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Channeling of 20–100 eV Si atoms above the Si(111) surface
334
CHANNELING
Applied Surface Science 29 (1987) 334-340 North-Holland, Amsterdam
OF 20-100 eV Si ATOMS ABOVE THE Si(ll1)
SURFACE
Brian W. DODSON Sandia National Laboratories, Albuquerque, NM 87185, USA Received 22 May 1987; accepted for publication 12 June 1987
The interaction of low energy silicon atoms with an unreconstructed (111) silicon surface has been studied using molecular dynamics techniques and an accurate description of the covalent Si-Si interaction. For angles of incidence below a critical value, a new phenomenon of “surface channeling” is observed. In “surface channeling”, the trajectory of the incoming particle is steered by short-range repulsive and long-range attractive interactions with the surface atoms parallel to, and roughly 2 A above, the surface of the substrate. Such surface channeling trajectories offer considerable promise for precision control of beam-induced growth.
Recent developments in the field of semiconductor devices have required materials with highly precise physical structures. Examples of such materials include superlattices, strained-layer structures, devices with buried ultrathin layers, and so on. The resulting devices can be very sensitive to the presence of defect structures. One approach to obtaining low defect densities is to adjust the substrate temperature during growth. However, a conflict often appears in the use of substrate temperature to control the quality of deposited material: if the temperature is too low, defects associated with unannealed states will appear, whereas if the temperature is too high, thermally induced defects will limit the film quality. For some systems an adequate window of temperatures exists between these two limits, but this is not always the case. A nonequilibrium approach to high-quality growth is to keep the bulk of the structure relatively cool during deposition while supplying additional excitation through some specific interaction with the surface. One proposed technique is low energy ion beam deposition, in which experimental studies have recently begun [l]. We have simulated the interaction of low energy (20-100 eV) atomic beams composed of silicon atoms with a silicon (111) surface. The many-body interaction potential and simulation method are first described, and are then applied to the problem of atoms impinging on the surface with a grazing (3”-30 “) angle of incidence. We predict regimes of beam energy and incidence angle where the initial interaction with the surface is inelastic and removes essentially all of the vertical momentum of the incoming atom. This results in a class of trajectories which we call “surface channeling”, in analogy to bulk channeling trajectories along low-index sym0169-4332/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
B. W. Do&on / Channeling of low energy Si atoms above Si(1 II)
335
metry directions in single crystals. Surface channeling trajectories are characterized by motion roughly parallel to and about 2 A above the substrate in which kinetic energy is only gradually lost to the substrate. Such behavior is not restricted to the unreconstructed Si(ll1) surface, but is expected to be a general feature of grazing low-energy beam-surface interactions. In the simulation of high energy (many keV) interactions, the usual approximation is that the ion-substrate interaction is spherically symmetric with no attractive part. These approximations are incorrect in the present regime, especially concerning materials which form highly directional covalent bonds. Thus, the silicon-silicon covalent bonding must be accurately described, which requires including many-body effects via an empirical potential. A many-body empirical potential for silicon recently introduced by Dodson [2] is used. This potential, which is based on an approach developed by Tersoff [3], avoids pathological behavior marring this earlier work. The potential is optimized to describe the high-density phases, ground state elastic properties, and surface structural properties of silicon, and has resulted in a useful description of many physical properties. This potential is based on a data set which is only concerned with deformation of the outer electron shell. As the momentum transfer in an individual scattering even rises, the inner shell structure will take on increasing importance. This raises suspicion that the small r behavior of the potential will be unphysical. The concern is reasonable, since the atomic cores, at small radius, will be harder than predicted by this empirical potential. For the present problem, however, this limitation on the accuracy of the potential is unimportant, since we are concerned with surface channeling trajectories. Such trajectories result from glancing interactions with the surface in which the normal component of momentum is absorbed by gentle inelastic interactions with many surface atoms. Thus, successful surface channeling requires a number of collisions in which the momentum transfer is small enough that the potential need only be accurate for relatively large radii. To study the interaction of a beam of energetic particles with a substrate, it is necessary to develop a simulation procedure which accurately treats the important physics of the problem without becoming so cumbersome that the simulation becomes intractable. In the current problem, we are concerned primarily with length scales of about ten nanometers, a few hundred atoms, and time scales of a picosecond or less. These restrictions make the problem easily accessible to conventional molecular dynamics techniques. In molecular dynamics the classical equations of motion for an assembly of interacting particles are integrated numerically. The result of such computation is a trajectory in phase space, representing a complete classical description of the system over the integration period. In the present case, the requirement that a many-body potential be used to provide an accurate description of covalent bonding means that the most
