Analysis and Calculation of Electronic Properties and Light Absorption

Article pubs.acs.org/JPCA

Analysis and Calculation of Electronic Properties and Light Absorption of Defective Sulfur-Doped Silicon and Theoretical Photoelectric Conversion Efficiency He Jiang and Changshui Chen* Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices and MOE Key Laboratory of Laser Life Science & Institute of Laser Life Science, South China Normal University, Guangzhou 510631, Guangdong, China ABSTRACT: Most material properties can be traced to electronic structures. Black silicon produced from SF6 or sulfur powder via irradiation with femtosecond laser pulses displays decreased infrared absorption after annealing, with almost no corresponding change in visible light absorption. The high-intensity laser pulses destroy the original crystal structure, and the doping element changes the material performance. In this work, the structural and electronic properties of several sulfur-doped silicon systems are investigated using first principle calculations. Depending on the sulfur concentration (level of doping) and the behavior of the sulfur atoms in the silicon lattice, different states or an absence of states are exhibited, compared with the undoped system. Moreover, the visible-infrared light absorption intensities are structure specific. The results of our theoretical calculations show that the conversion efficiency of sulfur-doped silicon solar cells depends on the sulfur concentrations. Additionally, two types of defect configurations exhibit light absorption characteristics that differ from the other configurations. These two structures produce a rapid increase in the theoretical photoelectric conversion efficiency in the range of the specific chemical potential studied. By controlling the positions of the atomic sulfur and the sulfur concentration in the preparation process, an efficient photovoltaic (PV) material may be obtainable. of surface, termed “black silicon”, has an improved light trapping performance and visually appears black. Subsequently, more manufacturing methods were reported, including reactive ion beam etching, metal-assisted etching, and electrochemical corrosion.5−7 Some studies found that the fabricated materials exhibited unique optical properties, including near-unity absorption in the near-infrared (1100−2500 nm).8−10 Recently, people have begun to study the performance of crystalline silicon supersaturated with sulfur as well as the influence of new doping elements, such as selenium and tellurium, on silicon.11−13 It has been well-established that chalcogen-hyperdoped (S, Se, and Te) silicon can induce an insulator−metal transition and has therefore been proposed to produce an intermediate-band in the silicon band gap.11,14−17 Nevertheless, the hyperdoping-induced changes lead to enhanced infrared absorption, and the effect of chalcogens in silicon requires further research and additional theoretical study. It also has been suggested that chalcogen-doped silicon could be used as a PV material because exhibits strong subband gap infrared absorption.18−21 However, most research has been focused on practical applications of black silicon solar cells, and although some new preparation methods that have resulted in significant progress have been proposed,22−26 the actual photoelectric conversion efficiencies still need to be

I. INTRODUCTION Silicon is the most important semiconductor material in modern industry and is widely used in electronic devices, photodetectors, photodiodes, and solar panel manufacturing.1 Silicon exists in the Earth’s crust in the form of compounds, with an abundance second only to oxygen. These abundant reserves make it the preferred material for the construction of solar cells; however, many shortcomings limit the applicability of silicon in the field of solar cells. For example, bands of sunlight exceeding 1100 nm cannot be absorbed by intrinsic silicon because of its wide band gap. Thus, many approaches have been developed to improve the light absorption characteristics and photoelectric conversion efficiencies of silicon-based solar cells. In 1997, Lupue and Martı ́ introduced a model for intermediate-band solar cells with a theoretical efficiency of 63.1%, which was based on the principle of detailed balance.2 Several methods can be used to fabricate this type of cell, such as the quantum size effect and the multiple quantum wells method.3 The simplest method that can be used to obtain an intermediate-band solar cell involves doping the material with another element so that the impurity levels will form in the forbidden band. One year after the introduction of Lupue and Martı ́’s model, a research group led by Professor Eric Mazur from Harvard University prepared new microstructures using femtosecond lasers to irradiate crystalline− silicon surfaces in the presence of sulfur-bearing gas.4 The surfaces of such silicon microstructures exhibit arrays of sharp conical spikes with a height of approximately 40 μm. This type © 2015 American Chemical Society

Received: November 27, 2014 Revised: March 18, 2015 Published: March 23, 2015 3753

