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Cathodoluminescence assessment of annealed silicon and a novel technique for estimating minority carrier lifetime in silicon
Materials Science and Engineering B 159–160 (2009) 194–197
Contents lists available at ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
Short communication
Cathodoluminescence assessment of annealed silicon and a novel technique for estimating minority carrier lifetime in silicon K.J. Fraser a , R.J. Falster b , P.R. Wilshaw a,∗ a b
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK MEMC Electronic Materials SpA, viale Gherzi 31, 28100 Novara, Italy
a r t i c l e
i n f o
Article history: Received 9 May 2008 Accepted 13 May 2008 Keywords: Doping effects Electron microscopy Optical properties Semiconductors Silicon Solar cells
a b s t r a c t The effect of low-temperature anneals (≤500 ◦ C) on Cz–Si minority carrier lifetime has been investigated using near-band-edge cathodoluminescence (CL). The low-temperature anneals are intended to produce efficient gettering by taking advantage of the increasing supersaturation of impurities as temperatures are reduced. It is found that the anneals affect the CL efficiency through several different mechanisms and that annealing under “dirty” conditions does not introduce significant amounts of electrically active impurities into the material. In order to aid the interpretation of experimental results, modelling of the effect of different sample parameters on CL is carried out. Using this theoretical work, an experimental method of measuring minority carrier lifetime using CL which is independent of surface recombination is developed. © 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
It has been shown using luminescence measurements [1–6] that high temperature (≥900 ◦ C) annealing of electronic grade Si samples containing ion implantation damage can induce significant gettering of Shockley–Read–Hall (SRH) recombination centres such as transition metal impurities. We report on new experiments investigating the effects of lower temperature anneals (500 ◦ C and below) on samples containing mechanically introduced dislocations. As annealing temperatures are reduced, the increased supersaturation of transition metal impurities increases the driving force for gettering so that, at least in principle, cleaner material can be produced. However, annealing at lower temperature results in reduced diffusivity, requiring longer anneals. It is hoped that, after testing on single-crystal Si, this technique will be applied to multicrystalline solar cell material, which contains higher concentrations of impurities and for which improved gettering may have a beneficial effect. Such long duration anneals would be very expensive to carry out under clean room conditions; however, at such low temperatures in-diffusion of surface contaminants should also be reduced, allowing the anneals to be carried out in dirty, but cheap, conditions.
Specimens were prepared from (1 0 0) n-type Cz-wafers with a wide variety of doping concentrations (∼1014 –1019 cm−3 ). Anneals were carried out at 500 ◦ C for 20–24 h in air, followed by slow cooling to 200 ◦ C and annealing for a further ∼120 h. This process will subsequently be termed ‘low-temperature annealing’ and was carried out in a standard metallurgical furnace. Selected samples were scratched on the back (unpolished) surface using SiC paper to introduce dislocations as potential gettering sites. Specimens were cleaned before and/or after heat treatment using laboratory grade chemicals. In many cases, HF etching was used to remove surface oxide in order to standardize the surface state prior to cathodoluminescence (CL) examination. Luminescence efficiency was measured using a Gatan MonoCL3 system and a liquid-nitrogen cooled North Coast E0-817L Ge photodiode attached to a JEOL 6500F scanning electron microscope. Experiments were carried out at room temperature using an accelerating voltage of 30 kV.
∗ Corresponding author. Tel.: +44 1865 273736. E-mail address: [email protected] (P.R. Wilshaw). 0921-5107/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2008.05.006
3. Results To test the hypothesis that low-temperature annealing in relatively dirty conditions is satisfactory, samples were prepared with intentional surface contamination. This was accomplished by scratching a high-purity Fe, Cu or Ni wire over the front surfaces of different samples prior to annealing. Fig. 1 shows values of CL peak height obtained from contaminated samples, compared with an as-received sample and a control specimen annealed at the same
K.J. Fraser et al. / Materials Science and Engineering B 159–160 (2009) 194–197
Fig. 1. CL band-to-band peak height measured from intentionally contaminated specimens compared with uncontaminated and as-received specimens, all HF etched before examination. Accelerating voltage = 30 kV and probe current = 150 nA.