336
B. W. Dodron / Channeling of low enera
Si atoms above Si(I 11)
time-consuming step in the procedure is the determination of the forces acting on each particle. Thus the Schofield method, a simple, although stable, low-order integration routine requiring one force calculation per time step, is used [4]. The resulting algorithm, using a timestep of 0.5 femtoseconds, has proven satisfactory for the class of problems considered here. The silicon substrate has an unreconstructed but relaxed (111) free surface, measures about 12 A wide and 80 A long (in the 110 direction), is 4 atomic layers in thickness, and totals 320 atoms. This is large enough that substrate lattice excitations do not disturb the dynamics of the incoming beam atom, but is small enough that the calculation remains practical. The silicon atoms in the incoming beam are assigned an initial position, direction, and velocity. The evolution of the resulting system was then calculated using the Schofield method. The calculation was continued until the incoming particle bounced off the surface, became adsorbed onto the substrate, or left the substrate behind (typically a few tenths of a picosecond). The results of a typical simulation run appear in fig. 1. The incoming silicon atom had a kinetic energy of 40 eV and an initial angle of incidence of 10’ relative to the surface of the substrate. As in all calculations reported here, the component of the initial velocity parallel to the surface is collinear with the surface (110) vector, so that the particle travels along the long dimension of the substrate. In fig. 1, the response of the substrate to the impact of the atom is ignored, and the atomic positions shown are simply the initial positions.
10
i;
00000000000000000000 0000000000000000000Q Fig. 1. The surface channeling trajectory of an energetic silicon atom interacting with an unreconstructed silicon (111) surface. The incoming atom initially has a kinetic energy of 40 eV and an angle of incidence of 10 “. The perpendicular momentum of the incoming atom is lost to the substrate through inelastic interactions, and the resulting trajectory is essentially parallel to, and about 2 A above, the surface of the substrate. Evaluation of the rate of energy loss indicates that the total range along the surface for this 40 eV atom is several thousand A.
B. W. Do&on / Channeling of low energy Si atoms above Si(ll1)
331
(The substrate response is of course included in the molecular dynamics simulation.) As the particle approaches the substrate, it begins to interact with the surface atoms. The kinetic energy increases slightly as the atom is attracted to the surface, but the interaction quickly turns repulsive and the particle bounces from the surface. However, the interaction with the surface atoms is sufficiently inelastic (because of substrate lattice excitations) that the particle does not escape from the lattice, but rather is trapped between the attractive and repulsive interactions with the surface of the substrate. The vertical oscillations in these competing fields damp out quickly as the atom undergoes further inelastic interaction with the substrate, and eventually settles down to motion nearly parallel to the surface of the substrate. The behavior seen in fig. 1 and described above is a general feature of low-angle beam-surface interactions in this energy range. We call this phenomenon “ surface channeling”, in analogy to the more conventional bulk channeling. In bulk channeling, a high energy atom is steered along the symmetry directions of a lattice by the combined effect of the repulsive potentials of the atoms making up the lattice. These interactions produce an attraction toward certain symmetry axes, and also provide a potential barrier against deviating from these axes. The analogy in surface channeling is that the competition between the long-range attractive potential and short-range repulsive potential generated by the surface of the substrate also serves to produce a potential well which guides the incoming atom along the surface. The (110) direction seems particularly favorable for channeling along the (111) surface, but it should occur along other directions at shallower angles of incidence. The initial location of the particle is not a strong influence on the surface channeling phenomenon. We cannot rule out the possibility that there may be impact points on the surface which are particularly unfavorable for surface channeling, but such were not found in the current work, in which roughly 100 trajectories were studied. It is clearly safe to say that, at a given angle of incidence and kinetic energy, surface channeling is (or is not) a generic behavior, the possibility of occasional special cases notwithstanding. For a given initial beam energy and orientation, there is a critical angle 8, below which we see surface channeling and above which either the particle scatters from or rapidly absorbs onto the surface (see fig. 2). Surface channeling vanishes rapidly when the critical angle is exceeded. The lowest energy atoms (20 eV) always undergo abrupt absorption (fig. 2a), whereas higher energy (40 and 100 eV) atoms always bounce off (fig. 2b) as the critical angle is exceeded. Since the higher energy atoms are expected to stick (by penetration) for steep enough angles, this suggest that, for higher initial energies, there is a second critical angle 4, separating scattering off the surface from rapid absorption onto the surface (see fig. 3). The critical angle for surface channeling is a function of the initial energy
338
B. W. Doakon / Channeling of low energy Si atoms above Si(lI1) (111)
II
3
I
000000
0000000000000
000000
0
000000
0
0
0
0
00000000
0000000000000
000000
0000000000000
b)
a)
Fig. 2. Atomic trajectories not resulting in surface channeling. (a) Initial kinetic energy of 20 eV, angle of incidence of 20°. Adsorption occurs immediately following the first collision with the surface. (b) Initial kinetic energy of 40 eV, angle of incidence of 12O. The incoming particle scatters immediately from the surface.
