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Determination of Acceptor Ratio and Iron Concentration in Co-doped Silicon
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 55 (2014) 519 – 525
4th International Conference on Silicon Photovoltaics, SiliconPV 2014
Determination of acceptor ratio and iron concentration in co-doped silicon Til Bartela,*, Fabien Gibajaa, Maxime Forsterb a
Calisolar GmbH, Magnusstrasse 11, 12489 Berlin, Germany Apollon Solar, 66, cours Charlemagne, 69002 Lyon, France
b
Abstract Low-cost photovoltaic grade feedstock using multiple dopants - mainly Boron and Phosphorous but also Gallium and trace amounts of Aluminum - is currently establishing itself on the market. In this paper, the measurement of dissolved iron by lifetime spectroscopy introduced on the incumbent Boron-only doped Silicon is adapted to materials with several acceptors. A detailed theoretical description is given and pitfalls are identified. Since precise knowledge of the relative acceptor concentrations is necessary for a correct iron determination, a novel method for measuring acceptor concentration fractions in Silicon is proposed. It uses lifetime spectra analysis to determine the crossover point position. Using this simple method, it is possible to fully analytically characterize compensated silicon doped with two acceptor types. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the scientific committee of the SiliconPV 2014 conference. Peer-review under responsibility of the scientific committee of the SiliconPV 2014 conference Keywords: Solar silicon; iron acceptor pairing; compensation; crossover point
1. Introduction Silicor Materials provides its customers with high quality Silicon feedstock purified through a metallurgical process. Its subsidiary, Calisolar GmbH, characterizes the material with regards to chemical purity and defect engineering. A particularity of this feedstock is that it already contains the doping elements Boron and Phosphorous. At earlier processing stages, trace amounts of Aluminum can also be present and at ingot production Gallium may be added for better resistivity control. The performance of cells made from such co-doped and compensated
* Corresponding author. Tel.: (+49) (0)30 6392 4580; fax: (+49) (0)30 6392 4584. E-mail address: [email protected]
1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the scientific committee of the SiliconPV 2014 conference doi:10.1016/j.egypro.2014.08.018
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Til Bartel et al. / Energy Procedia 55 (2014) 519 – 525
materials has been shown to perform equally to cells made from ultra high purity feedstock [1,2,3]. In some cases, compensation even reduces the recombination activity of some important recombinative defects [4,5], in particular interstitial iron and the pairs it forms with acceptors [6]. In the incumbent Boron only doped Silicon, the measurement of the minority carrier lifetime has proven a fast and reliable method to evaluate the concentration of the total dissolved iron [Fe] and the total acceptor concentration. The procedures are routinely used and have been standardized [7,8]. In this paper, the method is expanded to the measurement of [Fe] in materials with several acceptors of known concentration. Since the acceptor concentrations are often unknown or imprecise, a novel interpretation of the lifetime spectra is proposed to determine acceptor concentration fractions in Silicon co-doped with two acceptor types using crossover point determination. 2. Determining [Fe] in co-doped Si Dissolved Iron causes different defect states depending on the availability of acceptors acting as paring partners [4]. In the following, defect states commonly associated with iron are identified by the index j=1,…,5 for Fei, FeB, FeAl, FeGa, and FeIn respectively. Each defect type j is qualified by its density ሾܰ ሿ, trap energy level ܧ and capture cross sections for holes ߪǡ and for electrons ߪǡ . Using these parameters, the Shockley Read Hall (SRH) formalism allows the determination of the associated minority carrier lifetime ߬ at an injection density ο݊ according to ଵ ఛೕ
ሾேೕ ሿൈሺబ ାబ ାοሻ
ൌଵ
ൗఙ ణ ൈሺబ ାభǡೕ ାοሻାଵൗఙ ణ ൈሺబ ାభǡೕ ାοሻ ǡೕ ǡೕ
.
(1)
Here, ߴ is the thermal velocity, ݊ and are the equilibrium carrier concentrations, and ݊ଵǡ and ଵǡ are the SRH densities given as ಶ షಶೕ ೖ
݊ଵǡ ൌ ܰ ݁ݔ൛ି
ൟǡଵǡ ൌ ܰ ݁ݔ൛ି
ಶೕ షಶೇ ೖ
ൟ,
(2)
using the effective density of states NC and NV in the conduction and valence band edges located at EC and EV. kT is the thermal energy. Taking advantage of the fact that ͳΤ߬ is linear in the defect density ሾܰ ሿ, ߬ଵ is defined as the lifetime associated with a defect of singular density. Eq 1 then becomes ଵ ఛೕ
ൌ
ሾேೕ ሿ ఛೕభ
ൌ
ሾிሿൈఈೕ ఛೕభ
.
