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Strain effects in Ge surface cascades
Nuclear Instruments and Methods in Physics Research B 164±165 (2000) 482±486
www.elsevier.nl/locate/nimb
Strain eects in Ge surface cascades J. Tarus a, K. Nordlund a, J. Keinonen a, R.S. Averback a
b
Accelerator Laboratory, University of Helsinki, P.O. Box 43, Helsinki, FIN-00014, Finland b Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
Abstract By using classical molecular dynamics technique we have simulated the eects of 5 keV Xe atoms impinging on the strained Ge(1 0 0) 2 1 surface. We found that large adatom islands are formed on top of the amorphous zones created by the cascades. We also found that lattice atoms around the molten zone move radially inwards and thus cause strain relief in the sample. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 34.10.+x; 61.82.Fk; 34.50.Dy Keywords: Germanium; Simulation; Strain
1. Introduction Development in epitaxial growth methods has enabled the synthesis of pseudomorphic Si1ÿx Gex alloys in semiconductor technology. Heterojunction structures have many bene®ts over conventional homojunction approaches. One of the advantages is that the bandgap can be altered by changing the proportion of the Ge content and strain caused by the lattice mismatch [1]. The strained SiGe layers have been used, for example, for heterojunction bipolar transistors (HBTs) and modulation-doped ®eld eect transistors (MODFETs) [2,3]. Ion implantation oers immense bene®ts in the doping of semiconductor devices in the form of shallow and sharp dopant pro®les. The disadvantage of this technique is that irradiation produces
E-mail address: jura.tarus@helsinki.® (J. Tarus).
defects in the dopant area, which may alter the electronic properties of the devices. Furthermore, the defects can form dislocations and thus, in some cases, lead to undesirable strain relaxation [4]. Equally, as the irradiation can aect the strain, the strain can aect the outcome of collision cascades. We have thus studied the in¯uence of strain on surface cascades by classical molecular dynamics simulations of low-energy (5 keV) Xe recoils impinging on strained Ge(1 0 0) surface. From simulations we have analysed the number of adatoms, size of amorphous zones and amount of the strain relief. We will show that owing to the liquid± amorphous phase-transition an adatom island will be forced to the surface. 2. Computational details We used a modi®ed Stillinger±Weber potential to describe the Ge±Ge interactions [5]. The forces
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 1 1 3 8 - 6
J. Tarus et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 482±486
at small distances and for Xe±Ge pairs were evaluated from a repulsive potential calculated with the DMol program package [6]. 1 We had 262620 unit cells (108 160 atoms) in the simulation box with periodic boundary conditions in two dimensions. In these two directions whereas in we had a ®xed unit cell size of 5.433 A the third direction the box was allowed to relax with a (21) reconstruction on the surface. This in the free resulted in a unit cell size of 5.84 A direction. The initial temperature of the box was set to 0 K. The impinging Xe atoms had 5 keV of energy and 10° o-normal angle. The evolution of the cascade was simulated for 20 ps and after that we applied 5 ps quenching with the quench rate of 0.05 K/fs. A total of 8 events were simulated. A more detailed description of the simulation methods are given in [7]. The liquid regions in the cascade were determined by the method described in [5] and for the ®nal damage state analysis we applied the structural order parameter procedure [8,9]. All the atoms more than a/8 above the surface were declared as adatoms (a is the lattice constant).
3. Results In all the events, a large adatom island was formed by the collision cascade along with an amorphous zone inside the sample (see Fig. 1). Although adatom islands have been observed in metals [10], collision cascades in semiconductors usually tend to form craters [11]. To understand the eect we ®rst checked the atomic volumes in dierent structural phases. The average atomic volume in the liquid phase at 3 . This is about 7.4% smaller the 1250 K is 21.3 A than the atomic volume in crystalline structure at the same temperature. The average atomic volume 3 , which is in the amorphous phase at 0 K is 21.0 A 2.4% smaller than the atomic volume of the 1 DMol is a trademark of Bio. Sym. Inc., San Diego, California, USA.