of the beam. We have performed a large number of simulations at 20, 40, and 100 eV in order to identify the critical angles (respectively 18”, 10 O, and 5 “) for each initial energy. These figures yield the condition that the normal component of momentum, which must be carried away via inelastic interac0 w 0
30RAP ‘ID
ADSORPT
ION
w 1 ” s
15-
W ii E
1
0 Z
-
Cl
,
SURFACE
I
I
I
SO
0 BEAM Fig. 3. surface. become energy steered
CHANNELING
E,NERGY
I
100 (e’.‘)
Incidence angle versus beam energy phase plane for Si atoms incident on the Si(ll1) Incoming atoms with either low kinetic energy or large angle of incidence will quickly localized and adsorb at the surface (this region is marked RA for rapid adsorption). If the is above roughly 20 eV and the angle of incidence is sufficiently small, the atom will be into a surface channeling trajectory. At somewhat higher energies and intermediate incidence angles, the incoming atom scatters off the surface and does not stick.
B. W. Do&on / Channeling of low energy Si atoms above Si(ll1)
tion with the substrate, be a very weak function precisely, the critical perpendicular velocity is VP = 20.5 + 336/E,,
339
of beam energy. More (1)
where V, is in A/ps and E, is the beam energy in eV. The above information is summarized in an incidence angle versus beam energy phase diagram, which appears in fig. 3. The final point of interest is to consider the rate of energy loss experienced by a particle in the surface channeling mode. This can be evaluated directly from the computed trajectories by numerical differentiation. Upon doing so, the rate of energy loss is found to be nearly linear in kinetic energy of the surface channeling atom; in this energy range, aE/tlX=
0.000154 E - 0.0193,
(2)
where E is in eV and X is in A. Clearly, this relation cannot be extrapolated far outside of this energy range, but it does allow us to estimate the total surface channeling range along the surface as a function of initial beam energy. Crude estimates reveal that the surface channeling ranges will be thousands of A for the higher energy atoms. Direct calculation for the 20 eV atoms show that the linearity of the energy loss relation fails badly for smaller energies, and a surface channeling range of around 40 w is found before adsorption for these atoms, compared to perhaps 1000 A as predicted by eq. (2). The phenomenon called surface channeling described above must not be confused with the low angle trajectory focusing surface scattering described by Thompson and coworkers [5,6], or with the near-surface channeling mechanism proposed by Sizmann and Varelas [7]. In the first case, sometimes called surface semi-channeling, at certain surface orientations the incoming beam is focused by interaction with the surface atoms onto a second-layer row of atoms, whereupon very strong reflection from the surface with characteristic angular dependence takes place. In the second case, the beam atoms actually penetrate below the surface and channel within the bulk material near the surface, sometimes escaping from the surface when dechanneling takes place. In both cases the effects require high beam energies, the principal interaction with the substrate takes place below the surface layer, and the attractive part of the potential is unimportant. By contrast, in the surface channeling mechanism proposed here, very low energy atoms suffice to demonstrate the effect, the principal interaction generates bulk phonons through excitation of the surface atoms, and the attractive term in the potential is vital in predicting where the effect will appear. It is perhaps most similar to the mechanism proposed by Ohtsuki et al. [8], who predict a skipping motion when ions are scattered off a metal surface at grazing angles. The mechanism, however, is very different. They consider a surface potential resulting from dynamical
340
B. W. DorLFon / Channeling
of lowenergySi aionzs above Si(lll)
polarization of the valence electrons caused by the motion of the incident ion, which serves to trap the ion near the surface until neutralization of the ion takes place. This is a purely electronic effect requiring beam velocities much larger than those in the present calculation. The unreconstructed Si(ll1) surface and a beam orientation along the (110) surface direction represent a particularly favorable combination for surface channeling, as this surface is regular and fairly dense, even in the open diamond structure. However, we do not expect that surface ChaMeling is an effect limited to this surface. Preliminary simulation have been made on other beam orientations on the (111) surface, on the unreconstructed (100) surface, and on the reconstructed (100) and (111) surfaces. These early results indicate that surface channeling still appears in these cases, although it is limited to shallower angles of incidence. Surface channeling thus appears to be a generic feature of grazing low-energy beam-surface interactions in semiconductors. Helpful discussions with Paul Taylor and Tom Picraux are acknowledged. This work was performed at Sandia National Laboratories and was supported by USDOE contract DE-AC04-76DP00789.