time without contamination. All samples were HF etched before examination. It can be seen that the efficiencies of all the annealed specimens are very similar, indicating that at the temperatures used, intentional contamination of the surface before annealing does not result in any significant reduction in luminescence efficiency due to in-diffusion of metal atoms. Indeed, the annealed specimens show enhanced luminescence; this effect is discussed further below. Fig. 2 shows band-to-band CL efficiency as a function of doping concentration for as-received and low-temperature annealed samples. Samples with doping above 1017 cm−3 show no significant improvement in CL efficiency after annealing. Lower-doped samples show an increase in CL efficiency of up to a factor of 10 after annealing. However, as shown in Fig. 3, this increase is reduced to around a factor of 2 after HF etching. Note that no significant difference was observed between as-received samples before and after HF etching. The effect of HF etching can be understood in terms of the acid removing surface oxide produced during annealing. This oxide electrically passivates the surface, reducing the proportion of generated carriers which recombine non-radiatively at the sample’s front surface, thus increasing the luminescence observed. However, the fact that after oxide removal, annealed specimens still show greater luminescence than as-received ones indicates that the bulk radiative efficiency has increased. It is tempting to ascribe this increase to the gettering of non-radiative recombination centres, and hence a proportional increase in radiative recombination. However, annealing Si at low temperatures will also produce thermal donors [7], which may substantially increase the free carrier concentration and
Fig. 3. Integrated band-to-band CL efficiency as a function of doping concentration for (i) as-received and HF etched, (ii) low-temperature annealed and (iii) annealed and HF etched n-type samples. Accelerating voltage = 30 kV and probe current = 10 nA.
hence the radiative efficiency (since, as can be seen from Fig. 2, at low doping levels efficiency increases with doping). Resistivity measurements on as-received and annealed samples showed this to be the case. For example, material from a particular wafer was annealed similarly to those described above (the only difference being a temperature of 450 ◦ C for the initial step) and showed a similarly enhanced CL efficiency. It was found to have an initial resistivity of 7.8 cm, reducing to 1.6 cm after the anneal. This corresponds to an increase in free carrier concentration from 5.7 × 1014 to ∼3 × 1015 cm−3 , which is sufficient to account for the increase in luminescence efficiency induced by annealing. From this, it can be concluded that the present CL experiments provide no conclusive evidence for the effectiveness of low-temperature annealing to increase the purity of commercial single-crystal Si. However, although CL characterization of Si is a relatively widely used and rapid technique, it suffers from the drawback of yielding only one parameter – luminescence efficiency – which is dependent on several sample parameters including doping concentration, surface recombination velocity and minority carrier lifetime (which is controlled in turn by the rates of several different recombination paths). Thus, although CL efficiency is often taken as a measure of minority carrier lifetime, if this is to be achieved accurately, a detailed analysis of how the different sample parameters affect luminescence must be undertaken. This is presented in the next section. 3.1. Modelling of cathodoluminescence Modelling of the luminescence produced from a sample under electron beam excitation was carried out as follows. The specimen was split into an array of cells with cylindrical symmetry about the beam’s point of incidence. The CASINO program [8] was used to calculate the generation rate of electron–hole pairs in each cell as a function of position, probe current and accelerating voltage. The recombination rate of carriers in each cell was calculated, taking into account radiative band-to-band, Shockley–Read–Hall and Auger recombination (Eqs. (1)–(3)), along with surface recombination for the cells representing the sample surfaces. Recombination at the front surface was characterized by the surface recombination velocity S; at the back surface, where the electrical connection to the sample is located, an infinite recombination rate and thus a constant zero excess carrier concentration was assumed. Rbb = Bbb (np − n2i )
Fig. 2. CL band-to-band peak height as a function of doping concentration for (i) asreceived and (ii) low-temperature annealed samples. Accelerating voltage = 30 kV and probe current = 140–150 nA.
