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Growth and properties of SiGe multicrystals with microscopic compositional distribution for high-efficiency solar cells
Solar Energy Materials & Solar Cells 73 (2002) 305–320
Growth and properties of SiGe multicrystals with microscopic compositional distribution for high-efficiency solar cells Kazuo Nakajima*, Noritaka Usami, Kozo Fujiwara, Yoshihiro Murakami, Toru Ujihara, Gen Sazaki, Toetsu Shishido Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan Received 15 October 2001
Abstract The growth technique and physical properties of SiGe multicrystals with microscopic compositional distribution are demonstrated for new high-efficiency solar cells in which the wavelength dependence of the absorption coefficient can be freely designed by controlling the compositional distribution in the SiGe multicrystals. This growth technique is suitable for the practical casting method, and it is made up of melt growth of SiGe multicrystals with wide and microscopic distribution of the composition from Si to Ge all over the crystals. It is studied how much widely the microscopic compositional distribution in SiGe multicrystals grown from binary Si–Ge melts can be controlled by the melt composition and the cooling process. The range of the microscopic compositional distribution becomes wider as the starting Si concentration in the growth melt becomes larger. SiGe multicrystals with various microscopic compositional distribution can be freely controlled by optimizing the melt composition and the cooling process. The wavelength dependence of the absorption coefficient of such SiGe multicrystals can also be freely designed. Using the experimentally determined absorption coefficient of a SiGe crystal with microscopic compositional distribution, the short circuit photo-current of solar cells was calculated and it is demonstrated that the short circuit photocurrent can be much larger for SiGe with microscopic compositional distribution than for SiGe with uniform composition. Si thin film can be easily grown on such a SiGe multicrystal and the Si/SiGe heterostructure can be obtained. These results show that SiGe multicrystals with microscopic compositional distribution are hopeful for new high-efficiency solar cell applications by using the practical casting method. r 2002 Elsevier Science B.V. All rights reserved. *Corresponding author. Tel.: +81-22-215-2010; fax: +81-22-215-2011. E-mail address: [email protected] (K. Nakajima). 0927-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 4 8 ( 0 1 ) 0 0 2 1 6 - 1
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Keywords: SiGe; Multicrystal; Casting method; Melt growth; Solar cells; Compositional distribution; Absorption coefficient; High efficiency; Heterostructure
1. Introduction The low-cost casting method is widely used as a practical method to produce solar cells of Si multicrystals [1]. The most important problem to produce solar cells of Si multicrystals by the casting method is how to obtain higher conversion efficiency. Reduction of defects and stress in grains and at grain boundaries of Si multicrystals is the most certain solution of this problem. In order to obtain higher conversion efficiency, tandem solar cells which are made by several kinds of materials with different energy gaps such as SiGe/Si or GaAs/Ge [2] are generally used. However, the technologies to grow thin films and to prepare the tandem solar cells are highcost ones and the low-cost casting method has never been used for preparing them. If SiGe multicrystals whose absorption coefficient can be freely designed could be made for solar cells by using the practical casting method, the technology will largely impact on the development of practical solar cells with high efficiency. In this work, such a technique is presented by casting melt growth of SiGe multicrystals with microscopic compositional distribution and with wide distribution of energy gap from Si to Ge all over the crystals. Such SiGe multicrystals can be grown from Si–Ge binary melts. SiGe bulk crystals have been grown by the Czochralski [3–5], Bridgman [6] and floating zone melting [7] methods. In these crystals, Si composition gradually decreases as the crystals grow because of the use of limited amounts of Si–Ge growth melt. Generally, such graded compositional distribution appears in multicomponent crystals grown by cooling the melt. So, the growth method to obtain multicomponent single crystals such as SiGe and InGaAs with uniform composition has generally been studied by controlling compositional variation in the crystals due to depletion of solute elements in the binary or pseudo-binary melt during growth [8–11]. For multicrystalline SiGe solar cells, crystals with uniform composition also have been studied until now [12]. However, very few efforts have been made to obtain multicomponent multicrystals with microscopic compositional distribution or large lack of uniformity, and the compositional distribution in the multicrystals has never been put to practical use such as solar cells. The microscopic compositional distribution in the multicrystals may be controlled by growth parameters such as the cooling rate, the amount of supercooling and the melt composition, but it is not known how much wide microscopic compositional distribution can be obtained by controlling the growth parameters. In this work, it was studied how much widely the microscopic compositional distribution in SiGe multicrystals grown from binary melts with various compositions could be controlled by the cooling rate and the melt composition. The growth conditions to obtain SiGe multicrystals with large compositional distribution from Si
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to Ge all over the crystals were studied. Using the absorption coefficient of a SiGe crystal with microscopic compositional distribution, the short circuit photo-current of solar cells was calculated. The short circuit photo-current for a SiGe solar cell with microscopic compositional distribution was compared with that for a SiGe solar cell with uniform composition. The wavelength dependence of absorption coefficient of SiGe multicrystals with microscopic compositional distribution was also experimentally determined. A new heterostructure of solar cells which have a Si thin film epitaxially grown on such a SiGe multicrystal is proposed to obtain higher efficiency than that of multicrystalline Si solar cells. It is demonstrated that SiGe multicrystals with microscopic compositional distribution is useful for new highefficiency solar cells using the practical casting method.