(3)
In the last term, the concentration [Nj] of the iron in state j is expressed as a fraction ߙ of the total dissolved iron concentration ሾ݁ܨሿ ൌ σହሾ݁ܨሿ ൈ ߙ . The measured minority carrier lifetime ߬ in the sample can now be described as ଵ ఛ
ൌఛ
ଵ ೝ
ఈ
ሾ݁ܨሿ ൈ σହ ఛభೕ ,
(4)
ೕ
where ߬௧ describes lifetime limiting effects not related to iron. When a sample is illuminated with strong light, iron will be predominantly in its free, unpaired interstitial state. This state is referred to as the “free” state, even if some paired iron may subsist. When left in darkness, most of the iron will repair with acceptors. Accordingly this state is referred to as the “paired” state, even if some residual unpaired, i.e. free iron may remain. Using this terminology, the distribution factors after illumination will change ௗ to ߙ . The lifetimes measured in the sample in these states are referred to as ߬ and ߬ ௗ . In from ߙ
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Til Bartel et al. / Energy Procedia 55 (2014) 519 – 525
analogy with Si containing a single acceptor [9], the conversion factor relating ሾ݁ܨሿ to the change in lifetime between the paired and free state can now be defined using Eq 4: ଵ ఛೌೝ
െ
ଵ ఛೝ
ೝ
ೌೝ
ൌ ሾ݁ܨሿ ൈ ቊσହ
ఈೕ
ఛೕభ
െ σହ
ఈೕ
ఛೕభ
ቋ
(5)
Fig. 1. Lifetime measurements of a sample brought to the interstitial state and relaxing to a paired state. The lifetime is fitted with a triple exponential function as in [8].
To extract the concentration of iron ሾ݁ܨሿ from Eq 5, it is necessary to precisely determine the occupation ͲǤͻͷ fractions ߙ . After the breaking of iron-acceptor pairs, the interstitial state dominates the lifetime and ߙଵ ൏ ͲǤͲͳ). The is assumed. In darkness and at room temperature very few Fei will eventually remain unpaired (ߙଵ ௗ (j=2,3,4,5) will depend on the respective concentrations of the distribution among the available acceptors, ߙ paring partners, the pairing preference of the Fei, and its level of thermalization between the different acceptor types. The recommendations for the measurement of [Fei] presented in [8] equally apply to co-doped samples. In addition, special care must be given to the definition and determination of ߬ ௗ (called ߬ in [8]): since iron may redistribute between acceptors after a first repairing, multi-exponential fitting of the lifetime profiles becomes necessary in some cases [10]. This allows the determination of the lifetime at which the iron has paired with the next available acceptor as a result of its random diffusion through the Si matrix, but has not yet redistributed. In this state, ௗ are defined by the concentration fractions of the acceptor types in the sample as the occupation fractions ߙ was confirmed by DLTS for B and Al co-doped samples [11]. 2.1. Exemplary determination of Fei in Si co-doped with B, Ga and P For illustration, ሾ݁ܨሿ is determined on a multicrystalline brick made from solar grade silicon using the correct procedure described in the previous section and under the erroneous assumption of B as sole acceptor in the sample. At the location of measurement, a co-doping with B=1.4E16/cm³, Ga=3.1E15/cm³ and P=9.8E15/cm³ was determined according to the expected segregation behavior of these dopants. The sample is brought into the “free” ൌ ͲǤͻͷ) and the lifetime is then continuously tracked by quasi-steady state state by flashing with light (ߙଵ photoconductance decay resulting in the bulk lifetime profile shown in Fig 1 (measurements are taken in intervals increasing from 30 seconds to 15 minutes and evaluated at an injection density of 1E15/cm³). Within a few days, Fe
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Til Bartel et al. / Energy Procedia 55 (2014) 519 – 525 ௗ
