*IIIrd Generation Solar Cell DOI: http://dx.doi.org/10.5772/intechopen.95289*

*Solar Cells - Theory, Materials and Recent Advances*

for solar cell applications.

**2. Perovskites for photovoltaics**

In this chapter we focus on two most promising material for photovoltaic application. The basic overview of organometallic properties of perovskites and quantum dots from the point of view of photovoltaics and formulation description of the electronic structure in the form of a simplified effective Hamiltonian as an approximation of a tight tie will be presented. The electronic structure plays a key role in the photovoltaic effect and is responsible for the high efficiency of the effect. Additionally perovskites or quantum dots show the spin-orbit coupling in the general form, this coupling can increase the carrier's lifetime - the quantity important

Some perovskite-structured oxides have an internal electrical field, which plays an important role as it leads to the separation of electrons and holes generated in the process of light absorption. These oxides have the general structure of the ABO3 type. In general, there are quite a few different materials called perovskites, but the crystalline structure for all perovskites is similar. Perovskite oxides and, above all, organometallic halogen perovskites play an important role for photoelectronics and photovoltaics. Nonetheless perovskite oxides turned out to be inefficient in terms of photovoltaics. The interest in perovskite materials increased significantly towards the end of the last year a decade, when a series of works appeared showing the possibility of increasing efficiency in organometallic perovskites [1]. It turned out that there was a fairly broad class organometallic halide perovskites of the type CH3NH3PbX3 (X = I, Br, Cl), which show promising properties from the photovoltaic point of view. Although the first results gave relatively low photovoltaic efficiency, however this efficiency is quite fast it grew with new research. Besides, the conducted research did not show any significant restriction on the upper limit of the photovoltaic efficiency organometallic perovskites, which now reaches over 20%, which in turn gives hope for its further growth. The main advantages of organometallic halide perovskites are their relatively low levels price and relatively simple technology, which makes these materials competitive. Recent research results show that the efficiency of the laudatory prototypes of perovskite solar cell are already equalled and even exceeded the silicon based solar cell. Hence the great interest these materials from the point of view of application in photovoltaic cells [2, 3]. Of course, these materials also have weaknesses. One of these weaknesses is the lead toxicity they contain. The second is quite rapid degradation resulting from the sensitivity of photovoltaic cells based on them on humidity and the effect of ultraviolet radiation to which they are exposed. Therefore, the main lines of current research are not only aimed at further increasing efficiency photovoltaic, but also removing these undesirable weaknesses. As mentioned for photovoltaic the most interesting and promising are halide perovskites, the crystal structure of these materials has the general form ABX3, where A is the cation of the methylammonium group CH3NH3 for organometallic halide perovskites (metal cation for oxides), B is the metal cation Pb or Sn (the smaller metal cation in the case of oxides), while X is a Cl, Br or I anion for halide perovskites (O for oxides). The unit cell of the ABX3 perovskite crystal in the cubic phase is shown in **Figure 1**. One of the most promising materials is a perovskite with the chemical composition CH3NH3PbI3, because in this case the photovoltaic efficiency turned out to be the highest in this class of materials. It is worth noting, however, that the class of organometallic perovskites is in fact quite rich and contains many elements, which allows the use not only of single perovskites, but their more complex structures, e.g. double perovskites or systems composed of various materials [4]. The high photoelectric efficiency of organometallic perovskites is related to their electronic properties.

**340**

This material is a semiconductor with a band gap width of about 1.6 eV. The light absorption coefficient is very high while energy losses associated with the possibility of non-radiative electron processes (e.g., electron–hole recombination by phonons) are relatively low. Moreover, the mobility of the carriers (electrons and holes) in these perovskite materials is quite high due to the low effective mass of the carriers. All these properties underlie high photovoltaic efficiency. On the other hand, the physical mechanisms underlying these properties are not yet fully researched and elucidated.

The excellent photovoltaic properties of perovskites are related to their electronic structure, in particular to the quantum states of electrons and holes in the conduction and valence bands, respectively. In the case of organometallic halide perovskites these properties are related to the organic CH3NH3 positive ion and its orientation with respect to the crystallographic axes [5].

Even better results using perovskite material from energy harvesting point of view may be achieved using hybrid structure. Recent discovery by the group of Prof. Miyasaka of a highly efficient light-to-voltage conversion in hybrid organic–inorganic perovskites [6] made these material promising elements for photovoltaics, especially taking into account simple low-cost fabrication technology. The basic structure of the perovskite-based solar cell is presented in **Figure 2**.