2. Calculation of short circuit photo-current of solar cells For the SiGe multicrystals with microscopic compositional distribution, when the compositional ratio, R from 1.0 to 0 at 0.1 intervals is a (at x ¼ 1:0): b (at x ¼ 0:9): c (at x ¼ 0:8): d (at x ¼ 0:7): e (at x ¼ 0:6): f (at x ¼ 0:5): g (at x ¼ 0:4): h (at x ¼ 0:3): i (at x ¼ 0:2): j (at x ¼ 0:1): k (at x ¼ 0), the average composition, x of SixGe1x can be obtained x ¼ ð1:0a þ 0:9b þ 0:8c þ 0:7d þ 0:6e þ 0:5f þ 0:4g þ 0:3h þ 0:2i þ 0:1j þ 0kÞ =ða þ b þ c þ d þ e þ f þ g þ h þ i þ j þ kÞ:
ð1Þ
The absorption coefficient at the wavelength l can be obtained using the compositional ratio aðlÞ ¼ aSiðlÞ a þ aSi0:9 Ge0:1 ðlÞ b þ aSi0:8 Ge0:2 ðlÞ c þ aSi0:7 Ge0:3 ðlÞ d þ aSi0:6 Ge0:4 ðlÞ e þ aSi0:5 Ge0:5 ðlÞ f þ aSi0:4 Ge0:6 ðlÞ g þ aSi0:3 Ge0:7 ðlÞ h þ aSi0:2 Ge0:8 ðlÞ i þ aSi0:1 Ge0:9 ðlÞ j þ aGeðlÞ k
ð2Þ
and it can be freely changed by controlling the compositional distribution in the SiGe multicrystals even though the SiGe crystals with uniform composition have a unique absorption coefficient at the wavelength l: Fig. 1 shows the absorption coefficients of Si, Ge, Si0.5Ge0.5 and SiGe with microscopic compositional distribution by the compositional ratio of R ¼ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1: The absorption coefficient of SiGe with microscopic compositional distribution was derived from the experimental data of Si, Ge and Si0.5Ge0.5 [13]. The absorption range of SiGe with microscopic compositional distribution expands wider towards the longer wavelength region than that of SiGe with uniform composition, even though the average composition is same for both types of SiGe crystal. The wavelength dependence of the absorption coefficient can be freely controlled for SiGe with microscopic compositional distribution.
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Fig. 1. Absorption coefficient of Si, Ge, Si0.5Ge0.5 and SiGe with microscopic compositional distribution by the compositional ratio, R ¼ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1:
Using these absorption coefficients, the short circuit photo-current of solar cells prepared by both types of SiGe crystal with the same average composition of x ¼ 0:5 was calculated as a function of the wavelength (Fig. 2). The compositional ratio of the SiGe multicrystal with microscopic compositional distribution is R ¼ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1: The junction depth is 2 mm. Even though the average composition is same for both types of SiGe crystal, the short circuit photo-current can be larger for the SiGe solar cell with microscopic compositional distribution than for the SiGe solar cell with uniform composition. The photo-current can be much larger by optimizing the compositional ratio.
Fig. 2. Calculated short circuit photo-current of solar cells prepared by two SiGe crystals with microscopic compositional distribution ðR ¼ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1:Þ and with uniform composition (x ¼ 0:5) as a function of the wavelength. The junction depth is 2 mm. The average composition is same for both types of SiGe crystal.
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3. Experimental procedure of the growth of SiGe multicrystals Si–Ge binary melts for the growth of SiGe multicrystals were prepared by using polycrystalline Si and Ge chunks of semiconductor grade (10 nines). The Si and Ge chunks were chemically cleaned by HF:HNO3=1:1 and HF:H2O2=1.1, respectively. The Si and Ge chunks were mixed, set in a quartz crucible with an inside diameter of 1.5 cmf, and then sealed in a quartz ampoule in high vacuum. Six samples (A, B, C, D, E, and F) with several compositions were prepared. The weights of these samples are AðSi ¼ 0:662 g; Ge ¼ 13:62 g), BðSi ¼ 2:08 g; Ge ¼ 13:87 g), CðSi ¼ 1:66 g; Ge ¼ 3:71 g), DðSi ¼ 5:7 g; Ge ¼ 13:22 g), EðSi ¼ 2:5 g; Ge ¼ 5:7 g), and FðSi ¼ 2:50 g; Ge ¼ 5:71 g), and the Si atomic fraction x1Si of these melts is A=0.11, B=0.28, C=0.54, D=0.53, E=0.53, and F=0.53. Fig. 3 shows equilibrium tie-lines between the melt and solid compositions of these six samples on the Si–Ge binary phase diagram. For each samples, the left and right values represent the melt and solid equilibrium compositions, respectively. Each sample sealed in a quartz ampoule was heated up to 9001C at a heating rate of 101C/min, and then from 9001C to 13001C (for the samples A, B, C, D, and E) or to 14301C (for the sample F) at a heating rate of 21C/min. These samples were held at 13001C for 5 h and they were cooled to room temperature using different cooling rate for each sample. The samples A, B and C were cooled to 7001C at 101C/min and the sample D was slowly cooled to 7001C at 0.51C/min. Then, they were rapidly cooled to room temperature. The samples E and F were quenched from 13001C to room temperature in the atmosphere and into water, respectively. The compositional distribution was measured on the cross section of each multicrystal by energy dispersive X-ray (EDX) analysis. The diameter of the probe is about 2 mm. The composition at about 100 points on the cross section was measured at regular intervals of 250 mm.
Fig. 3. Equilibrium tie-lines between the melt and solid compositions of the six samples on the Si–Ge binary phase diagram.
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4. Experimental results of the growth of SiGe multicrystals Figs. 4 and 5 show the histograms of the compositional distribution of these six samples after cooling at several cooling rates. In Figs. 4 and 5, the vertical axis is the normalized number of points with same solid composition, and the horizontal axis is the Si composition of measured points on a cross section of a SiGe multicrystal. The total number of measured points for one sample is about 100. The Si composition, x is represented by the Si atomic fraction in SixGe1x and it is shown at regular intervals of 0.05. Xav means the average value of Si compositions in about 100 points. Fig. 4 shows the dependence of the compositional distribution on the melt composition, wlSi : The samples A, B and C have the different melt compositions as shown in Fig. 3. The cooling rate is 101C/min for these three samples. The maximum Si composition in the crystals increases as the starting Si composition of the melt increases, and it almost corresponds to the solid composition on the phase diagram. The range of the compositional distribution becomes wider as the starting Si composition of the melt increases. The shape of the histogram of the compositional distribution becomes more even or various solid compositions spread more uniformly in SiGe multicrystals as the starting Si composition of the melt increases. The number of points of the Ge-rich composition becomes larger as the starting Si composition becomes smaller because the large amount of Ge-rich melt finally remained without using for the crystal growth of SiGe and it crystallized rapidly. Xav increases as the starting Si composition increases, and Xav is almost around the starting Si composition. Fig. 5 shows the dependence of the compositional
Fig. 4. Histograms of the compositional distribution of the three samples with the almost melt compositions (x1Si ¼ 0:11; 0:28 and 0.54) after cooling at 101C/min.
