Improving the prediction capabilities of Binary Collision Approximation ion implant simulators
J.M. Hern´andez-Mangas, J. Arias, L. Bail´on, M. Jara´ız, J. Barbolla Dept. Electricidad y Electr´onica, Universidad de Valladolid, Spain. (September 26, 2001) An efficient Binary Collision Approximation (BCA) ion implant code with good prediction capabil- ities in semiconductor materials (Si, GaAs SiC) with only one fitting parameter for low implantation doses is presented. It includes specific interatomic potentials and recent improvements in physical models for inelastic stopping. A periodic ab initio full bond electron density for the target is used. Damage accumulation is supported using a modified Kinchin-Pease model. Also some of the BCA integration algorithms and target selection procedure have been refined. An algorithm commonly used for statistical noise reduction has been modified to also improve the noise reduction in the lateral and shallow zones. The agreement with experiments is good, even under channelling condi- tions and for different target materials. A comparison with experimental SIMS results for several projectiles and targets is presented.
I. INTRODUCTION namics (MD) technique is more accurate than BCA, it needs much longer calculation times. In addition, BCA Ion implantation is one of the main processes used for methods can be refined to improve their accuracy to meet the fabrication of modern integrated microelectronic de- current needs. vices, allowing controlled doping of the active regions. Historically, researchers have used several modeliza- The reliable prediction of dopant concentrations by sim- tion schemes to solve the problem of ion implantation. ulations is of great importance in order to save the cost The choice depends on material’s characteristics such as and time required by experiments. amorphous [6] or crystalline [7] targets, and also on the Accurate knowledge of the three-dimensional profile of description level of the problem: MD, BCA, Transport the implanted ions is crucial for current deep sub-micron Equation, etc. devices, as this distribution is closely related to the de- In the 60’s, the LSS theory [8,9] was introduced to sired electrical characteristics of the final device. The model ion implantation. In this theory the total stop- ability to accurately predict the lateral doping profiles as ping power was calculated as the sum of two independent well as the depth profiles in a computationally efficient contributions: nuclear (elastic) and electronic (inelastic). manner is important for optimum design and fabrica- The nuclear stopping was obtained by means of classical tion of advanced devices. Also dopant profiles implanted mechanics. The electronic stopping was assumed to be with high energies are needed to create retrograde wells. proportional to the ion velocity and it did not depend on Channelling of projectiles into the target must be taken either the ion direction or the individual collisions. This into account with physical models, because some projec- is a non-local stopping and sees the ion as moving in a tiles (e.g. boron into silicon) present a strong channelling uniform electron gas. This model did not follow the ion component [1–4]. trajectory into the target and did not take into account To be predictive for different materials and projectiles, the crystalline properties of the target. a simulation code must be able to simulate different im- An improved modelization was made in 1974 by Robin- plant conditions like angle, orientation, oxide layer, dose, son et al. [7,10,11] (MARLOWE code). This model con- etc., with the same set of adjustable parameters and mod- siders a crystalline target material with the BC approx- els. imation. It uses a symmetrically spherical electron den- Also, the ion implant simulator must allow a trade-off sity (ZBL density) that does not represent neither the between speed and accuracy [5]. All of these aspects have bonds of covalent targets nor the low electron density been studied by different groups and are now scattered at the interstitial zones. It also used integration algo- across different simulation codes. In