ARTICLE pubs.acs.org/JPCC
Theoretical Study of Chlorine for Silicon Nanocrystals Yeshi Ma, Xiaobo Chen, Xiaodong Pi,* and Deren Yang State Key Laboratory of Silicon Materials and Department of Materials Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China ABSTRACT: In the framework of density functional theory we show that a chlorine (Cl) atom prefers residing at the surface of silicon nanocrystals (Si NCs) in single coordination, passivating a Si atom. The surface of Si NCs is covered by H in a very Cl-poor environment, while it may be covered by both H and Cl in a less Cl-poor environment. The Cl coverage increases with the increase of the chemical potential of Cl. At rather high Cl coverage the NC structure is distorted. The band-edge recombination rates of Cl-passivated Si NCs may be significantly larger than that of completely H-passivated ones.
1. INTRODUCTION Si nanocrystals (NCs) hold great promise for applications in microelectronics,1 optoelectronics,2 photovoltaics,36 thermoelectrics,7 and bioimaging.8 The success of Si NCs in these applications, however, may ultimately depend on the control of impurities, which are introduced to Si NCs both intentionally and unintentionally. This is analogous to that happens to bulk Si. The intentional introduction of impurities is usually called doping. For instance, Si NCs have been doped with P and B to enhance the conductivity of Si NC-based structures.911 In contrast, some impurities are unintentionally introduced to Si NCs because they cannot be avoided during the synthesis and processing of Si NCs. Among the unintentionally introduced impurities, O has been subject to extensive research.12,13 To date, a variety of liquid-phase, solid-phase, and gas-phase approaches have been employed to synthesize Si NCs. In liquidphase approaches, SiCl4 is routinely used as the Si precursor.1417 Chlorine-containing compounds such as HCl and PCl3 are employed in the surface modification of Si NCs.18,19 In solidphase and gas-phase approaches, besides popularly used SiH4, both SiCl4 and SiH2Cl2 are also used as Si precursors.2025 Therefore, Cl is a possible unintentionally introduced impurity for Si NCs. Depending on the conditions of Si NC synthesis, Cl has been already detected in Si NC samples.15,20,24,25 It is generally assumed that Cl passivates the surface of Si NCs.15,20,26,27 Whether Cl can be incorporated inside Si NCs, however, has not been rigorously investigated. Puzder et al. theoretically showed that one Cl atom passivating the surface of a Si NC only slightly narrowed the bandgap of the Si NC.26 However, in Martinez et al.’s recent calculation, the bandgap of a Si NC significantly decreased if the NC surface was completely passivated by Cl.27 Experimental work has indicated that the amount of Cl introduced to Si NCs is adjustable.24,25 This implies that the coverage of Cl at the surface of Si NCs may range from 0 to 100% if Cl does reside at the NC surface. Therefore, it is r 2011 American Chemical Society
interesting to explore the dependence of the properties of Si NCs on the Cl coverage. In this work we have calculated the formation energy of Si NCs with Cl incorporated in different locations by using density functional theory (DFT). It is found that Cl indeed prefers residing at the surface of Si NCs. The surface of Si NCs is covered by H in a very Cl-poor environment, while it may be covered by both H and Cl in a less Cl-poor environment. The Cl coverage increases with the increase of the chemical potential of Cl. When the Cl coverage is rather high, structural distortion occurs to Si NCs. By investigating the electronic structures of Si NCs with different Cl coverage, we have gained insights into the effect of Cl on the optical properties of Si NCs.
2. MODEL AND METHOD Figure 1 shows the model of a Si NC, which is constructed by cutting out a spherical portion in an optimized bulk Si model. The bond length of SiSi in the NC is about 2.36 Å. The NC surface is passivated by H atoms. Three types of hydrides (SiH, SiH2, and SiH3) are at the NC surface. Before the impurity of Cl is introduced, the Si NC is in the form of Si71H84 with a diameter of ∼1.5 nm. We have considered a variety of bonding configurations for Cl at the NC surface. A Cl atom may substitute either a Si atom or a H atom at the NC surface. In the substitution of H the Cl atom actually passivates a Si atom at the NC surface.26,27 The site of a Si atom substituted or passivated by Cl at the NC surface is denoted by A, B, or C. The sites of A, B, and C correspond to the original passivation of Si by one H atom, two H atoms, and three H atoms, respectively. The approach that we use to denote surface Cl may be followed after an introduction to ClAp and ClBs (see our work on P-doped Si NCs for analogy28). Received: April 1, 2011 Revised: May 20, 2011 Published: May 28, 2011 12822
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Figure 1. Model of a Cl-incorporated Si NC, which is originally Si71H84 (1.5 nm in diameter). Si and H atoms are denoted by green and gray balls, respectively. Internal substitutional Cl atoms, substitutional Cl atoms at the NC surface, passivating Cl atoms, and interstitial Cl atoms are denoted by blue, red, black, and purple balls, respectively. The sites of A, B, and C for Si atoms correspond to the passivation of Si by one H atom, two H atoms, and three H atoms, respectively. A substitutional Cl atom inside the Si NC can be moved along a path from the center toward the subsurface, i.e., 1 f 2 f 3 f 4.