References [l] N. Herbots, B.R. Appleton, T.S. Noggle, S.J. Permycook, R.A. Zuhr and D.M. Zehner, in: Semiconductor-Based Heterojunctions, Eds. M.L. Green, J.E.E. Baglin, G.Y. Chin, H.W. Deckman, W. Mayo and D. Narasinham (The Metallurgical Society, Warrendale, PA, 1986). [2] B.W. Dodson, Phys. Rev. B35 (1987) 2795. [3] J. Tersoff, Phys. Rev. Letters 56 (1986) 632. [4] P. Schofield, Computer Phys. Commun. 5 (1973) 17. [5] A.D. Mat-wick, M.W. Thompson, B.W. Farmery and G.S. Harbinson, Radiation Effects 15 (1972) 195. [6] M.W. Thompson and H.J. Pabst, Radiation Effects 37 (1978) 105. [7] R. Sizmann and C. Varelas, Nucl. Instr. Methods 132 (1976) 633. [8] Y.H. Ohtsuki, K. Koyama and Y. Yamamura, Phys. Rev. B20 (1979) 5044.
CHANNELING
Applied Surface Science 29 (1987) 334-340 North-Holland, Amsterdam
OF 20-100 eV Si ATOMS ABOVE THE Si(ll1)
SURFACE
Brian W. DODSON Sandia National Laboratories, Albuquerque, NM 87185, USA Received 22 May 1987; accepted for publication 12 June 1987
The interaction of low energy silicon atoms with an unreconstructed (111) silicon surface has been studied using molecular dynamics techniques and an accurate description of the covalent Si-Si interaction. For angles of incidence below a critical value, a new phenomenon of “surface channeling” is observed. In “surface channeling”, the trajectory of the incoming particle is steered by short-range repulsive and long-range attractive interactions with the surface atoms parallel to, and roughly 2 A above, the surface of the substrate. Such surface channeling trajectories offer considerable promise for precision control of beam-induced growth.
