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Surface segregation behavior of Ge in comparison with B, Ga, and Sb: calculations using a first-principles method
Journal of Crystal Growth 201/202 (1999) 81}84
Surface segregation behavior of Ge in comparison with B, Ga, and Sb: calculations using a "rst-principles method Jiro Ushio*, Kiyokazu Nakagawa, Masanobu Miyao, Takuya Maruizumi Central Research Laboratory, Hitachi, Ltd., 1-280 Higashi-Koigakubo, Kokubunji-shi, Tokyo 185-8601, Japan
Abstract The potential energies of a Ge atom in the three top layers of Si(1 0 0) surfaces were evaluated by accurate density functional calculations of the model clusters and compared with the previously reported potential energies for B, Ga, and Sb. The order of resistance to surface segregation of all of these elements can be understood primarily by considering the bond energies between the element and Si atoms as the driving force for segregation. Though the potential energy curve for Ge has a minima in the "rst layer, it is so shallow that Ge shows a moderate tendency towards surface segregation. 1999 Elsevier Science B.V. All rights reserved. PACS: 68.35.!p; 68.60.!p Keywords: Molecular beam epitaxy; Surface segregation; Silicon; Germanium; Density functional theory
1. Introduction Molecular beam epitaxy (MBE) is expected to become a powerful tool for forming sharp doping pro"les and abrupt heterointerfaces because of its low-temperature growth process. However, many elements have been shown to segregate to the epitaxial surface during MBE growth. It is known that B, Ga, Sb, and Ge show di!erent behaviors in surface segregation during Si-MBE [1}5]. Though B and Ga both belong to group III, B is an excellent dopant which hardly segregates to the Si surface while Ga segregates easily. Moreover, Sb also has much less of a tendency to segregate than Ga.
* Corresponding author. Tel.: #81 423 23 1111, ext. 3114; fax: #81 423 27 7748; e-mail: [email protected].
However, these two dopants and Ge cause surface segregation much more easily than B. In our previous paper [6], we studied the surface-segregation behavior of B, Ga, and Sb, and concluded that the driving force for the segregation is the bond-energy di!erence between the dopant-Si and the Si}Si bonds. Here, we further investigate the surface segregation behavior of Ge and compare it with that of the dopants to identify the behavior characteristics of a group IV element.
2. Calculation details The behavior of an atom incorporated into the Si crystal can be explained by a two-state model with an appropriate potential for the atom. A schematic potential energy diagram is shown in Fig. 1. The
0022-0248/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 2 9 0 - 1
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J. Ushio et al. / Journal of Crystal Growth 201/202 (1999) 81}84
Fig. 1. Schematic energy diagram of the two-state model.
jumping rate for surface segregation is determined by the potential barrier, and the driving force of surface segregation is the energy di!erence between the surface (adsorbed) and subsurface (incorporated) states. We evaluated the potential energies of the Ge atom in the three top layers of a Si(1 0 0) surface by using accurate density functional calculations with a model cluster. For the calculation, we used the Si H cluster as the Si surface model; we used the same cluster in our previous paper [6]. Fig. 2 illustrates the cluster structure. The bridge site was taken as the adsorption site for Ge, as it was for B, Ga, and Sb. The potential energy for Ge was obtained taking into account the structural relaxation of the Si lattice by optimizing the positions of the nearest Si atoms around the adsorbed or incorporated Ge atom.
Fig. 2. Cluster model (an atom and Si H ) used to calculate the total energies of the cluster for the adsorbed and incorporated states of B, Ga, Ge, and Sb atoms on or in the Si(1 0 0) surface layers. The hydrogen atoms are not shown. The four locations where the atom was placed to calculate the adsorbed and incorporated states are indicated by the arrows.
To evaluate the potential barrier for the B, Ga, Ge, and Sb atoms in Fig. 1, we assumed a linear transit path of the atoms from the adsorption site to the incorporated site in the "rst Si layer then divided the line between the two sites into "ve parts of equal length. At each dividing point, the total energy was calculated by optimizing the positions of the nearest Si atoms. All the calculations were performed using the linear combination of Gaussian-type orbitalsmodel core-potential-density functional theory (LCGTO-MCP-DFT) program `deMona developed at the UniversiteH de Montre`al [7].
