Issue 
Eur. Phys. J. Appl. Phys.
Volume 94, Number 1, April 2021



Article Number  10101  
Number of page(s)  7  
Section  Semiconductors and Devices  
DOI  https://doi.org/10.1051/epjap/2021210015  
Published online  12 April 2021 
https://doi.org/10.1051/epjap/2021210015
Regular Article
Nickel and gold identification in ptype silicon through TDLS: a modeling study
Aix Marseille University, Université de Toulon, CNRS, IM2NP, Marseille 13397, France
^{*} email: olivier.palais@univamu.fr
Received:
18
January
2021
Accepted:
11
March
2021
Published online: 12 April 2021
In Silicon, impurities introduce recombination centers and degrade the minority carrier lifetime. It is therefore important to identify the nature of these impurities through their characteristics: the capture cross section σ and the defect level E_{t}. For this purpose, a study of the bulk lifetime of minority carriers can be carried out. The temperature dependence of the lifetime based on the ShockleyReadHall (SRH) statistic and related to recombination through defects is studied. Nickel and gold in ptype Si have been selected for the SRH lifetime modeling. The objective of the analysis is to carry out a study to evaluate gold and nickel identification prior to temperaturedependent lifetime measurements using the microwave phaseshift (μWPS) technique. The μWPS is derived from the PCD technique and is sensitive to lower impurity concentrations. It has been shown that both gold and nickel can be unambiguously identified from the calculated TDLS curves.
Note to the reader: Further to the publication of an erratum, the citation of the article was modified on 19 July 2021.
© S. Dehili et al. published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
In 2019, 27% of the global electricity generation was ensured by the use of renewable energies [1] and the energy mix is constantly evolving. This change is driven by environmental issues, climate change policies, economical and geopolitical motivations for energy independence. The penetration rate of solar energy remains low, it represents around 3% of global power output despite its high potential. Major drop in costs of solar equipment should, however, allow a strong growth of PV. The international energy agency (IEA) forecasts a solar photovoltaic power generation as high as 16% in 2050.
Due to its high availability, wellestablished technology showing high conversion efficiency and good durability, silicon dominates the photovoltaic market. Crystalline silicon wafers have a share up to 95% of the worldwide market [2]. Despite the highefficiency level of this technology, silicon ingot fabrication processes still face challenges in improving material properties by reducing defects and impurities concentrations.
During crystal growth and processing of silicon solar cells, the semiconductor material is at risk of contamination by impurities. Impurities are an obstacle to the improvement of the performances of solar cells as they are responsible for the degradation of the minority carrier lifetime [3]. The minority carrier lifetime is an important electronic property as it allows to assess the intrinsic quality of semiconductor materials for solar cells. Impurities were found to be detrimental to both ptype and ntype cell efficiency [4]. Moreover, they also contribute to the LightInducedDegradation (LID) phenomenon in both mc and monoSi [5,6]. In order to limit and mitigate the effects of impurities, it is important to quantify and identify their nature through the determination of their main characteristics: the concentration N_{t}, the capture cross section σ and the defect level E_{t}. In Silicon and other indirect band gap materials, the recombination of electrons and holes through defect levels in the band gap is dominated by the ShockleyReadHall (SRH) recombination mechanism. Lifetime spectroscopy (LS) methods allow for the lifetimelimiting defect parameters to be determined through the analysis of injection, temperature or temperature and injectiondependent minority carrier lifetime measurements.
This study sets out to study gold (Au) and nickel (Ni) contamination in Borondoped Silicon through temperaturedependent lifetime spectroscopy (TDLS) modeling. Even though gold contamination is of minor importance in silicon wafer manufacturing processes nowadays, its properties are well established. It can therefore be used for an accurate modeling of TDLS characteristics. Gold is a heavy 5d transition metal that strongly degrades the lifetime. Samples can easily be contaminated by mechanical contact or it can also be easily replated on wafers if using goldcontaminated solutions. As for Nickel, it is among the main impurities in device production, the contamination occurs by mechanical contact and it is also replated on wafer surfaces during wet chemical processes [7]. Ni exhibits high values of diffusivity and solubility [8,9]. It therefore precipitates quantitatively even during rapid quenching from high temperatures [10] and only less than 1% of the total solubility remains dissolved and forms electrically active defects. Unlike iron and chromium, Ni cannot be efficiently removed from wafers surface by cleaning procedures [11].