195
RSRH =
BSRH (np − n2i ) n + p + 2ni cosh(E/kT )
(1) (2)
196
K.J. Fraser et al. / Materials Science and Engineering B 159–160 (2009) 194–197
a result, SRH recombination dominates at low doping and Auger recombination at high doping, with radiative efficiency being maximized at intermediate doping. In addition, the modelled curves predict that gettering (through a reduction in BSRH ) and/or oxidation (through a reduction in S) only improves the CL efficiency of relatively low-doped material, which is consistent with experimental results where only lowdoped material shows improvement after annealing. This is due to Auger recombination being so fast in highly doped material that changes in SRH and/or surface recombination have virtually no effect on the total recombination rate. Likewise, generation of thermal donors in quantities sufficient to affect the total effective doping concentration in low-doped material will have a negligible effect on highly doped material. The simulation shows the importance of surface recombination in determining the efficiency. Reductions in efficiency of an order of magnitude or more are obtained when S is increased from 102 to 104 cm s−1 , and the effect is particularly noticeable for material with long bulk lifetimes. In addition, when surface recombination is fast, the efficiency becomes increasingly insensitive to bulk lifetime for long values of lifetime. These issues, together with the dependence of luminescence efficiency on doping (and hence on the presence of thermal donors), demonstrate that CL is not able to provide a simple measure of bulk lifetime unless both the specimen doping and surface recombination velocity are accurately known, which will rarely be the case. However, we propose a new technique that overcomes some of these difficulties. Consider a uniform specimen cut from a wafer which is then angle lapped to produce a taper of about 1◦ using, in our case,
Fig. 4. Modelled CL efficiency as a function of doping concentration and SRH recombination coefficient (assuming Fe as dominant impurity, with deep level 0.17 eV from band centre) for n-type specimens with a thickness of 600 m and front surface recombination velocities of (a) 104 cm s−1 and (b) 103 cm s−1 . Accelerating voltage = 30 kV and probe current = 10 nA.
RA = BAn n(np − n2i ) + BAp p(np − n2i )
(3)
Rx and Bx represent the rates and rate coefficients of bandto-band (subscript bb), Shockley–Read–Hall (subscript SRH) and Auger (subscript An/Ap) recombination respectively. n and p are the electron and hole concentrations, while ni is the intrinsic carrier concentration. E is the energy difference between the impurity deep level and the centre of the Si bandgap. Carrier transport between cells was calculated using the finite difference method together with the diffusion equation. The simulation was run using similar excitation conditions to our experiments until steady state was reached, at which point the radiative flux was integrated over the entire perturbed region and the luminescence efficiency calculated by comparing this to the total number of electron–hole pairs generated per second. Fig. 4 shows CL efficiency versus doping dependence for different sets of values of BSRH (which is directly proportional to impurity concentration) with S being 104 and 102 cm s−1 in Fig. 4a and b respectively. Note that the modelled values of efficiency represent the internal efficiency, not taking into account self-absorption, internal reflection and losses in the collection equipment. It can be seen that the numerically modelled doping dependence curves show the same characteristic features as the experimental ones. Both show an efficiency peak at intermediate doping concentrations. This can be explained by the differing doping dependencies of the three bulk recombination paths, radiative band-to-band, SRH, and Auger recombination. Under low injection conditions, these are directly proportional to, independent of and proportional to the square of doping concentration respectively. As
Fig. 5. Modelled, normalized CL efficiency as a function of sample thickness for 5.7 × 1014 cm−3 n-type specimens with indicated values of minority carrier lifetime for surface recombination velocities of (a) 104 cm s−1 and (b) 103 cm s−1 . Experimental data for short- and long-lifetime specimens is also presented with approximate lines of best fit (dotted lines). Accelerating voltage = 30 kV and probe current = 10 nA.
K.J. Fraser et al. / Materials Science and Engineering B 159–160 (2009) 194–197
grinding followed by Syton polishing. This results in a specimen of continuously varying thickness t with constant S at the top surface and, with suitable processing, infinite S at the bottom surface. At different locations along the specimen the CL efficiency is then partly determined by the minority carrier lifetime and specimen thickness since these together control the proportion of carriers reaching the back surface, where they recombine nonradiatively. Such specimens were modelled using the simulation described above. The resulting values of , when normalized according to Eq. (4), are presented in Fig. 5a and b for values of S of 104 and 103 cm s−1 respectively and a variety of minority carrier lifetimes. These values of S were chosen to represent surfaces free of passivating oxide. (t) =
(t) − (tmin ) (tmax ) − (tmin )
197
4. Conclusions The present work has shown that the effects of low-temperature annealing on minority carrier lifetime are difficult to quantify using CL due to the introduction of thermal donors and passivating surface oxide. However, it is clear that low-temperature annealing in dirty conditions does not introduce significant amounts of electrically active impurities into the material. With the aid of numerical modelling of carrier generation, diffusion and recombination, a method has been developed to measure minority carrier lifetime independent of surface recombination velocity by plotting normalized CL efficiency as a function of sample thickness. Initial results using this technique are promising. However, it can be seen from the modelled curves that distinguishing between very high values of minority carrier lifetime is difficult.
