Germany. Keywords: silicon, boron, oxygen, lifetime degradation

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1 Solid State Phenomena Vols (211) pp Online available since 211/Aug/16 at (211) Trans Tech Publications, Switzerland doi:1.428/ The Nature of Lifetime-Degrading Boron-Oxygen Centres Revealed by Comparison of p-type and n-type Silicon V.V.Voronkov 1a, R.Falster 1b, K.Bothe 2c, B.Lim 2d, J.Schmidt 2e 1 MEMC Electronic Materials, via Nazionale 59, 3912 Merano, Italy 2 Institute for Solar Energy Research Hameln (ISFH), Am Ohrberg 1, D-3186 Emmerthal, Germany a vvoronkov@memc.it, b rfalster@memc.it, c k.bothe@isfh.de, d lim@isfh.de, e j.schmidt@isfh.de Keywords: silicon, boron, oxygen, lifetime degradation Abstract. Illumination-induced degradation of minority carrier lifetime was studied in n-type Czochralski silicon co-doped with phosphorus and boron. The recombination centre that emerges is found to be identical to the fast-stage centre (FRC) known for p-si where it is produced at a rate proportional to the squared hole concentration, p 2. Since holes in n-si are excess carriers of a relatively low concentration, the time scale of FRC generation in n-si is increased by several orders of magnitude. The generation kinetics is non-linear, due to the dependence of p on the concentration of FRC and this non-linearity is well reproduced by simulations. The injection level dependence of the lifetime shows that FRC exists in 3 charge states (-1,, +1) possessing 2 energy levels. The recombination is controlled by both levels. The proper identification of FRC is a B s O 2 complex of a substitutional boron and an oxygen dimer. The nature of the major lifetime-degrading centre in n-si is thus different from that in p-si - where the dominant one (a slow-stage centre, SRC) was found to be B i O 2 a complex involving an interstitial boron. Introduction The minority carrier lifetime in boron- and oxygen- containing silicon is long known to degrade under illumination [1-3] an effect that is of a primary importance for solar cells. In Czochralskigrown p-si there are two kinds of degrading recombination centres [3] labelled FRC and SRC. They correspond to fast and slow stages of degradation, respectively. The major centre is SRC while FRC can be detected only after a short-time illumination. The saturated concentration of both centres was found [3] to be proportional to the boron concentration N B and to the squared oxygen concentration C ox 2. This led initially to the identification of both centres as a B s O 2 complex of a substitutional boron atom B s and an oxygen dimer O 2 [4]. Subsequent experiments with p-si co-doped with boron and phosphorus found [5-7] the concentration of SRC to be proportional not to N B but rather to the hole concentration p. This feature is consistent with the identification of SRC as a B i O 2 complex [8] that involves an interstitial boron atom B i rather than B s. This complex exists initially in a grown-in latent form of a low recombination activity. In the presence of excess electrons, it is recharged from +1 into the neutral state and then reconstructs into the recombination-active configuration, SRC. The nature of the other centre, FRC, remained however unclear. Recently [6, 9] lifetime degradation was observed in n-si co-doped with phosphorus and boron. In the present study more data on the lifetime degradation in compensated n-si are presented and used to identify the nature of FRC which is found to be the major lifetime-degrading centre in n-si. Experimental Samples were cut from a co-doped silicon crystal. The initial concentration in the melt was 6x1 16 cm -3 for boron and 9x1 16 cm -3 for phosphorus. The oxygen concentration C ox varied in a range (1 to 8) x1 17 cm -3 from seed to tail. The boron segregation coefficient (about.9) is so close to 1 that the boron concentration in the crystal is almost constant (excepting the very tail end), and equal to N B = 5.4x1 16 cm -3. The phosphorus concentration N P on the other hand increases along the crystal length. A small initial portion of the crystal is p-type, while the major portion is n-type, with All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, (ID: /8/11,1:53:12)