Modeling the minority carrier lifetime allows to assess the TDLS capability to identify Au and Ni in Borondoped Si and define the constraints for performing the measurements such as the temperature range.
2 Modeling
2.1 The Shockleyreadhall equation
The dependence of minority carrier lifetime in terms of temperature and injection level can be studied through TDLS, IDLS and TIDLS [12–16] (temperaturedependent, injectiondependent and temperature and injectiondependent lifetime spectroscopy respectively), based on the ShockleyReadHall (SRH) theory. The latter describes the trapassisted recombination statistic in semiconductors [17,18]. Defects introduce intermediate energy levels in the forbidden gap that can act as recombination centers for free carriers. These levels are characterized by the depth of the energy level E_{t}, the density N_{t} and the capture cross sections σ_{n} and σ_{p} for electrons and holes respectively.(1)
The SRH densities n_{1} and p_{1} represent the electrons and holes concentration when the defect and Fermi level coincide, and are expressed as:(2)
where n_{0} and p_{0} represent the carrier densities in the conduction and valence band respectively at thermal equilibrium. N_{c} and N_{v} are the effective densities of states in the conduction and valence band respectively. The capture time constants for electrons and holes, τ_{n0} and τ_{p0} respectively, are given by:(3)with and the electron and hole thermal velocity respectively.
Introducing the symmetry factor k, defined as,(4)
Equation (1) can be rewritten in terms of the symmetry factor:(5)
E_{t}, N_{t} and σ are characteristic to the impurity's nature and allow its identification. TDLS consists in fitting equation (1) to experimental temperaturedependent lifetime data in order to extract these quantities. It is therefore necessary to consider the temperature dependence of all the parameters in equation (1).
2.2 Parameters temperature dependence
The temperature dependence of the capture time constants τ_{n0}τ_{p0} arises from the electron and hole thermal velocity and the capture cross sections σ_{n} and σ_{p}.(6)where v_{the,h}^{300} the thermal velocities at room temperature, calculated as:(7)with m_{n} = 0.26m_{o} and m_{p} = 0.39m_{o} the electron and hole masses at 300 K and m_{0} the electron mass at rest.
The temperature dependence of the capture cross sections depends on the capture process involved. In silicon, Excitonic Auger [19] (EA) and multiphonon emission [20] (MPE) processes are dominant [21]. The EA process is relevant to deep impurities. When a free exciton meets an impurity, one of the particles is captured and the excess energy is transferred to the second one. Two subsequent EA processes are necessary for a complete electronhole recombination. In this case, the capture cross section shows a negative powerlaw temperature dependence and is expressed as [22]:(8)with α > 0.
In the MPE mechanism model, lattice vibrations cause for the free and bound carrier levels to cross which results in the capture of a free carrier. The excessive energy is dissipated through the emission of multiple phonons. MPE capture mechanism has a thermally activated behaviour, the capture cross section is expressed as:(9)
E_{a} being the energy that a free electron from the BC has to overcome in order to be captured by the defect.
For the effective densities of states, N_{c} and N_{v}, we consider the temperature dependence of the effective masses. They are expressed as [23]:(10)where k and h are Boltzmann and Planck's constants respectively, and the densityofstates effective masses in the BC and BV respectively given by [24]:(11)
With a, b, c, d, e, f, g, h and i constants given in Table 1 [24].
In equation (11), E_{g} (0) is the energy gap of silicon at 0K and is equal to 1.17 eV, the temperature dependence of the energy band gap is expressed as [25]:(12)where α = 73 × 10^{−4} ev/K is a temperature coefficient and β = 636 K a temperature offset.
The range in which TDLS data are acquired requires to also consider the temperature dependence of the carrier density. We distinguish three regimes:

the freezeout regime at low temperatures where the thermal energy is not sufficient to ionize the dopants atoms (p_{o} (T) < N_{A}).

the extrinsic regime at intermediate temperatures where the carrier density equals the doping (p_{o} (T) = N_{A}).

the intrinsic regime at high temperatures where the semiconductor is dominated by intrinsic conduction (p_{o} (T) > N_{A}).
Considering ptype silicon, the majority carrier density at thermal equilibrium is a piecewisedefined function, expressed as [26]:(13)where f_{A} is the ionization level, the fraction of ionized acceptor atoms:(14) with .
