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Diffusion modelling of low-energy ion-implanted BF2 in crystalline silicon: Study of fluorine vacancy effect on boron diffusion
Materials Science and Engineering B 154–155 (2008) 216–220
Contents lists available at ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
Diffusion modelling of low-energy ion-implanted BF2 in crystalline silicon: Study of fluorine vacancy effect on boron diffusion J. Marcon a,∗ , A. Merabet b a b
Laboratoire Electronique Microtechnologie et Instrumentation (LEMI), University of Rouen, 76821 Mont Saint Aignan, France Laboratoire de Physique et Mécanique des Matériaux Métalliques, Département d’O.M.P., Faculté des Sciences de l’Ingénieur, Université de Sétif, 19000 Sétif, Algeria
a r t i c l e
i n f o
Article history: Received 5 May 2008 Received in revised form 22 August 2008 Accepted 8 October 2008 Keywords: Boron Fluorine Transient enhanced diffusion Simulation
a b s t r a c t We have investigated and modelled the diffusion of boron implanted into crystalline silicon in the form of boron difluoride BF2 + . We have used published data for BF2 + implanted with an energy of 2.2 keV in crystalline silicon. Fluorine effects are considered by using vacancy-fluorine pairs which are responsible for the suppression of boron diffusion in crystalline silicon. Following Uematsu’s works, the simulations satisfactory reproduce the SIMS experimental profiles in the 800–1000 ◦ C temperature range. The boron diffusion model in silicon of Uematsu has been improved taking into account the last experimental data. © 2008 Elsevier B.V. All rights reserved.
1. Introduction For advanced technologies, there is a lack of calibrated physical models that enable accurate simulations of CMOS technologies down to channel lengths of 70–30 nm and below [1–5]. This work aims to develop predictive modelling of ultra-shallow junction (USJ) profiles for next generation CMOS devices. In the present paper, we will give a contribution to a deeper understanding of boron implantation within sub-keV regime. It has been previously reported that BF2 yields shallower junctions than B when implanted into crystal silicon at the same effective energy [6–9]. The role of the fluorine on transient enhanced diffusion has been recently studied by several authors [10–17]. It has been concluded that the boron TED suppression is a consequence of F-defect interaction [10–17]. In addition, it was shown that adding F to B reduced boron diffusion [10–17]. Fluorine redistribution after postimplantation annealing deviates from simple diffusion in silicon. Indeed, F migrates to the surface rapidly [18–22]. Our aim consists to improve the boron diffusion model in crystalline silicon published by Uematsu by taking into account the F–V pairs and the anomalous fluorine out-diffusion in silicon [23–27]. In the present work, we study the reaction of fluorine with selfinterstitials, vacancies and boron to understand the mechanism underlying the fluorine effect on the boron redistribution. Con-
∗ Corresponding author at: University of Rouen, IUT of Rouen, 76821 Mont Saint Aignan, France. Tel.: +33 2 35 14 63 55; fax: +33 2 35 14 00 50. E-mail address: [email protected] (J. Marcon). 0921-5107/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2008.10.001
cerning B and BF2 implantations (500 eV and 2.2 keV implantation energies, respectively), we have used published data [9]. B and BF2 implantations in crystalline silicon were carried out at a dose of 1015 cm−2 by Suzuki [9]. The rapid thermal annealing (RTA) were performed at 800, 900 and 1000 ◦ C [9]. To the author’s knowledge, there have been no reports of boron diffusion model implanted in crystalline silicon with ultra-low energy (500 eV B+ and 2.2 eV BF2 + ) including fluorine effect and fitting the boron experimental profiles in the 800–1000 ◦ C temperature range. 2. Model The boron diffusion model in silicon of Uematsu is based on kick-out mechanism including substituted dopants (Bs ), neutral boron interstitials (Bi ), positive and neutral silicon self-interstitials (I+ and I0 ) [23–27]. Boron diffusivity is based on Fair’s estimate [28]. While the kick-out diffusion model is extremely powerful, the large number of physical parameters used makes the calibration difficult [23–27,29]. In order to separate the influence of the parameters, a hierarchical step-by-step approach has been used by Uematsu [23–27]. Boron atoms in boron precipitates (B–B complexes [26]) and in boron clusters (B–I complexes [25]) have been considered. The simulation of high-concentration boron diffusion in silicon requires to take into account two species: the postimplantation clustering of boron below the boron solubility limit (Bm In clusters) [25,30,31] and the boron precipitation when the B concentration exceeds its solubility limit [26]. B clusters and B precipitates are assumed to be electrically inactive and immobile
J. Marcon, A. Merabet / Materials Science and Engineering B 154–155 (2008) 216–220
[25]. As Uematsu [26], we have considered that these two species exist simultaneously. During annealing, B clusters are dissolved to emit self-interstitials that contribute to TED. The transient activation of boron during post-implantation annealing is based on the concurrent formation of complexes comprising boron atoms and self-interstitials. Several other approaches have been followed to simulate this phenomenon [30,31]. Indeed, several versions of BICs model (boron interstitial clusters) have been proposed [30,31]. These models take into account a complex scheme of reaction leading to the formation of BICs [30,31]. A large number of equations have to be solved for a full implementation of a BIC model. To our knowledge, the influence of fluorine on BICs has not been studied. Consequently, in order to obtain the simplest model and in order to improve the boron diffusion mode of Uematsu [26], B clusters [25] and B precipitates [26] have been considered in our model. In order to take into account fluorine effect, the model of Uematsu has been improved. The following reactions have been used to take into account the fluorine and boron interaction [22,32,33]: FS + I ⇔ Fi
