Two Kinds of Hydrogen Monomers Manifested in Plasma-Exposed Silicon

In boron-doped silicon annealed in a plasma ambient (at 150°C), the reported hydrogen concentration profile and the hole profile cannot be simultaneously fitted assuming only one kind of in-diffusing hydrogen ions H of a definite parameterDK (whereD is the diffusivity of H and K is the equilibrium dissociation constant of the HB defect, the passivated boron). A good fit is possible only assuming two independent kinds of H—one of a larger value of DK and the other—of a smaller value. A concept of two independent atomic subsystems H(1) and H(2), each involving both positive and neutral charge states, is also useful to account for hydrogen pairing into dimers.


Introduction
Hydrogen impurity plays an important role in silicon materials-by passivating dopants and other defects [1][2][3][4][5][6]. In p-type and near-intrinsic Si, under equilibrium conditions, the dominant monomeric state of hydrogen is thought [7] to be H + (BC)-a positive ion in a bond-centred position. e acceptors (normally, boron B − ) are passivated by combining H + and B − into neutral defects HB. e data on hydrogen diffusion from a plasma ambient and on the related boron passivation were collected years ago, but they are still waiting for a proper analysis, in view of a growing interest to hydrogen as a powerful and promising tool to control the defects in Si. e degree of passivation-a ratio of passivated boron concentration [HB] and nonpassivated boron concentration A depth profile of hydrogen concentration C(z) includes a near-surface narrow region of a high concentration, and a bulk part where hydrogen is represented by free and trapped atomic species, H + and HB. e concentration [H + ] turns out [8] to be much smaller than [HB] or [B − ]. e shape of the C(z) profile, for a specified hydrogen concentration at the sample surface, depends [8] on a single material parameter D + K where D + is the diffusivity of H + . e value of D + K based on the reported C(z) profiles is about 6.5 × 10 4 cm −1 s −1 at 150°C being slightly different for different samples.
For one of the samples annealed at 150°C [9], also the hole profile p(z) is available along with C(z). Quite unexpectedly, fitting the p(z) profile (described in the next section) gives an essentially smaller value of D + K-about 10 4 cm −1 s −1 .
is seeming discrepancy is resolved if there are two independently diffusing hydrogen ions that we denote H + (1) and H + (2)-one of a larger D + K and the other of a smaller D + K. In the present paper, a theory of boron passivation by two independent ions H + (1) and H + (2) is considered and applied to fit some representative experimental profiles. spreading resistance profile R(z) were reported [9]. e resistance normalized by its bulk value R b is equal to the normalized specific resistivity ρ(z)/ρ b . With the known bulk resistivity ρ b , the resistivity profile ρ(z) is defined and converted into p(z) using a standard ASTM procedure. is p(z) profile is shown in Figure 1 by circles. e concentration profile C(z) for the same sample is displayed in Figure 2(a).
Since p � [B − ] − [H + ] and C � [HB] + [H + ], the two profiles p(z) and C(z) are complementary: their sum is a fixed total boron concentration N B . e profiles can be simulated [8] by solving an equation for diffusion and drift of H + accompanied by fast trapping and detrapping of H + by boron, which maintains the equilibrium relation (1) between the reacting species. e solution depends on the value of D + K and on the concentration of H + at the sample surface normalized by K; this ambient-controlled boundary parameter, [H + ]/K, is denoted X.
In Figure 1(a), the curve 1 was calculated with D + K � 8 × 10 4 cm −1 s −1 -the value deduced by fitting the concentration profile of Figure 2(a). e boundary parameter X was set to 21.2 to reproduce the penetration depth of hydrogen, 0.57 μm. Clearly, the computed curve is inconsistent with the experimental hole profile. A much better (although not quite satisfactory) fit is achieved with an essentially smaller value of D + K � 1.4 × 10 4 cm −1 s −1 and a larger X � 115 (the curve 2 in Figure 1(a)). is smaller value of D + K is however inconsistent with the shape of the C(z) profile in Figure 2(a).

A Concept of Two Kinds of H + Ions
To resolve this contradiction, we note that the information contained in the C(z) and p(z) profiles actually refers to different parts of the profiles. e C(z) bulk profile is comprised of a plateau portion (marked P in Figure 2(a)) and a tail portion (marked T). In the plateau, a small difference between C and N B cannot be accurately determined, and the informative part of the profile is only the tail. erefore, the deduced D + K parameter refers to the hydrogen ions within the tail.
For the p(z) profile, the nonpassivated boron concentration [B − ] is directly defined in the whole in-diffused region, allowing to find D + K for the H + ions within the plateau.
It can be thus concluded that there are actually two independent passivating hydrogen ions: H + (1) of a larger D + K dominating in the tail portion of the presently discussed hydrogen profile, and H + (2) of a smaller D + K dominating in the plateau part. e first one is assumed to be the abovementioned bond-centred ion H + (BC). e second one is in a different lattice location to be discussed later. Independent diffusion of these two species implies that there is a high energy barrier for transition from one state of H + to the other which prevents equilibration between them. e concentration ratio of the two species H + (1) and H + (2) at the sample surface depends on the plasma ambient, and it can have a strongly nonequilibrium value. It is thus possible that the H + (2) species is more significant under plasma exposure than under the equilibrium conditions. e hydrogen in-diffusion and resulting boron passivation should be now reconsidered taking into account simultaneous presence of two kinds of H + ions.