2 14 Gettering and Defect Engineering in Semiconductor Technology XIV a gradually increasing net doping n = N P N B and accordingly decreasing resistivity. The electron mobility µ n - controlled by the total concentration of charged scatterers, N = N P + N B = n + 2 N B is deduced as a function of N using the ASTM concentration-resistivity conversion curve for phosphorus-doped material. The resistivity of compensated material, ρ = 1 / [q µ n (N) n] where q is the electronic charge, is calculated as a function of n and N B. In this way a calibration curve n(ρ, N B ) is obtained. It is shown in Fig.1 for two values of N B : 5.4x1 16 and 7x1 16 cm -3 ; the former is expected near the seed end, the latter near the tail end. A remarkably weak sensitivity of the calibration curve to the assumed value of N B allows for a reliable conversion of measured ρ into n, independent of a sample location within the crystal. The samples, 15 micron thick, were passivated by a plasma-enhanced chemical vapour deposited silicon nitride to suppress surface recombination. They were illuminated by a halogen lamp for up to 2 weeks at a power density of P = 1 mw/cm 2, and sometimes at 4 mw/cm 2. The sample temperature, controlled by natural cooling, was about 3 o C and 5 o C, respectively. The illumination was occasionally interrupted to measure the hole lifetime τ p by photoconductivity decay at room temperature (RT). A short illumination pulse creates a high hole concentration p (~1 16 cm -3 ) that subsequently decays and p is monitored as a function of time. The reciprocal lifetime, 1/τ p = (-dp/dt) / p, is thus obtained in a wide range of p, down to about 1 12 cm -3. The electron concentration n is incremented by illumination. From now on, the dark value of n will be denoted n while the actual value is n = n + p. A lifetime value used to monitor the degradation corresponds to a standard injection level, p/n =.1. Results and discussion n, cm resistivity, Ohm.cm Fig.1 Electron concentration in dependence of the resistivity of compensated n-si at a specified boron concentration. Curve 1: N B = 5.4x1 16 cm -3 (seedend), curve 2: N B = 7x1 16 cm -3 (tail-end). An example of the evolution of the reciprocal lifetime of holes is shown in Fig.2 for a sample of ρ=.29 Ohm-cm (n = 3.3x1 16 cm -3 ) illuminated at 1 and 4 mw/cm 2 (the curves 1 and 2, respectively). Similar curves - discussed later - were found for other samples. The features of the generation curves in Fig.2 are though already sufficient to draw important conclusions about the lifetime-degrading centres in n-si, as discussed below. Comparison of lifetime-degrading centres in n-si and p-si. From previous studies [3, 5], the rate constant for generation of both SRC and FRC in p-si is concluded to be proportional to p 2. This dependence for SRC can be accounted for by assuming that a reconstruction from the neutral latent configuration into SRC proceeds through an intermediate +2 state involving the capture of two holes [8]. The rate equation for the concentration M of activated centres (either FRC or SRC) reads dm/dt = g (p/1 16 cm -3 ) 2 (M sat M), (1)

3 Solid State Phenomena Vols where M sat is the saturated value. The rate coefficient g was reported [3] to be about 3 h -1 for FRC, and.3 h -1 for SRC, at RT. Eq.(1) is linear at a low injection level. The exponential rise in M(t), from to M sat, has a distinct time scale in p-si. It is about 1 s for FRC and 3 h for SRC (for a typical doping level, p = 1 16 cm -3 ). The same equation (1), if applied now to n-si, becomes non-linear because holes are now excess carriers and p depends on the concentration M of already produced recombination centres. At P = 1 mw/cm 2, p starts at about 5x1 14 cm -3 and decreases down to 5x1 13 cm -3 upon accumulation of the recombination centres. The time scale of defect generation for both FRC and SRC is thus increased compared to p-si, by a factor ranging from 4x1 2 to 4x1 4 depending on the duration. The degradation process is extended over a long period of time as is indeed evident from the experimental data of Fig.2. At an increased light power (curve 2 in Fig.2), p 1/τp, 1/ms is increased and the degradation is accordingly accelerated. The expected time scale for SRC generation in n-si is extremely long. It is 1 h at the initial value of p but actually is much longer since p is already reduced after 1 h increasing the time scale up to 1 5 h. SRC is therefore not produced at all in n-si within the illumination times (less than 1 3 h) of the present experiments even if the latent B i O 2 defect exists in n-si. On the other hand, the expected time scale of FRC generation of about.3 to 3 h at P = 1 mw/cm 2, is consistent with the data shown in Fig.2 (curve 1). More than that, the numerical solution of Eq.