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Si : An Efficient Solar Cell Material Jiajun Linghu, Lei Shen, Ming Yang, Shuyan Xu, and Yuan Ping Feng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04032 • Publication Date (Web): 07 Jul 2017 Downloaded from http://pubs.acs.org on July 10, 2017

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The Journal of Physical Chemistry

Figure 1. (a) The unit cell of Si24 with the three nonequivalent atomic positions labeled as Site 1~3. (b) PDOS of Si atoms at the three nonequivalent atomic positions. (c) Band structure of Si24 calculated with the hybrid functional. The band gap value is given in the unit of eV. 73x133mm (300 x 300 DPI)

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Figure 2 Band structures (left panel) and PDOS (right panel) of (a) pure Si24 and (b) B-doped Si24, (c) Aldoped Si24, (d) Ga-doped Si24, (e) P-doped Si24, and (f) As-doped Si24. The Fermi level is indicated by the dashed pink line. The band gap value is given in the unit of eV. 136x457mm (300 x 300 DPI)


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Figure 3. Partial charge from the VBM or the CBM of B-doped Si24(a), and P-doped Si24(b). The Si atoms are shown in blue balls, and the dopant is shown in pink ball. 14x5mm (300 x 300 DPI)



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Si24: An Efficient Solar Cell Material Jiajun Linghu, † Lei Shen, ‡ Ming Yang, ¶ Shuyan Xu, § and Yuan Ping Feng †,∥,* †

Department of Physics, 2 Science Drive 3, National University of Singapore, 117551, Singapore

‡

Department of Mechanical Engineering, 9 Engineering Drive 1, National University of

Singapore, 117575, Singapore ¶

Institute of Materials Research and Engineering, A*-STAR, 2 Fusionopolis Way, 138634,

Singapore §

National Institute of Education, Nanyang Technological University, 637616, Singapore

∥

Centre for Advanced 2D Materials, 6 Science Drive 2, National University of Singapore,

117546, Singapore


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ABSTRACT

Si24, a recently synthesized allotrope of silicon, has received much attention due to its quasi-direct band gap around 1.3 eV. To explore its potential application in solar cell device, we investigated the doping effect on the electronic properties of Si24 using first-principles calculations. It is found that Si24 can be easily doped as both p- and n-type, respectively, and the dopants are readily ionized. Furthermore, the incorporation of these dopants only reduces the band gap of Si24 slightly, which remains in the ideal region for solar cells. Boron and phosphorus are identified as the most promising elements for the p-type and n-type doping in Si24, respectively, due to their low formation energies, small ionization energies, and small reductions in the band gap. These properties suggest great potential in constructing novel Si24 based p-n junction which is highly desired for future industrial application of photovoltaic devices.


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INTRODUCTION Silicon-based photovoltaic devices have been dominating the solar cell industry for several decades due to their elementary and technical advantages such as abundance, high stability, environmental-friendliness, and the relatively high photoelectric transfer efficiency. Even though the widely used crystal silicon in the diamond structure (d-Si) suffers from a number of shortcomings and other semiconductors such as GaAs show better efficiency, the economic advantages of silicon will keep it as the dominant material for the solar cell industry in the near future. The challenge is to improve the efficiency of silicon-based devices. D-Silicon is actually not an ideal material for photovoltaic applications due to two major factors. First, d-Si has low absorption efficiency in visible light region because its band gap (1.12 eV)1 is smaller than the optimal gap (1.4 eV) for achieving the maximum absorption efficiency for the AM1.5 solar spectrum.2 Second, d-Si is an indirect band gap semiconductor, in which its valence band maximum (VBM) and its conduction band minimum (CBM) appear at different crystal momentum (k-point), hence, its light absorption needs the assistance of phonon, leading to a much lower light absorption efficiency compared to direct band gap semiconductors whose VBM and CBM appears at the same k-point. Therefore, to improve the efficiency of siliconbased solar cell devices, it is desirable to have silicon allotropes with larger and direct energy gap, which has been the goal of numerous efforts in engineering silicon structures.3-7 Driven by this desire, various phases of silicon have been synthesized experimentally,8-10 among which the BC8 and R8 phases are found stable at the ambient condition.11-13 However, they are not suitable for solar cell applications because the BC8 phase is semimetallic,14 and the band gap of the R8 phase is too small (0.24 eV).15 Along with the experimental efforts, extensive


