Solar Solutions for the Future

*David M. Mulati and Timonah Soita*

### **Abstract**

The energy conversion efficiency and limits of perovskite/silicon solar cells are investigated. The influence of a layered approach in preventing lead leakage in perovskite solar cells is discussed. The highest efficiency perovskite tandem to date was achieved by pairing a perovskite top cell with a Si bottom cell in a four-terminal configuration, yielding 26.4%. Perovskite cell integrated with crystalline silicon cell to form a tandem solar device has shown high performance above the single pn-junction silicon devices. Although sufficient work and different strategies have been applied to increase efficiency in these devices, the tandem application has achieved efficiency of 29% in a short period.

**Keywords:** photovoltaics, conversion efficiency, perovskite solar cells and tandem solar cells

### **1. Introduction**

The growing demand of energy, has forced researchers to look for cheap alternative sources of energy. Among these cheap sources energy under investigations, photovoltaics is one of them. The International Energy Agency (IEA) has noted declining prices of photovoltaics and estimates solar systems in general to supply 5% of global electricity consumption in 2030. These estimates are likely to rising to 16% by 2050. This can only be achieved by increasing the global production of solar energy to 4600 GW by 2050 [1]. At the same time solar and wind energy is expected to contribute up to 50% of total energy generated. Reduced costs of energy generation and improvements in performance will lead to more penetration of solar energy across the globe. These coupled with more research, will make solar energy cheaper than fossil fuel in the near future. Using innovative new designs, researchers are continuously working to improve photovoltaic energy systems. This work is geared towards reducing the power generation cost by combining several materials in photovoltaic cells. The best cell efficiency of 39.2% has been demonstrated from multi-junction solar cells. However, it should be observed that this is applied in space technologies that have complex fabrication processes. Currently the theoretical efficiency of crystalline silicon (c-Si) based solar cells is approximately 26.7% and for thin film technology it is 23.4%. These solar cell technologies outlined above are mature, and already in production. However, the complexed of the production process and energy consumption needs to be reduced.

Currently inexpensive and easy to fabricate solar cells are under investigation by researchers. Most of these solar cell technologies are categorized as emerging PV

technologies. Examples include; organic solar cells, dye-sensitized solar cells, quantum dot solar cells; perovskite solar cells (PSC). PSC shows very promising results and can favorably compete with c-Si solar cells in terms of efficiency. Perovskite was discovered in the Ural Mountain, in Russia, and basically describes compounds having crystal structures like calcium titanium oxide (CaTiO3). The materials being used for newly developed PSC have their structure in the form of ABX structure where A, and B are cations and X is the bonding anion. In comparison, with traditional Si cells PSC absorbs sunlight with a hundred times thinner active layer. This ABX structure allows for variation in the energy gap by mixing and matching scenario where we can have multiple compounds by substituting any of the constituents. Within a decade of its inception, PSC has already overtaken thin film technology such as cadmium telluride (CdTe) or copper-indium-gallium-selenide (CIGS) and reached the level of c-Si solar cells. Already an efficiency of 25.2% for single junction PSC has been realized by a team led by Prof. Michael Saliba at KRICT2 whereas the theoretical efficiency for these PSC's are about 31%. When Perovskite solar cell is in tandem with other solar cell technologies, they give varying efficiencies. CIGS-perovskite tandem cells have shown efficiencies up to 21.5%, whereas, when combined with c-Si technology the perovskite-c-Si tandem cells have shown efficiencies up to 28% that shows better performance in comparison with a single pn-junction of silicon; and also single junction of PSC. The efficiency of the perovskite/c-Si tandem solar cells are in the range of 32.8% for gallium-indium-phosphide/gallium arsenide (GaInP/GaAs) tandem solar cells. This type of solar cells is realized through intensified processes and expensive manufacturing techniques. With more research the efficiency of the Perovskite/silicon tandem cell can get towards 30%. Although PV technology is not the most widely used energy source; due to low energy conversion efficiency and high initial system cost; in comparison to non-renewable energy sources; it is a fast growing energy source in the power sector [2–4]. So far, solar modules from c-Si single-junction solar cells have their conversion efficiency in the lab as 26.3% [5], while the upper theoretical energy conversion efficiency of a solar cell with a bandgap of 1.14 eV (e.g., silicon) is about 33.5% [6]. Multi-junction solar cell approach has been used to increase the theoretical limits of single-junction solar cells [7–13]. It has been shown that series connection of tandem solar cells can reach conversion efficiency in excess of 40% if proper material combination is selected for the top and bottom solar cell [6, 7]. Higher than 40% can be attained if the relationship of the cells is *E*G\_top = 0.5 *E*G\_bot + 1.14 eV, where *E*G\_top and *E*G\_bot are the bandgaps of the top and bottom diode absorbers. This equation holds true when the bottom cell bandgap is between 0.8.5 and 1.2 eV; hence several material combinations can be identified. One of the materials suitable as the bottom solar cell is c-Si with a bandgap of 1.14 eV. This has led to many activities focusing on the development of tandem solar cell using a c-Si bottom solar cell. With c-Si bottom solar cell; the highest conversion efficiency can be achieved if the bandgap of the top-cell is about 1.7 eV.