(1) (discussed below), using the value of g known for FRC from p-si, provides a good fit to the data as shown by the solid lines in Fig.2. In conclusion, the observed lifetime degradation in n-si is entirely due to FRC. This provides a nice opportunity to investigate the properties of FRC and to judge the nature of this recombination centre. Injection level dependence of the FRC-controlled lifetime. The reciprocal lifetime 1/τ p is composed of the contribution of FRC (1/τ pf ) and a contribution of background recombination centres (1/τ p ). The latter (assumed to be unchanged by illumination) is measured before the degradation run. The FRC-controlled lifetime, τ pf, is expressed as 1/(1/τ p - 1/τ p ). Both τ p and τ p are known in dependence of the injection level; the resulting value of τ pf is plotted in Fig.3 as a function of the p/n ratio for several samples of different electron concentration n (different resistivity). A similar plot for FRC in p-si is much simpler: it is a straight line (Fig.4) corresponding to recombination at a single deep recombination level. In this case, the well known Shockley-Read expression [1, 11] is simplified to: 1/τ nf = (α n M) / [1 + (α n /α p )(n/p)], (2) illumination time, h Fig.2 Variation of the reciprocal lifetime of holes in the course of illumination at two different light powers. Curve 1: 1 mw/cm 2, curve 2: 4 mw/cm 2. The resistivity of both n-si samples is close to.29 Ohm.cm.

4 142 Gettering and Defect Engineering in Semiconductor Technology XIV where α n and α p are the capture coefficients of an electron and a hole at the recombination level (a capture coefficient is the product of a capture cross section and the thermal velocity). The capture ratio deduced from Fig.4 is α n /α p = 65. This large value implies that electrons are captured by an attractive (positive) centre. In other words, the recombination level is a donor level (+1/). It is now convenient to use notations that show explicitly the charge state of a centre that captures a carrier: α n will be replaced with α + n, and α p with α p. A large capture ratio for the donor level, Q d = α + n /α p = 65, leads to a strongly pronounced increasing dependence of τ nf on n/p. In n-si such a one-level expression is not applicable. Fig.3 shows that τ pf is not a linear function of p/n and that the type of the dependence is different for samples of various n. A strong injection level dependence for the highest n (curve 1 in Fig.3) suggests that the holes are captured by attractive (negative) centre. A fit presented below leads to a capture ratio for holes and electrons α - p /α n 86. There are thus three charge states of FRC (-1,, +1) and accordingly two energy levels of this defect: a donor level (+1/) operating in p-si and an acceptor level (-1/) manifested in n-si. The non-linear curves of Fig.3 can be explained by recombination at a two-level centre when both acceptor and donor levels are essential. The recombination rate at a two-level centre is obtained in a way similar to [1, 11] using the quasi-steady state balance equations for the concentrations m -, m and m + of different charge states of the defect (with m + + m + m - = M): τpf, ms p /n Fig.3 Injection level dependence of the electron lifetime due to FRC for n-si samples of various electron concentration. 1: n = 3.3x1 16 cm -3 (ρ =.29 Ohm.cm), 2: n = 1.5x1 16 cm -3 (ρ =.9 Ohm.cm), 3: n = 1.85x1 15 cm -3 (ρ = 4.9 Ohm.cm). τnf, ms n /p Fig.4 Injection level dependence of the electron lifetime due to FRC in p-si, plotted by the data of ref.[3]. dm + /dt = - α n + n m + + α p p m =, (3) dm - /dt = - α p - (p m - - p a m ) + α n (n m n a m - ) =. (4) Eq.(4), for the acceptor level, includes thermal emission of holes and electrons (by and -1 states, respectively). The emission is described through the parameters p a and n a that have the meaning of carrier concentrations in the dark with the Fermi level coincident with the acceptor level [12].

