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Effect of dangling bonds of ultra-thin silicon film surface on electronic states of internal atoms
Applied Surface Science 258 (2012) 5265–5269
Contents lists available at SciVerse ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Effect of dangling bonds of ultra-thin silicon film surface on electronic states of internal atoms Eiji Kamiyama ∗ , Koji Sueoka 1 Department of Communication Engineering, Okayama Prefectural University, 111 Kuboki, Soja, Okayama 719-1197, Japan
a r t i c l e
i n f o
Article history: Received 1 October 2011 Received in revised form 3 February 2012 Accepted 4 February 2012 Available online 13 February 2012 Keywords: Silicon Film Density of states Dangling bond Mid-gap states
a b s t r a c t We investigate how dangling bonds at the surface of ultra-thin films affect electronic states inside the film by first principles calculation. In the calculation models, dangling bonds at the surface are directly treated, and the impact on the electronic states of the internal atoms was estimated. Models with a Hterminated surface at both sides have no state in the bandgap. Whereas, new states appear at around the midgap by removing terminated H at surfaces of one or both sides. These mid-gap states appear at all layers, the states of which decrease as the layer moves away from the surface with dangling bonds. The sum of local DOS corresponds to the number of dangling bonds of the model. If the activation rate is assumed as 2.0 × 10−5 , which is an ordinary value of thermal oxide passivation on Si (1 0 0) surface, volume concentration and surface concentration at the 18th layer from the surface in a 36-layer model are estimated to be 1.2 × 1014 cm−3 and 1.5 × 109 cm−2 , respectively. These numbers are comparable to the values, especially the dopant volume concentration of Si substrate used in current VLSI technology (∼1015 cm−3 ). Therefore, the midgap states inside ultra-thin films may degrade performance of the FinFETs. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Nanometer-scale ultra-thin films are now being applied to the structures of next-generation electronic devices [1] as well as their starting materials. Silicon-on-insulator (SOI) wafers are a candidate starting material and have an amorphous SiO2 layer as a base for silicon (Si) thin film [2–7], while Si films with silicon-on-nothing (SON) structures have nothing beneath them [8]. The flexibility of Si atoms located at the film/base interface of SOI wafers is restricted by their bonds with the base atoms. In contrast, Si atoms located at the free top surfaces of the Si film can easily form dimer structures such as those of a bulk surface, and the Si atoms just beneath the surface are expected to adjust to the deviations of the top surface atoms forming dimer structures. SOI wafers with a top Si film around 5 nm thick were expected to be used in electronic devices at one time [9]. Such films have around 30 layers of Si atoms. The surface effect is expected to become relatively large as the top Si film in SOI wafers and/or SON structures become thinner in thickness. Meanwhile, FinFETs are promising structures for next-generation
∗ Corresponding author. Tel.: +81 866 94 2136; fax: +81 866 94 2199. E-mail addresses: [email protected] (E. Kamiyama), [email protected] (K. Sueoka). 1 Tel.: +81 866 94 2136; fax: +81 866 94 2199. 0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2012.02.012
electrical devices. The heart of the FinFETs is a “Fin”-shaped Si thin film of nanometer-scale thickness [10]. Modeling of nanometer scale ultra-thin Si films with dimer structures at the surface was investigated using both conventional plate shaped models and two additional plate shaped models with different constraint conditions for atoms and cells [11]. The energy gains forming dimers in the models with no constrained atoms in the film were smaller than those in the models with constrained atoms at the center of the films and with fewer layers. The amount of deviation of all atoms deeper than the fifth layer in the models with no constrained atoms was also much higher than that in the models with constrained atoms. These facts indicate that the dimer formations deform the positions of atoms below the surface and increase the total energies as the sizes of the models increase, i.e., this energy increase is due to the deformation of internal atoms from the bulk positions, which are propagated from the surfaces that had dimers. For the reason stated above, the film surface and the internal atoms compete to stabilize the structure of ultra-thin Si (1 0 0) films as a whole. In the FinFETs, the structure of internal atoms of ultrathin films should be investigated because the signal current flows mainly in them. Whereas, the film surface can be controlled to prevent the deviations of internal atoms by the surface stabilizations. This kind control, technology for which is expected to be invented in future, is similar to an electronic passivation by SiO2 films to prevent the electronic states from forming at the Si film surface. The