3. Results and discussion When the incorporation of an atom di!erent from Si takes place, (incorporated atom)-Si bonds form and the Si}Si bonds dissociate. If the bond energy of the (incorporated atom)-Si bond is larger than that of the Si}Si bond, the incorporated state of the atom in the "rst layer should be more stable than the surface state, i.e., surface segregation is unlikely to occur. We calculated the single-bond energies of the B}Si, Ga}Si, Ge-Si, Sb}Si, and Si-Si bonds (Table 1). The bond energy of B}Si is higher than that of Si}Si, but those of Ga}Si, Ge}Si, and Sb}Si are lower. These bond energies determine the driving force for the surface segregation of the incorporated atom and must be the primary origin of the completely di!erent surface-segregation behavior of B, Ga, Ge, and Sb. The Ge}Si bond energy is just slightly (0.08 eV) less than the Si}Si bond. Based on this result and the conclusion of our previous paper, we can anticipate that Ge tends to segregate to the Si surface even though the tendency is weaker than for Ga and Sb. This agrees with our experimental observation [5]. The calculated potential energies for Ge are shown in Fig. 3 together with those for B, Ga, and Sb [7]. For Ge, the potential energy is at its minimum in the "rst layer, and even the energy in the second layer is lower than that at the surface. Therefore, Ge has a resistance to rather than a tendency towards surface segregation, but the resistance is very weak since the energy lowering is only about 0.3 eV. A considerable amount of Ge
J. Ushio et al. / Journal of Crystal Growth 201/202 (1999) 81}84 Table 1 Bond energies (in eV) of the B}Si, Ga}Si, Ge}Si, Sb}Si, and Si}Si single bonds and their bond lengths (in As ) for the B, Ga, Ge, and Sb atoms in the second and third Si surface layers Bond
B}Si Ga}Si Ge}Si Sb}Si Si}Si
Bond energy
4.32 3.42 3.65 3.11 3.73
Bond length Second layer
Third layer
2.01 2.32 2.38 2.56 2.36
2.08 2.36 2.36 2.51 2.36
Calculated for the bonds in H B}SiH , H Ga}SiH , H Ge}SiH , H Sb}SiH , and H Si}SiH . For B and Ga, the values are averages of the three dopantnearest-neighbor-Si bond lengths. For Ge and Sb, the values are averages of the four bond lengths to the four nearestneighbor Si atoms. Average of the four bond lengths between the Si atom in the third layer and the nearest neighbor Si atoms in the optimized structure of the Si H cluster without a dopant or Ge atom.
Fig. 3. Total energies of the Si clusters with the atoms of B, Ga, Ge, and Sb in the three surface layers of the Si(1 0 0) surface. The adsorbed state energy was taken as zero. The actual locations of the adsorbed and incorporated atoms are shown by the arrows in Fig. 2.
can move to the surface at a "nite temperature if there is no signi"cant potential barrier between the surface and "rst Si layers. In the third layer, where
83
the environment of the Ge atom is almost the same as in bulk Si (see the Ge}Si bond lengths in Table 1), the potential energy is almost zero since the bond energy for Ge}Si is very close to that for Si}Si. The potential curve for Ge is located between that for Ga and that for B showing the experimentally observed tendency to segregate; that is, a tendency weaker than Ga but stronger than B. To consider the dynamical aspect of surface segregation, evaluation of the potential barrier is necessary. Although Sb is less stable than Ga in the Si crystal (Fig. 3), the weaker tendency of Sb to segregate compared to that of Ga, as actually observed, can be explained by the smaller jumping rate of Sb due to its larger potential barrier. However, it is very computer-demanding to calculate an accurate barrier for the jump of an atom in the Si crystal. Here, we assumed that the transit path of each of the B, Ga, Ge, and Sb atoms in the jump is linear between the adsorption site (surface) and the incorporated site in the "rst Si layer and calculated more detailed potential energies on that path using the cluster model shown in Fig. 2. From the obtained potential energies we can obtain some approximate information about the potential energy surfaces for the jumping of the atoms. The more detailed potential energies of B, Ga, Ge, and Sb between the adsorption site and the incorporated site in the "rst layer are depicted in Fig. 4. The potential barriers for the atoms are about 0.7, 0.2, 0.5 and 1.5 eV for B, Ga, Ge, and Sb, respectively. The barrier for Ge corresponds to the jump from the location of layer number 0.4 to the surface. Though this barrier is rather large, the Ge atom seems to have a tendency to segregate to the surface, because the potential barrier between the "rst layer and the location of layer number 0.4 is about 0.1 eV and Ge can easily jump from the "rst layer to the location of layer number 0.4. The larger barrier of Sb, compared to that of Ga, allows Sb to jump from the "rst layer to the surface less frequently. This makes it more di$cult for Sb to segregate to the surface kinetically than for Ga. In conclusion, the surface segregation behavior of Ge on Si(1 0 0) can be explained by considering the bond-energy di!erence between Ge}Si and Si}Si a driving force for the segregation, as has been reported for the dopants B, Ga, and Sb. The
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J. Ushio et al. / Journal of Crystal Growth 201/202 (1999) 81}84
4. Summary The driving force of surface segregation of Ge on a Si(1 0 0) surface was investigated using accurate density functional theory, and was compared with the behavior of B, Ga, and Sb dopant atoms. The surface-segregation of all these elements can be understood primarily by comparing the bond energies of the X}Si and Si}Si bonds (X"B, Ga, Ge, Sb). The potential barrier, which controls the segregation rate, is small for Ge and Ga, but plays an important role in the segregation of Sb.