Recent developments in the field of semiconductor devices have required materials with highly precise physical structures. Examples of such materials include superlattices, strained-layer structures, devices with buried ultrathin layers, and so on. The resulting devices can be very sensitive to the presence of defect structures. One approach to obtaining low defect densities is to adjust the substrate temperature during growth. However, a conflict often appears in the use of substrate temperature to control the quality of deposited material: if the temperature is too low, defects associated with unannealed states will appear, whereas if the temperature is too high, thermally induced defects will limit the film quality. For some systems an adequate window of temperatures exists between these two limits, but this is not always the case. A nonequilibrium approach to high-quality growth is to keep the bulk of the structure relatively cool during deposition while supplying additional excitation through some specific interaction with the surface. One proposed technique is low energy ion beam deposition, in which experimental studies have recently begun [l]. We have simulated the interaction of low energy (20-100 eV) atomic beams composed of silicon atoms with a silicon (111) surface. The many-body interaction potential and simulation method are first described, and are then applied to the problem of atoms impinging on the surface with a grazing (3”-30 “) angle of incidence. We predict regimes of beam energy and incidence angle where the initial interaction with the surface is inelastic and removes essentially all of the vertical momentum of the incoming atom. This results in a class of trajectories which we call “surface channeling”, in analogy to bulk channeling trajectories along low-index sym0169-4332/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
B. W. Do&on / Channeling of low energy Si atoms above Si(1 II)
335
metry directions in single crystals. Surface channeling trajectories are characterized by motion roughly parallel to and about 2 A above the substrate in which kinetic energy is only gradually lost to the substrate. Such behavior is not restricted to the unreconstructed Si(ll1) surface, but is expected to be a general feature of grazing low-energy beam-surface interactions. In the simulation of high energy (many keV) interactions, the usual approximation is that the ion-substrate interaction is spherically symmetric with no attractive part. These approximations are incorrect in the present regime, especially concerning materials which form highly directional covalent bonds. Thus, the silicon-silicon covalent bonding must be accurately described, which requires including many-body effects via an empirical potential. A many-body empirical potential for silicon recently introduced by Dodson [2] is used. This potential, which is based on an approach developed by Tersoff [3], avoids pathological behavior marring this earlier work. The potential is optimized to describe the high-density phases, ground state elastic properties, and surface structural properties of silicon, and has resulted in a useful description of many physical properties. This potential is based on a data set which is only concerned with deformation of the outer electron shell. As the momentum transfer in an individual scattering even rises, the inner shell structure will take on increasing importance. This raises suspicion that the small r behavior of the potential will be unphysical. The concern is reasonable, since the atomic cores, at small radius, will be harder than predicted by this empirical potential. For the present problem, however, this limitation on the accuracy of the potential is unimportant, since we are concerned with surface channeling trajectories. Such trajectories result from glancing interactions with the surface in which the normal component of momentum is absorbed by gentle inelastic interactions with many surface atoms. Thus, successful surface channeling requires a number of collisions in which the momentum transfer is small enough that the potential need only be accurate for relatively large radii. To study the interaction of a beam of energetic particles with a substrate, it is necessary to develop a simulation procedure which accurately treats the important physics of the problem without becoming so cumbersome that the simulation becomes intractable. In the current problem, we are concerned primarily with length scales of about ten nanometers, a few hundred atoms, and time scales of a picosecond or less. These restrictions make the problem easily accessible to conventional molecular dynamics techniques. In molecular dynamics the classical equations of motion for an assembly of interacting particles are integrated numerically. The result of such computation is a trajectory in phase space, representing a complete classical description of the system over the integration period. In the present case, the requirement that a many-body potential be used to provide an accurate description of covalent bonding means that the most
336
B. W. Dodron / Channeling of low enera
Si atoms above Si(I 11)
time-consuming step in the procedure is the determination of the forces acting on each particle. Thus the Schofield method, a simple, although stable, low-order integration routine requiring one force calculation per time step, is used [4]. The resulting algorithm, using a timestep of 0.5 femtoseconds, has proven satisfactory for the class of problems considered here. The silicon substrate has an unreconstructed but relaxed (111) free surface, measures about 12 A wide and 80 A long (in the 110 direction), is 4 atomic layers in thickness, and totals 320 atoms. This is large enough that substrate lattice excitations do not disturb the dynamics of the incoming beam atom, but is small enough that the calculation remains practical. The silicon atoms in the incoming beam are assigned an initial position, direction, and velocity. The evolution of the resulting system was then calculated using the Schofield method. The calculation was continued until the incoming particle bounced off the surface, became adsorbed onto the substrate, or left the substrate behind (typically a few tenths of a picosecond). The results of a typical simulation run appear in fig. 1. The incoming silicon atom had a kinetic energy of 40 eV and an initial angle of incidence of 10’ relative to the surface of the substrate. As in all calculations reported here, the component of the initial velocity parallel to the surface is collinear with the surface (110) vector, so that the particle travels along the long dimension of the substrate. In fig. 1, the response of the substrate to the impact of the atom is ignored, and the atomic positions shown are simply the initial positions.
10
i;
00000000000000000000 0000000000000000000Q Fig. 1. The surface channeling trajectory of an energetic silicon atom interacting with an unreconstructed silicon (111) surface. The incoming atom initially has a kinetic energy of 40 eV and an angle of incidence of 10 “. The perpendicular momentum of the incoming atom is lost to the substrate through inelastic interactions, and the resulting trajectory is essentially parallel to, and about 2 A above, the surface of the substrate. Evaluation of the rate of energy loss indicates that the total range along the surface for this 40 eV atom is several thousand A.