an effort to analyze rithms that did not take into account the effect of the the prediction capabilities and computational efficiency neighboring atoms potential energy. As a result, it had a that can be attained with these models, we have gath- low predictive capability, it needs a number of fitting pa- ered them all into a single simulation code. The purpose rameters to match the experiments. This code has been of this paper is, therefore, to first describe the models greatly modified by many authors (e.g. [1,12]) implemented and then present an analysis of the perfor- A third simulation scheme for ion implantation was de- mance of the combined use of these models in terms of veloped by Ziegler, Biersack and Littmark (ZBL) [6] in prediction capabilities and computational efficiency. We 1985. It was a BCA Monte Carlo method for amorphous selected the binary collision approximation (BCA) in or- targets. The projectile trajectory is statistically followed der to achieve this because, although the Molecular Dy- selecting randomly a target atom, an impact parame-
1 ter and a distance (mean free path). The elastic part mass, TDebye is the Debye temperature of the target ob- of the collision was solved by classical mechanics obtain- tained experimentally [22] and A(T ) is the Debye func- ing the new position, direction and energy for both the tion [23]. projectile and target atom. To shorten the calculation Projectiles loose their energy both elastically and in- time it uses a magic formula that fits the solved equa- elastically by collisions with the atoms of the target mate- tions. The inelastic contribution was estimated using the rial. The binary collision approximation, used here, con- Brandt and Kitagawa theory [13]. It had two terms: the siders only the collision with one target atom at a time. proton stopping in a uniform electron gas, and a scaling Simultaneous collisions are modelled through a combina- factor for heavier projectiles. The proton stopping was tion of individual collisions [10] when needed (e.g. chan- fitted through experimental data. neling conditions). This model works sensibly well for amorphous targets, The scheme followed iteratively is: (i) search of target but it cannot be employed for crystalline targets. candidates (as in Ref. [7]); (ii) calculation of each bi- A highly modi- nary (individual) elastic collision; (iii) selection of actual fied MARLOWE code (UT-MARLOWE) was developed targets; (iv) calculation of non-local electronic losses for [1,14–16] at the University of Texas at Austin. It covered each binary collision considering the 3D periodic electron the most commonly used implant species into single crys- density following the asymptotic trajectories (tabulating tal silicon with explicit dependence on energy, dose, tilt this procedure with the actual trajectories would lead to and rotation angles, but the models used for stopping, a too high computational burden); (v) calculation of local damage, etc., are different depending on species, energy electronic losses for the simultaneous collision with all the range, etc. in order to match the experimental results. targets; (vi) finally, energy and momentum conservation CRYSTAL-TRIM [2] code was a combination between rules are applied and projectile and targets are moved to the MARLOWE and TRIM codes in order to be fast with their new positions. Specific explanations of these steps amorphous targets, but it uses many adjustable parame- will be given next. ters [17] both for the electronic stopping and the damage model to cover all the implant species and conditions. The University of Wien has developed VISTA- A. Elastic losses: specific screening functions MCIMPL that also needs many fitting parameters to match experiments. It implements a complex rare-event The nuclear interaction between the incident projectile model [18]. and the target atom is solved by classical mechanics [24]. Other attempts to model ion implantation have been A numerical integration of the movement equations for made using mixtures of the ones cited above or using MD. both particles is done. To speed up the implant simula- Molecular Dynamics is