Open access peer-reviewed chapter

Crystal Structures of CH3NH3PbI3 and Related Perovskite Compounds Used for Solar Cells

By Takeo Oku

Submitted: April 9th 2014Reviewed: September 18th 2014Published: October 22nd 2015

DOI: 10.5772/59284

Downloaded: 6068

1. Introduction

Recently, organic-inorganic hybrid solar cells with perovskite-type pigments have been widely fabricated and rapidly studied [12, 8, 11]. Solar cells with a perovskite structure have high conversion efficiencies and stability as the organic solar cells. Since a photoconversion efficiency of 15% was achieved [2], higher efficiencies have been reported for various device structures and processes [13, 23], and the photoconversion efficiency was increased up to 19.3% [27]. The photovoltaic properties of solar cells are strongly dependent on the fabrication process, hole transport layers, electron transport layers, nanoporous layers, interfacial microstructures, and crystal structures of the perovskite compounds. Especially, the crystal structures of the perovskite-type compounds, strongly affect the electronic structures such as energy band gaps and carrier transport, and a detailed analysis of them is mandatory.

In the present article, crystal structures of perovskite-type compounds such as CH3NH3PbI3 CH3NH3PbCl3, CH3NH3PbBr3, CsSnI3, CH3NH3GeCl3, and CH3NH3SnCl3, are expected for solar cell materials, are reviewed and summarized. Since these perovskite-type materials often have nanostructures in the solar cell devices, summarized information on the crystal structures would be useful for structure analysis on the perovskite-type crystals. The nanostructures of the solar cell devices are often analysed by using X-ray diffraction (XRD) and transmission electron microscopy (TEM), and the diffraction conditions are investigated and summarized. Transmission electron microscopy, electron diffraction, and high-resolution electron microscopy are powerful tools for structure analysis of solar cells [18] and perovskite-type structures in atomic scale [17, 19].

2. Synthesis of methylammonium trihalogenoplumbates (II)

There are various fabrication processes for the methylammonium trihalogenoplumbates (II) (CH3NH3PbI3) compound with the perovskite structures. Two typical synthesis methods for the CH3NH3PbI3 (MAPbI3) were reported [1]. MAPbI3 could be synthesised from an equimolar mixture of CH3NH3I and PbI2 using the reported method [8]. CH3NH3I was synthesised at first by reacting a concentrated aqueous solution of hydroiodic acid with methylamine, and the cleaned precipitant was mixed with PbI2 in gamma-butyrolactone to obtain the MAPbI3 product. Crystalline MAPbI3 was obtained by drop-casting the solutions on glass substrates, and annealed at 100 °C. Polycrystalline MAPbI3 could be also prepared by precipitation from a hydroiodic acid solution [22]. Lead(II) acetate was dissolved in a concentrated aqueous HI and heated. An HI solution with CH3NH2 was added to the solution, and black precipitates were formed upon cooling from 100 °C.

A typical fabrication process of the TiO2/CH3NH3PbI3 photovoltaic devices is also described here [28]. The details of the fabrication process is described in the reported paper [2] except for the mesoporous TiO2 layer [16]. The photovoltaic cells were fabricated by the following process. F-Doped tin oxide (FTO) substrates were cleaned using an ultrasonic bath with acetone and methanol and dried under nitrogen gas. The 0.30M TiOx precursor solution was prepared from titanium diisopropoxide bis(acetyl acetonate) (0.11 mL) with 1-butanol (1 mL), and the TiOx precursor solution was spin-coated on the FTO substrate at 3000 rpm for 30 s and annealed 125 °C for 5 min. This process was performed two times, and the FTO substrate was sintered at 500 °C for 30min to form the compact TiO2 layer. After that, mesoporous TiO2 paste was coated on the substrate by a spin-coating method at 5000 rpm for 30 s. For the mesoporous TiO2 layer, the TiO2 paste was prepared with TiO2 powder (Aerosil, P-25) with poly(ethylene glycol) in ultrapure water. The solution was mixed with acetylacetone and triton X-100 for 30min. The cells were annealed at 120 °C for 5min and at 500 °C for 30min. For the preparation of pigment with a perovskite structure, a solution of CH3NH3I and PbI2 with a mole ratio of 1:1 in γ-butyrolactone (0.5 mL) was mixed at 60 °C. The solution of CH3NH3I and PbI2 was then introduced into the TiO2 mesopores by spin-coating method and annealed at 100 °C for 15min. Then, the hole transport layer (HTL) was prepared by spin coating. As the HTLs, a solution of spiro-OMeTAD (36.1 mg) in chlorobenzene (0.5 mL) was mixed with a solution of lithium bis(trifluoromethylsulfonyl) imide (Li-TFSI) in acetonitrile (0.5 mL) for 12 h. The former solution with 4-tert-butylpyridine (14.4 μL) was mixed with the Li-TFSI solution (8.8 μL) for 30min at 70 °C. Finally, gold (Au) metal contacts were evaporated as top electrodes. Layered structures of the photovoltaic cells were denoted as FTO/TiO2/CH3NH3PbI3/HTL/Au.