(1)
Fi + V ⇔ FS
(2)
FS + V ⇔ FV
(3)
FV + I ⇔ FS
(4)
I+V⇔0
(5)
In the above equations, FS , Fi , FV, I and V refer to substitutional fluorine, interstitial fluorine, fluorine vacancy pairs, self-intertitials and vacancies, respectively. The main source of generation of fluorine interstitial is the kick-out reaction (1). Fluorine vacancy pairs also formed an important part of this model because they slow the rapid formation of fluorine interstitials. The fluorine surface flux is determined according the expression J = −kCx=0 where J corresponds to the flux of the mobile species at the surface, k is the surface recombination velocity of the mobile species and Cx=0 corresponds to the concentration of the mobile species at the surface. The initial I and V profiles have been obtained trough a UT-MARLOWE simulation [34]. Thus, the fluorine interstitials, the boron interstitials and the I and V point defects are the related mobile species in the set of reactions considered. The high-dose BF2 implantation in silicon is amorphizing [35] and the effect of end-of-range dislocations (EoR) should be taken into account [23]. In our model, the influence of EoR defects on selfinterstital behaviour is simulated in the same manner as Uematsu in the case of 2 × 1015 cm−2 40 keV BF2 implantation [23]. EoR defects are dislocations and act as both as sink or source of selfinterstitials. The solid-phase epitaxial regrowth (SPER) process of the amorphous region eliminates the damages in this region and damages beyond EoR defects remain and become a source of TED. Consequently, in the amorphous region, self-interstitial and vacancy concentrations have been assumed to be the equilibrium values. The as-implanted profiles (fluorine and boron) were read as interstitial fluorine and interstitial boron in the amorphous region. Paul et al. [35] have shown that the 1 × 1015 cm−2 2.2 keV BF2 implantation are amorphizing and TEM analysis reveals a 6 nm thick amorphous layer. The partial differential equations were solved using PROMIS [36]. Self-interstitial and vacancy concentrations have been assumed to be the equilibrium values at the Si surface [23–27]. Using as-implanted data, the initial profiles of boron species have been calculated using Uematsu’s expressions [24–27]. Since the B diffusion is proportional to the self-interstitial concentration, the tail shift of its profile represents the evolution of the excess self-interstitial concentration. Several features have been deduced
217
from the analysis of self-interstitial generation or annihilation: (i) the well-known phenomenon of the transient enhanced diffusion (TED), (ii) boron forms electrically inactive and immobile clusters, (iii) the dissolution of a SiB layer known as boride enhanced diffusion (BED) [37–39], and (iv) the EoR defects could act as a source for self-interstitials [23]. The self-interstitial supersaturation could be reduced by several phenomena: (i) the surface is generally believed to be the main sink for interstitials during TED, (ii) the need to take into account the trapping of self-interstitials by extended defects (Type I defects), (iii) Frenkel pair recombination term taking into account the recombination of self-interstitials could be included [40], (iv) the presence of fluorine could act as sinks for excess self-interstitials and reduces boron diffusion, and (v) the EoR defects could act as a sink for self-interstitials [23]. The B diffusion is also proportional to the interstitial boron concentration. Boron cluster and precipitate formation or annihilation could generate or capture interstitial boron and, consequently, modify the boron diffusion. Moreover, interstitial boron concentration could decrease near the surface by out-diffusion. The effect of so-called “superactivation” on boron diffusion is also taken into account [26]. The B superactivation is based on the experimental results that the active B concentration exceeds the B solubility at higher temperatures. It has been shown that the electrical activation of boron implanted in silicon is strongly correlated to its diffusion [26]. Then more it diffuses, more it is electrically active. 3. Simulations Fig. 1 shows the boron depth profiles and simulated results for the samples annealed at 800 ◦ C during 30 min and 1 h 30 min using the equilibrium diffusivity model. Fluorine effect, TED and BED have not been taken into account in these simulations. The break point in the boron profiles, near the surface, has been attributed to the precipitated boron and the boron interstitial clusters and thereby immobilised B atoms. In our model, these two species have been considered simultaneously. These experimental profiles cannot be fitted using equilibrium diffusivity model. We could deduce a reduction of B diffusion at 800 ◦ C below equilibrium conditions. This feature is very surprising since this is the opposite result to that obtained for the TED or BED boron diffusion in crystalline silicon. In order to study the fluorine effect on boron diffusion in crystalline silicon, Fig. 2 shows the boron depth profiles and simulated results for the samples annealed at 800 ◦ C during 30 min and 1 h 30 min
Fig. 1. Simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 800 ◦ C during 30 min and 1 h 30 min. B diffusion profiles under point defect equilibrium are reported. Experimental data are from Ref. [9].
