ISSN 10637826, Semiconductors, 2015, Vol. 49, No. 6, pp. 741–745. © Pleiades Publishing, Ltd., 2015. Original Russian Text © Ya.L. Shabelnikova, E.B. Yakimov, D.P. Nikolaev, M.V. Chukalina, 2015, published in Fizika i Tekhnika Poluprovodnikov, 2015, Vol. 49, No. 6, pp. 758–762.
PROCEEDINGS OF THE CONFERENCE “SILICON2014”, IRKUTSK, JULY 7–12, 2014
MICROCRYSTALLINE, NANOCRYSTALLINE, POROUS, AND COMPOSITE SEMICONDUCTORS
Quantitative Description of the Properties of Extended Defects in Silicon by Means of Electron and LaserBeamInduced Currents Ya. L. Shabelnikovaa*, E. B. Yakimova, D. P. Nikolaevb, and M. V. Chukalinaa a
Institute of Microelectronics Technology and HighPurity Materials, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia b Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051 Russia *email:
[email protected] Submitted November 27, 2014; accepted for publication December 4, 2014
Abstract—A solar cell on a wafer of multicrystalline silicon containing grain boundaries was studied by the inducedcurrent method. The sample was scanned by an electron beam and by a laser beam at two wave lengths (980 and 635 nm). The recorded inducedcurrent maps were aligned by means of a specially devel oped code, that enabled to analyze the same part of the grain boundary for three types of measurements. Opti mization of the residual between simulated inducedcurrent profiles and those obtained experimentally yielded quantitative estimates of the characteristics of a sample and its defects: the diffusion length of minor ity carriers and recombination velocity at the grain boundary. DOI: 10.1134/S1063782615060226
1. INTRODUCTION At present, multicrystalline silicon (mSi) is one of the main materials for the fabrication of solar cells. It is less expensive than its singlecrystal analog; how ever, the efficiency of solar cells fabricated from mSi is also lower because of extended structural defects (grain boundaries, dislocations) which are inevitably present in the material. Solving the problem of reduc ing the recombination activity of extended defects requires, among other things, the development of methods for the local diagnostics of semiconductor structures. A diagnostic technique should not only reveal a defect, but also provide quantitative informa tion about this defect (commonly, the recombination velocity Vs for a grain boundary) and about the sample under study as a whole (diffusion length L or lifetime of minority carriers). It would be most natural to obtain these data by the widely used method in which the electronbeaminduced current (EBIC) is mea sured, with a simulated inducedcurrent profile fitted to that experimentally measured. However, a short coming of the EBIC method is that the electron beam does not penetrate deep into the sample (to a depth of ~10 μm for an electronbeam energy of 20–30 keV). This means that, in the case of samples with a large dif fusion length, the inducedcurrent profile weakly depends on L, which leads to a large error in determin ing this parameter. By contrast, for the methods with current induced by Xray (XBIC) or laser (LBIC)
beams, the penetration depth of the beam into the sample is commonly large. Therefore, we suggest in the present study that the LBIC method be used in combination with the EBIC method and Vs and L be found as values at which the residuals are close to the minimum value for both methods. 2. EXPERIMENTAL The solar cell studied by the EBIC and LBIC methods was fabricated by the standard technique on a 150 × 150 mm multicrystalline silicon wafer with a thickness of 200 μm [1]. The wafer was cut from an ingot produced by casting. To reduce the reflection of visible light, its surface was textured. The EBIC study was carried out with a JSM 840 electron microscope at room temperature, a beam energy of 35 keV, and a beam current of ~10–10 A. The LBIC measurements were performed in a setup based on an optical micro scope and scanning table [1]. Semiconductor lasers with wavelengths of 980 (penetration depth ~150 μm [2]) and 635 nm (penetration depth ~4 μm [2]) used to produce the excitation light beam. The power of the lasers was 20 mW. Images of a solarcell fragment, obtained in the inducedcurrent (IC) mode, are shown in Fig. 1 (upper panels). The grain boundaries in mSi are places of enhanced carrier recombination, and, therefore, they are manifested in the images as dark lines.
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Fig. 1. Upper panels: images of a fragment of a solar cell (a) in the EBIC mode and in the LBIC mode under excitation at a wave length of (b) 980 and (c) 635 nm. Lower panels: corresponding images in the x, y coordinates after the alignment procedure.