3. Crystal structures of CH3NH3PbX3 (X=Cl, Br, or I) compounds

The crystals of methylammonium trihalogenoplumbates(II) (CH3NH3PbX3, X=Cl, Br, or I) have perovskite structures and provide structural transitionsupon heating [24], 22]. The crystal systems and transition temperatures are summarized in Table 1, as reported in the previous works [22, 21]. Atomic sites were indicated from the space group table [6]. Although the CH3NH3PbX3 perovskite crystals have a cubic symmetry for the highest temperature phase, the CH3NH3 ion is polar and has C3v symmetry, which should result in disordered cubic phase [14]. In addition to the disordering of the CH3NH3 ion, the halogen ions were also disordered in the cubic phase, as shown in Figure 1(a) and Table 2 [14]. Site occupancies were set as 1/4 for I and 1/12 for C and N. The CH3NH3 ion occupies 12 equivalent orientations of the C2 axis, and hydrogen atoms have two kinds of configurations on the C2 axis. Then, the total degree of freedom is 24 [21].

As the temperature decreases, the cubic phase is transformed in the tetragonal phase, as shown in Figure 1(b) and Table 3 [10]. The isotropic displacement parameters B were calculated as 8π2 Uiso. For the tetragonal phase, I ions are ordered, which resulted in the lower symmetry from the cubic phase. Site occupancies were set as 1/4 for C and N for the tetragonal CH3NH3PbI3. As the temperature decreases lower, the tetragonal phase is transformed in the orthorhombic systems, which is due to the ordering of CH3NH3 ions in the unit cell, as shown in Figure 1(c) and Table 4 [1].

Energy gaps of the CH3NH3PbI3 were also measured and calculated [1], as summrized in Table 5. The energy gap increases with increasing temperature from the ab-initio calculation, and the measured energy gap of ~1.5 eV is suitable for solar cell materials.

Crystal systemCubicCubicCubic
Transition temperature (K)177236330
Crystal systemTetragonalTetragonalTetragonal
Transition temperature (K)172149~154161
Crystal systemOrthorhombicOrthorhombicOrthorhombic

Table 1.

Crystal systems and transition temperatures of CH3NH3PbX3 (X=Cl, Br, or I).

AtomsitexyzB (Å2)

Table 2.

Structural parameters of cubic CH3NH3PbI3. Space group Pmm (Z=1), a=6.391 Å at 330 K. B is isotropic displacement parameter.

Figure 1.

Structure models of CH3NH3PbI3 with (a) cubic, (b) tetragonal and (c) orthorhombic structures.

AtomsitexyzB (Å2)

Table 3.

Structural parameters of tetragonal CH3NH3PbI3 at 220 K. Space group I4/mcm (Z=4), a=8.800 Å, c=12.685 Å. B is isotropic displacement parameter.

AtomsitexyzB (Å2)

Table 4.

Structural parameters of orthorhombic CH3NH3PbI3 at 100 K. Space group Pnma (Z=4), a=8.8362 Å, b=12.5804 Å, c=8.5551 Å. All occupancy factors 1.0. B is isotropic displacement parameter.

Crystal systemCubicTetragonalOrthorhombic
Measured energy gap (eV)1.51
Calculated energy gap (eV)1.31.431.61

Table 5.

Energy band gaps of CH3NH3PbI3.

AtomxyzB (Å2)

Table 6.

Structural parameters of cubic CH3NH3PbCl3. Space group Pm3m (Z=1), a=5.666 Å at 200 K. B is isotropic displacement parameter.

