Universitetet i Oslo

University of Oslo

AMKS Group

Surface Plasmonsand

Solar CellsM. Kirkengen, J. Bergli, Yu. M. Galperin

Surface Plasmons Solar Cell Basics

Combining the Concepts Experimental Encouragement 2: Thin Film CellExperimental Encouragement 1: Light Emitting Diode

Research Direction 1 – Guiding light Research Direction 2 – Direct Absorption

This work is financed by the Storforsk Program of the Norwegian Research Council.

For the idea to explore this field, we are grateful to prof. Alexander Ulyashin, IFE

The phenomenon known as Surface Plasmons can only exist in the interface between a metal and a dielectric material (like air). The plasmons are oscillations in the charge density of the metal surface, accompanied by an oscillating electromagnetic field in the dielectric material. The field decays exponentially away from the surface.

A special kind of Surface Plasmons can be excited on the surface of a metal particle when irradiated by light. In this case, the alternating positive and negative charge accumulations must match after completing a full circle. The number (n) of full periods is called the mode of the oscillation. The n=1 mode is usually the most important, and behaves exactly like a dipole.

n=1dipole

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n=2quadrupole

n=3

Blue denotes the particle, red, the electrons being moved around, greatly exaggerated.

The relation between the wavelength of the incoming light and the particle diameter determines the relative importance of the different modes. For wavelengths much longer than the diameter, the dipole mode dominates. For shorter wavelengths (or larger paticles), higher modes are also important. The figure to the left shows the scattered field at different wavelengths.=100r =5r =r

Because the frequency of the incoming light has to match the resonance frequency of the plasmons, it is possible to detect the plasmons by a marked peak in the scattering. The peak shifts with particle shape, size and the dielectric functions of the materials. To the right we see scattering due to gold nanoparticles, with a marked peak about 500nm. The earliest use of this effect includes the use of gold in ornamental glass. The red light in the rightmost picture is due to surface plasmons on gold nanoparticles, made in AD 1600...

Two proofs of the existence of surface plasmons on gold particles.

Solar Cells exist in many variations, but the type discussed here is the working horse of the solar cell industries, the one using silicon wafers. The main advantages of the silicon cell are its price, material availability, and the fact that the industry has been using silicon for computers for a long time.

To understand solar cells, one must understand the fundamental concepts of semiconductors. In a semiconductor, electrons can be in one of two bands, the valence band and the conduction band. At zero temperature, and with no doping, all electrons will be in the valence band, filling it completely. When exited by light, electrons may jump into the conduction band, leaving behind a hole, an unfilled position, in the valence band. Both the electron and the hole may then move around.

In addition, one can dope the semiconductor, either with n-type or p-type impurities. N-type impurities give an extra electron to the conduction band, p-type impurities create an extra hole. In solar cells, we use both, creating a p-n-junction. At the junction, conduction band electrons will be pushed one way, holes the other, creating a voltage. If the electrons reenter the valence band before leaving the cell, their energy is lost. This is called recombination, and is a major efficiency killer.

1) Light entering and leaving the cell2) Electrons giving up eccess energy as heat

3) Electron being pushed over the p-n-junction4) Electrons and holes leaving the cell

5) Recombination of electron-hole pairs (bad)

It is important to make sure that as much as possible of the light enters the cell, and that it stays there for as long as possible. To avoid reflection, one usually adds an Anti Reflection Coating (ARC). This creates a destructive interference between light being reflected at the interface between air and the ARC, and that reflected from the interface between ARC and silicon.

Texturing is used to make the light enter the cell at an angle, making its path through the cell as long as possible. This increases the probability that the light will excite an electron-hole pair.

Anti reflection coating

Active layer

Si p-n-junction

Rear contact, mirror, Al

Contacts (Ag)

At the University of New South Wales, Australia, experiments have been performed studying emission from silicon light emitting diodes. This is basically only a solar cell working backwards. Instead of light being absorbed, moving electrons to the conduction band and thereby creating a voltage, one can apply a voltage, which makes electrons move into the conduction band from the contacts, and when they fall down into the valence band, light is emitted.

When adding a layer of silver nanoparticles on top of the diode, the authors have found an up to 8-fold increase in emitted light. Because the processes are so similar, the observed increase in efficiency for LEDs indicates that a similiar increase should be possible for solar cells too.

Ref: Pillai et al, App. Phys: Letters 88, 161102 (2006)

While surface plasmons have been exploited in other applications for several decades, they are only now starting to be concidered for use in solar cells.

