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Adsorption characteristics composition of Ge and Si on 4H-SiC(0 0 0 1) surface
Journal of Crystal Growth 531 (2020) 125370
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Adsorption characteristics composition of Ge and Si on 4H-SiC(0 0 0 1) surface
T
⁎
Xiaomin He, Jichao Hu , Hongbin Pu, Yi Liang, Teng Jia Department of Electronic Engineering, Xi’an University of Technology, Xi’an 710048, China
A R T I C LE I N FO
A B S T R A C T
Communicated by Min Lu
Silicon (Si) and germanium (Ge) are two important materials for hetero-epitaxy of 4H-silicon carbide (4H-SiC), so the First-principles calculation is employed to compare the difference of the adsorptions of Ge and Si atoms on the surface of 4H-SiC(0 0 0 1) by calculating the adsorption energy, geometric optimization, charge populations and density of state. For the two different types, four common adsorption models (top, hcp, fcc, bridge) are studied. The calculation results of adsorption energy show that, for two different types of atoms, compared with other sites, the most stable adsorption site is top site. At the same time, another important feature is that Si atom is more stable on Si surface, while Ge atom is easier to diffuse on Si surface. The results of the diffusion barrier indicates that, compared with the adsorption of Si atoms, Ge atoms are more active on the adsorption surface, which is consistent with the adsorption energy. Charge populations results shows that there is obvious charge transfer between the adsorbed atom and the surface atom, which implies that Si-Ge bonds and Si-Si bonds are formed between the adsorbed atom and the surface atom. The behaviors of the DOS of Si are qualitatively similar to that of Ge adsorption. It can be seen from the dos results that there are great resonance peaks, which indicates the presence of strong interactions of adsorbed atom and surface atoms, but extent of depreciation is different.
Keywords: First-principles Adsorption Surface Si Ge
1. Introduction Although SiC based light control devices have been realized and have strong anti-interference ability, due to the forbidden band width of SiC materials, according to the relationship between the wavelength and the forbidden band width, 4H-SiC is only sensitive to ultraviolet light or shorter wavelength light, and is not sensitive to visible light and near-infrared light, so SiC light control devices can only be controlled by ultraviolet light source, which will be a long way degree increases the complexity and cost of the system. When it is not used properly, it can cause harm to human body and serious UV pollution to the environment, which limits the application range in the field of optoelectronics. In order to further expand its spectral response range to nearinfrared region, narrow band gap semiconductor Si and Ge are used as near-infrared sensitive layers [1,2]. To prepare the difference of the adsorptions of Ge and Si atoms on the surface of 4H-SiC (0 0 0 1). This paper mainly studies the adsorption from the theoretical aspect. In previous work, we have systematically studied the epitaxy growth of two kinds of atoms from the experimental aspect. Deposition of film on 4H-SiC is used by low-pressure chemical vapor deposition (LPCVD). high purity hydrogen (H2) is used as carrier gas respectively. Refs. [3–5] describe specific growth details. However, the 23.0% of lattice ⁎
mismatch between Ge(1 1 1) and 4H-SiC(0 0 0 1) can cause distortion or even dislocation near the interface. Si film has also been prepared on SiC [6–8]. For details, please refer to Ref. [6]. The Si films with [1 1 1] and [2 2 0] orientations have been successfully prepared on 6HSiC(0 0 0 1) substrate [9,10]. By studying the adsorption process, the atom diffusion and electron transfer processes can be understood and the properties of the Ge/4H-SiC(0 0 0 1) and Si/4H-SiC(0 0 0 1) interfacial systems can be further revealed. 2. Methodology In this paper, the studying is invested by the first-principles method. First-principles model parameters are very important. If the model parameters are not selected properly, the simulation results will be inaccurate. The first important parameter is potential. The electron-ion interaction is described by pseudopotential [11,12]. The generalized gradient approximation (PW91) [13] of Perdew GGA potentials is used to describe the exchange-correlation functional. PW91 represents a more inhomogeneous chemical environment [14,15]. Cutoff energy is a kind of plane wave which shows how much energy the plane wave takes after it expands. For the high-energy part, the proportion of cutoff energy is very small, and it affects the calculation speed, so it is not the
Corresponding author at: Department of Electronic Engineering, Xi’an University of Technology, Xi’an 710048, China. E-mail address: [email protected] (J. Hu).
https://doi.org/10.1016/j.jcrysgro.2019.125370 Received 15 July 2019; Received in revised form 18 November 2019; Accepted 19 November 2019 Available online 22 November 2019 0022-0248/ © 2019 Elsevier B.V. All rights reserved.
Journal of Crystal Growth 531 (2020) 125370
X. He, et al.
Fig. 1. Test of Cutoff energy. Fig. 3. Test of surface layers.
bigger the cutoff energy is, the better the truncation energy is. In this paper, the convergence of Eutoff energy is tested in Fig. 1. It is found that the system is stable when the truncation can reach 400 eV. In this paper, the single particle Kohn–Sham wave functions were expanded by a cutoff energy of 550 eV. In order to avoid the interaction between the slab and its periodic images, a vacuum region of 10 Å was embedded into the supercells. The Kohn–Sham equation was solved by the selfconsistent field (SCF) procedure with the SCF convergence threshold of 2e−6 eV/atom. A regular MonkhorstPack grid [16] with 7 × 7 × 1 kpoints was performed for the Sampling of the irreducible edge of Brillouin zone. Broyden–Fletcher–Goldfarb–Shanno (BFGS) [17] algorithm is considered to be the best quasi-Newton method with the best numerical effect, and has global convergence and superlinear convergence rate. In order to relax the minimum total energy of the supercells system, the BFGS algorithm with a convergence tolerance of 0.01 eV/Å was used to fulfill the geometry optimization.