5 Solid State Phenomena Vols Thermal emission is important only if the level is sufficiently close to either the conduction band or to the valence band. In Eq.(3) for the donor level, the thermal emission is neglected since this level is deep [3] somewhere above the mid-gap. It is now assumed that the acceptor level of FRC lies in the lower half of the gap (which means that FRC is a so called negative-u centre); n a in Eq.(4) can thus be neglected. This assumption allows for a good fit of the data shown in Fig.3. The recombination rate G is the flux of electrons to the centre, α n + nm + + α n nm (or equivalently, the net flux of holes, α p - (pm - - p a m ) + α p pm ). The resulting expression for G (the same for p-si and n-si) is: G = α n + α p - M n p (α n n + α p p) / [α n + α n n 2 + α p - α p p 2 + α n + α p - np + α p - α n + np a ]. (5) In case of n-si, the reciprocal hole lifetime is defined as G / p: 1/τ pf = (α p - M) (1 + y Q ) / [1 + y Q a (1 + y / Q d ) + Q a p a /n], (6) where y = p/n. Eq.(6) contains 3 capture ratios: Q a = α p - /α n (for the acceptor level), Q d = α n + /α p (for the donor level) and Q = α p /α n (for the neutral state of FRC). Since Q d is large, and y < 1, the term y / Q d in Eq.(6) will be neglected. The experimental curves τ p (y) for the samples shown in Fig.3 as well as for many other samples - are well reproduced by Eq.(6) with Q a = 86, Q = 7.4 and p a = 2.2x1 14 cm -3. The combination α p - M, is fitted individually for each sample. The deduced value of p a allows for locating the acceptor level position at.28 ev above the valence band. The uncertainty, caused by an unknown degeneracy factor [12], is about ±.3 ev. The thermal emission of holes by the neutral state (represented by p a ) plays an important role: without this term, the function τ pf (y) would be the same for all the samples. But this is not the case. The degree of the injection level dependence is characterised by the ratio of two values of τ pf : one at y 1 and the other at y. This ratio is equal to (1 + Q a ) / [(1 + Q ) (1 + Q a p a /n )] by Eq.(6). It is large at a high electron concentration n and corresponds to a pronounced increase in τ p (y) (the curve 1 in Fig.3). The lifetime ratio becomes 1 at n = p a (1 + Q ) / (1 Q /Q a ) = 2x1 15 cm -3 at which point there is no dependence on p/n. At still smaller n the injection level dependence of τ p would be decreasing. Indeed, for a sample of the lowest n = 1.85x1 15 cm -3 (the curve 3 in Fig.3) there is a slight decrease in τ pf upon increasing the injection level. In case of p-si, the reciprocal electron lifetime, G / n, is expressed from Eq.(5) through the same parameters: 1/τ nf = (α n + M) (1 + x / Q ) / [1 + x Q d (1 + x / Q a ) + p a /p], (7) where x = n/p. The capture ratios Q a and Q deduced above from the data on n-si - are large, and x < 1, p a << p for p-si. Eq.(7) is then simplified and becomes equivalent to Eq.(2). In other words, the recombination at the two-level FRC centre in p-si is controlled by only the donor level. The main reason for this simplification is a small capture ratio α n /α p = 1 / Q. The capture of electrons by the recharged centre (FRC ) can accordingly be neglected in comparison to capturing by FRC +. Simulation of the degradation kinetics in n-si. The generation (activation) of FRC is described by the same kinetic equation (1) for both p-si and n-si. The process is a reconstruction, from a latent configuration (denoted LCF) into FRC. A detailed reconfiguration model is to be presented elsewhere. A central point of the model is that the reconstruction proceeds not directly from LCF to FRC but through an intermediate (transient) configuration TCF. The forward flux LCF TCF is proportional to p 2. A peculiarity of n-si is that at very low p a backward transition, TCF LCF, also becomes important. Thus the net transition rate includes an additional factor:

