Modelling boron diffusion in heavily implanted low-pressure chemical vapor deposited silicon thin films during thermal post-implantation annealing

Thin Solid Films 517 (2009) 1961–1966

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Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f

Modelling boron diffusion in heavily implanted low-pressure chemical vapor deposited silicon thin films during thermal post-implantation annealing Salah Abadli ⁎, Farida Mansour Department of Electronics, University Mentouri Route d'Ain EL-Bey Constantine, Constantine 25000, Algeria

a r t i c l e

i n f o

Article history: Received 19 July 2007 Received in revised form 30 August 2008 Accepted 21 October 2008 Available online 29 October 2008 Keywords: Boron Model Diffusion Silicon LPCVD Crystallization Annealing

a b s t r a c t We have investigated and modelled boron (B) diffusion in heavily implanted silicon (Si) thin films deposited from disilane (Si2H6) by low pressure chemical vapor deposition (LPCVD) at low temperatures. A comprehensive one-dimensional two-stream diffusion model adapted to the particular structure of deposited Si films and to the effects of high B concentrations has been developed. This model includes B clustering in grains as well as in grain boundaries. In addition, the effects of Si-films crystallization, during thermal post-implantation annealing, on B diffusion as well as on B clusters formation and dissolution were considered. The effects of clustering, growth of grains, dopant-enhanced grains growth and the driving force for grains growth were coupled with the dopant diffusion coefficients and the process temperature based on thermodynamic concepts. To investigate complex B diffusion in heavily implanted Si films deposited by LPCVD, we have used experimental profiles obtained by secondary ion mass spectroscopy (SIMS) for B implantation with doses of 1 × 1015 at./cm2, 4 × 1015 at./cm2 and 5 × 1015 at./cm2 at an energy of 15 keV. Thermal post-implantation anneals were carried out at relatively low-temperatures (700 °C and 850 °C) for various short-times of 1 min to 15 min. The good adjustment of the simulated profiles with the experimental SIMS profiles allowed the validation of this model. It was found that the simulation well reproduces the experimental SIMS profiles when the growth of grains and immobile B clusters are considered. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Polycrystalline-silicon (poly-Si) is a key element of today's advanced very-large-scale-integration and ultra-large-scale-integration technology. He forms an adherent oxide, absorbs and re-emits dopants, absorbs heavy metals (gettering), has good step coverage if deposited by chemical vapor deposition, has high-conductivity if heavily doped and has a compatible work function for metal-oxidesemiconductor (MOS) devices. These properties make of poly-Si an element of concentrated research for broad applications in present electronic components technology [1–5]. The growth of thin layers by low pressure chemical vapor deposition (LPCVD) is one of the most important techniques for deposition of thin films in modern technology. The reasons of a wide application of the LPCVD method are in possibility of deposition of different elements and compounds at relatively low temperatures in amorphous and crystalline phase with high degree of uniformity and purity. Indeed, the good control of deposition mechanisms of these films permits their use in high performance integrated circuits [4,5]. The heavily doped poly-Si is now the more used gates material in complementary MOS technology. Boron (B) is the most widely used p-type dopant in modern microelectronic devices due its high solid solubility in Si. It is usually ⁎ Corresponding author. Tel.: +213 554 267 349. E-mail address: [email protected] (S. Abadli). 0040-6090/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2008.10.048

ion implanted into Si films, followed by a thermal post-implantation annealing which electrically activates the B and removes implant damage. Recently, p+ doped poly-Si gate electrodes have been used instead of n+ poly-Si ones for p channel MOS field-effect transistors to convert the buried-channel operations to surface-channel ones [5–7]; which are scalable to deep submicrometer dimensions. However, B penetration from p+ poly-Si gate electrodes through such thin gate oxide layers and into the underlying Si channel region has become a severe problem [3–7], because a high carrier activation in the poly-Si is simultaneously required to prevent the gate depletion effect; which degrades the drivability of devices. As technology generations advance and devices become smaller, it is necessary to create very shallow junctions with high-concentrations of electrically active B. Two related processes limit the realization of this goal: (i) the transient enhanced diffusion (TED) of the B during the thermal post-implantation annealing and (ii) the formation of electrically inactive B clusters and B precipitates. TED and the formation of B–Si interstitial clusters or B–B precipitates make the formation of ultra-shallow low-resistivity junctions difficult. Concerning TED in single-crystal Si, it is now well established that {311} self-interstitial clusters produced by ion-implantation damage are the sources of self-interstitials that enhance the B diffusion [8–11]. Furthermore, high-concentration B will lead to B clustering and B precipitation, which reduce electrical activation. However, the observed TED in Si thin films obtained by LPCVD is not yet well

