Restricting the angular range in which a photovoltaic system emits light, is a promising but rather unexplored approach to enhance conversion efficiency. In this paper we analyze and discuss the effect of a directionally selective filter on the absorption of light and the generation of charge carriers in a germanium solar cell. A directionally selective filter transmits photons of perpendicular incidence and reflects photons under oblique incidence in a given spectral range. To investigate its effect on light trapping, we perform reflection and quantum efficiency measurements. The reflection measurements show that a wavelength dependent absorption enhancement is induced by the application of the directionally selective filter. We calculate a maximum absorption enhancement of 45% at λ ≈ 1900 nm. We show that the absorption enhancement is caused by light trapping of non-absorbed and scattered light and is not due to a suppression of radiative processes. A trapping of photons generated by radiative recombination could not be detected. Measurements of the quantum efficiency confirm the results of the reflection measurements. The generation of charge carriers is increased by up to 33% at λ ≈1900 nm. A comparison of path length enhancement factors calculated from reflection and quantum efficiency measurements indicates a low parasitic absorption in the solar cell device.
©2011 Optical Society of America
Light trapping is one of the major approaches of solar cell research today [1–3] to increase the efficiency of photovoltaic devices. Light trapping is indispensable for absorption enhancement in thin solar cells  or is used to provide a better light transport in optical concentrators [5,6].
One approach to realize light trapping is the restriction of the angular range into which the solar cell emits radiation. This restriction has several effects. One is a light trapping effect [7,8] which overcomes the Yablonovitch limit. Another is a change of the thermodynamic working conditions of the solar cell [9–12] which results in an increased detailed balance efficiency limit. Different concepts for the realization of directionally selective systems were proposed. Examples for such concepts are selectively emitting surfaces , the use of micro lens arrays  or the use of directionally selective filters . In this paper we use directionally selective filters.
The basic concept of this approach is the combination of a directionally selective filter and a process in the solar cell which results in a directional redistribution of light. The principle is depicted in Fig. 1 . An ideal directionally selective filter is characterized by a certain critical angle θc(λ) that defines the acceptance range of the filter and which may depend on the wavelength λ. Light with a polar angle smaller than θc(λ) is transmitted by the filter, light with a greater polar angle is reflected. The acceptance range shall especially include the directions of incident sunlight. This technique therefore requires tracking, if the acceptance range is very small. Incident light passes the filter and impinges on the solar cell. Ideally, in the solar cell, light either contributes to current and voltage generation or it leaves the cell again. In the following we consider two loss mechanisms inherent to solar cells in detail.
One of these mechanisms is radiative recombination; here an electron-hole pair recombines under emission of a photon. As this process has no preferred direction, the emission process is isotropic. It is important in the following that this process is connected with a change of the light wavelength between absorption and emission. Light is absorbed in the complete absorption range of the semiconductor material. In case of germanium this is nearly all light below the band edge wavelength of ca. λ = 1850 nm. Emission of radiation, on the other hand, occurs close to this band edge wavelength  due to thermalization.
Another loss mechanism is incomplete absorption of light. Close to the band edge, the absorption coefficient of the semiconductor is small resulting in large absorption lengths. (Note that light emitted by radiative recombination is in turn also poorly absorbed.) If the absorption length exceeds the effective thickness of the solar cell, light traverses the solar cell without being absorbed, is reflected at the back side and leaves it through the front surface again. As the solar cell investigated in this paper had no texture, the direction of the unabsorbed light is only changed by imperfections on the layer boundaries. For this reason, the directional distribution of the light rays is narrow.
Light emitted by radiative processes as well as scattered light can take one of three paths. Light subject to total internal reflection (TIR) inside the solar cell is trapped (i) until it is absorbed or leaves the solar cell after another scattering or absorption / emission process. Light inside the acceptance range of the filter is either absorbed or traverses the filter and is lost (ii). Light within the escape cone of TIR but outside the acceptance range of the directionally selective filter is trapped by the filter and enters the solar cell again (iii). This light trapping by the filter causes additional absorption and charge carrier generation which can be detected in comparative measurements.
Experiments similar to the ones shown in this paper have been performed for thin film solar cells made of amorphous silicon. The ability of the light trap to increase absorption and quantum efficiency has been demonstrated [15,16]. In this paper we investigate the effects of a directionally selective filter on the absorption in a germanium solar cell. By using a flat front surface instead of a scattering texture we can distinguish between radiative processes and scattering because of the different directional distributions of these processes. The aim of this approach is to develop a procedure which allows us to investigate radiative processes in a solar cell with simple reflection measurements.