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those of Fig. 1(a) to evaluate the effect of the dangling bonds at the surface only, apart from the deformations of dimerization. For comparisons, dangling bonds of some models were later terminated by hydrogen (H) atoms to eliminate their effects. The smearing value for calculating density of states was set at 0.05 eV to obtain an appropriate resolution between states. The calculations of first principles analysis were based on the local density approximation [12,13] using the ultra-soft pseudopotential method [14] and the plane waves as a basis set for efficient structure optimization. The expression proposed by Perdew et al. [15] was used for the exchange-correlation energy in the generalized gradient approximation (GGA). The CASTEP code was used to solve the Kohn-Sham equation self-consistently with the threedimensional periodic boundary condition [16]. The density mixing method [17] and BFGS geometry optimization method [18] were used to optimize the electronic structure and atomic configurations, respectively. Only the neutral charge state of the systems was considered in this study. The calculations were performed for the system at a temperature of absolute zero. Additionally, k-point sampling was tested at 3 × 7 × 1 and 3 × 6 × 1 special points of the Monkhorst–Pack grid [19]. The cutoff energy of the plane waves was also tested at 310 eV and 350 eV. Fig. 2 shows charge density distributions in the z-direction of a 48 layers bulk model for each condition: (a) 3 × 7 × 1 special points and cutoff energy at 350 eV; (b) 3 × 6 × 1 special points and cutoff energy at 350 eV; and (c) 3 × 7 × 1 special points and cutoff energy at 310 eV. Each peak of the charges in all figures is at the position corresponding to the bonding center between two Si atoms. This fact shows the bonding has a covalent nature. The grids of charge density distributions are determined automatically by CASTEP. Condition (c) was not uniformly distributed because grids of the model in the z-direction of the cell were divided not into 480 parts like (a) and (b) but 450 parts. Condition (a) was most uniformly distributed. Hence, we will apply condition (a) from here.
3. Results and discussion Fig. 1. (a) Bulk model with 48 layers along z-direction in unit cell and two atoms in each layer. (b) A example of a Si film model that has 16 layers with vacuum slabs. In this model, atoms had been removed from the Fig. 1(a) after the geometrical optimization. Models with the number of layers (16, 20, 24, 28, 32, and 36) were also calculated.
surface of an ultra-thin film can certainly affect the electronic carriers inside the film, differing from that of a bulk. How dangling bonds at the film surface affect the inside of the ultra-thin films, which are used in devices like FinFETs, should be investigated because the surface states generally come from the remained dangling bonds after the passivation at the surface. In this paper, we investigate the effect of dangling bonds at the surface of ultra-thin films on electronic states inside the film by first principles calculation. In the calculation model, dangling bonds are directly treated and the impact on the electronic states at the internal atoms was estimated. 2. Simulation details First, we fabricated a bulk model that had 48 layers along the z-direction in the unit cell and two atoms in each layer, as shown in Fig. 1(a). An example of a Si film model that has 16 layers with vacuum slabs is shown in Fig. 1(b), in which atoms had been removed from the Fig. 1(a) after the geometrical optimization. The numbers of layers calculated were 16, 20, 24, 28, 32, and 36 in the models shown in Fig. 1(b). After that, the total energy, charge density distribution and local density of states (LDOS) were calculated while all atom positions were kept the same as
Fig. 3 shows charge density distributions in the z-direction of film models normalized by a bulk (i.e., Fig. 2(a)): (a) shows a whole cell in horizontal axis and a full range of the density in vertical axis; (b) shows a whole cell in horizontal axis and a magnified range of the density around unity in vertical axis from (a); and (c) shows a center area of films in horizontal axis and a far magnified range of the density around unity in vertical axis from (b). In a film, charges crowd around the atom positions more than a bulk. This trend reaches its maximum at the second layer and second maximum at the third layer from the surface of films. At the fourth and fifth layers, the charges also have peaks but the baselines are far lower than the bulk (unity). The deviations of charges in internal portions of the films that have more layers become fewer than those of the near surface portions, and about 0.001% at the center of the film of a 36-layer model. A dangling bond at a Si (1 0 0) surface atom remains even after dimer formation. Hence, the charge distribution in internal portions of the films does not change very much after dangling bonds decrease and the internal atoms are deformed by the dimer formation at the surface. Fig. 4 compares calculated Si atom self-energies of a bulk and films. The self-energies of films were deduced by the subtraction between total energies of next layer number models. The differences are very small and within the range of 0.001 eV. We discussed similar comparison in our previous paper [20] and showed a possibility of self-energy of a Si atom in the film that is about 0.005 eV lower than that in the Si bulk. However, this result shows that films and a bulk do not obviously differ. Our previous results showed a difference because they must have had an error of first principles
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Fig. 3. Charge density distributions in z-direction of film models normalized by bulk: (a) shows whole cell in horizontal axis and full range of density in vertical axis; (b) shows whole cell in horizontal axis and magnified range of density around unity in vertical axis from (a); (c) shows center area of films in horizontal axis and far magnified range of density around unity in vertical axis from (b).