very time consuming (orders of tion, a look-up table is previously calculated. A repul- magnitude more than BCA). However, in the near future, sive Coulombic screened potential is used. The screening MD may be the technique of choice for very low energies. function can be selected among several universal and spe- Our starting point has been the MARLOWE scheme cific ones. By default a universal screening function due [7] but it has been completely rewritten in C++ to ZBL [6] is used. [12,19,20]. A physical model with only one adjustable Other universal screening functions (Bohr, Moli`ere parameter [21] has been used for the electronic stopping [25], Lenz-Jensen [26], Thomas-Fermi [27]) have been using a novel integration method. Also to speed-up the tested [28]. We use specific screening functions, when simulator a new statistical noise reduction scheme has available, for each projectile-target combination obtained been implemented. by ab-initio methods [6] (e.g. with DMol code [29]) to reduce the number of approximations used by the sim- ulator. When no specific screening function is available II. PHYSICAL MODELS the best suited seems to be the ZBL one. It has a mean error of 2.1% with respect to specific ones [6]. Projectiles are simulated following their complete tra- jectory as well as the trajectories of the recoils generated (full cascade development). The target material is mod- B. Inelastic losses: physical models elled as crystalline, polycrystalline or amorphous [7]. For polycrystalline targets a random rotation of the whole It has been found necessary [21] to include inelastic crystal is made before each ion implant. For amorphous, energy loss due to collisions (local), and energy loss due a random rotation of the crystal is done before each col- to background electronic stopping (non-local) as two dis- lision. tinct mechanisms in order to obtain good simulation re- Thermal vibrations are considered using a Debye tem- sults under a range of channelling conditions [28,30,31]. perature model. The RMS amplitude of the thermal dis- It is not possible to assume that one of these processes is A placement varies with the target temperature as RMS = dominant and fit it to accurately model energy losses for 1/2 12.063464 (A(T )/(TDebyeM)) where M is the atomic different implant energies and directions.
2 The non-local inelastic stopping accounts for the aver- R[38,39] as proposed by Beardmore et al. [21]: ∆Ei = F dr age energy loss of the ion as it travels along the interstitial trajectory ij where volume of the target. It is due to the interaction between the nucleus of the projectile and the target’s electrons. 1/3h F 2 ¯ v − v This electronic stopping is given by the modified Brandt- ij = πa (ˆj ˆi) "2 B Ã ! Ã !# Kitagawa [13] theory with only one adjustable parameter 1/3 1/3 r0 2 Z αR 2 Z (1 − α)R [4,32], s . This stopping is calculated as Z I A + Z I B (4) Z A a B a S Z∗ v,r0 2S v,r dx non local = [ 1 ( s )] p( s) (1) trajectory with Z Z∗ S ∞ Φ2(x) where 1 represents the effective charge of the ion, p I W dx r ( )= x (5) is the electronic stopping power for a proton and s = W (3/(4πρ))1/3 the one-electron radius (ρ is the local elec- h i−1 tron density). The r0 value is related to the effective 1/6 s and α = 1+(ZB/ZA) ,Φ(x) being the universal electron density of the target and depends on the ion- screening function [6], ZA,ZB the atomic numbers (ZA ≥ target combination [4]. 2 1/3 ZB), R the atomic separation, a =(9π /128) aB, and According to Brandt and Kittagawa the effective a Z∗ Z γ v,r0 B the Bohr radius. As mentioned by Firsov [39], at suf- charge is defined as: 1 = 1 ( s ) with " # ficiently high ion velocities the electrons of the two atoms µ ¶2 will not have the time necessary for free interaction, and 4Λ γ v,r0 q v C r0 − q v therefore the transfer of energy will diminish. Following ( s )= ( )+ ( s )(1 ( )) ln 1+ r0 (2) s Ref. [40] we have accounted for this fact by damping out the energy transfer beyond a critical velocity (vc =0.7vB, where q(v) is the ionization fraction, C(r0) depends s where vB is the Bohr velocity), as: weakly on the target, but can be approximated to 0.5 and