When combining well established c-Si solar cell technology with other material systems or fabrication process; a number of crucial aspects must be considered. Although amorphous silicon has a fav0urable bandgap of 1.7 eV, its tail states hinder it in being applied on the formation of tandem cell with high values of open circuit voltage. This is a condition for attaining high efficiency in a tandem structure [14–18]. Also silicon oxide/c-Si based quantum dot and quantum well have been researched for the top solar cell material. Un-successfully the two materials have shown comparatively low conversion efficiency. Although, compound semiconductors have been researched as potential top solar cell absorber material; high fabrication temperatures, the lattice mismatch between silicon and compound semiconductors, and the fabrication cost are the biggest hindrances to its application. In the last decade; the perovskite material system has attracted a lot of research either for single-junction solar cells or as material for perovskite/silicon tandem solar cells [18–25]. This has shown high energy conversion efficiencies, with open-circuit voltages close to the theoretical limit of silicon material [26–33]. In addition, a variety of deposition methods at low temperatures can be used in the fabrication of a perovskite top solar cell on a c-Si bottom solar cell. Conversion efficiencies above 20% have been realized with perovskite singlejunction solar cells [34–38].

The perovskite/silicon tandem solar cells have both high and low band gap material in a single device; enabling the device to be active in both long and short wavelength regions of the electromagnetic spectrum, where each wavelength region can effectively be converted to electric power resulting in high efficiencies. Also perovskite SCs (solar cells) have unique properties like high absorption coefficient, variable bandgap, high defect tolerance, high open circuit voltage, abundant availability of its constituent elements and easy processability. Perovskite SCs can use the high energy blue and green light much more efficiently than silicon SCs. We note that perovskite/ silicon tandem solar cells with high efficiencies is only possible if the perovskite top solar cell and the silicon bottom solar cell operate at a value very near to their theoretical limit. It is worth noting that, perovskite/silicon tandem solar cells with certified energy conversion efficiencies above 27% have been achieved [39]. The realization of solar cells with higher energy conversion efficiencies approaching or even exceeding 30% is feasible in the near future.

## **2. The basics of photovoltaic cells**

A solar cell is an electrical device which converts the energy of sunlight directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon. The solar cells structure consists of either a p-n junction or p-i-n junction [4, 40]. Initially the incident radiation directed on the surface are absorbed resulting in the creation of electron/hole pairs. Then these photo generated electron/hole pairs are separated by the electric field and subsequently collected at the terminals. The charge collection of the photo generated charges occurs due to diffusion, drift or the combination of both transport processes to the contacts of the solar cell. **Figure 1** provides an overview of different solar cells. Note that schematic figures are not to scale.