Fig. 2. Charge density distributions in z-direction of 48-layer bulk model for each condition: (a) 3 × 7 × 1 special points and cutoff energy at 350 eV; (b) 3 × 6 × 1 special points and cutoff energy at 350 eV; (c) 3 × 7 × 1 special points and cutoff energy at 310 eV.
analysis in the modelling, where different cell size models were calculated by the same k-point sampling condition. Fig. 5 shows the total DOS of Si atoms in 16-layer models with and without H-terminated surfaces (Si–H bond length was set at 0.154 nm) around the bandgaps. The model with a H-terminated surface at both sides shows a 0.7 eV-wide bandgap, which is wider than that of a typical bulk value (0.6 eV) calculated by using the expression of exchange-correlation energy proposed by Perdew et al. This bandgap change must come from a quantum confinement effect because the 36-layer model with an H-terminated surface at both sides shows a value close to the bulk. Any models like them with an H-terminated surface at both sides had no state in the bandgap. Whereas, removing terminated-H changes the total DOS drastically. The point to find is that new states are made to appear at around the midgap (∼0.4 eV) by removing terminated H at surfaces of one or both sides. This thought to correspond to the fact
Fig. 4. Comparison of calculated Si atom self-energies of bulk and films.
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Fig. 5. Total DOS of 16-layer models with and without H-terminated surface around bandgaps. Fig. 7. LDOS for each layer of 36-layer model [11].
that charges crowd around the atom positions more than a bulk in Fig. 3. The LDOS for each layer of a 16-layer model with terminatedH at the surfaces of one side was also calculated and is shown in Fig. 6. The same as in Fig. 5, mid-gap states can be seen at all layers, states of which decrease as the layer moves away from the surface with dangling bonds. The Si films models with dimer structures at both side surfaces were investigated by adding dimer structures to Fig. 1(b)-type models and geometrically optimizing the atoms and the cell. Fig. 7 shows a LDOS for each layer of the 36-layer model with citing results from our previous work [11]. The LDOS peak around 0.4 eV remained, but the peak height decreased to 1/4. The main part of LDOS moved to and formed new states around 0.6 eV, which came from bonding orbitals in the dimers. Notice that the amount of LDOS at 0.4 eV in the center of the film with dimer structures at surfaces of both sides is close to that of the film with no dimer structures at surfaces of either side, shown in Fig. 6. Fig. 8 shows LDOS dependence of midgap states in various models/conditions on the distance from the surfaces. This figure compares between (1) a 36-layer model without a H-terminated
Fig. 6. LDOS for each layer of 16-layer model with terminated H at surface of one side.
surface but showing LDOS only at from the first layer to the 18th layer, (2) a 16-layer model without a H-terminated surface, and (3) a 16-layer model with a H-terminated surface at one side. The LDOS in all models decrease as the distances from the surface increase. Surprisingly, they show the same exponential decrease in LDOS. The sum of LDOS in from first to 18th layers of a 36-layer model is 3.94 electrons and almost equal to the number of dangling bonds at one side of the model. This is thought to correspond to a fact that states of dangling bonds generally appear at midgap. This number can convert into 5.5 × 1021 cm−3 and 1.3 × 1015 cm−2 , as respectively a volume concentration and a surface concentration, where 0.714 nm3 of the volume of 18 layers and 0.298 nm2 of the surface area in the model are used. If the activation rate is assumed as 2.0 × 10−5 , which is an ordinary value of thermal oxide passivation on a Si (1 0 0) surface, these numbers reduce to 1.1 × 1017 cm−3 and 2.6 × 1010 cm−2 . At the 18th layer from the surface in a 36-layer model, LDOS retains 2.6 × 10−4 electrons/eV, which can convert into 5.8 × 1018 cm−3 and 7.7 × 1013 cm−2 . Considering the
Fig. 8. LDOS dependence of midgap states on the distance from surfaces in various models/conditions: (1) 36-layer model without H-terminated surface but showing LDOS only at from first to 18th layer; (2) 16-layer model without H-terminated surface; (3) 16-layer model with H-terminated surface at one side.