References
Fig. 4. The total energies of the Si cluster with the atoms of B, Ga, Ge, and Sb between the surface site and the subsurface site in the "rst layer. The transit between the two sites was assumed to be linear.
potential barriers for Ge and Ga are small and only weakly a!ect the behavior of Ge and Ga, but that for Sb is much larger and decreases the surface segregation of Sb.
[1] G.E. Becker, J.C. Bean, J. Appl. Phys. 48 (1977) 3395. [2] K. Nakagawa, M. Miyao, Y. Shiraki, Thin Solid Films 183 (1989) 315. [3] J.C. Bean, Appl. Phys. Lett. 33 (1978) 654. [4] H. Jorke, Surf. Sci. 193 (1988) 569. [5] K. Nakagawa, M. Miyao, J. Appl. Phys. 69 (1991) 3058. [6] J. Ushio, K. Nakagawa, M. Miyao, T. Maruizumi, Phys. Rev. B 58 (1998) 3932. [7] D.R. Salahub, R. Fournier, P. Mlynarski, I. Papai, A. StAmant, J. Ushio, in: J. Labanowski, J. Andzelm (Eds.), Density Functional Methods in Chemistry, Springer, New York, 1991, p. 77.
Surface segregation behavior of Ge in comparison with B, Ga, and Sb: calculations using a "rst-principles method Jiro Ushio*, Kiyokazu Nakagawa, Masanobu Miyao, Takuya Maruizumi Central Research Laboratory, Hitachi, Ltd., 1-280 Higashi-Koigakubo, Kokubunji-shi, Tokyo 185-8601, Japan
Abstract The potential energies of a Ge atom in the three top layers of Si(1 0 0) surfaces were evaluated by accurate density functional calculations of the model clusters and compared with the previously reported potential energies for B, Ga, and Sb. The order of resistance to surface segregation of all of these elements can be understood primarily by considering the bond energies between the element and Si atoms as the driving force for segregation. Though the potential energy curve for Ge has a minima in the "rst layer, it is so shallow that Ge shows a moderate tendency towards surface segregation. 1999 Elsevier Science B.V. All rights reserved. PACS: 68.35.!p; 68.60.!p Keywords: Molecular beam epitaxy; Surface segregation; Silicon; Germanium; Density functional theory
1. Introduction Molecular beam epitaxy (MBE) is expected to become a powerful tool for forming sharp doping pro"les and abrupt heterointerfaces because of its low-temperature growth process. However, many elements have been shown to segregate to the epitaxial surface during MBE growth. It is known that B, Ga, Sb, and Ge show di!erent behaviors in surface segregation during Si-MBE [1}5]. Though B and Ga both belong to group III, B is an excellent dopant which hardly segregates to the Si surface while Ga segregates easily. Moreover, Sb also has much less of a tendency to segregate than Ga.
* Corresponding author. Tel.: #81 423 23 1111, ext. 3114; fax: #81 423 27 7748; e-mail: [email protected].
However, these two dopants and Ge cause surface segregation much more easily than B. In our previous paper [6], we studied the surface-segregation behavior of B, Ga, and Sb, and concluded that the driving force for the segregation is the bond-energy di!erence between the dopant-Si and the Si}Si bonds. Here, we further investigate the surface segregation behavior of Ge and compare it with that of the dopants to identify the behavior characteristics of a group IV element.