B. W. Do&on / Channeling of low energy Si atoms above Si(ll1)
331
(The substrate response is of course included in the molecular dynamics simulation.) As the particle approaches the substrate, it begins to interact with the surface atoms. The kinetic energy increases slightly as the atom is attracted to the surface, but the interaction quickly turns repulsive and the particle bounces from the surface. However, the interaction with the surface atoms is sufficiently inelastic (because of substrate lattice excitations) that the particle does not escape from the lattice, but rather is trapped between the attractive and repulsive interactions with the surface of the substrate. The vertical oscillations in these competing fields damp out quickly as the atom undergoes further inelastic interaction with the substrate, and eventually settles down to motion nearly parallel to the surface of the substrate. The behavior seen in fig. 1 and described above is a general feature of low-angle beam-surface interactions in this energy range. We call this phenomenon “ surface channeling”, in analogy to the more conventional bulk channeling. In bulk channeling, a high energy atom is steered along the symmetry directions of a lattice by the combined effect of the repulsive potentials of the atoms making up the lattice. These interactions produce an attraction toward certain symmetry axes, and also provide a potential barrier against deviating from these axes. The analogy in surface channeling is that the competition between the long-range attractive potential and short-range repulsive potential generated by the surface of the substrate also serves to produce a potential well which guides the incoming atom along the surface. The (110) direction seems particularly favorable for channeling along the (111) surface, but it should occur along other directions at shallower angles of incidence. The initial location of the particle is not a strong influence on the surface channeling phenomenon. We cannot rule out the possibility that there may be impact points on the surface which are particularly unfavorable for surface channeling, but such were not found in the current work, in which roughly 100 trajectories were studied. It is clearly safe to say that, at a given angle of incidence and kinetic energy, surface channeling is (or is not) a generic behavior, the possibility of occasional special cases notwithstanding. For a given initial beam energy and orientation, there is a critical angle 8, below which we see surface channeling and above which either the particle scatters from or rapidly absorbs onto the surface (see fig. 2). Surface channeling vanishes rapidly when the critical angle is exceeded. The lowest energy atoms (20 eV) always undergo abrupt absorption (fig. 2a), whereas higher energy (40 and 100 eV) atoms always bounce off (fig. 2b) as the critical angle is exceeded. Since the higher energy atoms are expected to stick (by penetration) for steep enough angles, this suggest that, for higher initial energies, there is a second critical angle 4, separating scattering off the surface from rapid absorption onto the surface (see fig. 3). The critical angle for surface channeling is a function of the initial energy
338
B. W. Doakon / Channeling of low energy Si atoms above Si(lI1) (111)
II
3
I
000000
0000000000000
000000
0
000000
0
0
0
0
00000000
0000000000000
000000
0000000000000
b)
a)
Fig. 2. Atomic trajectories not resulting in surface channeling. (a) Initial kinetic energy of 20 eV, angle of incidence of 20°. Adsorption occurs immediately following the first collision with the surface. (b) Initial kinetic energy of 40 eV, angle of incidence of 12O. The incoming particle scatters immediately from the surface.
of the beam. We have performed a large number of simulations at 20, 40, and 100 eV in order to identify the critical angles (respectively 18”, 10 O, and 5 “) for each initial energy. These figures yield the condition that the normal component of momentum, which must be carried away via inelastic interac0 w 0
30RAP ‘ID
ADSORPT
ION
w 1 ” s
15-
W ii E
1
0 Z
-
Cl
,
SURFACE
I
I
I
SO
0 BEAM Fig. 3. surface. become energy steered
CHANNELING
E,NERGY
I
100 (e’.‘)
Incidence angle versus beam energy phase plane for Si atoms incident on the Si(ll1) Incoming atoms with either low kinetic energy or large angle of incidence will quickly localized and adsorb at the surface (this region is marked RA for rapid adsorption). If the is above roughly 20 eV and the angle of incidence is sufficiently small, the atom will be into a surface channeling trajectory. At somewhat higher energies and intermediate incidence angles, the incoming atom scatters off the surface and does not stick.