reaches a thermodynamical equilibrium by redistributing from one acceptor type to the other. As a result ߙ (j=2,4) is not trivially defined. However, since the initial pairing of iron with the next neighboring acceptor is ௗ will be equal to the relative usually fast enough to neglect redistribution immediately after the initial pairing, ߙ concentrations of the acceptors at this moment. To properly determine the lifetime at this point, it is necessary to record a lifetime trace until at least the first exponential has saturated, ideally until the following decays can be approximated by fitting. In Fig 1, the experimental data is fitted with the sum of three exponentials. As presented in [10], the second and third exponentials describe redistribution effects between the different dopants. The fitting results from the first exponential are used to determine ߬ ௗ after the initial repairing. Taking into account the concentration fractions ௗ ௗ ؆ ͲǤͺʹǡ ߙସ ؆ ͲǤͳͺ ) and with Eq 5, of the two dopants, the paired fractions are determined ( ߙଶ ሾ݁ܨሿ=8.4E10/cm³ is calculated. For comparison a single exponential fit of the same data (not shown) assuming the ௗ ؆ ͳ) erroneously yields ሾ݁ܨሿ=1.7E11/cm³. sample contains only Boron (ߙଶ 3. Determination of acceptor concentration fraction by crossover point determination The crossover point (COP) defines an excess charge carrier density Δେ at which the lifetime becomes independent of the pairing state of the iron. It represents a characteristic signature of iron in Si and allows the extraction of the acceptor concentration fraction as described in this section. Since the total acceptor concentration can be obtained with the same measurement [8], it can be used to fully quantitatively analyze a material co-doped with two acceptors. If the resistivity is measured, the compensation with a donor can also be extracted. In the following, the theoretical framework for determining acceptor fractions is presented. The expected position of Δେ for a material containing multiple dopants is found by setting Eq 5 to zero. For two dopants, the equation becomes lengthy but is readily solved analytically (see Appendix A). In addition to the defect parameters, net doping and the temperature [12,13], Δେ now becomes a function of the relative ௗ ). If the distribution probability of Fei to the different distribution of the iron between the acceptors (i.e. ߙ acceptors is known and the defect parameters are very different for every acceptor type, a measurement of the crossover point allows the extraction of the concentration fraction between the two acceptor types. Depending on temperature, net doping and recombination parameters, a crossover must not necessarily exist for all concentration ratios. Δେ was calculated for p-type Si sample co-doped with B and either Ga or In since these defects have been characterized in the literature (see Appendix B for details). Note that the reported recombination parameters scatter widely if measured independently. For FeGa and FeIn only one set of values was found. For the interesting FeAl defect, the set of recombination parameters remains incomplete at this time. Fig 2 plots the crossover position as a function of the B fraction for a sample containing either additional Ga or In under the assumption that Fei is distributed according to the respective concentration fractions of the acceptors. A net doping p0=1E16/cm³ and a temperature of 300K was chosen for this example. The COP position is expected to shift towards lower injection by about one order of magnitude when Ga gradually replaces B as a dopant. The trend is even more pronounced for In. Since the shift is important, a good sensitivity for the acceptor fractions can be expected. Experimentally, the measurement of the COP is complicated by trapping effects that can dominate the photoconductance at low injection densities. Quasi steady state photoluminescence may provide an alternative method to avoid trapping artefacts. In addition, when the lifetime within the sampled area is inhomogeneous, the injection density reached may also vary locally. Averaging over the area will induce an error in the determination of the injection density. First experimental results illustrating a practical application of the crossover point method will be published elsewhere [15]. 4. Summary In this paper, the measurement of the interstitial iron concentration by lifetime measurement is adapted to silicon co-doped simultaneously with B, Ga, In and Al. Further, it is proposed to use a characteristic signature of iron in the lifetime spectra (crossover point position) to determine the relative concentrations of acceptors in p-type silicon co-
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doped with two acceptors. Using the proposed modeling, lifetime spectroscopy becomes a simple analytical tool to determine the concentrations of up to three dopants in compensated p-type Silicon containing iron.