In the next section we describe the used solar cell, the directionally selective filter and the applied measurement setups in detail. Following that, we present reflection measurements to characterize the absorption enhancement due to directional selectivity caused by scattering and radiative processes respectively. The reflection measurements are complemented by quantum efficiency measurements to characterize the effect of the directionally selective filter on the generation of charge carriers. Finally, we compare results obtained from reflection and quantum efficiency measurements by means of calculated path length enhancement factors.
2. Description of samples and measurement setup
2.1 Solar cell and directionally selective filter
For the presented measurements we used a germanium solar cell with a flat front surface and a thickness of d = 220 µm. In this cell no scattering mechanisms are included so that non-absorbed light is only marginally scattered and has a narrow directional distribution when escaping from the cell. Light emitted by radiative processes, on the other hand, has a wide angular distribution. The different spectral and angular characteristics of non-absorbed light and light emitted by radiative recombination will enable us to distinguish between these processes.
One way to create directional selectivity makes use of the Bragg effect, a mechanism applying to many photonic crystals, e.g. to Rugate filters  or the 3D photonic crystal called opal . The Bragg effect predicts a blue shift of a characteristic assigned to a certain wavelength λ0 with increasing angles of incidence according to
Such a characteristic is for example the wavelength corresponding to the lower edge of a reflection plateau of an edge filter λedge. We have used such an edge filter to create a light trap for a germanium solar cell. Figure 2a shows the measured reflection characteristics of the filter for normal incidence and the external quantum efficiency (EQE) of the used germanium solar cell. The reflection edge of the filter for normal incidence is located at λ = 1880 nm, close to the absorption edge of the solar cell. For light under normal incidence, the filter causes only minor reflection losses. Figure 2b shows the simulated angular dependence of the reflection characteristic of the same filter. For a wavelength λedge(θc) below λedge(0), the filter is transparent for normal incidence. If the direction of incidence is tilted, the reflection peak shifts towards the blue. At a certain critical angle θc, the reflection edge reaches the wavelength λedge(θc). For the wavelength λedge(θc) the filter, therefore, provides directional selectivity with an angular acceptance range defined by θc. The filter was attached to the solar cell simply by placing it on top. Optical coupling was not used.
2.2 Setup for reflection measurement
To characterize the light trapping effect induced by the directionally selective filter on the absorption in the germanium solar cell we performed reflection measurements using a spectrometer and an integrating sphere. These measurements were carried out for the solar cell with and without filter on top. Reflection measurements produce indirect information about the absorption in the solar cell, as the solar cell system is opaque for all considered wavelengths. We therefore have
Using the integrating sphere we performed measurements of the diffuse and direct reflectance. The corresponding measurement setups are depicted in Fig. 3 . In Fig. 3a, the setup for measuring the total reflectance of the system is shown. In this measurement the normal of the sample is tilted 4° away from the direction of incidence. In that way, directly reflected light is not reflected back to its source but hits the wall of the integrating sphere, is scattered and eventually detected. In that way specularly as well as diffuse reflected light is detected. Figure 3b shows the setup for measuring the diffuse fraction of the reflected light. In the shown configuration, the sample is not tilted and specularly reflected light escapes from the integrating sphere through the entrance opening. For this reason, only the diffuse fraction of the reflected light remains in the sphere and is detected. As we expect the non-absorbed light to be reflected mostly specularly, this measurement is especially sensitive to light emitted by radiative recombination.
3. Experimental results
3.1 Reflection measurement
The results obtained from the measurements of the total reflection are shown in Fig. 4a and 4b. We compare a measurement of a device reflection with filter Rwith to one of the device reflection without filter Rwithout. From Eq. (2) it follows that the change in the calculated absorption induced by the filter is the difference ΔA = Rwithout - Rwith = Awith - Awithout (cf. Fig. 4a). The relative absorption increase is represented by the ratio Awith / Awithout (Fig. 4b). Shown as well in Fig. 4 is the filter transmission. The obtained results resemble those obtained for a light trap for an amorphous silicon solar cell [15,16].
