In the following we will describe several applications of the DSC Module in tiberCAD to investigate different aspects and possible architectures of DSCs. The applications involve simulations in 1 and 3 dimensions.

The first application is a 1D simulation of a DSC. The aim is to study the effect of the variation of several physical parameters (absorption spectrum of the dye, electron mobility and TiO₂ thickness) on the efficiency of the device.

Then, we will see three 3D simulations describing some novel topologies of DSC, namely a cell where the illuminated surface and the electron collection surface are decoupled, a DSC wrapped around an optical fiber and a Back-contact cell (BC-DSC).

EFFICIENCY MAPS

The fundamental figure of merit which characterizes a solar cell is the energy conversion efficiency.

Using a simple 1D model of a DSC, we can study how the efficiency varies for a standard illumination of 1.5 AM Sun, by modifying some geometrical and physical parameters of the cell: absorption coefficient, electron mobility and TiO₂ thickness.

The first and third parameters can be easily modified by changing the molecular dye and increasing the layer of paste deposited for the cell
construction. The second parameter is more complex to change, different sintering processes or
nanostructuring of the TiO₂ can help to modulate and control the electron mobility.

The efficiency maps (shown below) are the result of hundreds of simulations with small variations of the parameters under investigation. The low absorption case is shown on the left while high absorption on the right.

Passing from a lower to a higher cell absorption we notice that also the behavior of the efficiency as a function of electron mobility and TiO₂ thickness changes radically. In the low absorption case, a larger thickness is needed in order to achieve the maximum efficiency (between 15 and 25 μm).
A large portion of light is absorbed far from the illuminated contact and then a larger active layer is needed in order to collect light efficiently.

Thus, for highly transparent modules (for example for applications of DSCs integrated with building facades and windows) we need larger thicknesses of TiO₂  but consequently higher mobilities.

On the contrary, in the case of a high absorption, all the light is harvested close to the photoanode and then all electrons are generated there. A high mobility has a small impact over the efficiency. A large thickness, instead, can even reduce the final efficiency, because a portion of the active layer contribute to recombination only.

THREE CASES OF 3D CELL SIMULATION

1. TOP FINGERED MODEL

In the first geometry (see below) the metallic contact for the anode is on one side of the device, spatially separated from the transparent surface for light absorption.
In this way, the illuminated surface and the electron collection surface, made by metallic fingers, are decoupled, avoiding the problem of the shadowing induced by the metallic fingers or the presence of the conductive oxide for electron collection.

In the figures below, the calculated electron generation (left) and recombination (right) are shown in short circuit condition.
The decoupling of illumination and collection surfaces changes the density distribution inside the cell.
In fact, the highest electron photogeneration is concentrated close to the illuminated surface, on the contrary recombination occurs in the volume of TiO₂ farthest from the collection surface, thus at the bottom of the cell. In the left figure the current flux lines are plotted to show the path followed by charge carriers. It is found that this decoupled cell has a slightly better short circuit current and conversion efficiency.

2. CYLINDRICAL CELL MODEL

The second geometry (see below) shows a completely different device. It is a potential new application for photovoltaics where the active region of the cell can be placed far from the direct light source. In fact, the light reaches the active region through an optical fiber which acts like a light-pipe. Similar devices can have interesting applications in medicine and for tandem cells.

Here we focus on the effect on internal density distribution due to a spatial modulation in the illumination. The light intensity is modulated along the axis of the cylindric cell. The decaying exponent is assumed equal to 0.01 µm^-1. The generation in the  cell is  shown  in  the  figure above  at  right, where the light intensity decays along the black arrow.
The effect of this non-homogeneous light intensity is that the path of the current for triiodide, as well as for the other charge carriers, changes from a radial current to a diagonal current. The current of the ionic species concentrates on the corner, where the light intensity is lower. This non-homogeneity in the illumination, which may occur due to a bad coupling between the TiO₂ and the core of the optical fiber, may have large consequences over the final efficiency.

3. BC-DSC MODEL

The final case of 3D cell model is a Back-contact cell (BC-DSC).
This is a monolithic back-contact DSC based on an array of two interdigitated finger electrodes located on one common substrate.

This architecture presents two advantages:

1. No need of FTO on the collection side
2. Optical transmission losses avoided

Here is a cross-section of the FEM mesh of the 3D model of the cell, showing the interdigitated anode and cathode contacts.

Below is a 3-D picture of the BC-DSC modelled with tiberCAD.

Finally, here is the calculated electron current in the designed structure.

REFERENCES

A.Gagliardi et al., J Comput Electron (2011) 10:424–436

D.Gentilini et al., Opt Quant Electron (2012) 44:155–160

Dongchuan Fu et al., Adv. Mater. 2010, 22, 4270–4274