Acknowledgements This work was supported under BMWi grant KF2794102AG2.
Appendix A. Theoretical simulation of ઢܖ۱ ۾۽in Si co-doped with two acceptors The COP is analytically derived from Eq 5 for the exemplary case of silicon doped with B and Ga. Other acceptors can easily be implemented by using the correct defect parameters. From the condition that the lifetime at the COP is independent of the state of the Fe it follows from Eq 5: ೌೝ
σହ
ఈೕ
ೝ
ିఈೕ
ൌͲ
ఛೕభ
(6)
Without loss of generality the “free” state can be assumed to be exclusively composed of a population of free Fei (ߙி ൌ ͳ). In analogy, the “paired” state can be assumed to be composed exclusively of Fe paired with either a B or a Ga acceptor. Replacing the j indices according to the defect names (Table 1), Eq 6 now become ଵ భ ఛಷ
ೌೝ
ೌೝ
ൌ
ఈಷಳ
భ ఛಷಳ
ఈಷಸೌ
(7)
భ ఛಷಸೌ
The injection density dependency Δ which solves this equation, is contained within the single defect lifetimes ߬ଵ . Expanding these lifetimes according to their definition (Eq 1) yields బ ାబ ାΔ୬ ଵ ଵൗ ఙǡಷ ణכ൫బ ାభǡಷ ାΔ୬൯ା ൗఙǡಷ ణൈ൫బ ାభǡಷ ାΔ୬൯
ൌ
ೌೝ
ೌೝ
ఈಷಸೌ ൈሺబ ାబ ାΔ୬ሻ ఈಷಳ ൈሺబ ାబ ାΔ୬ሻ ଵ ଵൗ ଵൗ ൈሺ ൈሺబ ାభǡಷಸೌ ାΔ୬ሻ ା ାΔ୬ሻା ା ାΔ୬ሻ ା ାΔ୬ሻାଵൗఙ ൈሺ ൈሺ ൗ బ భǡಷಳ బ భǡಷಳ బ భǡಷಸೌ ఙǡಷಸೌ ణ ఙǡಷಳ ణ ఙǡಷಳ ణ ǡಷಸೌ ణ
(8)
The numerators and the thermal velocity ߴ simplify out. The following short hand notations are introduced: ȱ୨ ൌ ͳൗߙ ߪǡ ൈ ൫݊ ݊ଵǡ Δ൯ ͳൗߙ ߪǡ ൈ ൫ ଵǡ Δ൯ ͳൗ ͳൗ ͳ ൌ ቀᇣᇧ ͳᇧ ൗᇧ ߙᇧ ߪᇧ ߙ ߪǡ ൈ ൫݊ ݊ଵǡ ൯ ൗߙ ߪǡ ൈ ൫ ଵǡ ൯ ߙᇧ ᇧ ǡ ߪ ᇧ ᇧᇤᇧ ᇧǡ ᇧᇥቁ ൈ Δ ᇣᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇤᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇥ ఙೕషభ
ൌ
ߪିଵ Δ
ೕ
ܿ
Where ߙ represent the population ratios used in Eq 7. Substituting these short hand notations in Eq 8 and transposing leads to ȱୣ ȱୣୋୟ ൌ ȱୣ୧ ൈ ሼȱୣୋୟ ȱୣ ሽ
(9)
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Til Bartel et al. / Energy Procedia 55 (2014) 519 – 525
Factoring out the left hand side results in ିଵ ିଵ ିଵ ିଵ ߪிீ ൈ Δଶ ሾߪி ܿிீ ߪிீ ܿி ሿ ൈ Δ ܿி ܿிீ ȱୣ ȱୣୋୟ ൌ ߪி
And the right hand side yields ȱୣ୧ ൈ ሼȱୣୋୟ ȱୣ ሽ ିଵ ିଵ ିଵ ൌ ሺߪி Δ ܿி ሻ ൈ ሼߪி Δ ܿி ߪிீ Δ ܿிீ ሽ ିଵ ିଵ ିଵ ൌ ሺߪி Δ ܿி ሻ ൈ ሼሾߪி ߪிீ ሿΔ ܿி ܿிீ ሽ ିଵ ିଵ ିଵ ିଵ ሿ ିଵ ିଵ ሻ ൈ Δଶ ሾܿி ൈ ሺߪி ߪி ൌ ߪி ൈ ሾߪி ߪிீ ߪிீ ൈ ሺܿி ܿிீ ሻሿ ൈ Δ ܿி ൈ ሼܿி ܿிீ ሽ
Gathering this in Eq 9 gives a polynomial of second order in Δ: ିଵ ିଵ ିଵ ሻെߪ ିଵ ିଵ ሿ ଶ ሾߪி ൈ ሺߪி ߪிீ ி ߪிீ ൈ Δ ିଵ ିଵ ିଵ ିଵ ିଵ ሾܿி ൈ ሺߪி ߪிீ ሻ ߪி כሺܿி ܿிீ ሻ െ ߪி ܿிீ െ ߪிீ ܿி ሿ ൈ Δ ܿி ൈ ሺܿி ܿிீ ሻ െ ܿி ܿிீ ൌ Ͳ
This polynomial in Δ can be solved using the quadratic formula and results in two distinct roots. One root is negative and has no physical meaning, the other root is positive and represents the injection density at the COP Δେ . In addition to its usual dependencies (temperature, net doping, defect parameters), Δେ has now become a ௗ (contained within ܿ and ߪ ). It can be used to determine the distribution of function of the pairing fraction ߙ the Fei between two acceptors. Note that since Δେ Ͳͳͳ بȀ ³ is expected, ݊ , ݊ଵǡி , ݊ଵǡிீ , and ଵǡி may all be neglected for p-type silicon at temperatures below 400K, however this does not significantly simplify the equations and was not applied here.
Appendix B. Recombination parameters of Fe related defects Note that values that have been reported repeatedly scatter widely and we rely on the recommendation in [12]. Data for FeGa, FeIn and FeAl is scarce or missing altogether. Table 1. Energy levels and capture cross sections of Fei related defects in Si as used in this paper. Defect
ܧ ሺܸ݁ሻ
ߪǡ ሺܿ݉²ሻ
ߪǡ ሺܿ݉²ሻ
1
Fei
ܧ௩ ͲǤ͵ͺ
4E-14
7E-17
[6]
2
FeB
ܧ െ ͲǤʹ
5E-15
3E-15
[14]
3
FeAl
ܧ௩ ͲǤͳ͵ܽ݊݀ͲǤʹ
??
2E-14 to 4E-15
[6]
4
FeGa
ܧ௩ ͲǤʹ
4E-14
2E-14
[13]
5
FeIn
ܧ௩ ͲǤͳͷ
3.5E-13
1.5E-14
[13]
Index j
Reference
References [1] M. Kaes, M. Heuer, F. Kirscht, A. Turenne, T. Jester, Metallurgically purified silicon for photovoltaics, to be presented at EUPVSEC 2014 [2] F. Cocco, D. Grosset-Bourbange, P. Rivat, G. Quost, J. Degoulange, R. Einhaus, M. Forster, H. Colin, PHOTOSIL UMG silicon: Industrial evaluation by multi-c p-type ingots and solar cells, Proceedings of the 28th European Photovoltaic Solar Energy Conference, Paris, France, (2013) [3] M. Forster, P. Wagner, J. Degoulange, R. Einhaus, G. Galbiati, F. E. Rougieux, Andrés Cuevas and E. Fourmond, Impact of compensation on the boron and oxygen-related degradation of upgraded metallurgical-grade silicon solar cells Solar Energy Materials and Solar Cells 120, 390 (2014),.
