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Monte Carlo simulation of two-dimensional distributions of implanted ions in a crystalline silicon target
22
Nuclear
Instruments
and Methods
in Physics
Research
B34 (1988) 22-26
North-Holland,
Amsterdam
MONTE CARLO SIMULATION OF TWO-DIMENSIONAL DISTRIBUTIONS OF IMPLANTED IONS IN A CRYSTALLINE SILICON TARGET A.M.
MAZZONE
CNR-Istituto Received
LAMEL,
15 December
Via Castagnoli I, 40126 Bologna, Itai) 1987 and in revised form 14 March
1988
In this work a Monte Carlo method is used to analyze two-dimensional ion distributions in a crystalline show under which conditions nonnegligible lateral and in-depth tails may appear in these distributions.
1. Introduction The problem of the lateral penetration of ions has been examined from a theoretical point of view in numerous papers. Generally, such analyses are based on the assumption of a random arrangement of the target atoms and no account is taken of the actual structure of the silicon lattice. However a series of papers [1,6] has recently emphasized the importance of the minor channels near the (100) axis. In such works experimental and calculated one-dimensional profiles are presented which show light and heavy, low-energy, ions to have profiles with channelled tails even for a nominally random orientation of the target. When the ion distribution is examined in two dimensions (that is laterally and in depth) the question then arises whether such tails remain located in the vicinity of the ion incidence point or whether there is also a deep penetration along the lateral direction. In fact, a normal condition for an ion to have a long lateral range is the occurrence of large-angle collisions. Such a requirement is opposite to channelling. In this paper a Monte Carlo simulation is used to evaluate the spatial distribution of Bf and As+ ions in a crystalline silicon matrix. The masses and the energies have been chosen in such a way as to guarantee large acceptance angles for axial and planar channelling. As will be seen, the two-dimensional distributions show complex features not directly deducible from the concept of a critical angle.
2. The method The simulation study channelling simulation follows, moving particle. A
method is the one used in ref. [7] to in GaAs. We recall here that the collision by collision, the path of the small section of the crystal (contain-
0168-583X/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
silicon target. The results
ing approximately 40 atoms) is constructed around the ion path and the scatterer is chosen to be the atom nearest to the ion whose impact parameter is lower than 0.5~~ [8] (aa = 0.54 nm is the lattice parameter in silicon). The model of the target projectile interaction is based on the usual assumptions of binary collisions and separate elastic and inelastic losses. A refined universal potential [9] is used for the elastic losses and the standard velocity-proportional LSS expression, in the form reported in [lo], is used for the inelastic losses. Reference is made to [8] for the modelling of lattice vibrations, for the deflection generated by the electron scattering and for the treatment of simultaneous collisions. As discussed in [8,11] the evaluation of simultaneous collisions involves some elements of arbitrariness. In the present calculations a simultaneous deflection is induced only by those atoms whose distance, measured along the path of the projectile, is lower than O.Ola,. These collisions, in which two scatterers act simultaneously, are a few percent of the total. However, if their number is increased by one order of magnitude, changes of the order of lo-30%, at the maximum, are found only in those regions of the in-depth profiles where the fraction of the stopped ions is < 0.01. Furthermore all the general trends remain unaltered. The sample orientation is defined by the tilt angle 0 and the rotation angle +. The tilt and the rotation are about the (001) axis. In the following the orientations corresponding to the offset angles (0 = 0 o ), (0 = 7.5 O, +=O”) and (B=7.5”, cp=l9”) will be indicated as axial, planar and random, respectively. The spatial distribution of ions is referred to cylindrical coordinates (R, Z) [12] with the in-depth Z axis directed along the (001) axis. The ion beam is aligned with the Z axis. As in [13] the distribution of velocity directions within the incident beam is modelled by assuming (i) a Gaussian distribution for the angle with the beam axis (the di-