#### **Figure 1.**

*Perovskite crystal unit cell, a - large cation (methylammonium group CH3NH3), B - smaller cation (Pb or Sn), X - anion (I, Br or Cl).*

#### **Figure 2.**

*Schematic picture of a hybrid organic–inorganic perovskite solar cell. (figure source: USA). Department of Energy website.*

The first two compounds of this family investigated by Prof. Miyasaka group, that is CH3NH3PbBr3 and CH3NH3PbI3, deposited on the TiO2 surface, demonstrated a good power conversion efficiency η higher than 3% (now reaching as high as 20%, similar to that in best conventional semiconductor-based solar cell) accompanied by the open-circle voltage Voc higher that 0.6 V and generated current density Jsc higher than 5.5 mA/cm<sup>2</sup> . These results of Prof. Miyasaka group attracted a great deal of attention and caused a tide of research in this field.

These compounds belong to the family of perovskite structures, similar to the high- temperature superconductors, where the main element is represented by Cu-O octahedrons. Although some structure elements of these groups of materials are similar, their physical properties are very different. In general, all the perovskites are known for formation of different structures and a variety of temperature-induced structural transitions.

Due to a large variety of the organic cations, the entire family of hybrid organicinorganic perovskites potentially contains more than 1000 members [7], all different in their properties. Structure-wise, the main element of these compounds as presented in two-dimensional projection in **Figure 3** is an octahedron built by metal and halogen ions, these elements are surrounded by organic layers.

Despite several years of extensive research efforts, many microscopic properties, which can help in the understanding of the high photovoltaic efficiency in these compounds, remain unknown. This holds true even for CH3NH3PbI3 and

**343**

*IIIrd Generation Solar Cell*

negatively charged PbI<sup>−</sup>

efficiency.

1000 W/m<sup>2</sup>

V ∼ 108

*DOI: http://dx.doi.org/10.5772/intechopen.95289*

HC(NH2)2PbI3 - the leaders of the race for the low-cost high photovoltaic efficiency. Electrical properties such as conductivity of these compounds can strongly depend on the temperature since due to a relatively soft lattice, various structural phase transitions occur in the temperature range of the order of 100 K - the property common for all perovskite structures, as mentioned above. Here we review and analyze properties of these materials in the context of their applicability for photovoltaics and connect these properties to the processes related to their possibly high

Typical hybrid perovskite structure has the known form of a vertex-sharing networks of BX6 octahedrons as shown in **Figure 3**, which can be modeled as

due mainly to the metal and halogen orbitals. Mutual overlap of these orbitals determines the matrix elements of interatomic hopping and, in turn, the band structure, corresponding to direct-band semiconductors with the bandgap Eg. This gap can be evaluated by different techniques. The overlap of the orbitals forms a relatively small effective mass of the carriers as well as the optical properties of these systems. The sunlight has the following physical properties of our interest. Its spectrum corresponds to maximum in the green light region at photon energies ω close to 2.2 eV. This implies that the main contribution to the absorption in hybrid perovskites starts from the infrared part of the sunlight spectrum and its intense visible and ultraviolet parts can be used efficiently. The specific intensity of sun-

light at the Earth's surface at a sunny day is of the order of 1000 W/m<sup>2</sup>

corresponds to the free carrier bulk (3D) generation rate of the order of

Simultaneously, current J produced in such a sample of S = 1 cm2

somewhat less than this basic estimate.

emissions of phonons.

the performance of a photovoltaic cell, one can establish that the energy flux of

1021 s−1 cm−3; corresponding to two-dimensional (2D) concentration injection rate 1018 s−1 cm−2. Although the exact electrodynamics of solar cells is very complex [8], by using the Gauss theorem for the electric field produced by charge distribution, one can obtain that this concentration corresponds to the rate of the voltage generation. The resulting bias V is of the order of (dV/dt) × G−1, where G−1 is the characteristic time corresponding to the relaxation of the optical injection, e.g. by electron–hole recombination or trapping carriers by lattice defects, leading to

order of 0,1 A. These numbers demonstrate that the first perovskite solar cells produced voltage close the maximal one, although the generated current was

 corresponds to the photon flux of the order of 1018 s−1 cm−2. Being totally absorbed in a layer of the thickness of L ∼ 10 μm (10−3 cm), this photon flux

) × G−1. With the reasonable estimation of G−1 ∼ 10−9 s the value of V ∼ 0,1 V.