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J. Marcon, A. Merabet / Materials Science and Engineering B 154–155 (2008) 216–220
Table 1 Reduction and enhancement factors of boron diffusion in the case of B+ (500 eV) and BF2 + (2.2 keV) implantations. Experimental data are from Ref. [9]. 800 ◦ C 0.5 h B+ BF2 +
×2.0
900 ◦ C 1 h 30 min ×1.5 Reduction of B diffusion
Fig. 2. Simulated and experimental profiles for 500 eV B+ implanted in crystalline silicon annealing at 800 ◦ C during 30 min and 1 h 30 min. B diffusion profiles under point defect equilibrium are also reported. Calculated profiles are also shown relative to the 30 min and 1 h 30 min diffusion cycles, extracted by using a factor 2 and 1.5 of the equilibrium diffusivity. Experimental data are from Ref. [9].
using the equilibrium diffusivity model in the case of 500 eV B+ implantation. Extremely interesting feature emerges. Indeed, we could deduce an enhancement of B diffusion at 800 ◦ C annealing in the case of 500 eV B+ implantation. Calculated profiles are also reported relative to the 30 min and 1 h 30 min annealing cycle and using a factor of 2 and 1.5 of the equilibrium diffusivity. Consequently, boron diffusion mechanisms in the case of B+ and BF2 + implantations are not similar (enhancement and reduction of boron diffusion, respectively). Table 1 lists the reduction or enhancement factor relative to the equilibrium diffusivity model in the case of B+ (500 eV) and BF2 + (2.2 keV) implantations in crystalline silicon during annealing (800, 900 and 1000 ◦ C). First, we could deduce an enhancement of B diffusion at 900 and at 1000 ◦ C in the case of BF2 + implantation but the B diffusion has been reduced in comparison with the case of B+ implantation. Secondly, contrary to the case of 500 eV B+ implantation, we could deduce that there is no BED effect at these temperatures because it has been shown that BED effect increase highly with temperature.
1000 ◦ C
150 s
300 s
10 s
20 s
×2.5 ×1.5
×2.5 ×1.5
×4.0 ×1.8
×3.0 ×1.4
Fig. 3. Simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 1000 ◦ C during 10 and 20 s. Experimental data are from Ref. [9].
Fig. 6 shows the fluorine depth profiles and simulated results for the sample annealed at 800 ◦ C. The initial and the profile after annealing (800 ◦ C) of substitutional boron are also shown. Fluorine redistribution after post-implantation annealing deviates from simple diffusion in silicon [18–22]. For implantation below the amorphization threshold, a strong surface-oriented diffusion was observed [18–22]. F atoms are immobile below 500 ◦ C and F migrates to the surface and leaves the silicon in the 550–800 ◦ C [18]. The out-diffusion of these F atoms takes place in the 900–1100 ◦ C temperature range [18]. Such an anomalous diffusion phenomenon has been observed for nitrogen diffusion in silicon [32–33]. The interaction between the self-interstitials and fluorine during annealing has been explained as follows: the abundance of vacancies, generated during the implantation and liberated during the annealing, makes probable that most of the F atoms are released to substitutional positions and to fluorine vacancy cluster. During annealing, fluorine vacancy cluster is converted to substitutional fluorine (FV + I ⇒ FS ) and substitutional
4. Results and discussion Under our experimental conditions, simulations have shown that the effect of EoR defects are negligible because the surface proximity (6 nm) [35]. Indeed, the surface is the main sink for self-interstitials during TED. Consequently, contrary to 40 keV BF2 implantation experiments (a/c interface at 50 nm [23]), in our case of 2.2 keV BF2 implantation (a/c interface at 6 nm [35]), the EoR defects near the surface don’t play a key role. Figs. 3–5 show the boron depth profiles and simulated results for the samples annealed at 1000, 900 and 800 ◦ C. A good approximation between experimental and simulated profiles has been obtained using the boron diffusion model for the samples annealed at 1000 and 900 ◦ C and using the fluorine vacancy interaction for the sample annealed at 800 ◦ C.