ClAp means that the Cl atom passivates a Si atom at an A site, while ClBs means that the Cl atom substitutes a Si atom at a B site. In addition to all kinds of Cl configurations at the surface of a Si NC, we have also considered substitutional and interstitial Cl inside the NC. When a substitutional Cl atom is moved from the center toward the subsurface layer in a Si NC, a path is identified by 1 f 2 f 3 f 4, as shown in Figure 1. Substitutional Cl is denoted as ClS1, ClS2, ClS3, or ClS4 according to the location of Cl on the path (Figure.1). It is noted that ClS4 is bonded to surface SiH3 to form SiH3Cl, which is dissociated from the NC after structure optimization. Therefore, ClS4 cannot be actually formed. There exist two possible interstitial sites for Cl. The interstitial Cl close to the center is denoted by ClI1, while that near the surface is denoted by ClI2. We have also studied Cl coverage at the surface of a Si NC. Cl25%, Cl50%, Cl75%, Cl89%, and Cl100% are used to denote Si71H63Cl21, Si71H42Cl42, Si71H21Cl63, Si71H9Cl75, and Si71Cl84, respectively. In the study of Cl coverage Cl passivates Si atoms at the NC surface. The placement of Cl is arranged to achieve a homogeneous distribution of Cl at the NC surface. The optimization of Si NC structures and the calculation of total energies are performed with the modeling program DMOL3. In the framework of all-electron DFT, the Perdew BurkeErnzerhof (PBE) correlation exchange functional at the generalized gradient approximation (GGA) level is adopted. Double numerical basis sets augmented with p-polarization functions (DNP basis sets) are used as the atomic orbital basis functions. A high self-consistent field (SCF) convergence threshold of 106 is employed to ensure accurate calculation. The maximum forces on all of the atoms in the optimized structures are less than 0.002 Ha/Å. When a Si NC is excited, an electron in the highest occupied molecular orbital (HOMO) transits to the lowest unoccupied molecular orbital (LUMO), leaving a hole in the HOMO. After the HOMOLUMO transition, the relaxed geometry of the Si NC at the excited state is obtained by structural and electronic optimization. For both the ground state and excited state, the HOMOLUMO gaps are readily calculated once the Si NC optimization is finished. For a Si NC larger than 1 nm, the excitation energy of the NC is similar to the HOMOLUMO
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Figure 2. Formation energy of a pure or Cl-incorporated Si NC with respect to Cl chemical potential. In the direction indicated by the arrow, the formation energy increases in the order pure, ClCs, ClCp, ClAp, ClBp, ClS3, ClBs, ClAs, ClI2, ClI1, ClS2, and ClS1. Lines for Si NCs with Cl coverage of 25%, 50%, 75%, 89%, and 100% are indicated in the figure.
gap of the NC at the ground state.26,29 The emission energy of the NC is similar to the HOMOLUMO gap of the NC at the excited state. Such similarities are adopted to determine the excitation energy and emission energy of Si NCs in this work. Radiative band-edge recombination rates for Si NCs are numerically calculated in momentum space by using Fermi’s golden rule:30 ! 16π2 ne2 ∧ 2 Ri, f ¼ ð1Þ 2 2 3 Ei, f jÆϕi j p jϕf æj 3p m c ϕi and ϕf are the wave function of the HOMO and that of the LUMO at the first excited state of a Si NC, respectively. Ei,f is the HOMO-LUMO transition energy between states i and f, m is the electron rest mass, e is the electronic charge, n is the refractive index of Si NCs, c is the velocity of light, and ^p is the momentum operator. Both phonon-assisted and non-phonon-assisted electronic transitions may occur in Si NCs.31 In this work, however, we only consider non-phonon-assisted ones in the calculation of radiative band-edge recombination rates. The matrices of all the HOMO/LUMO wave functions are obtained by discretely sampling three-dimension space with a grid space of 0.2 Å.