23
A.M. Mazzone / Simulation of two-dimensional distributions of implanted ions
vergency is the straggling parameter of such a Gaussian) and that (ii) the component in the plane orthogonal to the beam axis is subdi~d~ at random into two planar components. The simulation refers to the case of a point source irradiation. The ion incidence point is (R *, 2 = 0). The randomisation of the ion paths is achieved by varying R* at random with uniform probability in the interval (a further r~do~sing factor is obviously O-R,, offered by a nonzero beam divergency). According to the assumption of a point source R has to be kept as small as possible with respect to the lateral straggling parameter of the ion distribution to avoid an artificial shift of the trajectories along the lateral direction. The choice of the value 0.4 nm was based on the following considerations. For the axial orientation the projection of the channel onto the (x, y) plane is a square whose diagonal has a length equal to 0.3 nm. Consequently = 0.3 nm is the width of a nonreducible cell and, R asmtch, represents a realistic incidence condition for the ions entering a (001) channel. The value 0.4 nm avoids some artificial concentration of the incidence points near the origin. For the planar orientation R,, = 0.4 nm includes approximately two crystallographic cells. For off-axis implants the incidence condition is not critical. That was shown by several test calculations using different R,, values. 5000 to 10000 pseudo-particles stories were used to construct the profiles reported below. With this sampling the fluctuations of the ion projected range and of the second order moments fall in the range l-2% and 5-7%, respectively. In the following, data on ion penetration through an oxide layer are reported. In such cases the simulation method is the one used in ref. [14] with only the difference that the refined potential [9] has been substituted for the standard Lindhard potential. As a final point we wish to discuss the limits of validity of the calculations. In the first place it has to be recalled that the sim~ation applies to those implantation conditions which maintain the crystalline nature of the target, that is implants below the threshold for amorphisation or on a heated substrate. In the second place one has to account for dechanneling factors, such as for instance the misalignements within the scattering chamber, the divergency of the beam and the thickness of the native oxide, which represent uncertain inputs for the simulation. Usually the divergency of the beam is between 0.5’ and lo and the thickness of the native oxide l-2 nm. Some insight into the role played by these factors is given in fig. 1. The figure describes the d~h~ne~ng effects arising from a beam with 7” divergency and from and oxide coating equal to 1 nm. It is seen that the scattering within the oxide defocusses the beam which acquires a divergency approximately equal to 7O (as shown by the similarity of the through-
t
’
I
I
I
I
B+ 5 keV
I
OXIDE COATIN
I”
50 100 DEPTH [nml Fig. 1. In-depth distribution of B+ ions, 5 keV, dose equal to 2 X 1Or4cm-*. Axial channeling. Broken line = 0 ’ beam divergency, thick line = 7 o beam divergency, thin line = through-oxide implant, oxide thickness 1 nm. The points on the continuous curve are SIMS me~urements from ref. [l].