As the filter was not optically coupled to the solar cell, reflection losses occur for all incident wavelengths. These reflection losses result in a reduced calculated absorption which can be noticed for wavelengths below λ = 1700 nm. The agreement of ΔA with the filter transmission, as shown in Fig. 4, confirms this issue. For wavelengths above λ = 1700 nm, however, the curves diverge. The additional absorption found in this spectral range is caused by the directionally selective light trap. For wavelengths between λ = 1750 nm and λ = 1900 nm, the gain induced by light trapping exceeds the reflection losses. Close to λ = 1900 nm, the light trapping increases the solar cell absorption by up to 45% as shown in Fig. 4b.
To distinguish between effects caused by scattering of non absorbed light and by radiative recombination, we need to understand the functionality of the spectrometer in the integrating sphere. The spectrometer varies the wavelength of incident light and measures the intensity of the light returning to the detector. It is important to note, that the detected light is not resolved by wavelength but it is assumed that the detected light has the same wavelength as the incident light. The spectrometer will therefore detect light that was subject to a spectral shift with the wrong wavelength.
The wavelengths of photons emitted by radiative are close to the band edge of the semiconductor material and are therefore trapped by angular confinement. In the presented measurements, light emitted by radiative processes should add a contribution that is proportional to the absorption and depends on the lifetime of the generated charge carriers. For wavelengths between λ = 1000 nm and λ = 1700 nm this contribution can be assumed to be more or less constant. For higher wavelengths we would expect a decrease in emission intensity, due to the lower material absorptance close to the band edge. None of these features are found in Fig. 4. Non-absorbed and scattered light, on the other hand, is not subject to a spectral shift. Therefore, it is detected at the correct spectral position. A measurement of scattered light should therefore show a strong spectral dependence and an increase with increasing wavelength, due to the better light trapping close to the reflection edge of the filter.
From this argument we conclude, that the main source for trapped light detected in this measurement is non absorbed and scattered radiation. Light emitted by radiative recombination could, however, add a small contribution. This issue is addressed in the following section.
To quantify the light trapping of light emitted by radiative processes, we performed measurements of the diffuse reflection of the solar cell. As shown in Fig. 3b, we assume that in this setup most of the light that has not been subject to an absorption event leaves the integrating sphere and only the light emitted by radiative recombination is detected. To characterize the light trapping effect induced by the filter we performed two measurements. First, we measured the diffuse reflection of the solar cell with filter on top. Following that, we measured the diffuse reflection of the solar cell with a glass plate on top. The comparison to a system with glass plate on top is necessary as the filter was not optically coupled to the solar cell. For this reason, a certain light trapping is provided by reflections at the filter substrate, which is also a glass plate. As we expect an almost constant contribution of light emitted by radiative processes, we would otherwise not be able to distinguish between an offset coming from the reflection of a glass surface and trapping of light emitted by radiative processes.
To deduce information on light trapping of emitted radiation we subtracted the reflection of a solar cell covered with a glass plate from the reflection obtained for the solar cell covered with a filter. Again, as the devices are completely opaque, this calculation gives the change in absorption induced by the filter. The result is shown in Fig. 5 .
From the result shown in this figure we draw several conclusions:
- 1. The assumption that non-absorbed light is reflected mostly direct is correct. This can be seen in Fig. 5a; less than 10% of the incident light is subject to diffuse reflection.
- 2. Above the reflection edge, the filter blocks most of the light independent of the direction whereas the glass plate is still transparent. This explains the large reflection differences between the samples obtained for wavelengths above λ = 1850 nm (cf. Fig. 5b).
- 3. Photons emitted by radiative processes are not detected. Following the argument given earlier, an increase in absorption with little spectral dependence is expected for light emitted by radiative processes. The filter induces no detectable light trapping for incident light with wavelengths below λ = 1850 nm (cf. Fig. 5b).
We conclude therefore that the effect induced by the directionally selective filter on the absorption of a germanium solar cell is caused by non absorbed and scattered light only. Effects caused by light emitted by radiative processes are below the resolution of this simple method.
Taking into account these considerations, the relative absorption enhancement shown in Fig. 4b seems comparably large. In the investigated wavelength range, however, germanium is a poor absorber. The number of photons additionally absorbed is therefore comparably small. Introducing a more efficient scattering mechanism into germanium, the light trapping could be greatly improved.
3.2 Quantum efficiencies
In a second measurement series the external quantum efficiency was detected to investigate the effect of the directionally selective filter on the generation of charge carriers within the solar cell. The EQE was measured for a solar cell without and with filter. The difference and the ratio of the EQEs are shown in Fig. 6a and Fig. 6b.