v/vB for v 3 density than the ZBL one. We expected this should be III. COMPUTING ALGORITHMS a good approximation for non-polar covalent materials (e.g. silicon). A. Inelastic losses: integration methods Figure 1 shows the differences between the ZBL, IADS { } and true bond densities along the 111 direction for a We have observed that the integration schemes for the silicon target. It is clear that the ZBL density does not two energy loss components can play a critical role in represent accurately some regions (in particular, intersti- order to achieve the degree of accuracy demanded by tial regions). current technology, particularly under channeling condi- A comparison between the common electron distri- tions. As a result, we are using an integration method butions [28,30,31], reveals the necessity for a three- that is a hybrid between molecular dynamics and the dimensional description of the covalent nature of silicon. BCA model, in order to improve the numerical integra- This necessity is extensible, and even more important, tions. for other compound semiconductors. For silicon targets { } For the non-local electronic losses the straight projec- the main differences were observed in the 110 chan- tile incoming trajectory is sampled (see Fig. 2, where nel direction [28]. Simulations without free parameters a straight movement is considered for the projectile be- [43] have also proven the necessity of using a 3D electron tween P1 and P2 and target from T1 to T2) having into density distribution. account the potential energy at each point due to the surrounding neighbors, Ep(x), the elastic energy trans- fer to the target, E (x), and also the electronic losses D. Damage accumulation T accumulated upto this point, Snon local(x). The local ki- netic energy for the projectile is calculated as: Ec(x)= In order to deal with high dose implantations the sim- Ec0 − ET (x) − Snon local(x) − Ep(x) where Ec0 is the ini- ulator must include some damage accumulation model. tial kinetic energy at this collision. The ET (x) value is It will be important especially in channelling cases. Al- calculated by linear interpolationp between its initial and though we have implemented the full cascade develop- final values. Since v = 2Ec/M1 the non-local electronic ment, due to practical reasons (mainly the speed of the losses can be integrated using equation (1). simulator) we have begun implementing damage accumu- The local inelastic losses are integrated along the lation based on Kinchin-Pease theory [1,44] as a first ap- straight incoming and outgoing trajectories (Figure 2) proximation. In a near future we plan to include the full of the projectile. Straight displacements are assumed for cascade development in damage accumulation as a slower the target. At each point, the force Fij between the pro- but more accurate option. The modelization of damage jectile and the target is evaluated using equation (4). The has two parts: the defect generation/recombination and outgoing trajectory is followed long enough to account for the damage simulation. The damage simulation will be all the interaction. At this stage we consider the contri- described in the Computing Algorithms section. butions of the electron densities of all the targets involved n The number of point defects generated, , is propor- in the collision. tional to the energy, E, lost by nuclear scattering in each sector: kE B. Statistical noise improvement algorithm n = (8) 2Ed In order to reduce the calculation time and to improve where k =0.8 is a constant and Ed is the displacement the accuracy of the simulated profiles a three-dimensional threshold energy. For boron implantation into silicon rare event algorithm is implemented [45]. The straight- Ed = 15 eV. Part of the point defects generated recom- forward way to obtain a statistically significant concen- bines with other defects, so the net increase of point de- tration at all depths of the profile is to run many simu- fects after recombination, ∆n, is given by: lated cascades. Most of the ions will stop near the main peak. The majority of the computer effort will not im- N prove the accuracy of the tail or low