483
3 ) at the same temperature strained crystal (21.5 A and about 7.1% smaller volume than the equilibrium crystalline structure. The average maximum number of liquid atoms during cascades is 3832 and is reached at 0.3 ps (see Fig. 2). When the liquid cools it forms an amorphous zone where the average number of atoms is 2852, ranging from 2410 to 3172. Average number of adatoms formed by the cascades is 121.25 ranging from 39 to 227. In Fig. 2 we can also see the average hzi for atoms that at some point have been part of the liquid (excluding sputtered atoms). The ®rst dip in the graph is purely ballistic. As the number of liquid atoms decreases the hzi and the number of adatoms increase. The maximum number of adatoms, which is about twice as large as the ®nal number, is reached after 3 ps. At this time the number atoms in the liquid has decreased to about a third of the maximum. The second bump in hzi originates from the oscillation of the box as the movement of the surface clearly shows. Fig. 3 shows the average pressure in x- and ydirections during the cascades. We can see that the pressure drops from the initial value of 4.63 GPa to 4.17 GPa, with the lowest ®nal pressure being 4.12 GPa and highest 4.25 GPa. In the event where we had the largest strain relief we also had the highest number of amorphous atoms and adatoms, whereas in the case of smallest strain relief the corresponding numbers were lowest. As the size of the box in¯uences the amount of strain relief, the above mentioned pressure ®gures should be considered as qualitative values. By drawing the initial and ®nal positions of the atoms we can also visually examine the amount of the strain relief in the lattice (see Fig. 4). Atoms near the sides of the cascade seem to have moved towards the cascade area, whereas atoms below have moved deeper into the bulk. Separate amorphous zones inside the crystal can cause strain and force atoms above it to move upwards. Strain relief seems to favor the h1 1 0i direction and this results in a four-leaf clover pattern on the surface in case of symmetrical amorphous zone (see Fig. 5).
484
J. Tarus et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 482±486
Fig. 1. The ®nal position of atoms after one cascade is shown. Atom sizes correspond to their structural order parameter. The bigger the atom, the further its local environment is from crystalline structure. A large adatom island is formed above the amorphous zone.
Fig. 2. The average number of adatoms and atoms in liquid zone during cascades. The average movement, hzi, of the atoms that at some point have been part of the liquid and the average change in the surface position during the cascades are shown also.
4. Discussion The results show that large adatom clusters are formed during the liquid±amorphous phase-transition. First, a liquid is formed and as the atomic
Fig. 3. The average pressure in x- and y-directions during cascades.
volume of the liquid atoms is somewhat smaller than the atomic volumes at the surrounding lattice, the lattice atoms relax radially inwards to the soft liquid core causing the pressure in the liquid to rise. As the liquid cools the transition to the amorphous phase further increases the pressure
J. Tarus et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 482±486
485
are joined. Darker end of Fig. 4. A side view of one cascade event. Initial and ®nal positions of atoms that have moved more than 0.5 A the line points the ®nal position of the atom whereas the lighter end points the initial position of the atom. Black line indicates the initial surface position.
are joined. Darker end of Fig. 5. A top view of one cascade event. Initial and ®nal positions of atoms that have moved more than 0.5 A the line points the ®nal position of the atom whereas the lighter end points the initial position of the atom.
owning to its lower density causing formation of an adatom island on the surface. On the same time atoms below the amorphous zone are pushed deeper into the bulk and thus create strain in zdirection. The increase of the strain perpendicular
to the surface after ion bombardment has also been observed experimentally [4]. The experimental value for the density of the amorphous state is about 1% greater than the crystalline density [12]. Since the potential used
486
J. Tarus et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 482±486
here gives too small of an atomic volume for the amorphous state he eect shown here should be even bigger in real Ge. Although as thick strained Ge layers cannot be formed experimentally as those used in the simulations, the formation of adatoms clusters and strain relief can be expected to occur in real semiconductor structures. These include at least such common structures as strained Si1ÿx Gex layers, and strained compound semiconductors. Thus the eect found here could have consequences for processing of shallow junctions or other thin semiconductor structures processed by ion implantation. In conclusion, by using classical molecular dynamic simulations of cascades formed by 5 keV Xe atoms in strained Ge we have shown that large adatom clusters are formed on the surface and the strain relief can happen to some extent without any dislocations. Acknowledgements The research was supported by the Academy of Finland under projects No. 39190 and 44215. One of us (J.T.) thanks the Academy of Finland for travel expense grant. Grants of computer time
from the Center for Scienti®c Computing in Espoo, Finland are gratefully acknowledged.