The minority carrier density is calculated using:(15)with n_{i} the intrinsic carrier density, function of the effective density of states in the BC and BV and the bandgap energy E_{g}:(16)
3 Results
3.1 Gold contamination
In the silicon lattice, gold occupies substitutional sites and acts as a twolevel defect [27] thus introducing two energy levels, a donor and an acceptor [28,29].
The temperature dependence of the capture cross sections associated to the gold levels was measured in ntype Si [30]. As gold is not known for forming complexes in Si, the capture cross sections are expected to be the same in ptype Si. The activation energy and capture cross sections for the gold levels are summarized in Table 2.
In ptype Si, the lifetime of minority carriers is dominated by the donor level [31–33].
We consider goldcontaminated ptype silicon with a Boron doping of N_{A} = 10^{15} cm^{−3} and a gold concentration of N_{t} = 10^{12} cm^{−3}. At low and intermediate temperatures (T < 500 K), for a low injection level (Δn ≪ p_{0} + n_{0}) and ptype doping (n_{0} ≪ p_{0}), equation (1) reduces to:(17)
At high temperature, the approximation does not hold, n_{0} increases as we enter the intrinsic conduction. At low temperature, as p_{1} → 0 the lifetime can be approximated by τ_{n0} (Eq. (3)) as shown in Figure 1. The thermal velocity being known, N_{t} × σ_{n} can be determined. In the hypothesis of a known impurity concentration N_{t}, fitting the low temperature part of the SRH lifetime to equation (3) and multiplying the result by the electron thermal velocity v_{the}, an electron capture cross section of σ_{n} = 2.12 × 10^{−11}T ^{−1.96} is obtained.
To extract the energy depth ΔE_{t}, we use the Defect Parameter Solution Surface (DPSS) method developed by Rein and Glunz [15]. The method consists of leastsquaresfitting the TDLS data while varying the energy depth ΔE_{t} through the whole band gap (ΔE_{t} ∈ [0, 1.12 eV]) and optimizing the symmetry factor k for each energy depth. The DPSS results in two curves, the optimal symmetry factor kDPSS and the least square fitting error Chi^{2}DPSS as a function of E_{c} − E_{t}.
Applying the DPSS analysis to the TDLS curve of Figure 1, it results in the two curves of Figure 2. We get two solutions as the least squares fit error is minimized by two distinct defect parameters, one in each half of the band gap with the same energy depth located at E_{c} − E_{t} = 0.34 eV and E_{t} − E_{v} = 0.34 eV with optimal k values of k = 1.16 and k = 0 respectively.
Activation energy and capture cross sections of gold donor, gold acceptor and substitutional nickel in silicon.
Fig. 1
Calculated TDLS curve (thick solid line) of Aucontaminated ptype Si ([Au] = 10^{12}cm^{−3}, N_{A} = 10^{15}cm^{−3}) and the electron capture time constant τ_{n0} (dashed line). Below 250 K, approximating the TDLS curve by τ_{n0} allows the Tdependent capture crosssection σ_{n} (T) extraction. 
Fig. 2
Resulting DPSS diagram obtained from leastsquaresfitting the TDLS lifetime data shown in Figure 1 using the extracted capture cross section σ_{n} (T) = 2.12 × 10^{−11} × T ^{−1.96}. Two solutions are obtained from Chi^{2}DPSS curve minimum position, E_{c} − E_{t} = 0.34 eV with k = 1.16 and E_{t} − E_{v} = 0.34 eV with k = 0. With a smaller Chi^{2} value by almost two orders of magnitude, the solution in the second half of the bandgap is identified as the true solution. 
3.2 Nickel contamination
At room temperature, only substitutional nickel remains in Si as unstable interstitial nickel disappears by outdiffusion or precipitation [7]. The parameters associated to substitutional Nickel (Ni_{s}) were determined by Rein [26] using TDLS (Tab. 2) and were used for the modeling of the lifetime curves.
We consider nickelcontaminated ptype silicon with a Boron doping of N_{A} = 10^{15} cm^{−3} and a nickel concentration of N_{t} = 10^{12}cm^{−3}. At low and intermediate temperatures (T < 500 K), for a low injection level (Δn ≪ p_{0} + n_{0}), ptype doping (n_{0} ≪ p_{0}) and for a defect in the upper half of the gap, equation (1) reduces to:(18)
At low temperature, the lifetime is approximated by the electron capture time constant τ_{n0} (Eq. (3)) as shown in Figure 3. In the hypothesis of a known impurity concentration N_{t}, fitting the low temperature part of the SRH lifetime to equation (3) leads to an electron capture cross section of σ_{n} = 4.56 × 10^{−11}T ^{−2.4}.
