Spatially resolved photocurrent-spectroscopy and spatially resolved current-voltage characteristics are introduced as new methods to characterize solar cells. A combination of these two methods is shown to localize and characterize deficiencies and structural damages in processed solar cells with high spatial resolution. The local external and internal quantum efficiencies as well as the local characteristic parameters of the p-n junction like the short circuit current, the saturation current, the ideality factor, and the optically induced shunt resistance can be determined quantitatively. Both, a slab of a damaged and an undamaged (GaIn)(NAs) concentrator solar cell, are used as test structures. Upon these test structures domains with a high concentration of impurities in the crystal structure and structural imperfections in the upper contact region are identified and analyzed. Additional numerical simulations prove the reliability and show limits of the methods.
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The material and structural quality determines the conversion efficiency of a solar cell [1,2]. Optimizing the manufacturing process with respect to these parameters is of crucial importance. Preferentially, this is performed before mass production, in order to combine high conversion efficiencies with a low processing effort. Prototypes therefore have to be tested accurately. Spatially resolved photocurrent-spectroscopy (SRPS) offers various possibilities to characterize such prototypes. The photocurrent generated by a focused laser beam is mapped on the entire cell with high spatial resolution, showing the general material quality, the quality of the p-n junction as well as damages in the upper contacts. The cell is biased in an SRPS experiment in contrast to the light-beam induced current (LBIC) method which works without applied voltage [3,4]. The advantages of a reverse bias are twofold: i) the signal to noise ratio is improved and ii) the lateral diffusion of the photoexcited carriers is reduced. Both effects enable a much higher spatial resolution of the solar cell characterization. The voltage-dependence of the photocurrent yields spatially resolved current-voltage characteristics (SRIV) and thus, provides important information about the p-n junction and local shunt resistances. In this paper, the applicability and reliability of SRPS and SRIV is demonstrated under various experimental conditions. Both methods are confirmed and substantiated by extensive numerical simulations.
The compound (GaIn)(NAs) is used for the spectral range around 1 eV in multijunction concentrator solar cells [5–8]. A damaged (GaIn)(NAs) solar cell is used as test structure. A second, undamaged (GaIn)(NAs) cell with the same layer structure but different size serves as a reference. The damaged cell has an inhomogeneous density of non-radiative recombination centers in the active region of the p-n junction as well as several broken contacts and a localized mechanical defect at the surface. These two structures are perfectly suited to evaluate SRPS and SRIV in terms of their applicability and reliability under realistic conditions.
Numerical simulations of SRPS and SRIV measurements are performed in order to interpret the experimental data. The model takes in account both, the current-voltage (I-V) characteristics of the p-n junction with possible shunt resistances as well as the conductivities of the cap layer and the upper contacts. A particular parameter set is determined for each simulation since these quantities depend on the intensity and the wavelength of the incident laser beam.
2.1 Experimental setup
A solar cell under reverse bias is locally illuminated by a chopped beam from a semiconductor laser diode. The beam is focused on a pinhole with a diameter of 50 µm. The transmitted part is imaged on the sample to a spot diameter of 30 µm, determining the spatial resolution of the measurements, which can easily be adjusted by simply changing the pinhole. A digital multimeter monitors the bias which is applied by a programmable voltage source. The voltage drop on a series resistor is measured by lock-in technique [9,10] so that only the photogenerated current of the illuminated spot contributes to the signal.
Diffusion of generated carriers into dark regions around the illuminated spot becomes increasingly important for small spot diameters. Therefore one has to ensure that the drift velocities of the generated electrons and holes significantly exceed their initial velocities due to the excess energy after photogeneration. A reverse bias increases the drift velocity and therefore lowers carrier losses due to diffusion processes. Furthermore the signal to noise ratio is increased lowering the experimental effort and the duration of the measurement.
The sample is mounted on a motorized two-dimensional translation stage which has an accuracy of 100 nm. A SRPS map of the whole sample is then obtained with a spatial resolution of 30 µm, ultimately restricted by the diameter of the incident laser beam only. The SRIV measurements are performed by determining the I-V characteristics when a specific spot is photoexcited. Here special attention has to be paid on diffusion of generated carriers as their drift velocities as well as the depletion layer width change during the experiment.
The wavelength of the incident laser beam must be between the band gap of the cap layer and of the active material. A wavelength of 980 nm was chosen for the measurements presented here. The chopping frequency of 330 Hz was chosen not be too high in order to avoid unwanted, distorting resonances.
