separately. However, LS is sensitive to the actual recombination channels which limit the material quality and hence the conversion efficiency of the solar cell, while from DLTS measurements the impact for material quality cannot be decided.
In summary, it can be concluded that DLTS is the workhorse for analyzing the defect parameters of point-like defects in silicon, while lifetime spectroscopy has special advantages for accessing the defect centers which actually limit the material quality and hence the solar cell efficiency. A combination of both methods can result in a defect level to be fully characterized.
11.3 Summary and comparison of experimental results
The defect parameters of the different point-like impurities which were determined within this work are summarized in Tab. 11.6.
Manganese-related defect levels in p-type silicon were investigated in Chap. 7. For the manganese-boron defect configuration (MnB), DLTS measurements yielded an energy level at (EV + 0.55) ±0.02 eV and a majority carrier capture cross section of σp = 3.5×10-13 cm2. Combining these results with an IDLS analysis (being based on QSS-PC measurements), the minority carrier capture cross section could be determined to σn = 2.1×10-12 cm2 (k = 6.0). TDLS measurements (being based on µW-PCD measurements) at low temperatures revealed the temperature-dependence of the minority carrier capture cross section σ(T) ~ T -1.6, indicating recombination via excitonic Auger capture.
For the interstitial defect configuration of manganese, TDLS measurements at high temperatures revealed a defect level located at EC – 0.45 (0.405 – 0.495) eV with a ratio of the capture cross sections of k = 9.4 (3.2 – 19.0). Both found defect levels correspond very well with values reported in literature.
From dynamic TDLS measurements, the association time constant of the formation of manganese-boron pairs could be determined and can be represented by the expression τassoc = 8.3×105 K-1 cm-3 (T / Ndop) exp(0.67 eV / kB T). From these measurements, the diffusivity coefficient D0 and the migration enthalpy HM of manganese in silicon was determined (in a temperature range from 70°C to 120°C) to be D0 = 6.9×10-4 cm2 s-1and HM = 0.67 eV.
Tab. 11.6: List of the defect parameters determined in this work.
Capture cross sections Impurity Energy level
(eV)
Titanium-related defect levels in p-type silicon were investigated in Chap. 8. Two distinct defect levels were found using TDLS analysis being based on QSS-PL measurements and IDLS analysis being based on QSS-PC measurements. For the deep defect level, an energy level of EC – 0.47 (0.44 – 0.49) eV with a ratio of the capture cross sections of k = 13 (7 – 21) was determined. The temperature-dependence of the minority carrier capture cross section was measured to be σ(T) ~ T−1.22.
For the shallow defect level that titanium introduces into the silicon band gap, in accordance with literature reports, an energy level of EC – 0.08 (0.06 – 0.13) eV could be determined. The temperature-dependence of the minority carrier capture cross section was measured to be σ(T) ~ T−1.70.
Aluminum-related defect levels in p-type silicon were investigated in Chap. 9. DLTS measurements using two different measurement setups yielded an energy depth of (EV + 0.44) ±0.02 eV and a majority carrier capture cross section of
11.3 Summary and comparison of experimental results 155
σp = 3.6×10-13 cm2. Combining these results with an IDLS analysis (being based on QSS-PC measurements), the minority carrier capture cross section could be determined to σn = 3.1×10-10 cm2 (k = 870).
Tungsten-related defect levels in p-type silicon were investigated in Chap. 10. Using DLTS measurements, an energy depth of (EV + 0.38) ±0.03 eV and a majority carrier capture cross section of σp = 4.8×10-16 cm2 could be extracted. Comparing these values with recent values determined by T-IDLS, namely (EV + 0.34) ±0.02 eV and k = 9.6, a small discrepancy between the two measurement methods is existent.
12 Conclusions
The present work was concerned with the analysis of electrically active defects in silicon for solar cells. Analysis of such defects was performed using the two different characterization techniques deep-level transient spectroscopy and lifetime spectroscopy. The challenge of the present work was the in-depth comparison of the different measurement and evaluation techniques as well as the experimental use of these techniques for accessing the defect parameters of various impurities in silicon material.
