The effect of enclosing a nanowire (NW) radial pn junction photovoltaic (PV) element inside a nanoring optical antenna to enhance the electric field in the near field region has been investigated. Five different materials for the NW (Si, Ge, GaAs, GaInP and InGaAs) have been selected to maximize the absorbed solar spectrum. In addition, the position and diameter of the NW are varied through a random distribution to optimize the power conversion efficiency. Results show that the ring antenna geometry and the NW random spatial distribution are effective in both spectral widening and field concentration which result in an increase of the cell conversion efficiency.
© 2012 OSA
Radial pn junction nanowire array solar cell is a PV device consisting of arrays of semiconducting nanowires [1,2]. This radial geometry enables decoupling the requirements for light absorption and carrier extraction into orthogonal spatial directions. Each individual pn junction wire in the cell is long in the direction of incident light, allowing for maximum light absorption, but thin in the orthogonal direction, thereby allowing for effective carrier collection. Different materials namely Si, Ge, GaAs, GaInP and InGaAs are investigated.
Specially-designed nanostructured optical ring antennas are used to split the incident solar spectrum and to concentrate the electric field in lateral spatial locations coinciding with the location of the NWs of the optimized bandgap energy . Optical antennas are able to concentrate light on a scale much smaller than the wavelength . This is a subject receiving an extensive attention in physics, optics and antenna engineering due to their potential of enhancing the efficiency of photo-detection, light emission, sensing, heat transfer and spectroscopy. Metal nanostructures act as optical antennas because free electrons are in resonance with the incident photons. These nonpropagating excitations of the conduction electrons, known as localized surface plasmon resonances, can produce an enhanced electromagnetic field localized around the metal nanostructures. Plasmon-coupling induced in the near-field region is employed to enhance the absorption efficiency of optical materials in solar cells. The investigation of localized surface plasmons in metal nanoparticles has received intense interest owing to a number of related unique and useful optical properties, such as confinement of light at the metal surface and control of both the far-field and near-field distribution of light. Another exciting direction for plasmonic researches is photovoltaic applications. Design approaches based on plasmonics for high-efficiency solar-cell have been proposed [5,6]. Herein, we focus on the use of silver nanoring antennas to enhance the spectral efficiency of the photovoltaic nanowire. Silver is used as it is the best known reflector of visible light although, aluminum outdoes it in limited parts of the visible spectrum .
Besides the ability to concentrate the electromagnetic field, ring resonator antenna is selected also for spectral splitting. At resonance, this antenna structure uniformly enhances the electric field within the ring cavity. Coupling and interaction between the inner and outer surfaces result in dipolar excitations with energy levels that can generally be categorized into a lower energy dipolar symmetric bonding mode and a higher energy dipolar anti-symmetric anti-bonding mode. As the plasmon interaction between the inner and outer surfaces increases, the splitting between these hybridized modes increases . The rings are thus able to red-shift peaks to lower energies and achieve a better tuning range. This reduces the material losses, retardation effects and radiation damping.
2. Modeling and simulation
Simulation of the proposed structure has been performed using COMSOL Multiphysics , where Maxwell’s equations are solved in three dimensions to calculate the absorption coefficient of the NW. An analytical model is then used to determine the total efficiency of the NW . AM1.5G is assumed and all the used NWs are of 1 µm height with varying radii according to the material used. We have used a radius value of 100 nm for Si and for Ge. For GaAs, GaP and InP the radii were 200 nm, 220 nm and 250 nm respectively. Each NW has a lower limit in its radius value to avoid a fully depleted pn junction . Increasing the NW radius above this lower limit will increase the number of absorbed photons and hence increases the power conversion efficiency. A maximum is reached when the radius is equal to approximately the diffusion length of the NW material . Any further increase will cause a higher carrier recombination rates which will eventually decrease the cell efficiency. It is to be noted that the chosen values for the height and the radius of the NW are only taken as a reference for showing the percentage of the enhancement in the power conversion efficiency. NWs with longer height up to the value of the diffusion length of the material have an increasing efficiency .
The loop antenna structure is simulated with a gap source excitation, where a lumped port of one voltage source is assumed across the feeding gap. A wavelength of 650 nm is considered for the light radiation when the thickness of the loop is 100 nm (outer radius – inner radius). The complex permittivity of silver is taken to be εr = −26.64 + i1.66 at this wave length .
3. Results and discussions
3.1 Nanoring antenna effect
For maximum efficiency of a PV cell, it is important to absorb most of the incoming photons. This necessitates a minimum material thickness, which forms the primary cost determinant. On the other hand, the presence of nearby nanoparticle antennas can enhance carrier generation and hence the efficiency of the PV cell through several distinct ways. Plasmonic nanoparticles have large optical cross sections and can efficiently collect and scatter photons into the far field. Some of these photons may become coupled into in-plane waveguide modes in the cell material. This increases the photon absorption probability. Also, the spatially localized high-momentum near-field photons created near an optical antenna can directly generate carriers in an indirect gap semiconductor (like silicon) even without phonon assistance. Finally, there is the possibility of direct charge-carrier injection from the nanoparticle into the semiconductor.
