13 Optical Absorption-Solar Cell and Photodetectors

Dr. Ayushi Paliwal and Dr. Monika Tomar

1. Introduction

Optical absorption is a fundamental process which is exploited when optical energy is converted into electrical energy. Solar cells and photodetectors are the best examples convert electrical energy into optical energy. When the light is shinning on a semiconductor sample, if the energy of the individual photons is greater than the semiconductor band gap, then the photons can be absorbed, transferring their energy to an electron. This process, elevates the electron from the valence band into the conduction band. The absorption process therefore creates an electron-hole pair (EHP), because it results in an electron in the conduction band, and a hole in the valence band. When the covalent bond is broken, the electron is free to move in the crystal lattice of the semiconductor (it is now in the conduction band). The energy required to break a covalent bond is Eg, If the photon energy is less than Eg, it doesn’t carry enough energy to break a covalent bond and free an electron for conduction. Since electrons cannot occupy the forbidden states between the valence and conduction bands, a photon with energy less than Eg cannot be absorbed and will pass through the sample. In other words, an electron must either be in a covalent bond or free, not in between. The photon energy at which the transition between absorbing and non-absorbing behavior takes place will correspond to the band gap energy. Because the transition between absorption and transmission is gradual, we will see that the shape of the transition will provide insight into some of the details of the electron interband transitions (this is a transition between energy states in valence band and conduction band). The transition region is called the ‘absorption edge’.

2. Optical absorption

From the wave–particle duality principle we can draw the inference that light waves can also be treated as particles. These particles are called Photons. The energy of a photon is given by E = hν, where h is Plank’s constant and ν is the frequency. Wavelength and energy can parallely be related by,

where E corresponds to the photon energy (eV) and c represents the speed of light.

Photon–semiconductor interaction can take place via different mechanisms. For example, photons interact with the semiconductor lattice hence the photon energy is converted into heat. Photons also interact with the impurity atoms, these impurity atoms can be any one of donors or acceptors, or they also can interact with defects existing within the semiconductor. However, the most sought out and basic photon interaction process is the interaction of photon with valence electrons. When a photon collides with a valence electron, enough energy can be imparted to the electros which elevates them towards the conduction band. Such a process leads to the creation of electron–hole pairs and hence generates excess carrier concentrations.

2.1 Photon Absorption Coefficient

The incident photons falling on the surface of semiconductor may be adsorbed at the surface only or propagate deep inside the semiconductor by illuminating it with light. This is dependent on the bandgap energy i.e. Eg of the semiconductor and also on the energy of incident photons. Hence, figure 1 shows the three different cases for the energy of photons equal to, greater than or less than the band gap energy. Considering first case i.e. the photon energy is less than Eg where the photons will not be absorbed readily. This indicates the semiconductor appears to be transparent where all the light will be transmitted through the material. An interaction between incident photons and valence electrons occurs for incident energy, E = hν ≥ Eg and elevating it into the conduction band. There is a maximum probability of this interaction, since the valence band contains a very high ratio of electrons in comparison to conduction band which mostly has many empty states. This interaction leads to creation of an electron-hole pair i.e. a hole in the valence band and consecutively an electron in the conduction band. When hν > Eg, there will be a dissipation of energy as heat in the semiconductor due to additional amount of kinetic energy attained by an extra electron–hole pair created.

Consider, the photon flux intensity denoted by Iν (x) which is expressed in terms of energy/cm2-s. The variation of incident photon intensity for a differential length dx is shown in figure 2(a) which describes an incident photon flux at a position x and the corresponding photon flux emerging at a distance x + dx. Thus, for a distance dx, the energy absorbed per unit time is given by,

αIν(x)d(x) (2)

where α represent the absorption coefficient which can be defined as the relative number of photons which are absorbed per cm by the material.

Using Figure 2(a), we get

Thus, above equation (5) denotes that the photon flux intensity decreases exponentially with distance as we go through the semiconductor. Figure 2(b) describes the photon flux intensity as a function of depth (x) in the semiconductor for two general values of absorption coefficient. For a large absorption coefficient the photons are readily absorbed over a relatively short distance. The absorption coefficient of the semiconductor is a very strong function of photon energy and also the bandgap energy of the semiconductor.

Figure 3 describes the variation in absorption coefficient which plotted as a function of wavelength for various semiconductors. The value absorption coefficient shows rapid increase for hν >Eg , or for λ < 1.24/Eg . The semiconductor appears transparent to photons in the energy range hν < Eg as the value of absorption coefficient is very small.

