Scattering and Absorption

The basic principles for the functioning of plasmonic-enhanced solar cells include scattering and absorption of light due to the deposition of metal nano-particles. Silicon does not absorb light very well. For this reason, more light needs to be scattered across the surface in order to increase the absorption. It has been found that metal nano-particles help to scatter the incoming light across the surface of the silicon substrate. The equations that govern the scattering and absorption of light can be shown as:

• ${\displaystyle C_{scat}={\frac {1}{6\pi }}\left({\frac {2\pi }{\lambda }}\right)^{4}|\alpha |^{2}}$

This shows the scattering of light for particles which have diameters below the wavelength of light.

• ${\displaystyle C_{abs}={\frac {2\pi }{\lambda }}{\text{Im}}[\alpha ]}$

This shows the absorption for a point dipole model.

• ${\displaystyle \alpha =3V\left[{\frac {\epsilon _{p}/\epsilon _{m}-1}{\epsilon _{p}/\epsilon _{m}+2}}\right]}$

This is the polarizability of the particle. V is the particle volume. ${\displaystyle \epsilon _{p}}$ is the dielectric function of the particle. ${\displaystyle \epsilon _{m}}$ is the dielectric function of the embedding medium. When ${\displaystyle \epsilon _{p}=-2\epsilon _{m}}$ the polarizability of the particle becomes large. This polarizability value is known as the surface plasmon resonance. The dielectric function for metals with low absorption can be defined as:

• ${\displaystyle \epsilon =1-{\frac {\omega _{p}^{2}}{\omega ^{2}+i\gamma \omega }}}$

In the previous equation, ${\displaystyle \omega _{p}}$ is the bulk plasma frequency. This is defined as:

• ${\displaystyle \omega _{p}^{2}=Ne^{2}/m\epsilon _{0}}$

N is the density of free electrons, e is the electronic charge and m is the effective mass of an electron. ${\displaystyle \epsilon _{0}}$ is the dielectric constant of free space. The equation for the surface plasmon resonance in free space can therefore be represented by:

• ${\displaystyle \alpha =3V{\frac {\omega _{p}^{2}}{\omega _{p}^{2}-3\omega ^{2}-i\gamma \omega }}}$

Many of the plasmonic solar cells use nano-particles to enhance the scattering of light. These nano-particles take the shape of spheres, and therefore the surface plasmon resonance frequency for spheres is desirable. By solving the previous equations, the surface plasmon resonance frequency for a sphere in free space can be shown as:

• ${\displaystyle \omega _{sp}={\sqrt {3}}\omega _{p}}$

As an example, at the surface plasmon resonance for a silver nanoparticle, the scattering cross-section is about 10x the cross-section of the nanoparticle. The goal of the nano-particles is to trap light on the surface of the SC. The absorption of light is not important for the nanoparticle, rather, it is important for the SC. One would think that if the nanoparticle is increased in size, then the scattering cross-section becomes larger. This is true, however, when compared with the size of the nanoparticle, the ratio (${\displaystyle CS_{scat}/CS_{particle}}$) is reduced. Particles with a large scattering cross section tend to have a broader plasmon resonance range.

Wavelength dependence

Surface plasmon resonance mainly depends on the density of free electrons in the particle. The order of densities of electrons for different metals is shown below along with the type of light which corresponds to the resonance.

• Aluminum - Ultra-violet
• Silver - Ultra-violet
• Gold - Visible
• Copper - Visible

If the dielectric constant for the embedding medium is varied, the resonant frequency can be shifted. Higher indexes of refraction will lead to a longer resonant wavelength.

Light trapping

The metal nano-particles are deposited at a distance from the substrate in order to trap the light between the substrate and the particles. The particles are embedded in a material on top of the substrate. The material is typically a dielectric, such as silicon or silicon nitride. When performing experiment and simulations on the amount of light scattered into the substrate due to the distance between the particle and substrate, air is used as the embedding material as a reference. It has been found that the amount of light radiated into the substrate decreases with distance from the substrate. This means that nano-particles on the surface are desirable for radiating light into the substrate, but if there is no distance between the particle and substrate, then the light is not trapped and more light escapes.

The surface plasmons are the excitations of the conduction electrons at the interface of metal and the dielectric. Metallic nano-particles can be used to couple and trap freely propagating plane waves into the semiconductor thin film layer. Light can be folded into the absorbing layer to increase the absorption. The localized surface plasmons in metal nano-particles and the surface plasmon polaritons at the interface of metal and semiconductor are of interest in the current research. In recent reported papers, the shape and size of the metal nano-particles are key factors to determine the incoupling efficiency. The smaller particles have larger incoupling efficiency due to the enhanced near-field coupling. However, very small particles suffer from large ohmic losses.^[19]

Nevertheless, in certain types of nanostructured solar cells, such as the emerging quantum-dot intermediate band solar cells, the highly intense scattered near-field produced in the vicinity of plasmonic nanoparticles may be exploited for local absorption amplification in the quantum dots that are embedded in a host semiconductor.^[20][21]