Til Bartel et al. / Energy Procedia 55 (2014) 519 – 525 [4] MacDonald and A. Cuevas, Recombination in compensated crystalline silicon for solar cells, J. Appl. Phys. 109 43704 (2011) [5] S. Dubois, N. Enjalbert, and J. P. Garandet., Effects of the compensation level on the carrier lifetime of crystalline silicon, Appl. Phys. Lett. 93 32114 (2008) [6] A. Istratov, H. Hieslmair, and E. R. Weber, Appl. Phys. A 69, 13 (1999). [7] Semiconductor Equipment and Materials International, SEMI PV13-0813 [8] J. Tan, D. Macdonald, F. Rougieux and A. Cuevas, Accurate measurement of the formation rate of iron–boron pairs in silicon, Semicond. Sci. Technol. 26 (2011) [9] D. H. Macdonald, L. J. Geerligs, A. Azzizi, Iron detection in crystalline silicon by carrier lifetime measurements for arbitrary injection and doping, J. App. Phys 95 1021 (2004) [10] T. Bartel, F. Gibaja, O. Graf, D. Gross, M. Kaes, M. Heuer, F. Kirscht, C. Möller, K. Lauer, Dynamics of iron-acceptor-pair formation in co-doped silicon, Appl. Phys. Lett. 103 202109 (2013) [11] K. Mishra, M. Banan, J. Moody, S. Chandrasekhar, Effect of iron complexes on the minority carrier lifetime in B, Al, and P doped silicon, The Electrochemical Society, Proceedings of the Symposium on Diagnostic Techniques for Semiconductor Materials and Devices, 131 (1994) [12] J. E. Birkholz, K. Bothe, D. Macdonald, J. Schmidt Electronic properties of iron-boron pairs in crystalline silicon by temperature- and injection-level-dependent lifetime measurements, J. Appl. Phys. 97 103708 (2005) [13] J. Schmidt, D. Mcdonald, Recombination activity of iron-gallium and iron-indium pairs in silicon, J. Appl. Phys. 97, 113712 (2005) [14] D. Macdonald, T. Roth, P. N. K. Deenapanray, T. Trupke and R. A. Bardos Doping dependence of the carrier lifetime crossover point upon dissociation of iron-boron pairs in crystalline silicon, Appl. Phys. Lett. 89 142107 (2006) [15] T. Bartel, F. Gibaja, M. Kaes, A. Turenne Quantification of Iron Redistribution between Acceptors in co-doped Silicon, to be presented at the IEEE PVSC in Denver (2014)
525
ScienceDirect Energy Procedia 55 (2014) 519 – 525
4th International Conference on Silicon Photovoltaics, SiliconPV 2014
Determination of acceptor ratio and iron concentration in co-doped silicon Til Bartela,*, Fabien Gibajaa, Maxime Forsterb a
Calisolar GmbH, Magnusstrasse 11, 12489 Berlin, Germany Apollon Solar, 66, cours Charlemagne, 69002 Lyon, France
b
Abstract Low-cost photovoltaic grade feedstock using multiple dopants - mainly Boron and Phosphorous but also Gallium and trace amounts of Aluminum - is currently establishing itself on the market. In this paper, the measurement of dissolved iron by lifetime spectroscopy introduced on the incumbent Boron-only doped Silicon is adapted to materials with several acceptors. A detailed theoretical description is given and pitfalls are identified. Since precise knowledge of the relative acceptor concentrations is necessary for a correct iron determination, a novel method for measuring acceptor concentration fractions in Silicon is proposed. It uses lifetime spectra analysis to determine the crossover point position. Using this simple method, it is possible to fully analytically characterize compensated silicon doped with two acceptor types. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the scientific committee of the SiliconPV 2014 conference. Peer-review under responsibility of the scientific committee of the SiliconPV 2014 conference Keywords: Solar silicon; iron acceptor pairing; compensation; crossover point
1. Introduction Silicor Materials provides its customers with high quality Silicon feedstock purified through a metallurgical process. Its subsidiary, Calisolar GmbH, characterizes the material with regards to chemical purity and defect engineering. A particularity of this feedstock is that it already contains the doping elements Boron and Phosphorous. At earlier processing stages, trace amounts of Aluminum can also be present and at ingot production Gallium may be added for better resistivity control. The performance of cells made from such co-doped and compensated
* Corresponding author. Tel.: (+49) (0)30 6392 4580; fax: (+49) (0)30 6392 4584. E-mail address: [email protected]
1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the scientific committee of the SiliconPV 2014 conference doi:10.1016/j.egypro.2014.08.018
520
Til Bartel et al. / Energy Procedia 55 (2014) 519 – 525
materials has been shown to perform equally to cells made from ultra high purity feedstock [1,2,3]. In some cases, compensation even reduces the recombination activity of some important recombinative defects [4,5], in particular interstitial iron and the pairs it forms with acceptors [6]. In the incumbent Boron only doped Silicon, the measurement of the minority carrier lifetime has proven a fast and reliable method to evaluate the concentration of the total dissolved iron [Fe] and the total acceptor concentration. The procedures are routinely used and have been standardized [7,8]. In this paper, the method is expanded to the measurement of [Fe] in materials with several acceptors of known concentration. Since the acceptor concentrations are often unknown or imprecise, a novel interpretation of the lifetime spectra is proposed to determine acceptor concentration fractions in Silicon co-doped with two acceptor types using crossover point determination. 2. Determining [Fe] in co-doped Si Dissolved Iron causes different defect states depending on the availability of acceptors acting as paring partners [4]. In the following, defect states commonly associated with iron are identified by the index j=1,…,5 for Fei, FeB, FeAl, FeGa, and FeIn respectively. Each defect type j is qualified by its density ሾܰ ሿ, trap energy level ܧ and capture cross sections for holes ߪǡ and for electrons ߪǡ . Using these parameters, the Shockley Read Hall (SRH) formalism allows the determination of the associated minority carrier lifetime ߬ at an injection density ο݊ according to ଵ ఛೕ
ሾேೕ ሿൈሺబ ାబ ାοሻ
ൌଵ
ൗఙ ణ ൈሺబ ାభǡೕ ାοሻାଵൗఙ ణ ൈሺబ ାభǡೕ ାοሻ ǡೕ ǡೕ
.