DOI: 10.1021/jp511852w J. Phys. Chem. A 2015, 119, 3753−3761

Article

The Journal of Physical Chemistry A

Figure 1. Different positions of sulfur atoms in the silicon lattice (Si ⟨110⟩ plane). (a) SSi215: isolated sulfur atom located at a substitutional site. (b) S2Si214: two sulfur atoms located at nearest-neighbor substitutional sites. (c) SI−USi216 and (d) SI−USi108: sulfur atoms located at interstitial-unbonded sites. (e) SI‑2BSi216, (f) SI‑3BSi216, (g) SI‑4BSi216, (h) SI‑6BSi216, and (i) SI−ISi108: sulfur atoms located at interstitial-bonded sites. The gray and yellow spheres represent silicon and sulfur atoms, respectively.

simultaneously describe the exchange and correlation potentials. Norm-conserving pseudopotentials35 were employed for the calculation of optical properties. Calculations of the band structure and the density of states were performed with the Becke 3-parameter Lee−Yang−Parr (B3LYP)36−39 functional using the norm-conserving pseudopotential method. A planewave energy cutoff of 250 eV was employed for the calculation of the atomic relaxation, and a cutoff of 500 eV was used to investigate the electronic and optical properties. The total energy converged to 5 × 10−7 eV/atom in the self-consistent calculation. The energy change, maximum force, maximum stress, and maximum displacement tolerances were set to 5 × 10−6 eV/atom, 0.01 eV/Å, 0.02 GPa and 5 × 10−4 Å, respectively. The models consisted of a 3 × 3 × 3 supercell (216 atoms) that corresponded to the conventional cubic cell of bulk silicon. For the sampling of the Brillouin zone (BZ), the atomic relaxation and electronic properties and the optical properties were calculated using 3 × 3 × 3 and 5 × 5 × 5 kpoint grids, respectively, which were generated according to the Monkhorst−Pack40 scheme. The following equation was employed to calculate the formation energies41 of each model:

further improved. Additionally, the analyses carried out in previous studies have focused only on the origin of the infrared absorption enhancement. As a result, more theoretical calculations are required to determine to what extent this material can contribute to increasing the efficiency of solar cells as well as the best configuration to achieve this goal. In this work, density functional theory (DFT)27,28 was used to simulate and analyze three types of defect structures in sulfur-hyperdoped (exceeding 1020 cm−3) crystalline silicon, in which the sulfur atoms occupy substitutional, interstitialunbonded, and interstitial-bonded positions in the lattice. Following the structural optimization process, the electronic properties and light-absorption characteristics of these systems were investigated. We find that the dopants can form an intermediate band of structure-dependent electronic states within the silicon band gap and that a strong below-band gap absorption appears. Furthermore, by comparing the theoretical limiting conversion efficiencies of the different defect configurations, we have discovered structures with high conversion efficiencies that have never been previously reported. In Section II, the methods and geometrically optimized structures are presented. The results and a discussion regarding the electronic and light absorption properties of these systems are contained in Section III, in addition to a calculation of the conversion efficiency of a solar cell based on the obtained absorptivities. Finally, the conclusions are presented in Section IV.

⎡⎛ ⎤ E (N ) ⎞ εf = lim ⎢⎜E(N ± 1) ∓ 0 ⎟ − E 0 (N )⎥ N →∞⎣⎝ N ⎠ ⎦

(1)

where E0(N) is the ground state energy at ideal positions and N is the number of atoms in the crystal (N = 216 was used in this work), E(N ± 1) is the energy of a crystal with one atom more/ fewer than the ideal crystal. Ignoring the effects of temperature and pressure, we have calculated a formation energy of 3.63 eV for a structure that contains a vacancy in the silicon crystal. This value is similar to that reported in previous experimental studies.42 Different positions of the sulfur atom in a silicon lattice (Si ⟨110⟩ plane) are shown in Figure 1. The identifiers, sulfur concentrations, and the formation energies of each model are listed in Table 1. All of the models strictly adhere to valencebond theory so that Si and S can form no more than four and six bonds, respectively. Sulfur concentrations of 0.5 (ca. 2.3 × 1020 cm−3), 0.9, 3, 6, and 9% sulfur atoms were introduced at substitutional sites in silicon, and these cases are denoted as SSi215, S2Si214, S6Si210, S12Si204, and S18Si198, respectively. On the