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Fig. 5. Histograms of the compositional distribution of the four samples with the different same melt composition (x1Si ¼ 0:53) after cooling at several cooling rates (0.51C/min, 101C/min, quench in the atmosphere, and quench into water).
distribution on the cooling rate. The samples C, D, E, and F have almost the same melt composition of about 0.5. These four samples were grown by the different cooling rates. The cooling rates of the samples C and D are 101C/min and 0.51C/min, respectively. The samples E and F were quenched from 13001C to room temperature in the atmosphere and into water, respectively. By comparing the figures of the samples C and D, it is known that these two samples have almost the same value of the maximum Si composition in the crystals and it corresponds to the solid composition on the phase diagram. The range of the compositional distribution is almost the same for these two samples. However, the compositional distribution is very different with each other. The number of points of the Si-rich composition becomes larger and the shape of the histogram for the compositional distribution becomes more uneven as the cooling rate becomes smaller as shown in Fig. 5(a) because there is enough time for the sample D to grow crystals with equilibrium solid composition. For the samples E and F, the shape of the histogram for the compositional distribution has a concave curvature as shown in Figs. 5(c) and (d),
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the number of points becomes larger at both Si- and Ge-rich compositions. There is not enough time for atoms to diffuse to grow crystals with a uniformly spread compositional distribution, so at first crystals with the Si-rich composition grow and then crystals with the Ge-rich composition grow from the remained melt. By comparison between Figs. 5(c) and (d) for the samples E and F, both peaks of the histogram at the Si- and Ge-rich sides approach a little more to the starting Si composition of the melt (wlSi ¼ 0:53) as the cooling rate becomes larger. Xav is almost around the starting Si composition and Xav is almost equal for the four samples. The range of the compositional distribution does not strongly depend on the cooling rate. Fig. 6 shows the EDX mapping of (a) Si and (b) Ge elements on a 16 mmf cross section of a typical sample whose growth conditions are very similar to the sample B. The structure is a mixture of the blade-like and matrix crystals. Most of Si elements are included in the center of the blade-like crystals because they are first solidified. The periphery of the blade-like crystals is Ge-rich. Fig. 7 shows the structure of a blade-like crystal in sample A, and (a) the compositional distribution of Si in the blade-like crystals and (b) the compositional distribution of Si across the blade-like crystal. The Si composition is almost constant in the center of the blade-like crystal. The Si composition decreases rapidly near the periphery and become smaller in the matrix crystal. Fig. 8 shows the X-ray image of the 5 mm 5 mm cross sections of the three samples A, B and C, and it shows the Si composition dependence of the grown structure. The blade-like crystals become larger as the starting Si composition of the melt increases. Fig. 9 shows the X-ray image of the 5 mm 5 mm and 2 mm 2 mm cross sections of the three samples C, D and E, and of the sample F,
Fig. 6. EDX mapping of (a) Si and (b) Ge elements on the 16 mmf cross section of a typical sample whose growth conditions are very similar to the sample B.
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Fig. 7. Microscopic compositional distribution of Si in the sample A. (a) shows the Si compositional distribution in a blade-like crystal. The Si composition is almost constant in the center of the crystal. (b) shows the Si compositional distribution across the blade-like crystal.
respectively. It shows the cooling rate dependence of the grown structure. The bladelike crystals become larger as the cooling rate becomes smaller.
5. Experimental procedure and results of absorption coefficient of SiGe multicrystals Spectroscopic ellipsometry was performed on mirror-polished samples by using commercially available system (Sopra GESP-5). The measurements were carried out in the range of 250–850 nm at room temperature. The diameter of the incident light was changed to investigate microscopic properties of each grain or macroscopic properties.
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Fig. 8. X-ray image of the 5 mm 5 mm cross sections of the three samples A, B and C, and it shows the Si composition dependence of the grown structure.
Fig. 10 compares the extinction coefficient of a SiGe multicrystal with average Si composition of 0.11 grown at cooling rate of 101C/min. The three spectra represent for Si-rich blade crystal (open circles), Ge-rich matrix (open triangles), and the average of the large area (solid circles), respectively. The former two spectra were obtained by focusing the incident light in particular regions. On the other hand, the average was measured by defocusing the incident light, which corresponds to macroscopic properties of the crystal. The focused two spectra show systematic variation depending on the microscopic composition. The defocused spectrum shows intermediate property. Therefore, it can be concluded that microscopic compositional distribution controls the macroscopic properties.
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Fig. 9. X-ray image of the 5 mm 5 mm and 2 mm 2 mm cross sections of the three samples C, D and E, and of the sample F, respectively, and it shows the cooling rate dependence of the grown structure.
Fig. 11 compares extinction coefficients of a SiGe multicrystal with average Si composition of 0.53, and a SiGe crystal with uniform composition of 0.49 grown by liquid phase epitaxy (LPE) [13]. It is noted that the increased absorption is clearly identified in lower energies in the SiGe multicrystal compared with LPE-grown material although the averaged composition is even Si-rich. This result demonstrates the impact of microscopic compositional distribution, which indicates that drastic change in the macroscopic properties is possible by small addition of Ge. This is quite important for the solar cell applications since increase of the amount of Ge causes increase of the production cost and decrease of the open circuit voltage.
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Fig. 10. Extinction coefficient of a SiGe multicrystal with average Si composition of 0.11 for Si-rich region (open circles), Ge-rich region (open triangles), and the average of the large area for evaluation of macroscopic property (solid circles). The sample was grown at cooling rate of 101C/min.
Fig. 11. Comparison of extinction coefficients of a SiGe multicrystal (mc-SiGe) with an average Si composition of 0.53, and SiGe with uniform composition of 0.49 grown by LPE.