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investigated. B redistribution in these thin films is strongly affected by the morphological structure of deposited Si films (poly-Si or amorphous-Si films), which are function of deposition conditions. An additional complexity is that the morphological structure of deposited Si films changes during annealing with grains growing in size. To the author's knowledge, this complex redistribution is not yet given in a clear and single way in literature. Ones suggest that B segregate to the grain boundaries [12,13], while others require the possibility of B clustering in grains as well as in grain boundaries [14]. This paper aims to develop a fundamental understanding of the B transport mechanisms inside Si obtained by LPCVD and developing a model for the process. This has become an essential step which will make possible the optimization of the manufacturing process of very shallow junctions and thus, to propose solutions to surmount the established problems. Based on the one-dimensional Fick's laws, we present a theoretical one-dimensional two-stream diffusion model adapted to the particular structure of Si-LPCVD and to the effects of high B concentrations. This model consists of two coupled partial differential equations for diffusion. The first equation is associated to the B diffusion inside the grains and the second equation is associated to the B diffusion within grain boundaries. These two partial differential equations are coupled by an expression which introduces the impurities exchange between the grains and the grain boundaries; by associating the effects of high B concentrations, B trapping-emission as well as segregation.

used as references and initial conditions during the next theoretical simulation step (simulation step of diffusion profiles after annealing). Starting from the calculations carried out using the expression given by Solmi et al. [17] (Csol = 9.25 × 1022 exp(−0.73/KT)), we can be

2. Experimental details and initial doping profiles In this paper, we investigated two type of Si films chemically vapor deposited at a low pressure (26.6 Pa) with a various thickness onto thermally oxidized single-crystal Si substrates; p-type (111) Sisubstrates with thermal oxide SiO2 of 120 nm-thickness. The first type, consists of approximately 200 nm-thick Si films deposited at 480 °C by thermal decomposition of disilane (Si2H6) inside a low pressure chemical vapor deposition reactor. These films are then B implanted with the doses of 1 × 1015 atoms/cm2 and 5 × 1015 atoms/cm2 by an energy of 15 keV [3]. The second type, consists of approximately 335 nm-thick Si films deposited at 465 °C by LPCVD from disilane under total pressure of 26.6 Pa. These films are then B implanted with a dose of 4 × 1015 atoms/cm2 by an energy of 15 keV [15]. The experimental doping profiles have been obtained by secondary ion mass spectrometry (SIMS) using a CAMECA IMS4F measuring device [3,15], which enables us to obtain impurity concentration profiles as a function of the samples depth. Fig. 1a, b and c show the experimental SIMS total B concentration profiles obtained after ion implantation (before annealing) for films deposited at 480 °C and B implanted with 1 × 1015 at/cm2–15 keV, films deposited at 465 °C and B implanted with 4 × 1015 at/cm2–15 keV and films deposited at 480 °C and B implanted with 5 × 1015 at/cm2–15 keV, respectively. In order to avoid long B redistributions, thermal post-implantation anneals were carried out at relatively low temperatures (700 °C and 850 °C) for various short-times ranging between 1 and 15 min, in a conventional furnace and nitrogen ambient. The initial total B distribution profiles (after ion implantations) have been simulated without any difficulties using the analytical Gaussian expression. This expression is identified by the next three following parameters: the ion implantation dose Qd; the projected range Rp; and the straggle or the standard deviation ΔRp; given by the following form [16]:  2 ! x−Rp Q C ðxÞ = pffiffiffiffiffiffi d exp − 2ΔR2p 2πΔRp

ð1Þ

Fig. 1a, b and c show also the good adjustment of SIMS profiles and simulated profiles (profiles before annealing). These profiles will be

Fig. 1. Simulated (●) and SIMS (—) total B distribution profiles, before annealing, for Sifilms (a) deposited at 480 °C and B implanted with 1 × 1015 at./cm2–15 keV; (b) deposited at 465 °C and B implanted with 4 × 1015 at./cm2–15 keV; (c) deposited at 480 °C and B implanted with 5 × 1015 at./cm2–15 keV.

