Therefore, the substitutional and quasi-substitutional configurations will not be discussed further in this work and we will focus our discussion on the four interstitial configurations (ScI, ScSI, ScTI, ScHI) in the following.
Then, the optical properties of the four interstitial configurations in 2 × 2 × 2 supercell are investigated and compared to that of bulk-silicon by calculating their dielectric functions and optical absorption coefficients in Fig. 2. The dielectric functional curves show that a strong peak appears centered at around 3.5 eV for all of these configurations and bulk-silicon. Obviously, the strong peak is assigned to the contribution of host material, that is, electrons are promoted directly from VB to CB. For the four interstitial configurations (ScI, ScSI, ScTI, ScHI), another low frequency peak appears centered at around 0.5 eV and is approximately 1 eV wide. In addition, the dielectric functional curves of the four interstitial configurations are almost coincide with each other, which suggests that the four interstitial configurations have the same optical properties. While for the bulk-silicon, the dielectric functional value at low frequencies tends to zero, which is due to the existence of the band gap of bulk-silicon.
Fig. 2 Dielectric function (imaginary part) (a) and absorption (b) of bulk silicon, bond-center interstitial configuration (ScI), split <110> position (ScSI), tetrahedral interstitial configuration (ScTI), and hexagonal interstitial configuration (ScHI) in 2 × 2 × 2 supercell.
The optical absorption coefficients of these configurations are also shown in Fig. 2(b) together with that of bulk silicon. The results indicate that a broad sub-band gap absorption band from 0.2 to 1.5 eV appears for all of the four interstitial configurations and their absorption curves are almost coincide with each other, which is in accordance with the dielectric functional results. Therefore, it is not difficult to get the conclusion that the low frequency peaks of these curves in these configurations should be associated with the existence of Sc in silicon lattice. Some of the positions of Sc in silicon may change the electronic band structure of bulk silicon and thus influence its optical properties.
In order to explore the causes leading to the sub-band gap absorption, we calculated the electronic band structures of these interstitial configurations and the results are shown in Fig. 3. The results indicate that, for the four interstitial configurations, all of them can form an impurity band in the silicon band gap and the impurity band is crossed by the Fermi energy. Due to the high atomic concentration of Sc (1.5 at.%), the impurity band formed by the interstitial Sc atom overlaps with the conduction band (CB). The electronic band structures of these configurations are all very similar, which is the reason why these interstitial configurations have similar optical properties. For the configurations of ScI, ScSI, ScTI, and ScHI, the valance band maximum (VBM) are separated from the Fermi level by 0.543, 0.553, 0.552, and 0.54eV, respectively, lower than the band gap of pure silicon. Therefore, the sub-band gap absorption of the compound should be due to the introduction of impurity band which decreases the transition energy minimum of electrons. Owing to the similar optical properties and band structures of these interstitial configurations, we will discuss one of these compounds in lower atomic concentrations of Sc in the following to observe the changes of the optical properties.
Fig. 3 Electronic band structures of the bond-center interstitial configuration (ScI) (a), split interstitial configuration (ScSI) (b), tetrahedral interstitial configuration (ScTI) (c), and hexagonal interstitial configuration (ScHI) (d) in 2 × 2 × 2 supercell.
We studied the optical properties of the bond-center interstitial configuration of ScI in 2 × 2 × 3, 2 × 3 × 3, and 3 × 3 × 3 silicon supercells, and compared them to that of the 2 × 2 × 2 one. The impurity atomic concentrations for these supercells are 1 at.%, 0.69 at.%, and 0.46 at.%, respectively. Figures 4(a) and 4(b) give the dielectric function and absorption of the models, respectively. From the dielectric function curves we find that the low-frequency peak increases firstly and then decreases sharply as the supercell grow in size. For the 2 × 3 × 3 supercell, the low-frequency peak is especially strong compared to the other supercells. While for the 3 × 3 × 3 supercell, the dielectric function value at low-frequency tending to zero. The absorption coefficients of these configurations give the same results to the dielectric functional analysis: the 2 × 3 × 3 supercell offers the highest sub-band gap absorption; while for the 3 × 3 × 3 supercell, the sub-band gap absorption band disappears. The results indicate that the sub-band gap absorption of the bond-center interstitial configuration is not only result from the existence of Sc, but also relevant to the concentration of Sc. The best atomic concentration for the bond-center interstitial position of Sc is 0.69 at.%, which offers the highest sub-band gap absorption of the material. However, at a lower concentration of 0.46 at.%, the sub-band gap absorption disappears. Considering the lowest formation energy of the interstitial configurations, we conclude that the sub-band gap of absorption of the compound would maintain stability after thermal annealing.
Fig. 4 Dielectric function (imaginary part) (a) and optical absorption coefficient (b) of the bond-center interstitial configuration of ScI in 2 × 2 × 2, 2 × 2 × 3, 2 × 3 × 3, and 3 × 3 × 3 silicon supercells.
4. Conclusion
In summary, Sc in silicon play an important role in the optical properties of silicon. Especially for the interstitial configurations of Sc, they are more stable in silicon than the substitutional and quasi-substitutional ones and can lead to the sub-band gap absorption. The electronic band structural studies indicate that the sub-band gap absorption is attributed to introduction of impurity band in silicon band gap. By computing the optical properties of the bond-center interstitial configuration in different supercells, we find that the Sc atomic concentration of 0.69 at.% can largely enhance the sub-band gap absorption. The special effect of Sc on the properties of silicon will make the material having potential application in silicon-based infrared photodetectors, and our work will have some guidance to the experiment .
Funding
PhD Early Development Program of Henan Normal University (qd14207); Key Research Program of Henan Province Office of Education (15A140007, 15A140008); Cutting-edge Technology Research Program of Henan Province (122300410230).
References and links
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