(1)
Here, ߴ is the thermal velocity, ݊ and are the equilibrium carrier concentrations, and ݊ଵǡ and ଵǡ are the SRH densities given as ಶ షಶೕ ೖ
݊ଵǡ ൌ ܰ ݁ݔ൛ି
ൟǡଵǡ ൌ ܰ ݁ݔ൛ି
ಶೕ షಶೇ ೖ
ൟ,
(2)
using the effective density of states NC and NV in the conduction and valence band edges located at EC and EV. kT is the thermal energy. Taking advantage of the fact that ͳΤ߬ is linear in the defect density ሾܰ ሿ, ߬ଵ is defined as the lifetime associated with a defect of singular density. Eq 1 then becomes ଵ ఛೕ
ൌ
ሾேೕ ሿ ఛೕభ
ൌ
ሾிሿൈఈೕ ఛೕభ
.
(3)
In the last term, the concentration [Nj] of the iron in state j is expressed as a fraction ߙ of the total dissolved iron concentration ሾ݁ܨሿ ൌ σହሾ݁ܨሿ ൈ ߙ . The measured minority carrier lifetime ߬ in the sample can now be described as ଵ ఛ
ൌఛ
ଵ ೝ
ఈ
ሾ݁ܨሿ ൈ σହ ఛభೕ ,
(4)
ೕ
where ߬௧ describes lifetime limiting effects not related to iron. When a sample is illuminated with strong light, iron will be predominantly in its free, unpaired interstitial state. This state is referred to as the “free” state, even if some paired iron may subsist. When left in darkness, most of the iron will repair with acceptors. Accordingly this state is referred to as the “paired” state, even if some residual unpaired, i.e. free iron may remain. Using this terminology, the distribution factors after illumination will change ௗ to ߙ . The lifetimes measured in the sample in these states are referred to as ߬ and ߬ ௗ . In from ߙ
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analogy with Si containing a single acceptor [9], the conversion factor relating ሾ݁ܨሿ to the change in lifetime between the paired and free state can now be defined using Eq 4: ଵ ఛೌೝ
െ
ଵ ఛೝ
ೝ
ೌೝ
ൌ ሾ݁ܨሿ ൈ ቊσହ
ఈೕ
ఛೕభ
െ σହ
ఈೕ
ఛೕభ
ቋ
(5)
Fig. 1. Lifetime measurements of a sample brought to the interstitial state and relaxing to a paired state. The lifetime is fitted with a triple exponential function as in [8].
To extract the concentration of iron ሾ݁ܨሿ from Eq 5, it is necessary to precisely determine the occupation ͲǤͻͷ fractions ߙ . After the breaking of iron-acceptor pairs, the interstitial state dominates the lifetime and ߙଵ ൏ ͲǤͲͳ). The is assumed. In darkness and at room temperature very few Fei will eventually remain unpaired (ߙଵ ௗ (j=2,3,4,5) will depend on the respective concentrations of the distribution among the available acceptors, ߙ paring partners, the pairing preference of the Fei, and its level of thermalization between the different acceptor types. The recommendations for the measurement of [Fei] presented in [8] equally apply to co-doped samples. In addition, special care must be given to the definition and determination of ߬ ௗ (called ߬ in [8]): since iron may redistribute between acceptors after a first repairing, multi-exponential fitting of the lifetime profiles becomes necessary in some cases [10]. This allows the determination of the lifetime at which the iron has paired with the next available acceptor as a result of its random diffusion through the Si matrix, but has not yet redistributed. In this state, ௗ are defined by the concentration fractions of the acceptor types in the sample as the occupation fractions ߙ was confirmed by DLTS for B and Al co-doped samples [11]. 2.1. Exemplary determination of Fei in Si co-doped with B, Ga and P For illustration, ሾ݁ܨሿ is determined on a multicrystalline brick made from solar grade silicon using the correct procedure described in the previous section and under the erroneous assumption of B as sole acceptor in the sample. At the location of measurement, a co-doping with B=1.4E16/cm³, Ga=3.1E15/cm³ and P=9.8E15/cm³ was determined according to the expected segregation behavior of these dopants. The sample is brought into the “free” ൌ ͲǤͻͷ) and the lifetime is then continuously tracked by quasi-steady state state by flashing with light (ߙଵ photoconductance decay resulting in the bulk lifetime profile shown in Fig 1 (measurements are taken in intervals increasing from 30 seconds to 15 minutes and evaluated at an injection density of 1E15/cm³). Within a few days, Fe