Figure 1 shows the increase in the electric field inside a Si NW (approximately 100 times) due to the presence of the optical nanoring antenna. This increase in the electric field reflects on the absorption capabilities of the material located in the near field region and consequently affects the power conversion efficiency of the photovoltaic nanowire.
The obtained efficiency of the modified structure is found to be 5.8% while that of the NW without antenna is 5.28% , which is about 10% increase. Other advantage of the proposed structure is the existence of an approximately uniform electric field in the near field region of the optical antenna across the axis. Spectrum widening is another phenomena associated with nanoring antenna. This phenomenon affects the absorption of the material across the illuminated wavelengths, and achieves a better tuning range on the external quantum efficiency (EQE). The EQE is defined as the ratio of the number of charge carriers collected by the solar cell to the number of incident photons of a given energy shining on the solar cell from outside. EQE tuning is due to the interaction between the inner and outer surfaces of the optical nanoring antenna. As presented in Fig. 2 , a widening in external quantum efficiency in Si nanowire is observed. A red-shift peak located at 700 nm is reduced to a lower value with a decrease in EQE from 75% to 73% causing a wider tuning range for Si NW.
3.2 Spectrally distributed nanowire array
Materials with different band-gap have different spectral regions for optimal energy conversion. The optimized combination of materials can cover a larger spectral range and therefore has a higher total efficiency. A variety of semiconductor materials , namely Si, Ge, GaAs, GaInP and InGaAs that cover portions of the solar spectrum, have been used. A 5×5 array has been simulated using these materials each in a row, where the spacing between each two elements is constant and equals to 500 nm. The results show that this uniform array structure will not increase the electric field inside each wire over the 100 times already obtained from the presence of the nanoring antennas. However, as shown in Fig. 3 , the selected five materials cover a wide band in the solar spectrum according to their band-gaps. It's clear that GaAs (a direct band-gap material) has the highest EQE while Ge (an indirect band-gap material) has the lowest EQE.
3.3 Spatial and spectral distributed array
Another parameter which has been taken into consideration is the wire positioning in the array. Due to the photonic properties of wire arrays, the positions of the wires influence the performance considerably and need to be carefully chosen . A ten elements array in a 3×3 µm2 area is designed using uniform random distribution by determining the x-y positioning, diameter and the material used for each nanowire. The x and y component varies from 0 to 3 µm, the diameter varies from 100 to 250 nm while the materials is chosen randomly from the five previously selected materials. The selected random distribution is based on nonrandom physical law, namely the minimization of the electrostatic surface potential during clustering. The electrostatic surface potential is given by Eq. (1) :Fig. 4 . Ten wires are chosen in the array instead of nine, as nine wires in the area 3×3 µm2 results in a too regular structure. A considerable increase in the electric field inside the nanowire of about 10000 times that of a single NW without nanoring antenna is observed , which reflects on the efficiency of the nanowires. The calculated efficiency is 6.6% for Si NW and 15.2% for GaAs NW. Compared with the 5.28% for Si and 14.14% for GaAs found in standalone NW without nanorings , this indicates a 25% increase for Si and 7.5% increase for GaAs.
In order to increase the efficiency of NW photovoltaic, a nanoring antenna has been used to concentrate the electric field in its near field region. Different materials (Si, Ge, GaAs, GaInP and InGaAs) have been selected to maximize the absorbed solar spectrum. In addition, a random array configuration has been implemented while varying both the position and the diameter of the NW following a minimization algorithm to optimize the power conversion efficiency. The proposed array topology considers the spectral distribution through the use of different materials with different band-gaps and the hot spot effect due to the existence of a nanoring antenna which concentrates the electric field in its near field region. An increase in the power conversion efficiency by 25% for Si NW and 7.5% for GaAs NW is achieved when comparing the case of random array with antennas against a standalone NW without antenna.
References and links
1. B. M. Kayes, C. E. Richardson, N. S. Lewis, and H. A. Atwater, “Radial pn junction nanorod solar cells: device physics principles and routes to fabrication in silicon,” in Proceedings of the 31th IEEE Photovoltaic Specialists Conference, Florida, USA (January 3–7, 2005).
2. S. Abdellatif, K. Kirah, H. Ghali, and W. Anis, “A comparison between Si and GaAs nanowire-based photovoltaic devices,” Proc. SPIE 8204, 820412 (2011). [CrossRef]
3. H.-S. Philip Wong, P. Peumans, M. Brongersma, and Y. Nishi, “Lateral nanoconcentrator nanowire multijunction photovoltaic cells,” GCEP Progress Report (Stanford University, 2011).
6. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]
8. COMSOL, Version 4.2. http://www.comsol.com.
9. P. P. Altermatt, Y. Yang, T. Lange, A. Schenk, and R. Brendel, “Simulation of optical properties of Si wire cells,” in Proceedings of the 34th IEEE Photovoltaic Specialists Conference, Philadelphia, USA (June 7–12, 2009).