Applying the DPSS analysis to the TDLS curve of Figure 3 using this extracted capture cross section results in the two curves of Figure 4.
Two solutions are highlighted by the DPSSChi^{2} curve minimums, one in each half of the band gap located at E_{c} − E_{t} = 0.40 eV and E_{t} − E_{v} = 0.41 eV with optimal DPSSk values of k = 0.83 and k = 0.16 respectively. The solution in the second half of the gap (E_{t} − E_{v} = 0.41 eV) representing the global minimum of the DPSSChi^{2} curve could stand out as the true solution, however the solution does not correspond to the true level of Nickel.
Applying the DPSS using the τ_{n0} value used for the TDLS curve modeling gives a distinct solution at the right position of the Ni defect level E_{c} − E_{t} = 0.40 eV (DPSS diagram not shown). This means that the small offset that appears in Figure 3 resulting from the approximation of the low temperature part of the TDLS curve by equation (3) is enough to throw the solution in the wrong half of the gap.
Since we can accurately extract the temperature dependence of τ_{n0} from the NiTDLS curve at low temperature, we can modify the DPSS optimized parameters to reduce the error related to the approximation. Inputting only the temperature dependence of τ_{n0} in the leastsquaresfitting routine, we carry a DPSS analysis optimizing both the symmetry factor k, and the N_{t} × σ_{0} product. The DPSS diagram now results in three curves, the optimal symmetry factor kDPSS, the N_{t} × σ_{0} product denoted ADPSS and the least square fitting error Chi^{2} as a function of E_{c} − E_{t}.
Using the extracted temperature dependence of τ_{n0} ∝ T ^{2.4}, it results in the three curves of Figure 5. Two solutions are highlighted by the Chi^{2}DPSS curve minimum, one in each half of the band gap with the same energy depth and close values of A = N_{t} × σ_{0}. The solutions are located at E_{c} − E_{t} = 0.40 eV and E_{t} − E_{v} = 0.41 eV with optimal kDPSS and ADPSS values of k = 0.89, A = 49.5 cm^{−1} and k = 0.28, A = 46.7 cm^{−1} respectively.
Fig. 3
Calculated TDLS curve (thick solid line) of Nicontaminated ptype ([Ni] = 10^{12}cm^{−3}, N_{A} = 10^{15}cm^{−3}) and the electron capture time constant τ_{n0} (dashed line). Below 270K, approximating the TDLS curve by τ_{n0} allows the Tdependent capture crosssection σ_{n} (T) extraction. 
Fig. 4
Resulting DPSS diagram obtained from leastsquaresfitting the TDLS lifetime data shown in Figure 1 using the extracted capture cross section σ_{n} (T) = 4.56 × 10^{−11} × T ^{−2.4}. Two solutions are obtained from Chi^{2}DPSS curve minimum position, E_{c} − E_{t} = 0.40 eV with k = 0.83 and E_{t} − E_{v} = 0.41 eV with k = 0.16. Even though the second solution shows a lower Chi^{2} value, the solution does not correspond to the true Ni defect level. 
Fig. 5
Resulting DPSS diagram obtained from leastsquaresfitting the TDLS lifetime data shown in Figure 1 only using the extracted temperature dependence of the capture cross section (T ^{−2.4}) as an input. The diagram results in three curves, (a) the optimized symmetry factor k (b) optimized N_{t} × σ_{0} denoted ADPSS and (c) the leastsquares fit error Chi^{2}. Two solutions are highlighted by the Chi^{2}DPSS curve minimum position, E_{c} − E_{t} = 0.40 eV with k = 0.89, A = 49.5 cm^{−1} and E_{t} − E_{v} = 0.41 eV with k = 0.28, A = 46.7 cm^{−1}. The Chi^{2}DPSS curve allows the true defect parameters identification from the position of its global minimum in the upper bandgap half. 
4 Discussion
The analysis of temperaturedependent lifetime data does not allow to quantify unknown impurities as the impurity concentration N_{t} cannot be separated from the product N_{t} × σ_{n} (T).
We can however extract the temperature dependence of the electron capture cross section in the case of gold or nickel contamination in ptype Si. At low temperature, the temperature dependence of the lifetime arises from the electron capture cross section σ_{n} (T) and the known electron thermal velocity .