II. METHODS AND MODELS The influence of the interatomic distance on the performance of materials, such as the calculation of energy gaps and the Mott transition, has been discussed in previous studies.29,30 The introduction of sulfur atoms into the silicon crystal lattice necessarily results in changes in the atomic distances and lattice structure. Additionally, the effects due to this type of modification become enhanced as the sulfur concentration is increased. In this work, we have used a first-principle calculation within DFT to explore these changes by employing the CASTEP ab initio total energy program.31 For the structural optimization process, the generalized gradient approximation (GGA)32 in the Perdew, Burke, and Ernzerhof (PBE)33 scheme with ultrasoft pseudopotentials34 was used to 3754


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concentration is 0.9% due to the interaction between two sulfur atoms (see Figure 1d). In this case, we find that the Si−Si bond exhibits several different lengths in the vicinity of the sulfur atoms, with a maximum length of 3.47 Å, thus indicating that the bond is more prone to rupture. The models in which a single sulfur atom could occupy two-, three-, four-, and 6-fold coordinated interstitial positions in the silicon lattice are denoted as SI‑2BSi216, SI‑3BSi216, SI‑4BSi216, and SI‑6BSi216, respectively, and the corresponding structures are displayed in Figure 1 (panels e, f, g, and h). A Si−S−Si buckling angle of 122.4° was found for SI‑2BSi216, which is smaller than the Si− O−Si buckling angle in silica (143.6°). This result can be attributed to sulfur having a larger number of extranuclear electrons compared to oxygen. In the structure shown in Figure 1g, the sulfur atom lies at the same position as shown in Figure 1c. The only difference is in the four bonds the sulfur forms with the nearby silicon atoms. This bond formation is relatively difficult because the formation energy of SI‑4BSi216 is higher than that of SI−USi216. An unsaturated bond exists in the SI‑3BSi216 system; therefore, some of the electrons are in a metastable state. We thus conclude that this structure could transform between SSi215 and SI‑2BSi216 under certain conditions. Another two-sulfur-atom configuration, SI−ISi108, is shown in Figure 1i. This system contains no unsaturated bonds and exhibits one of the longest Si−Si bond lengths (3.80 Å), which may also be prone to rupture. In substitutional configurations, the lattice vibration, which is caused by irradiation by sunlight, is actually a vibration of twodimensional atomic chains (it can also be considered as primitive-cell vibration). When sulfur atoms are substituted into the silicon positions, the resonance mode emerges because the atomic mass of sulfur is greater than that of silicon, thus causing resonance absorption. In interstitial-unbonded and 4-fold coordinated configurations, the lattice wave is a resonance of the entire crystal lattice that results from the particular position of the dopants. The intensity of this resonance absorption is greater than that for substitutional configurations. The frequencies of the localized lattice vibrations are concentrated in the infrared band; consequently, these frequencies can cause infrared absorption. However, some of the defect configurations do not form impurity levels because the local lattice periodicity is destroyed by the dopants. These configurations do not contribute to infrared absorption. Band structure and light absorption are further discussed in Sections III.A. and III.C.

Table 1. Sulfur Concentrations, Identifiers, and Formation Energies of Each Modela sulfur atom position substitution

interstitialunbonded interstitial-bonded

identifier

sulfur concentration (%)

formation energy (eV)

SSi215 S2Si214 S6Si210 S12Si204 S18Si198 SI−USi216

0.5 0.9 3 6 9 0.5

−3.22 −3.85 3.34 3.53 3.67 0

SI−USi108 SI‑2BSi216 SI‑3BSi216 SI‑4BSi216 SI‑6BSi216 SI−ISi108

0.9 0.5 0.5 0.5 0.5 0.9

1.01 −3.05 −2.97 0.82 −0.84 1.54

a

The sulfur concentrations of 0.5 and 0.9% were considered based on ref 20.