The results obtained from EQE-measurements resemble qualitatively those obtained from reflection measurements. The additional filter reflection causes reflection losses for all wavelengths; the EQE is decreased. The light trapping effect induced by directional selectivity enhances the generation of charge carriers in the spectral range between λ = 1700 nm and λ = 1900 nm. Close to this latter wavelength, the external quantum efficiency is increased by 33% due to an application of the directionally selective filter. Taking into account the comparably large uncertainties for these considerations (represented by the two different measurement curves shown in Fig. 4), the EQE results (Fig. 5) are in good qualitative agreement with the absorption results (Fig. 4).
The comparably small difference between the enhancements in reflection and quantum efficiency indicate that, other than in amorphous silicon , no or only little parasitic absorption occurs in the germanium solar cell.
It has to be said that the presented method at the current stage and in the investigated spectral range is very cost intensive and provides only a small increase in generated current. The situation could be improved by further developed directionally selective filters that are less expensive and cover a larger spectral range.
3.3 Path length enhancement
In a previous publication  we have discussed how the path length enhancement induced by the directionally selective filter can be quantified. We have presented two different approaches, one based on reflection data and one based on external quantum efficiency data. The path length enhancement factor based on the reflection measurements κR is given byFig. 7 .
To indicate the variation in the calculated path length enhancement factors obtained from reflection measurements, we used the two reflection measurements already used in Fig. 4a and 4b. The results obtained from these measurements are represented by the red and the brown curve in Fig. 7. In the wavelength range around λ = 1900 nm reflection and quantum efficiency of the solar cell drop fast (cf. Fig. 2a and 2b) and already small deviations can result in considerable discrepancies in the difference between two measurements. Additionally, the logarithm in Eqs. (2) and (3) amplifies this effect.
Taking this variation into account, the enhancement factors obtained from reflection and EQE data are in good agreement. Additional absorption induced by the filter is efficiently transferred into the generation of electron hole pairs; parasitic effects are not found. The absence of parasitic effects marks a clear difference to the results obtained for the light trap realized for solar cells made of amorphous silicon  for which large differences between Kr and KEQE were found that are due to parasitic absorption probably in TCO. A comparison with amorphous silicon also shows that the light trapping in germanium could benefit greatly from more efficient scattering; the path length enhancement factors found for amorphous silicon are more than five times higher than the ones shown here.
4. Summary and conclusions
In this paper we have investigated the effect induced by a directionally selective filter on a germanium solar cell. The directionally selective filter causes light trapping for radiation that impinges onto the surface under oblique angles and with a wavelength close to the band gap. In a germanium solar cell, there are two sources for such radiation. The first source is light emitted by radiative recombination. Characteristic for this radiation is that a change of wavelength occurs between the absorption and emission process. The second source is non-absorbed and scattered light.
To characterize the light trapping effect we performed reflection measurements with an integrating sphere. From these measurements we calculated the total and diffuse absorption within the solar cell. We found a light trapping effect that shows a strong dependence on the incident light wavelength and is strongest close to the reflection edge of the filter. The light trapping results in a wavelength dependent absorption enhancement. We calculated values of up to 45% close to the band edge of germanium (λ ≈1900 nm). The wavelength dependence of the effect indicates that the main source for the absorption enhancement is non absorbed and scattered light. Light emitted by radiative processes plays only a marginal role. This result was confirmed by measurements of the diffuse reflection.
In a subsequent set of measurements we detected the external quantum efficiencies for the solar cell with and without directionally selective filter. The results obtained here are in good agreement with the reflection measurements. The generation and collection of charge carriers was enhanced by up to 33% close to λ = 1900 nm. This result confirms that photonic light trapping also works for a weakly scattering germanium solar cell. The light trapping effect could be enhanced by introducing further scattering mechanism like a roughened surface into the solar cell. The small differences between the results obtained from reflection and quantum efficiency measurements suggest a negligible parasitic absorption in the germanium solar cell.
Finally, we calculated path length enhancement factors from reflection and quantum efficiency data. These factors show that the path length within the solar cell is increased by the directionally selective filter considerably. The maximum enhancement factors obtained from different measurements range between 25% and 50%. Furthermore, the enhancement factors calculated for the different data confirm that the absorbed light contributes to current generation and is not absorbed parasitically.
The BMBF project NANOVOLT (03SF0322) is gratefully acknowledged. The authors thank Prof. Uwe Rau from Forschungszentrum Jülich for his support. The authors also thank Prof. Gottfried Bauer, Sebastian Knabe and Florian Heidemann from University of Oldenburg for fruitful discussion.
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