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informed that via implantation doses of 1 × 1015 at./cm2, 4 × 1015 at./ cm2 and 5 × 1015 at./cm2 the B concentration exceeds its solubility limit in the studied Si films. In this case, the doping excess precipitates and forms inactive and immobile clusters [11,18]. Precisely, the state of B linked to this parameter, particularly in poly-Si, was not given in obvious and single way in the literature. It has been suggest that B forms precipitates (B–B) to the grain boundaries if the impurity concentration exceeds its solubility limit [12,13]. At the same time, others researchers indicated that B forms also electrically inactive and immobile interstitial clusters in crystalline Si structure [8,19], so at the grains. The possibility of clustering even at concentrations below the solubility limit under the supersaturation of self-interstitials in crystalline Si has been also proposed [8,11]. 3. Diffusion model Recently, a lot of models had been proposed to permit the understanding and the simulation of complex mechanisms of B redistribution and activation in Si during thermal post-implantation annealing [11,14,15]. Based on the ideas and the results of each model, we describe now a more detailed model adapted to the particular structure of Si-LPCVD and to the effects of very strong-concentrations. The diffusion mechanism is controlled by two partial differential equations, signifying two dopant concentrations, coupled by a term representing the dopant transfer rate between the grains and the grain boundaries. The two dopant concentrations are coupled by dopant transfer or exchange due to grains-growth, lateral diffusion, trapping-emission and segregation to the grain boundaries. Therefore, the total dopant concentration (Ctot) will be divided between the grains (Cg) and the grain boundaries (Cgb). The effects linked to the strong-concentrations were combined with the effective dopant diffusion coefficients in grains and grain boundaries. As result, for a one-dimensional two-stream diffusion mechanism, this model is given by the next coupled continuity equations for the two dopant populations Cg and Cgb:     Cgb ACg ACg A Deff = −keff Cg − g t Ax At Ax kseg

eff ACgb ACgb Dgb ALg A Deff = + C gb Ax At Ax Lg gb Ax

!

ð2Þ

  Cgb + keff Cg − t kseg

ð3Þ

where Cg is the individual dopant concentration in the grains, Cgb is the individual dopant concentration in the grain boundaries, keff t is the effective dopant transfer rate between grains and grain boundaries as a result of grain boundary motion related to the grain growth kinetics, kseg is the effective dopant segregation coefficient between the grains and the grain boundaries and Lg is the average grain size. The Eqs. (2) and (3) have standard flux terms and are coupled together by the transfer of dopant atoms from the grains to the grain boundaries or vice versa. Indeed, the total B concentration in the studied layers is the sum of the two individual concentrations Cgb and Cg (Ctot = Cg + Cgb). Therefore, it is necessary to deduce two theoretical initial B distribution profiles (for each distribution profile) starting from the previously simulated profiles shown in Fig. 1. This step was completed using the studies of Puchner et al. [14], Uematsu [11] and Sadovnikov [20]. The solubility limit Csol is taken to calculate the active impurity concentration in grains Cg starting from the total impurity concentration Ctot. The reported expression of Csol given by Solmi et al. [17] was multiplied in our case by a factor of about 3 to have used values of Csol for our investigated Si thin films. Deff and Deff g gb are respectively, the effective dopant diffusion coefficients inside the grains and the grain boundaries. They take

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into account of all the possible effects considered in this study. These coefficients are identified by the next expressions:

Deff g

0 1  2m !−1 Cg Cg 1 + βðp=ni Þ B C = Di @1 + qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA 1 + m 1+β Csol C 2 + 4n2 g

Deff gb

ð4Þ

i

0 1    Cgb 1 + βðp=ni Þ B −Eb C = Fa Di @1 + qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA 1−exp 1+β KT C 2 + 4n2 gb