basis of the results of Warrender,43 we have determined that a sulfur-doping concentration of more than 10% can be obtained under the best-achievable laser melting conditions; thus, the concentrations of 3, 6, and 9% used in this work are reasonable. Additionally, it has been previously reported that the substitutional position for a single sulfur dopant atom (see Figure 1a) is preferred,44 which is consistent with our calculated formation energies. We have also performed calculations on a configuration containing two isolated substitutional sulfur atoms (results not shown). The results show that the formation energy is larger (0.61 eV) than that of a model in which two sulfur atoms are placed at nearest-neighbor substitutional positions. This result indicates that double sulfur atoms will bond energetically in a silicon crystal under low energies, which is also consistent with the results of a previous study.44 An elongated S−S bond length of 3.17 Å was found in the case of S2Si214 (see Figure 1b), which is longer than the S−S bonds in α-S (2.06 Å). This means that the delocalization of the electrons around the sulfur atoms is enhanced. Furthermore, our data show that both the Si−Si and Si−S bond lengths become shorter as the sulfur concentration is increased from 0.5 to 9%. This phenomenon is due to the larger number of electrons introduced into the crystal lattice, which leads to strong electron−electron interactions. This behavior is similar to a Mott transition30 in that hyperdoping with sulfur can induce a phase transition in the silicon. We have also determined that an increasingly strong metallicity emerges as the sulfur concentration is increased. For the models with sulfur concentrations of 0.5 and 0.9%, the sulfur atoms are located at interstitial-unbonded sites in the silicon lattice and are denoted as SI‑USi216 and SI‑USi108, respectively (Figure 1, panels c and d, respectively). We repeatedly performed a geometry optimization process on these structures to confirm their correctness and to simultaneously ensure that they correspond to the lowest energy structures. No bonds are formed between the sulfur and silicon atoms in the two models. In SI−USi216, the sulfur atom is equidistant from the four nearby silicon atoms, which are confined in the crystal lattice. In this case, the introduced sulfur atom stretched the Si−Si bond length over the range of 2.35−2.40 Å. This result indicates that the delocalization of all of the electrons is enhanced under the perturbation of sulfur atoms. A local nonperiodic structure emerges in the lattice when the sulfur

III. RESULTS AND DISCUSSION A. Band Structure. The band structures of SSi215, S2Si214, and SI‑6BSi216 are shown in Figure 2 (panels a, b, and c, respectively). The band structures corresponding to other sulfur concentrations are not shown here because the impurity bands are indistinguishable. To accurately determine the location of the impurity levels relative to the band edge and the configuration of the system, we have employed the B3LYP level of theory (calculated value: 1.64 eV) rather than GGA (calculated value: 0.59 eV). This has allowed us to calculate the band structure and address the band gap underestimation problem (experimental value: 1.12 eV). Figure 2 clearly shows that the impurity band exists in the band gap and that the bandwidth increases with increasing sulfur concentration. As displayed in Figure 2a, a narrow impurity band (0.22 eV) emerges at approximately 0.51 eV below the conduction band edge, which is consistent with the results of previous studies.16 3755


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Figure 2. Corresponding band structure of each model. The red line represents the impurity bands, and the dotted line at 0 eV represents the Fermi level. The coordinates of the k-points in the BZ are K(0,0,0.5), Λ(0,0.5,0), Γ(0,0,0), and M(0,0.5,0.5).

Figure 3. Corresponding band structure of each model. The red line represents the impurity bands, and the dotted line at 0 eV represents the Fermi level. The coordinates of the k-points in the BZ are K(0,0,0.5), Λ(0,0.5,0), Γ(0,0,0), and M(0,0.5,0.5).