0
oxide and 7” divergency profiles) and induces a remarkable dechanneling. The calculation indicates, however, that if the divergency of the beam is equal to lo the dechanneling is limited to the ions which would reach a depth between 130 and 150 nm in the case of a perfectly collimated beam (the profile corresponding to 1’ divergency has been omitted in fig. 1 for the sake of clarity in the figure). In fig. 1 SIMS measurements from ref. [l] are also reported. A good agreement is noticed with the calculated t~~ou~-o~de profile. In the following a 7* beam divergency is used as a representative estimate of the native oxide coating. In fact, for the energies and masses here considered, a perfectly collimated beam acquires a divergency of approximately 7” traversing an oxide l-2 nm thick. We add that, similarly to our procedure, a 7 o beam divergency was used in ref. [14] to simulate the experiments reported in ref. [l]. A third, and more complex element for uncertainty, is represented by the evaluation of the energy losses. In fact channeled particles come to a stop in a regime dominated by electronic stopping. For heavy ions at low energy a good experimental information on electronic stopping for axes and planes is not at present available. Consequently we attribute a tentative meaning to the results reported in the following paragraph. For light
24
A.M. Mazzone / Simulation of two-dimensional distributions of implanted ions
Table 1 Average projected range ( RP) and in-depth and lateral straggling parameters (dR and dR,, respectively) for different target
w=exp;@=o”;Ref [ll =exp;9=19?6~Ref [1I l
orientations
Target orientation
RP
$27
pn”m;
As+ 50 keV, 0 o beam divergency Planar (7.50,0”) 89.5 Random (7.5 O, 19 o ) 38.3
73.6 24.3
6.0 9.0
B+ 10 keV, 0 o beam divergency Planar (7.5 O, 0 Q) 14.5 Random (7.5 O, 19 o ) 47.0
47.6 30.5
16.0 19.0
Bf 10 keV, 7 ’ beam divergency Planar (7.5 O,O“) 61.8 Random (7.5 O, 19 o ) 57.9
41.8 41.0
18.0 19.0
WI
Kd 0
I
I
50
I
I
II
I
100
DEPTH [nml Fig. 2. In-depth distribution of Bf ions, 5 keV, dose equal to 2~10’~ cme2, for the random and planar orientation of the target. The continuous curves are SIMS measures from [l]. Note that the experimental profiles for + = 45” and 19O fall one on the other.
ions a limited comparison with experiments is possible. Calculated Bt implants for two planar orientations respectively) and one nominally (+=O” and $=45”, random (+ = 19 ” ) are compared in fig. 2 with the experiments from ref. [l]. It is seen that the simple LSS expression leads to reasonably correct results, although channeling in the (110) planes (+ = 0 ” ) is overestimated.
3. Results
The following data refer to a light (B+) and a heavy (As+) ion. The energies (10 keV for Bf and 50 keV for As+) are chosen in such a way as to obtain comparable projected ranges of a few tens nanometers. Furthermore two sets of calculation are constantly referred to. In one, the beam is perfectly collimated and the results are illustrative of the typical properties of the scattering in the crystal. In the other set the beam divergency is nonzero and the simulation is more representative of the actual experimental conditions. The main features of the spatial distribution of the ions are summarized in table 1. In the table the average projected range (R,) and the straggling parameters along the Z and R directions, d R, and d R, respec-
tively, are reported for different target orientations. In the case of B+ a comparison is also made between a 0 o and 7 o beam divergency. It is seen that for the planar orientation the ion distribution constantly shows longer R, and dR, and slightly shorter dR,. We recall that a typical ion path is roughly composed of two pieces. In the near surface region, where the primary energy is high, the ion maintains its original direction. In this region its energy is slowly drained by the interaction with the electron subsystem and by nuclear, small-angle collisions. At greater depths, a series of nuclear collisions with large momentum exchanges deflects the ion trajectory and brings the ion deeply along the lateral direction. Obviously in such collisions the ion closely approaches the atomic strings. For a channelled ion this condition is fulfilled only at great depth when its energy has considerably decayed. Consequently the lateral penetration is limited. A typical channelled trajectory, if compared to a random one, appears elongated in depth and laterally shorter. A further important point shown by the table is the effect of the beam divergency. For the planar orientation, similarly to the results for axial channeling shown in fig. 1, sizeable divergency causes an appreciable dechanneling. The effect is reversed for the random orientation, which exhibits a considerable enhancement of R,. This result is not new. As discussed in refs. [13,16], extra-scattering centres become active which may feed ions into the channels. To this point the calculations do not suggest relevant departures from the features of channelling as they are generally understood. More interesting data come from the inspection or the ion profiles reported in the following figs. 3-5. These figures show: (i) the in-depth distribution of the total implanted charge (thick line);
25
A.M. Mazzone / Simulation of two-dimensional distributions of implanted ions
6=25’,
S=O’.