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computational studies have been carried out to design new phases of Si with desired properties. For example, Botti et al.16 performed a structural search using the minima hopping method and predicted several metastable silicon phases, including M-10, C2221, imma, cmcm, P-1, and P21/c structure, with band gaps ranging from 0.8 to 1.5 eV. Xiang and his colleagues17 proposed a cubic Si20 phase with a quasi-direct gap of 1.55 eV. Similarly, using particle swarm optimization algorithm, Wang et al.18 predicted six novel silicon structures, with band gaps varying between 0.81 and 1.25 eV. Lee et al.19 and Amsler et al.20 also generated a number of silicon phases with direct or quasi-direct band gaps in the range of 0.29 to 1.8 eV. Most of these theoretical predictions, however, have not been verified experimentally. More recently, Kim et al.21 synthesized a silicon phase with the cmcm symmetry. The 24atom unit cell of Si24 can be obtained by removing sodium atoms from the Na4Si24 precursor. This Si24 structure is found to have an indirect band gap of 1.29 eV and a slightly large direct band gap of 1.39 eV, which are close to the optimal value (1.4 eV) for solar cell applications. In addition, its light absorption efficiency is estimated to be higher than that of d-Si in the visible light range. These suggest that Si24 is a promising material for solar cell applications. Obviously, further studies are necessary to evaluate Si24 for solar energy application. For example, an important issue for solar cell application is whether the material can be easily doped to p- and n-type and form p-n junction, and how the doping affects its electronic structure. In the present study, we perform first-principles calculations to investigate the doping properties of Si24. Our calculations predict that both p- and n-type Si24 can be easily achieved by doping with group III and group V elements, respectively, particularly boron and phosphorous. Furthermore, Si24 is found to have similar doping properties as d-Si. Based on these properties, we can expect that p-n junction of Si24 can be easily fabricated and Si24 can be an efficient solar cell material.


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COMPUTATIONAL METHODS All calculations are carried out using the density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP), with the projector-augmented-wave (PAW)22 method for the electron-ion interaction and the Perdew-Burke-Ernzerhof (PBE)23 exchangecorrelation functional. The cutoff energy for the plane-wave expansion of electron wave function is set at 400 eV, and the force on each atom is relaxed until it is smaller than 0.01 eV/Å in all calculations. It is well known that standard DFT exchange-correlation (XC) functionals within local density approximation (LDA) or generalized gradient approximation (GGA) seriously underestimate band gaps of semiconductors by as much as 50% for some materials, due to the spurious electron self-interaction and lack of the derivative discontinuities of the XC functional24. Various approaches such as GGA+U,25 hybrid functional,26-28 GW,29 etc. have been developed to address this issue. The hybrid functional method, which is performed by mixing a fraction of nonlocal exact exchange energy with PBE exchange, is accepted as a practical approach due to its accuracy and relatively low demand for computational resources and is widely used to calculate the electronic structures of semiconductors. In this work, the HSE06 hybrid functional30-31, with 34% exact exchange energy, is applied in band structure calculation to obtain a more reliable band gap. Doping is modeled using a 3×1×1 supercell containing 72 atoms which is sufficient to minimize the potential Coulomb interaction among dopants. The Monkhorst-Pack scheme with 9×3×3 and 3×3×3 k-point meshes are used for the unit cell and supercell calculations, respectively. The formation energy of a doping defect X in charge state q is given by:32 (X ) = tot (X ) − tot (bulk) − ∑ + ( + + ∆)

(1)