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reaches a thermodynamical equilibrium by redistributing from one acceptor type to the other. As a result ߙ (j=2,4) is not trivially defined. However, since the initial pairing of iron with the next neighboring acceptor is ௗ will be equal to the relative usually fast enough to neglect redistribution immediately after the initial pairing, ߙ concentrations of the acceptors at this moment. To properly determine the lifetime at this point, it is necessary to record a lifetime trace until at least the first exponential has saturated, ideally until the following decays can be approximated by fitting. In Fig 1, the experimental data is fitted with the sum of three exponentials. As presented in [10], the second and third exponentials describe redistribution effects between the different dopants. The fitting results from the first exponential are used to determine ߬ ௗ after the initial repairing. Taking into account the concentration fractions ௗ ௗ ؆ ͲǤͺʹǡ ߙସ ؆ ͲǤͳͺ ) and with Eq 5, of the two dopants, the paired fractions are determined ( ߙଶ ሾ݁ܨሿ=8.4E10/cm³ is calculated. For comparison a single exponential fit of the same data (not shown) assuming the ௗ ؆ ͳ) erroneously yields ሾ݁ܨሿ=1.7E11/cm³. sample contains only Boron (ߙଶ 3. Determination of acceptor concentration fraction by crossover point determination The crossover point (COP) defines an excess charge carrier density Δେ at which the lifetime becomes independent of the pairing state of the iron. It represents a characteristic signature of iron in Si and allows the extraction of the acceptor concentration fraction as described in this section. Since the total acceptor concentration can be obtained with the same measurement [8], it can be used to fully quantitatively analyze a material co-doped with two acceptors. If the resistivity is measured, the compensation with a donor can also be extracted. In the following, the theoretical framework for determining acceptor fractions is presented. The expected position of Δେ for a material containing multiple dopants is found by setting Eq 5 to zero. For two dopants, the equation becomes lengthy but is readily solved analytically (see Appendix A). In addition to the defect parameters, net doping and the temperature [12,13], Δେ now becomes a function of the relative ௗ ). If the distribution probability of Fei to the different distribution of the iron between the acceptors (i.e. ߙ acceptors is known and the defect parameters are very different for every acceptor type, a measurement of the crossover point allows the extraction of the concentration fraction between the two acceptor types. Depending on temperature, net doping and recombination parameters, a crossover must not necessarily exist for all concentration ratios. Δେ was calculated for p-type Si sample co-doped with B and either Ga or In since these defects have been characterized in the literature (see Appendix B for details). Note that the reported recombination parameters scatter widely if measured independently. For FeGa and FeIn only one set of values was found. For the interesting FeAl defect, the set of recombination parameters remains incomplete at this time. Fig 2 plots the crossover position as a function of the B fraction for a sample containing either additional Ga or In under the assumption that Fei is distributed according to the respective concentration fractions of the acceptors. A net doping p0=1E16/cm³ and a temperature of 300K was chosen for this example. The COP position is expected to shift towards lower injection by about one order of magnitude when Ga gradually replaces B as a dopant. The trend is even more pronounced for In. Since the shift is important, a good sensitivity for the acceptor fractions can be expected. Experimentally, the measurement of the COP is complicated by trapping effects that can dominate the photoconductance at low injection densities. Quasi steady state photoluminescence may provide an alternative method to avoid trapping artefacts. In addition, when the lifetime within the sampled area is inhomogeneous, the injection density reached may also vary locally. Averaging over the area will induce an error in the determination of the injection density. First experimental results illustrating a practical application of the crossover point method will be published elsewhere [15]. 4. Summary In this paper, the measurement of the interstitial iron concentration by lifetime measurement is adapted to silicon co-doped simultaneously with B, Ga, In and Al. Further, it is proposed to use a characteristic signature of iron in the lifetime spectra (crossover point position) to determine the relative concentrations of acceptors in p-type silicon co-
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doped with two acceptors. Using the proposed modeling, lifetime spectroscopy becomes a simple analytical tool to determine the concentrations of up to three dopants in compensated p-type Silicon containing iron.
Acknowledgements This work was supported under BMWi grant KF2794102AG2.