models named top, hcp, fcp and bridge. The adsorption model of Si atom on 4H-SiC surface is similar to that of Ge atom. The only difference is that Si atom is used to replace Ge atom while keeping other structures unchanged. In this structure, the 4H-SiC(0 0 0 1) surface is simulated by the thickness of an atomic layer. If the thickness is too small, it cannot represent the surface model. In order to find the number of atomic layers that can represent the surface, the convergence of the surface structure with different atomic layer thickness is tested in Fig. 3. It can be found that when the number of atomic layers reaches ten, the surface energy is basically stable. In the simulation calculation, ten layers of atoms are used as surface models, and only six layers of atoms on the surface are allowed to move freely, while the atoms on the back remain unchanged. Vertical distance d of the Ge and Si adatom from the surface layer is a very important parameter. Once this parameter is unreasonable, the calculation will not converge or the result will be wrong. If the distance d between the adsorbed atom and the surface atom is too large, the bonding between the atoms will not be possible. If the distance between the atoms is too small, it will not conform to the bonding law of the atoms. Therefore, in the early stage, we used the results of energy calculation to predict the initial distance d. For the Ge adsorption, the optimal parameters of the top model is 2.5 Å, the others are 2.4 Å. While for Si adsorption, the optimal parameters of the top model is 2.4 Å, the other position are 2.3 Å. We find that the optimal distance parameters of the four models are very close to the actual covalent bond performance distance. We can also find that
3. Results and discussion 3.1. Adsorption model The adsorption model of Ge atom on SiC(0 0 0 1) surface is shown in the following Fig. 2. Because there are two surfaces when the surface model of 4H-SiC(0 0 0 1) is established, in order to restrain the influence of another surface, one of the two surfaces adsorbs Ge atom and the other is passivated by hydrogen (H) atom. The four adsorption
Fig. 2. Top view and front view of the adsorption model of Ge atom on SiC(0 0 0 1) surface. Green represents the adsorbed atom Ge, yellow represents Si atom, gray represents C atom and white represents H atom. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
2
Journal of Crystal Growth 531 (2020) 125370
X. He, et al.
trend of bond length is the same as that of energy: the larger the energy, the smaller the bond length. For two models, the bond length c of top is the shortest. The bond length c of hcp is longest, this is mainly because that the number of atoms around the atoms at different adsorption sites is different, resulting in different stability. For the adsorbed atoms at the top, there is one atom around them, for the bridged atoms, there are two atoms around them, but for the adsorbed atoms at other locations, there are three atoms around them. According the definition of D, we calculated the barrier heights of two adsorption models. The diffusion barrier of Ge adsorption is 0.29 eV and the diffusion barrier of Si adsorption is 0.39 eV. This indicates that for Ge adsorption, it is necessary to cross the barrier height of 0.29 eV from the most stable state to the most stable state adjacent to it, while for Si, it is necessary to cross the barrier height of 0.39 eV. The diffusion barrier of Ge adsorption is less than the diffusion barrier of Ge adsorption, also indicating that the Si adsorption atoms are more stable than Ge adsorption. The larger the diffusion barrier, the more difficult it is for atoms to diffuse on the surface.
Table 1 Adsorption energies Eads, Diffusion barrier D, the bond length c and the initial distance d of different adsorption sites. Ge (D = 0.29 eV)
Si (D = 0.39 eV)
Adsorption position
Eads (eV)
c (Å)
d (Å)
Eads (eV)
c (Å)
d (Å)
top fcc hole hcp hole bridge
1.92 1.63 1.39 1.63
2.49 2.97 3.02 2.84
2.49 2.38 2.44 2.37
2.18 1.76 1.54 1.79
2.41 2.88 2.91 2.76
2.41 2.27 2.31 2.28
the optimal parameters of Ge adsorption is smaller than Si adsorption. The difference of initial distance d between Si adsorption and Ge adsorption is mainly due to the difference of electronegativity caused by the different electron distribution of the two atoms. The difference of electronegativity between Si and Ge is mainly due to the different electronic structures of the two atoms. Ge atom has one more layer of electrons than Si atom, which leads to stronger electronegativity.