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activation rate, the LDOSs inside ultra-thin film reduce to 1.2 × 1014 cm−3 and 1.5 × 109 cm−2 . These numbers are comparable to the ordinary values, especially the dopant volume concentration of a Si substrate used in a current electronic device technology (∼1015 cm−3 ). These dopant concentration substrates are expected to continue to be used in FinFETs in future. Therefore, the midgap states inside ultra-thin films, mentioned above, may degrade performance of the FinFETs. The midgap states will appear on the surfaces of lightly doped Si samples as well as the intrinsic Si films calculated in this study. The positive charges on the surface of p-type Si samples after a diluted HF dip were detected by alternating current surface photovoltage method [21]. This result can be explained by the existence of the midgap states as the followings. Some Si atoms at the surface are thought to be missing H atoms after the diluted HF dip and have dangling bonds. In such a case, the dopant B atoms inside the surface get electrons from the midgap states originated from these dangling bonds since the Fermi level locates at lower than the mid-gap position in p-type Si. Therefore, the surface Si atoms with dangling bonds show positive charges.
film with no dimer structures. The sum of LDOS from first to 18th layers of a 36-layer model with no dimer structures is 3.94 electrons and almost equal to the number of dangling bonds at one side of the model. This number can convert into 5.5 × 1021 cm−3 and 1.3 × 1015 cm−2 as a volume concentration and a surface concentration, respectively. If the activation rate is assumed as 2.0 × 10−5 , which is an ordinary value of thermal oxide passivation on Si (1 0 0) surface, these numbers reduce to 1.1 × 1017 cm−3 and 2.6 × 1010 cm−2 , respectively. At the 18th layer from the surface in a 36-layer model, LDOS retains 2.6 × 10−4 electrons/eV, which can convert into 5.8 × 1018 cm−3 and 7.7 × 1013 cm−2 . Considering the activation rate, the LDOSs inside ultra-thin film reduce to 1.2 × 1014 cm−3 and 1.5 × 109 cm−2 . These numbers are comparable to the ordinary values, especially the dopant volume concentration of the Si substrate used in a current electronic device technology. These dopant concentration substrates are expected to continue to be used in FinFET in future. Therefore, the midgap states inside ultra-thin films may degrade performance of the FinFETs.
4. Conclusions
[1] International Technology Roadmap for Semiconductors, 2009 Edition, International Roadmap Committee. [2] T.R. Anthony, J. Appl. Phys. 58 (1985) 1240. [3] T. Yonehara, K. Sakuguti, N. Sato, Appl. Phys. Lett. 64 (1994) 2108. [4] M. Bruel, B. Aspar, A.J. Auberton-Herve, Jpn. J. Appl. Phys. 36 (1997) 1636. [5] K. Izumi, M. Doken, H. Ariyoshi, Electron. Lett. 14 (1978) 593. [6] S. Nakashima, K. Izumi, J. Mater. Res. 7 (1992) 788. [7] O.W. Holland, D. Fathy, D.K. Sadana, Appl. Phys. Lett. 69 (1996) 674. [8] I. Mizushima, T. Sato, S. Taniguchi, Y. Tsunashima, Appl. Phys. Lett. 77 (2000) 3290. [9] International Technology Roadmap for Semiconductors, 2005 Edition, International Roadmap Committee. [10] D. Hisamoto, W.-C. Lee, J. Kedzierski, E. Anderson, H. Takeuchi, A. Asano, T.-J. King, J. Bokor, C. Hu, A Foldered-channel MOSFET for Deep-sub-tenth Micron Era, IEDM Tech. Dig., nm15.7, San Francisco, USA, December, 1998, pp.1032–1034. [11] E. Kamiyama, K. Sueoka, Surf. Sci., submitted. [12] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. [13] W. Kohn, L. Sham, Phys. Rev. 140 (1965) A1133. [14] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [15] J. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [16] The CASTEP code is available from Accelrys Software Inc. [17] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [18] T. Fischer, J. Almlof, J. Phys. Chem. 96 (1992) 9768. [19] H. Monkhorst, J. Pack, Phys. Rev. B 13 (1976) 5188. [20] E. Kamiyama, K. Sueoka, J. Electrochem. Soc. 157 (2010) H323. [21] H. Shimizu, Y. Sanada, Jpn. J. Appl. Phys. 50 (2011) 111301.