Recently, the plasmonic asymmetric modes of nano particles have found to favor the broadband optical absorption and promote the electrical properties of solar cells. The simultaneously plasmon-optical and plasmon-electrical effects of nanoparticles reveal a promising feature of nanoparticle plasmon.^[13]

Shape choice of nano-particles

Multiple energy levels

The idea for multiple energy level solar cells is to basically stack thin film solar cells on top of each other. Each thin film solar cell would have a different band gap which means that if part of the solar spectrum was not absorbed by the first cell then the one just below would be able to absorb part of the spectrum. These can be stacked and an optimal band gap can be used for each cell in order to produce the maximum amount of power. There are multiple options for how each cell can be connected, such as serial or parallel. The serial connection is desired because the output of the solar cell would just be two leads.

The lattice structure in each of the thin film cells needs to be the same. If it is not then there will be losses. The processes used for depositing the layers are complex. They include Molecular Beam Epitaxy and Metal Organic Vapour Phase Epitaxy. The current efficiency record is made with this process but doesn't have exact matching lattice constants. The losses due to this are not as effective because the differences in lattices allows for more optimal band gap material for the first two cells. This type of cell is expected to be able to be 50% efficient.

Lower-quality materials that use cheaper deposition processes are being researched as well. These devices are not as efficient, but the price, size and power combined allow them to be just as cost effective. Since the processes are simpler and the materials are more readily available, the mass production of these devices is more economical.

Hot carrier cells

A problem with solar cells is that the high energy photons that hit the surface are converted to heat. This is a loss for the cell because the incoming photons are not converted into usable energy. The idea behind the hot carrier cell is to utilize some of that incoming energy which is converted to heat. If the electrons and holes can be collected while hot, a higher voltage can be obtained from the cell. The problem with doing this is that the contacts which collect the electrons and holes will cool the material. Thus far, keeping the contacts from cooling the cell has been theoretical. Another way of improving the efficiency of the solar cell using the heat generated is to have a cell which allows lower energy photons to excite electron and hole pairs. This requires a small bandgap. Using a selective contact, the lower energy electrons and holes can be collected while allowing the higher energy ones to continue moving through the cell. The selective contacts are made using a double barrier resonant tunneling structure. The carriers are cooled which they scatter with phonons. If a material has a large bandgap of phonons then the carriers will carry more of the heat to the contact and it won't be lost in the lattice structure. One material which has a large bandgap of phonons is indium nitride. The hot carrier cells are in their infancy but are beginning to move toward the experimental stage.

Plasmonic-electrical solar cells

Having unique features of tunable resonances and unprecedented near-field enhancement, plasmon is an enabling technique for light management. Recently, performances of thin-film solar cells have been pronouncedly improved by introducing metallic nanostructures. The improvements are mainly attributed to the plasmonic-optical effects for manipulating light propagation, absorption, and scattering. The plasmonic-optical effects could: (1) boost optical absorption of active materials; (2) spatially redistribute light absorption at the active layer due to the localized near-field enhancement around metallic nanostructures. Except for the plasmonic-optical effects, the effects of plasmonically modified recombination, transport and collection of photocarriers (electrons and holes), hereafter named plasmonic-electrical effects, have been proposed by Sha, etal.^[40][41] For boosting device performance, they conceived a general design rule, tailored to arbitrary electron to hole mobility ratio, to decide the transport paths of photocarriers.^[41] The design rule suggests that electron to hole transport length ratio should be balanced with electron to hole mobility ratio. In other words, the transport time of electrons and holes (from initial generation sites to corresponding electrodes) should be the same. The general design rule can be realized by spatially redistributing light absorption at the active layer of devices (with the plasmonic-electrical effect). They also demonstrated the breaking of space charge limit in plasmonic-electrical organic solar cell.^[40] Recently, the plasmonic asymmetric modes of nano particles have found to favor the broadband optical absorption and promote the electrical properties of solar cells. The simultaneously plasmon-optical and plasmon-electrical effects of nanoparticles reveal a promising feature of nanoparticle plasmon.^[13][42]

Ultra-thin plasmonic wafer solar cells

Reducing the silicon wafer thickness at a minimized efficiency loss represents a mainstream trend in increasing the cost-effectiveness of wafer-based solar cells. Recently, Zhang et al. have demonstrated that, using the advanced light trapping strategy with a properly designed nano-particle architecture, the wafer thickness can be dramatically reduced to only around 1/10 of the current thickness (180 μm) without any solar cell efficiency loss at 18.2%. Nano-particle integrated ultra-thin solar cells with only 3% of the current wafer thickness can potentially achieve 15.3% efficiency combining the absorption enhancement with the benefit of thinner wafer induced open circuit voltage increase. This represents a 97% material saving with only 15% relative efficiency loss. These results demonstrate the feasibility and prospect of achieving high-efficiency ultra-thin silicon wafer cells with plasmonic light trapping.^[43]