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where tot (X ) is the total energy of the supercell with the defect, X, tot (bulk) is the total energy of bulk (undoped) Si24 supercell. is the number of atoms of type (host atoms or dopant) that have been added to ( >0) or removed from ( < 0) the supercell to construct the defect, and are the corresponding chemical potential. In this work, Si24 and pure metal of aluminum, gallium, and arsenic are used as the source of the Si, Al, Ga, and As element to obtain the chemical potential, respectively. For the boron element, it has many allotropes such as αrhombohedral, α-tetragonal, β-rhombohedral, β-tetragonal, and γ-boron phase, among which the β-rhombohedral phase is most stable and selected as the origin of boron in our calculation. In addition, phosphorus owns four common allotropes, white, red, violet, and black, among which the least reactive and thermodynamically stable black phosphorous is used as the source of phosphorus element. is the Fermi energy that is varied within the band gap with respect to the VBM ( = 0 at the VBM), hence, is affected by the reference of the VBM. However, the existence of defect would give rise to a constant shift in the electrostatic potential of VBM between defect supercell and the bulk. To align the VBM, a method was proposed by Van de Walle and his colleagues that the energy of VBM, i.e. the term in the formula, is firstly calculated in bulk, and subsequently, the potential in the imperfect supercell is measured at where far from the defect and compared with that in the bulk, achieving the potential shift ∆. Therefore, the VBM in defect supercell can be aligned to that in bulk through adding ∆ to .32-33 Based on the defect formation energy, the thermodynamic transition level ( /! ) is defined as the Fermi level position where the formation energies of a defect with charge states and ! are equal:32

( /! ) =

"# ($ %& ;"( )*) + "# ($ %, ;"( )*) , +&

(2)


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One thing worth to note is that, in the formation energy calculation of charged defect, the Fermi level changes from the VBM to the CBM in the system. Meanwhile, the position of transition level is decided by the energy differences between different charge states. Hence, the accuracy of the transition level is also affected by the band gap problem caused by general DFT functional. Therefore, the HSE06 method with 34% exact exchange energy is also used in all the calculations related to the formation energy of charged defect, as well as the transition levels.

RESULTS AND DISCUSSION The atomistic structure of Si24 is shown in Figure 1a. The unit cell of the orthorhombic structure contains 24 Si atoms occupying three non-equivalent sites (labeled as Site-1~3). The calculated projected density of states (PDOS), shown in Figure 1b, indicate that the Si atoms at these different sites contribute almost equally to the total density of states (DOS). As seen clearly in the calculated HSE06 band structure shown in Figure 1c, Si24 is a semiconductor with an indirect band gap of 1.29 eV which is in excellent agreement with the measured value.21 The VBM is located at the Γ point but the CBM is near the mid-point along the Γ-X line (Details of the reciprocal space and high symmetry k-points are given in Figure S1 in the supporting information). It is also noted that the direct band gap at Γ is 1.35 eV, only 0.06 eV larger than the indirect band gap. This suggests simultaneous optical transitions corresponding to the indirect and the direct band gap, therefore a high solar adsorption efficiency, and potential for further band structure engineering of Si24-based devices. In contrast, d-Si is an indirect band gap semiconductor, but the energy difference between its indirect and direct band gap is as large as 2.28 eV.34


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Figure 1. (a) The unit cell of Si24 with the three nonequivalent atomic positions labeled as Site 1~3. (b) PDOS of Si atoms at the three nonequivalent atomic positions. (c) Band structure of Si24 calculated with the hybrid functional. The band gap value is given in the unit of eV. The basic component of a solar cell device is the p-n junction. To produce a p-n junction, it is essential to dope the semiconductor to p-type and n-type which are traditionally done by substituting Si with group III and group V elements, respectively. Here, we carry out first principles calculations to investigate the feasibility of realizing p-type and n-type Si24. Group III elements B, Al, and Ga are considered for p-type doping, while group V elements P and As are investigated for n-type doping. Doped Si24 is modeled by introducing one dopant into the 3×1×1 Si24 supercell, which corresponds to a doping concentration of 1.39%. Both the interstitial and