We investigated how dangling bonds at the surface of ultra-thin films affect electronic states inside the film by first principles calculation. In the calculation model, dangling bonds are directly treated and estimate the impact on the electronic states at the internal atoms. In a film, charges crowd around the atom positions more than a bulk. This trend reaches its maximum at the second layer and second maximum at the third layer from the surface of films. At the fourth and fifth layers, the charges also have peaks but the baselines are far lower than the bulk. The deviations of charges in internal portions of the films that have more layers become fewer than those of the surface portions, and about 0.001% at the center of the film of a 36-layer model. Any models with an H-terminated surface at both sides had no state in the bandgap. Whereas, new states are made to appear at around the midgap by removing terminated-H at surfaces of one or both sides. These mid-gap states appear at all layers, states of which decreases as the layer moves away from the surface with dangling bonds. In the models with dimer structures at both side surfaces, the amount of LDOS at the midgap is close to that of the
References
Contents lists available at SciVerse ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Effect of dangling bonds of ultra-thin silicon film surface on electronic states of internal atoms Eiji Kamiyama ∗ , Koji Sueoka 1 Department of Communication Engineering, Okayama Prefectural University, 111 Kuboki, Soja, Okayama 719-1197, Japan
a r t i c l e
i n f o
Article history: Received 1 October 2011 Received in revised form 3 February 2012 Accepted 4 February 2012 Available online 13 February 2012 Keywords: Silicon Film Density of states Dangling bond Mid-gap states
a b s t r a c t We investigate how dangling bonds at the surface of ultra-thin films affect electronic states inside the film by first principles calculation. In the calculation models, dangling bonds at the surface are directly treated, and the impact on the electronic states of the internal atoms was estimated. Models with a Hterminated surface at both sides have no state in the bandgap. Whereas, new states appear at around the midgap by removing terminated H at surfaces of one or both sides. These mid-gap states appear at all layers, the states of which decrease as the layer moves away from the surface with dangling bonds. The sum of local DOS corresponds to the number of dangling bonds of the model. If the activation rate is assumed as 2.0 × 10−5 , which is an ordinary value of thermal oxide passivation on Si (1 0 0) surface, volume concentration and surface concentration at the 18th layer from the surface in a 36-layer model are estimated to be 1.2 × 1014 cm−3 and 1.5 × 109 cm−2 , respectively. These numbers are comparable to the values, especially the dopant volume concentration of Si substrate used in current VLSI technology (∼1015 cm−3 ). Therefore, the midgap states inside ultra-thin films may degrade performance of the FinFETs. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Nanometer-scale ultra-thin films are now being applied to the structures of next-generation electronic devices [1] as well as their starting materials. Silicon-on-insulator (SOI) wafers are a candidate starting material and have an amorphous SiO2 layer as a base for silicon (Si) thin film [2–7], while Si films with silicon-on-nothing (SON) structures have nothing beneath them [8]. The flexibility of Si atoms located at the film/base interface of SOI wafers is restricted by their bonds with the base atoms. In contrast, Si atoms located at the free top surfaces of the Si film can easily form dimer structures such as those of a bulk surface, and the Si atoms just beneath the surface are expected to adjust to the deviations of the top surface atoms forming dimer structures. SOI wafers with a top Si film around 5 nm thick were expected to be used in electronic devices at one time [9]. Such films have around 30 layers of Si atoms. The surface effect is expected to become relatively large as the top Si film in SOI wafers and/or SON structures become thinner in thickness. Meanwhile, FinFETs are promising structures for next-generation
∗ Corresponding author. Tel.: +81 866 94 2136; fax: +81 866 94 2199. E-mail addresses: [email protected] (E. Kamiyama), [email protected] (K. Sueoka). 1 Tel.: +81 866 94 2136; fax: +81 866 94 2199. 0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2012.02.012