Structural parameters of cubic CH3NH3PbCl3 and CH3NH3PbBr3 are summarized as Table 6 and 7, respectively [14, 15]. They have similar structure parameters compared with the cubic CH3NH3PbI3, except for the lattice constants. Lattice parameters of these compounds are strongly depedent on the size of halogen ions, as shown in Figure 2. As summarized in Table 8, ion radii of halogen elements increase with increasing atomic numbers, which affect the lattice constants of CH3NH3PbX3, as observed in Figure 2.

AtomxyzB (Å2)

Table 7.

Structural parameters of cubic CH3NH3PbBr3. Space group Pm3m (Z=1), a=5.933 nm at 298 K. B is isotropic displacement parameter.

Hologen elementF-Cl-Br-I-
Ion radius (Å)1.331.811.962.20
14 group elementGe2+Sn2+Pb2+
Lattice parameters0.730.931.18

Table 8.

Ion radii of halogen and 14 group elements.

Figure 2.

Lattice constants of CH3NH3PbX3 (X=Cl, Br, or I).

4. X-ray diffraction of CH3NH3PbI3

Microstructure of the perovskite phases can be investigated by X-ray diffraction (XRD). The XRD will indicate that the sample is a single phase or mixed phase. If the sample consists of nanoparticles or nanocrystals, the crystallite size can be estimated from the full width at half maximum (FWHM). From the XRD data, analyses of high-resolution TEM image and electron diffraction would become easier. If the sample is a known material, plane distances (d) and indices can be clarified from the diffraction peaks of XRD. When the sample has an unknown structure, the values of the plane distances can be obtained by the XRD, which will effectively stimulate the structure analysis.

Calculated X-ray diffraction patterns on the CH3NH3PbI3 with cubic, tetragonal and orthorhombic structures is shown in Figure 3, and calculated X-ray diffraction parameters of cubic, tetragonal and orthorhombic CH3NH3PbI3 are listed in Table 9, 10, and 11, respectively. For the cubic phase, site occupancies were set as 1/4 for I and 1/12 for C and N. Structure factors were averaged for each index. Site occupancies were set as 1/4 for C and N for the tetragonal CH3NH3PbI3. Figure 4 is an enlarged calculated X-ray diffraction patterns of CH3NH3PbI3. Reflection positions of 211 and 213 inconsistent with cubic symmetry for tetragonal structure are indicated by asterisks, which would be helpful for the distinction between the cubic and tetragonal phase [1].

Index2θ (°)d-spacing (Å)|F|Relative intensity (%)Multiplicity
1 0 013.84496.3910107.11006
1 1 019.62794.519146.31812
1 1 124.09903.689829.438
2 0 027.89733.1955164.3556
2 1 031.26952.858193.45624
2 1 134.34232.609144.41024
2 2 039.86332.2596136.03512
2 2 142.39422.130384.02324
3 0 042.39422.130376.056
3 1 044.80822.021035.9424
3 1 147.12371.92708.60.224
2 2 249.35551.8449116.1108
3 2 051.51491.772569.51024
3 2 153.61141.708135.9548
4 0 057.64581.5978100.946
4 1 059.59561.550066.81348

Table 9.

Calculated X-ray diffraction parameters of cubic CH3NH3PbI3. Equivlent indices were combined. Space group Pm3m (Z=1), a=6.391 Å at 330 K. F is structure factor.

Figure 3.

Calculated X-ray diffraction patterns of CH3NH3PbI3 with cubic, tetragonal and orthorhombic structures.

Figure 4.

Enlarged calculated X-ray diffraction patterns of CH3NH3PbI3 with cubic, tetragonal and orthorhombic structures. *Reflection positions inconsistent with cubic symmetry for tetragonal structure.