The DPSS analysis of the Aucontaminated ptype Si TDLS curve highlighted two solutions located at E_{c} − E_{t} = 0.34 eV and E_{t} − E_{v} = 0.34 eV with optimal k values of k = 1.16 and k = 0 respectively. These two solutions differ in their DPSSChi^{2} value. In this case, the method allows us to determine which of the solutions correspond to the true defect parameter as the Chi² value of the solution E_{t} − E_{v} = 0.34 eV and k = 0 in the lower half of the gap is almost two orders of magnitude smaller than the solution in the upper half of the gap. The corresponding optimized kDPSS value of k = 0 is due to the fact that the TDLS curve does not depend on the symmetry factor as given by the approximation of equation (18). Therefore, in the case of gold we cannot deduce a value for the hole capture cross section from the kDPSS result.
For the DPSS results extracted from the TDLS curve of Nicontaminated ptype Si, although the solution in the lower half of the bandgap E_{t} − E_{v} = 0.41 eV is distinguished by a lower Chi^{2} value in Figure 4, it does not correspond to the true Ni level. Both solutions being of the same order of magnitude, we cannot formally conclude regarding the position of the defect level. The ambiguity in these results arises from the approximation of the lifetime data at low temperature. For DPSS to yield unambiguous results, an accurate determination of the electron capture time constant is necessary.
In the case of both Ni and Au, as we can accurately extract the temperature dependence of τ_{n0} at low temperature, instead of inputting τ_{n0} in the DPSS leastsquaresfitting routine, we now only input its temperature dependence and optimize both the symmetry factor kDPSS and the N_{t} × σ_{0} product denoted ADPSS. In the case of Nickel, the solutions are located at E_{c} − E_{t} = 0.40 eV and E_{t} − E_{v} = 0.41eV with optimal kDPSS and ADPSS values of k = 0.89, A = 49.5 cm^{−1} and k = 0.28, A = 46.7 cm^{−1} respectively. The solution in the upper bandgap half (E_{c} − E_{t} = 0.40 eV) has a Chi^{2}DPSS value more than an order of magnitude smaller than the solution in the lower bandgap half. Therefore, E_{c} − E_{t} = 0.40 eV, k = 0.89 and A = 49.5 cm^{−1} represent the true defect parameters. In the hypothesis of a known impurity concentration (here N_{t} = 10^{12}cm^{−3}), using the ADPSS value and the extracted temperature dependence, the total electron capture cross section is given by σ_{n} = 4.95 × 10^{−11}T ^{−2.4}.
The kDPSS value results in an almost 30% overestimation of the symmetry factor k = 0.7 used for the TDLS curve modeling leading to an underestimation of the hole capture cross section σ_{p}, but the result remains in the same order of magnitude. Since the capture cross section of both holes and electrons follows the same temperature law, using the kDPSS value we can deduce the hole capture cross section at 300 K σ_{p}:.
The capture cross section values used for the temperaturedependent lifetime modeling for Nickel were given by Rein [26]. The given value of the hole capture cross section was extracted using the optimized kDPSS value assuming that the capture process for both holes and electrons is the same, the symmetry factor being temperature independent. Thus, the hole capture cross section was assigned the same temperature dependence as the one extracted for electrons. However, the hypothesis of a constant symmetry factor does not hold for all impurities according to the literature as given by the capture cross sections of Au [30], Fe [34] and Ti [35]. The hole capture cross section has the effect of modifying both quantitatively and qualitatively the TDLS curve for Nicontaminated Si depending on its model.
All the temperaturedependent lifetime data were calculated in the 120650K range. Extracting the temperature dependence of the capture cross section σ_{n} requires for the data to be obtained at sufficiently low temperatures. Not including the high temperature part of the curve in the fit routine does not prevent the energy depth and position of the defect to be determined.
Measured TDLS data are subject to uncertainties. The DPSSChi^{2} curve allows to estimate an error on the extracted defect parameters from the minimum peak width by setting a limit for the tolerated DPSSChi^{2} value.
This study is a preliminary study for the development of a characterization bench based on the microwave phaseshift technique (μWPS) for the determination of impurities in silicon. μWPS [36] is a sensitive (10^{9}cm^{−3} limit [37]), contactless technique carried out at low level of carrier injection based on the measurement of the phaseshift between the modulated light excitation signal and the intensity of the reflected microwaves.