3.3. Mulliken charge population 3.2. Adsorption energy and geometric optimization Population refers to the distribution of electrons in atomic orbitals. Analyzing this population is helpful for understanding the bonding of atoms in molecules. In this part, we study the charge distribution of two kinds of adsorbed atoms used by Mulliken charge population. The results are shown in the Table 2. The electronic arrangement of ground Ge atom and Si atom are as follows: 4s24p2 and 3s23p2, two electrons occupy the s and p orbitals, respectively. After the adsorption, the electrons of the s orbital of the adsorbed atom are transferred to the p orbital. Because of sp3 orbital hybridization, each silicon atom on the surface of SiC contains 1/4 s orbital electrons and 3/4p orbital electrons, so the s orbital of Si atom on the surface contains one electron and the p orbital contains three electrons. It can be found that, after relaxation, electron transfer from sorbital to p-orbital of adsorbed atoms. It can also be seen from Table 2 that, for the Ge adsorption, the number of electrons obtained by adsorbing atoms is very small (top(0.05e), fcc(0.04e), hcp(0.01e), and bridge(0.03e)). The corresponding surface atom loses more electrons (0.99e, 0.93e, 0.92e and 0.93e). For the Si adsorption, we observe gains of 0.06e, 0.04e, 0.00e and 0.03e of Si(a), which was also very few. The surface Si(s) of top site also losses Lost more electrons (0.97e, 0.91e, 0.89e and 0.91e), we found that all the adsorbed atoms get electrons, and all the surface atoms lose electrons. The electrons obtained by adsorbing atoms are mainly from surface atoms. The electron transfer between the adsorbed atom and the surface atom mainly comes from the contributions of Ge(4s) orbitals, Ge(4p) orbitals, Si(3s) orbitals and Si(3p) orbitals, indicating that a SieGe bond and SieSi bond are formed between the adsorbed atom and the surface. Therefore, the bonding between the adsorbed atom and the surface atom can be confirmed by the atomic charge population. It can also be seen that the charges located at the adatom bonded to surface Si atoms are very small, which suggests that the bonding is weak. In order to compare the difference of
Adsorption energy and geometric optimization of the adsorption models (top, hcp, fcc, bridge) of Si and Ge were studied. The result is shown in Table 1.The formula for calculating the adsorption energy is as follows: Eads = −(Esystem − Esubstrate − NEadatom)/ N . Where Esubstrate stands for the energy of the clean substrate, Esystem stands for the energy of an supercells system and Eadatom stands for the energy of a free adsorbed atom. N represents the number of adsorbed atoms. In this formula, because there is only one adsorbed atom, N is equal to 1. Diffusion barrier (D) is an important index to describe the diffusion degree of adsorbed atoms. The definition of D is the difference between the adsorption energy of the most stable position and the adsorption energy of the sub-stable position. After the models are relaxed, In order to achieve the most stable state, the initial distance d (the distance between adsorbed atoms and the adsorption surface) and the bond length c (the bond length between the adsorbed atom and the nearest atom of the surface) change accordingly. The results are also listed in Table 1. For the Ge adsorption, the optimal parameters d of the top model is 2.5 Å, the others are 2.4 Å. After relaxation, the distances corresponding to top, fcc, hcp and bridge are respectively as followed: 2.49 Å, 2.38 Å, 2.44 Å, 2.37 Å. The maximum change is only 0.04 Å. While for Si adsorption, the optimal parameters of the top model is 2.4 Å, the other position are 2.3 Å. The corresponding relaxation distances of the four models are: 2.41 Å for top, 2.27 Å for fcc, 2.31 Å for hcp and 2.28 Å for bridge. It can also be seen that the variation d is very small. This indicates that the initial distance (d) setting is closer to the actual distance. It can be seen that the larger the formula of Eads, the lower the energy of the system, and the more stable the whole adsorption system is. For the adsorption model of Ge atom, the maximum Eads is 1.92 eV at the top, the next is 1.63 eV at the fcc and hcp, and 1.39 eV at the bridge. For the adsorption model of Si atom, the maximum Eads is 2.18 eV at the top, the next is 1.79 eV at the bridge, 1.76 eV at the fcc and 1.54 eV at the hcp. For both models of Ge and Si adsorption, the energy of the top model is biggest, which implies that the most stable adsorption site for both adsorption models is the top site. This is mainly due to the strong interaction between surface atoms and adsorbed atoms. Compared with Ge adsorption, the adsorption energy of Si adsorption is larger, which indicates that Si atom is more stable on Si surface, while Ge tom is easier to diffuse on Si surface. For the adsorption model of Ge atom, the bond lengths c order of the four models from small to large is as follows: top(2.49 Å) < brige (2.84 Å) < fcc(2.97 Å) < hcp(3.02 Å). For the adsorption model of Si atom, the bond lengths order of the four models from small to large is as:top(2.41 Å) < brige(2.76 Å) < fcc(2.88 Å) < hcp(2.91 Å). The
Table 2 Population analysis of adsorbed atom Ge and Si. top Ge
Si
3
fcc
hcp
bridge
orbital
Ge
Si
Ge
Si
Ge
Si
Ge
Si
S P charge
1.73 2.32 −0.05
1.08 1.93 0.99
1.81 2.23 −0.04
1.10 1.97 0.93
1.83 2.18 −0.01
1.12 1.95 0.92
1.81 2.22 −0.03
1.10 1.97 0.93
orbital S P charge
Si(a) 1.71 2.35 −0.06
Si(s) 1.08 1.95 0.97
Si(a) 1.80 2.24 −0.04
Si(s) 1.10 1.99 0.91
Si(a) 1.83 2.17 −0.00
Si(s) 1.12 1.99 0.89
Si(a) 1.81 2.22 −0.03
Si(s) 1.10 1.99 0.91
Journal of Crystal Growth 531 (2020) 125370
X. He, et al.
Fig. 4. Density of state of model of Ge adsorption.