Fig. 4. Simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 900 ◦ C during 150 and 300 s. Experimental data are from Ref. [9].
J. Marcon, A. Merabet / Materials Science and Engineering B 154–155 (2008) 216–220
219
Table 2 Parameters used in the simulations. eq
DI CI
Self-interstitials
= 9.14 × 102 exp(−4.84/kT ) [23]
Interstitial boron
Di = 3.17 exp(−3.59/kT) [23,28]
Boron limit solubility
CSol = 9.25 × 1022 exp(−0.73/kT) [26,42]
Vacancies
CV = 1.4 × 1023 exp(−2.0/kT ) [41]; DV = 3 × 10−2 exp(−1.9/kT) [41]
Fluorine (F diffusion coefficient and FV cluster dissolution)
At T = 800 ◦ C; DF = 10−13 cm2 s−1 ; kF = 2 × 10−13 cm−3 s−1
Fig. 5. Simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 800 ◦ C during 30 min and 1 h 30 min. Experimental data are from Ref. [9].
fluorine is converted in interstitial fluorine (FS + I ⇒ Fi ). The presence of fluorine vacancy clusters give an undersaturation of the local self-interstitial concentration since any self-interstitial would be able to recombine and annihilate with vacancies and fluorine vacancy clusters. Since boron diffusion in silicon is mediated by self-interstitials, an undersaturation of the self-interstitials concentration would give rise to a suppression of the boron diffusion. The dissociation of substitutional fluorine in interstitial fluorine and the fast diffusion of the liberated interstitial fluorine below the SIMS sensitivity explain the surface oriented fluorine diffusion in silicon. In our model, FI2 and F2 I2 [22] clusters have not been taken into account because our aim was to obtain the simplest model to explain the boron diffusion implanted in crystalline silicon in the form of BF2 + .
eq
According to this fluorine diffusion model, several features have been deduced: (i) at temperature near 800 ◦ C and for short anneal, the fluorine implant suppresses the enhanced boron diffusion due to the under-saturation of self-interstitials; (ii) at temperature near 800 ◦ C and for long anneal or for the 900–1100 ◦ C temperature range, the fluorine is not effective in suppressing the enhanced boron diffusion because the majority of fluorine during anneal is located near the surface and considerable fluorine dose has been lost by F out-diffusion. Consequently, the reduction of boron diffusion by fluorine implant is a transient phenomenon which is high at low temperature and decreases with time. The parameters used in the simulation are summarized in Table 2. This model needs to be improved to extract fluorine parameters as functions of temperature. Major part of the fundamental parameters has been taken from literature: equilibrium concentrations, diffusivities, boron solubility, boron precipitate and BI cluster dissolutions [23–27,29,41,42]. Recently, using several experimental results, Impellizzeri et al. [14–16], Kham et al. [11,13] and El Mubarek et al. [10,11] have shown that the responsible for boron diffusion reduction by fluorine is the presence of fluorine cluster. It has been shown that the fluorine diffusion profiles after anneals are not affected by the presence of boron [16]. This feature indicates that there is no direct interaction between boron and fluorine. These experimental results confirm our model [10–16]. Moreover, positron annihilation spectroscopy has directly confirms the presence of fluorine vacancy clusters in fluorine implanted silicon [43–45]. 5. Conclusion We have studied high-concentration dopant diffusion profiles in crystalline silicon implanted with low-energy BF2 + (2.2 keV). The diffusion of boron in ion implanted BF2 + is slightly lower than the coefficient of B in ion implanted B+ . The presence of vacancy-fluorine clusters gives an undersaturation of the selfinterstitial concentration and the boron diffusion has been reduced. A good agreement has been obtained between experimental and simulated profiles in the 800–1000 ◦ C temperature range. In a previous paper, we have correctly simulated the enhanced diffusion of boron implanted in crystalline silicon (500 eV B+ ) [29]. We have concluded that neglecting the dissolution of the SiB layer (boride enhanced diffusion) would lead to the underestimation of the boron diffusion. In this paper, we have correctly simulated the reduction of boron diffusion implanted in crystalline silicon (2.2 keV BF2 + ). We conclude that neglecting the interaction of fluorine with point defects would lead to the overestimation of the boron diffusion. Finally, we have improved the boron diffusion model of Uematsu in the case of ultra-lowenergy boron in crystalline silicon (500 eV B+ and 2.2 keV BF2 + implants). References
Fig. 6. Initial, simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 800 ◦ C during 1 h 30 min. Experimental data are from Ref. [9].