concentration zones. ∆n = nfsurv(1 − ) (9) Nα With the atom splitting scheme [45] at certain depths, f the ion is split into two virtual ions with half statistical where surv is the fraction of point defects surviving weight of unsplit ion. The virtual ions generated have both intracascade and intercascade recombination and the same position and velocity as the parent ion. Their it is adjusted for each implanted kind of projectile (e.g. f . N final trajectories are, however, different due to the ther- surv =006 for boron into silicon), is the previous mal vibration effects. In the end, we obtain practically local defect density, and Nα is the local defect density N the same number of virtual ions at each bin of the his- necessary to reach amorphization (e.g. for silicon α is togram profile improving the statistics on low concentra- ten percent of the atomic density). tion zones. In the ion implant simulation there are two rare event cases of particular interest to be considered to 4 improve the statistics of the impurity profile: the deep generally a percentage of the initial energy. Ions that region (channeled ions) and the shallow region. verify this condition are likely to stop nearby. Second, a positional condition: we consider the shallow region (Fig. 5) defined by Wshallow = pd(Dmax − Dmin), 1. Channelled ions where Dmax is the maximum depth reached by an im- planted ion, Dmin is the positive minimum depth of the This case occurs when the projectile travels through a current profile and pd is the percentage of the whole pro- crystal channel. It looses its energy mainly by inelastic file that the user considers to be the shallow region. We interaction without experiencing hard nuclear (elastic) divide Wshallow into N equal zones. Initially the projec- collisions. We monitor the total distance travelled by the tile is considered to have index 0 (nindex = 0, with unity ion to improve statistics at both the deep and the lateral statistical weight). When the first condition (E ≤ Eth) regions. is met we compare the current depth of the projectile, D In general, we define a border di as either a depth projectile with the border that defines the next index as reached by the ion or as the total distance travelled by Dprojectile 5 the total number of real ions to be simulated. We apply simulator [6]. Since the profile shape is the same, Fig- periodic boundary conditions at the lateral borders of ure 7 shows only the projected range versus projectile each sector. The local defect density, N, is a measure energy for boron, arsenic and phosphorous implants into of the amorphization of each sector in the crystal. If amorphous silicon. A very good agreement is obtained. the sector is completely amorphous, a random rotation Simultaneous collision treatment is necessary to correctly of the crystal lattice is performed for each collision as simulate [10] the channelling effect in crystalline targets. in MARLOWE [7]. For a partially amorphized section Since TRIM was designed for amorphous materials, it the rotation probability is N/Nα. After the collision, the does not include such treatment. However, at low veloci- original crystal orientation is restored. ties, there are simultaneous collisions even in amorphous materials. This leads to an underestimation of the stop- ping by TRIM that is more relevant at low velocities D. Speeding up the calculation (heavy ions, low energies), as can be seen in the inset of Fig. 7 for As. Several strategies have been employed throughout the For crystalline targets we compare our simulation re- code to speed up the calculation. When possible, lookup sults directly with SIMS experimental profiles obtained tables [12] previously calculated are used: elastic interac- from the literature [16,21,32,42]. Figures 8, 9 and 10 rep- tion, local and non-local inelastic losses, etc. The tables resent boron implanted into silicon for several energies are calculated and stored in disk, for future use, for each and implant conditions showing good agreement with projectile-target atom combination. experiments including very low energy (Fig. 8), chan- nelling conditions (Fig. 9) and high energy (Fig. 10). All implants use the same (and only) fitting parameter r0 . E. Selection of the target atoms s =185. Figures 11, 12 and 13 show implants of arsenic into sil- BCA needs a method to select the next target atoms icon for several energies and implant conditions. For this r0 . to collide with. We begun using the MARLOWE [7] tar- ion-target combination we use s =20 for all conditions. get atom selection method. It accepts target atoms that In Figure 14 we can see phosphorous into silicon im- are in the direction of ion movement and have an im- plants also with several energies and implant conditions. The value employed for r0 is 1.85, identical to the boron- pact parameter smaller than a given value (p 6 silicon. [4] David Cai, Niels Gronbech-Jensen, C.M. Snell, and K.M. Figure 17 represents 40, 100 and 300 keV arsenic im- Beardmore. Phys. Rev. B, 54(23):17147–17157, 1996. plants into 6H-SiC with the same conditions cited above [5] International Technology Roadmap for Semiconductors. r0 . Semiconductor Industry Association, 1999. ( s =175). Again, they match very well. [6] J.F. Ziegler, J.P. Biersack, and U. Littmark. Pergamon Press, New York, 1985. C. Other target materials [7] Mark T. Robinson and Ian M. Torrens. Phys. Rev. B, 9(12):5008–5024, 1974. [8] J. Lindhard and M. Scharff. Phys. Rev., 124:128–130, Other interesting semiconductor materials are the III- 1961. V semiconductors, like gallium arsenide. Special charac- [9] J. Lindhard, M. Scharff, and H.E. Schiott. Dan. Vidensk. teristics for this material are a very low Debye temper- Seksk. Mat. Fys. Medd., 33(14):1–42, 1963. ature (360 K) and its softness. The damage accumula- [10] Mark Hou and Mark T. Robinson. Nucl. Instr. and N · 20 tion will be important even for low doses ( α =6 10 Meth., 132:641–645, 1976. 3 f . at/cm , surv =009). [11] Mark T. Robinson. Phys. Rev. B, 40(16):10717–10726, Figure 18 shows silicon into GaAs (REO: Random 1989. { } r0 . Equivalent Orientation) and 100 channel, s =20) im- [12] J. Arias, M. Jaraiz, L. Pelaz, L. Bail´on, and J. Barbolla. 13 2 plants at 150 keV, 3 · 10 at/cm compared with SIMS Nucl. Instr. and Meth. B, 102:228–231, 1995. profiles [47], and it shows a comparison between selenium [13] W. Brandt and M. Kitagawa. Phys. Rev. B, 25(9):5631– { } r0 . into GaAs (REO and 100 channel, s =17) implants 5637, 1982. at 300 keV, 3 · 1013 at/cm2, and SIMS profiles [47]. [14] S.H. Yang, S. Morris, S. Tian, K. Karab, A.F. Tasch, P.M. Echenique, R. Capaz, and J. Joannopoulos. In Mat. Res. Soc. Symp., 1995. V. CONCLUSIONS [15] G. Wang, S. Tian, M. Morris, B. Obradovich, G. Bala- murugan, and A. Tasch. Microelectronic Device Technol- A new BCA ion implant simulator is reported. It gath- ogy, Austin TX, USA, SPIE-Int., Soc. Opt. Eng., pages 324–333, 1997. ers some of the best physical models and simulation algo- [16] University of Texas at Austin. rithms, including a novel hybrid integration scheme for http://homer.mer.utexas.edu/TCAD/utmarlowe, 1999. the inelastic energy losses. It also uses an ab initio phys- [17] Matthias Posselt, Bruno Schmidt, Thomas Feudel, and ical description of the electron distribution for the target Norbert Strecker. Materials Science Engineering B, atoms. For low implant doses, the simulator is capa- 71:128–136, 2000. ble of predicting the impurity implant profiles for a wide [18] W. Bohmayr, A. Burenkov, J. Lorenz, H. Ryssel, and range of projectile atoms and target materials with only S. Selberherr. IEEE Trans. Semic. Manuf, 8(4):402–407, r0 one adjustable parameter ( s ) for each projectile-target 1995. material combination. For high doses, there are two ad- [19] J. Arias, M. Jaraiz, J.E. Rubio, L. Pelaz, L.A. Marqu´es, ditional fitting parameters (fsurv, Nα). and J. Barbolla. Journal Mat. Sci. and Tech., 11:1191– 1193, 1995. [20] J. Arias, J. Hern´andez, M. Jaraiz, L. Bail´on, and ACKNOWLEDGMENTS J. Barbolla. In Conferencia de Dispositivos Electr´onicos, Barcelona, 1997. This work was performed under the auspices of the [21] Keith M. Beardmore and Niels Gronbech-Jensen. Phys. Junta de Castilla y Le´on (VA 14/00B) and the DGICYT Rev. E, 57(6):7278–7287, 1998. project No. PB 