6 144 Gettering and Defect Engineering in Semiconductor Technology XIV f = p / (p + a), (8) The parameter a is to be fitted. The kinetic equation (1) is modified by including the factor f. The actual quantity that controls the lifetime is the product Y = α p - M, and the kinetic equation for Y(t) reads dy/dt = f g (p/1 16 cm -3 ) 2 (Y sat Y), (9) To solve this non-linear equation for the effective FRC concentration, Y(t), the hole concentration p should be expressed through Y by the balance equation of production and recombination of electron-hole pairs: J / d = G = p / τ p = p (1/ τ p + 1/τ pf ), (1) where J is the number of pairs produced per unit area and time, and d is the sample thickness. Light is absorbed within a narrow near-surface layer, but the carriers are quickly spread by diffusion over the sample depth. For d = 15 µm, the homogenization time by diffusion, (d/π) 2 /D h, where D h is the hole diffusivity, is about 2 µs and much shorter than the lifetime. The number of pairs produced per unit volume is J/d. To use the Eq.(1), the scaling ratio S = J/P between the carrier production rate J and the light power density P should be specified. J is approximately equal to P divided by the average photon energy, leading to S 2.5x1 15 (assuming that J is in cm -2 s -1 and P is in mw/cm 2 ). The factor S should be tuned individually for every illumination run since the actual value of P may deviate somewhat from the nominal value of 1 or 4 mw/cm 2. The tuned value of S was found to be 1/τp, 1/ms illumination time, h Fig.5 Variation of the reciprocal lifetime of holes for illumination at 1 mw/cm 2, for two n-si samples. Curve 1:.65 Ohm.cm (n = 1.4x1 16 cm -3 ), curve 2: 1.5 Ohm.cm (n = 8.9x1 15 cm -3 ). scattered within ±2% around the above-mentioned seed value. Both τ p and τ pf in Eq,(1) depend on p. For τ p this dependence is relatively weak and it was taken from the experiment. For τ pf, the analytical expression (6) was used with the best-fit parameters listed above. The rate constant g in Eq.(9) was fixed at a value known [3] for FRC in p-si: 4 h -1 at 3 o C (at 1 mw/cm 2 ) and 65 h -1 at 5 o C (at 4 mw/cm 2 ). The fitting of the degradation curves, of the type shown in Fig.2, consists only in a slight tuning of the scaling ratio S and in a proper choice of the parameter a in Eq.(8). The best fit is achieved at a 2x1 14 cm -3. With this value, the factor f is close to 1 at the beginning of the illumination. It is reduced to about.3 by the end of the run. The additional factor f is therefore not of a crucial importance but it helps to improve the fit quality. The calculated curves are shown in Fig.2 by the solid lines. Similarly calculated curves for other samples, of smaller n, also provide a good (although not ideal) reproduction of the data as illustrated in Fig.5 The only exception is the sample of the lowest n = 1.85x1 15 cm -3 (not shown), where a discrepancy between the computed and experimental curves is significant. A possible reason may be a very strong compensation of phosphorus by boron for this sample (n is much

7 Solid State Phenomena Vols smaller than N P ) which may lead to a strong non-uniformity. Even still, the data for this sample can be well reproduced by a more sophisticated model, in which LCF exists in two different configurations, both of which transform into the same FRC configuration, but at a different rate. This advanced model (to be described in more detail elsewhere) leads also to a better reproduction of the data for the other samples. The nature of FRC. The FRC concentration in p-si can be characterized simply by 1/τ nf at a fixed injection level. In n-si, however, this cannot be done since the hole lifetime depends also on n. A proper way is to use the above-mentioned quantity Y = α p - M, expressed by Eq.(6) through τ pf and n. The saturated value, Y sat = α p - M sat is shown in Fig.6 for samples of different n. FRC, unlike SRC, is not a B i O 2 defect. Indeed, the grown-in concentration of B i O 2 is proportional to p in p-si which comes from a single-positive charge of B i [8]. This concentration becomes negligible in intrinsic material. In n-si the charge state of B i changes to -1 [13], and the B i O 2 concentration increases in proportion to n. The FRC concentration shown in Fig.6 does not however increase in this way. An alternative attribution of FRC to B s O 2, is on the other hand quite consistent with the data of Fig.6. First, the boron concentration N B is almost the same for all the samples, and the grown-in concentration of B s O 2 (in its latent