gain and loss electrons between the absorption surface and the clean surface, the charge population of the clean surface is calculated. The Si atom on the clean surface lost 1.04 electrons, which was more than that on the Ge adsorption surface (top (0.99e), fcc (0.93e), hcp (0.92e), bridge (0.93e)) and that on Si adsorption surface (top (0.97e), fcc (0.91e), hcp (0.89e), bridge (0.91e)), indicating that the new energy level may be introduced into the forbidden band to enhance the surface activity. 3.4. Densities of states Density of states denotes the number of electrons allowed per unit energy range. Because atomic orbitals are mainly divided by energy, the density of states can reflect the distribution of electrons in each orbit and the bonding between atoms. The densities of states results of electronic structure of Ge and Si on 4H-SiC(0 0 0 1) system is analyzed in Figs. 4 and 5. Fig. 6 shows the distribution of the density of states of the clean adsorbed surface. Firstly, we can see from Fig. 4 that the energy levels of a single Ge atom are relatively split without the energy band characteristics of Ge
Fig. 6. Density of state of clean 4H-SiC(0 0 0 1) surface.
crystal. Secondly, we can also see from the Fig. 6 that a new defect energy level appears in the band gap on a clean surface, which is caused by the surface hanging bond of SiC. Thirdly, due to the difference of adsorption sites of the adsorbed atom, there is a different degree of localization of the adsorbed atoms and surface atoms. It can be seen,
Fig. 5. Density of state of model of Si adsorption. 4
Journal of Crystal Growth 531 (2020) 125370
X. He, et al.
compared with the DOS of the clean 4H-SiC(0 0 0 1) Si-face, that the DOS of the surface of the top site, bridge site, fcc site and hcp site has a significant depreciation of the DOS at the Fermi level. The defect energy levels of the surface of the top site almost disappeared, indicating that the adsorbed atoms completely passivated the surface hanging bonds. Lastly, we can also found from the Fig. 4 that there are great resonance peaks, which indicates the presence of strong interactions of adsorbed atom and surface atoms. It can see from Fig. 5 that the energy levels of a single Si atom are relatively split without the energy band characteristics of Si crystal. The behaviors of the DOS of Si are qualitatively similar to that of Ge adsorption, but extent of depreciation is different. Seen from Figs. 5 and 6, for top adsorption, the density of states on the adsorption surface almost disappears, indicating that the system is the most stable at this time and that the top position is the most stable adsorption position.
Investigation. Hongbin Pu: Investigation. Yi Liang: Formal analysis. Teng Jia: Formal analysis.
4. Conclusions
References
In this paper, the adsorptions of Ge and Si atoms on the surface of 4H-SiC(0 0 0 1) were studied. For both models of Ge and Si adsorption, the most stable adsorption site is the top site. Compared with Ge adsorption, the adsorption energy of Si adsorption is larger, which indicates that Si atom is more stable on Si surface, while Ge atom is easier to diffuse on Si surface. Diffusion barrier also indicates that the Si adsorption atoms are more stable than Ge adsorption. For two models, the bond length c of top is the shortest and the distance d of the corresponding position is the longest. The bond length c of hcp is longest, while the distance d of the corresponding position is the shortest. It can be found from the charge populations that the bonding between the adsorbed atom and the surface atom can be confirmed. It can also be seen that the charges located at the adatom bonded to surface Si atoms are very small, which suggests that the bonding is weak. The behaviors of the DOS indicate the presence of strong interactions of adsorbed atom and surface atoms.
[1] Q. Chu, L. Li, C. Zhu, Y. Zang, S. Lin, Y. Han, Mater. Lett. 211 (2018) 133–137. [2] L.B. Li, Z.M. Chen, Y. Zang, CrystEngComm 18 (2016) 5681. [3] Y.L. Han, H.B. Pu, Y. Zang, L.B. Li, Optoelectron. Adv. Mater. Rapid Commun. 10 (9–10) (2016) 737–739. [4] K. Alassaad, V. Souli’ere, F. Cauwet, Acta Mater. 75 (2014) 219–226. [5] P.M. Gammon, A. Perez-Tom’as, M.R. Jennings, et al., J. Appl. Phys. 107 (12) (2010) 124512. [6] F. Zhu, Z.M. Chen, L.B. Li, et al., Chin. Phys. B 18 (11) (2009) 4966–4969. [7] Y. Zang, Z.M. Chen, L.B. Li, S.F. Zhao, IEEE International Conference on Electron Devices and Solid-State Circuits, 2009, pp. 306–309. [8] L.B. Li, Z.M. Chen, Y. Yang, Mater. Lett. 65 (2011) 1257–1260. [9] L.B. Li, Z.M. Chen, L.F. Xie, Mater. Lett. 93 (2013) 330–332. [10] L.F. Xie, Z.M. Chen, L.B. Li, C. Yang, X.M. He, N. Ye, Appl. Surf. Sci. 261 (2012) 88–91. [11] D. Vanderbilt, Phys. Rev. B: Condens. Matter 41 (11) (1990) 7892. [12] K. Laasonen, A. Pasquarello, R. Car, Phys. Rev. B: Condens. Matter 47 (16) (1993) 10142. [13] K. Burke, J.P. Perdew, Y. Wang, Electronic Density Functional Theory, Springer, US, 1998, pp. 81–111. [14] G. Jomard, T. Petit, L. Magaud, Phys. Rev. B 60 (23) (1999) 15624–15627. [15] A. Christensen, E.A. Carter, Phys. Rev. B 58 (12) (1998) 8050–8064. [16] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [17] T.H. Fischer, J. Almlof, J. Phys. Chem. 96 (24) (1992) 9768–9774.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was supported financially by the Natural Science Foundation of Shaanxi Province (Grants no. 19JK0571). This work was supported financially by Doctoral Scientific Research Foundation of Xi’an University of Technology (Grant no. Y201605).
