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Mechanisms of boron diffusion in silicon and germanium
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FIG. 1.

Chemical profiles SIMS of B atoms after implantation (0.5 keV, 1 × 1015/cm2) in Ge pre-amorphized Si, and after different thermal processes (750 °C-15 min, 1000 °C spike, 1300 °C single or multiple flash anneals). A boron profile is also reported as a reference sample (grown by chemical vapor deposition, CVD). The kinks (shown by arrows) in the annealed profiles indicate the formation of an immobile B peak (due to B clustering). Reprinted with permission from F. Severac, J. Appl. Phys. 107, 123711 (2010). Copyright 2010 American Institute of Physics.

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FIG. 2.

Chemical profile of B as-implanted in α-Si (0.5 keV, 1 × 1015/cm2) and after annealing at 500 °C for 40 min. Reprinted from R. Duffy et al., Appl. Phys. Lett. 84, 4283 (2004). Copyright 2004 American Institute of Physics.

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FIG. 3.

Chemical profile of B in the as-amorphized sample (dotted line) and after annealing at 500 °C, 8 h (circles) or 650 °C, 250 s (squares), with the simulations following the best fit procedures (solid lines). Experimental drawing in the inset. Reprinted with permission from S. Mirabella et al., Phys. Rev. Lett. 100, 155901 (2008). Copyright (2008) The American Physical Society.

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FIG. 4.

Transient effect in the effective B diffusivity measured in the high (squares) and the low (circles) B boxes, with simulation curves (solid lines). Dotted lines represent the B diffusivity in c-Si multiplied by a 105 factor, for each annealing temperature.

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FIG. 5.

Cu decoration technique for profiling the coordination defects in undoped (circles) or 8 × 1020 B/cm3 enriched (stars) α-Si. Cu was implanted (dotted line, 15 keV, 1 × 1016/cm2) in unrelaxed (closed symbols) and relaxed (open symbols) samples, and Cu profiles have been measured after diffusion annealing at 200 °C, 1 h. Cu concentration in undoped Si is lower than in B enriched Si, regardless of the relax status.

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FIG. 6.

Arrhenius plot for the diffusivities of dangling bond (D d , left axis) and of B per unit of dangling bond density (α, right axis), with the relative fits (dotted lines) and equations. Reprinted with permission from S. Mirabella et al., Phys. Rev. Lett. 100, 155901 (2008). Copyright (2008) The American Physical Society.

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FIG. 7.

Schematic representation of the atomistic mechanism of B diffusion in amorphous Si. An immobile, 3-fold coordinated, B atom jumps to an adjacent site through the exchange of a dangling bond (db) and the temporary restoring of a metastable, 4-fold coordinated configuration.

Image of FIG. 8.

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FIG. 8.

Diffusivity of Boron and Gallium in silicon as a function of the normalized hole concentration. The linear trend over almost three orders of magnitude indicates that the mobile BI pair is in the neutral charge state. Reprinted with permission from R. B. Fair and P. N. Pappas, J. Electrochem. Soc. 122, 1241 (1975). Copyright 1975 The Electrochemical Society.

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FIG. 9.

Diffusion of a B delta (grown by molecular beam epitaxy) annealed at 900 °C for 5 min in N2 ambient (left panel) or at 625 °C for 110 h in dry O2 ambient (right panel). The different shapes of the diffused profiles were simulated (continuous lines) with the interstitial mediated diffusion model. Reprinted with permission from N. E. B. Cowern et al., Phys. Rev. Lett. 67, 212 (1991). Copyright (1991) The American Physical Society.

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FIG. 10.

Chemical profile (symbols) of 11B spike before (squares) and after diffusion annealing at 700 °C for the samples with different doping backgrounds (triangles for 10B doping or circles for 31P doping). The continuous lines are the best fits to the data.

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FIG. 11.

Diffusivity (a), migration rate (b), and mean diffusion length (c) as a function of p/ni (hole concentration normalized to the intrinsic carrier concentration at 700 °C, equal to 0.92 × 1018/cm3 (Ref. 40 )). Symbols are referred to experimental data (squares to B doping, circles to P doping and stars to As doping) while lines are simulation based on the models in Ref. 14 considering or not the B pairing with As or P (a) and (b), and the B mobile species as the BI 0 complex with or without the BI complex (c). Above the graph, the varying doping condition together with the main reaction leading to the diffusion have been indicated.

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FIG. 12.