electrical devices. The heart of the FinFETs is a “Fin”-shaped Si thin film of nanometer-scale thickness [10]. Modeling of nanometer scale ultra-thin Si films with dimer structures at the surface was investigated using both conventional plate shaped models and two additional plate shaped models with different constraint conditions for atoms and cells [11]. The energy gains forming dimers in the models with no constrained atoms in the film were smaller than those in the models with constrained atoms at the center of the films and with fewer layers. The amount of deviation of all atoms deeper than the fifth layer in the models with no constrained atoms was also much higher than that in the models with constrained atoms. These facts indicate that the dimer formations deform the positions of atoms below the surface and increase the total energies as the sizes of the models increase, i.e., this energy increase is due to the deformation of internal atoms from the bulk positions, which are propagated from the surfaces that had dimers. For the reason stated above, the film surface and the internal atoms compete to stabilize the structure of ultra-thin Si (1 0 0) films as a whole. In the FinFETs, the structure of internal atoms of ultrathin films should be investigated because the signal current flows mainly in them. Whereas, the film surface can be controlled to prevent the deviations of internal atoms by the surface stabilizations. This kind control, technology for which is expected to be invented in future, is similar to an electronic passivation by SiO2 films to prevent the electronic states from forming at the Si film surface. The
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those of Fig. 1(a) to evaluate the effect of the dangling bonds at the surface only, apart from the deformations of dimerization. For comparisons, dangling bonds of some models were later terminated by hydrogen (H) atoms to eliminate their effects. The smearing value for calculating density of states was set at 0.05 eV to obtain an appropriate resolution between states. The calculations of first principles analysis were based on the local density approximation [12,13] using the ultra-soft pseudopotential method [14] and the plane waves as a basis set for efficient structure optimization. The expression proposed by Perdew et al. [15] was used for the exchange-correlation energy in the generalized gradient approximation (GGA). The CASTEP code was used to solve the Kohn-Sham equation self-consistently with the threedimensional periodic boundary condition [16]. The density mixing method [17] and BFGS geometry optimization method [18] were used to optimize the electronic structure and atomic configurations, respectively. Only the neutral charge state of the systems was considered in this study. The calculations were performed for the system at a temperature of absolute zero. Additionally, k-point sampling was tested at 3 × 7 × 1 and 3 × 6 × 1 special points of the Monkhorst–Pack grid [19]. The cutoff energy of the plane waves was also tested at 310 eV and 350 eV. Fig. 2 shows charge density distributions in the z-direction of a 48 layers bulk model for each condition: (a) 3 × 7 × 1 special points and cutoff energy at 350 eV; (b) 3 × 6 × 1 special points and cutoff energy at 350 eV; and (c) 3 × 7 × 1 special points and cutoff energy at 310 eV. Each peak of the charges in all figures is at the position corresponding to the bonding center between two Si atoms. This fact shows the bonding has a covalent nature. The grids of charge density distributions are determined automatically by CASTEP. Condition (c) was not uniformly distributed because grids of the model in the z-direction of the cell were divided not into 480 parts like (a) and (b) but 450 parts. Condition (a) was most uniformly distributed. Hence, we will apply condition (a) from here.
3. Results and discussion Fig. 1. (a) Bulk model with 48 layers along z-direction in unit cell and two atoms in each layer. (b) A example of a Si film model that has 16 layers with vacuum slabs. In this model, atoms had been removed from the Fig. 1(a) after the geometrical optimization. Models with the number of layers (16, 20, 24, 28, 32, and 36) were also calculated.
surface of an ultra-thin film can certainly affect the electronic carriers inside the film, differing from that of a bulk. How dangling bonds at the film surface affect the inside of the ultra-thin films, which are used in devices like FinFETs, should be investigated because the surface states generally come from the remained dangling bonds after the passivation at the surface. In this paper, we investigate the effect of dangling bonds at the surface of ultra-thin films on electronic states inside the film by first principles calculation. In the calculation model, dangling bonds are directly treated and the impact on the electronic states at the internal atoms was estimated. 2. Simulation details First, we fabricated a bulk model that had 48 layers along the z-direction in the unit cell and two atoms in each layer, as shown in Fig. 1(a). An example of a Si film model that has 16 layers with vacuum slabs is shown in Fig. 1(b), in which atoms had been removed from the Fig. 1(a) after the geometrical optimization. The numbers of layers calculated were 16, 20, 24, 28, 32, and 36 in the models shown in Fig. 1(b). After that, the total energy, charge density distribution and local density of states (LDOS) were calculated while all atom positions were kept the same as