6=7.5’. 0=199
div=O’
6=75’, @=O”.div=7’
dlv=O’
I(34h-
0
50
100
150
0
50
100
150
200
lo4.0
50
100
150
0
50
100
150
200
DEPTH hml
DEPTH hml
Fig. 3. In-depth distributions of As+ ions, 50 keV, 0” beam divergency. The thick line represents the one-dimensional profile. The thin line indicates the in-depth distribution of ions with 0 < R < dR, and the broken line the one of ions with
Fig. 5. In-depth distributions of B+ ions, 10 keV, 7O beam divergency. Symbols as in fig. 3.
dR, < R i 2dR,.
(ii) the in-depth
distribution of the charge located between R = 0 and R, (thin line) and between R, and 2R, (broken line). R, is assumed equal to the d R, value for the given implant conditions. Fig. 3 refers to As+ 50 keV, O” beam divergency, and compares a random and a planar orientation. In the first case it is seen that the fraction located in the inner and outward cylinder approximately coincide. In the second case the difference between the two lateral distributions is approximately of one order of magnitude. As discussed above, this limited lateral penetration is a normal feature of channelled trajectories. The corresponding B+ profiles are shown in fig. 4. As shown in the figure, for the random orientation the features of B+ are similar to the ones of As+. The planar case is more complex. An increase of randomisation is noticed at depths I R, where the fraction of ions located in the outward cylinder appears consider-
ably increased with respect to As+. However also the fraction of well channeled trajectories reaching depths of 100-150 nm is increased, with respect to As+, in both cylinders. This behaviour is not easily deducible from the use of one critical angle. Within such approach one would expect for the two ions only an increase or a decrease of channeling (paralleled by a decrease or increase of the lateral penetration) according to the ratio between the critical angles. Fig. 5 examines the effects of the defocussing of the beam (7 ’ divergency). It is seen that: (i) for the planar orientation dechannelling is the prevailing effect. (ii) on the contrary, for the random orientation an increase of channelling, especially evident at depths > 100 nm, is observed. However this re-channelling is also associated with an extended penetration along the lateral direction so that the distributions in the outward and inward shell reach the same level. In conclusion these simulations suggest that open trajectories, of great extension in either the lateral or the in-depth direction, are accessible to the ions. The probability of being conveyed along one of these unforeseen channels depends in a complex manner on the actual arrangement of the scattering centres, on the features of scattering and on external factors, like for instance the oxide coating. This work has been supported by Projetto Finalizzato Materioli e Dispositivi per 1’Elettronica - CNR. References
150 0 50 DEPTH Lnml
100
150
200
Fig. 4. In-depth distributions of B+ ions, 10 keV, O” beam divergency. Symbols as in fig. 3 above.
[l] A.E. Michel, R.H. Kastl, S.R. Mader, B.J. Mader and J.A.
Gardner, Appl. Phys. Lett. 44 (1984) 404. [2] F. Ziegler and R.F. Lever, Appl. Phys. Lett. 46 (1985) 385. [3] M.D. Giles and J.F. Gibbons, IEEE Trans. Electron. Devices ED-32 (1985) 1918.
26
A.M. Mazzone / Simulation
oftwo-dimensional $istributions of implanted ions
[4] M. Hautala, Mater. Res. Sot. Symp. Proc., eds. B.R. Appleton, F.H. Eisen and T.W. Sigmon (Mater. Res. Sot., ~ttsburgh, 1985) vol. 45, p. 105. [5] O.S. Oen, Nucl. Instr. and Meth. B13 (1986) 495. [6] T. Takeda, S. Tazawa and A. Yoshii, IEEE Trans. Electron. Devices ED-33 (1986) 1278. [7] F. Garofalo and A.M. Mazzone, Phys. Status Solidi (a) 98 (1986) 517. [S] M.T. Robinson and I.M. Torrens, Phys. Rev. B9 (1974) 5008. [9] J. Lindhard, M. Scharff and H.E. Schiott, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 33 (1963) no. 14. [lo] J. Biersack and J.F. Ziegler, Ion Implantation Techniques, eds. H. Ryssel and H. Glaswishing (Springer, Berlin and Heidelberg, 1982) p. 122.