Therefore, it would be desirable to reduce the amount of Ge as small as possible while keeping the improvement of the absorption coefficient. From this viewpoint, the next step will be to use Si-rich binary SiGe melt as a starting material. The reason for the reduction in higher energies is unclear. Native oxides at the surface might play a role, which was not taken into account to calculate extinction coefficient.
6. Discussion For the growth of SiGe crystals, every effort is made to obtain bulk crystals and thin films with a uniform composition. However, very few efforts have been made to obtain multicomponent crystals with large compositional distribution. Fig. 12 shows the schematic phase diagram of the Si–Ge binary system. For the near equilibrium growth from the melt with the Si composition of x1a ; the Si
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Fig. 12. Schematic phase diagram of the Si–Ge binary system. The most Ge-rich composition is xsb ; and crystals with more Ge-rich composition than xsb cannot be obtained.
composition of the firstly grown crystal is xsa ; the composition of the crystal varies along the solidus line, then the final crystal with the composition of the crystal varies along the solidus line, then the final crystal with the composition of xsb ð¼ x1a Þ is grown from the finally remained melt with x1b : So, the most Ge-rich composition is xsb ; and crystals with more Ge-rich composition than xsb cannot be obtained. In Fig. 4, the composition of the firstly grown crystals for the samples A, B and C is almost equal to the composition of xsa expected by the phase diagram. However, crystals with more Ge-rich composition than xsb are largely grown using the cooling rate of 101C/min because the growth condition is far from the equilibrium one. For the growth at the cooling rate of 0.51C/min, the composition of the crystal may vary along the solidus line because enough time for atoms to diffuse in the melt and crystal is given. However, smaller amount of crystals with more Ge-rich composition than xsb is obtained. So, even 0.51C/min is much higher in comparison with the near equilibrium growth. For the growth using the very high cooling rate such as the samples E and F, the solidus and liquidus lines shift from the equilibrium lines as shown by the dotted lines in Fig. 12. In this case, it is very difficult for atoms to diffuse in the firstly grown crystal with Si-rich composition. So, the average composition in the firstly grown crystal shifts to Si-rich, on the contrary the melt composition shifts to Ge-rich. Finally, Ge-rich crystals are grown from the remained melt. Therefore, the compositional distribution shown in Figs. 5(c) and (d) is obtained. The amount of Ge-rich crystals increases as the cooling rate becomes almost higher. For the growth under the extremely highest cooling rate, the crystal composition xsb may exceedingly approach to the starting melt composition x1a : The SiGe solar cells with microscopic compositional distribution has two important merits. The first one is that the SiGe multicrystals can be grown by using the low-cost and practical casting method. So, large-size wafers can be easily obtained. The second one is that the compositional distribution in the SiGe multicrystals can be freely controlled and the wavelength dependence of physical
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properties such as absorption coefficient can be freely designed. So, the solar cells prepared by SiGe multicrystals with microscopic compositional distribution can absorb the wider wavelength range of the solar spectrum than Si solar cells do and they have a possibility to realize solar cells with higher efficiency than the efficiency of Si solar cells. New solar cells with new merits and with higher conversion efficiency can be expected by optimizing the microscopic compositional distribution and the device structure. The efficiency of SiGe solar cells with microscopic compositional distribution strongly depends on the design of the solar cells. It is expected that Si/SiGe heterostructure solar cells with a Si thin film epitaxially grown on a SiGe multicrystal
Fig. 13. Si/SiGe heterostructure prepared by growing a Si thin film on a SiGe multicrystal with microscopic compositional distribution using MBE.
Fig. 14. Si/SiGe solar cell structure with p–n junction in the Si thin film and with columnar structure of the SiGe multicrystal.
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have the Si thin film with high quality and the Si/SiGe heterostructure with a wide wavelength range of absorption of the solar spectrum, and such solar cells may have higher efficiency than that of multicrystalline Si solar cells. Such Si/SiGe heterostructure can be easily grown as shown in Fig. 13. The heterostructure was prepared by growing a Si thin film on a SiGe multicrystal with microscopic compositional distribution using the molecular beam epitaxial (MBE) method. The surface of the Si thin film is very smooth. Fig. 14 shows an example of the Si/SiGe solar cell structures. The p2n junction is made in the Si thin film, and the SiGe multicrystal with microscopic compositional distribution has columnar structure. The stress calculation [14,15] will also be very important to know the effect of stress distribution in the heterostructure of the SiGe solar cells.
7. Conclusions The microscopic compositional distribution in SiGe multicrystals grown from binary melts was found to be freely controlled by the melt composition and the cooling process. The maximum Si composition in the multicrystals almost corresponds to the solid composition on the phase diagram. The range of the compositional distribution becomes wider as the starting Si composition of the melt increases, and it does not strongly depend on the cooling rate. The range of the compositional distribution can be made much wider than that predicted by the Si– Ge phase diagram when nonequilibrium growth conditions are used. The shape of the histogram of the compositional distribution becomes more even or various solid compositions spread more uniformly in SiGe multicrystals when the starting Si composition of the melt is 0.54 and the cooling rate is 101C/min. The Si-rich bladelike and Ge-rich matrix crystals constitute the SiGe multicrystals. The wavelength dependence of the absorption coefficient can be freely controlled for SiGe multicrystals with microscopic compositional distribution. The experimentally determined absorption range of a SiGe multicrystal with microscopic compositional distribution expands wider towards the longer wavelength region than that of SiGe with uniform composition, even though the average composition is same for both types of SiGe crystal. The short circuit photo-current can be larger for the SiGe solar cell with microscopic compositional distribution than for the SiGe solar cell with uniform composition, even though the average composition is same. The Si/SiGe heterostructure was prepared by growing a Si thin film on a SiGe multicrystal by MBE, and a Si/SiGe solar cell structure was proposed. Such SiGe multicrystals with microscopic compositional distribution could be hopeful for new solar cell applications using the practical casting method.
Acknowledgements This work was partly supported by the Grant-in-Aid from The Thermal & Electric Energy Technology Foundation and New Energy and Industrial Technology
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Development Organization (NEDO). This work was also partly supported by the Grant-in-Aid from Yamada Science Foundation. The authors wish to acknowledge the helpful discussions with Prof. A. Yamamoto in Fukui University, and the helpful assistance of Mrs. M. Ohmori, H. Kimura and K. Obara.