Figure 4 shows how bang gap energy of semiconductor material is related to the light spectrum. It can be seen that silicon and gallium arsenide are able to absorb the radiation in visible spectrum, on the other hand gallium phosphide, for example, will be transparent to the red spectrum

2.2 Electron–Hole Pair Generation Rate

It is known that electron–hole pairs are created when the semiconducting material absorbs photons having energy greater than Eg. The intensity Iv(x) is in units of energy/cm 2–s and αIv (x) quantifies the rate at which energy is absorbed per unit volume. Assuming, one electron-hole pair is created with adsorption of one photon at an energy hν, then electron-hole pair generation rate is given by,

It can be noted that photon flux is given by the ratio of Iv(x) to hν. If we take the average then an efficiency factor is multiplied to Equation (1.6) as the absorbed photon produces less than one electron–hole pair.

3 Solar Cells

A solar cell is a device which converts photon power (solar power) into electrical and also delivers this power to the load. Solar cell comprises of a p-n junction where a voltage is not applied across the junction. These devices act as the power supply of satellites, space vehicles and other electrical/ electronic modules. In order to understand the fabrication/ physics of solar cells we will consider a simple pn junction solar cell having uniform generation of excess charge carriers.

3.1 Why use Solar Cells?

Solar cells are low maintenance, long lasting sources of energy and provide cost-effective power supplies for people remote from the main electricity grids. It is also a non-polluting and silent source of electricity. This coupled with the fact that solar cells are convenient and flexible source of small amounts of renewable and sustainable power, as well as a means to reduce global warming.

3.2 The pn Junction Solar Cell

The pn junction based photovoltaic(PV) cells are the most common type of solar cells. Figure 5 shows a pn junction based solar cell panel where an array of photovoltaic cells are connected in series to form a panel together to generate significant amount of power. The electron and hole pairs which are knocked out by light energy flow freely to form current. The array of solar cells also called as a solar panel is also provided with metal contacts at the top and bottom of PV cells. These metal contacts are used to draw current to be used as an external power.

The solar radiation falling on pn junction is absorbed selectively by various regions of the photovoltaic cell. The radiations with smallest wavelength are absorbed by the n-type semiconducting region present at the top of the cell. The electrons and holes consequently created diffuse towards the front finger electrode and junction respectively as described in figure 6. Similarly medium wavelength radiation creates electron-hole pairs in the depletion region whereas the longest wavelength radiation penetrates to the p-type semiconductor leading to similar outcome.

Figure 7 describes a pn junction which is connected to a load resistance, R. Initially when zero bias voltage is applied across the junction, as describes by the figure an electric filed exists in the space charge region. The photons incident on the solar cell create electron–hole pairs in the space charge region. These electron-hole pairs will be swept out, hence producing the photocurrent IL in the reverse-biased direction as described in figure 7.

Due to the photocurrent IL a voltage drop occurs across the resistive load. The photocurrent forward biases the pn junction. This forward-bias voltage sets up a forward-bias current IF which can be seen in the figure. The net pn junction current, in the reverse-biased direction, is

I = IL – IF = IL – IS [exp (qV/KT) -1] (7)

Where Is is the reverse saturation current and K is the Boltzmann constant.

The ideal diode equation has been used here. The forward biasing of diode reduces the electric field strength in the space charge region. Though the field strength decreases substantially it does not go to zero and the field direction also remains unchanged. The photocurrent is always in the reverse-biased direction and the net solar cell current is also always in the reverse-biased direction.

Consider, the two limiting cases of interest. First case is the short-circuit condition occurs when R = 0 so that V = 0. In this case, the current corresponds to the short-circuit current, or

I = Isc = IL  (8)

The second limiting case corresponds to the open-circuit condition and occurs when R→ infinity. In this case, the net current is zero and correspondingly the voltage produced is called as the open-circuit voltage. The photocurrent is just balanced by the forward-biased junction current, so we have

I = 0 = IL – IS [exp (qVoc/KT) -1] (9)

We can find the open circuit voltage Voc as

Figure 8: I-V characteristics of a pn junction solar cell.

The power delivered to the load using equation 1.7 is,

The value of Vm may be determined by trial and error. Figure 8 shows the maximum power rectangle where Im is the current when V = Vm.

The pn type solar cell can also be represented by the equivalent circuits as described in figure 9.

Figure 9: Equivalent circuit of solar cell (a) Ideal pn junction solar cell, V and (b) Parallel and series resistances Rs and Rp.