  −Ea Di = D0 exp KT

ð5Þ

i

ð6Þ

where Di is the intrinsic diffusion coefficient in single-crystal silicon, K is the Boltzmann constant, T is the annealing temperature in Kelvin, Ea is the activation energy, p is the holes concentration, ni is the electron intrinsic concentration, Csol is the solubility limit for the dopant species, β is a statistical factor for charged vacancies, m is the medium number of B interstitial atoms trapped in a cluster (small B clusters), Fa is a constant pre-exponential factor for the adjustment of the intrinsic diffusivity in the grain boundaries and Eb is the energy barrier height to the grain boundaries. The intrinsic diffusivity Di in single-crystal silicon varies exponentially with the temperature T and the activation energy Ea associated with the diffusion process. In this study, we took the very used value of Ea = 3.46 eV [21,22], which is the default value for single-crystal Si. D0 is the diffusivity pre-exponential factor (D0 = 0.76 cm2 s− 1) [22]. The effective diffusion coefficients are greatly linked to the effects of high B concentrations (excess of Csol). They depend also on the charged vacancies concentration in the interior grains because vacancies with different charge states accelerate impurities diffusivity. β is the ratio of the diffusivity induced by the positively charged vacancies on the global diffusivity induced by the neutral vacancies (β = D+i /D0i ) [15,21]. eff In addition, Deff gb and Dg depend of holes concentration p and intrinsic concentration ni. Moreover, Deff g depends of the doping solubility limit Csol, as well as of the small interstitial-clusters formation by means of a medium number m of B–Si atoms trapped in cluster [11,14]. Concerning the effective diffusion coefficient in the grain boundaries Deff gb , it is well controlled by the trapping and the segregation to the grain boundaries. These two effects are obviously related to the energy barrier height Eb to the grain boundaries [20]. Eb depends on the impurity concentration, the average size of the grains and the traps density [23,24]. Fa is a pre-exponential factor for the adjustment of the intrinsic diffusivity within the grain boundaries (case of Si-LPCVD films); since the effective diffusivity of dopant atoms in single-crystal Si is different to that in polycrystalline Si [21]. It represents the ratio Dpoly/Dmono because the B diffusion coefficient in poly-Si is generally much higher than the default diffusion coefficient in single-crystal Si [13,21]. This pre-exponential factor can be some hundreds to some thousand. As an example, a value of about 104 reported by Probst et al. [21] and a value of about 102–103 reported by Sadovnikov [20]. It depends strongly on the films deposition conditions and the treatment conditions after deposition. The coupling between the two diffusion partial differential Eqs. (2) and (3) is ensured by a term representing the effective dopant transfer from the grains to the grain boundaries and vice versa. The net effective transfer rate is given by [20,25]: keff t =

Dg Lg

! 4 1 2α ALg + pffiffiffiffiffiffiffiffi + Lg 2 Dg t Lg At

ð7Þ

The effective doping transfer rate between the grains and the grain boundaries depends mainly on the average grain size Lg and its

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growth during thermal annealing (morphological structure changes and recrystallization). α is a factor of adjustment [25]; in this work we consider α = 1. In real poly-Si, the crystallites have a distribution of sizes and irregular shapes. For more simplification, we assume that poly-Si is composed of identical crystallites having a grain size of Lg. The grains of poly-Si are assumed to be squares growing from initial grain size Lg0 (Lg0 depends on deposition conditions). The grainsgrowth is proportional to the square root of time [20,26]: Lg ðt Þ =

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2g0 + 2γt

ð8Þ

Lg(t) represents the average grains size after time t and Lg0 represents the initial average grains size after deposition of poly-Si layer. γ is a parameter which depends on the grain boundary mobility and the grain boundary energy [26] (γ = 4.6 × 10− 2 exp(−1.36/KT) µm2/s). Its value depends on the local Fermi level. Concerning the dopant segregation, it can be described by the studies of Mandurah et al. [27] and of Swaminathan et al. [28]. It is identified by the next expression: kseg = 2kseg0