The results in Figure 2b show that the impurity bands are located across the Fermi level and are closer to the conduction band edge. Additionally, they exhibit large fluctuations, which indicate that the delocalization of the electrons on the same band is enhanced. With higher sulfur concentrations (greater than 0.9%), the bandwidth is widened, and the impurity bands merge with the conduction band. Additionally, the Fermi level gradually approaches the conduction band edge and enters it. Therefore, excessive doping alters the nature of the silicon and produces the metallicity in the system, which is consistent with the discussion in section II. In other words, if the energies are sufficiently high to allow an increase in the doping concentration, very strong bonds will be formed in the material. When a silicon crystal is doped at a high concentration (greater than 0.9%) with sulfur by high-energy pulsed-laser doping, the band structure and formation energy lead us to hypothesize that sulfur atoms are not substitutionally trapped completely in the silicon crystal. We therefore believe that the system will undergo cellular breakdown and may instead form several interstitial configurations, thus resulting in its decomposition into single Si−S metal nanoclusters/nanoparticles (as opposed to forming a mass). Breakdown phenomena such as this become more pronounced with increasing impurity concentration. Moreover, the systems appeared to be trending toward an insulator-to-metal transition at 0.5% because the dopants produce deep donor levels in the band gap. However, at 0.9%, the system appears to be completely metallic in nature. This result is also consistent with previous experimental results whereby an insulator-to-metal transition occurred at sulfur concentrations between 0.4 and 0.9% in sulfur-doped silicon.15 The impurity states shown in Figure 2c are similar to those in Figure 2b in that the bands are located across the Fermi level, and SI‑6BSi216 also exhibits metallicity. Figure 3 shows the band structure of the models in which the sulfur atoms are located at interstitial positions in silicon. No impurity bands are formed for SI−USi108, SI‑2BSi216, and SI−ISi108; therefore, they are not shown. As shown in Figure 3b, an energy band is located near the valence band edge, which indicates that the electrons in this band remain in a metastable state. This phenomenon is consistent with the discussion regarding this model in Section II. Specifically, the unpaired electrons can form a deep donor state or bound state as the

conditions change. We find that the bonding between sulfur and silicon is covalent in SI‑2BSi108 and SI−ISi108 because there is no intermediate band in the band gap, thus indicating that the dopant electrons are in a bound state. As shown in Figure 3 (panels a and c), a relatively narrow impurity band (0.09 eV) emerges at 0.39 eV toward the valence band edge, which belongs to shallow donor levels. As shown in Figure 1 (panels c and g), the lattices have a center-of-inversion symmetry when the sulfur atom locates at such a central position. The surrounding silicon atoms form a perturbation, which lowers the impurity level. This situation is completely different from that shown in Figure 2b. Thus, the key factor that influences the electronic properties of these systems is the positions of the dopant atoms in the crystal lattice rather than their bonding character. We have found the different impurity states by comparing Figures 2 and 3. As shown in Figure 2, the impurity levels are located at the conduction band edge, which is responsible for the metallicity that emerges in these systems. In contrast, for the systems shown in Figure 3, the impurity levels are located at the top of the valence band, which does not produce the same change in behavior. Therefore, the doping concentration as well as the positions of dopant atoms affect the behavior of these materials. Other defect structures with locally destroyed periodicity also do not form impurity levels in the forbidden band; thus, structural periodicity is one of the key factors determining the impurity levels. B. Density of States. Some of the defect configurations, including SI‑USi108, SI‑2BSi216, SI‑3BSi216, and SI‑ISi108, do not have an intermediate band in their energy gap. These models are not discussed in further detail here. Figure 4 (panels a−e) shows the electronic partial density of states (PDOS) for SSi215, S2Si214, SI‑USi216, SI‑4BSi216, and SI‑6BSi216. From Figure 4a, we can clearly see an appreciable contribution of the Si p and S s electrons (see red and blue lines, respectively) near EF, which indicates that the Si and S atoms form hybridizations that should be σ bands. In Figure 4b, a relatively wide electronic DOS peak appears at EF, which indicates that the electrons on these bands are no longer at the bound state. Additionally, we do not find evidence that a covalent bond is formed between two sulfur atoms, which indicates the formation of a coordination bond. As the sulfur concentration becomes 3756


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configurations, particularly that of SI‑4BSi216. Figure 4e shows the PDOS for SI‑6BSi216. There is one DOS peak on each side of EF, indicating that the bonding between Si and S is strongly covalent. However, it must also contain the antibonding interactions between Si p and S p. C. Light Absorption. We have performed calculations of the optical properties of the studied system using the dielectric function to determine absorption coefficients. To facilitate the calculation of the conversion efficiency, the conversion between the absorption coefficient α and absorptivity κ (i.e., extinction coefficient) was performed using the formula

α = 4πκ /λ

(2)

where λ is the wavelength. The relation between the wavelength λ and the frequency ν is given by

ν = c/λ

(3)

where c is the speed of light. We also used the relation

E = hν

(4)

where h is the Planck constant and E is the photon energy. Combining eqs 2, 3, and 4, the relation between the absorption coefficient α and the absorptivity κ can be expressed in terms of the photon energy E. κ=

