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The Physics of Industrial Crystalline Silicon Solar Cells

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The Physics of Industrial Crystalline Silicon Solar Cells Author's personal copy CHAPTER ONE The Physics of Industrial Crystalline Silicon Solar Cells Otwin Breitenstein Max Planck Institute of Microstructure Physics, Halle, Germany Contents 1. Introduction and Chapter Methodology 1 2. Basic Theory of Solar Cells 4 2.1 Solar cell in thermal equilibrium 4 2.2 Biased solar cell 8 2.3 Analysis of the bulk lifetime 13 2.4 Depletion region recombination 18 2.5 Illuminated solar cell 20 2.6 Reverse current 23 3. Theory Versus Experiment 24 4. Origins of Nonideal Characteristics 26 4.1 The depletion region recombination (second diode) current 27 4.2 The diffusion (first diode) current 37 4.3 The ohmic current 44 4.4 The reverse current 48 4.5 Relation between dark and illuminated characteristics 59 5. Summary and Outlook 67 Acknowledgments 70 References 70 1. INTRODUCTION AND CHAPTER METHODOLOGY Solar cells made from silicon wafers are the oldest type of solar cells, which were developed in Bell Laboratories in the 1950s for space applica- tions. While the first silicon solar cell made in 1953 had an energy conver- sion efficiency of 6%, already in 1958 the “Vanguard 1” satellite was powered by 108 silicon solar cells having an efficiency of 10.5% (http:// en.wikipedia.org/wiki/Solar_cell#History_of_solar_cells). Today, the Semiconductors and Semimetals, Volume 89 # 2013 Elsevier Inc. 1 ISSN 0080-8784 All rights reserved. http://dx.doi.org/10.1016/B978-0-12-381343-5.00001-X Author's personal copy 2 Otwin Breitenstein world efficiency record for crystalline silicon solar cells is at 25% (Green et al., 2012), and typical industrial cells are already approaching 20% (Song et al., 2012). This impressive advancement was only possible based on a deep understanding of the physics underlying these solar cells. Note that semiconductor physics is a relatively young science. The theory of a p–n junction was developed only in 1949 (Shockley, 1949), the papers describ- ing the Shockley–Read–Hall (SRH) recombination statistics appeared in 1952 (Hall, 1952; Shockley and Read, 1952), and in 1957 the diode theory became extended to generation and recombination processes in the deple- tion region (Sah et al., 1957). Until now, these are the basic papers for understanding the physics of solar cells. Today, this theory is an integral part of textbooks on semiconductor physics and technology (see, e.g., Sze and Ng, 2007). This chapter will not replace such a textbook. For understanding it, basic knowledge in solid state and semiconductor physics is required. This chapter basically consists of two parts. In the first part, the established theory of the operation of solar cells is reviewed. Here the most important relations describing a solar cell are derived and made physically clear. Then the pre- dictions of this theory are compared with typically measured solar cell char- acteristics, which reveal significant deviations from the theory. The main focus of the second part of this chapter is to point on the reasons for these deviations and explain their physical origins. The widely accepted model electrically describing silicon solar cells is the so-called two-diode model, which will be discussed in the following section. However, as mentioned above, the current–voltage (I–V ) characteristics of industrial silicon solar cells show significant deviations from the classical two-diode model predictions. This holds particularly for cells made from multicrystalline material, which contain high concentrations of crystal defects like grain boundaries, dislocations, and precipitates, fabricated by the so-called vertical gradient freeze (Trempa et al., 2010) or Bridgman method (Mu¨ller et al., 2006). Even the characteristics of industrial mono- crystalline cells, which do not contain these crystal defects, deviate from the theoretical predictions. In particular, the so-called depletion region recombination current or second diode current is usually several orders of magnitude larger than expected, and its ideality factor is significantly larger than the expected value of two. This nonideal behavior was observed already very early and tentatively attributed to the existence of metallic precipitates or other defects in the depletion region (Queisser, 1962). In that work (Queisser, 1962) it was already suspected that local leakage currents could be responsible for the nonideal diode behavior, and it was speculated that Author's personal copy The Physics of Industrial Crystalline Silicon Solar Cells 3 the edge region of a cell could significantly contribute to these nonideal cur- rents. Later on, this nonideal behavior was attempted to be explained also under the assumption of a homogeneous current flow by attributing it to trap-assisted tunneling (Kaminski et al., 1996; Schenk and Krumbein, 1995). However, in crystalline silicon solar cells, the defect levels responsible for this effect could never be identified. There were attempts to explain the large ideality