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Contents lists available at ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
Diffusion modelling of low-energy ion-implanted BF2 in crystalline silicon: Study of fluorine vacancy effect on boron diffusion J. Marcon a,∗ , A. Merabet b a b
Laboratoire Electronique Microtechnologie et Instrumentation (LEMI), University of Rouen, 76821 Mont Saint Aignan, France Laboratoire de Physique et Mécanique des Matériaux Métalliques, Département d’O.M.P., Faculté des Sciences de l’Ingénieur, Université de Sétif, 19000 Sétif, Algeria
a r t i c l e
i n f o
Article history: Received 5 May 2008 Received in revised form 22 August 2008 Accepted 8 October 2008 Keywords: Boron Fluorine Transient enhanced diffusion Simulation
a b s t r a c t We have investigated and modelled the diffusion of boron implanted into crystalline silicon in the form of boron difluoride BF2 + . We have used published data for BF2 + implanted with an energy of 2.2 keV in crystalline silicon. Fluorine effects are considered by using vacancy-fluorine pairs which are responsible for the suppression of boron diffusion in crystalline silicon. Following Uematsu’s works, the simulations satisfactory reproduce the SIMS experimental profiles in the 800–1000 ◦ C temperature range. The boron diffusion model in silicon of Uematsu has been improved taking into account the last experimental data. © 2008 Elsevier B.V. All rights reserved.
1. Introduction For advanced technologies, there is a lack of calibrated physical models that enable accurate simulations of CMOS technologies down to channel lengths of 70–30 nm and below [1–5]. This work aims to develop predictive modelling of ultra-shallow junction (USJ) profiles for next generation CMOS devices. In the present paper, we will give a contribution to a deeper understanding of boron implantation within sub-keV regime. It has been previously reported that BF2 yields shallower junctions than B when implanted into crystal silicon at the same effective energy [6–9]. The role of the fluorine on transient enhanced diffusion has been recently studied by several authors [10–17]. It has been concluded that the boron TED suppression is a consequence of F-defect interaction [10–17]. In addition, it was shown that adding F to B reduced boron diffusion [10–17]. Fluorine redistribution after postimplantation annealing deviates from simple diffusion in silicon. Indeed, F migrates to the surface rapidly [18–22]. Our aim consists to improve the boron diffusion model in crystalline silicon published by Uematsu by taking into account the F–V pairs and the anomalous fluorine out-diffusion in silicon [23–27]. In the present work, we study the reaction of fluorine with selfinterstitials, vacancies and boron to understand the mechanism underlying the fluorine effect on the boron redistribution. Con-
∗ Corresponding author at: University of Rouen, IUT of Rouen, 76821 Mont Saint Aignan, France. Tel.: +33 2 35 14 63 55; fax: +33 2 35 14 00 50. E-mail address: [email protected] (J. Marcon). 0921-5107/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2008.10.001
cerning B and BF2 implantations (500 eV and 2.2 keV implantation energies, respectively), we have used published data [9]. B and BF2 implantations in crystalline silicon were carried out at a dose of 1015 cm−2 by Suzuki [9]. The rapid thermal annealing (RTA) were performed at 800, 900 and 1000 ◦ C [9]. To the author’s knowledge, there have been no reports of boron diffusion model implanted in crystalline silicon with ultra-low energy (500 eV B+ and 2.2 eV BF2 + ) including fluorine effect and fitting the boron experimental profiles in the 800–1000 ◦ C temperature range. 2. Model The boron diffusion model in silicon of Uematsu is based on kick-out mechanism including substituted dopants (Bs ), neutral boron interstitials (Bi ), positive and neutral silicon self-interstitials (I+ and I0 ) [23–27]. Boron diffusivity is based on Fair’s estimate [28]. While the kick-out diffusion model is extremely powerful, the large number of physical parameters used makes the calibration difficult [23–27,29]. In order to separate the influence of the parameters, a hierarchical step-by-step approach has been used by Uematsu [23–27]. Boron atoms in boron precipitates (B–B complexes [26]) and in boron clusters (B–I complexes [25]) have been considered. The simulation of high-concentration boron diffusion in silicon requires to take into account two species: the postimplantation clustering of boron below the boron solubility limit (Bm In clusters) [25,30,31] and the boron precipitation when the B concentration exceeds its solubility limit [26]. B clusters and B precipitates are assumed to be electrically inactive and immobile
J. Marcon, A. Merabet / Materials Science and Engineering B 154–155 (2008) 216–220
[25]. As Uematsu [26], we have considered that these two species exist simultaneously. During annealing, B clusters are dissolved to emit self-interstitials that contribute to TED. The transient activation of boron during post-implantation annealing is based on the concurrent formation of complexes comprising boron atoms and self-interstitials. Several other approaches have been followed to simulate this phenomenon [30,31]. Indeed, several versions of BICs model (boron interstitial clusters) have been proposed [30,31]. These models take into account a complex scheme of reaction leading to the formation of BICs [30,31]. A large number of equations have to be solved for a full implementation of a BIC model. To our knowledge, the influence of fluorine on BICs has not been studied. Consequently, in order to obtain the simplest model and in order to improve the boron diffusion mode of Uematsu [26], B clusters [25] and B precipitates [26] have been considered in our model. In order to take into account fluorine effect, the model of Uematsu has been improved. The following reactions have been used to take into account the fluorine and boron interaction [22,32,33]: FS + I ⇔ Fi