References [1] G.L. Patton, S.S. Iyer, S.L. Delage, S. Tiwari, J.C. Stork, IEEE Elect. Dev. Lett. 9 (1988) 165. [2] A.M. Sembian, M. Konuma, I. Silier, A. Gutjahr, N. Rollb uhler, F. Banhart, S.M. Babu, P. Ramasamy, Thin Solid Films 336 (1998) 116. [3] S.S. Iyer, G.L. Patton, J.C. Stork, B.S. Meyerson, D.L. Harame, IEEE Transactions on Electron Devices 36 (1989) 2043. [4] P. Kringhùj, J.M. Glasko, R.G. Elliman, Nucl. Instr. and Meth. B 96 (1995) 276. [5] K. Nordlund, M. Ghaly, R.S. Averback, M. Caturla, T. Diaz de la Rubia, J. Tarus, Phys. Rev. B 57 (1998) 7556. [6] K. Nordlund, N. Runeberg, D. Sundholm, Nucl. Instr. and Meth. B 132 (1997) 45. [7] J. Tarus, K. Nordlund, A. Kuronen, J. Keinonen, Phys. Rev. B 58 (1998) 9907. [8] H. Zhu, R.S. Averback, M. Nastasi, Philos. Mag. A 71 (1995) 735. [9] K. Nordlund, R.S. Averback, Phys. Rev. B 56 (1997) 2421. [10] K. Nordlund, J. Keinonen, M. Ghaly, R.S. Averback, Nature 398 (1999) 49. [11] M. Ghaly, K. Nordlund, R.S. Averback, Philos. Mag. A 79 (1999) 795. [12] T.M. Donovan, E.J. Ashley, W.E. Spicer, Phys. Lett. 40 (1970) 1.
www.elsevier.nl/locate/nimb
Strain eects in Ge surface cascades J. Tarus a, K. Nordlund a, J. Keinonen a, R.S. Averback a
b
Accelerator Laboratory, University of Helsinki, P.O. Box 43, Helsinki, FIN-00014, Finland b Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
Abstract By using classical molecular dynamics technique we have simulated the eects of 5 keV Xe atoms impinging on the strained Ge(1 0 0) 2 1 surface. We found that large adatom islands are formed on top of the amorphous zones created by the cascades. We also found that lattice atoms around the molten zone move radially inwards and thus cause strain relief in the sample. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 34.10.+x; 61.82.Fk; 34.50.Dy Keywords: Germanium; Simulation; Strain
1. Introduction Development in epitaxial growth methods has enabled the synthesis of pseudomorphic Si1ÿx Gex alloys in semiconductor technology. Heterojunction structures have many bene®ts over conventional homojunction approaches. One of the advantages is that the bandgap can be altered by changing the proportion of the Ge content and strain caused by the lattice mismatch [1]. The strained SiGe layers have been used, for example, for heterojunction bipolar transistors (HBTs) and modulation-doped ®eld eect transistors (MODFETs) [2,3]. Ion implantation oers immense bene®ts in the doping of semiconductor devices in the form of shallow and sharp dopant pro®les. The disadvantage of this technique is that irradiation produces
E-mail address: jura.tarus@helsinki.® (J. Tarus).