Fig. 3 shows charge density distributions in the z-direction of film models normalized by a bulk (i.e., Fig. 2(a)): (a) shows a whole cell in horizontal axis and a full range of the density in vertical axis; (b) shows a whole cell in horizontal axis and a magnified range of the density around unity in vertical axis from (a); and (c) shows a center area of films in horizontal axis and a far magnified range of the density around unity in vertical axis from (b). In a film, charges crowd around the atom positions more than a bulk. This trend reaches its maximum at the second layer and second maximum at the third layer from the surface of films. At the fourth and fifth layers, the charges also have peaks but the baselines are far lower than the bulk (unity). The deviations of charges in internal portions of the films that have more layers become fewer than those of the near surface portions, and about 0.001% at the center of the film of a 36-layer model. A dangling bond at a Si (1 0 0) surface atom remains even after dimer formation. Hence, the charge distribution in internal portions of the films does not change very much after dangling bonds decrease and the internal atoms are deformed by the dimer formation at the surface. Fig. 4 compares calculated Si atom self-energies of a bulk and films. The self-energies of films were deduced by the subtraction between total energies of next layer number models. The differences are very small and within the range of 0.001 eV. We discussed similar comparison in our previous paper [20] and showed a possibility of self-energy of a Si atom in the film that is about 0.005 eV lower than that in the Si bulk. However, this result shows that films and a bulk do not obviously differ. Our previous results showed a difference because they must have had an error of first principles
E. Kamiyama, K. Sueoka / Applied Surface Science 258 (2012) 5265–5269
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Fig. 3. Charge density distributions in z-direction of film models normalized by bulk: (a) shows whole cell in horizontal axis and full range of density in vertical axis; (b) shows whole cell in horizontal axis and magnified range of density around unity in vertical axis from (a); (c) shows center area of films in horizontal axis and far magnified range of density around unity in vertical axis from (b).
Fig. 2. Charge density distributions in z-direction of 48-layer bulk model for each condition: (a) 3 × 7 × 1 special points and cutoff energy at 350 eV; (b) 3 × 6 × 1 special points and cutoff energy at 350 eV; (c) 3 × 7 × 1 special points and cutoff energy at 310 eV.
analysis in the modelling, where different cell size models were calculated by the same k-point sampling condition. Fig. 5 shows the total DOS of Si atoms in 16-layer models with and without H-terminated surfaces (Si–H bond length was set at 0.154 nm) around the bandgaps. The model with a H-terminated surface at both sides shows a 0.7 eV-wide bandgap, which is wider than that of a typical bulk value (0.6 eV) calculated by using the expression of exchange-correlation energy proposed by Perdew et al. This bandgap change must come from a quantum confinement effect because the 36-layer model with an H-terminated surface at both sides shows a value close to the bulk. Any models like them with an H-terminated surface at both sides had no state in the bandgap. Whereas, removing terminated-H changes the total DOS drastically. The point to find is that new states are made to appear at around the midgap (∼0.4 eV) by removing terminated H at surfaces of one or both sides. This thought to correspond to the fact
Fig. 4. Comparison of calculated Si atom self-energies of bulk and films.
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Fig. 5. Total DOS of 16-layer models with and without H-terminated surface around bandgaps. Fig. 7. LDOS for each layer of 36-layer model [11].
that charges crowd around the atom positions more than a bulk in Fig. 3. The LDOS for each layer of a 16-layer model with terminatedH at the surfaces of one side was also calculated and is shown in Fig. 6. The same as in Fig. 5, mid-gap states can be seen at all layers, states of which decrease as the layer moves away from the surface with dangling bonds. The Si films models with dimer structures at both side surfaces were investigated by adding dimer structures to Fig. 1(b)-type models and geometrically optimizing the atoms and the cell. Fig. 7 shows a LDOS for each layer of the 36-layer model with citing results from our previous work [11]. The LDOS peak around 0.4 eV remained, but the peak height decreased to 1/4. The main part of LDOS moved to and formed new states around 0.6 eV, which came from bonding orbitals in the dimers. Notice that the amount of LDOS at 0.4 eV in the center of the film with dimer structures at surfaces of both sides is close to that of the film with no dimer structures at surfaces of either side, shown in Fig. 6. Fig. 8 shows LDOS dependence of midgap states in various models/conditions on the distance from the surfaces. This figure compares between (1) a 36-layer model without a H-terminated
Fig. 6. LDOS for each layer of 16-layer model with terminated H at surface of one side.