In an experiment performed at the University of California, San Diego, using an amorphous silicon, thin film cell, a small improvement was found when applying gold nanoparticles (8%).

However, the additional treatment needed to add the nanoparticles has probably created a lot of unwanted impurities leading to electron-hole recombination. This experiment demonstrates both the potential of using surface plasmons, and the need for improved cell designs and production methods.

Ref: Derkacs et. Al. App. Phys Letters 89, 093103 (2006)

The Current-Voltage curve tells us which voltage gives the optimal power. Power = Current times Voltage

By adding a layer of metal particles with diameter much less than the wavelength at the top of the cell, we can increase the scattering at the surface, without increasing reflection.

It is important that the scattering should have a maximum fitting the energy spectrum of the light used by the solar cell. This means we have to be able to tune the plasmon resonance to the optimal frequency, using correct materials, and maybe even shaping the particles. This can be a challenge, as they should be only about 50 nm across to avoid reflection!

Why does it work – how can we make it work better?

One of the main limitations of the silicon solar cell is the fact that the momentum of the highest energy state of the valence band does not match the momentum of the lowest energy state of the conduction band. A photon carrying exactly the energy difference between the bands cannot carry enough momentum to also allow momentum conservation. Therefore, for photons near the band gap, only indirect transitions are possible. Indirect transitions involve a phonon to supply the extra momentum. These transitions are a lot less likely than direct transitions, which is why silicon cells have to be relatively thick, compared to cell made from GaAs or similar materials.

However, it is known that the electric field near an emitting dipole has components that do not radiate. These fields can be very strong compared to the field radiated from the dipole, and are localized around the emitter. Not surprisingly, they are called the ”near field”.

Mathematically, we can represent the total field from an emitting dipole as a fourier series, that is as a sum of harmonically oscillating components with different wavelengths. When we write the interaction between the field and the electrons in the semiconductor, we find that some of these components actually allow momentum conservation. It is therefore possible that the surface plasmons in the nanoparticles can give direct transitions, even in silicon. These transitions must be expected to occur close to the nanoparticles. If this mechanism turns out to be important, it can greatly reduce the necessary thickness for a silicon cell, reducing both material costs and recombination losses. Exact calculations are in progress.

Conduction band minimum

Valence band maximum

Silicon band structure

The near field decays orders of magnitude in less than a wavelenght(r is the radius of the green circle)

=100r

Surprising obstacleAfter many decades of research and industrial use of silicon, we were quite surprised to find that the wave function at the conduction band minimum is not known. Several approximations exist, but none are perfect. We had to settle on using the Tight Binding Approximation, allowing the coefficients of the expansion to be determined in experiment by someone else.

One of the most popular approaches to explaining why surface plasmons work for solar cells is to look at the optics of the problem only. In this approach, one assumes that the improvement can be explained by the fact that light emitted from the nanoparticle will travel along a longer path within the cell before exiting, or even be bound to a guided mode (experiencing total reflection), and thus not leave until it is absorbed. We have therefore looked closely at how light is emitted from a dipole located at an interface.

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In the same way, by the reciprocity principle, the dipole can emit light into angles that should normally not be accessible when light goes from air into the silicon. In addition, evanescent components of the field from the dipole, components that normally do not radiate energy away, but only exist as a ”near field”, can be transformed into radiating components by crossing the interface. Thus while a dipole in air would radiate symmetrically backwards and forwards, a dipole near an interface may end up radiating a very large proportion of its energy over the interface, as shown in the figure. To be able to cover more realistic situations, we have expanded on Mertz’ calculations using transfer matrix theory, to allow situations with multiple interfaces, or anisotropic polarization of the dipole, due to deformed nanoparticles.

Radiation from a dipole very near an interface. The angle of total reflection is at the maximum of the side lobes to the left. The figures to the right show a dipole in open air and the orientation of the dipole relative to the interface.

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z

1 (dielectric)

2 metal+++

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Following previous calculations by Mertz, we have used the reciprocity principle, which says that a dipole emits and receives with the same efficiency. By looking at how light from different directions can reach the dipole, we can find out how effectively the dipole emits towards those directions. If we have a dipole in air beside a silicon surface, we meet the phenomenon of frustrated total reflection. In total reflection, the light does enter slightly into the neighboring material before it is reflected. If the dipole can absorb energy from the wave before it is returned, the reflection is ”frustrated”.

Ref. J. Mertz, J. Opt. Soc. Am. B 17,11 (Nov 2000)

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When reflected at an interface, the plane wave has an exponentially decreasing component on the other side of the interface. A Dipole within the decaying field can still absorb energy.

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