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Growth and properties of SiGe multicrystals with microscopic compositional distribution for high-efficiency solar cells Kazuo Nakajima*, Noritaka Usami, Kozo Fujiwara, Yoshihiro Murakami, Toru Ujihara, Gen Sazaki, Toetsu Shishido Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan Received 15 October 2001
Abstract The growth technique and physical properties of SiGe multicrystals with microscopic compositional distribution are demonstrated for new high-efficiency solar cells in which the wavelength dependence of the absorption coefficient can be freely designed by controlling the compositional distribution in the SiGe multicrystals. This growth technique is suitable for the practical casting method, and it is made up of melt growth of SiGe multicrystals with wide and microscopic distribution of the composition from Si to Ge all over the crystals. It is studied how much widely the microscopic compositional distribution in SiGe multicrystals grown from binary Si–Ge melts can be controlled by the melt composition and the cooling process. The range of the microscopic compositional distribution becomes wider as the starting Si concentration in the growth melt becomes larger. SiGe multicrystals with various microscopic compositional distribution can be freely controlled by optimizing the melt composition and the cooling process. The wavelength dependence of the absorption coefficient of such SiGe multicrystals can also be freely designed. Using the experimentally determined absorption coefficient of a SiGe crystal with microscopic compositional distribution, the short circuit photo-current of solar cells was calculated and it is demonstrated that the short circuit photocurrent can be much larger for SiGe with microscopic compositional distribution than for SiGe with uniform composition. Si thin film can be easily grown on such a SiGe multicrystal and the Si/SiGe heterostructure can be obtained. These results show that SiGe multicrystals with microscopic compositional distribution are hopeful for new high-efficiency solar cell applications by using the practical casting method. r 2002 Elsevier Science B.V. All rights reserved. *Corresponding author. Tel.: +81-22-215-2010; fax: +81-22-215-2011. E-mail address: [email protected] (K. Nakajima). 0927-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 4 8 ( 0 1 ) 0 0 2 1 6 - 1
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Keywords: SiGe; Multicrystal; Casting method; Melt growth; Solar cells; Compositional distribution; Absorption coefficient; High efficiency; Heterostructure
1. Introduction The low-cost casting method is widely used as a practical method to produce solar cells of Si multicrystals [1]. The most important problem to produce solar cells of Si multicrystals by the casting method is how to obtain higher conversion efficiency. Reduction of defects and stress in grains and at grain boundaries of Si multicrystals is the most certain solution of this problem. In order to obtain higher conversion efficiency, tandem solar cells which are made by several kinds of materials with different energy gaps such as SiGe/Si or GaAs/Ge [2] are generally used. However, the technologies to grow thin films and to prepare the tandem solar cells are highcost ones and the low-cost casting method has never been used for preparing them. If SiGe multicrystals whose absorption coefficient can be freely designed could be made for solar cells by using the practical casting method, the technology will largely impact on the development of practical solar cells with high efficiency. In this work, such a technique is presented by casting melt growth of SiGe multicrystals with microscopic compositional distribution and with wide distribution of energy gap from Si to Ge all over the crystals. Such SiGe multicrystals can be grown from Si–Ge binary melts. SiGe bulk crystals have been grown by the Czochralski [3–5], Bridgman [6] and floating zone melting [7] methods. In these crystals, Si composition gradually decreases as the crystals grow because of the use of limited amounts of Si–Ge growth melt. Generally, such graded compositional distribution appears in multicomponent crystals grown by cooling the melt. So, the growth method to obtain multicomponent single crystals such as SiGe and InGaAs with uniform composition has generally been studied by controlling compositional variation in the crystals due to depletion of solute elements in the binary or pseudo-binary melt during growth [8–11]. For multicrystalline SiGe solar cells, crystals with uniform composition also have been studied until now [12]. However, very few efforts have been made to obtain multicomponent multicrystals with microscopic compositional distribution or large lack of uniformity, and the compositional distribution in the multicrystals has never been put to practical use such as solar cells. The microscopic compositional distribution in the multicrystals may be controlled by growth parameters such as the cooling rate, the amount of supercooling and the melt composition, but it is not known how much wide microscopic compositional distribution can be obtained by controlling the growth parameters. In this work, it was studied how much widely the microscopic compositional distribution in SiGe multicrystals grown from binary melts with various compositions could be controlled by the cooling rate and the melt composition. The growth conditions to obtain SiGe multicrystals with large compositional distribution from Si
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to Ge all over the crystals were studied. Using the absorption coefficient of a SiGe crystal with microscopic compositional distribution, the short circuit photo-current of solar cells was calculated. The short circuit photo-current for a SiGe solar cell with microscopic compositional distribution was compared with that for a SiGe solar cell with uniform composition. The wavelength dependence of absorption coefficient of SiGe multicrystals with microscopic compositional distribution was also experimentally determined. A new heterostructure of solar cells which have a Si thin film epitaxially grown on such a SiGe multicrystal is proposed to obtain higher efficiency than that of multicrystalline Si solar cells. It is demonstrated that SiGe multicrystals with microscopic compositional distribution is useful for new highefficiency solar cells using the practical casting method.