(4)
The shapes of the resulting profiles are independent of S to a good approximation over a wide range of values. The progression of the profile’s shape from short to long lifetime is clear; short-lifetime material gives a profile that increases abruptly at low thickness and then becomes flat at high thickness, while long-lifetime material gives a profile with an almost constant gradient. Unfortunately, the technique is still insensitive to changes in lifetime for long lifetimes when the resulting minority carrier diffusion length is of the same order as the thickness of the starting wafer. However, these simulations show that the minority carrier lifetime of material can be estimated using a tapered specimen and comparing measured CL efficiency values normalized using Eq. (4) to modelled ones using the simulation. Also presented in Fig. 5 is experimental data from one long-lifetime and one short-lifetime specimen indicating general agreement with the simulation.
Acknowledgement One of the authors (KJF) was supported by an EPSRC studentship. References [1] W.L. Ng, M.A. Lourenc¸o, R.M. Gwilliam, S. Ledain, G. Shao, K.P. Homewood, Nature 410 (2001) 192–194. [2] D.J. Stowe, S.A. Galloway, S. Senkader, K. Mallik, R.J. Falster, P.R. Wilshaw, Physica B 340 (2003) 710–713. [3] N.A. Sobolev, A.M. Emel’yanov, E.I. Shek, V.I. Vdovin, Physica B 340–342 (2003) 1031–1035. ¨ [4] J.M. Sun, T. Dekorsky, W. Skorupa, B. Schmidt, A. Mucklich, M. Helm, Phys. Rev. B 70 (2004), 155316-1-11. [5] M. Kittler, T. Arguirov, A. Fischer, W. Seifert, Opt. Mater. 27 (2005) 967–972. [6] K.J. Fraser, D.J. Stowe, S.A. Galloway, S. Senkader, K. Mallik, R.J. Falster, P.R. Wilshaw, Phys. Stat. Sol. C 4 (2007) 2977–2980. [7] C.S. Fuller, R.A. Logan, J. Appl. Phys. 28 (1957) 1427–1436. [8] P. Hovington, D. Drouin, R. Gauvin, Scanning 19 (1997) 1–14.
Contents lists available at ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
Short communication
Cathodoluminescence assessment of annealed silicon and a novel technique for estimating minority carrier lifetime in silicon K.J. Fraser a , R.J. Falster b , P.R. Wilshaw a,∗ a b
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK MEMC Electronic Materials SpA, viale Gherzi 31, 28100 Novara, Italy
a r t i c l e
i n f o
Article history: Received 9 May 2008 Accepted 13 May 2008 Keywords: Doping effects Electron microscopy Optical properties Semiconductors Silicon Solar cells
a b s t r a c t The effect of low-temperature anneals (≤500 ◦ C) on Cz–Si minority carrier lifetime has been investigated using near-band-edge cathodoluminescence (CL). The low-temperature anneals are intended to produce efficient gettering by taking advantage of the increasing supersaturation of impurities as temperatures are reduced. It is found that the anneals affect the CL efficiency through several different mechanisms and that annealing under “dirty” conditions does not introduce significant amounts of electrically active impurities into the material. In order to aid the interpretation of experimental results, modelling of the effect of different sample parameters on CL is carried out. Using this theoretical work, an experimental method of measuring minority carrier lifetime using CL which is independent of surface recombination is developed. © 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
It has been shown using luminescence measurements [1–6] that high temperature (≥900 ◦ C) annealing of electronic grade Si samples containing ion implantation damage can induce significant gettering of Shockley–Read–Hall (SRH) recombination centres such as transition metal impurities. We report on new experiments investigating the effects of lower temperature anneals (500 ◦ C and below) on samples containing mechanically introduced dislocations. As annealing temperatures are reduced, the increased supersaturation of transition metal impurities increases the driving force for gettering so that, at least in principle, cleaner material can be produced. However, annealing at lower temperature results in reduced diffusivity, requiring longer anneals. It is hoped that, after testing on single-crystal Si, this technique will be applied to multicrystalline solar cell material, which contains higher concentrations of impurities and for which improved gettering may have a beneficial effect. Such long duration anneals would be very expensive to carry out under clean room conditions; however, at such low temperatures in-diffusion of surface contaminants should also be reduced, allowing the anneals to be carried out in dirty, but cheap, conditions.