2.2 Sample structure
Figure 1 shows a photograph of the damaged solar cell of 5 mm x 5 mm size which is used as the first test structure. A rhombic horizontal busbar is located 0.5 mm away from the bottom of the cell. It is connected to a horizontal finger at a distance of 0.5 mm from the top by five vertical fingers, having spacings of 1 mm. The distances between the vertical fingers and the edges are 0.5 mm. Each finger is 8 µm wide while the busbar has a width of 320 µm in the center. All contacts are 2.2 µm thick and consist of an Ag/Au/Ti/Pd/Ge alloy with 91% of Ag. They are connected to an external contact by five bond-wires on the busbar which are protected from mechanical damage by a spot of resin. The magnified pictures at the side of the photograph reveal a mechanical surface defect with a size of about 200 µm on the lower right-hand side of the cell located between fingers four and five. The fingers themselves exhibit several cracks as well. Additional broken fingers are indicated by red ellipses.
The cross section of the cell is schematically depicted in Fig. 2 . The three green-shaded layers form the active region where the incident light is absorbed. The two topmost layers of this region are Te-doped n-type (GaIn)(NAs) and Mg-doped p-type (GaIn)(NAs) forming the p-n junction. This structure is covered by n-type layers of Te-doped GaAs, (AlGa)As, and a thick GaAs cap forming the n-contact. The (AlGa)As additionally serves as an etch stop for the post epitaxial processing and as a hole barrier preventing the photogenerated holes from diffusing to the surface. A buffer layer of Mg-doped p-type GaAs and the p-doped GaAs substrate form the bottom p-contact. The material quality of the (GaIn)(NAs) layers was investigated at various spots by time-resolved photoluminescence [11–13]. For low excitation densities, a considerably shorter carrier lifetime and photoluminescence intensity is observed in the upper left-hand corner of the cell compared to other regions. This observation is attributed to an elevated concentration of non-radiative recombination centers [14,15].
The undamaged reference cell has the same layer and contact structure but a different size. It is 10 mm wide and 10 mm long. The rhombic horizontal busbar is located 400 µm away from the bottom and has a width of 360 µm in the center. Twelve vertical fingers connect the bar with a horizontal finger at a distance of 400 µm from the top. The vertical fingers are spaced by about 830 µm. Their distances to both edges measure about 400 µm. Each finger is 8 µm broad. Again, all these contacts have a thickness of 2.2 µm and consist of the same alloy. Seven bond wires connect the busbar to an external contact.
Both solar cell structures were grown by metal-organic vapour-phase epitaxy on (001) GaAs in a commercially available, horizontal reactor system (AIX200) using hydrogen carrier gas at a low reactor pressure of 50 hPa. Due to the metastability of the (GaIn)(NAs) material system low substrate temperatures had to be chosen in order to achieve significant N incorporation. In this case the substrate temperature was fixed to 550°C with a growth rate of 1 µm/h. Metal-organic sources efficiently decomposing at low temperatures like the group V sources tertiarybutylarsine (TBAs) and the unsymmetric dimethylhydrazine (UDMHy) had to be used as a consequence of the low growth temperature. As group III sources, trimethylgallium (TMGa) and trimethylindium (TMIn) were applied. Te from diethyltellurium (DETe) was used as n-dopant and Mg from dicyclopentadienylmagnesium (Cp2Mg) as p-dopant, respectively. A post-growth annealing step was applied to the solar cell structures to reduce the defect density. Details on the growth of (GaIn)(NAs) and the optimization of the post growth annealing can be found in [16,17]. The electrical characteristics of the (GaIn)(NAs) material are summarized in .
For all simulations, the damaged cell is divided into domains measuring 30 µm x 30 µm each, corresponding to the spatial resolution of the experimental setup. Figure 3 shows the assumed circuit diagram for these domains. A photodiode and a light-dependent resistor represent the active region which are connected to their four neighbors by ohmic resistors forming the cap layer and the upper contacts. These resistors are assumed not to be photosensitive as the photon energy of the incident laser beam is smaller than the band gaps of the cap layers. The resistances are calculated from the corresponding specific resistances [19–23] taking into account the dimensions of the cap layers and the contacts. The resistance of the bottom contact is assumed to be small with respect to the top contact and therefore neglected in the model. Thus, the domains are grounded at the lower side. According to Kirchhoff’s laws, the specific geometry of the sample leads to a set of 167 x 167 implicit equations which determine the voltage at every domain and have to be solved numerically.