[ll] M. Hou and M.T. Robinson, Nucl. In&. and Meth. 132 (1976) 641. HZ] M.T. Robinson, Phys. Rev. B27 (1983) 5347. [13] A.M. Mazzone, Philos. Mag. Lett. 55 (1987) 235. [14] A.M. Mazzone and G. Rocca, IEEE Trans. Comp. Aided Design 3 (1984) 64. [15] N. Azziz, K.W. Brannon, G.R. Srinivasan, Mater. Res. Sot. Symp. Proc., eds. B.R. Appleton, F.H. Eisen and T.W. Sigmon (Mater. Res. Sot., Pittsburgh, 1985) p. 109. 1161 M. Ha&ala, Nucl. Instr. and Meth. B15 (1986) 75. [17] O.S. Oen and M.T. Robinson, Nucl. In&r. and Meth. 132 (1976) 647.
Nuclear
Instruments
and Methods
in Physics
Research
B34 (1988) 22-26
North-Holland,
Amsterdam
MONTE CARLO SIMULATION OF TWO-DIMENSIONAL DISTRIBUTIONS OF IMPLANTED IONS IN A CRYSTALLINE SILICON TARGET A.M.
MAZZONE
CNR-Istituto Received
LAMEL,
15 December
Via Castagnoli I, 40126 Bologna, Itai) 1987 and in revised form 14 March
1988
In this work a Monte Carlo method is used to analyze two-dimensional ion distributions in a crystalline show under which conditions nonnegligible lateral and in-depth tails may appear in these distributions.
1. Introduction The problem of the lateral penetration of ions has been examined from a theoretical point of view in numerous papers. Generally, such analyses are based on the assumption of a random arrangement of the target atoms and no account is taken of the actual structure of the silicon lattice. However a series of papers [1,6] has recently emphasized the importance of the minor channels near the (100) axis. In such works experimental and calculated one-dimensional profiles are presented which show light and heavy, low-energy, ions to have profiles with channelled tails even for a nominally random orientation of the target. When the ion distribution is examined in two dimensions (that is laterally and in depth) the question then arises whether such tails remain located in the vicinity of the ion incidence point or whether there is also a deep penetration along the lateral direction. In fact, a normal condition for an ion to have a long lateral range is the occurrence of large-angle collisions. Such a requirement is opposite to channelling. In this paper a Monte Carlo simulation is used to evaluate the spatial distribution of Bf and As+ ions in a crystalline silicon matrix. The masses and the energies have been chosen in such a way as to guarantee large acceptance angles for axial and planar channelling. As will be seen, the two-dimensional distributions show complex features not directly deducible from the concept of a critical angle.