The spectroscopic evaluation of the injection- and temperature-dependent excess carrier lifetime is based on a reliable measurement. Different physical mechanisms can be utilized for accessing the excess carrier lifetime. Photoconductance-based measurements are well-established but are prone to measurement artifacts due to trapping of minority carriers and depletion region modulation at low injection densities. Recently, photoluminescence-based excess carrier lifetime measurements emerged, allowing for reliable measurements of the excess carrier lifetime even at very low injection densities. These excess carrier lifetime data, acquired in a wide injection range, are fundamental for the subsequent analysis of the underlying defect parameters using advanced lifetime spectroscopy.
Fig. 12.1: Schematic of the effect of photon reabsorption. The longer the path is for the photoluminescence photons within the silicon sample, the more get reabsorbed, reducing the detectable photoluminescence light intensity.
However, the effect of photon reabsorption complicates temperature-dependent measurements of the excess carrier lifetime using the photoluminescence-based measurement technique (see Fig. 12.1). Within this work, it was possible to derive a carrier lifetime and temperature-dependent correction matrix, which allows for reliable measurements of the excess carrier lifetime in a large temperature range. This
correction matrix is developed from analytical findings based on the generalized Planck radiation law as well as from subsequent numerical simulations of the measurable photoluminescence radiation.
Based on the findings of the temperature-dependent photon reabsorption, the coefficient of radiative recombination was investigated in detail using the photoluminescence-based measurement technique. These measurements were independent of the intrinsic carrier concentration and were found to give a good correlation with values reported in literature.
By means of different intentionally titanium-contaminated p-type silicon samples the reliability of the temperature-dependent photoluminescence-based measurements was investigated. A sound agreement between the different samples was observed, showing the good accuracy of the derived correction due to photon reabsorption. For the titanium-related defect levels, these temperature-dependent photoluminescence measurements, in conjunction with injection-dependent photoconductance measurements, resulted in an identification of two related defect levels. One shallow defect level was either found to be located in the band gap half of the minority carriers at EC - Et = 0.08 (+0.05, −0.02) eV, or in the band gap half of the majority carriers at EC - Et = 1.024 (+0.006, –0.007) eV. Comparison with literature values measured by means of deep-level transient spectroscopy strongly suggests the solution being located in the band gap half of the minority carriers and thus representing the true defect parameters. The deeper titanium-related defect level of these samples was unambiguously found to be located in the band gap half of the minority carriers at an energy depth of EC - Et = 0.47 (+0.02, −0.03) eV with a corresponding symmetry factor of k = 13 (+8, −6). Since no such deep defect level has been observed in literature so far, it is not very likely that this deep defect center found out here is also related to interstitial titanium. A comparison with literature values suggest a cross-contamination of the samples with vanadium or chromium, both having a defect level being located at EC - Et = 0.45 eV.
With intentionally manganese-contaminated p-type silicon samples, two different defect configurations were found, depending on the temperature and the illumination conditions of the sample. For the interstitial defect configuration of manganese, temperature-dependent lifetime measurements at high temperatures revealed a defect level located at EC – Et = (0.45 ± 0.05) eV with a ratio of the capture cross sections of k = 9.4 (+9.6, -6.2). Concerning the defect related to manganese-boron pairs, deep-level transient spectroscopy measurements below room temperature unambiguously identified the deep defect level to be located at an energy level of
12 Conclusions 159
Et - EV = (0.55 ±0.02) eV with a majority carrier capture cross section of σp = 3.5×10-13 cm2. From injection-dependent lifetime spectroscopy measurements the corresponding symmetry factor k = σn/σp , could be determined to k = 6.0 (implying σn = 2.1×10-12 cm2). From dynamic temperature-dependent excess carrier lifetime measurements with changing illumination and temperature, the temperature-dependent association time constant of the formation of manganese-boron pairs could be determined and can be represented by the expression τassoc = 8.3×105 K-1 cm-3 (T / Ndop) exp(0.67 eV / kB T). From these measurements, the diffusivity coefficient D0 and the migration enthalpy HM of manganese in silicon were determined (in a temperature range from 70°C to 120°C) to be D0 = 6.9×10-4 cm2 s-1 and HM = 0.67 eV. Compared with literature values for the diffusivity, this is two times faster than expected, but in perfect analogy to the findings with iron-boron pairs, with regard to similar experimental techniques.