(1)
Fi + V ⇔ FS
(2)
FS + V ⇔ FV
(3)
FV + I ⇔ FS
(4)
I+V⇔0
(5)
In the above equations, FS , Fi , FV, I and V refer to substitutional fluorine, interstitial fluorine, fluorine vacancy pairs, self-intertitials and vacancies, respectively. The main source of generation of fluorine interstitial is the kick-out reaction (1). Fluorine vacancy pairs also formed an important part of this model because they slow the rapid formation of fluorine interstitials. The fluorine surface flux is determined according the expression J = −kCx=0 where J corresponds to the flux of the mobile species at the surface, k is the surface recombination velocity of the mobile species and Cx=0 corresponds to the concentration of the mobile species at the surface. The initial I and V profiles have been obtained trough a UT-MARLOWE simulation [34]. Thus, the fluorine interstitials, the boron interstitials and the I and V point defects are the related mobile species in the set of reactions considered. The high-dose BF2 implantation in silicon is amorphizing [35] and the effect of end-of-range dislocations (EoR) should be taken into account [23]. In our model, the influence of EoR defects on selfinterstital behaviour is simulated in the same manner as Uematsu in the case of 2 × 1015 cm−2 40 keV BF2 implantation [23]. EoR defects are dislocations and act as both as sink or source of selfinterstitials. The solid-phase epitaxial regrowth (SPER) process of the amorphous region eliminates the damages in this region and damages beyond EoR defects remain and become a source of TED. Consequently, in the amorphous region, self-interstitial and vacancy concentrations have been assumed to be the equilibrium values. The as-implanted profiles (fluorine and boron) were read as interstitial fluorine and interstitial boron in the amorphous region. Paul et al. [35] have shown that the 1 × 1015 cm−2 2.2 keV BF2 implantation are amorphizing and TEM analysis reveals a 6 nm thick amorphous layer. The partial differential equations were solved using PROMIS [36]. Self-interstitial and vacancy concentrations have been assumed to be the equilibrium values at the Si surface [23–27]. Using as-implanted data, the initial profiles of boron species have been calculated using Uematsu’s expressions [24–27]. Since the B diffusion is proportional to the self-interstitial concentration, the tail shift of its profile represents the evolution of the excess self-interstitial concentration. Several features have been deduced
217
from the analysis of self-interstitial generation or annihilation: (i) the well-known phenomenon of the transient enhanced diffusion (TED), (ii) boron forms electrically inactive and immobile clusters, (iii) the dissolution of a SiB layer known as boride enhanced diffusion (BED) [37–39], and (iv) the EoR defects could act as a source for self-interstitials [23]. The self-interstitial supersaturation could be reduced by several phenomena: (i) the surface is generally believed to be the main sink for interstitials during TED, (ii) the need to take into account the trapping of self-interstitials by extended defects (Type I defects), (iii) Frenkel pair recombination term taking into account the recombination of self-interstitials could be included [40], (iv) the presence of fluorine could act as sinks for excess self-interstitials and reduces boron diffusion, and (v) the EoR defects could act as a sink for self-interstitials [23]. The B diffusion is also proportional to the interstitial boron concentration. Boron cluster and precipitate formation or annihilation could generate or capture interstitial boron and, consequently, modify the boron diffusion. Moreover, interstitial boron concentration could decrease near the surface by out-diffusion. The effect of so-called “superactivation” on boron diffusion is also taken into account [26]. The B superactivation is based on the experimental results that the active B concentration exceeds the B solubility at higher temperatures. It has been shown that the electrical activation of boron implanted in silicon is strongly correlated to its diffusion [26]. Then more it diffuses, more it is electrically active. 3. Simulations Fig. 1 shows the boron depth profiles and simulated results for the samples annealed at 800 ◦ C during 30 min and 1 h 30 min using the equilibrium diffusivity model. Fluorine effect, TED and BED have not been taken into account in these simulations. The break point in the boron profiles, near the surface, has been attributed to the precipitated boron and the boron interstitial clusters and thereby immobilised B atoms. In our model, these two species have been considered simultaneously. These experimental profiles cannot be fitted using equilibrium diffusivity model. We could deduce a reduction of B diffusion at 800 ◦ C below equilibrium conditions. This feature is very surprising since this is the opposite result to that obtained for the TED or BED boron diffusion in crystalline silicon. In order to study the fluorine effect on boron diffusion in crystalline silicon, Fig. 2 shows the boron depth profiles and simulated results for the samples annealed at 800 ◦ C during 30 min and 1 h 30 min
Fig. 1. Simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 800 ◦ C during 30 min and 1 h 30 min. B diffusion profiles under point defect equilibrium are reported. Experimental data are from Ref. [9].