Arrhenius plot of (a) diffusivity divided by p/ni (hole concentration normalized to the intrinsic carrier concentration) and of (b) migration frequency divided by the diffusivity, as extracted from diffusion of a 11B spike in intrinsic (closed squares) or p-type doped (open circles) conditions. Upper panel shows the energy barrier to the diffusion of the mobile BI 0 species. Lower panel represents the energy barriers to the formation of the BI or BI + complex (in the two diffusion channels), with respect to the energy level of the diffusing BI 0 complex.

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FIG. 13.

Energetics of B diffusion process in crystalline Si. Substitutional B ( ) can give mobile BI pair by interaction with I 0 or I ++ with energy barriers of 4.1 and 4.4 eV, respectively. The BI species moves through negative BI (only in n-type conditions, not shown here) or neutral BI 0 saddle points. This last is the main mechanism with a 3.45 eV total activation energy. The pairing of substitutional B with As or P n-dopant is also indicated, causing a strong increase in the diffusion energy cost.

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FIG. 14.

Chemical (SIMS) and electrical (spreading resistance profiling, SRP) profiles of 25 keV, 2 × 1014 B/cm2 implanted in crystalline Si and annealed at 800 °C for different times. The B profile is composed of an immobile, non-active part, and a diffusing part, with a concentration threshold at ∼3 × 1018 B/cm3. Reprinted from N. E. B. Cowern et al., J. Appl. Phys. 66, 6191 (1990). Copyright 1990 American Institute of Physics.

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FIG. 15.

Chemical profiles of a B multidelta structure grown by MBE and implanted with Si ions in the shallower region. (Upper panel) Thermal annealing at 790 °C induces the B TED in all the spikes, while the BIC formation causing the immobile peaks occurs only in the shallower region. Lower panel reports the simulation of the Is distribution after implantation and the de-convolution of the B profiles in mobile and immobile fractions. Reprinted from L. Pelaz et al., Appl. Phys. Lett. 70, 2285 (1997). Copyright 1997 American Institute of Physics.

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FIG. 16.

Superimposition of BICs features observed by TEM (cross-sectional view) and chemical profiling (SIMS), taken from the same MBE sample (with an embedded B box) implanted with Si ions and annealed at 815 °C, 5 min. Small dark spots, with typical contrast of dislocation loops (as shown in the inset), are observed at the depth of 220 nm where the immobile part of the chemical profile is recorded. A schematic of the experiment is also shown. Reprinted from S. Boninelli, Appl. Phys. Lett. 91, 031905 (2007). Copyright 2007 American Institute of Physics.

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FIG. 17.

Schematic map of B-I clusters energetics (referred to the perfect lattice) as a function of the composition (as BnIm clusters). BIC evolution towards different configuration occurs through B (oblique red lines) or Si (vertical blue lines) interstitials exchange with the hosting lattice. Four main regions have been defined: SB for clusters with less than 4 B atoms, LBLI (large BICs low interstitial), LBB (large BICs barrier), and LBHI (large BICs high interstitial) with a larger number of B atoms. Reprinted from M.Aboy et al., J. Appl. Phys. 110, 073524 (2011). Copyright 2011 American Institute of Physics.

Image of FIG. 18.

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FIG. 18.

Chemical profiles of B as-implanted in Ge (20 keV and 6×1014/cm2) and after annealing at 850 °C for 24 h, with fitting lines. Reprinted from S.Uppal et al., J. Appl. Phys. 90, 4293 (2001). Copyright 2001 American Institute of Physics.

Image of FIG. 19.

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FIG. 19.

B diffusion induced by dissolution of EOR defects. The average number of B diffusion events (gt, closed squares, left axis) and the EOR strain integral (S, open squares, right axis) are reported into an Arrhenius plot. The lines are fit to the data considering the exponential functions reported into the graph (parameters A, B, and C account for the initial and saturation values).

Image of FIG. 20.

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FIG. 20.

Ion irradiation effects on the chemical profiles of B in Ge. Starting sample (i.e., the as-grown sample after the 1 h 600 °C annealing, dotted line) and those further irradiated at 150 °C with the 300 keV, 1 × 1016 H+/cm2 (continuous line) or 3 MeV, 8 × 1013 O+/cm2 (dashed-dotted line) are reported, together with a non-implanted sample thermally annealed at 350 °C for the longer implant time (dashed line).

Image of FIG. 21.

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FIG. 21.