2. The method The simulation study channelling simulation follows, moving particle. A
method is the one used in ref. [7] to in GaAs. We recall here that the collision by collision, the path of the small section of the crystal (contain-
0168-583X/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
silicon target. The results
ing approximately 40 atoms) is constructed around the ion path and the scatterer is chosen to be the atom nearest to the ion whose impact parameter is lower than 0.5~~ [8] (aa = 0.54 nm is the lattice parameter in silicon). The model of the target projectile interaction is based on the usual assumptions of binary collisions and separate elastic and inelastic losses. A refined universal potential [9] is used for the elastic losses and the standard velocity-proportional LSS expression, in the form reported in [lo], is used for the inelastic losses. Reference is made to [8] for the modelling of lattice vibrations, for the deflection generated by the electron scattering and for the treatment of simultaneous collisions. As discussed in [8,11] the evaluation of simultaneous collisions involves some elements of arbitrariness. In the present calculations a simultaneous deflection is induced only by those atoms whose distance, measured along the path of the projectile, is lower than O.Ola,. These collisions, in which two scatterers act simultaneously, are a few percent of the total. However, if their number is increased by one order of magnitude, changes of the order of lo-30%, at the maximum, are found only in those regions of the in-depth profiles where the fraction of the stopped ions is < 0.01. Furthermore all the general trends remain unaltered. The sample orientation is defined by the tilt angle 0 and the rotation angle +. The tilt and the rotation are about the (001) axis. In the following the orientations corresponding to the offset angles (0 = 0 o ), (0 = 7.5 O, +=O”) and (B=7.5”, cp=l9”) will be indicated as axial, planar and random, respectively. The spatial distribution of ions is referred to cylindrical coordinates (R, Z) [12] with the in-depth Z axis directed along the (001) axis. The ion beam is aligned with the Z axis. As in [13] the distribution of velocity directions within the incident beam is modelled by assuming (i) a Gaussian distribution for the angle with the beam axis (the di-
23
A.M. Mazzone / Simulation of two-dimensional distributions of implanted ions
vergency is the straggling parameter of such a Gaussian) and that (ii) the component in the plane orthogonal to the beam axis is subdi~d~ at random into two planar components. The simulation refers to the case of a point source irradiation. The ion incidence point is (R *, 2 = 0). The randomisation of the ion paths is achieved by varying R* at random with uniform probability in the interval (a further r~do~sing factor is obviously O-R,, offered by a nonzero beam divergency). According to the assumption of a point source R has to be kept as small as possible with respect to the lateral straggling parameter of the ion distribution to avoid an artificial shift of the trajectories along the lateral direction. The choice of the value 0.4 nm was based on the following considerations. For the axial orientation the projection of the channel onto the (x, y) plane is a square whose diagonal has a length equal to 0.3 nm. Consequently = 0.3 nm is the width of a nonreducible cell and, R asmtch, represents a realistic incidence condition for the ions entering a (001) channel. The value 0.4 nm avoids some artificial concentration of the incidence points near the origin. For the planar orientation R,, = 0.4 nm includes approximately two crystallographic cells. For off-axis implants the incidence condition is not critical. That was shown by several test calculations using different R,, values. 5000 to 10000 pseudo-particles stories were used to construct the profiles reported below. With this sampling the fluctuations of the ion projected range and of the second order moments fall in the range l-2% and 5-7%, respectively. In the following, data on ion penetration through an oxide layer are reported. In such cases the simulation method is the one used in ref. [14] with only the difference that the refined potential [9] has been substituted for the standard Lindhard potential. As a final point we wish to discuss the limits of validity of the calculations. In the first place it has to be recalled that the sim~ation applies to those implantation conditions which maintain the crystalline nature of the target, that is implants below the threshold for amorphisation or on a heated substrate. In the second place one has to account for dechanneling factors, such as for instance the misalignements within the scattering chamber, the divergency of the beam and the thickness of the native oxide, which represent uncertain inputs for the simulation. Usually the divergency of the beam is between 0.5’ and lo and the thickness of the native oxide l-2 nm. Some insight into the role played by these factors is given in fig. 1. The figure describes the d~h~ne~ng effects arising from a beam with 7” divergency and from and oxide coating equal to 1 nm. It is seen that the scattering within the oxide defocusses the beam which acquires a divergency approximately equal to 7O (as shown by the similarity of the through-
t
’
I
I
I
I
B+ 5 keV
I
OXIDE COATIN
I”
50 100 DEPTH [nml Fig. 1. In-depth distribution of B+ ions, 5 keV, dose equal to 2 X 1Or4cm-*. Axial channeling. Broken line = 0 ’ beam divergency, thick line = 7 o beam divergency, thin line = through-oxide implant, oxide thickness 1 nm. The points on the continuous curve are SIMS me~urements from ref. [l].