Boron Passivation by Two Independent In-
Diffusing H + Ions e inferred existence of two independent H + ions is most essential for a plasma-induced acceptor (boron) passivation. In this case, there are two different structural forms of passivated boron HB: the HB(1) originates from trapping H + (1), and HB(2) from trapping H + (2). A transport equation of Reference [8] is applicable to each of the two H + /HB subsystems: e subsystem index I is either 1 or 2. e concentration [HB(I)] in the left-hand part represents the total concentration for the subsystem I, neglecting a small contribution of free ions [8]. e flux J(I) in Equation (2) After that, each of the two transport equations (2) contains only one parameter, either D + (1)K(1) or D + (2)K(2). At 150°C, D + (1)K(1) is already defined to be 8 × 10 4 cm −1 s −1 while D + (2)K(2) is on the order of 10 4 cm −1 s −1 , and only a small adjustment of this parameter is required; the best-fit value was found to be D + (2)K(2) � 9.6 × 10 3 is is the only equation through which one subsystem affects the other. e diffusion problem involves two ambient-dependent boundary parameters (2). e surface value of [B − ] is expressed through these parameters from Equations (4) and (3): e best fit of the hole profile is shown by the solid curve in Figure 1 is curve reproduces the measured p(z) profile much better than the curves 1 and 2 in Figure 1(a), which are based on only one kind of H + ion.
e computed concentration profile C(z)-for the parameter set specified above-is shown by the solid curve in Figure 2(a). e reported hydrogen penetration depth [9] was a bit larger for the C(z) pro le in comparison with the p(z) pro le.
is small discrepancy may be due to some inaccuracy in a crater depth z in the SIMS technique, and it was adjusted by rescaling the experimental C(z) pro le-by multiplying all the values of z by a scaling factor 0.86. is rescaled pro le-shown in Figure 2(a) by the circles-is well consistent with the predicted pro le, the solid curve. e near-surface high-concentration region (marked S in Figure 2(a)) was modelled here as in-di usion of slow hydrogen dimers H 2C [10] produced at the surface. e concentration pro le of dimers is described by an erfc function with an apparent di usivity 3 × 10 −15 cm 2 /s, which is close to that expected for H 2C [10]. e dimeric contribution 2[H 2C ] is simply added to that resulting from indi usion and trapping of H + (1) and H + (2).
To illustrate a speci c e ect of a simultaneous transport of two H + /HB subsystems, the two components of the passivated boron, [HB(1)] and [HB (2)], are shown separately in Figure 2(b). e HB(2) dominates in the major part of the passivated region, while HB(1) dominates within the tail portion. A qualitative explanation is that the species H + (2), due to a large X (2) [H + (2)]/K(2), occupy the major part of boron traps down to some depth, while the H + (1) species, facing a low concentration of remaining B − traps, easily penetrate to a larger depth and thus control the tail part of the pro le.

Fitting Concentration Profile for Lower Doping Level
Another example of a concentration pro le with a wellresolved tail (N B 10 17 cm −3 , annealed at 150°C for 30 min [11]), is shown in Figure 3 a di usion length of H 2A dimers-moderately mobile species observed in samples saturated with hydrogen at high T and subsequently quenched [12,13]. is kind of dimers is formed by a pairing reaction H 0 (1) + H + (1) at a known rate [10]; the neutral monomer H 0 (1) is a minor but extremely fast species located in a tetrahedral interstice. However, the computed concentration [H 2A ], due to this pairing reaction, turns out to be much smaller than N B [8] and cannot account for the S-component. Now, with two independent subsystems of monomeric hydrogen, more pairing reactions can proceed involving H 0 (1) and H + (2) or HB(2) and these ones can be more e cient. e reaction H 0 (1) + HB(2) seems preferable since [HB (2) where the pairing kinetic coe cient β, for the di usionlimited reaction, is e actual value of β can be smaller, and it should be treated as a tting parameter with the upper limit given by Equation (6). All the parameters in Equation (6) were speci ed [8], and the upper limit for β is 6 × 10 12 Backward dissociation of H 2A into H 0 (1) + HB(2) proceeds by H 2A + B − + h + at a rate proportional to p 2 . It is neglected at a relatively low temperature of 150°C and a moderate hole concentration.
To reproduce the C(z) pro le in Figure 3(a), we use for D + (2)K(2) the previously deduced value, 9.6 × 10 3 cm −1 s −1 . e parameter D + (1)K(1) was a bit reduced, down to 5 × 10 4 cm −1 s −1 , for a better reproduction of the tail. e di usivity D 2A of H 2A dimer is known [10,14,15] to be 2 × 10 −13 cm 2 /s at 150°C (for the deuterium isotope). e remaining parameters are the two boundary ratios X(1) and X (2), and the pairing coe cient β; their tted values are X(1) 10.3, X(2) 21.7 and β 4 × 10 12 cm −3 s −1 . e latter value is only slightly smaller than the upper limit of 6 × 10 12 cm −3 s −1 . e corresponding best-t pro le is shown by the solid curve in Figure 3 For illustration, also the individual pro les of HB(1) and HB(2) are displayed in Figure 3 from Reference [16], is shown in Figure 4(a). is pro le has quite a similar shape but the width of the S-component corresponds to a smaller di usivity D 2A , and the tail is relatively steep corresponding to a smaller D + (1)K(1). is is understood if, in spite of the same nominal temperature for the pro les of Figures 3(a) and 4(a), the actual temperature is somewhat lower (roughly, by 15°C) for the latter case. To t the tail of the pro le of Figure 4