5 Conclusion
Recombination through defect levels in the band gap of silicon has the impact of limiting the minority carrier lifetime inducing efficiency losses in crystalline silicon. The study of the temperaturedependent lifetime of minority carriers in gold and nickelcontaminated ptype Si showed that the exploitation of the TDLS curves allow to identify both impurities through their defect level ΔE_{t} and electron capture cross section σ_{n} (T). TDLS does not allow to quantify the impurities through the determination of N_{t} and data have to be acquired over a wide range from low to high temperatures. The low temperature part allows the temperaturedependence of the electron capture time constant τ_{n0} to be extracted while the whole curve is used for the defect parameter solution surface (DPSS) fit routine. Optimizing both the symmetry factor k and the N_{t} × σ_{0} product, the DPSS allows the unambiguous determination of the defect energy depth and bandgap half position.
The development of an experimental setup for TDLS data acquisition based on the microwave phaseshift technique is currently ongoing and will allow to compare simulation results with experimental data. A secondary goal will be to extend the study to other detrimental impurities such as iron and chromium.
Author contribution statement
S. Dehili conducted the modeling study and wrote the manuscript. D. Barakel, L. Ottaviani and O. Palais supervised the work and the data analysis. All authors commented on previous versions of the manuscript, read and approved the final manuscript.
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Cite this article as: Sarra Dehili, Damien Barakel, Laurent Ottaviani, Olivier Palais, Nickel and gold identification in ptype silicon through TDLS: a modeling study, Eur. Phys. J. Appl. Phys. 94, 10101 (2021)
All Tables
Activation energy and capture cross sections of gold donor, gold acceptor and substitutional nickel in silicon.
All Figures
Fig. 1
Calculated TDLS curve (thick solid line) of Aucontaminated ptype Si ([Au] = 10^{12}cm^{−3}, N_{A} = 10^{15}cm^{−3}) and the electron capture time constant τ_{n0} (dashed line). Below 250 K, approximating the TDLS curve by τ_{n0} allows the Tdependent capture crosssection σ_{n} (T) extraction. 

In the text 
Fig. 2
Resulting DPSS diagram obtained from leastsquaresfitting the TDLS lifetime data shown in Figure 1 using the extracted capture cross section σ_{n} (T) = 2.12 × 10^{−11} × T ^{−1.96}. Two solutions are obtained from Chi^{2}DPSS curve minimum position, E_{c} − E_{t} = 0.34 eV with k = 1.16 and E_{t} − E_{v} = 0.34 eV with k = 0. With a smaller Chi^{2} value by almost two orders of magnitude, the solution in the second half of the bandgap is identified as the true solution. 

In the text 
Fig. 3
Calculated TDLS curve (thick solid line) of Nicontaminated ptype ([Ni] = 10^{12}cm^{−3}, N_{A} = 10^{15}cm^{−3}) and the electron capture time constant τ_{n0} (dashed line). Below 270K, approximating the TDLS curve by τ_{n0} allows the Tdependent capture crosssection σ_{n} (T) extraction. 

In the text 
Fig. 4
Resulting DPSS diagram obtained from leastsquaresfitting the TDLS lifetime data shown in Figure 1 using the extracted capture cross section σ_{n} (T) = 4.56 × 10^{−11} × T ^{−2.4}. Two solutions are obtained from Chi^{2}DPSS curve minimum position, E_{c} − E_{t} = 0.40 eV with k = 0.83 and E_{t} − E_{v} = 0.41 eV with k = 0.16. Even though the second solution shows a lower Chi^{2} value, the solution does not correspond to the true Ni defect level. 

In the text 
Fig. 5
Resulting DPSS diagram obtained from leastsquaresfitting the TDLS lifetime data shown in Figure 1 only using the extracted temperature dependence of the capture cross section (T ^{−2.4}) as an input. The diagram results in three curves, (a) the optimized symmetry factor k (b) optimized N_{t} × σ_{0} denoted ADPSS and (c) the leastsquares fit error Chi^{2}. Two solutions are highlighted by the Chi^{2}DPSS curve minimum position, E_{c} − E_{t} = 0.40 eV with k = 0.89, A = 49.5 cm^{−1} and E_{t} − E_{v} = 0.41 eV with k = 0.28, A = 46.7 cm^{−1}. The Chi^{2}DPSS curve allows the true defect parameters identification from the position of its global minimum in the upper bandgap half. 

In the text 
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