0
oxide and 7” divergency profiles) and induces a remarkable dechanneling. The calculation indicates, however, that if the divergency of the beam is equal to lo the dechanneling is limited to the ions which would reach a depth between 130 and 150 nm in the case of a perfectly collimated beam (the profile corresponding to 1’ divergency has been omitted in fig. 1 for the sake of clarity in the figure). In fig. 1 SIMS measurements from ref. [l] are also reported. A good agreement is noticed with the calculated t~~ou~-o~de profile. In the following a 7* beam divergency is used as a representative estimate of the native oxide coating. In fact, for the energies and masses here considered, a perfectly collimated beam acquires a divergency of approximately 7” traversing an oxide l-2 nm thick. We add that, similarly to our procedure, a 7 o beam divergency was used in ref. [14] to simulate the experiments reported in ref. [l]. A third, and more complex element for uncertainty, is represented by the evaluation of the energy losses. In fact channeled particles come to a stop in a regime dominated by electronic stopping. For heavy ions at low energy a good experimental information on electronic stopping for axes and planes is not at present available. Consequently we attribute a tentative meaning to the results reported in the following paragraph. For light
24
A.M. Mazzone / Simulation of two-dimensional distributions of implanted ions
Table 1 Average projected range ( RP) and in-depth and lateral straggling parameters (dR and dR,, respectively) for different target
w=exp;@=o”;Ref [ll =exp;9=19?6~Ref [1I l
orientations
Target orientation
RP
$27
pn”m;
As+ 50 keV, 0 o beam divergency Planar (7.50,0”) 89.5 Random (7.5 O, 19 o ) 38.3
73.6 24.3
6.0 9.0
B+ 10 keV, 0 o beam divergency Planar (7.5 O, 0 Q) 14.5 Random (7.5 O, 19 o ) 47.0
47.6 30.5
16.0 19.0
Bf 10 keV, 7 ’ beam divergency Planar (7.5 O,O“) 61.8 Random (7.5 O, 19 o ) 57.9
41.8 41.0
18.0 19.0
WI
Kd 0
I
I
50
I
I
II
I
100
DEPTH [nml Fig. 2. In-depth distribution of Bf ions, 5 keV, dose equal to 2~10’~ cme2, for the random and planar orientation of the target. The continuous curves are SIMS measures from [l]. Note that the experimental profiles for + = 45” and 19O fall one on the other.
ions a limited comparison with experiments is possible. Calculated Bt implants for two planar orientations respectively) and one nominally (+=O” and $=45”, random (+ = 19 ” ) are compared in fig. 2 with the experiments from ref. [l]. It is seen that the simple LSS expression leads to reasonably correct results, although channeling in the (110) planes (+ = 0 ” ) is overestimated.
3. Results
The following data refer to a light (B+) and a heavy (As+) ion. The energies (10 keV for Bf and 50 keV for As+) are chosen in such a way as to obtain comparable projected ranges of a few tens nanometers. Furthermore two sets of calculation are constantly referred to. In one, the beam is perfectly collimated and the results are illustrative of the typical properties of the scattering in the crystal. In the other set the beam divergency is nonzero and the simulation is more representative of the actual experimental conditions. The main features of the spatial distribution of the ions are summarized in table 1. In the table the average projected range (R,) and the straggling parameters along the Z and R directions, d R, and d R, respec-
tively, are reported for different target orientations. In the case of B+ a comparison is also made between a 0 o and 7 o beam divergency. It is seen that for the planar orientation the ion distribution constantly shows longer R, and dR, and slightly shorter dR,. We recall that a typical ion path is roughly composed of two pieces. In the near surface region, where the primary energy is high, the ion maintains its original direction. In this region its energy is slowly drained by the interaction with the electron subsystem and by nuclear, small-angle collisions. At greater depths, a series of nuclear collisions with large momentum exchanges deflects the ion trajectory and brings the ion deeply along the lateral direction. Obviously in such collisions the ion closely approaches the atomic strings. For a channelled ion this condition is fulfilled only at great depth when its energy has considerably decayed. Consequently the lateral penetration is limited. A typical channelled trajectory, if compared to a random one, appears elongated in depth and laterally shorter. A further important point shown by the table is the effect of the beam divergency. For the planar orientation, similarly to the results for axial channeling shown in fig. 1, sizeable divergency causes an appreciable dechanneling. The effect is reversed for the random orientation, which exhibits a considerable enhancement of R,. This result is not new. As discussed in refs. [13,16], extra-scattering centres become active which may feed ions into the channels. To this point the calculations do not suggest relevant departures from the features of channelling as they are generally understood. More interesting data come from the inspection or the ion profiles reported in the following figs. 3-5. These figures show: (i) the in-depth distribution of the total implanted charge (thick line);
25
A.M. Mazzone / Simulation of two-dimensional distributions of implanted ions
6=25’,
S=O’.