In-Diffusion Profiles in Lightly Doped n-Si
In lightly doped n-Si, the observed concentration pro les C(z) include a near-surface component (labelled S) and a bulk component (labelled B). Two representative examples [3,17] are shown in Figure 5. e pro le is insensitive to variations in the electron concentration suggesting that it is formed by neutral hydrogen species while H + is not now essential. Each component is well described as resulting from pairing of some in-di using species of a di usivity D at a rate where c(z) is a steady-state depth pro le of the in-di using species and r is the capture (pairing) radius. With a variable S Dc used instead of c, the depth pro le obeys a simple equation: e solution of Equation (9) depends on one material parameter D/r and one boundary parameter S 0 -a surface value of S(z): e characteristic penetration depth L equals [(D/r)/(4πS 0 /3)] 1/2 . e total hydrogen concentration C(z) is mostly due to produced pairs of in-di using defects (while a contribution c of the source species themselves is negligible [8]). e diffusion of produced pairs is neglected on the time and depth scales of the pro les; then, With the deduced shape parameters L and G 0 , the ratio D/r is calculated as (4π/9)G 0 L 4 .
For the S-component, the deduced ratio D/r [8] is close to the value expected for a hydrogen species responsible for a slow stage of tritium loss at 400 to 500°C [18]-from samples saturated with the tritium isotope at high T and quenched. e di usivity of this mysterious species is much higher than D 2A but much smaller than the known atomic hydrogen di usivity [19], and this species was tentatively identi ed [10] as a "fast dimer" H 2B . Accordingly, the S-component was attributed to H 2B pairing into tetramers. An alternative treatment is possible, but it will not be discussed in the present paper. Regarding the B-component, there were two di culties [8]: (1) e value of D/r for this component was orders of magnitude smaller than the value of D/r for the neutral tetrahedral monomer H 0 (1). (2) e deduced values of D/r were strongly di erent for two close temperatures: 150°C (Figure 4(a), D/r 0.8 cm/s) and 125°C (Figure 4(b), D/r 0.015 cm/s). A huge di erence-by a factor of 53-is too large for any reasonable temperature dependence of D/r. Now, a concept of two di erent atomic subsystems o ers a simple solution to these puzzles if we assume that H + (2) is a part of a subsystem H(2) that includes also a neutral species H 0 (2), dominating in intrinsic and n-type Si (which implies that the donor level of H(2) is below the midgap). e B-component can be then ascribed to dimers produced by interpairing H 0 (1) + H 0 (2) or self-pairing H 0 (2) + H 0 (2).
ere are two extreme cases: Case 1. e equilibration time between H 0 (1) and H 0 (2) is shorter than the anneal duration. en, the two species coexist in the equilibrium ratio and di use together, as one species of an apparent di usivity D a averaged over the two species: where R 21 is the equilibrium concentration ratio of H 0 (2) and H 0 (1). In the D/r ratio deduced from the shape of the B-component, the apparent di usivity D is equal to D a . We assume that this situation is valid at a higher T 150°C-for the pro le of Figure 5(a). With a di usion-limited capture radius, r 0.5 nm, the di usivity D a 4 × 10 −8 cm 2 /s. e di usivity of atomic hydrogen [19] extrapolated down to 150°C is 1.4 × 10 −8 cm 2 /s (for the deuterium isotope). is di usivity is averaged over all the atomic species present in intrinsic Si, including the major one, H + (1), and therefore it is smaller than D a (which is averaged only over the neutral states). Yet, the di erence between the two di usivities is not very large showing that H 0 (2) in intrinsic Si gives a small but signi cant contribution to the total concentration.