2. Calculation details The behavior of an atom incorporated into the Si crystal can be explained by a two-state model with an appropriate potential for the atom. A schematic potential energy diagram is shown in Fig. 1. The
0022-0248/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 2 9 0 - 1
82
J. Ushio et al. / Journal of Crystal Growth 201/202 (1999) 81}84
Fig. 1. Schematic energy diagram of the two-state model.
jumping rate for surface segregation is determined by the potential barrier, and the driving force of surface segregation is the energy di!erence between the surface (adsorbed) and subsurface (incorporated) states. We evaluated the potential energies of the Ge atom in the three top layers of a Si(1 0 0) surface by using accurate density functional calculations with a model cluster. For the calculation, we used the Si H cluster as the Si surface model; we used the same cluster in our previous paper [6]. Fig. 2 illustrates the cluster structure. The bridge site was taken as the adsorption site for Ge, as it was for B, Ga, and Sb. The potential energy for Ge was obtained taking into account the structural relaxation of the Si lattice by optimizing the positions of the nearest Si atoms around the adsorbed or incorporated Ge atom.
Fig. 2. Cluster model (an atom and Si H ) used to calculate the total energies of the cluster for the adsorbed and incorporated states of B, Ga, Ge, and Sb atoms on or in the Si(1 0 0) surface layers. The hydrogen atoms are not shown. The four locations where the atom was placed to calculate the adsorbed and incorporated states are indicated by the arrows.
To evaluate the potential barrier for the B, Ga, Ge, and Sb atoms in Fig. 1, we assumed a linear transit path of the atoms from the adsorption site to the incorporated site in the "rst Si layer then divided the line between the two sites into "ve parts of equal length. At each dividing point, the total energy was calculated by optimizing the positions of the nearest Si atoms. All the calculations were performed using the linear combination of Gaussian-type orbitalsmodel core-potential-density functional theory (LCGTO-MCP-DFT) program `deMona developed at the UniversiteH de Montre`al [7].
3. Results and discussion When the incorporation of an atom di!erent from Si takes place, (incorporated atom)-Si bonds form and the Si}Si bonds dissociate. If the bond energy of the (incorporated atom)-Si bond is larger than that of the Si}Si bond, the incorporated state of the atom in the "rst layer should be more stable than the surface state, i.e., surface segregation is unlikely to occur. We calculated the single-bond energies of the B}Si, Ga}Si, Ge-Si, Sb}Si, and Si-Si bonds (Table 1). The bond energy of B}Si is higher than that of Si}Si, but those of Ga}Si, Ge}Si, and Sb}Si are lower. These bond energies determine the driving force for the surface segregation of the incorporated atom and must be the primary origin of the completely di!erent surface-segregation behavior of B, Ga, Ge, and Sb. The Ge}Si bond energy is just slightly (0.08 eV) less than the Si}Si bond. Based on this result and the conclusion of our previous paper, we can anticipate that Ge tends to segregate to the Si surface even though the tendency is weaker than for Ga and Sb. This agrees with our experimental observation [5]. The calculated potential energies for Ge are shown in Fig. 3 together with those for B, Ga, and Sb [7]. For Ge, the potential energy is at its minimum in the "rst layer, and even the energy in the second layer is lower than that at the surface. Therefore, Ge has a resistance to rather than a tendency towards surface segregation, but the resistance is very weak since the energy lowering is only about 0.3 eV. A considerable amount of Ge
J. Ushio et al. / Journal of Crystal Growth 201/202 (1999) 81}84 Table 1 Bond energies (in eV) of the B}Si, Ga}Si, Ge}Si, Sb}Si, and Si}Si single bonds and their bond lengths (in As ) for the B, Ga, Ge, and Sb atoms in the second and third Si surface layers Bond
B}Si Ga}Si Ge}Si Sb}Si Si}Si
Bond energy
4.32 3.42 3.65 3.11 3.73
Bond length Second layer
Third layer
2.01 2.32 2.38 2.56 2.36
2.08 2.36 2.36 2.51 2.36
Calculated for the bonds in H B}SiH , H Ga}SiH , H Ge}SiH , H Sb}SiH , and H Si}SiH . For B and Ga, the values are averages of the three dopantnearest-neighbor-Si bond lengths. For Ge and Sb, the values are averages of the four bond lengths to the four nearestneighbor Si atoms. Average of the four bond lengths between the Si atom in the third layer and the nearest neighbor Si atoms in the optimized structure of the Si H cluster without a dopant or Ge atom.