αch 4πE

(5)

The dependence of the absorptivity on the photon energy for SSi215, S2Si214, S6Si210, S12Si204, S18Si198, and SI‑6BSi216 are presented and compared to that of undoped Si (denoted as Si216) in Figure 5a. The calculation parameters used when calculating the absorption coefficient of Si216 were the same as those employed in the other models of this study. The experimental value of the absorptivity of crystalline silicon (at T = 300 K) was used as a reference45 and is displayed as the black dotted line in Figure 5a. Additionally, the AM1.5G solar spectrum46 is also shown in the background of the figure for reference. As was the case in the discussion of electronic properties, various models having no intermediate-band electronic states in their band gap exhibited almost the same absorption spectrum as that of undoped Si, and the results for these systems are not shown. Conversely, some of the models that do contain an intermediate band in their band gap exhibit an enhanced below-band gap absorption that is broadened with increased sulfur concentration. Regarding the absorptivity of SSi215 (the red dotted line in Figure 5a), an approximately 0.2 eV-wide infrared absorption peak appears at an energy of approximately 0.5 eV. These results agree quite well with experimental measurements in which a broad mid-infrared optical absorption peaking near 0.5 eV was observed for sulfurhyperdoped silicon.12 For S2Si214, an approximately 0.2 eV-wide peak appears at an energy of approximately 0.6 eV, which is higher than that of SSi215. This higher absorption peak is due to the wide intermediate band in which the electronic levels are slightly closer to the conduction band, which arises due to the contribution from the bonding of two sulfur atoms. From the absorptivities of S6Si210, S12Si204, and S18Si198, an obvious improvement can be found in the visible-infrared waveband and can be attributed to the larger number of defects introduced. With an increase in the sulfur concentration, the dopant atoms become more closely spaced, resulting in a strong electron−electron interaction; consequently, the band gap cannot be distinguished. Although there are more free electrons

Figure 4. PDOSs for (a) SSi215, (b) S2Si214, (c) SI−USi216, (d) SI‑4BSi216, and (e) SI‑6BSi216. The Si s, Si p, S s, and S p density of states are represented by the black, red, blue, and pink lines, respectively.

increasingly high (the diagrams are not shown), the impurity bands merge with the conduction band and exhibit no energy gap at EF. Meanwhile, the electronic DOSs exhibit no obvious peak value, which means that the electron states have significant delocalization. In other words, the system exhibits strong conductivity with increasing sulfur concentration. Additionally, the Si p and S p orbitals exhibit some obvious formants with increasing quantity as the sulfur concentration is increased. This further confirms that the Si−S bond strength becomes increasingly large with the introduction of excess dopants and indicates the formation of a nonpolar bond. The PDOSs for SI−USi216, and SI‑4BSi216 are given in Figure 4 (panels c and d, respectively). Figure 4c clearly shows that the pink line has an obvious peak at approximately 0 eV, which indicates that the impurity bands near EF are completely composed of S p electrons. Similarly, in Figure 4d, there is a DOS peak near EF that mainly arises from S p electrons; however, another peak emerges at approximately −0.4 eV, which indicates that the Si−S bond energy is likely to be low. By combining the structural characteristics and PDOSs we find that, in SI−USi216 no bond forms between S and Si but more free electrons come from S. In SI‑4BSi216, ionic bonds should exist between S and Si, which can form electric dipole moments when they undergo relative vibration. Therefore, these results could confirm that the two models will display a stronger below-band gap absorption that is better than those of other 3757