2. Calculation of short circuit photo-current of solar cells For the SiGe multicrystals with microscopic compositional distribution, when the compositional ratio, R from 1.0 to 0 at 0.1 intervals is a (at x ¼ 1:0): b (at x ¼ 0:9): c (at x ¼ 0:8): d (at x ¼ 0:7): e (at x ¼ 0:6): f (at x ¼ 0:5): g (at x ¼ 0:4): h (at x ¼ 0:3): i (at x ¼ 0:2): j (at x ¼ 0:1): k (at x ¼ 0), the average composition, x of SixGe1x can be obtained x ¼ ð1:0a þ 0:9b þ 0:8c þ 0:7d þ 0:6e þ 0:5f þ 0:4g þ 0:3h þ 0:2i þ 0:1j þ 0kÞ =ða þ b þ c þ d þ e þ f þ g þ h þ i þ j þ kÞ:
ð1Þ
The absorption coefficient at the wavelength l can be obtained using the compositional ratio aðlÞ ¼ aSiðlÞ a þ aSi0:9 Ge0:1 ðlÞ b þ aSi0:8 Ge0:2 ðlÞ c þ aSi0:7 Ge0:3 ðlÞ d þ aSi0:6 Ge0:4 ðlÞ e þ aSi0:5 Ge0:5 ðlÞ f þ aSi0:4 Ge0:6 ðlÞ g þ aSi0:3 Ge0:7 ðlÞ h þ aSi0:2 Ge0:8 ðlÞ i þ aSi0:1 Ge0:9 ðlÞ j þ aGeðlÞ k
ð2Þ
and it can be freely changed by controlling the compositional distribution in the SiGe multicrystals even though the SiGe crystals with uniform composition have a unique absorption coefficient at the wavelength l: Fig. 1 shows the absorption coefficients of Si, Ge, Si0.5Ge0.5 and SiGe with microscopic compositional distribution by the compositional ratio of R ¼ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1: The absorption coefficient of SiGe with microscopic compositional distribution was derived from the experimental data of Si, Ge and Si0.5Ge0.5 [13]. The absorption range of SiGe with microscopic compositional distribution expands wider towards the longer wavelength region than that of SiGe with uniform composition, even though the average composition is same for both types of SiGe crystal. The wavelength dependence of the absorption coefficient can be freely controlled for SiGe with microscopic compositional distribution.
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Fig. 1. Absorption coefficient of Si, Ge, Si0.5Ge0.5 and SiGe with microscopic compositional distribution by the compositional ratio, R ¼ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1:
Using these absorption coefficients, the short circuit photo-current of solar cells prepared by both types of SiGe crystal with the same average composition of x ¼ 0:5 was calculated as a function of the wavelength (Fig. 2). The compositional ratio of the SiGe multicrystal with microscopic compositional distribution is R ¼ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1: The junction depth is 2 mm. Even though the average composition is same for both types of SiGe crystal, the short circuit photo-current can be larger for the SiGe solar cell with microscopic compositional distribution than for the SiGe solar cell with uniform composition. The photo-current can be much larger by optimizing the compositional ratio.
Fig. 2. Calculated short circuit photo-current of solar cells prepared by two SiGe crystals with microscopic compositional distribution ðR ¼ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1:Þ and with uniform composition (x ¼ 0:5) as a function of the wavelength. The junction depth is 2 mm. The average composition is same for both types of SiGe crystal.
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3. Experimental procedure of the growth of SiGe multicrystals Si–Ge binary melts for the growth of SiGe multicrystals were prepared by using polycrystalline Si and Ge chunks of semiconductor grade (10 nines). The Si and Ge chunks were chemically cleaned by HF:HNO3=1:1 and HF:H2O2=1.1, respectively. The Si and Ge chunks were mixed, set in a quartz crucible with an inside diameter of 1.5 cmf, and then sealed in a quartz ampoule in high vacuum. Six samples (A, B, C, D, E, and F) with several compositions were prepared. The weights of these samples are AðSi ¼ 0:662 g; Ge ¼ 13:62 g), BðSi ¼ 2:08 g; Ge ¼ 13:87 g), CðSi ¼ 1:66 g; Ge ¼ 3:71 g), DðSi ¼ 5:7 g; Ge ¼ 13:22 g), EðSi ¼ 2:5 g; Ge ¼ 5:7 g), and FðSi ¼ 2:50 g; Ge ¼ 5:71 g), and the Si atomic fraction x1Si of these melts is A=0.11, B=0.28, C=0.54, D=0.53, E=0.53, and F=0.53. Fig. 3 shows equilibrium tie-lines between the melt and solid compositions of these six samples on the Si–Ge binary phase diagram. For each samples, the left and right values represent the melt and solid equilibrium compositions, respectively. Each sample sealed in a quartz ampoule was heated up to 9001C at a heating rate of 101C/min, and then from 9001C to 13001C (for the samples A, B, C, D, and E) or to 14301C (for the sample F) at a heating rate of 21C/min. These samples were held at 13001C for 5 h and they were cooled to room temperature using different cooling rate for each sample. The samples A, B and C were cooled to 7001C at 101C/min and the sample D was slowly cooled to 7001C at 0.51C/min. Then, they were rapidly cooled to room temperature. The samples E and F were quenched from 13001C to room temperature in the atmosphere and into water, respectively. The compositional distribution was measured on the cross section of each multicrystal by energy dispersive X-ray (EDX) analysis. The diameter of the probe is about 2 mm. The composition at about 100 points on the cross section was measured at regular intervals of 250 mm.
Fig. 3. Equilibrium tie-lines between the melt and solid compositions of the six samples on the Si–Ge binary phase diagram.
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4. Experimental results of the growth of SiGe multicrystals Figs. 4 and 5 show the histograms of the compositional distribution of these six samples after cooling at several cooling rates. In Figs. 4 and 5, the vertical axis is the normalized number of points with same solid composition, and the horizontal axis is the Si composition of measured points on a cross section of a SiGe multicrystal. The total number of measured points for one sample is about 100. The Si composition, x is represented by the Si atomic fraction in SixGe1x and it is shown at regular intervals of 0.05. Xav means the average value of Si compositions in about 100 points. Fig. 4 shows the dependence of the compositional distribution on the melt composition, wlSi : The samples A, B and C have the different melt compositions as shown in Fig. 3. The cooling rate is 101C/min for these three samples. The maximum Si composition in the crystals increases as the starting Si composition of the melt increases, and it almost corresponds to the solid composition on the phase diagram. The range of the compositional distribution becomes wider as the starting Si composition of the melt increases. The shape of the histogram of the compositional distribution becomes more even or various solid compositions spread more uniformly in SiGe multicrystals as the starting Si composition of the melt increases. The number of points of the Ge-rich composition becomes larger as the starting Si composition becomes smaller because the large amount of Ge-rich melt finally remained without using for the crystal growth of SiGe and it crystallized rapidly. Xav increases as the starting Si composition increases, and Xav is almost around the starting Si composition. Fig. 5 shows the dependence of the compositional
Fig. 4. Histograms of the compositional distribution of the three samples with the almost melt compositions (x1Si ¼ 0:11; 0:28 and 0.54) after cooling at 101C/min.