3. ALIGNMENT OF IMAGES OBTAINED IN THE INDUCEDCURRENT MODE To apply the results of measurements by different methods for determining the soughtfor parameters L and Vs, it was necessary to solve the problem of the alignment of three images recorded in the IC mode. It was assumed from the very beginning that there exists a projective transformation that aligns any two images of three. The projective transformation of a plane has eight parameters and can be uniquely expressed via coordinates of any four points of common positions if the coordinates of each point are known in both images. In the given triad of images, we could find four points uniquely identified in all images, and this cir cumstance made it possible to calculate the transfor mation parameters. In the process, other wellidenti fied features were also aligned, which confirms the ini tial hypothesis about the transformation type. The results obtained in the case of alignment of the images are shown in Fig. 1 (lower panels). The line in the figure marks that part of the grain boundary for which the inducedcurrent profile being analyzed [Ic(x)] was chosen. For the EBIC method, this profile is shown in Fig. 2a. The contrast of the induced cur rent was defined as C(x) = 1 – Ic(x)/I(x), where I(x) is the induced current whose value is not affected by the
grain boundary, or, in other words, the defectfree cur rent. It was approximated with a curve shown by the dashed line in Fig. 2a. Figure 2b shows the contrast profiles. The highest contrast corresponds to LBIC at a wavelength of 980 nm, for which the penetration depth of the scanning beam is maximum. 4. MODEL FOR CONTRAST CALCULATION The induced current was simulated as was done in the calculations described in [3, 4]. The induced cur rent was calculated as a convolution of the function of electron–hole pair generation, g(x, y, z), and the col lection probability, ψ(x, y, z) [5]. The collection prob ability was set by the expression obtained by Donolato [6] for the case in which a perpendicular to surface grain boundary is present in a sample. For the LBIC method, we used the approximation of a generation function proportional to the laserbeam intensity [7], 2 2 2 i.e., g(x, y, z) = exp ( – Mz ) exp [ – ( x + y )/2σ ] , where σ is the beam width, and M is the photonabsorption coefficient, i.e., the quantity determining the penetra tion depth. In the case of the EBIC method, for the generation function determination of the Werner model [8] was used. In contrast to the frequently used Donolato model [9], it takes into account the effect of SEMICONDUCTORS
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backscattered electrons. The contrast was calculated as C = 1 – Ic/I, where I is the induced current in a defectfree sample. 5. DETERMINATION OF THE DIFFUSION LENGTH AND RECOMBINATION VELOCITY For the contrast profiles in Fig. 2, obtained via EBIC and LBIC (λ = 980 and 635 nm) measure ments, we calculated the residual functions dx ( C – C ) ∫ ⋅ 100% dx C ∫ 2
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between the experimental (Cex) and simulated (Cm) contrasts. The simulation was performed for a space chargeregion (SCR) width of W = 0.1 μm and diffu sion coefficient of D = 36 cm2/s. During the calcula tion of the EBIC contrast, the generation volume was determined by the transport length s0 = 13.3 μm that corresponds to an electron energy of 35 keV, the elec tronprobe width was estimated as d = 10 nm. For the LBIC method, the photonabsorption coefficient was set as M = 67 × 10–4 μm–1 for a wavelength of 980 nm SEMICONDUCTORS
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and M = 0.25 μm–1 for 635 nm, that corresponds to the absorption depths in [2]. The residual was calcu lated as a function of the diffusion length L and recombination velocity Vs. For the LBIC method, the laser beam width σ was the third variable parameter. Figure 3 shows the results obtained for calculations of the residuals: Nev_EBIC function for the EBIC con trast and Nev_LBIC_980 and Nev_LBIC_635 for the LBIC contrast at wavelengths of 980 and 635 nm. It can be seen from the images that the level surfaces of the residual functions are elongated and have a strongly nonspherical shape. Conventional optimiza tion techniques, such as the coordinatewise descent and random search methods, do not work well with Table 1. Parameter values at which the residuals reach the minimum value Residual function
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functions of this kind. Therefore, their minima were found in a search for the smallest element in the array of values of the residual functions. The values of the functions were calculated for L from 4 to 604 μm and σ from 4 to 100 μm with a step of 4 μm and for Vs in the range (0.04–0.84) × 105 cm/s with a step of 0.02 × 105 cm/s. The parameters L, Vs, and σ at which the residuals reach their minimum values are listed in Table 1, and Fig. 4 shows the contrast profiles calcu lated for these values in comparison with the experi mental curves. For Nev_LBIC_980, the minimum was found at Vs = 0.84 × 105 cm/s, which is the limiting value for the range in which the residuals were calculated. How ever, additional estimates demonstrated that this residual continues to gradually decrease with increas ing Vs; in particular, the minimum value is 4.6% at Vs = 106 cm/s. It can be seen from data in Table 1 that the minima of the residuals lie at different points in the space of the opimized parameters. This means that the results obtained using only a single method, EBIC or LBIC, are insufficient for determining the diffusion length and recombination velocity. Therefore, the question of finding the parameters at which all the three residuals were close to the minimum value was posed.