defects in the dopant area, which may alter the electronic properties of the devices. Furthermore, the defects can form dislocations and thus, in some cases, lead to undesirable strain relaxation [4]. Equally, as the irradiation can aect the strain, the strain can aect the outcome of collision cascades. We have thus studied the in¯uence of strain on surface cascades by classical molecular dynamics simulations of low-energy (5 keV) Xe recoils impinging on strained Ge(1 0 0) surface. From simulations we have analysed the number of adatoms, size of amorphous zones and amount of the strain relief. We will show that owing to the liquid± amorphous phase-transition an adatom island will be forced to the surface. 2. Computational details We used a modi®ed Stillinger±Weber potential to describe the Ge±Ge interactions [5]. The forces
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 1 1 3 8 - 6
J. Tarus et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 482±486
at small distances and for Xe±Ge pairs were evaluated from a repulsive potential calculated with the DMol program package [6]. 1 We had 262620 unit cells (108 160 atoms) in the simulation box with periodic boundary conditions in two dimensions. In these two directions whereas in we had a ®xed unit cell size of 5.433 A the third direction the box was allowed to relax with a (21) reconstruction on the surface. This in the free resulted in a unit cell size of 5.84 A direction. The initial temperature of the box was set to 0 K. The impinging Xe atoms had 5 keV of energy and 10° o-normal angle. The evolution of the cascade was simulated for 20 ps and after that we applied 5 ps quenching with the quench rate of 0.05 K/fs. A total of 8 events were simulated. A more detailed description of the simulation methods are given in [7]. The liquid regions in the cascade were determined by the method described in [5] and for the ®nal damage state analysis we applied the structural order parameter procedure [8,9]. All the atoms more than a/8 above the surface were declared as adatoms (a is the lattice constant).
3. Results In all the events, a large adatom island was formed by the collision cascade along with an amorphous zone inside the sample (see Fig. 1). Although adatom islands have been observed in metals [10], collision cascades in semiconductors usually tend to form craters [11]. To understand the eect we ®rst checked the atomic volumes in dierent structural phases. The average atomic volume in the liquid phase at 3 . This is about 7.4% smaller the 1250 K is 21.3 A than the atomic volume in crystalline structure at the same temperature. The average atomic volume 3 , which is in the amorphous phase at 0 K is 21.0 A 2.4% smaller than the atomic volume of the 1 DMol is a trademark of Bio. Sym. Inc., San Diego, California, USA.
483
3 ) at the same temperature strained crystal (21.5 A and about 7.1% smaller volume than the equilibrium crystalline structure. The average maximum number of liquid atoms during cascades is 3832 and is reached at 0.3 ps (see Fig. 2). When the liquid cools it forms an amorphous zone where the average number of atoms is 2852, ranging from 2410 to 3172. Average number of adatoms formed by the cascades is 121.25 ranging from 39 to 227. In Fig. 2 we can also see the average hzi for atoms that at some point have been part of the liquid (excluding sputtered atoms). The ®rst dip in the graph is purely ballistic. As the number of liquid atoms decreases the hzi and the number of adatoms increase. The maximum number of adatoms, which is about twice as large as the ®nal number, is reached after 3 ps. At this time the number atoms in the liquid has decreased to about a third of the maximum. The second bump in hzi originates from the oscillation of the box as the movement of the surface clearly shows. Fig. 3 shows the average pressure in x- and ydirections during the cascades. We can see that the pressure drops from the initial value of 4.63 GPa to 4.17 GPa, with the lowest ®nal pressure being 4.12 GPa and highest 4.25 GPa. In the event where we had the largest strain relief we also had the highest number of amorphous atoms and adatoms, whereas in the case of smallest strain relief the corresponding numbers were lowest. As the size of the box in¯uences the amount of strain relief, the above mentioned pressure ®gures should be considered as qualitative values. By drawing the initial and ®nal positions of the atoms we can also visually examine the amount of the strain relief in the lattice (see Fig. 4). Atoms near the sides of the cascade seem to have moved towards the cascade area, whereas atoms below have moved deeper into the bulk. Separate amorphous zones inside the crystal can cause strain and force atoms above it to move upwards. Strain relief seems to favor the h1 1 0i direction and this results in a four-leaf clover pattern on the surface in case of symmetrical amorphous zone (see Fig. 5).
484
J. Tarus et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 482±486
Fig. 1. The ®nal position of atoms after one cascade is shown. Atom sizes correspond to their structural order parameter. The bigger the atom, the further its local environment is from crystalline structure. A large adatom island is formed above the amorphous zone.