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results, we have discovered that this incredible absorptivity is mostly due to the sulfur atom. As mentioned above, these two models feature the same sulfur atom position, which is equidistant from four nearby Si atoms due to the balance of atomic forces. On the one hand, the involvement of sulfur causes the relaxation in the silicon lattice and leads to the delocalization of electron states. Moreover, the strong electron−nucleus coupling effect occurs close to the intersection of the potential energy surface formed by the Si and S atoms; therefore, the electrons around the potential energy surface can mutually convert between the different quantum states. However, the nature of the remarkable absorptivity remains to be elucidated. For the substitutional and 6-fold coordinated configurations, the impurity levels are close to the bottom of the conduction band and belong to the deep donor level. The introduction of more sulfur atoms leads to a higher concentration of free electrons, which improves the conductivity. However, the deep level acts as the recombination center, thus resulting in a decrease in the carrier lifetime and a reduction in the carrier mobility due to carrier scattering. In contrast, the impurity levels are close to the top of the valence band and belong to the shallow level in SI‑USi216 and SI‑4BSi216. The electrons in these energy states can only be ionized at slightly higher temperatures (room temperature and higher) and form free carriers to conduct electricity. D. Photoelectric Conversion Efficiency. The method used in this study to determine the photoelectric conversion efficiency limits for sulfur-doped silicon solar cells is based on the principle of detailed balance.47 We assume that the absorption of a photon can excite an electron−hole pair without any energy loss. According to Planck’s law, the sulfurdoped silicon absorbs sunlight and emits a number of photons per second according to

Figure 5. Dependence of the absorptivity on the photon energy. (a) The absorptivities of SSi215, S2Si214, S6Si210, S12Si204, S18Si198, and SI‑6BSi216. The absorptivity of undoped Si is plotted with the black line. Experimental results (black dotted line) and the AM1.5G solar spectrum (gray background) are displayed for reference. (b) The absorptivities of SI‑USi216 and SI‑4BSi216.

N=

2n2π h3c 2

2

∫ exp[(E −κ(Eμ))/E kT ] − 1 dE

(6)

where h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, T is the temperature of the blackbody (T = 300 K for the solar cell), n is the refractive index of the medium (n = 1 for air), E is the energy of the radiation (0.49 to 4.20 eV in this paper), and κ is the absorptivity of the body (i.e., extinction coefficient; eq 5). Additionally, μ is the chemical potential48 associated with the emitted radiation and must be less than the band gap of the material. The chemical potential is related to the internal voltage of the solar cell by

to enhance infrared absorption, the absorptivity values are below average in the ultraviolet region, particularly for S18Si198. Because the coupling takes place between the sub-bands, lowenergy-level electrons are excited into the higher levels, followed by immediate recombination with the holes and eventual relaxation back to the low levels. On the basis of this analysis, we have determined that the transition between single sub-bands does not effectively contribute to the electronic transmission. Furthermore, the large overlap of the energy levels renders most of the impinging photons useless. This weak absorption could also be due to the large number of recombination centers. Moreover, an abnormal, declining infrared absorption occurs for sulfur concentrations of between 6 and 9%. This may be due to the influence of sub-band coupling as well. Thus, we can conclude that the maximum value of the infrared absorption must be in the 3−9% concentration range. The SI‑6BSi216 system exhibits an enhancement at infrared wavelengths as well, but there is no obvious peak in its absorptivity values, and the intensities are lower than those of the other models. Figure 5b shows the absorptivities of SI‑USi216 and SI‑4BSi216. As expected, the remarkable absorptivity from the infrared to the ultraviolet region is observed. On the basis of the PDOS

μ = qV

(7)

where q is the charge of an electron. The numerical value of V is approximately equal to the chemical potential when units of J s−1 and eV are used, respectively (V ≈ 0.999 μ). The current density generated by the absorption of the incident photons is J = qfc N

(8)

where fc is related to the solid angle of the photoelectric emission. Therefore, the output power of the sulfur-doped silicon solar cell can be calculated from Pout = Jμ

(9)

If the sun is a blackbody with a temperature of Ts (6000 K) then the incident power is given by 3758


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Pin = fs σTs 4

introduction of more impurities can enhance the absorption of visible-infrared light (see Figure 5a, red and blue dotted lines). The conversion efficiencies of SI‑USi216 and SI‑4BSi216 are shown in Figure 6 with pink and green crosses, respectively. The conversion efficiencies rapidly increase with increasing chemical potential beginning at 0.4 eV, whereas the increase is extremely slow from 0.3 to 0.4 eV. However, because these two models exhibited a narrow band gap, we cannot ensure that a chemical potential higher than 0.4 eV can be achieved in the process of photoelectric conversion. Moreover, the chemical potential will decline if the intensity of the solar radiation energy is insufficient because intense solar radiation is required to produce high chemical potentials. However, highly intense solar radiation also leads to high temperatures, which cause lattice disturbances in the cell that result in increased electron scattering and thus decreased conductivity. Therefore, in practice, the efficiency of these systems will be lower.