Appendix A. Theoretical simulation of ઢܖ۱ ۾۽in Si co-doped with two acceptors The COP is analytically derived from Eq 5 for the exemplary case of silicon doped with B and Ga. Other acceptors can easily be implemented by using the correct defect parameters. From the condition that the lifetime at the COP is independent of the state of the Fe it follows from Eq 5: ೌೝ
σହ
ఈೕ
ೝ
ିఈೕ
ൌͲ
ఛೕభ
(6)
Without loss of generality the “free” state can be assumed to be exclusively composed of a population of free Fei (ߙி ൌ ͳ). In analogy, the “paired” state can be assumed to be composed exclusively of Fe paired with either a B or a Ga acceptor. Replacing the j indices according to the defect names (Table 1), Eq 6 now become ଵ భ ఛಷ
ೌೝ
ೌೝ
ൌ
ఈಷಳ
భ ఛಷಳ
ఈಷಸೌ
(7)
భ ఛಷಸೌ
The injection density dependency Δ which solves this equation, is contained within the single defect lifetimes ߬ଵ . Expanding these lifetimes according to their definition (Eq 1) yields బ ାబ ାΔ୬ ଵ ଵൗ ఙǡಷ ణכ൫బ ାభǡಷ ାΔ୬൯ା ൗఙǡಷ ణൈ൫బ ାభǡಷ ାΔ୬൯
ൌ
ೌೝ
ೌೝ
ఈಷಸೌ ൈሺబ ାబ ାΔ୬ሻ ఈಷಳ ൈሺబ ାబ ାΔ୬ሻ ଵ ଵൗ ଵൗ ൈሺ ൈሺబ ାభǡಷಸೌ ାΔ୬ሻ ା ାΔ୬ሻା ା ାΔ୬ሻ ା ାΔ୬ሻାଵൗఙ ൈሺ ൈሺ ൗ బ భǡಷಳ బ భǡಷಳ బ భǡಷಸೌ ఙǡಷಸೌ ణ ఙǡಷಳ ణ ఙǡಷಳ ణ ǡಷಸೌ ణ
(8)
The numerators and the thermal velocity ߴ simplify out. The following short hand notations are introduced: ȱ୨ ൌ ͳൗߙ ߪǡ ൈ ൫݊ ݊ଵǡ Δ൯ ͳൗߙ ߪǡ ൈ ൫ ଵǡ Δ൯ ͳൗ ͳൗ ͳ ൌ ቀᇣᇧ ͳᇧ ൗᇧ ߙᇧ ߪᇧ ߙ ߪǡ ൈ ൫݊ ݊ଵǡ ൯ ൗߙ ߪǡ ൈ ൫ ଵǡ ൯ ߙᇧ ᇧ ǡ ߪ ᇧ ᇧᇤᇧ ᇧǡ ᇧᇥቁ ൈ Δ ᇣᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇤᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇧᇥ ఙೕషభ
ൌ
ߪିଵ Δ
ೕ
ܿ
Where ߙ represent the population ratios used in Eq 7. Substituting these short hand notations in Eq 8 and transposing leads to ȱୣ ȱୣୋୟ ൌ ȱୣ୧ ൈ ሼȱୣୋୟ ȱୣ ሽ
(9)
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Til Bartel et al. / Energy Procedia 55 (2014) 519 – 525
Factoring out the left hand side results in ିଵ ିଵ ିଵ ିଵ ߪிீ ൈ Δଶ ሾߪி ܿிீ ߪிீ ܿி ሿ ൈ Δ ܿி ܿிீ ȱୣ ȱୣୋୟ ൌ ߪி
And the right hand side yields ȱୣ୧ ൈ ሼȱୣୋୟ ȱୣ ሽ ିଵ ିଵ ିଵ ൌ ሺߪி Δ ܿி ሻ ൈ ሼߪி Δ ܿி ߪிீ Δ ܿிீ ሽ ିଵ ିଵ ିଵ ൌ ሺߪி Δ ܿி ሻ ൈ ሼሾߪி ߪிீ ሿΔ ܿி ܿிீ ሽ ିଵ ିଵ ିଵ ିଵ ሿ ିଵ ିଵ ሻ ൈ Δଶ ሾܿி ൈ ሺߪி ߪி ൌ ߪி ൈ ሾߪி ߪிீ ߪிீ ൈ ሺܿி ܿிீ ሻሿ ൈ Δ ܿி ൈ ሼܿி ܿிீ ሽ
Gathering this in Eq 9 gives a polynomial of second order in Δ: ିଵ ିଵ ିଵ ሻെߪ ିଵ ିଵ ሿ ଶ ሾߪி ൈ ሺߪி ߪிீ ி ߪிீ ൈ Δ ିଵ ିଵ ିଵ ିଵ ିଵ ሾܿி ൈ ሺߪி ߪிீ ሻ ߪி כሺܿி ܿிீ ሻ െ ߪி ܿிீ െ ߪிீ ܿி ሿ ൈ Δ ܿி ൈ ሺܿி ܿிீ ሻ െ ܿி ܿிீ ൌ Ͳ
This polynomial in Δ can be solved using the quadratic formula and results in two distinct roots. One root is negative and has no physical meaning, the other root is positive and represents the injection density at the COP Δେ . In addition to its usual dependencies (temperature, net doping, defect parameters), Δେ has now become a ௗ (contained within ܿ and ߪ ). It can be used to determine the distribution of function of the pairing fraction ߙ the Fei between two acceptors. Note that since Δେ Ͳͳͳ بȀ ³ is expected, ݊ , ݊ଵǡி , ݊ଵǡிீ , and ଵǡி may all be neglected for p-type silicon at temperatures below 400K, however this does not significantly simplify the equations and was not applied here.
Appendix B. Recombination parameters of Fe related defects Note that values that have been reported repeatedly scatter widely and we rely on the recommendation in [12]. Data for FeGa, FeIn and FeAl is scarce or missing altogether. Table 1. Energy levels and capture cross sections of Fei related defects in Si as used in this paper. Defect
ܧ ሺܸ݁ሻ
ߪǡ ሺܿ݉²ሻ
ߪǡ ሺܿ݉²ሻ
1
Fei
ܧ௩ ͲǤ͵ͺ
4E-14
7E-17
[6]
2
FeB
ܧ െ ͲǤʹ
5E-15
3E-15
[14]
3
FeAl
ܧ௩ ͲǤͳ͵ܽ݊݀ͲǤʹ
??
2E-14 to 4E-15
[6]
4
FeGa
ܧ௩ ͲǤʹ
4E-14
2E-14
[13]
5
FeIn
ܧ௩ ͲǤͳͷ
3.5E-13
1.5E-14
[13]
Index j
Reference
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