Fig. 2. The average number of adatoms and atoms in liquid zone during cascades. The average movement, hzi, of the atoms that at some point have been part of the liquid and the average change in the surface position during the cascades are shown also.
4. Discussion The results show that large adatom clusters are formed during the liquid±amorphous phase-transition. First, a liquid is formed and as the atomic
Fig. 3. The average pressure in x- and y-directions during cascades.
volume of the liquid atoms is somewhat smaller than the atomic volumes at the surrounding lattice, the lattice atoms relax radially inwards to the soft liquid core causing the pressure in the liquid to rise. As the liquid cools the transition to the amorphous phase further increases the pressure
J. Tarus et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 482±486
485
are joined. Darker end of Fig. 4. A side view of one cascade event. Initial and ®nal positions of atoms that have moved more than 0.5 A the line points the ®nal position of the atom whereas the lighter end points the initial position of the atom. Black line indicates the initial surface position.
are joined. Darker end of Fig. 5. A top view of one cascade event. Initial and ®nal positions of atoms that have moved more than 0.5 A the line points the ®nal position of the atom whereas the lighter end points the initial position of the atom.
owning to its lower density causing formation of an adatom island on the surface. On the same time atoms below the amorphous zone are pushed deeper into the bulk and thus create strain in zdirection. The increase of the strain perpendicular
to the surface after ion bombardment has also been observed experimentally [4]. The experimental value for the density of the amorphous state is about 1% greater than the crystalline density [12]. Since the potential used
486
J. Tarus et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 482±486
here gives too small of an atomic volume for the amorphous state he eect shown here should be even bigger in real Ge. Although as thick strained Ge layers cannot be formed experimentally as those used in the simulations, the formation of adatoms clusters and strain relief can be expected to occur in real semiconductor structures. These include at least such common structures as strained Si1ÿx Gex layers, and strained compound semiconductors. Thus the eect found here could have consequences for processing of shallow junctions or other thin semiconductor structures processed by ion implantation. In conclusion, by using classical molecular dynamic simulations of cascades formed by 5 keV Xe atoms in strained Ge we have shown that large adatom clusters are formed on the surface and the strain relief can happen to some extent without any dislocations. Acknowledgements The research was supported by the Academy of Finland under projects No. 39190 and 44215. One of us (J.T.) thanks the Academy of Finland for travel expense grant. Grants of computer time
from the Center for Scienti®c Computing in Espoo, Finland are gratefully acknowledged.
References [1] G.L. Patton, S.S. Iyer, S.L. Delage, S. Tiwari, J.C. Stork, IEEE Elect. Dev. Lett. 9 (1988) 165. [2] A.M. Sembian, M. Konuma, I. Silier, A. Gutjahr, N. Rollb uhler, F. Banhart, S.M. Babu, P. Ramasamy, Thin Solid Films 336 (1998) 116. [3] S.S. Iyer, G.L. Patton, J.C. Stork, B.S. Meyerson, D.L. Harame, IEEE Transactions on Electron Devices 36 (1989) 2043. [4] P. Kringhùj, J.M. Glasko, R.G. Elliman, Nucl. Instr. and Meth. B 96 (1995) 276. [5] K. Nordlund, M. Ghaly, R.S. Averback, M. Caturla, T. Diaz de la Rubia, J. Tarus, Phys. Rev. B 57 (1998) 7556. [6] K. Nordlund, N. Runeberg, D. Sundholm, Nucl. Instr. and Meth. B 132 (1997) 45. [7] J. Tarus, K. Nordlund, A. Kuronen, J. Keinonen, Phys. Rev. B 58 (1998) 9907. [8] H. Zhu, R.S. Averback, M. Nastasi, Philos. Mag. A 71 (1995) 735. [9] K. Nordlund, R.S. Averback, Phys. Rev. B 56 (1997) 2421. [10] K. Nordlund, J. Keinonen, M. Ghaly, R.S. Averback, Nature 398 (1999) 49. [11] M. Ghaly, K. Nordlund, R.S. Averback, Philos. Mag. A 79 (1999) 795. [12] T.M. Donovan, E.J. Ashley, W.E. Spicer, Phys. Lett. 40 (1970) 1.