Index2θ (°)d-spacing (Å)|F|Relative intensity (%)Multiplicity
0 0 213.95136.3425477.0602
1 1 014.22166.2225442.51004
1 1 219.97304.4418116.878
2 0 020.16474.4000211.6114
2 1 123.65093.7587195.72716
2 0 224.60413.6152227.6178
0 0 428.11493.1713852.4452
2 2 028.66843.1113744.0664
2 1 331.01762.8808184.51416
1 1 431.64052.8255410.3338
2 2 232.01482.7933331.7218
3 1 032.13872.7828511.0498
2 0 434.84412.5727180.558
3 1 235.18812.5483199.61216
3 2 137.49402.3967117.9416
2 2 440.58742.2209665.6508
4 0 040.99032.2000566.6184
2 1 542.35262.1323165.5616
0 0 642.73432.1142415.042
3 2 342.74182.1138109.2216
4 1 142.93542.1047277.81516
3 1 443.21692.0917479.94516
4 0 243.50432.0785222.458
3 3 043.59982.0742225.324
4 2 046.09011.9677317.288
2 0 647.68441.9056155.228
4 1 347.69131.9053265.21116
4 0 450.44451.8076523.0198
3 2 551.94461.7589106.0116
2 2 652.27161.7487303.668
4 3 152.44421.7433171.5416
3 3 452.68641.7359218.238
5 1 053.01651.7258307.968
3 1 654.45991.6834165.0316
4 2 454.86321.6720294.61016
2 1 755.80451.6460149.8216
4 1 556.28041.6332250.9716
4 3 356.59631.6249171.4316
0 0 858.12851.5856657.652
4 4 059.36001.5556423.944
1 1 860.17391.5365353.368

Table 10.

Calculated X-ray diffraction parameters of tetragonal CH3NH3PbI3. Space group I4/mcm (Z=4), a=8.800 Å, c=12.685 Å at 220 K.

Index2θ (°)d-spacing (Å)|F|Relative intensity (%)Multiplicity
0 2 014.06796.2902462.7672
1 0 114.39896.1463408.51004
1 1 116.03565.522532.818
2 0 020.08134.4181238.792
1 2 120.18284.3961106.978
0 0 220.74834.2775225.272
2 0 122.63243.9255239.3144
1 0 223.08163.8501231.4124
0 3 123.60823.7654168.364
2 1 123.72393.747386.838
1 1 224.15393.6816128.778
2 2 024.60293.6154172.864
0 2 225.15593.5372132.934
2 2 126.74713.3302221.7168
1 2 227.13233.2838256.6218
0 4 028.35363.1451834.3512
2 0 229.03163.0732627.4554
2 3 029.34023.0415108.224
1 3 231.51912.836180.928
1 4 131.93792.7998373.2328
3 0 132.11302.7850560.5354
0 1 332.15842.7811155.634
2 2 232.39652.7612304.2208
1 0 332.97802.7139473.6244
2 4 034.99122.5622239.454
3 2 135.21352.5465244.8118
0 4 235.39492.5339225.254
1 2 336.01262.4918317.4188
2 4 136.57992.4545193.668
1 4 236.87172.4357185.868
3 0 237.02622.4259145.824
2 1 338.20652.3536127.438
1 3 339.52042.2784101.418
4 0 040.81482.2091432.062
2 4 241.02832.1980555.9418
4 0 142.21642.1389281.754
0 0 442.21892.1388305.732
2 5 142.64672.1183161.038
1 5 242.90362.1062142.928
3 3 243.03982.0999157.938
0 6 043.10732.0967330.632
3 4 143.36162.085506.1308
4 2 043.37832.0843145.814
2 3 343.46432.0803157.538
1 0 443.49912.0787318.364
1 4 344.03522.0547429.7218
1 1 444.11972.0509140.728
4 2 144.71462.0250292.598
0 2 444.71692.0249202.124
1 6 145.68011.9844100.818
1 2 445.94141.9738258.078
4 0 246.21361.9628352.164
3 2 346.58321.948173.018
2 5 246.61441.946893.918
2 0 447.17281.9251308.854
3 4 247.28171.9209124.018
0 5 348.19251.8867181.824
4 2 248.54891.8737135.728
1 3 448.85981.8625183.138
2 6 149.22661.8494148.328
1 5 349.35031.8451124.918
1 6 249.45671.8414175.338
2 2 449.47361.8408218.748
4 4 050.4421.8077403.474
4 4 151.63671.7686236.348
0 4 451.63881.7686287.334
0 7 151.94701.7588234.224
4 0 352.34511.7464135.014
2 5 352.71091.735182.518
1 4 452.74101.7342270.658
2 6 252.81231.7320242.348
5 0 152.85551.7307280.334
4 1 352.88581.7298121.218
3 1 453.39461.7145162.928
3 6 154.75481.6751197.838
3 2 454.98391.6686176.928
4 4 255.10981.6651333.988
2 7 055.12351.6647160.714
4 5 055.29311.6600194.814
1 6 355.32261.6592258.848
2 4 455.95641.6419290.558
1 2 556.66931.6229166.928
2 1 558.23951.5829131.818
0 8 058.65871.5726586.052
4 0 460.17131.5366266.924

Table 11.