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Fig. 5. Histograms of the compositional distribution of the four samples with the different same melt composition (x1Si ¼ 0:53) after cooling at several cooling rates (0.51C/min, 101C/min, quench in the atmosphere, and quench into water).
distribution on the cooling rate. The samples C, D, E, and F have almost the same melt composition of about 0.5. These four samples were grown by the different cooling rates. The cooling rates of the samples C and D are 101C/min and 0.51C/min, respectively. The samples E and F were quenched from 13001C to room temperature in the atmosphere and into water, respectively. By comparing the figures of the samples C and D, it is known that these two samples have almost the same value of the maximum Si composition in the crystals and it corresponds to the solid composition on the phase diagram. The range of the compositional distribution is almost the same for these two samples. However, the compositional distribution is very different with each other. The number of points of the Si-rich composition becomes larger and the shape of the histogram for the compositional distribution becomes more uneven as the cooling rate becomes smaller as shown in Fig. 5(a) because there is enough time for the sample D to grow crystals with equilibrium solid composition. For the samples E and F, the shape of the histogram for the compositional distribution has a concave curvature as shown in Figs. 5(c) and (d),
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the number of points becomes larger at both Si- and Ge-rich compositions. There is not enough time for atoms to diffuse to grow crystals with a uniformly spread compositional distribution, so at first crystals with the Si-rich composition grow and then crystals with the Ge-rich composition grow from the remained melt. By comparison between Figs. 5(c) and (d) for the samples E and F, both peaks of the histogram at the Si- and Ge-rich sides approach a little more to the starting Si composition of the melt (wlSi ¼ 0:53) as the cooling rate becomes larger. Xav is almost around the starting Si composition and Xav is almost equal for the four samples. The range of the compositional distribution does not strongly depend on the cooling rate. Fig. 6 shows the EDX mapping of (a) Si and (b) Ge elements on a 16 mmf cross section of a typical sample whose growth conditions are very similar to the sample B. The structure is a mixture of the blade-like and matrix crystals. Most of Si elements are included in the center of the blade-like crystals because they are first solidified. The periphery of the blade-like crystals is Ge-rich. Fig. 7 shows the structure of a blade-like crystal in sample A, and (a) the compositional distribution of Si in the blade-like crystals and (b) the compositional distribution of Si across the blade-like crystal. The Si composition is almost constant in the center of the blade-like crystal. The Si composition decreases rapidly near the periphery and become smaller in the matrix crystal. Fig. 8 shows the X-ray image of the 5 mm 5 mm cross sections of the three samples A, B and C, and it shows the Si composition dependence of the grown structure. The blade-like crystals become larger as the starting Si composition of the melt increases. Fig. 9 shows the X-ray image of the 5 mm 5 mm and 2 mm 2 mm cross sections of the three samples C, D and E, and of the sample F,
Fig. 6. EDX mapping of (a) Si and (b) Ge elements on the 16 mmf cross section of a typical sample whose growth conditions are very similar to the sample B.
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Fig. 7. Microscopic compositional distribution of Si in the sample A. (a) shows the Si compositional distribution in a blade-like crystal. The Si composition is almost constant in the center of the crystal. (b) shows the Si compositional distribution across the blade-like crystal.
respectively. It shows the cooling rate dependence of the grown structure. The bladelike crystals become larger as the cooling rate becomes smaller.
5. Experimental procedure and results of absorption coefficient of SiGe multicrystals Spectroscopic ellipsometry was performed on mirror-polished samples by using commercially available system (Sopra GESP-5). The measurements were carried out in the range of 250–850 nm at room temperature. The diameter of the incident light was changed to investigate microscopic properties of each grain or macroscopic properties.
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Fig. 8. X-ray image of the 5 mm 5 mm cross sections of the three samples A, B and C, and it shows the Si composition dependence of the grown structure.
Fig. 10 compares the extinction coefficient of a SiGe multicrystal with average Si composition of 0.11 grown at cooling rate of 101C/min. The three spectra represent for Si-rich blade crystal (open circles), Ge-rich matrix (open triangles), and the average of the large area (solid circles), respectively. The former two spectra were obtained by focusing the incident light in particular regions. On the other hand, the average was measured by defocusing the incident light, which corresponds to macroscopic properties of the crystal. The focused two spectra show systematic variation depending on the microscopic composition. The defocused spectrum shows intermediate property. Therefore, it can be concluded that microscopic compositional distribution controls the macroscopic properties.
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Fig. 9. X-ray image of the 5 mm 5 mm and 2 mm 2 mm cross sections of the three samples C, D and E, and of the sample F, respectively, and it shows the cooling rate dependence of the grown structure.
Fig. 11 compares extinction coefficients of a SiGe multicrystal with average Si composition of 0.53, and a SiGe crystal with uniform composition of 0.49 grown by liquid phase epitaxy (LPE) [13]. It is noted that the increased absorption is clearly identified in lower energies in the SiGe multicrystal compared with LPE-grown material although the averaged composition is even Si-rich. This result demonstrates the impact of microscopic compositional distribution, which indicates that drastic change in the macroscopic properties is possible by small addition of Ge. This is quite important for the solar cell applications since increase of the amount of Ge causes increase of the production cost and decrease of the open circuit voltage.
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Fig. 10. Extinction coefficient of a SiGe multicrystal with average Si composition of 0.11 for Si-rich region (open circles), Ge-rich region (open triangles), and the average of the large area for evaluation of macroscopic property (solid circles). The sample was grown at cooling rate of 101C/min.
Fig. 11. Comparison of extinction coefficients of a SiGe multicrystal (mc-SiGe) with an average Si composition of 0.53, and SiGe with uniform composition of 0.49 grown by LPE.
Therefore, it would be desirable to reduce the amount of Ge as small as possible while keeping the improvement of the absorption coefficient. From this viewpoint, the next step will be to use Si-rich binary SiGe melt as a starting material. The reason for the reduction in higher energies is unclear. Native oxides at the surface might play a role, which was not taken into account to calculate extinction coefficient.