factors solely by the influence of the series resistance (McIntosh, 2001; van der Heide et al., 2005). As will be shown in Section 4.1, this explanation is not sufficient for interpreting large ideality factors in well-processed cells. It has turned out that the key for a detailed understanding of the dark characteristic of solar cells is the spatially resolved mapping of the local cur- rent density of solar cells in the dark. Until now, all textbooks dedicated to solar cells still generally assume that a solar cell behaves homogeneously, e.g., (Green, 1998; Wu¨rfel, 2005). Until 1994, there was no experimental technique available that could map the dark forward current of a solar cell with sufficient accuracy. In principle, this current can be mapped by infrared (IR) thermography (Simo and Martinuzzi, 1990). However, since silicon is a good conductor of heat, the thermal signals are generally weak and the images appear blurred. Therefore, conventional IR thermography is only able to image breakdown currents under a reverse bias of several Volts, and the obtained spatial resolution is very poor (several mm, see Simo and Martinuzzi, 1990). The first method enabling a sensitive imaging of the dark forward current with a good spatial resolution was the “Dynamic Precision Contact Thermography” (DPCT) method (Breitenstein et al., 1994, 1997). Here a very sensitive miniature temperature sensor was probing the cell surface point-by-point in contact mode, and in each position the cell bias was square-pulsed and the local surface temperature modulation was measured and evaluated over some periods according to the lock-in principle. This technique already reached a sensitivity in the 100 mK range (standard thermography: 20–100 mK), and, due to its dynamic nature, the spatial resolution was well below one mm. Its only limitation was its low speed; taking a 100 100 pixel image took several hours. Therefore, DPCT was later replaced by IR camera-based lock-in thermography (LIT). This technique was developed already before it was introduced to photovoltaics (Kuo et al., 1988), and since then it was mainly used in nondestructive testing, hence for “looking below the surface of bodies” (Busse et al., 1992). In the following, LIT was also used for inves- tigating local leakage currents in integrated circuits (Breitenstein et al., 2000) Author's personal copy 4 Otwin Breitenstein and in solar cells (Breitenstein et al., 2001). Meanwhile, LIT is a widely used standard imaging method for characterizing solar cells, which is commercially available. Details to its basics, realization, and application are given in (Breitenstein et al., 2010a). Since the illuminated I–V characteristic of asolarcelliscloselyrelatedtoitsdarkcharacteristic,LIT can even be used for performing a detailed local analysis of the efficiency of inhomogeneous solar cells (Breitenstein, 2011, 2012). In the last years, in addition to LIT, also camera-based electroluminescence (EL) and photoluminescence (PL) imaging methods have been developed for the local characterization of inhomogeneous solar cells. An overview over these methods and their comparison to LIT-based methods can be found in Breitenstein et al. (2011a). The topics covered in this chapter are as follows: • Section 2: Basic Theory of Solar Cells – Section 2.1: Solar cell in thermal equilibrium – Section 2.2: Biased solar cell – Section 2.3: Analysis of the bulk lifetime – Section 2.4: Illuminated solar cell – Section 2.5: Reverse current • Section 3: Theory Versus Experiment • Section 4: Origins of Nonideal Characteristics – Section 4.1: The depletion region recombination (second diode) current – Section 4.2: The diffusion (first diode) current – Section 4.3: The ohmic current – Section 4.4: The reverse current – Section 4.5: Relation between dark and illuminated characteristics • Section 5: Summary and Outlook 2. BASIC THEORY OF SOLAR CELLS 2.1. Solar cell in thermal equilibrium Figure 1.1A shows qualitatively the band scheme of an nþ–p junction, including its ohmic contacts, as it is present in usual industrial solar cells, in thermal equilibrium. Particularly, the x-axis is not to scale, in reality the emitter thickness is a factor of 500 smaller than the base thickness. 20 3 “nþ–p” means that the n-side is much more highly doped (up to 10 cmÀ ) Author's personal copy The Physics of Industrial Crystalline Silicon Solar Cells 5 Figure 1.1 Schematic band diagram (A), profile of the space charge density (B), and profile of the electric fields (C) in an nþ–p junction, assuming homo- geneous nondegenerate emitter doping, including its ohmic contacts (ME metal), ¼ not to scale. Author's personal copy 6 Otwin Breitenstein 16 3 than the p-side of the junction (typically 10 cmÀ ), which holds for typical P-diffused p-base solar cells. Moreover, for keeping the explanations simple, the nþ-type emitter in Fig. 1.1 is assumed to be homogeneously and nondegenerately doped, in contrast to real diffused emitters. Figure 1.1B shows the local space charge densities and (C) the electric fields in this device, both also not to scale.
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