The light-induced transitions produce electron–hole pairs in the energy interval E > Eg, where Eg is the fundamental gap at the R − point of the Brillouin zone. The fundamental gap can be understood from the Coulomb energy arguments for the energy necessary to transfer electron from halogen to the IV-group heavy ion.

A qualitative plot of injected distribution of electrons in the energy representation is presented in **Figure 4**. This strongly nonequilibrium distribution then relaxes to the quasi equilibrium which, as we will see below, determines the performance of the photovoltaic devices. The relaxation process is mainly attributed to the multiple

The energy relaxation processes are understood even less sufficiently than the origin of the carrier's finite mobility. Indeed, due to a complex unit cell structure, crystals possess a large variety of phonon branches (of the order of 100) of different nature and symmetry. Here we propose a simple picture of the relaxation due to electron–phonon coupling. The analysis done in [9] shows that coupling to acoustic

ing to a relatively strong electric field of the order of 102

3 elements. The bandstructure and optical properties are

–103

correspond-

V/m. To understand

area, is of the

**Figure 3.** *Typical crystal structure of hybrid organic–inorganic perovskite compounds.*

## *IIIrd Generation Solar Cell DOI: http://dx.doi.org/10.5772/intechopen.95289*

*Solar Cells - Theory, Materials and Recent Advances*

of attention and caused a tide of research in this field.

temperature-induced structural transitions.

ions, these elements are surrounded by organic layers.

*Typical crystal structure of hybrid organic–inorganic perovskite compounds.*

higher than 5.5 mA/cm<sup>2</sup>

The first two compounds of this family investigated by Prof. Miyasaka group, that is CH3NH3PbBr3 and CH3NH3PbI3, deposited on the TiO2 surface, demonstrated a good power conversion efficiency η higher than 3% (now reaching as high as 20%, similar to that in best conventional semiconductor-based solar cell) accompanied by the open-circle voltage Voc higher that 0.6 V and generated current density Jsc

These compounds belong to the family of perovskite structures, similar to the high- temperature superconductors, where the main element is represented by Cu-O octahedrons. Although some structure elements of these groups of materials are similar, their physical properties are very different. In general, all the perovskites are known for formation of different structures and a variety of

Due to a large variety of the organic cations, the entire family of hybrid organicinorganic perovskites potentially contains more than 1000 members [7], all different in their properties. Structure-wise, the main element of these compounds as presented in two-dimensional projection in **Figure 3** is an octahedron built by metal and halogen

Despite several years of extensive research efforts, many microscopic properties, which can help in the understanding of the high photovoltaic efficiency in these compounds, remain unknown. This holds true even for CH3NH3PbI3 and

. These results of Prof. Miyasaka group attracted a great deal

**342**

**Figure 3.**

HC(NH2)2PbI3 - the leaders of the race for the low-cost high photovoltaic efficiency. Electrical properties such as conductivity of these compounds can strongly depend on the temperature since due to a relatively soft lattice, various structural phase transitions occur in the temperature range of the order of 100 K - the property common for all perovskite structures, as mentioned above. Here we review and analyze properties of these materials in the context of their applicability for photovoltaics and connect these properties to the processes related to their possibly high efficiency.

Typical hybrid perovskite structure has the known form of a vertex-sharing networks of BX6 octahedrons as shown in **Figure 3**, which can be modeled as negatively charged PbI<sup>−</sup> 3 elements. The bandstructure and optical properties are due mainly to the metal and halogen orbitals. Mutual overlap of these orbitals determines the matrix elements of interatomic hopping and, in turn, the band structure, corresponding to direct-band semiconductors with the bandgap Eg. This gap can be evaluated by different techniques. The overlap of the orbitals forms a relatively small effective mass of the carriers as well as the optical properties of these systems.