3. RESULTS AND DISCUSSION During the synthesis of Si NCs, thermodynamic equilibrium is usually established.911,1419 This justifies the use of formation energy to compare the relative stability of Si NCs.32 We calculate the formation energy (Ef) of a Si NC (SixHyClz) by using Ef ¼ EðSix Hy Clz Þ xμSi yμH zμCl
ð2Þ
E(SixHyClz) is the total energy of the Si NC at ground state. x, y, and z are the numbers of Si, H, and Cl atoms, respectively. μSi, μH, and μCl are the chemical potentials of Si, H, and Cl, respectively. Figure 2 shows the dependence of Ef on μCl for all kinds of Si NCs by using μSi (7874.84 eV) and μH (15.84 eV) for the total energy per atom of bulk Si and hydrogen gas at 0 K, respectively. It is clear that Ef for all kinds of Cl-incorporated Si NCs linearly decreases as μCl increases. We consider that Si71H84 12823
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Figure 3. (a) Model of a Si NC with the Cl coverage of 89%. (b) Model of a Si NC with the Cl coverage of 100%. Si, H, and Cl atoms are denoted by green, gray, and black balls, respectively. Significantly stretched bonds in (b) are indicated by blue color.
is a pure Si NC. Since there is no Cl in the pure Si NC, it is natural that Ef for the pure Si NC does not change with μCl. We assume that in a Cl-poor environment μCl is smaller than the total energy per atom of chlorine gas at 0 K (12 517.6 eV). It is then clearly seen in Figure 2 that Ef for the pure Si NC (completely passivated by H) is the lowest in a very Cl-poor environment (μCl < 12 519.3 eV). This predicts that no Cl is incorporated in Si NCs as the amount of H is enough to make a very Cl-poor environment. As the NC-synthesis environment becomes less Cl-poor (μCl > 12 519.3 eV), there exist Clincorporated Si NCs with Ef smaller than that for the pure Si NC, implying the incorporation of Cl during the synthesis of Si NCs. We should note that for all the Cl-incorporated Si NCs with the lowest Ef in the different ranges of μCl Cl is always at the NC surface (Figure 2). ClCs, ClCp, ClAp, and ClBp are the most likely formed Cl configurations at the NC surface with similar Ef. A Cl atom in each of these four configurations is in single coordination, passivating a Si atom at the NC surface. With the increase in μCl the number of the above four configurations increases to enhance the Cl coverage at the NC surface, short of the formation of interstitial Cl inside a Si NC and substitutional Cl both at the NC surface (except ClCs) and inside the NC. It is found that as the Cl coverage reaches 89% NC structure distortion occurs, as shown in Figure 3. Bond angles are significantly changed in a Si NC with the Cl coverage of 89% (Figures 1 and 3a). Although the changes of bond angles are not very large in a Si NC with the Cl coverage of 100%, there exist severely stretched bonds. Their lengths increase by ∼13% (Figure 3b). It is likely that the NC structure distortion induced by the high Cl coverage leads to the vulnerability of Si NCs. For instance, Si NCs with high Cl coverage may be decomposed by ion bombardment in plasma. This may explain the unsuccessful plasma synthesis of Si NCs in an environment with a relatively high μCl.24,25 It has been experimentally found that H2 must be added to scavenge Cl in a SiCl4-based plasma synthesis of Si NCs. The underlying mechanism is that H2 adjusts μCl to avoid the formation of easily decomposed Si NCs with high Cl coverage. We now move to investigate the electronic and optical properties of Cl-incorporated Si NCs. Given the possibility of formation, we focus on Si NCs with the Cl coverage ranging from one Cl atom (ClCs, ClCp, ClAp, and ClBp) to 100%. Figure 4 shows energy-level diagrams for these Cl-incorporated Si NCs together with the pure Si NC at ground state. It is clear that a onecoordinated Cl atom at the NC surface only very slightly reduces the bandgap of Si NCs, consistent with previous theoretical
Figure 4. Energy-level diagram for a pure or Cl-incorporated Si NC. Filled (empty) circles indicate that the energy levels are occupied (unoccupied) by electrons.