We constructed the summary residual S = (Nev_EBIC + Nev_LBIC_980 + Nev_LBIC_635)/3, and also the halfsums of the residuals S12 = (Nev_EBIC + Nev_LBIC_980)/2, S23 = (Nev_LBIC_980 + Nev_LBIC_635)/2, S13 = (Nev_EBIC + Nev_LBIC_635)/2. The coordinates and values of the minima for these functions are listed in Table 2. The minimum value of the summary residual is 20.8% and the values of the summandresiduals at the point of its minimum are 22, 26.7, and 13.8%. Thus, despite the extended shape of the minima of the residuals (Fig. 3), it is impossible to find a point in the space of parameters {L, Vs, σ} at which all three residuals differ from their minimum values by less than a factor of 3–4. In addition, it should be noted in an analysis of the data in Tables 1 and 2 that the minimum value of the residual Nev_LBIC_635 (14.3%) is several times the values for the remaining two discrepancies (5.3% for Nev_EBIC and 4.7% for Nev_LBIC_980). The same refers to the halfsums of the residuals for LBIC at 635 nm with EBIC (15.3%) and with LBIC at 980 nm (18.6%). This suggests that the results of measure ments with a laser beam at 635 nm are not informative and should not be used for determination of the diffu
Table 2. Parameters at which the summary residuals reach the minimum value Summary residual
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sion length and recombination velocity. Therefore, the values of L and Vs should be found from the minimum of the halfsum S12 of the residuals for EBIC and LBIC at 980 nm. In this way, we found a diffusion length of 160 μm, a recombination velocity of 0.18 × 105 cm/s, and laserbeam width of 29 μm. The contrast profiles calculated for these values are shown in Fig. 5b. Fig ure 5a shows the residual S12 . It can be noted that the level lines of this function have a substantially less elongated shape than that for the residuals in Fig. 3. This suggests that methods of automated search for the minimum will work well with this residual. 6. CONCLUSIONS Thus, a method was described for determining the diffusion length and recombination velocity at a grain boundary by inducedcurrent methods. It should be noted that the results obtained in measurements by the EBIC and LBIC methods were for the first time used in combination for determining the characteristics of a sample and its defect. It was shown that the results of LBIC measurements at a wavelength of 635 nm, for which the signalgeneration depth is only ~4 μm, can not be used to determine L and Vs. SEMICONDUCTORS
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ACKNOWLEDGMENTS The study was financially supported by the Russian Foundation for Basic Research (project nos. 1307 00970 and 130200021). REFERENCES 1. E. B. Yakimov and V. I. Orlov, J. Surf. Invest.: Xray, Synchrotron Neutron Tech. 8, 839 (2014). 2. Properties of Crystalline Silicon, Ed. by R. Hull (INSPEC, London, 1999). 3. Ya. L. Shabelnikova, E. B. Yakimov, M. V. Grigor’ev, R. R. Fakhrtdinov, and V. A. Bushuev, Tech. Phys. Lett. 38, 913 (2012). 4. Ya. L. Shabelnikova and E. B. Yakimov, J. Surf. Invest.: Xray, Synchrotron Neutron Tech. 6, 894 (2012). 5. S. Donolato, Appl. Phys. Lett. 46, 270 (1985). 6. S. Donolato, J. Appl. Phys. 54, 1314 (1982). 7. T. Wilson and E. M. McCabe, J. Appl. Phys. 61, 191 (1988). 8. U. Werner, F. Koch, and G. Oelgart, J. Phys. D: Appl. Phys. 21, 116 (1988). 9. S. Donolato, Phys. Status Solidi 65, 649 (1981).
Translated by M. Tagirdzhanov