form) decreases along the crystal (and hence with increasing n ) due to a reduction in C ox. To take this effect into account, Y sat was corrected multiplied by [C ox ()/C ox ] 2 where C ox () refers to the seed end. The corrected Y sat, 1/ms Fig.6 Saturated effective concentration of FRC in n- Si (open circles) in dependence of the electron concentration. The values corrected for an oxygen variation are shown by filled rhombs. values (filled rhombs in Fig.6) show no systematic dependence on n. Second, the absolute value of Y sat in Fig.6 can be predicted using the known data for the saturated FRC-controlled lifetime in p-si - where the effective FRC concentration, X = α + n M, is expressed through τ nf by Eq.(2). The saturated concentration, X sat, is proportional to N B and C 2 ox in boron-only doped Si [3]: X sat = α n + M sat = (28 ms -1 ) (N B /1 16 cm -3 ) (C ox /1 18 cm -3 ) 2. (11) If FRC is B s O 2, then the saturated concentration in n-si, Y sat = α p - M sat, is given by the right-hand part of Eq.(11) multiplied by the rescaling ratio α p - /α n +. This ratio is expressed through the already known parameters as Q a / (Q Q d ) =.18. The prefactor 28 ms -1 for X sat in p-si is then replaced with 5 ms -1 for Y sat in n-si. With N B = 5.4x1 16 cm -3 and C ox = 1 18 cm -3, the predicted Y sat is 27 ms -1. This value is not very different from the experimental values of Fig.6. This supports strongly identification of FRC as a B s O 2 complex n, cm -3

8 146 Gettering and Defect Engineering in Semiconductor Technology XIV Summary Comparison of lifetime degradation in boron-containing p-si and n-si Czochralski samples has revealed a striking difference between these two materials. In p-si two kinds of lifetime-degrading centres are known to emerge during illumination: FRC (found after a short illumination) and SRC (dominant during subsequent illumination). The major centre, SRC, was identified as a B i O 2 complex involving an interstitial boron atom B i. In n-si only FRC is generated within the actual illumination time since the time scale for production of both centres is greatly increased (due to a lower hole concentration) and becomes enormously long for SRC. The injection level dependence of the lifetime shows that FRC exists in 3 charge states and possesses 2 energy levels, a donor one and an acceptor one. Both levels contribute into recombination in n-si, but only the donor level is essential in p-si. The accumulation kinetics of FRC in the course of illumination of n-si samples is well reproduced by simulations, taking into account that the hole concentration depends on the current FRC concentration. The saturated FRC concentration in n-si was found to be independent of the electron concentration, and well predicted by the data for p-si assuming that FRC is a B s O 2 complex involving a substitutional boron atom B s. In conclusion, the major lifetime-degrading centre is B i O 2 (SRC) in p-si but B s O 2 (FRC) in compensated n-si. References [1] H. Fischer and W. Pschunder, Proc. 1-th IEEE Photovoltaic Specialists Conference (IEEE N.Y. 1973), p.44. [2] S. W. Glunz, S. Rein, J. Y. Lee, and W. Warta, J. Appl. Phys. 9, 2397 (21). [3] K. Bothe, and J. Schmidt, J. Appl. Physics 99, 1371 (26). [4] J. Schmidt and K. Bothe, Phys. Rev. B 69, 2417 (24). [5] D. Macdonald, F. Rougieux, A. Cuevas, B. Lim, J. Schmidt, M. Di Sabatino, and L. J. Geerligs, J. Appl. Phys. 15, 9374 (29). [6] B. Lim, F. Rougieux, D. Macdonald, K. Bothe and J. Schmidt, J.Appl. Phys. 18, (21) [7] J. Geilker, W. Kwapil, and S. Rein, J. Appl. Phys. 19, (211). [8] V. V. Voronkov, and R. Falster, J. Appl. Phys. 17, 5359 (21). [9] T. Schulz-Kuchly, J. Veirman, S. Dubois and D. R. Heslinga, Appl. Phys. Letters 96, 9355 (21). [1] W. Shockley and W. T. Read, Phys. Rev. 87, 835 (1952). [11] R. N. Hall, Phys. Rev. 87, 387 (1952). [12] J. S. Blackmore, Semiconductor Statistics, Pergamon, N.Y. (1962). [13] R. D. Harris, J. L. Newton and G. D. Watkins, Phys. Rev. B 36, 194 (1987).

9 Gettering and Defect Engineering in Semiconductor Technology XIV doi:1.428/ The Nature of Lifetime-Degrading Boron-Oxygen Centres Revealed by Comparison of P-Type and N-Type Silicon doi:1.428/

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