CRediT authorship contribution statement Xiaomin He: Data curation, Writing-origainanl draft. Jichao Hu:
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Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Adsorption characteristics composition of Ge and Si on 4H-SiC(0 0 0 1) surface
T
⁎
Xiaomin He, Jichao Hu , Hongbin Pu, Yi Liang, Teng Jia Department of Electronic Engineering, Xi’an University of Technology, Xi’an 710048, China
A R T I C LE I N FO
A B S T R A C T
Communicated by Min Lu
Silicon (Si) and germanium (Ge) are two important materials for hetero-epitaxy of 4H-silicon carbide (4H-SiC), so the First-principles calculation is employed to compare the difference of the adsorptions of Ge and Si atoms on the surface of 4H-SiC(0 0 0 1) by calculating the adsorption energy, geometric optimization, charge populations and density of state. For the two different types, four common adsorption models (top, hcp, fcc, bridge) are studied. The calculation results of adsorption energy show that, for two different types of atoms, compared with other sites, the most stable adsorption site is top site. At the same time, another important feature is that Si atom is more stable on Si surface, while Ge atom is easier to diffuse on Si surface. The results of the diffusion barrier indicates that, compared with the adsorption of Si atoms, Ge atoms are more active on the adsorption surface, which is consistent with the adsorption energy. Charge populations results shows that there is obvious charge transfer between the adsorbed atom and the surface atom, which implies that Si-Ge bonds and Si-Si bonds are formed between the adsorbed atom and the surface atom. The behaviors of the DOS of Si are qualitatively similar to that of Ge adsorption. It can be seen from the dos results that there are great resonance peaks, which indicates the presence of strong interactions of adsorbed atom and surface atoms, but extent of depreciation is different.
Keywords: First-principles Adsorption Surface Si Ge
1. Introduction Although SiC based light control devices have been realized and have strong anti-interference ability, due to the forbidden band width of SiC materials, according to the relationship between the wavelength and the forbidden band width, 4H-SiC is only sensitive to ultraviolet light or shorter wavelength light, and is not sensitive to visible light and near-infrared light, so SiC light control devices can only be controlled by ultraviolet light source, which will be a long way degree increases the complexity and cost of the system. When it is not used properly, it can cause harm to human body and serious UV pollution to the environment, which limits the application range in the field of optoelectronics. In order to further expand its spectral response range to nearinfrared region, narrow band gap semiconductor Si and Ge are used as near-infrared sensitive layers [1,2]. To prepare the difference of the adsorptions of Ge and Si atoms on the surface of 4H-SiC (0 0 0 1). This paper mainly studies the adsorption from the theoretical aspect. In previous work, we have systematically studied the epitaxy growth of two kinds of atoms from the experimental aspect. Deposition of film on 4H-SiC is used by low-pressure chemical vapor deposition (LPCVD). high purity hydrogen (H2) is used as carrier gas respectively. Refs. [3–5] describe specific growth details. However, the 23.0% of lattice ⁎
mismatch between Ge(1 1 1) and 4H-SiC(0 0 0 1) can cause distortion or even dislocation near the interface. Si film has also been prepared on SiC [6–8]. For details, please refer to Ref. [6]. The Si films with [1 1 1] and [2 2 0] orientations have been successfully prepared on 6HSiC(0 0 0 1) substrate [9,10]. By studying the adsorption process, the atom diffusion and electron transfer processes can be understood and the properties of the Ge/4H-SiC(0 0 0 1) and Si/4H-SiC(0 0 0 1) interfacial systems can be further revealed. 2. Methodology In this paper, the studying is invested by the first-principles method. First-principles model parameters are very important. If the model parameters are not selected properly, the simulation results will be inaccurate. The first important parameter is potential. The electron-ion interaction is described by pseudopotential [11,12]. The generalized gradient approximation (PW91) [13] of Perdew GGA potentials is used to describe the exchange-correlation functional. PW91 represents a more inhomogeneous chemical environment [14,15]. Cutoff energy is a kind of plane wave which shows how much energy the plane wave takes after it expands. For the high-energy part, the proportion of cutoff energy is very small, and it affects the calculation speed, so it is not the
Corresponding author at: Department of Electronic Engineering, Xi’an University of Technology, Xi’an 710048, China. E-mail address: [email protected] (J. Hu).
https://doi.org/10.1016/j.jcrysgro.2019.125370 Received 15 July 2019; Received in revised form 18 November 2019; Accepted 19 November 2019 Available online 22 November 2019 0022-0248/ © 2019 Elsevier B.V. All rights reserved.
Journal of Crystal Growth 531 (2020) 125370
X. He, et al.
Fig. 1. Test of Cutoff energy. Fig. 3. Test of surface layers.
bigger the cutoff energy is, the better the truncation energy is. In this paper, the convergence of Eutoff energy is tested in Fig. 1. It is found that the system is stable when the truncation can reach 400 eV. In this paper, the single particle Kohn–Sham wave functions were expanded by a cutoff energy of 550 eV. In order to avoid the interaction between the slab and its periodic images, a vacuum region of 10 Å was embedded into the supercells. The Kohn–Sham equation was solved by the selfconsistent field (SCF) procedure with the SCF convergence threshold of 2e−6 eV/atom. A regular MonkhorstPack grid [16] with 7 × 7 × 1 kpoints was performed for the Sampling of the irreducible edge of Brillouin zone. Broyden–Fletcher–Goldfarb–Shanno (BFGS) [17] algorithm is considered to be the best quasi-Newton method with the best numerical effect, and has global convergence and superlinear convergence rate. In order to relax the minimum total energy of the supercells system, the BFGS algorithm with a convergence tolerance of 0.01 eV/Å was used to fulfill the geometry optimization.