Specimens were prepared from (1 0 0) n-type Cz-wafers with a wide variety of doping concentrations (∼1014 –1019 cm−3 ). Anneals were carried out at 500 ◦ C for 20–24 h in air, followed by slow cooling to 200 ◦ C and annealing for a further ∼120 h. This process will subsequently be termed ‘low-temperature annealing’ and was carried out in a standard metallurgical furnace. Selected samples were scratched on the back (unpolished) surface using SiC paper to introduce dislocations as potential gettering sites. Specimens were cleaned before and/or after heat treatment using laboratory grade chemicals. In many cases, HF etching was used to remove surface oxide in order to standardize the surface state prior to cathodoluminescence (CL) examination. Luminescence efficiency was measured using a Gatan MonoCL3 system and a liquid-nitrogen cooled North Coast E0-817L Ge photodiode attached to a JEOL 6500F scanning electron microscope. Experiments were carried out at room temperature using an accelerating voltage of 30 kV.
∗ Corresponding author. Tel.: +44 1865 273736. E-mail address: [email protected] (P.R. Wilshaw). 0921-5107/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2008.05.006
3. Results To test the hypothesis that low-temperature annealing in relatively dirty conditions is satisfactory, samples were prepared with intentional surface contamination. This was accomplished by scratching a high-purity Fe, Cu or Ni wire over the front surfaces of different samples prior to annealing. Fig. 1 shows values of CL peak height obtained from contaminated samples, compared with an as-received sample and a control specimen annealed at the same
K.J. Fraser et al. / Materials Science and Engineering B 159–160 (2009) 194–197
Fig. 1. CL band-to-band peak height measured from intentionally contaminated specimens compared with uncontaminated and as-received specimens, all HF etched before examination. Accelerating voltage = 30 kV and probe current = 150 nA.
time without contamination. All samples were HF etched before examination. It can be seen that the efficiencies of all the annealed specimens are very similar, indicating that at the temperatures used, intentional contamination of the surface before annealing does not result in any significant reduction in luminescence efficiency due to in-diffusion of metal atoms. Indeed, the annealed specimens show enhanced luminescence; this effect is discussed further below. Fig. 2 shows band-to-band CL efficiency as a function of doping concentration for as-received and low-temperature annealed samples. Samples with doping above 1017 cm−3 show no significant improvement in CL efficiency after annealing. Lower-doped samples show an increase in CL efficiency of up to a factor of 10 after annealing. However, as shown in Fig. 3, this increase is reduced to around a factor of 2 after HF etching. Note that no significant difference was observed between as-received samples before and after HF etching. The effect of HF etching can be understood in terms of the acid removing surface oxide produced during annealing. This oxide electrically passivates the surface, reducing the proportion of generated carriers which recombine non-radiatively at the sample’s front surface, thus increasing the luminescence observed. However, the fact that after oxide removal, annealed specimens still show greater luminescence than as-received ones indicates that the bulk radiative efficiency has increased. It is tempting to ascribe this increase to the gettering of non-radiative recombination centres, and hence a proportional increase in radiative recombination. However, annealing Si at low temperatures will also produce thermal donors [7], which may substantially increase the free carrier concentration and
Fig. 3. Integrated band-to-band CL efficiency as a function of doping concentration for (i) as-received and HF etched, (ii) low-temperature annealed and (iii) annealed and HF etched n-type samples. Accelerating voltage = 30 kV and probe current = 10 nA.