Fig. 3. Total energies of the Si clusters with the atoms of B, Ga, Ge, and Sb in the three surface layers of the Si(1 0 0) surface. The adsorbed state energy was taken as zero. The actual locations of the adsorbed and incorporated atoms are shown by the arrows in Fig. 2.
can move to the surface at a "nite temperature if there is no signi"cant potential barrier between the surface and "rst Si layers. In the third layer, where
83
the environment of the Ge atom is almost the same as in bulk Si (see the Ge}Si bond lengths in Table 1), the potential energy is almost zero since the bond energy for Ge}Si is very close to that for Si}Si. The potential curve for Ge is located between that for Ga and that for B showing the experimentally observed tendency to segregate; that is, a tendency weaker than Ga but stronger than B. To consider the dynamical aspect of surface segregation, evaluation of the potential barrier is necessary. Although Sb is less stable than Ga in the Si crystal (Fig. 3), the weaker tendency of Sb to segregate compared to that of Ga, as actually observed, can be explained by the smaller jumping rate of Sb due to its larger potential barrier. However, it is very computer-demanding to calculate an accurate barrier for the jump of an atom in the Si crystal. Here, we assumed that the transit path of each of the B, Ga, Ge, and Sb atoms in the jump is linear between the adsorption site (surface) and the incorporated site in the "rst Si layer and calculated more detailed potential energies on that path using the cluster model shown in Fig. 2. From the obtained potential energies we can obtain some approximate information about the potential energy surfaces for the jumping of the atoms. The more detailed potential energies of B, Ga, Ge, and Sb between the adsorption site and the incorporated site in the "rst layer are depicted in Fig. 4. The potential barriers for the atoms are about 0.7, 0.2, 0.5 and 1.5 eV for B, Ga, Ge, and Sb, respectively. The barrier for Ge corresponds to the jump from the location of layer number 0.4 to the surface. Though this barrier is rather large, the Ge atom seems to have a tendency to segregate to the surface, because the potential barrier between the "rst layer and the location of layer number 0.4 is about 0.1 eV and Ge can easily jump from the "rst layer to the location of layer number 0.4. The larger barrier of Sb, compared to that of Ga, allows Sb to jump from the "rst layer to the surface less frequently. This makes it more di$cult for Sb to segregate to the surface kinetically than for Ga. In conclusion, the surface segregation behavior of Ge on Si(1 0 0) can be explained by considering the bond-energy di!erence between Ge}Si and Si}Si a driving force for the segregation, as has been reported for the dopants B, Ga, and Sb. The
84
J. Ushio et al. / Journal of Crystal Growth 201/202 (1999) 81}84
4. Summary The driving force of surface segregation of Ge on a Si(1 0 0) surface was investigated using accurate density functional theory, and was compared with the behavior of B, Ga, and Sb dopant atoms. The surface-segregation of all these elements can be understood primarily by comparing the bond energies of the X}Si and Si}Si bonds (X"B, Ga, Ge, Sb). The potential barrier, which controls the segregation rate, is small for Ge and Ga, but plays an important role in the segregation of Sb.
References
Fig. 4. The total energies of the Si cluster with the atoms of B, Ga, Ge, and Sb between the surface site and the subsurface site in the "rst layer. The transit between the two sites was assumed to be linear.
potential barriers for Ge and Ga are small and only weakly a!ect the behavior of Ge and Ga, but that for Sb is much larger and decreases the surface segregation of Sb.
[1] G.E. Becker, J.C. Bean, J. Appl. Phys. 48 (1977) 3395. [2] K. Nakagawa, M. Miyao, Y. Shiraki, Thin Solid Films 183 (1989) 315. [3] J.C. Bean, Appl. Phys. Lett. 33 (1978) 654. [4] H. Jorke, Surf. Sci. 193 (1988) 569. [5] K. Nakagawa, M. Miyao, J. Appl. Phys. 69 (1991) 3058. [6] J. Ushio, K. Nakagawa, M. Miyao, T. Maruizumi, Phys. Rev. B 58 (1998) 3932. [7] D.R. Salahub, R. Fournier, P. Mlynarski, I. Papai, A. StAmant, J. Ushio, in: J. Labanowski, J. Andzelm (Eds.), Density Functional Methods in Chemistry, Springer, New York, 1991, p. 77.