models named top, hcp, fcp and bridge. The adsorption model of Si atom on 4H-SiC surface is similar to that of Ge atom. The only difference is that Si atom is used to replace Ge atom while keeping other structures unchanged. In this structure, the 4H-SiC(0 0 0 1) surface is simulated by the thickness of an atomic layer. If the thickness is too small, it cannot represent the surface model. In order to find the number of atomic layers that can represent the surface, the convergence of the surface structure with different atomic layer thickness is tested in Fig. 3. It can be found that when the number of atomic layers reaches ten, the surface energy is basically stable. In the simulation calculation, ten layers of atoms are used as surface models, and only six layers of atoms on the surface are allowed to move freely, while the atoms on the back remain unchanged. Vertical distance d of the Ge and Si adatom from the surface layer is a very important parameter. Once this parameter is unreasonable, the calculation will not converge or the result will be wrong. If the distance d between the adsorbed atom and the surface atom is too large, the bonding between the atoms will not be possible. If the distance between the atoms is too small, it will not conform to the bonding law of the atoms. Therefore, in the early stage, we used the results of energy calculation to predict the initial distance d. For the Ge adsorption, the optimal parameters of the top model is 2.5 Å, the others are 2.4 Å. While for Si adsorption, the optimal parameters of the top model is 2.4 Å, the other position are 2.3 Å. We find that the optimal distance parameters of the four models are very close to the actual covalent bond performance distance. We can also find that
3. Results and discussion 3.1. Adsorption model The adsorption model of Ge atom on SiC(0 0 0 1) surface is shown in the following Fig. 2. Because there are two surfaces when the surface model of 4H-SiC(0 0 0 1) is established, in order to restrain the influence of another surface, one of the two surfaces adsorbs Ge atom and the other is passivated by hydrogen (H) atom. The four adsorption
Fig. 2. Top view and front view of the adsorption model of Ge atom on SiC(0 0 0 1) surface. Green represents the adsorbed atom Ge, yellow represents Si atom, gray represents C atom and white represents H atom. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
2
Journal of Crystal Growth 531 (2020) 125370
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trend of bond length is the same as that of energy: the larger the energy, the smaller the bond length. For two models, the bond length c of top is the shortest. The bond length c of hcp is longest, this is mainly because that the number of atoms around the atoms at different adsorption sites is different, resulting in different stability. For the adsorbed atoms at the top, there is one atom around them, for the bridged atoms, there are two atoms around them, but for the adsorbed atoms at other locations, there are three atoms around them. According the definition of D, we calculated the barrier heights of two adsorption models. The diffusion barrier of Ge adsorption is 0.29 eV and the diffusion barrier of Si adsorption is 0.39 eV. This indicates that for Ge adsorption, it is necessary to cross the barrier height of 0.29 eV from the most stable state to the most stable state adjacent to it, while for Si, it is necessary to cross the barrier height of 0.39 eV. The diffusion barrier of Ge adsorption is less than the diffusion barrier of Ge adsorption, also indicating that the Si adsorption atoms are more stable than Ge adsorption. The larger the diffusion barrier, the more difficult it is for atoms to diffuse on the surface.
Table 1 Adsorption energies Eads, Diffusion barrier D, the bond length c and the initial distance d of different adsorption sites. Ge (D = 0.29 eV)
Si (D = 0.39 eV)
Adsorption position
Eads (eV)
c (Å)
d (Å)
Eads (eV)
c (Å)
d (Å)
top fcc hole hcp hole bridge
1.92 1.63 1.39 1.63
2.49 2.97 3.02 2.84
2.49 2.38 2.44 2.37
2.18 1.76 1.54 1.79
2.41 2.88 2.91 2.76
2.41 2.27 2.31 2.28
the optimal parameters of Ge adsorption is smaller than Si adsorption. The difference of initial distance d between Si adsorption and Ge adsorption is mainly due to the difference of electronegativity caused by the different electron distribution of the two atoms. The difference of electronegativity between Si and Ge is mainly due to the different electronic structures of the two atoms. Ge atom has one more layer of electrons than Si atom, which leads to stronger electronegativity.