The combined application of deep-level transient spectroscopy and injection-dependent lifetime spectroscopy is an efficient way to obtain the defect parameters of the lifetime-limiting defect in intentionally aluminum-contaminated p-type silicon.
From the various energy levels reported in literature, we identified by means of deep-level transient spectroscopy one single energy deep-level at an energy depth of Et - EV = (0.44 ±0.02) eV with a majority carrier capture cross section of σp = 3.6×10-13 cm2 (at T = 200 K). The corresponding symmetry factor k can be determined from injection-dependent excess carrier lifetime measurements and was determined to be k = 870. The minority carrier capture cross section can be calculated as σn = 3.1×10-10cm2, wherefore a temperature-independent symmetry factor was assumed.
DLTS measurements of an intentionally tungsten-contaminated p-type silicon sample resulted in an extracted deep defect level of Et - EV = (0.38 ± 0.03) eV with a majority carrier capture cross section of σp = 4.8×10-16cm2.
The photoluminescence-based excess carrier lifetime measurement technique was found to be an excellent complement to the widely established photoconductance-based measurement technique. For samples with high excess carrier lifetimes, photoluminescence measurements can be carried out independent of other measurement techniques, while the photoluminescence signal has to be calibrated using other techniques for samples with low carrier lifetimes. Overall, an excellent agreement between the different investigated excess carrier lifetime measurement techniques was found.
Having investigated and certified the accuracy of the photoluminescence technique, new challenges can be approached using this approach. Recently we proposed a method for measuring the excess carrier lifetime of epitaxial layers of crystalline thin-film solar cells [151, 152], for which a patent is filed. This is all the more important since established techniques are not capable of measuring the excess carrier lifetimes of multi-layer samples reliably so far. Investigating different kinds of semiconductor materials using variable types of photoluminescence sensors promises interesting insights and results, too.
Finally, the physically different defect characterization methods, deep-level transient spectroscopy and lifetime spectroscopy, were analyzed and compared in detail. Due to the fact that with none of the methods the defect parameters of an electrically active defect level can be accessed completely, it was found that the combination of different methods is largely beneficial. On the one hand, deep-level transient spectroscopy is effective in determining the energy level and (with limited accuracy) the carrier capture cross section of the majority carriers. Furthermore, the defect concentration can be estimated using this well-established technique. On the other hand, lifetime spectroscopy determines the actual recombination strength of the defect levels dominating the samples performance, making the defect energy and the ratio of the carrier capture cross sections accessible. Especially if being based on photoluminescence measurements, reliable results for these defect parameters can be gained. Throughout this work, these different defect characterization techniques were applied successfully to different intentionally contaminated silicon samples.
Tab. 12.1: Summary of the investigated defects and their respective energy levels within the silicon band gap. The samples have been investigated by means of deep-level transient spectroscopy (DLTS) and lifetime spectroscopy (LS). A more detailed compilation may be found in Tab. 11.6.
Impurity Energy level (eV) Techniques
Manganese-Boron (MnB) EV + 0.55 DLTS, LS
Interstitial manganese (Mni) EC – 0.45 LS
Titanium, shallow level (Tishallow) EC – 0.08 LS Titanium, deep level (Tideep) EC – 0.47 LS
Aluminum (Al) EV + 0.44 DLTS, LS
Tungsten (W) EV + 0.38 DLTS
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