Table 1. Excitation Energy (Eex), Emission Energy (Eem), and Recombination Rate (R) for a Pure or Cl-Incorporated Si NC R (106 s1)
Eex (eV)
Eem (eV)
pure
3.00
2.70
ClCs
2.95
2.49
5.1
ClAp
2.98
2.53
294.5
ClBp
2.99
2.50
9.7
ClCp
2.99
2.67
29.6
Cl25%
2.80
2.53
7.8
Cl50% Cl75%
2.45 2.06
2.32 1.04
118.2 26.0
2.9
work.26 With the increase in the number of one-corordinated Cl atoms at the NC surface, the bandgap of Si NCs decreases. The bandgap reduction mainly results from the significant lowering of the LUMO. It is seen that deep energy levels appear as the Cl coverage increases to be 89% and 100%. We find that these deep energy levels are related to the NC structure distortion induced by the high Cl coverage. Since deep energy levels usually quench the band-edge light emission from Si NCs,30 we exclude Si NCs with the high Cl coverage (89 and 100%) in the calculation of emission energy and the rates of the radiative band-edge recombination of Si NCs. The results are tabulated in Table 1 together with excitation energy. It is seen that the emission energy is smaller than the excitation energy for all the presented Si NCs, consistent with the well-known Stokes shift. Both the excitation energy and emission energy decrease after the incorporation of Cl. The decrease is more prominent for higher Cl coverage. Please note that the actual excitation energy and emission energy of a Si NC should be larger than those shown in Table 1. This is because in DFT excitation energy and emission energy are routinely underestimated by ∼12 eV.33,34 However, we should point out that the relative order between the values of Eex (Eem) is not affected by the underestimation. Although the recombination rate does not monotonically change with the Cl coverage, it increases by up to 2 orders of magnitude after the incorporation of Cl. This indicates that the Cl passivation of Si NCs may be a route to obtain highly efficient luminescence from Si NCs. We notice that 12824
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The Journal of Physical Chemistry C the recombination rates of Si NCs with Cl at the surface have not yet been experimentally obtained. Since the efficiency of luminescence is proportional to the recombination rate, we can correlate the calculated recombination rates with experimentally observed luminescence. Nozaki et al. have recently observed that small addition of H2 results in more efficient luminescence from Si NCs synthesized in SiCl4-based plasma than large addition of H2.25 Such a luminescence enhancement may be actually due to the increase in recombination rate, which is enabled by the Cl passivation of Si NCs in a H-poor (i.e., Cl relatively rich) environment.
4. CONCLUSION In conclusion, we have shown that Cl is most likely onecoordinated at the surface of Si NCs, passivating Si atoms. It is rather hard for Cl to be incorporated inside Si NCs. In a very Cl-poor environment the surface of Si NCs is covered by H. As the environment becomes less Cl-poor, however, the surface of Si NCs may be covered by both H and Cl. The Cl coverage increases with the increase of the chemical potential of Cl. The problem of rather high Cl coverage is the distortion of NC structure, facilitating the decomposition of Si NCs. For Cl-incorporated Si NCs without deep energy levels introduced in the NC bandgap, the band-edge recombination rates are larger than that of completely H-passivated Si NCs. Both the excitation energy and emission energy of Si NCs decrease with the increase in the Cl coverage. Insights gained in this work may guide the tuning of the properties of Si NCs by controlling the impurity of Cl, which is present in a variety of popular NC synthesis environments. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT R. Gresback and Dr. T. Nozaki at the Tokyo Institute of Technology are thanked for commenting on our manuscript. We are grateful to Shanghai Supercomputer Center for providing computation resources. This work was mainly supported by the National Basic Research Program of China (973 Program) under Grant 2007CB613403. Partial support from the National Natural Science Foundation of China (Grants 50902122 and 50832006), Research Fund for the Doctoral Program of Higher Education of China (Grant 20090101120157), Scientific Research Foundation for Returned Scholars from the Ministry of Education of China (Grant [2009]1341), the Ministry of Human Resources & Social Security of China (Grant 20100129), and Major Scientific program of Zhejiang Province (Grant 2009C01024-2) is acknowledged. ’ REFERENCES
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