6. Discussion For the growth of SiGe crystals, every effort is made to obtain bulk crystals and thin films with a uniform composition. However, very few efforts have been made to obtain multicomponent crystals with large compositional distribution. Fig. 12 shows the schematic phase diagram of the Si–Ge binary system. For the near equilibrium growth from the melt with the Si composition of x1a ; the Si
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Fig. 12. Schematic phase diagram of the Si–Ge binary system. The most Ge-rich composition is xsb ; and crystals with more Ge-rich composition than xsb cannot be obtained.
composition of the firstly grown crystal is xsa ; the composition of the crystal varies along the solidus line, then the final crystal with the composition of the crystal varies along the solidus line, then the final crystal with the composition of xsb ð¼ x1a Þ is grown from the finally remained melt with x1b : So, the most Ge-rich composition is xsb ; and crystals with more Ge-rich composition than xsb cannot be obtained. In Fig. 4, the composition of the firstly grown crystals for the samples A, B and C is almost equal to the composition of xsa expected by the phase diagram. However, crystals with more Ge-rich composition than xsb are largely grown using the cooling rate of 101C/min because the growth condition is far from the equilibrium one. For the growth at the cooling rate of 0.51C/min, the composition of the crystal may vary along the solidus line because enough time for atoms to diffuse in the melt and crystal is given. However, smaller amount of crystals with more Ge-rich composition than xsb is obtained. So, even 0.51C/min is much higher in comparison with the near equilibrium growth. For the growth using the very high cooling rate such as the samples E and F, the solidus and liquidus lines shift from the equilibrium lines as shown by the dotted lines in Fig. 12. In this case, it is very difficult for atoms to diffuse in the firstly grown crystal with Si-rich composition. So, the average composition in the firstly grown crystal shifts to Si-rich, on the contrary the melt composition shifts to Ge-rich. Finally, Ge-rich crystals are grown from the remained melt. Therefore, the compositional distribution shown in Figs. 5(c) and (d) is obtained. The amount of Ge-rich crystals increases as the cooling rate becomes almost higher. For the growth under the extremely highest cooling rate, the crystal composition xsb may exceedingly approach to the starting melt composition x1a : The SiGe solar cells with microscopic compositional distribution has two important merits. The first one is that the SiGe multicrystals can be grown by using the low-cost and practical casting method. So, large-size wafers can be easily obtained. The second one is that the compositional distribution in the SiGe multicrystals can be freely controlled and the wavelength dependence of physical
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properties such as absorption coefficient can be freely designed. So, the solar cells prepared by SiGe multicrystals with microscopic compositional distribution can absorb the wider wavelength range of the solar spectrum than Si solar cells do and they have a possibility to realize solar cells with higher efficiency than the efficiency of Si solar cells. New solar cells with new merits and with higher conversion efficiency can be expected by optimizing the microscopic compositional distribution and the device structure. The efficiency of SiGe solar cells with microscopic compositional distribution strongly depends on the design of the solar cells. It is expected that Si/SiGe heterostructure solar cells with a Si thin film epitaxially grown on a SiGe multicrystal
Fig. 13. Si/SiGe heterostructure prepared by growing a Si thin film on a SiGe multicrystal with microscopic compositional distribution using MBE.
Fig. 14. Si/SiGe solar cell structure with p–n junction in the Si thin film and with columnar structure of the SiGe multicrystal.
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have the Si thin film with high quality and the Si/SiGe heterostructure with a wide wavelength range of absorption of the solar spectrum, and such solar cells may have higher efficiency than that of multicrystalline Si solar cells. Such Si/SiGe heterostructure can be easily grown as shown in Fig. 13. The heterostructure was prepared by growing a Si thin film on a SiGe multicrystal with microscopic compositional distribution using the molecular beam epitaxial (MBE) method. The surface of the Si thin film is very smooth. Fig. 14 shows an example of the Si/SiGe solar cell structures. The p2n junction is made in the Si thin film, and the SiGe multicrystal with microscopic compositional distribution has columnar structure. The stress calculation [14,15] will also be very important to know the effect of stress distribution in the heterostructure of the SiGe solar cells.
7. Conclusions The microscopic compositional distribution in SiGe multicrystals grown from binary melts was found to be freely controlled by the melt composition and the cooling process. The maximum Si composition in the multicrystals almost corresponds to the solid composition on the phase diagram. The range of the compositional distribution becomes wider as the starting Si composition of the melt increases, and it does not strongly depend on the cooling rate. The range of the compositional distribution can be made much wider than that predicted by the Si– Ge phase diagram when nonequilibrium growth conditions are used. The shape of the histogram of the compositional distribution becomes more even or various solid compositions spread more uniformly in SiGe multicrystals when the starting Si composition of the melt is 0.54 and the cooling rate is 101C/min. The Si-rich bladelike and Ge-rich matrix crystals constitute the SiGe multicrystals. The wavelength dependence of the absorption coefficient can be freely controlled for SiGe multicrystals with microscopic compositional distribution. The experimentally determined absorption range of a SiGe multicrystal with microscopic compositional distribution expands wider towards the longer wavelength region than that of SiGe with uniform composition, even though the average composition is same for both types of SiGe crystal. The short circuit photo-current can be larger for the SiGe solar cell with microscopic compositional distribution than for the SiGe solar cell with uniform composition, even though the average composition is same. The Si/SiGe heterostructure was prepared by growing a Si thin film on a SiGe multicrystal by MBE, and a Si/SiGe solar cell structure was proposed. Such SiGe multicrystals with microscopic compositional distribution could be hopeful for new solar cell applications using the practical casting method.
Acknowledgements This work was partly supported by the Grant-in-Aid from The Thermal & Electric Energy Technology Foundation and New Energy and Industrial Technology
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Development Organization (NEDO). This work was also partly supported by the Grant-in-Aid from Yamada Science Foundation. The authors wish to acknowledge the helpful discussions with Prof. A. Yamamoto in Fukui University, and the helpful assistance of Mrs. M. Ohmori, H. Kimura and K. Obara.
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