egb Lg

ð9Þ

enon is dominating. Consequently, each parameter affect the diffusion profile behaviour differently. Thus, a particular SIMS profile cannot be reproduced with one single set of these parameters because different phenomena are dominating in different regions. The simulation, which reproduces very well the experimental SIMS profiles, illustrate the significant role of Si crystallization (self-diffusion) and that of dopant trapping and segregation for the reproduction of the diffusion profiles. Figs. 2–4 show a satisfactory superposition of simulated total B profiles after annealing and SIMS profiles. These figures show B concentrations (cm− 3) as a function of Si films depth (µm). We notice good matching, particularly for the profiles shoulder that occurs near the B solubility limit concentration (Csol). Indeed, high-concentration B will lead to the formation of immobile B clusters (B–Si) and B precipitates (B–B), which of course reduce electrical activation [8–15]. Starting from the realized simulation, we notice that effective B diffusivity inside the grains is not very different to that in the grain boundaries for these investigated films. This is justified by the significant reduction of the B diffusion within grain boundaries caused by the important trapping-segregation mechanism or by means of the significant grain boundary width (amorphous Si-films deposited at lower temperatures) [27]. It indicates that the effective B

kseg0 is the thermal equilibrium grain boundary segregation coefficient and egb is the average width of a grain boundary. Segregation coefficient is described by the expression analogous to one obtained by Mandurah et al. [27] and to that in Sadovnikov [20] (kseg0 =k0 exp(0.456/ KT)). Concerning the used estimated values of Eb, they have been obtained from the following relations [23,24]: • For total impurity concentration Ctot lower than a critical concentration C⁎ (Ctot < C⁎), the energy barrier Eb is calculated from Eq. (10)

Eb =

q2 L2g 8e

ð10Þ

Ctot

• For total impurity concentration Ctot higher than a critical concentration C⁎ (Ctot > C⁎), the energy barrier Eb is calculated from Eqs. (11) and (12) Eb i

q2 Nt2 if EF −Eb >> KT 8eCtot

Eb i

Eg Nt + KTln q 2 Nc

sffiffiffiffiffiffiffiffiffiffi! Ctot if EF −Eb << KT 2eEb

ð11Þ

ð12Þ

where Eg is the band-gap energy, Eb is the barrier height, EF is the Fermi level, Nc is the effective density of states relative to the conduction band, Nt is the density of trapping states at the grain boundaries and ε is the dielectric permittivity of poly-Si. The critical concentration C⁎ is determined by the expression given by Kim et al. [26] and Mandurah et al. [29] (C⁎ = Nt/2r; were r is the average grain radius). 4. Results and discussion The simulated B diffusion profiles were obtained by means of numerical resolution of the partial differential Eqs. (2) and (3) while using an implicit method of finite differences with specified boundary conditions and initial conditions. These profiles were adjusted thereafter to the experimental SIMS profiles. The good adjustment is obtained by varying independently the values of the following set of parameters: Lg0, Fa, m, β and kseg0; each of which has a clear physical meaning. Each of these parameters has a leading effect on a particular part of the diffusion profile where the associated physical phenom-

Fig. 2. Simulated profiles (symbols) and SIMS profiles (lines) of B concentrations after 15 min annealing at 850 °C for deposited films at 480 °C and implanted with (a) 1 × 1015 at./cm2–15 keV and (b) 5 × 1015 at./cm2–15 keV. (●) total B concentration Ctot; (□) individual B concentration in the grains Cg; (○) individual B concentration in the grain boundaries Cgb.

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Fig. 3. Simulated profiles (symbols) and SIMS profile (line) of B concentrations after 15 min annealing at 700 °C for deposited films at 465 °C and implanted with 4 × 1015 at./cm2– 15 keV. (●) total B concentration Ctot; (□) individual B concentration in the grains Cg; (○) individual B concentration in the grain boundaries Cgb.