(10)

where fs is related to the solid angle of photoelectric absorption and σ is the Stefan−Boltzmann constant. Therefore, the theoretical conversion efficiency of sulfur-doped silicon solar cells is P η = out Pin (11) For the maximum conversion efficiency, fc/fs must be equal to 1. Combining eqs 9, 10, and 11, and given a value of μ, the efficiency η can be calculated. Figure 6 shows the relation between the theoretical photoelectric conversion efficiency and the chemical potential.

IV. CONCLUSION In this paper, we have discussed the electronic properties of different forms of sulfur-doped silicon with various configurations of the sulfur atom in the silicon lattice and over a range of sulfur concentrations. Some of the defect configurations form different intermediate bands in the band gap, resulting in varying degrees of the enhancement of visible-infrared light absorption, while others do not exhibit these characteristics. In the analysis of the light absorption, we find that the infrared absorption is enhanced upon increasing the doping concentration, with the best concentration being within the range from approximately 3 to 9%. However, it may be difficult to achieve more than 1% doping concentration in the present doping techniques, which is only theoretically possible, but from a perspective of electronic structure and optical absorption properties, it is still worth considering. Analyzing the theoretical efficiencies reveals that introducing dopant atoms enhances the conversion efficiency to some extent (∼0.5 at. %). Two model systems display high conversion efficiencies in a certain range, but these efficiencies are lower than that of undoped silicon and slowly increase for chemical potentials of 0.3−0.4 eV. However, obtaining such a particular defect structure is very challenging, that is, nearly impossible to achieve the position of precise control at present. Although, we have not yet prepared such structures, this is a phenomenon worthy of attention. Silicon remains the preferred material for producing solar cell panels. Reducing their cost of production and improving their conversion efficiencies are important goals for the scientific community. Thus, consider it our responsibility to explore new theories and methods. Finally, we suggest that focus on taking into account the position of dopant atoms and concentration, which maybe can influence the PV conversion.

Figure 6. Dependence of the theoretical limiting conversion efficiencies on the chemical potential.

Consider now the intermediate-band gap absorbers described by Luque and Martı2́ (the theoretical limiting conversion efficiency of intermediate-band solar cells do not exceed 63.1%), the actual band gap of crystalline silicon, and the likely range of chemical potential required for practical applications. We consider these constraints and use a specific range of chemical potential to calculate various defect configurations. For sulfur concentrations greater than 0.9%, we conclude unequivocally that such materials cannot be applied to photovoltaic energy conversion because they exhibit strong metallicity. Therefore, we do not discuss the conversion efficiency of these systems. In Figure 6, it is clear that the efficiency is higher when the dopants are introduced into the silicon lattice. As shown in the results, the conversion efficiency of S2Si214 is not particularly ideal compared to SSi215. Compared to the efficiency of Si216 (at μ = 0.65 eV), the conversion efficiency at sulfur concentrations of 0.5 and 0.9% is higher by approximately 7 and 5.7%, respectively. This result indicates that even though the sulfur concentration is increased by approximately 0.4%, the conversion efficiency reduces by approximately 1.3%. However, the band gap narrowed with increased sulfur concentration (see Figure 2, panels a and b), which leads to the decrease in the chemical potential and therefore the internal voltage. However, the AM1.5G solar spectra show that most of the light reaching Earth is concentrated in the visible-infrared region. Therefore, from a practical point of view, improving the conversion efficiency by increasing the doping concentration is feasible because the

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AUTHOR INFORMATION

Corresponding Author

*Address: Room 503, Laser Building, South China Normal University, Tianhe District, Guangzhou city, Guangdong Prov., China. E-mail: [email protected]. Tel: (+86) 135 4457 2096. Fax: 0086 + 20 + 85211768. Notes

The authors declare no competing financial interest. 3759


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ACKNOWLEDGMENTS This work was cofunded by the Science and Technology Program of Guangzhou, China (Grant 2014J4100028) and the Open Science Foundation of the Key Laboratory of Environmental Optics and Technology, CAS (Grant 2005DP1730652013-04).

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