## How do polymer solar cells work

Henrik Friis DamThue Trofod Larsen-Olsen

Like all solar cells, the polymer solar cell converts light into electricity, by converting a flux of photons (light) into a flux of charged particles (a current). This conversion process is made possible by the combination of several types of materials, all having distinct electrical and optical characteristics as described in the text presenting the polymer solar cell layer stack, but most importantly is the inclusion of semiconductors.

This text will explain how polymer solar cell is able to generate electricity, and will do so in three sections signifying the three main steps of the conversion process which can be summarized in brief

1. A photon incident on a semiconductor, having an energy that exceeds the semiconductor band gap, excites an electron to an unoccupied state above band gap, creating an electron-hole (e-h) pair.
2. The electron-hole pair is subsequently separated over a built-in gradient in the electrochemical potential of the solar cell.
3. Finally, the electron and hole is collected at opposite electrodes and led to recombine after being put to work in an external circuit.

Figure 1. The working principle of the solar cell. Light enters the cell through the transparent anode, and is absorbed in the bulk heterojunction layer through generation of excitons (1). The excitons diffuse in the bulk heterojunction until they either recombine or reach a donor-acceptor interface, where they separate into electrons (black) and holes (white) (2). The electrons and holes will then move to the respective anode and cathode, through the donor and acceptor material phase (3).

In the following these three steps will be elaborated, while a graphical summary is shown in figure 1.

### Absorption of light

The materials responsible for the absorption of light in the polymer solar cell are the organic semiconductors making up the active layer. This class of materials is characterized by having a band gap of certain gap energy ($E_{g}$). This gap signifies the energetic separation between the valence electrons and the nearest free electronic states, for organic semiconductors this is defined as the difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) as illustrated in Figure 2a $$E_g = E_{LUMO} - E_{HOMO}.$$ A material is generally considered a semiconductor when $E_{g}$ is greater than the thermal energy available at realistic temperatures (e.g. around room temperature), whereby valence electrons cannot be excited to the conduction states simply by thermal activation, rendering the material non-conductive. In the dark that is. Because the absorption of a photon of energy greater than $E_{g}$ can excite an electron from the HOMO to the LUMO state $$E_{photon} = \frac{c \cdot h}{\lambda_{photon}} \geq E_g$$ where $\lambda_{photon}$ is the wavelength of the light, $c$ is the speed of light and $h$ is Planck’s constant. As shown in figure 2b, the absorption of the photon by excitation of en electron from the HOMO state to a state above the LUMO level, leaves behind an unoccupied valence state, termed a ‘hole’, and the photon energy now resides as the potential energy difference between this excited electron-hole pair. However, as there is a continuum of states above the LUMO level, the excited electron will quickly undergo thermal relaxation, ending up at the LUMO level. This signifies that all of the photon energy exceeding the gap energy will be lost as heat ($E_{thermal~loss} = E_{photon}-E_g$), as is illustrated in Figure 2c.

Figure 2: (a) An organic semiconductor in the dark, with a band gap of energy Eg. (b) Incident light of energy greater than the energy gap excites an electron from the HOMO state to the LUMO state. (c) The photon energy greater than the gap energy is ‘lost’ by thermal relaxation to the LUMO level.

With this in mind, one can make some very important considerations about the general design of a solar cell: In order to optimize the solar cell design one must consider the balancing of the number of photons that are absorbed with the energy that is lost ($E_{thermal loss}$). To do this one of course also need to know how many photons are available. This is given by the solar spectrum, shown in figure 3. Considerations such as these determine the optimum band gap energy and also the theoretical limit to solar cell efficiency. This was done by Shockley and Queisser in their seminal work from 1961 defining the so-called ‘detailed balance limit’.DOI:10.1063/1.1736034

Figure 3. The solar spectrum incident on the atmosphere, compared with the ground level spectrum used for standard test conditions.