98-0398. [22] G. Buschhorn, E. Diedrich, W. Kufner, M. Rzepka, H. Genz, P. Hoffmann-Stascheck, and A. Richter. Phys. Rev. B, 55(10):6196–6202, 1997. [23] Charles Kittel. Introducci´on a la f´ısica del estado s´olido. VI. REFERENCES Revert´e, Barcelona, 1993. [24] J.B. Marion. Classical dynamics of particles and systems. Academic Press, Inc., New York, 1986. [25] G. Moliere. Z.f. Naturforsch, A2:133, 1947. [26] W. Lenz. Z.f. Physik, 77:713, 1947. [27] A. Sommerfeld. Z.f. Physik, 77:722, 1932. [28] Jes´us Hern´andez. PhD thesis, University of Valladolid, Valladolid, Spain, 2000. [1] Kevin M. Klein, Changae Park, and A.F. Tasch. IEEE [29] DMol is a trademark of Bio Sym Inc., San Diego, CA., Trans. Elect. Dev., 39(7):1614–1621, 1992. 2000. [2] M. Posselt. Rad. Eff. Def. Sol., 130, 1994. [30] J. Hern´andez, M. Jaraiz, J. Arias, L. Bail´on, J. Barbolla, [3] Cheruvu S. Murthy and G.R. Srinivasan. IEEE Trans. A. Rubio, and J.L. Orantes. In Conferencia de Disposi- Elect. Dev., 39(2):264–273, 1992. tivos Electr´onicos, Madrid, 1999. 7 [31] J. Hern´andez, M. Jaraiz, J. Arias, J. Barbolla, L. Bail´on, FIG. 1. Differences between ZBL, IADS and true bond { } and A. Rubio. In Mat. Res. Soc. Spring Meeting, San densities along 111 direction. Francisco, 1998. [32] David Cai, C.M. Snell, Keith M. Beardmore, and N. Gronbech-Jensen. Int. J. Modern Physics C, 9(3):459– 470, 1998. Integration trajectory P3 [33] S. Kreussler, C. Varelas, and W. Brandt. Phys. Rev. B, Real trajectory 23(82), 1981. [34] Richard J. Mathar and Matthias Posselt. Phys. Rev. B, 51(1):107–116, 1995. [35] P.M. Echenique, R.M. Nieminen, and R.H. Ritchie. Solid P State Communications, 37:779–781, 1981. P1 2 [36] H.A. Bethe. Ann. Phys. (N.Y.), 5:325, 1930. [37] Angel Rubio. (private communication). Dpto. F´ısica Te´orica, Facultad de Ciencias, Univ. de Valladolid, 1997. x T2 [38] L.M. Kishinevskii. Bull. Acad. Sci. USSR, Phys Ser, 26:11433, 1962. T1 T [39] O.B. Firsov. Sov. Phys. JETP, 36:1076–1080, 1959. 3 [40] S. Morris, D. Lin, S.H. Yang, S. Tian, K. Parab, and A.F. FIG. 2. Schematics for the local and non-local inelastic Tasch. In Mat. Res. Soc. Symp. Proc., Vol. 396:27, 1996. stopping integration algorithms. [41] M.J. Dort, P.H. Woerlee, and A.J. Walker. Solid State Electronics, 37(3):411–414, 1994. [42] K.M. Klein, C. Park, and A.F. Tasch. Nucl. Instr. and Meth. B, 59/60:60–64, 1991. 1/2 VIRTUAL ION [43] J. Sillamp¨aa, K. Nordlund, and J. Keinonen. Phys. Rev. 1/32 B, 62(5):3109–3116, 2000. [44] G.H. Kinchin and R.S. Pease. Rep. Progress Phys., 18:1– 1/32 51, 1955. 1/1 1/32 [45] J.M. Hern´andez-Mangas, J.Arias, M. Jara´ız, L. Bail´on, REAL ION and J. Barbolla. Nucl. Instr. and Meth. B, 174:433–438, 1/16 1/32 2001. 1/16 [46] S. Ahmed, C.J. Barbero, T.W. Sigmon, and J.W. Erick- 1/32 son. J. Appl. Phys., 77(12):6194–6200, 1995. 1/32 [47] R.G. Wilson and V.R. Deline. Appl. Phys. Lett., 1/16 37(9):793–796, 1980. 1/32 [48] P. Packman, H. Kennel, S. Thompson, S. Corcoran, and 1/32 M. Taylor. In 11th Int. Conf, on Ion Implantation Tech- 1/16 nology, pages 539–542, 1997. d1 d2 d3 d4 d5 FIG. 3. Rare event algorithm with lateral or depth en- hancement scheme. VII. FIGURES 1019 Without rare event With rare event 100000 True bond ZBL 18 ) 10 10000 IADS 3 ) 3 1000 1017 100 10 Concentration (at/cm 1016 1 Electron density (electron/A 0.1 1015 0 10 20 30 40 50 60 70 80 0.01 Depth (nm) 0 0.2 0.4 0.6 0.8 1 FIG. 4. Implantation of B (tilt=7◦, rotation=30◦) → Si <111> axis (a.u) {100}, 2 keV simulated with Nion = 2000 real ion with and without the trajectory-length selection scheme. 8 1/1 FIG. 7. Boron, Phosphorous and Arsenic into amorphous REAL silicon. Comparison between TRIM and this work simulation ION results. The inset shows, for arsenic, the differences found 1/16 with and without the simultaneous collision (SC) treatment. 1/4 1/16 1/8 VIRTUAL This work ION SIMS 1/16 1019 500 eV 1/8 1/8 ) 1/16 3 2000 eV 1/16 1018 1/16 ZONE 4 ZONE 3 ZONE 2 ZONE 1 ZONE 0 17 Concentration (at/cm 10 Wshallow FIG. 5. Rare event algorithm with shallow region enhance- ment scheme. 