Calculated X-ray diffraction parameters of orthorhombic CH3NH3PbI3. Space group Pnma (Z=4), a=8.8362 Å, b=12.5804 Å, c=8.5551 Å at 100 K. B is isotropic displacement parameter. All occupancy factors 1.0.

Calculated X-ray diffraction patterns of CH3NH3PbI3 with various FWHM values are shown in Figure 5. When the crystallite sizes decrease, the FWHM values increase, and different peak intensities are observed in Figure 5.

Figure 6 is an enlarged calculated X-ray diffraction patterns of CH3NH3PbI3. With increasing FWHM values, the diffraction peaks of 200 and 110 seem to be combined, which should be very careful for the XRD structure analysis.

Figure 5.

Calculated X-ray diffraction patterns of CH3NH3PbI3 with various FWHM values.

Figure 6.

Enlarged calculated X-ray diffraction patterns of CH3NH3PbI3 with various FWHM values.

5. Electron diffraction of CH3NH3PbI3

When the sample amount, sample area or film thickness is smaller, it is difficult to obtain the necessary diffraction amplitude by XRD. Since the amount is enough for the TEM observation, only TEM observation may be applied to obtain the structure data. To obtain the information on the fundamental atomic arrangements, electron diffraction patterns should be taken along the various directions of the crystal, and the fundamental crystal system and lattice constants may be estimated. Then, high-resolution TEM observation and composition analysis by energy dispersive X-ray spectroscopy are performed, and the approximate atomic structure model is constructed. Most of the materials have similar structures to the known materials, and the structures will be estimated if the database on the known structures is available. For example, lots of new structures were found for high-Tc superconducting oxides, which have basic perovskite structures, and the approximate atomic structure models can be constructed from the high-resolution TEM images, electron diffraction patterns, and composition analysis of the elements [17, 19].

If a structure of the TEM specimen is known, observation direction of the crystal should be selected, and electron diffraction pattern along the direction should be estimated. Any regions selected by the selected area aperture can be observed in electron diffraction patterns, and the structure can be easily analyzed by comparing TEM images with electron diffraction patterns. When electron diffraction pattern is observed in the selected area, the diffraction pattern is often inclined from the aimed direction, which is noticed from the asymmetry of the electron diffraction pattern. The sample holder can be usually tilted along two directions, and the specimen should be tilted as the diffraction pattern shows center symmetry. Atomic structure models of cubic CH3NH3PbI3 observed along varioius directions are shown in Figure 7. Note that the atomic positions of CH3, NH3 and I are disordered as observed in the structure models. Corresponding electron diffraction patterns of cubic CH3NH3PbI3 calculated along the [100], [110], [111] and [210] directions are shown in Figure 8.

Atomic structure models of tetragonal CH3NH3PbI3 observed along [001], [100], [021], [221] and [110] are shown in Figure 9, which correspond to [001], [110], [111], [210] and [100] of cubic phase in Figure 8, respectively. Atomic positions of I are fixed for the tetragonal phase, and only atomic positions of CH3 and NH3 are disordered. For the tetragonal phase, the crystal symmetries are lowered as indicated by arrows in Figure 9(c) and 9(e). Several diffraction spots in Figure 9 have different diffraction intensities compared with Figure 8, which would be due to the different crystal symmetry of the CH3NH3PbI3 compound.

High-resolution TEM observations have been performed for the perovskite materials [20], and the nanostructures were discussed. Although TEM is a powerful tool for nanostructured materials, sample damage by electron beam irradiation should be avoided, because the CH3NH3PbI3 are known to be unstable during annealing at elevated temperatures. Several TEM results have been reported for the CH3NH3PbI3 and CH3CH2NH3PbI3, and the structures were discussed by electron diffraction and high-resolution images in these works [1, 9, 28].

Figure 7.