Temperature effect on the shape of diffused B profile: lower temperatures (upper panel) lead to long exponential tails because of the long migration length. Chemical B profile in the starting sample (dashed line) and after 200 keV H+ implant performed at 200 °C (upper panel, line plus up triangles), 400 °C (upper panel, line plus stars), 750 °C (lower panel, line plus down triangles), and 800 °C (lower panel, line plus diamonds). A reference for thermal diffusion at 800 °C is also plotted in panel (b) (line plus open circles). Reprinted from G. G. Scapellato et al., Nucl. Instrum. Methods Phys. Res. B 282, 811 (2012). Copyright (2012) Elsevier.

Image of FIG. 22.

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FIG. 22.

Arrhenius plot of the diffusion length (λ) for B diffusion in Ge, under several conditions. Enhanced diffusion conditions are reported for samples irradiated at different temperatures with 3 MeV O+ (star), or with 200 keV H+ (triangles), or with 300 keV H+ (squares), and also for samples annealed after 300 keV H+ irradiation at room temperature (crossed squares). Thermal conditions are also reported for annealing (with no implantation) at 755 °C and 800 °C (open circles). Dashed red line is a fit of λ values obtained in high temperature regime (550-800 °C).

Image of FIG. 23.

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FIG. 23.

Effect of embedded GeO2 nanoclusters on B diffusion in Ge. Boron profiles in MBE-Ge sample after O implantation (black dashed line), and after annealing at 650 °C for 30 (orange open squares), 120 (blue open triangles), and 180 (green stars) min. A homogeneous broadening of the B profiles is observed, evidencing at 650 °C a transient enhanced diffusion of B lasting up to 120 min. Reprinted from G. G. Scapellato, Phys. Rev. B 84, 024104 (2011). Copyright (2011) The American Physical Society.

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/content/aip/journal/jap/113/3/10.1063/1.4763353
2013-01-16
2014-04-25

Abstract

B migration in Si and Ge matrices raised a vast attention because of its influence on the production of confined, highly p- doped regions, as required by the miniaturization trend. In this scenario, the diffusion of B atoms can take place under severe conditions, often concomitant, such as very large concentration gradients, non-equilibrium point defect density, amorphous-crystalline transition, extrinsic doping level, co-doping, B clusters formation and dissolution, ultra-short high-temperature annealing. In this paper, we review a large amount of experimental work and present our current understanding of the B diffusion mechanism, disentangling concomitant effects and describing the underlying physics. Whatever the matrix, B migration in amorphous (α-) or crystalline (c-) Si, or c-Ge is revealed to be an indirect process, activated by point defects of the hosting medium. In α-Si in the 450-650 °C range, B diffusivity is 5 orders of magnitude higher than in c-Si, with a transient longer than the typical amorphous relaxation time. A quick B precipitation is also evidenced for concentrations larger than 2 × 1020 B/cm3. B migration in α-Si occurs with the creation of a metastable mobile B, jumping between adjacent sites, stimulated by dangling bonds of α-Si whose density is enhanced by B itself (larger B density causes higher B diffusivity). Similar activation energies for migration of B atoms (3.0 eV) and of dangling bonds (2.6 eV) have been extracted. In c-Si, B diffusion is largely affected by the Fermi level position, occurring through the interaction between the negatively charged substitutional B and a self-interstitial (I) in the neutral or doubly positively charged state, if under intrinsic or extrinsic (p-type doping) conditions, respectively. After charge exchanges, the migrating, uncharged BI pair is formed. Under high n-type doping conditions, B diffusion occurs also through the negatively charged BI pair, even if the migration is depressed by Coulomb pairing with n-type dopants. The interplay between B clustering and migration is also modeled, since B diffusion is greatly affected by precipitation. Small (below 1 nm) and relatively large (5-10 nm in size) BI clusters have been identified with different energy barriers for thermal dissolution (3.6 or 4.8 eV, respectively). In c-Ge, B motion is by far less evident than in c-Si, even if the migration mechanism is revealed to be similarly assisted by Is. If Is density is increased well above the equilibrium (as during ion irradiation), B diffusion occurs up to quite large extents and also at relatively low temperatures, disclosing the underlying mechanism. The lower B diffusivity and the larger activation barrier (4.65 eV, rather than 3.45 eV in c-Si) can be explained by the intrinsic shortage of Is in Ge and by their large formation energy. B diffusion can be strongly enhanced with a proper point defect engineering, as achieved with embedded GeO2 nanoclusters, causing at 650 °C a large Is supersaturation. These aspects of B diffusion are presented and discussed, modeling the key role of point defects in the two different matrices.

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Scitation: Mechanisms of boron diffusion in silicon and germanium
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/3/10.1063/1.4763353
10.1063/1.4763353
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