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substitutional doping are considered. However, the calculated defect formation energies (Table 1) indicate that all dopants prefer substituting a Si atom rather than the interstitial sites. The defect formation energy for substitutional doping ranges from -0.03 eV to 0.81 eV which are much lower compared to those at the interstitial sites (9.03~11.40 eV). Due to the high formation energies, doping at the interstitial sites can essentially be ruled out. In the following, we focus our discussion on substitution doping only. Furthermore, a dopant can substitute a Si atom at any of the three inequivalent sites. The calculated formation energies differ by less than 0.1 eV and their electronic structures are also very similar. In Table 1, we list the lowest formation energy in each case. It is also noted that the defect formation energies of various dopants considered are quite low and the highest value is 0.72 eV, corresponding to substitution of Al for Si. At the same time, the intrinsic defects have much higher formation energies (Table S1 in the supporting information). This suggests that both p- and n-type doping can be easily realized in Si24 using these elements as the dopants. Results of our calculations also indicate that it is relatively easy to achieve n-type doping in Si24. In particular, the negative formation energy for PSi suggests that this doping process is an exothermic reaction,35 and can occur spontaneously.36 This could be due to the similar atomic radius of Si and P and the small structural changes induced by the substitution of P for Si atom. The P-Si bond in P-doped Si24 differs by 0.5% compared to the SiSi bond in the undoped Si24. For other dopants, the bond length varies by 2.5% to 6%.


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Table 1. Formation energy ( E f ) for substitutional and interstitial defects, calculated ionization energy (ε ) of various dopants in Si24. The calculated ( ε d − Si Cal.) and experimental ionization energy ( ε d − Si Exp.) of the same defect in diamond silicon are included for comparison. B

Al

Ga

P

As

E f (substitutional) (eV)

0.60

0.72

0.49

-0.03

0.24

E f (interstitial) (eV)

11.40

9.56

9.03

9.99

10.04

0.08~0.12

0.10~0.14

0.09~0.13

0.09~0.13

0.11~0.15

ε d − Si Cal. (eV)

0.06

0.09

0.10

0.06

0.08

ε d − Si Exp. (eV)a

0.045

0.067

0.072

0.045

0.054

ε

a

(eV)

Reference37

For n- and p-type doping, another crucial parameter is the ionization energy which should be as low as possible so that the excess charges introduced by the dopants can break away from them and become conducting charges.37 For the dopants considered here, the ionization energy is given by the thermodynamic transition level between the neutral (0) and the +1 (for donors) or -1 (for acceptors) charged states of the defect. The thermodynamic transition level also determines the electronic behavior and is often used as the basis for experimental detection or identification of the defect.33 However, it was reported that transition level derived from defect formation energies is reliable for deep transition levels,38 but questionable for shallow levels.39-40 Here, we benchmark our calculations for Si24 against the experimental ionization energy and theoretical value, calculated using the same method, of d-Si whose doping properties are well known. As can be seen in Table 1, the calculated ionization energies of d-Si are close but generally larger than the experimental values. More importantly, the calculated ionization energies show the


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correct chemical trend. By comparing the calculated ionization energy for Si24 with the value of d-Si, dopant ionization in Si24 can be assessed relative to that in d-Si. A couple of points are worth noting in the calculations. First, the dipole correction on the total energy of the system with charged defect should be scaled by the dielectric constant of the system. In the absence of the experimental dielectric constant for Si24, we used the calculated value which is usually larger than the experimental one (the difference is about 9% for d-Si, see Table S2 in supporting information). Therefore, the calculation would provide an upper bound for the ionization energy. Second, due to the anisotropic structure of Si24, the dielectric tensor has three different diagonal elements which lead to different values of the calculated ionization energy. In Table 1, the range of ionization energy calculated using these dielectric constants is listed for each dopant. On the whole, the ionization energies of various dopants in Si24 are slightly higher than but close to those in d-Si, indicating similar p- and n-type conductivity in doped Si24 and d-Si. Our calculations also show that B and P are the most favorable dopant to produce p- and n-type conductivity, respectively. Meanwhile, the ionization energy of Ga is slightly lower than that of Al, in contrast to the trend in d-Si. The effective doping of Si24 by the elements being studied is confirmed by the calculated electronic structures and PDOS, as shown in Figure 2. It is clear that doping with group III element, B, Al, and Ga, introduces an acceptor level which mixes with the valance band of Si24 and pins the Fermi level at the valence band, resulting in p-type semiconductors. On the contrary, doping with group V element, P and As, produces a donor level which is combined with the conduction band, resulting in n-type semiconductors. Orbital contributions to the states near the Fermi level can be seen in the calculated PDOS, where for p-type doping, the VBM mainly consists of p-orbitals of the Si atom and the dopant, while for n-type doping, the CBM is a