### Charge separation

In polymer solar cells, the electron-hole pair which was created through absorption is held together by coulomb forces, forming a quasi-particle called an exciton. However, in order for the solar cell to generate electricity the electron and hole must be separated, and subsequently collected at electrodes of opposite polarity. In order to accomplish this, the exciton bond must be broken. This is done by introducing a secondary organic semiconductor in the active layer, which has an energetically lower lying LUMO-level, such that electron transfer between the two types of semiconductor is favorable. For this reason the material with the highest LUMO is called the electron donor while the other is called the electron acceptor. And so in order for electron transfer to be favorable the following condition must be true, with $E_{exc-b}$ being the exciton bond energy $$E^{donor}_{LUMO} - E^{acceptor}_{LUMO} \geq E_{exc-b}$$ In state-of-the-art polymer solar cells the donor material is most often a conjugated polymer, while the acceptor is often a small molecule based on the C60 fullerene. As the absorption of the highly symmetric C60 molecule is rather low compared with the highly absorbing donor polymer, most of the excitons are generated in the donor phase and electrons are transferred to the acceptor. However, for excitons generated in the acceptor, the following must hold true in order for holes to be transferred from the acceptor to the donor $$E^{donor}_{HOMO} - E^{acceptor}_{HOMO} \geq E_{exc-b}$$ As the exciton only has a certain lifetime before it collapses, and the electron recombines with the hole; the characteristic distance between an exciton generation site and a donor/acceptor interface must be on order of 5-10 nm (see e.g. Deibel & Dyakonov DOI:10.1088/0034-4885/73/9/096401). At the same time, the photons need to traverse a certain thickness of active layer, often on the order of 100 nm, in order for most of them to be absorbed. For this reason, the donor-acceptor structure in the active layer becomes all important for the efficiency of the polymer solar cell. For instance a simple bilayer heterojunction device, as imagined in figure 4a, is not an optimal device layout because only a region, e.g. on the order of 10 nm, on each side of the junction would contribute to current generation, while around 100 nm of material is needed to absorb most of the available light. Rather what is needed is a 3D nanoscale phase separation in the active layer, which sufficiently increases the junction area. If one were able to fabricate this optimal active layer, it might be imagined to look like the ‘comb’-structure in figure 4b. Such nanoscale structuring of soft materials is complicated, but can be done using e.g. imprint lithography.DOI:10.1063/1.2715036DOI:10.1002/adma.200702650 However, what has proven to be the most successful way of fabricating the optimal active layer for a polymer solar cell is in many ways also the simplest imaginable; by simply dissolving and mixing the donor and acceptor materials in a common solvent, and casting the active layer from the solution mixture. Upon drying, the materials separate into distinct phases, which effectively distribute the heterojunction throughout the bulk of the active layer, as illustrated in figure 4c, hereby forming what is referred to as the bulk heterojunction (BHJ).

Figure 4. Three different ways to structure the bulk morphology of a donor-acceptor heterojunction solar cells. (a) is a simple bilayer structure, (b) is an imagined idealized controlled morphology, with nanostructured ‘comb’-structure of the donor and acceptor, while (c) is an illustration of the bulk heterojunction, where the nanostructured donor-acceptor phase separation is formed by solution casting from a bulk mixture of donor and acceptor.

### Charge collection

Upon separation of the exciton into an electron and a hole at a donor/acceptor interface, the electron and hole will move in the acceptor and donor phases respectively. To generate current the charges must be collected at separate electrodes, i.e. holes at the cathode and electrons at the anode, as seen in figure 1. In the bilayer and ‘comb’-structured devices (figure 4a and b) this is facilitated by the clear separation of the donor and acceptor phases, whereby the donor/acceptor interface becomes an effective barrier for charges to run to the wrong electrode. In the case of the BHJ (figure 4c) the phase orientations are random and percolation paths of pure donor or acceptor material can connect the two electrodes. Instead the current flow is controlled by the use of electrodes having sufficiently different work functions. Such that the anode electrode is chosen as a high work function material and the cathode selected as a low work function metal. As seen in Figure 1, the holes will travel to the high work function anode and the electrons to the low work function cathode. Alternatively, or additionally, modification layers are inserted between the BHJ layer and the electrodes, matched to allow only a specific charge carrier type to pass to the corresponding electrode, as will be discussed further in the next section.

## Current weather

Temperature: 4.88 °C
Sample temp: 8.42 °C