3.3 Conversion Efficiency and Solar Concentration

Conversion efficiency of a solar cell is termed as the ratio of output electrical power(Pm) to the incident optical power(Pin). So, in order to have the maximum power output, we can write

Isc is the maximum possible current and Voc is defined as the maximum possible voltage in the solar cell. The ratio ImVm/IscVoc is called the fill factor and is a measure of the realizable power from a solar cell. Typically, the value of fill factor is between 0.7 and 0.8 as can be seen in Figure 10(equivalent circuit of sloar cell) the series resistance Rs and the parallel resistance Rp can determine the value of Isc and Voc. For ideal case Rs must be zero and Rp should be infinite. A deviation from these ideal characteristics reduces the area of maximum power rectangle (Fig 10). Due to this the efficiency and fill factor of the solar cell decreases. This can be seen clearly in the figure 10.

4 Heterojunction Solar Cells

Normally a conventional solar cell consists of a pn junction which has unitary semiconductor bandgap energy. On exposure to the solar radiations, the photons possessing energy less than the bandgap energy Eg will not lead to an electrical output. On the other hand a photon with energy greater than Eg contributes to efficient output and fraction of photon energy that is greater than Eg will eventually only be dissipated as heat. In order to reduce the cost of solar cell and to improve the efficiency we can also use heterojunction solar cells. In the fabrication of heterojucntion solar cells thin films of polycrystalline material are deposited by methods such as PECVD(Plasma Enhanced Chemical Vapour Deposition). As we can see in the figure 11, a heterojucntion is formed between GaAs and AlGaAs having different band gaps. The AlGaAs acts as the n type semiconductor and GaAs acts as the the p type semiconductor. The photons enter through the GaAs creating electron-hole pairs and the remaining photons are passed to AlGaAs further creating charges. These solar cells show good absorption properties and, low cost.

5. Efficiency

The solar spectral irradiance (power per unit area per unit wavelength) is shown in Figure 12 where air mass zero represents the solar spectrum found outside the earth’s atmosphere and air mass one is the solar spectrum at the earth’s surface at noon.

Despite our best efforts of the scientists, silicon based solar cells are not able to achieve very high efficiency and the maximum efficiency possible for them is 28%. There are many factors which affect the efficiency of a solar cell. They can be,

• Transformation of certain amount of surplus photon energy into heat rather than to electrical energy.
• Due to inherent physical limits imposed by the material, single loss mechanisms (photons with too little energy are not absorbed, surplus photon energy is transformed into heat) cannot be further improved.
• There are other loss mechanisms i.e. electrical resistance losses in the semiconductor and the connecting cable.
• Since, different semiconductor materials or their combinations are suited only for specific spectral ranges leading to the usage of a specific portion of the solar radiant energy.
• The disrupting influence of material contamination, surface effects and crystal defects.

In order to overcome these deficits thin film technologies have been explored for fabrication of solar cells. Nanocrystals and quantum dots are also being used for fabrication of solar cells.

In order to increase the absorption of light intensity on the surface of solar cells, the incident photons need to be concentrated onto a solar cell leading to an increase in the light intensity falling on solar cells by hundred folds. This, in turn further increases the intensity concentration leading to a significant increase in short-circuit current with light concentration while the open-circuit voltage increases only slightly. Figure 12 shows the ideal solar cell efficiency at 300 K for two values of solar concentration. We can see that the conversion efficiency increases only slightly with optical concentration. The primary advantage of using concentration techniques is to reduce the overall system cost since an optical lens is less expensive than an equivalent area of solar cells.

Inverted pyramid texture can also be used for absorbing radiation as shown in figure 13. This geometry reduces the reflection losses and enhances the absorption probability of solar cells. Tandem cells can also be used (figure 13 (a)). Two thin film cells are connected back to back where energetic photons are absorbed at the first stage and the photons which pass across the first cell are absorbed in the second cell (figure 13(b)).

Figure 13: (a) Inverted pyramid texture geometry of solar cells, (b) Two thin film cells are connected back to back where energetic photons are absorbed at the first stage and the photons which pass across the first cell are absorbed in the second cell.

Solar cells are a novel and promising candidate for clean energy for generations to come. With the exponential degradation in the fossil fuel reserves it is no surprise that we have shifted our focus on solar energy. The results after extensive work on solar cell technology are rousing and inspiring, but it is also clearly visible that we have barely scratched the surface and a lot still needs to be done.

6. Summary

Optical absorption i.e. Photon Absorption Coefficient and Electron–Hole Pair Generation Rate.Pn junction solar cells were discussed in detail along with their current vs. voltage characteristics. Factors on which conversion efficiency of solar depends were also discussed.

Heterojunction solar cells were discussed in detail.