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hybridization of s- and p-orbitals of Si and the dopant. Compared to other dopants, the p-orbital of Ga has a higher intensity near the VBM, indicating the dominant role of the Ga-p-orbital near the Fermi level.

Figure 2 Band structures (left panel) and PDOS (right panel) of (a) pure Si24 and (b) B-doped Si24, (c) Aldoped Si24, (d) Ga-doped Si24, (e) P-doped Si24, and (f) As-doped Si24. The Fermi level is indicated by the dashed pink line. The band gap value is given in the unit of eV.


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It is worth noting that doping with these elements does not introduce any obvious defect levels in the band gap of Si24. Due to the low ionization energy, the donor and acceptor levels are mixed with the CBM or VBM, respectively, resulting in a small reduction of the band gap. The amount of the band gap narrowing is about 7%, 24%, 12%, 8% and 0.8% for B, Al, Ga, P, and As doping, respectively. The shapes of the CBM and the VBM are preserved and not much affected by the doping. In addition, the extra electron and hole introduced by the dopants are delocalized, as shown in Figure 3 for P- and B-doped Si24. Similar charge delocalization is found in other n-type and p-type Si24 and the details are given in Figure S2 in the supporting information. The delocalized charge distributes along the close-packed atomic chains in the [100] direction (x-axis). Thus, good conductivity can be expected along the [100] direction for both n-type and p-type Si24.

Figure 3. Partial charge from the VBM or the CBM of B-doped Si24(a), and P-doped Si24(b). The Si atoms are shown in blue balls, and the dopant is shown in pink ball.


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CONCLUSION In conclusion, based on detailed first-principles calculations, we found that the formation energies of group III and group V element doped Si24 are very low, p- and n-type Si24 and their junction can be easily produced. The dopants have low ionization energies and therefore can be easily ionized. The donor level below the conduction band minimum is mixed with the conduction band and the acceptor level above the valence band maximum hybridizes with the valence band, leading to a small reduction of the band gap, without affecting the shapes of the CBM and VBM. These doping properties are very similar to that of d-Si. On the other hand, even though the band gap is reduced slightly by doping, the band gaps of B-, Ga-, P- and As-doped Si24 remain in the ideal range (1.1 ~ 1.7 eV) for solar cell applications. In addition, the existence of a direct energy gap with a gap value close to that of the indirect gap effectively makes Si24 a quasi-direct energy gap material which will lead to much more efficient light absorption, compared to d-Si. Even though overall efficiency of a solar cell device depends on other dynamic factors such as rate of electron and hole recombination, one can expect that the combined effect of the optimal band gap and the efficient light absorption will lead to higher efficiency of Si24 based devices than the current solar cell devices based on d-Si. For practical use, we suggest P and B as the best dopant for n-type and p-type doping, respectively, because of their relatively low formation energy, low ionization energy, and band gap closer to the ideal value.


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ASSOCIATED CONTENT Supporting Information The reciprocal space with high-symmetry k-point path of Si24. Formation energy of intrinsic defects in Si24. Dielectric constant of d-Si and Si24. (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ACKNOWLEDGMENT The authors are indebted to Prof. Fan Haiming, Dr. Zhou Jun, and Mr. Yang Tong for helpful discussions. The computational resources were provided by Centre for Advanced 2D Materials, National University of Singapore


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Si24: An Efficient Solar Cell Material - The Journal of Physical

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