diffusivity along the grain boundaries is strongly affected by the morphological structure changes of the Si films. The effective diffusion coefficient within grain boundary depends much on Eb, Lg and thus on the density of trapping states Nt. In this study, Nt was found to be of the order of 5 × 1012 cm− 2, while the grain boundary width egb is fixed at 13 Å (Si-LPCVD films, 465 °C, 4 × 1015 at./cm2, 15 keV). It is about twice that obtained experimentally by Mandurah et al. [29] using a conditions not very different of our LPCVD conditions. The used parameter k0 is equal to 5.2 × 10− 9. It means that the effect of segregation for B in these conditions is about 4 times as low as for arsenic [27,29]. For Si-LPCVD films obtained at 465 °C, the satisfactory adjustment appears when the initial average grain size Lg0 of the order of 100 Å or less than this value has been used. This last value is approximately 8 times lower than that obtained in experiments by Akhtar et al. [30] using atomic force microscopy for poly-Si films obtained by LPCVD at 620 °C starting from silane SiH4. This is justified by the almost amorphous films deposited at lower temperature (465 °C) [15]. We assume that the deposited films by LPCVD at 465 °C starting from disilane Si2H6 provides grains of very small sizes with an important density (Lg0 < 100 Å). These grains are further grouped in the form of very small clusters of various silicon-atoms (Si–Si). In each cluster, the grains maintain their individual identity [30]. However, for Si-LPCVD films obtained at 480 °C, the satisfactory fit appears if we used the initial average grain size Lg0 of the order of 160 Å or more than this value. During B implantation in Si-LPCVD films, B clusters and B precipitates are formed rapidly (B–B and B–Si complexes). Thermal post-implantation annealing at 700 °C and 850 °C diminishes the clusters density and increases the grains size; grain boundaries are eliminated by grains growth through normal recrystallization. The grain length increase during annealing from the nearly clusters or starting from the near disordered regions; some grains grow at the expense of neighbouring grains. Growth kinetic or recrystallization is normal if the films are undoped. However, if the films are heavily doped, grains growth is greatly influenced and enhanced. This dopant-enhanced grain growth is a strong function of the dopant concentration. The grain-growth enhancement is limited at very high B concentrations (CB >Csol) because B-clusters and Bprecipitates excess impede grain boundary elimination. The driving force for grain growth is the reduction in grain boundary energy Eb as grain boundaries are eliminated by grain growth. In consequence, it has been postulated that vacancies with different charge states (which depend on the location of the Fermi level EF in the band gap) accelerate grain-

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boundary migration. The recrystallization is not uniform along the film depth because the doping concentration is not uniform. It is very possible that three regions of different grains sizes exist after some annealing time: a region of large and almost uniform grains, a region of medium size and less uniform grains, and a region of smaller grains grouped in the form of clusters basically nonuniform. The dopant diffusivity in each region is influenced by the crystallization velocity rate and the effects of impurity concentration. As the grains grow faster, the total grain boundary volume decreases and thus the concentration in the grain boundary drops. The dopant atoms are transported with the self atoms into the surrounding crystalline grains due to the movement of the grain boundaries related to the grain growth. In growth kinetics, grains grow at the expense of neighbouring grain boundaries. As mentioned before, grain growth is a strong function of the dopant concentration and so is maximum near the peak region of the B profile. In this peak region, the B clusters (B–Si) and the B precipitates (B–B) are quickly surrounded by the important Si-atoms migration (self-diffusion) or crystallization generated by the growth of crystallites to construct larger grains (primary and secondary crystallization). As it can be seen from Figs. 2b, 3 and 4, the nonreduction in the peak of the B profiles from the as-implanted profiles is because of Csol effects and slow B transfer-kinetics towards larger grains. The boron atoms in B precipitates and boron atoms in B clusters are rapidly surrounded before their dissolution and thereafter enclosed in large crystallites as a result of a considerable self-diffusion of Si occurring in this region. It can be clearly seen that in the peak region of the B profiles (CBtot >Csol) much of the B is immobile in the grains; since grain boundary eff volume is considerably reduced. Dgb and Dgeff are considerably decreased in this region. However, near and below solubility limit Csol, the activity of B is more and more significant and the driving force for grain growth is less considerable than before. Hence, most of the B is in the grain boundaries. Thus, for medium B concentrations (ni
Fig. 4. Simulated (symbols) and SIMS (lines) profiles of total B concentrations after annealing at 700 °C for 1 min, 5 min, and 15 min for deposited films at 465 °C and implanted with 4 × 1015 at./cm2–15 keV.

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of the B profiles (CBtot
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