6=7.5’. 0=199
div=O’
6=75’, @=O”.div=7’
dlv=O’
I(34h-
0
50
100
150
0
50
100
150
200
lo4.0
50
100
150
0
50
100
150
200
DEPTH hml
DEPTH hml
Fig. 3. In-depth distributions of As+ ions, 50 keV, 0” beam divergency. The thick line represents the one-dimensional profile. The thin line indicates the in-depth distribution of ions with 0 < R < dR, and the broken line the one of ions with
Fig. 5. In-depth distributions of B+ ions, 10 keV, 7O beam divergency. Symbols as in fig. 3.
dR, < R i 2dR,.
(ii) the in-depth
distribution of the charge located between R = 0 and R, (thin line) and between R, and 2R, (broken line). R, is assumed equal to the d R, value for the given implant conditions. Fig. 3 refers to As+ 50 keV, O” beam divergency, and compares a random and a planar orientation. In the first case it is seen that the fraction located in the inner and outward cylinder approximately coincide. In the second case the difference between the two lateral distributions is approximately of one order of magnitude. As discussed above, this limited lateral penetration is a normal feature of channelled trajectories. The corresponding B+ profiles are shown in fig. 4. As shown in the figure, for the random orientation the features of B+ are similar to the ones of As+. The planar case is more complex. An increase of randomisation is noticed at depths I R, where the fraction of ions located in the outward cylinder appears consider-
ably increased with respect to As+. However also the fraction of well channeled trajectories reaching depths of 100-150 nm is increased, with respect to As+, in both cylinders. This behaviour is not easily deducible from the use of one critical angle. Within such approach one would expect for the two ions only an increase or a decrease of channeling (paralleled by a decrease or increase of the lateral penetration) according to the ratio between the critical angles. Fig. 5 examines the effects of the defocussing of the beam (7 ’ divergency). It is seen that: (i) for the planar orientation dechannelling is the prevailing effect. (ii) on the contrary, for the random orientation an increase of channelling, especially evident at depths > 100 nm, is observed. However this re-channelling is also associated with an extended penetration along the lateral direction so that the distributions in the outward and inward shell reach the same level. In conclusion these simulations suggest that open trajectories, of great extension in either the lateral or the in-depth direction, are accessible to the ions. The probability of being conveyed along one of these unforeseen channels depends in a complex manner on the actual arrangement of the scattering centres, on the features of scattering and on external factors, like for instance the oxide coating. This work has been supported by Projetto Finalizzato Materioli e Dispositivi per 1’Elettronica - CNR. References
150 0 50 DEPTH Lnml
100
150
200
Fig. 4. In-depth distributions of B+ ions, 10 keV, O” beam divergency. Symbols as in fig. 3 above.
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Gardner, Appl. Phys. Lett. 44 (1984) 404. [2] F. Ziegler and R.F. Lever, Appl. Phys. Lett. 46 (1985) 385. [3] M.D. Giles and J.F. Gibbons, IEEE Trans. Electron. Devices ED-32 (1985) 1918.
26
A.M. Mazzone / Simulation
oftwo-dimensional $istributions of implanted ions
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