The sunlight has the following physical properties of our interest. Its spectrum corresponds to maximum in the green light region at photon energies ω close to 2.2 eV. This implies that the main contribution to the absorption in hybrid perovskites starts from the infrared part of the sunlight spectrum and its intense visible and ultraviolet parts can be used efficiently. The specific intensity of sunlight at the Earth's surface at a sunny day is of the order of 1000 W/m<sup>2</sup> corresponding to a relatively strong electric field of the order of 102 –103 V/m. To understand the performance of a photovoltaic cell, one can establish that the energy flux of 1000 W/m<sup>2</sup> corresponds to the photon flux of the order of 1018 s−1 cm−2. Being totally absorbed in a layer of the thickness of L ∼ 10 μm (10−3 cm), this photon flux corresponds to the free carrier bulk (3D) generation rate of the order of 1021 s−1 cm−3; corresponding to two-dimensional (2D) concentration injection rate 1018 s−1 cm−2. Although the exact electrodynamics of solar cells is very complex [8], by using the Gauss theorem for the electric field produced by charge distribution, one can obtain that this concentration corresponds to the rate of the voltage generation. The resulting bias V is of the order of (dV/dt) × G−1, where G−1 is the characteristic time corresponding to the relaxation of the optical injection, e.g. by electron–hole recombination or trapping carriers by lattice defects, leading to V ∼ 108 ) × G−1. With the reasonable estimation of G−1 ∼ 10−9 s the value of V ∼ 0,1 V. Simultaneously, current J produced in such a sample of S = 1 cm2 area, is of the order of 0,1 A. These numbers demonstrate that the first perovskite solar cells produced voltage close the maximal one, although the generated current was somewhat less than this basic estimate.

The light-induced transitions produce electron–hole pairs in the energy interval E > Eg, where Eg is the fundamental gap at the R − point of the Brillouin zone. The fundamental gap can be understood from the Coulomb energy arguments for the energy necessary to transfer electron from halogen to the IV-group heavy ion.

A qualitative plot of injected distribution of electrons in the energy representation is presented in **Figure 4**. This strongly nonequilibrium distribution then relaxes to the quasi equilibrium which, as we will see below, determines the performance of the photovoltaic devices. The relaxation process is mainly attributed to the multiple emissions of phonons.

The energy relaxation processes are understood even less sufficiently than the origin of the carrier's finite mobility. Indeed, due to a complex unit cell structure, crystals possess a large variety of phonon branches (of the order of 100) of different nature and symmetry. Here we propose a simple picture of the relaxation due to electron–phonon coupling. The analysis done in [9] shows that coupling to acoustic

#### **Figure 4.**

*Interband transitions caused by different photons, and electron distribution over the energy states, as injected. The behavior of the distribution at energies close to the minimum of the conduction band Ec is due to small density of states* ∼ *E E* − *<sup>c</sup> while the high-energy behavior is mainly determined by decrease in the spectral density of the incident light. Emin corresponds to the bottom of the conduction band.*

phonons (with the frequency linear in the momentum) would lead to high mobilities of the order of 103 cm2 V−1 s−1 and, therefore, this coupling is not the limiting factor for the observed low mobilities. Therefore, we concentrate on the relevant coupling to optical phonons. The coupling is due to the asymmetry of the field and change of the hopping integrals due to change in the interatomic distances. The value of the deformation potential constant is attributed to two main effects. First effect is the change in the site energy, corresponding to atomic displacement in the crystal field formed by its interaction with surrounding ions. Second effect is the changing in the overlap transfer integrals between the iodine and the lead orbitals, contributing to the electron energy as well.

The energy relaxation of the photoexcited electrons due to electron–phonon coupling with optical phonons, is relatively fast and occurs on the time scale of the order of 10 ps. This fast relaxation demonstrates that a thermalized room-temperature energy distribution is quickly produced. As a result, the performance of the photovoltaic elements with typical involved time scales of the order of 1–10 ns, is determined by the thermalized distributions, where the static local defects, either charged or not, structural disorder, and low-frequency optical phonons can play a role for the kinetics of the carriers distributions. The relation of these energy relaxation processes to the photovoltaic performance of real solar cells needs experimental studies and remains to be investigated.

The light absorption is efficient due to the band structure of perovskite materials having a direct bandgap close to 1.5 eV in the vertex point of the Brillouin zone. As a result, almost the entire sunlight spectrum can be absorbed. The efficiency of the absorption, in addition, is enhanced by relatively large momentum matrix elements between the group-IV heavy metal and halogen atoms resulting from their spatial overlap what makes perovskite material promising material for III generation of photovoltaic.