3.3. Mulliken charge population 3.2. Adsorption energy and geometric optimization Population refers to the distribution of electrons in atomic orbitals. Analyzing this population is helpful for understanding the bonding of atoms in molecules. In this part, we study the charge distribution of two kinds of adsorbed atoms used by Mulliken charge population. The results are shown in the Table 2. The electronic arrangement of ground Ge atom and Si atom are as follows: 4s24p2 and 3s23p2, two electrons occupy the s and p orbitals, respectively. After the adsorption, the electrons of the s orbital of the adsorbed atom are transferred to the p orbital. Because of sp3 orbital hybridization, each silicon atom on the surface of SiC contains 1/4 s orbital electrons and 3/4p orbital electrons, so the s orbital of Si atom on the surface contains one electron and the p orbital contains three electrons. It can be found that, after relaxation, electron transfer from sorbital to p-orbital of adsorbed atoms. It can also be seen from Table 2 that, for the Ge adsorption, the number of electrons obtained by adsorbing atoms is very small (top(0.05e), fcc(0.04e), hcp(0.01e), and bridge(0.03e)). The corresponding surface atom loses more electrons (0.99e, 0.93e, 0.92e and 0.93e). For the Si adsorption, we observe gains of 0.06e, 0.04e, 0.00e and 0.03e of Si(a), which was also very few. The surface Si(s) of top site also losses Lost more electrons (0.97e, 0.91e, 0.89e and 0.91e), we found that all the adsorbed atoms get electrons, and all the surface atoms lose electrons. The electrons obtained by adsorbing atoms are mainly from surface atoms. The electron transfer between the adsorbed atom and the surface atom mainly comes from the contributions of Ge(4s) orbitals, Ge(4p) orbitals, Si(3s) orbitals and Si(3p) orbitals, indicating that a SieGe bond and SieSi bond are formed between the adsorbed atom and the surface. Therefore, the bonding between the adsorbed atom and the surface atom can be confirmed by the atomic charge population. It can also be seen that the charges located at the adatom bonded to surface Si atoms are very small, which suggests that the bonding is weak. In order to compare the difference of
Adsorption energy and geometric optimization of the adsorption models (top, hcp, fcc, bridge) of Si and Ge were studied. The result is shown in Table 1.The formula for calculating the adsorption energy is as follows: Eads = −(Esystem − Esubstrate − NEadatom)/ N . Where Esubstrate stands for the energy of the clean substrate, Esystem stands for the energy of an supercells system and Eadatom stands for the energy of a free adsorbed atom. N represents the number of adsorbed atoms. In this formula, because there is only one adsorbed atom, N is equal to 1. Diffusion barrier (D) is an important index to describe the diffusion degree of adsorbed atoms. The definition of D is the difference between the adsorption energy of the most stable position and the adsorption energy of the sub-stable position. After the models are relaxed, In order to achieve the most stable state, the initial distance d (the distance between adsorbed atoms and the adsorption surface) and the bond length c (the bond length between the adsorbed atom and the nearest atom of the surface) change accordingly. The results are also listed in Table 1. For the Ge adsorption, the optimal parameters d of the top model is 2.5 Å, the others are 2.4 Å. After relaxation, the distances corresponding to top, fcc, hcp and bridge are respectively as followed: 2.49 Å, 2.38 Å, 2.44 Å, 2.37 Å. The maximum change is only 0.04 Å. While for Si adsorption, the optimal parameters of the top model is 2.4 Å, the other position are 2.3 Å. The corresponding relaxation distances of the four models are: 2.41 Å for top, 2.27 Å for fcc, 2.31 Å for hcp and 2.28 Å for bridge. It can also be seen that the variation d is very small. This indicates that the initial distance (d) setting is closer to the actual distance. It can be seen that the larger the formula of Eads, the lower the energy of the system, and the more stable the whole adsorption system is. For the adsorption model of Ge atom, the maximum Eads is 1.92 eV at the top, the next is 1.63 eV at the fcc and hcp, and 1.39 eV at the bridge. For the adsorption model of Si atom, the maximum Eads is 2.18 eV at the top, the next is 1.79 eV at the bridge, 1.76 eV at the fcc and 1.54 eV at the hcp. For both models of Ge and Si adsorption, the energy of the top model is biggest, which implies that the most stable adsorption site for both adsorption models is the top site. This is mainly due to the strong interaction between surface atoms and adsorbed atoms. Compared with Ge adsorption, the adsorption energy of Si adsorption is larger, which indicates that Si atom is more stable on Si surface, while Ge tom is easier to diffuse on Si surface. For the adsorption model of Ge atom, the bond lengths c order of the four models from small to large is as follows: top(2.49 Å) < brige (2.84 Å) < fcc(2.97 Å) < hcp(3.02 Å). For the adsorption model of Si atom, the bond lengths order of the four models from small to large is as:top(2.41 Å) < brige(2.76 Å) < fcc(2.88 Å) < hcp(2.91 Å). The
Table 2 Population analysis of adsorbed atom Ge and Si. top Ge
Si
3
fcc
hcp
bridge
orbital
Ge
Si
Ge
Si
Ge
Si
Ge
Si
S P charge
1.73 2.32 −0.05
1.08 1.93 0.99
1.81 2.23 −0.04
1.10 1.97 0.93
1.83 2.18 −0.01
1.12 1.95 0.92
1.81 2.22 −0.03
1.10 1.97 0.93
orbital S P charge
Si(a) 1.71 2.35 −0.06
Si(s) 1.08 1.95 0.97
Si(a) 1.80 2.24 −0.04
Si(s) 1.10 1.99 0.91
Si(a) 1.83 2.17 −0.00
Si(s) 1.12 1.99 0.89
Si(a) 1.81 2.22 −0.03
Si(s) 1.10 1.99 0.91
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Fig. 4. Density of state of model of Ge adsorption.