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Table 1 Reduction and enhancement factors of boron diffusion in the case of B+ (500 eV) and BF2 + (2.2 keV) implantations. Experimental data are from Ref. [9]. 800 ◦ C 0.5 h B+ BF2 +
×2.0
900 ◦ C 1 h 30 min ×1.5 Reduction of B diffusion
Fig. 2. Simulated and experimental profiles for 500 eV B+ implanted in crystalline silicon annealing at 800 ◦ C during 30 min and 1 h 30 min. B diffusion profiles under point defect equilibrium are also reported. Calculated profiles are also shown relative to the 30 min and 1 h 30 min diffusion cycles, extracted by using a factor 2 and 1.5 of the equilibrium diffusivity. Experimental data are from Ref. [9].
using the equilibrium diffusivity model in the case of 500 eV B+ implantation. Extremely interesting feature emerges. Indeed, we could deduce an enhancement of B diffusion at 800 ◦ C annealing in the case of 500 eV B+ implantation. Calculated profiles are also reported relative to the 30 min and 1 h 30 min annealing cycle and using a factor of 2 and 1.5 of the equilibrium diffusivity. Consequently, boron diffusion mechanisms in the case of B+ and BF2 + implantations are not similar (enhancement and reduction of boron diffusion, respectively). Table 1 lists the reduction or enhancement factor relative to the equilibrium diffusivity model in the case of B+ (500 eV) and BF2 + (2.2 keV) implantations in crystalline silicon during annealing (800, 900 and 1000 ◦ C). First, we could deduce an enhancement of B diffusion at 900 and at 1000 ◦ C in the case of BF2 + implantation but the B diffusion has been reduced in comparison with the case of B+ implantation. Secondly, contrary to the case of 500 eV B+ implantation, we could deduce that there is no BED effect at these temperatures because it has been shown that BED effect increase highly with temperature.
1000 ◦ C
150 s
300 s
10 s
20 s
×2.5 ×1.5
×2.5 ×1.5
×4.0 ×1.8
×3.0 ×1.4
Fig. 3. Simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 1000 ◦ C during 10 and 20 s. Experimental data are from Ref. [9].
Fig. 6 shows the fluorine depth profiles and simulated results for the sample annealed at 800 ◦ C. The initial and the profile after annealing (800 ◦ C) of substitutional boron are also shown. Fluorine redistribution after post-implantation annealing deviates from simple diffusion in silicon [18–22]. For implantation below the amorphization threshold, a strong surface-oriented diffusion was observed [18–22]. F atoms are immobile below 500 ◦ C and F migrates to the surface and leaves the silicon in the 550–800 ◦ C [18]. The out-diffusion of these F atoms takes place in the 900–1100 ◦ C temperature range [18]. Such an anomalous diffusion phenomenon has been observed for nitrogen diffusion in silicon [32–33]. The interaction between the self-interstitials and fluorine during annealing has been explained as follows: the abundance of vacancies, generated during the implantation and liberated during the annealing, makes probable that most of the F atoms are released to substitutional positions and to fluorine vacancy cluster. During annealing, fluorine vacancy cluster is converted to substitutional fluorine (FV + I ⇒ FS ) and substitutional
4. Results and discussion Under our experimental conditions, simulations have shown that the effect of EoR defects are negligible because the surface proximity (6 nm) [35]. Indeed, the surface is the main sink for self-interstitials during TED. Consequently, contrary to 40 keV BF2 implantation experiments (a/c interface at 50 nm [23]), in our case of 2.2 keV BF2 implantation (a/c interface at 6 nm [35]), the EoR defects near the surface don’t play a key role. Figs. 3–5 show the boron depth profiles and simulated results for the samples annealed at 1000, 900 and 800 ◦ C. A good approximation between experimental and simulated profiles has been obtained using the boron diffusion model for the samples annealed at 1000 and 900 ◦ C and using the fluorine vacancy interaction for the sample annealed at 800 ◦ C.