hence the radiative efficiency (since, as can be seen from Fig. 2, at low doping levels efficiency increases with doping). Resistivity measurements on as-received and annealed samples showed this to be the case. For example, material from a particular wafer was annealed similarly to those described above (the only difference being a temperature of 450 ◦ C for the initial step) and showed a similarly enhanced CL efficiency. It was found to have an initial resistivity of 7.8 cm, reducing to 1.6 cm after the anneal. This corresponds to an increase in free carrier concentration from 5.7 × 1014 to ∼3 × 1015 cm−3 , which is sufficient to account for the increase in luminescence efficiency induced by annealing. From this, it can be concluded that the present CL experiments provide no conclusive evidence for the effectiveness of low-temperature annealing to increase the purity of commercial single-crystal Si. However, although CL characterization of Si is a relatively widely used and rapid technique, it suffers from the drawback of yielding only one parameter – luminescence efficiency – which is dependent on several sample parameters including doping concentration, surface recombination velocity and minority carrier lifetime (which is controlled in turn by the rates of several different recombination paths). Thus, although CL efficiency is often taken as a measure of minority carrier lifetime, if this is to be achieved accurately, a detailed analysis of how the different sample parameters affect luminescence must be undertaken. This is presented in the next section. 3.1. Modelling of cathodoluminescence Modelling of the luminescence produced from a sample under electron beam excitation was carried out as follows. The specimen was split into an array of cells with cylindrical symmetry about the beam’s point of incidence. The CASINO program [8] was used to calculate the generation rate of electron–hole pairs in each cell as a function of position, probe current and accelerating voltage. The recombination rate of carriers in each cell was calculated, taking into account radiative band-to-band, Shockley–Read–Hall and Auger recombination (Eqs. (1)–(3)), along with surface recombination for the cells representing the sample surfaces. Recombination at the front surface was characterized by the surface recombination velocity S; at the back surface, where the electrical connection to the sample is located, an infinite recombination rate and thus a constant zero excess carrier concentration was assumed. Rbb = Bbb (np − n2i )
Fig. 2. CL band-to-band peak height as a function of doping concentration for (i) asreceived and (ii) low-temperature annealed samples. Accelerating voltage = 30 kV and probe current = 140–150 nA.
195
RSRH =
BSRH (np − n2i ) n + p + 2ni cosh(E/kT )
(1) (2)
196
K.J. Fraser et al. / Materials Science and Engineering B 159–160 (2009) 194–197
a result, SRH recombination dominates at low doping and Auger recombination at high doping, with radiative efficiency being maximized at intermediate doping. In addition, the modelled curves predict that gettering (through a reduction in BSRH ) and/or oxidation (through a reduction in S) only improves the CL efficiency of relatively low-doped material, which is consistent with experimental results where only lowdoped material shows improvement after annealing. This is due to Auger recombination being so fast in highly doped material that changes in SRH and/or surface recombination have virtually no effect on the total recombination rate. Likewise, generation of thermal donors in quantities sufficient to affect the total effective doping concentration in low-doped material will have a negligible effect on highly doped material. The simulation shows the importance of surface recombination in determining the efficiency. Reductions in efficiency of an order of magnitude or more are obtained when S is increased from 102 to 104 cm s−1 , and the effect is particularly noticeable for material with long bulk lifetimes. In addition, when surface recombination is fast, the efficiency becomes increasingly insensitive to bulk lifetime for long values of lifetime. These issues, together with the dependence of luminescence efficiency on doping (and hence on the presence of thermal donors), demonstrate that CL is not able to provide a simple measure of bulk lifetime unless both the specimen doping and surface recombination velocity are accurately known, which will rarely be the case. However, we propose a new technique that overcomes some of these difficulties. Consider a uniform specimen cut from a wafer which is then angle lapped to produce a taper of about 1◦ using, in our case,
Fig. 4. Modelled CL efficiency as a function of doping concentration and SRH recombination coefficient (assuming Fe as dominant impurity, with deep level 0.17 eV from band centre) for n-type specimens with a thickness of 600 m and front surface recombination velocities of (a) 104 cm s−1 and (b) 103 cm s−1 . Accelerating voltage = 30 kV and probe current = 10 nA.
RA = BAn n(np − n2i ) + BAp p(np − n2i )
(3)
Rx and Bx represent the rates and rate coefficients of bandto-band (subscript bb), Shockley–Read–Hall (subscript SRH) and Auger (subscript An/Ap) recombination respectively. n and p are the electron and hole concentrations, while ni is the intrinsic carrier concentration. E is the energy difference between the impurity deep level and the centre of the Si bandgap. Carrier transport between cells was calculated using the finite difference method together with the diffusion equation. The simulation was run using similar excitation conditions to our experiments until steady state was reached, at which point the radiative flux was integrated over the entire perturbed region and the luminescence efficiency calculated by comparing this to the total number of electron–hole pairs generated per second. Fig. 4 shows CL efficiency versus doping dependence for different sets of values of BSRH (which is directly proportional to impurity concentration) with S being 104 and 102 cm s−1 in Fig. 4a and b respectively. Note that the modelled values of efficiency represent the internal efficiency, not taking into account self-absorption, internal reflection and losses in the collection equipment. It can be seen that the numerically modelled doping dependence curves show the same characteristic features as the experimental ones. Both show an efficiency peak at intermediate doping concentrations. This can be explained by the differing doping dependencies of the three bulk recombination paths, radiative band-to-band, SRH, and Auger recombination. Under low injection conditions, these are directly proportional to, independent of and proportional to the square of doping concentration respectively. As
Fig. 5. Modelled, normalized CL efficiency as a function of sample thickness for 5.7 × 1014 cm−3 n-type specimens with indicated values of minority carrier lifetime for surface recombination velocities of (a) 104 cm s−1 and (b) 103 cm s−1 . Experimental data for short- and long-lifetime specimens is also presented with approximate lines of best fit (dotted lines). Accelerating voltage = 30 kV and probe current = 10 nA.