B. W. Do&on / Channeling of low energy Si atoms above Si(ll1)
tion with the substrate, be a very weak function precisely, the critical perpendicular velocity is VP = 20.5 + 336/E,,
339
of beam energy. More (1)
where V, is in A/ps and E, is the beam energy in eV. The above information is summarized in an incidence angle versus beam energy phase diagram, which appears in fig. 3. The final point of interest is to consider the rate of energy loss experienced by a particle in the surface channeling mode. This can be evaluated directly from the computed trajectories by numerical differentiation. Upon doing so, the rate of energy loss is found to be nearly linear in kinetic energy of the surface channeling atom; in this energy range, aE/tlX=
0.000154 E - 0.0193,
(2)
where E is in eV and X is in A. Clearly, this relation cannot be extrapolated far outside of this energy range, but it does allow us to estimate the total surface channeling range along the surface as a function of initial beam energy. Crude estimates reveal that the surface channeling ranges will be thousands of A for the higher energy atoms. Direct calculation for the 20 eV atoms show that the linearity of the energy loss relation fails badly for smaller energies, and a surface channeling range of around 40 w is found before adsorption for these atoms, compared to perhaps 1000 A as predicted by eq. (2). The phenomenon called surface channeling described above must not be confused with the low angle trajectory focusing surface scattering described by Thompson and coworkers [5,6], or with the near-surface channeling mechanism proposed by Sizmann and Varelas [7]. In the first case, sometimes called surface semi-channeling, at certain surface orientations the incoming beam is focused by interaction with the surface atoms onto a second-layer row of atoms, whereupon very strong reflection from the surface with characteristic angular dependence takes place. In the second case, the beam atoms actually penetrate below the surface and channel within the bulk material near the surface, sometimes escaping from the surface when dechanneling takes place. In both cases the effects require high beam energies, the principal interaction with the substrate takes place below the surface layer, and the attractive part of the potential is unimportant. By contrast, in the surface channeling mechanism proposed here, very low energy atoms suffice to demonstrate the effect, the principal interaction generates bulk phonons through excitation of the surface atoms, and the attractive term in the potential is vital in predicting where the effect will appear. It is perhaps most similar to the mechanism proposed by Ohtsuki et al. [8], who predict a skipping motion when ions are scattered off a metal surface at grazing angles. The mechanism, however, is very different. They consider a surface potential resulting from dynamical
340
B. W. DorLFon / Channeling
of lowenergySi aionzs above Si(lll)
polarization of the valence electrons caused by the motion of the incident ion, which serves to trap the ion near the surface until neutralization of the ion takes place. This is a purely electronic effect requiring beam velocities much larger than those in the present calculation. The unreconstructed Si(ll1) surface and a beam orientation along the (110) surface direction represent a particularly favorable combination for surface channeling, as this surface is regular and fairly dense, even in the open diamond structure. However, we do not expect that surface ChaMeling is an effect limited to this surface. Preliminary simulation have been made on other beam orientations on the (111) surface, on the unreconstructed (100) surface, and on the reconstructed (100) and (111) surfaces. These early results indicate that surface channeling still appears in these cases, although it is limited to shallower angles of incidence. Surface channeling thus appears to be a generic feature of grazing low-energy beam-surface interactions in semiconductors. Helpful discussions with Paul Taylor and Tom Picraux are acknowledged. This work was performed at Sandia National Laboratories and was supported by USDOE contract DE-AC04-76DP00789.
References [l] N. Herbots, B.R. Appleton, T.S. Noggle, S.J. Permycook, R.A. Zuhr and D.M. Zehner, in: Semiconductor-Based Heterojunctions, Eds. M.L. Green, J.E.E. Baglin, G.Y. Chin, H.W. Deckman, W. Mayo and D. Narasinham (The Metallurgical Society, Warrendale, PA, 1986). [2] B.W. Dodson, Phys. Rev. B35 (1987) 2795. [3] J. Tersoff, Phys. Rev. Letters 56 (1986) 632. [4] P. Schofield, Computer Phys. Commun. 5 (1973) 17. [5] A.D. Mat-wick, M.W. Thompson, B.W. Farmery and G.S. Harbinson, Radiation Effects 15 (1972) 195. [6] M.W. Thompson and H.J. Pabst, Radiation Effects 37 (1978) 105. [7] R. Sizmann and C. Varelas, Nucl. Instr. Methods 132 (1976) 633. [8] Y.H. Ohtsuki, K. Koyama and Y. Yamamura, Phys. Rev. B20 (1979) 5044.