**Figure 1a** above is a typical diagram of a c-Si homo-junction solar cell. It is assumed that absorption of high energy photons is done in the whole of p-n junction. Electron/hole pairs that are produced are predominantly transferred by charge diffusion process. Hetero junction solar cell that consists of a c-Si absorber and amorphous silicon contact layers is shown in **Figure 1b**. The hetero junction structure when compared with traditional homo-junction solar cells, there is a minimization of optical losses, particularly in the emitter. As a result we have high short-circuit current density and high open-circuit voltages. Generally, amorphous silicon p- and n-layers are used to form electrical contacts. The main charge transport mechanism in c-Si is charge diffusion; since it has high diffusion length. The p-i-n structure is currently applied in many thin-film solar cells. In this arrangement the intrinsic material layer is placed between the p-type material and n-type material. The charge collection process is done by a drifting mechanism of the electron/hole pairs to the contacts. **Figure 1c** shows a typical homo-junction of an amorphous silicon thin-film solar cell. A

#### **Figure 1.**

*Typical schematic diagrams of (a) homo-junction solar cell of c-Si, (b) hetero junction solar cell for a c-Si and amorphous silicon, (c) homo-junction thin-film solar cell for amorphous silicon, (d) hetero junction thin-film solar cell for perovskite, and (e) tandem solar cell of perovskite/silicon with layers showing different materials.*

heterojunction thin-film solar cell is shown in **Figure 1d**. A perovskite layer is used as an absorber of the incident photon. Different kinds of materials for electron transporting/hole blocking layers are being researched for a possible contact layer. Similarly other materials are under investigation for hole transporting/electron blocking layers. For example, transparent conductive oxides (TCO) are being used as contact layers. Perovskites can be applied to conventional silicon, thus combining the strengths of both material classes: Silicon, in this case, utilizes sunlight in the red and infrared range of the solar spectrum efficiently, while perovskites are good at converting blue light. "If the materials, i.e. perovskites on silicon, are stacked on top of each other, the efficiencies of already commercial silicon cells can be increased considerably. This tandem idea has the potential to herald a solar revolution. Basically the critical parameter to characterizing a solar cell is the energy conversion efficiency. This is typically given by the ratio of the electrical output power density to the optical input power density. The standard optical input spectrum of air mass 1.5 is normally used [41]. The relationship of the efficiency with the physics of solar cell parameters involves short-circuit current density, fill factor, and open-circuit voltage. The shortcircuit current density is obtained when the applied voltage is equal to zero, such that *J* (*V* = 0) = *J*sc, while the open circuit voltage is also obtained when the current is equal

to zero, i.e., *J*(*V* = *V*oc) = 0. The maximum power density output for a typical solar cell is given by the product of *V*mp and *J*mp i.e., (Vmp � *J*mp), where *V*mp and *J*mp are the voltage and current density at the maximum power point (MPP). These two parameters are derived from the current–voltage characteristic, of a solar cell.

$$\eta = \frac{V\_{\rm mp} \times J\_{\rm mp}}{P\_{\rm in}} = \frac{V\_{\rm oc} \times J\_{\rm sc} \times FF}{P\_{\rm in}} \tag{1}$$

Hence the fill factor can be calculated by Eq. (2):

$$\text{FF} = \frac{V\_{\text{mp}} \times J\_{\text{mp}}}{V\_{\text{oc}} \times J\_{\text{sc}}} \tag{2}$$

An ideal solar cell can be described by Eq. (3):

$$J(v) = J\_o \left\{ \exp\left(\frac{qV}{KT\_{\text{cell}}}\right) - 1 \right\} - J\_{\text{sc}} \tag{3}$$

From this Eq. (3); *q* is the elementary charge, *V* is the applied voltage, *k* is the Boltzmann constant,*T*cell is the solar cell temperature, and *J*<sup>0</sup> is the saturation current density. The open-circuit voltage of the solar cell can be determined by using Eq. (4):

$$V\_{\rm oc} = \frac{kT\_{\rm cell}}{q} \ln\left(\frac{J\_{\rm sc}}{J\_{\rm o}} + \mathbf{1}\right) \simeq \frac{kT\_{\rm cell}}{q} \ln\left(\frac{J\_{\rm sc}}{J\_{\rm o}}\right) \tag{4}$$

Understanding the fundamental limits in the energy conversion process of solar cells and determining a potential upper limit of the energy conversion efficiency is important in developing high-efficiency solar cells [42].