1016 0 10 20 30 40 50 60 70 80 90 Depth (nm) 1018 Without rare event algorithm ◦ ◦ { } With rare event algorithm FIG. 8. Boron (0 ,0 )into 100 silicon implant (500 and 2000 eV) comparison between SIMS profiles [21] and the cur- rent work simulation results. ) 17 3 10 1016 1018 This work 13 -2 SIMS 35 keV, 10 cm 13 -2 15 400 keV, 2 10 cm 10 80 keV Concentration (at/cm 140 keV ) 3 1014 1017 1013 0 500 1000 1500 2000 2500 Depth (nm) FIG. 6. Profile comparison for an implantation of B Concentration (at/cm ◦ ◦ (7 ,30 ) → Si {100}, 1 MeV simulated with Nion = 2000 real ion with an without the shallow region enhancement scheme. 1016 0 200 400 600 800 1000 1200 1400 1600 1800 104 Depth (nm) FIG. 9. Boron (0◦,0◦) with 35 and 80 keV and boron (0.6◦,0◦) with 140 and 400 keV implants into {100} silicon, 1 ◦ 10 (with a 15 A˚ SiO2 layer, 0.5 divergency) comparison between 3 10 SIMS profiles [4,48] and the current work simulation results. Arsenic detail 100 102 Phosphorous 103 104 Boron Arsenic Projected range (nm) 101 This work TRIM This work (w/o SC) 100 102 103 104 105 106 107 Energy (eV) 9 FIG. 12. Arsenic (0◦,0◦) with 15 and 180 keV into {100} 15 keV This work silicon implant comparison between SIMS profiles [32] and the SIMS 1018 80 keV current work simulation results. 280 keV 2400 keV ) 3 700 keV 1019 This work SIMS 1017 15 keV ) 3 18 Concentration (at/cm 10 16 10 17 0 500 1000 1500 2000 2500 3000 3500 4000 10 Concentration (at/cm Depth (nm) ◦ ◦ FIG. 10. Boron (7 ,30 )into{100} silicon implant (15, 80, 100 keV 280, 700 and 2400 keV, with a 15 A˚ SiO2 layer) comparison 50 keV between SIMS profiles [4,16] and the current work simulation 1016 results. 0 200 400 600 800 1000 1200 1400 1600 1800 Depth (nm) FIG. 13. Arsenic (0◦,0◦) with 15, 50 and 100 keV into {110} silicon implant comparison between SIMS profiles [16] 1019 This work and the current work simulation results. 15 keV SIMS 100 keV ) 3 18 This work 10 SIMS 1018 15 keV ) 3 100 keV 1017 Concentration (at/cm 500 keV 1017 1500 keV 16 10 Concentration (at/cm 0 50 100 150 200 250 300 350 400 Depth (nm) FIG. 11. Arsenic (8◦,30◦) with 15 and 100 keV into {100} silicon implant comparison between SIMS profiles [32] and the 1016 current work simulation results. 0 500 1000 1500 2000 Depth (nm) FIG. 14. Phosphorous (0◦,0◦) with 15 and 100 keV and ◦ ◦ 1019 phosphorous (10 ,15 ) with 500 and 1500 keV into {100} sil- This work icon implant comparison between SIMS profiles [21] and the 15 keV SIMS current work simulation results. ) 3 1018 180 keV 1017 Concentration (at/cm 1016 0 200 400 600 800 1000 1200 Depth (nm) 10 1022 This work 40 keV This work 15 keV, 8 1015 at/cm2 SIMS 100 keV SIMS 21 10 1019 300 keV 80 keV, 8 1015 at/cm2 ) 3 1020 ) 3 1018 1019 13 2 Conc. (at/cm 1018 10 at/cm Concentration (at/cm 17 80 keV, 1013 at/cm2 10 1017 1016 1016 0 100 200 300 400 500 600 700 800 900 0 50 100 150 200 250 300 350 400 450 500 Depth (nm) Depth (nm) ◦ ◦ FIG. 15. High dose, 8 · 1015 at/cm2, boron (0◦,0◦) with 15 FIG. 17. Arsenic (12.5 ,30 ) into 6H-SiC, 40, 100 and 300 13 13 14 and 80 keV into {100} silicon implant comparison between keV implants with doses of 2 · 10 ,9.9 · 10 and 1.1 · 10 2 SIMS profiles [16] and the current work simulation results. at/cm respectively. The orientation of the wafer flat is ◦ The low dose simulation results are also shown for compari- {1120¯ } and the wafers are cut 3.5 off-axis from the {0001} son. plane toward the {1120¯ } direction [46]. 90 keV This work 30 keV This work SIMS SIMS 1018 1019 195 keV ) ) 3 3 500 keV 1 MeV 1018 Si (0,0), 150 keV 1017 Si (7,30), 150 keV Concentration (at/cm 17 10 Concentration (at/cm 16 10 1016 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 Depth (nm) Depth (nm) FIG. 16. Aluminum (12.5◦,30◦) into 6H-SiC, 30, 90, 195, 500 and 1000 keV implants with doses of 3 · 1013,7.9 · 1013, Se (7,30), 300 keV This work 3.8 · 1014,3· 1013 and 3 · 1013 at/cm2 respectively. The orien- SIMS ◦ tation of the wafer flat is {1120¯ } and the wafers are cut 3.5 1018 { } { ¯ } off-axis from the 0001 plane toward the 1120 direction ) [46]. 3 Se (0,0), 300 keV 1017 Concentration (at/cm 1016 0 200 400 600 800 1000 Depth (nm) FIG. 18. (Top) Silicon at 150 keV and (bottom) Selenium at 300 keV (REO and {100} channel) implanted [47] into GaAs. 11