K.J. Fraser et al. / Materials Science and Engineering B 159–160 (2009) 194–197
grinding followed by Syton polishing. This results in a specimen of continuously varying thickness t with constant S at the top surface and, with suitable processing, infinite S at the bottom surface. At different locations along the specimen the CL efficiency is then partly determined by the minority carrier lifetime and specimen thickness since these together control the proportion of carriers reaching the back surface, where they recombine nonradiatively. Such specimens were modelled using the simulation described above. The resulting values of , when normalized according to Eq. (4), are presented in Fig. 5a and b for values of S of 104 and 103 cm s−1 respectively and a variety of minority carrier lifetimes. These values of S were chosen to represent surfaces free of passivating oxide. (t) =
(t) − (tmin ) (tmax ) − (tmin )
197
4. Conclusions The present work has shown that the effects of low-temperature annealing on minority carrier lifetime are difficult to quantify using CL due to the introduction of thermal donors and passivating surface oxide. However, it is clear that low-temperature annealing in dirty conditions does not introduce significant amounts of electrically active impurities into the material. With the aid of numerical modelling of carrier generation, diffusion and recombination, a method has been developed to measure minority carrier lifetime independent of surface recombination velocity by plotting normalized CL efficiency as a function of sample thickness. Initial results using this technique are promising. However, it can be seen from the modelled curves that distinguishing between very high values of minority carrier lifetime is difficult.
(4)
The shapes of the resulting profiles are independent of S to a good approximation over a wide range of values. The progression of the profile’s shape from short to long lifetime is clear; short-lifetime material gives a profile that increases abruptly at low thickness and then becomes flat at high thickness, while long-lifetime material gives a profile with an almost constant gradient. Unfortunately, the technique is still insensitive to changes in lifetime for long lifetimes when the resulting minority carrier diffusion length is of the same order as the thickness of the starting wafer. However, these simulations show that the minority carrier lifetime of material can be estimated using a tapered specimen and comparing measured CL efficiency values normalized using Eq. (4) to modelled ones using the simulation. Also presented in Fig. 5 is experimental data from one long-lifetime and one short-lifetime specimen indicating general agreement with the simulation.
Acknowledgement One of the authors (KJF) was supported by an EPSRC studentship. References [1] W.L. Ng, M.A. Lourenc¸o, R.M. Gwilliam, S. Ledain, G. Shao, K.P. Homewood, Nature 410 (2001) 192–194. [2] D.J. Stowe, S.A. Galloway, S. Senkader, K. Mallik, R.J. Falster, P.R. Wilshaw, Physica B 340 (2003) 710–713. [3] N.A. Sobolev, A.M. Emel’yanov, E.I. Shek, V.I. Vdovin, Physica B 340–342 (2003) 1031–1035. ¨ [4] J.M. Sun, T. Dekorsky, W. Skorupa, B. Schmidt, A. Mucklich, M. Helm, Phys. Rev. B 70 (2004), 155316-1-11. [5] M. Kittler, T. Arguirov, A. Fischer, W. Seifert, Opt. Mater. 27 (2005) 967–972. [6] K.J. Fraser, D.J. Stowe, S.A. Galloway, S. Senkader, K. Mallik, R.J. Falster, P.R. Wilshaw, Phys. Stat. Sol. C 4 (2007) 2977–2980. [7] C.S. Fuller, R.A. Logan, J. Appl. Phys. 28 (1957) 1427–1436. [8] P. Hovington, D. Drouin, R. Gauvin, Scanning 19 (1997) 1–14.