Atomic structure models of cubic CH3NH3PbI3 observed along (a) perspevtive view, (b) [100], (c) [110], (d) [111] and (e) [210].

Figure 8.

Calculated electron diffraction patterns of cubic CH3NH3PbI3 along (a) [100], (b) [110], (c) [111] and (d) [210].

Figure 9.

Atomic structure models of tetragonal CH3NH3PbI3 observed along (a) [001], (b) [100], (c) [021], (d) [221] and (e) [110] and (f) perspevtive view.

Figure 10.

Calculated electron diffraction patterns of tetragonal CH3NH3PbI3 along (a) [001], (b) [100], (c) [021], (d) [221] and (e) [110].

6. Other compounds with perovskite structures for solar cells

In addition to CH3NH3PbX3 (X=Cl, Br, or I) compounds, various perovskite compounds with perovskite structures for solar cells have benn reported and summarized [1]. Crystal systems and temperatures of CsSnI3 are listed in Table 12, which has very similar structures and phase transitions [3] compared with the CH3NH3PbX3. Solar cells with F-doped CsSnI2.95F0.05 provided an photo-conversion efficiency of 8.5% [4].

Temperature (K)300350478
Crystal systemOrthorhombicTetragonalCubic
Space groupPnmaP4/mbmPmm
Lattice parametersa = 8.6885 Å
b = 12.3775 Å
c = 8.3684 Å
a = 8.7182 Å
c = 6.1908 Å
a = 6.1057 Å

Table 12.

Crystal systems and temperatures of CsSnI3.

Temperature (K)2250370475
Crystal systemMonoclinicOrthorhombicTrigonalCubic
Space groupP21 /nPnmaR3mPmm
Lattice parametersa = 10.9973 Å
b = 7.2043 Å
c = 8.2911 Å
α = 90.470°
a = 11.1567 Å
b = 7.3601 Å
c = 8.2936 Å
a = 5.6784 Å
α = 90.945°
a = 5.6917 Å

Table 13.

Crystal systems and temperatures of CH3NH3GeCl3.

Similar structures of CH3NH3GeCl3 and CH3NH3SnCl3 are shown in Table 13 and 14, respectively [28, 26]. Ion radii of Ge and Sn ions are listed in Table 8, and they can be substituted for the Pb atoms in CH3NH3PbX3. Lead-free CH3NH3SnI3 solar cells were developed, which provided 5.7% efficiency [7]. (CH3CH2NH3)PbI3 with a 2H perovskite structure was reported, which privided 2.4% efficiency [9]. Perovskite oxides such as [KNbO3]0.9[BaNi0.5Nb0.5O3-x]0.1 were found to have an energy gap of ~1.4 eV, which would also be expected as solar cell materials [5].

Temperature (K)297318350478
Crystal systemTriclinicMonoclinicTrigonalCubic
Space groupP1PcR3mPmm
Lattice parametersa = 5.726 Å
b = 8.227 Å
c = 7.910 Å
α = 90.40°
β = 93.08°
γ = 90.15°
a = 5.718 Å
b = 8.236 Å
c = 7.938 Å
β = 93.08°
a = 5.734 Å
α = 91.90°
a = 5.760 Å

Table 14.

Crystal systems and temperatures of CH3NH3SnCl3.

7. Conclusion

Crystal structures of perovskite-type CH3NH3PbI3 compounds with cubic, tetragonal and orthorhombic structures were reviewed and summarized, and X-ray diffraction parameters and diffraction patterns were calculated and presented. Electron diffraction patterns were also calculated along various crystal directions and discussed. Other perovskite compounds such as CH3NH3PbCl3, CH3NH3PbBr3, CH3NH3GeCl3, CH3NH3SnCl3, and CsSnI3 were also reviewed, which are expected as next generation, organic-inorganic hybrid solar cells with high photo-conversion efficiencies.


The author would like to acknowledge M. Zushi and A. Suzuki for fruitful discussion on the perovskite materials for solar cells.

© 2015 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Takeo Oku (October 22nd 2015). Crystal Structures of CH3NH3PbI3 and Related Perovskite Compounds Used for Solar Cells, Solar Cells - New Approaches and Reviews, Leonid A. Kosyachenko, IntechOpen, DOI: 10.5772/59284. Available from:

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