Case 2.
e equilibration time is longer than the anneal duration. en, the two species di use independent of each other. If, in addition, the concentration of H 0 (1) is so small that interpairing can be neglected in comparison with self-pairing of H 0 (2), then the apparent di usivity D will be identical to D 0 (2). is situation may hold at a lower temperature of 125°C. Assuming again a di usion-limited capture radius, r 0.5 nm, we specify the di usivity of the neutral H 0 (2) species at 125°C: D 0 (2) 7.5 × 10 −10 cm 2 /s. If a representative di usivity prefactor, 0.01 cm 2 /s is further adopted, the migration energy of H 0 (2) is estimated to be 0.56 eV. e D 0 (2) di usivity extrapolated from 125°C to 150°C is then 2 × 10 −9 cm 2 /s-much smaller than the averaged di usivity D a deduced above to be 4 × 10 −8 cm 2 /s. By Equation (12), it is concluded that the hydrogen transport at 150°C is mostly due to H 0 (1), while the total concentration of the neutral species is mostly due to H 0 (2). e expression (12) is then simpli ed to D a D 0 (1)/R 21 .
A huge di erence between the apparent di usivities D at 125 and 150°C is now attributed to a di erent meaning of the apparent di usivity D for these two cases: a relatively low di usivity D 0 (2) at a lower T, and a much higher average di usivity D a (enhanced by a contribution of fast H 0 (1) species) at a higher T.

Summary
Penetration of H + hydrogen ions from a plasma ambient into a boron-doped sample is limited by their trapping by boron into HB neutral defects. It is controlled by the surface concentration of H + and by a single material parameter D + K-a product of the H + di usivity D + and the equilibrium dissociation constant K of the HB defects. Under an assumption of only one kind of H + , of a de nite value of D + K, it is impossible to reproduce simultaneously the hydrogen concentration pro le C(z) and the hole pro le p(z) measured for the same sample at 150°C: the former can be well tted only with a relatively large D + K while the latter can be roughly fitted only with a much smaller D + K. is difficulty is overcome by assuming two different kinds of H + ions, H + (1) and H + (2), one of a larger D + K and the other of a smaller D + K. ey in-diffuse-without an exchange between them-and get trapped by B − into two different kinds of passivated boron, HB(1) and HB (2). A transport of each species is affected by the presence of the other species through the hole concentration that depends on the total amount of passivated boron, [HB(1)] + [HB (2)]. e deduced D + K at 150°C is about 6 × 10 4 cm −1 s −1 for H + (1) and close to 10 4 cm −1 s −1 for H + (2). Relative contributions of the two species depend on their concentrations at the sample surface controlled by a composition of the ambient (hydrogen plasma). In one example, H + (2) was found to be the major passivating species down to some depth, leaving a low concentration of nonoccupied boron traps. In that case, H + (1) easily diffuse through the passivated region and control the hydrogen concentration within a tail of the profile.
In another example (at a lower doping level), the H + (2) ions are spent on formation of hydrogen dimers and do not penetrate deep; the sample bulk is then dominated by the species of the first kind.
It is assumed that H + (1) is an ion in the bond-centred position that is dominant under the equilibrium conditions in intrinsic Si. is one is equilibrated with a minor but highly mobile neutral species H 0 (1) in the tetrahedral location. Also, the H + (2) species seems to be present along with a neutral state H 0 (2), of a much higher concentration than H 0 (1). In the early stage of discussing the hydrogen properties in Si, it was argued that, due to its small size, a hydrogen atom should occupy a tetrahedral interstice remaining neutral. Now, we revive this notion assuming that the H 0 (1) is actually an excited state of the neutral tetrahedral hydrogen while the ground state corresponds to H 0 (2). ere should be a high energy barrier for transition between these two states, which retards an exchange between them. e reported hydrogen profiles in lightly doped n-Si for 125 and 150°C suggest that the exchange is negligible at 125°C but relatively fast at 150°C. e hydrogen profiles normally include a near-surface part of a very high concentration. is "S-component" of a profile cannot be ascribed to the unique reason; it is specific for particular samples: (i) In near-intrinsic Si, the S-component is clearly caused by self-pairing of some in-diffusing neutral species different from H 0 (1) and H 0 (2)-presumably the fast hydrogen dimer H 2B . e true nature of this species is still to be established. (ii) In samples moderately doped with boron, the S-component (relatively wide) can be attributed to formation of moderately mobile dimers H 2A by interpairing reaction H 0 (1) + HB(2). (iii) In heavily doped samples, the S-component is seemingly due to slow dimers H 2C that are formed at the surface (or close to the surface) and in-diffuse into the bulk.

Conflicts of Interest
e authors declare that they have no conflicts of interest.