### **3. Solar cell conversion efficiency limit**

The maximum conversion efficiency is the theoretical energy conversion limit of a semi-conductor –based solar cell. In deriving the limit we shall assume that the solar cell is described by a single-junction solar cell, which consists of a semiconductor with a constant bandgap. The light beam with photo energies equal or greater than the bandgap is absorbed, while photons with energies smaller than the bandgap are not absorbed. All the photo generated electron/hole pairs are assumed to be collected at contacts. Therefore the recombination of electron/hole pairs is not considered but only thermalization and absorption losses are taken into consideration. Thermalization losses occur for energies larger than the bandgap while absorption losses occur for photon energies smaller than the bandgap [42]. The absorbed photon flux density of the sun by the solar cell, is given by Eq. (5) [6, 42]:

$$F\_{\text{cell}}(T = T\_{\text{sun}}) = \frac{2\pi}{h^3 c^2} \int\_{E\_t}^{\infty} \frac{E^2 \text{d}E}{\exp\left(\frac{E}{kT\_{\text{sun}}}\right) - \mathbf{1}} \tag{5}$$

where *h*, *c*, *k*, and *E*<sup>g</sup> are Planck's constant, speed of light, Boltzmann constant, and energy bandgap of the photovoltaic material. The photon flux can be approximated by Eq. (6):

**Figure 2.**

*Ultimate conversion efficiency and Shockley-Queisser limit of single-junction solar cells as a function of the bandgap. A blackbody spectrum at 6000 K and an AM 1.5G spectrum were used for the calculations.*

$$F\_{\rm cell}(T = T\_{\rm sun}) = \frac{2\pi}{h^3 c^2} \int\_{E\_\rm \rm g}^{\rm ss} \exp\left(-\frac{E}{kT\_{\rm sun}}\right) E^2 d\mathbf{E} \quad = \int\_{E\_\rm \rm g}^{\rm ss} \mathcal{Q}\_{\rm sun} d\mathbf{E} \tag{6}$$

where *ϕ*sun is the blackbody radiation flux of the sun, which is given by Eq. (7):

$$\mathcal{Q}\_{\text{sun}} = \frac{2\pi}{h^3 c^2} \times E^2 \times \exp\left(\frac{-E}{k T\_{\text{sun}}}\right) \tag{7}$$

The photocurrent density of the solar cell is given by *J* = *q* � *F*cell (*T* = *T*sun). The electrical output power density of the solar cell is calculated by Eq. (8):

$$P\_{\rm out} = J \times V = q \times F\_{\rm cell} (T = T\_{\rm sun}) \times \frac{E\_{\rm g}}{q} = F\_{\rm cell} (T = T\_{\rm sun}) \times E\_{\rm g} \tag{8}$$

The input sun power density is given by Eq. (9) [42]:

$$P\_{\rm in} = \frac{2\pi}{h^3 c^2} \int\_{E\_\rm E}^{\infty} \frac{E^3 \rm dE}{\exp\left(\frac{E}{kT\_{\rm sun}}\right) - 1} \cong \frac{2\pi^5 (kT\_{\rm sun})^4}{15h^3 c^2} \tag{9}$$

From the above Eqs. (8) and (9), the energy conversion efficiency of a solar cell can be determined by *η* = *P*out/*P*in.

Using the blackbody spectrum at *T* = 6000 K and AM 1.5 global spectrum, the solar cell gives a maximum conversion efficiency of 44% and 49%, respectively, for an ideal bandgap of 1.1 eV as shown in **Figure 2**.

### **4. Methodology**

Multi-level approach is employed for effective designing of tandem perovskite/ silicon solar cell. This approach includes improving the performance of individual layers in each cell; examining the charge transport between each layer when they are stacked, and finally efficient light in-coupling between top and bottom cells (**Figure 3**).