Fig. 4. Simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 900 ◦ C during 150 and 300 s. Experimental data are from Ref. [9].
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Table 2 Parameters used in the simulations. eq
DI CI
Self-interstitials
= 9.14 × 102 exp(−4.84/kT ) [23]
Interstitial boron
Di = 3.17 exp(−3.59/kT) [23,28]
Boron limit solubility
CSol = 9.25 × 1022 exp(−0.73/kT) [26,42]
Vacancies
CV = 1.4 × 1023 exp(−2.0/kT ) [41]; DV = 3 × 10−2 exp(−1.9/kT) [41]
Fluorine (F diffusion coefficient and FV cluster dissolution)
At T = 800 ◦ C; DF = 10−13 cm2 s−1 ; kF = 2 × 10−13 cm−3 s−1
Fig. 5. Simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 800 ◦ C during 30 min and 1 h 30 min. Experimental data are from Ref. [9].
fluorine is converted in interstitial fluorine (FS + I ⇒ Fi ). The presence of fluorine vacancy clusters give an undersaturation of the local self-interstitial concentration since any self-interstitial would be able to recombine and annihilate with vacancies and fluorine vacancy clusters. Since boron diffusion in silicon is mediated by self-interstitials, an undersaturation of the self-interstitials concentration would give rise to a suppression of the boron diffusion. The dissociation of substitutional fluorine in interstitial fluorine and the fast diffusion of the liberated interstitial fluorine below the SIMS sensitivity explain the surface oriented fluorine diffusion in silicon. In our model, FI2 and F2 I2 [22] clusters have not been taken into account because our aim was to obtain the simplest model to explain the boron diffusion implanted in crystalline silicon in the form of BF2 + .
eq
According to this fluorine diffusion model, several features have been deduced: (i) at temperature near 800 ◦ C and for short anneal, the fluorine implant suppresses the enhanced boron diffusion due to the under-saturation of self-interstitials; (ii) at temperature near 800 ◦ C and for long anneal or for the 900–1100 ◦ C temperature range, the fluorine is not effective in suppressing the enhanced boron diffusion because the majority of fluorine during anneal is located near the surface and considerable fluorine dose has been lost by F out-diffusion. Consequently, the reduction of boron diffusion by fluorine implant is a transient phenomenon which is high at low temperature and decreases with time. The parameters used in the simulation are summarized in Table 2. This model needs to be improved to extract fluorine parameters as functions of temperature. Major part of the fundamental parameters has been taken from literature: equilibrium concentrations, diffusivities, boron solubility, boron precipitate and BI cluster dissolutions [23–27,29,41,42]. Recently, using several experimental results, Impellizzeri et al. [14–16], Kham et al. [11,13] and El Mubarek et al. [10,11] have shown that the responsible for boron diffusion reduction by fluorine is the presence of fluorine cluster. It has been shown that the fluorine diffusion profiles after anneals are not affected by the presence of boron [16]. This feature indicates that there is no direct interaction between boron and fluorine. These experimental results confirm our model [10–16]. Moreover, positron annihilation spectroscopy has directly confirms the presence of fluorine vacancy clusters in fluorine implanted silicon [43–45]. 5. Conclusion We have studied high-concentration dopant diffusion profiles in crystalline silicon implanted with low-energy BF2 + (2.2 keV). The diffusion of boron in ion implanted BF2 + is slightly lower than the coefficient of B in ion implanted B+ . The presence of vacancy-fluorine clusters gives an undersaturation of the selfinterstitial concentration and the boron diffusion has been reduced. A good agreement has been obtained between experimental and simulated profiles in the 800–1000 ◦ C temperature range. In a previous paper, we have correctly simulated the enhanced diffusion of boron implanted in crystalline silicon (500 eV B+ ) [29]. We have concluded that neglecting the dissolution of the SiB layer (boride enhanced diffusion) would lead to the underestimation of the boron diffusion. In this paper, we have correctly simulated the reduction of boron diffusion implanted in crystalline silicon (2.2 keV BF2 + ). We conclude that neglecting the interaction of fluorine with point defects would lead to the overestimation of the boron diffusion. Finally, we have improved the boron diffusion model of Uematsu in the case of ultra-lowenergy boron in crystalline silicon (500 eV B+ and 2.2 keV BF2 + implants). References
Fig. 6. Initial, simulated and experimental profiles for 2.2 keV BF2 + implanted in crystalline silicon annealing at 800 ◦ C during 1 h 30 min. Experimental data are from Ref. [9].
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