surface but showing LDOS only at from the first layer to the 18th layer, (2) a 16-layer model without a H-terminated surface, and (3) a 16-layer model with a H-terminated surface at one side. The LDOS in all models decrease as the distances from the surface increase. Surprisingly, they show the same exponential decrease in LDOS. The sum of LDOS in from first to 18th layers of a 36-layer model is 3.94 electrons and almost equal to the number of dangling bonds at one side of the model. This is thought to correspond to a fact that states of dangling bonds generally appear at midgap. This number can convert into 5.5 × 1021 cm−3 and 1.3 × 1015 cm−2 , as respectively a volume concentration and a surface concentration, where 0.714 nm3 of the volume of 18 layers and 0.298 nm2 of the surface area in the model are used. If the activation rate is assumed as 2.0 × 10−5 , which is an ordinary value of thermal oxide passivation on a Si (1 0 0) surface, these numbers reduce to 1.1 × 1017 cm−3 and 2.6 × 1010 cm−2 . At the 18th layer from the surface in a 36-layer model, LDOS retains 2.6 × 10−4 electrons/eV, which can convert into 5.8 × 1018 cm−3 and 7.7 × 1013 cm−2 . Considering the
Fig. 8. LDOS dependence of midgap states on the distance from surfaces in various models/conditions: (1) 36-layer model without H-terminated surface but showing LDOS only at from first to 18th layer; (2) 16-layer model without H-terminated surface; (3) 16-layer model with H-terminated surface at one side.
E. Kamiyama, K. Sueoka / Applied Surface Science 258 (2012) 5265–5269
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activation rate, the LDOSs inside ultra-thin film reduce to 1.2 × 1014 cm−3 and 1.5 × 109 cm−2 . These numbers are comparable to the ordinary values, especially the dopant volume concentration of a Si substrate used in a current electronic device technology (∼1015 cm−3 ). These dopant concentration substrates are expected to continue to be used in FinFETs in future. Therefore, the midgap states inside ultra-thin films, mentioned above, may degrade performance of the FinFETs. The midgap states will appear on the surfaces of lightly doped Si samples as well as the intrinsic Si films calculated in this study. The positive charges on the surface of p-type Si samples after a diluted HF dip were detected by alternating current surface photovoltage method [21]. This result can be explained by the existence of the midgap states as the followings. Some Si atoms at the surface are thought to be missing H atoms after the diluted HF dip and have dangling bonds. In such a case, the dopant B atoms inside the surface get electrons from the midgap states originated from these dangling bonds since the Fermi level locates at lower than the mid-gap position in p-type Si. Therefore, the surface Si atoms with dangling bonds show positive charges.
film with no dimer structures. The sum of LDOS from first to 18th layers of a 36-layer model with no dimer structures is 3.94 electrons and almost equal to the number of dangling bonds at one side of the model. This number can convert into 5.5 × 1021 cm−3 and 1.3 × 1015 cm−2 as a volume concentration and a surface concentration, respectively. If the activation rate is assumed as 2.0 × 10−5 , which is an ordinary value of thermal oxide passivation on Si (1 0 0) surface, these numbers reduce to 1.1 × 1017 cm−3 and 2.6 × 1010 cm−2 , respectively. At the 18th layer from the surface in a 36-layer model, LDOS retains 2.6 × 10−4 electrons/eV, which can convert into 5.8 × 1018 cm−3 and 7.7 × 1013 cm−2 . Considering the activation rate, the LDOSs inside ultra-thin film reduce to 1.2 × 1014 cm−3 and 1.5 × 109 cm−2 . These numbers are comparable to the ordinary values, especially the dopant volume concentration of the Si substrate used in a current electronic device technology. These dopant concentration substrates are expected to continue to be used in FinFET in future. Therefore, the midgap states inside ultra-thin films may degrade performance of the FinFETs.
4. Conclusions
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We investigated how dangling bonds at the surface of ultra-thin films affect electronic states inside the film by first principles calculation. In the calculation model, dangling bonds are directly treated and estimate the impact on the electronic states at the internal atoms. In a film, charges crowd around the atom positions more than a bulk. This trend reaches its maximum at the second layer and second maximum at the third layer from the surface of films. At the fourth and fifth layers, the charges also have peaks but the baselines are far lower than the bulk. The deviations of charges in internal portions of the films that have more layers become fewer than those of the surface portions, and about 0.001% at the center of the film of a 36-layer model. Any models with an H-terminated surface at both sides had no state in the bandgap. Whereas, new states are made to appear at around the midgap by removing terminated-H at surfaces of one or both sides. These mid-gap states appear at all layers, states of which decreases as the layer moves away from the surface with dangling bonds. In the models with dimer structures at both side surfaces, the amount of LDOS at the midgap is close to that of the
References