gain and loss electrons between the absorption surface and the clean surface, the charge population of the clean surface is calculated. The Si atom on the clean surface lost 1.04 electrons, which was more than that on the Ge adsorption surface (top (0.99e), fcc (0.93e), hcp (0.92e), bridge (0.93e)) and that on Si adsorption surface (top (0.97e), fcc (0.91e), hcp (0.89e), bridge (0.91e)), indicating that the new energy level may be introduced into the forbidden band to enhance the surface activity. 3.4. Densities of states Density of states denotes the number of electrons allowed per unit energy range. Because atomic orbitals are mainly divided by energy, the density of states can reflect the distribution of electrons in each orbit and the bonding between atoms. The densities of states results of electronic structure of Ge and Si on 4H-SiC(0 0 0 1) system is analyzed in Figs. 4 and 5. Fig. 6 shows the distribution of the density of states of the clean adsorbed surface. Firstly, we can see from Fig. 4 that the energy levels of a single Ge atom are relatively split without the energy band characteristics of Ge
Fig. 6. Density of state of clean 4H-SiC(0 0 0 1) surface.
crystal. Secondly, we can also see from the Fig. 6 that a new defect energy level appears in the band gap on a clean surface, which is caused by the surface hanging bond of SiC. Thirdly, due to the difference of adsorption sites of the adsorbed atom, there is a different degree of localization of the adsorbed atoms and surface atoms. It can be seen,
Fig. 5. Density of state of model of Si adsorption. 4
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compared with the DOS of the clean 4H-SiC(0 0 0 1) Si-face, that the DOS of the surface of the top site, bridge site, fcc site and hcp site has a significant depreciation of the DOS at the Fermi level. The defect energy levels of the surface of the top site almost disappeared, indicating that the adsorbed atoms completely passivated the surface hanging bonds. Lastly, we can also found from the Fig. 4 that there are great resonance peaks, which indicates the presence of strong interactions of adsorbed atom and surface atoms. It can see from Fig. 5 that the energy levels of a single Si atom are relatively split without the energy band characteristics of Si crystal. The behaviors of the DOS of Si are qualitatively similar to that of Ge adsorption, but extent of depreciation is different. Seen from Figs. 5 and 6, for top adsorption, the density of states on the adsorption surface almost disappears, indicating that the system is the most stable at this time and that the top position is the most stable adsorption position.
Investigation. Hongbin Pu: Investigation. Yi Liang: Formal analysis. Teng Jia: Formal analysis.
4. Conclusions
References
In this paper, the adsorptions of Ge and Si atoms on the surface of 4H-SiC(0 0 0 1) were studied. For both models of Ge and Si adsorption, the most stable adsorption site is the top site. Compared with Ge adsorption, the adsorption energy of Si adsorption is larger, which indicates that Si atom is more stable on Si surface, while Ge atom is easier to diffuse on Si surface. Diffusion barrier also indicates that the Si adsorption atoms are more stable than Ge adsorption. For two models, the bond length c of top is the shortest and the distance d of the corresponding position is the longest. The bond length c of hcp is longest, while the distance d of the corresponding position is the shortest. It can be found from the charge populations that the bonding between the adsorbed atom and the surface atom can be confirmed. It can also be seen that the charges located at the adatom bonded to surface Si atoms are very small, which suggests that the bonding is weak. The behaviors of the DOS indicate the presence of strong interactions of adsorbed atom and surface atoms.
[1] Q. Chu, L. Li, C. Zhu, Y. Zang, S. Lin, Y. Han, Mater. Lett. 211 (2018) 133–137. [2] L.B. Li, Z.M. Chen, Y. Zang, CrystEngComm 18 (2016) 5681. [3] Y.L. Han, H.B. Pu, Y. Zang, L.B. Li, Optoelectron. Adv. Mater. Rapid Commun. 10 (9–10) (2016) 737–739. [4] K. Alassaad, V. Souli’ere, F. Cauwet, Acta Mater. 75 (2014) 219–226. [5] P.M. Gammon, A. Perez-Tom’as, M.R. Jennings, et al., J. Appl. Phys. 107 (12) (2010) 124512. [6] F. Zhu, Z.M. Chen, L.B. Li, et al., Chin. Phys. B 18 (11) (2009) 4966–4969. [7] Y. Zang, Z.M. Chen, L.B. Li, S.F. Zhao, IEEE International Conference on Electron Devices and Solid-State Circuits, 2009, pp. 306–309. [8] L.B. Li, Z.M. Chen, Y. Yang, Mater. Lett. 65 (2011) 1257–1260. [9] L.B. Li, Z.M. Chen, L.F. Xie, Mater. Lett. 93 (2013) 330–332. [10] L.F. Xie, Z.M. Chen, L.B. Li, C. Yang, X.M. He, N. Ye, Appl. Surf. Sci. 261 (2012) 88–91. [11] D. Vanderbilt, Phys. Rev. B: Condens. Matter 41 (11) (1990) 7892. [12] K. Laasonen, A. Pasquarello, R. Car, Phys. Rev. B: Condens. Matter 47 (16) (1993) 10142. [13] K. Burke, J.P. Perdew, Y. Wang, Electronic Density Functional Theory, Springer, US, 1998, pp. 81–111. [14] G. Jomard, T. Petit, L. Magaud, Phys. Rev. B 60 (23) (1999) 15624–15627. [15] A. Christensen, E.A. Carter, Phys. Rev. B 58 (12) (1998) 8050–8064. [16] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [17] T.H. Fischer, J. Almlof, J. Phys. Chem. 96 (24) (1992) 9768–9774.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was supported financially by the Natural Science Foundation of Shaanxi Province (Grants no. 19JK0571). This work was supported financially by Doctoral Scientific Research Foundation of Xi’an University of Technology (Grant no. Y201605).
CRediT authorship contribution statement Xiaomin He: Data curation, Writing-origainanl draft. Jichao Hu:
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