The simulation of a SRPS map is performed in two steps. First, the voltage distribution under illumination of a specific domain is calculated iteratively. Thereby a fixed voltage at every site where a bond wire is connected to the busbar is assumed as boundary condition. This voltage corresponds to the applied bias. Subsequently, the total current flowing through the whole cell is computed by means of the obtained voltage distribution. This calculation has to be repeated for each domain since the voltage distribution depends on which domain is illuminated. Specific parameter sets for both cases have to be determined since the characteristics of the photodiodes and the light-dependent resistors are different depending on whether they belong to the illuminated domain or not. These parameters are deduced from measurements of the I-V characteristics. Secondly, the total background current flowing through the dark cell is calculated accordingly, assuming that the bias does not change. The difference between these two values is the desired photocurrent.
These calculations are very complex for several reasons. First, the number of domains is large. Second, the required numerical precision in the voltage of typically 11 decimal places is demanding and third, step one of the calculation has to be repeated for each of the 167 x 167 = 27889 domains to obtain a whole SRPS map. Therefore, a distributed computer cluster with an equivalent of typically more than 50 standard Pentium 4 desktop PCs is used for the simulations [24,25].
The boundary condition of a constant bias for both the illuminated and the dark cell is equivalent to the assumption that the voltage source biasing the cell has no inner resistance and that there is no series resistor in the circuit. Therefore, the experimental data have to be corrected accordingly before the experimental SRPS maps are compared to the simulation. This correction is demanding if the cell is strongly forward biased. Hence, the boundary condition for the simulation of SRIVs has to be more accurate. This is done by adding a corresponding series resistor to the assumed circuit diagram which is placed between the voltage source and the sites where the bond wires are connected to the resistor grid. Therefore the bias for the illuminated case is reduced by the voltage drop at this resistor caused by the additional current. This more accurate boundary condition is not applied for the simulation of SRPS maps since it makes the simulation even more demanding.
3.1 Experimental evaluation of the SRPS method
A series of SRPS maps with varying bias voltages and laser intensities has been measured at room temperature for the systematic experimental evaluation of the SRPS method. The results are shown in Figs. 4 –6 and compared to each other in the following. All laser intensities are given in continuous wave equivalent.
Figure 4 shows two normalized SRPS maps of the damaged solar cell measured at laser intensities of 2.1 W/cm2 and 890 W/cm2. The bias is 0.5 V. The experimental uncertainties are below 3.0% and 0.9%, respectively. For reverse and small forward biases, the measured photocurrent is in a good approximation:
In this formula Rs is the series resistance in the experimental setup and Rsh is the total shunt resistance of the dark cell which can be deduced from the corresponding I-V characteristic. The current I(Rs = 0) corresponds to the local photocurrent generated by the incident laser beam. Thus, a correction for series resistances in the experimental setup is just a multiplication by a constant factor and therefore not necessary for normalized SRPS maps.
The fingers, the busbar, and the bond wires are clearly visible and ease the orientation on the cell. A large drop in the photocurrent of about 75% with respect to the surrounding is observed in both maps in the upper left-hand corner. This drop is caused predominantly by a considerably higher concentration of impurities in the crystal structure of the p-n junction, as stated in subsection 2.2 above. Of course, the broken fingers also reduce the measured signal but this effect is much weaker as revealed by the simulations in subsection 3.2 below. The mechanical surface defect is clearly visible between the fourth and the fifth finger on the right-hand side of the cell. It shows up in both maps by a photocurrent drop of about 60% with respect to the surrounding. The map with the higher laser intensity is slightly more inhomogeneous. This is due to a relatively high voltage drop in the cap layer caused by the large induced photocurrent, which leads to a significant current in forward direction of the non-illuminated part of the p-n junction.
Two normalized SRPS maps of the damaged solar cell measured at reverse bias voltages of 0.5 V and 2.5 V are depicted in the left half of Fig. 5 . A laser intensity of 8.9 W/cm2 was chosen for both maps. The experimental uncertainties are below 1.6% and 0.6%, respectively. Again, a correction for series resistances in the experimental setup is unnecessary.
The cell appears more homogeneous with increasing bias. This is caused by a stronger contribution of optically induced shunt resistances to the measured photocurrent as this part scales linearly with the applied bias, whereas the contribution of the p-n junction is nearly constant. Shunt resistances, which do not depend on illumination, do not contribute to the signal as the measurement is differential. This will be also shown in subsection 3.4 below. Therefore the clear difference between the two maps reveals that optically induced shunt resistances play a significant role for the local I-V characteristics of the sample. This is an evidence for imperfections in the p-n junction and reveals another benefit of biasing the cell.
A distinct increase of the relative photocurrent is observed with increasing bias at some sites indicated by red arrows where the fingers are broken. The reason for this feature may be the missing cap layer at these sites. The rough, low reflecting surface leads to a better coupling of the incident laser beam into the p-n junction if the contact metal is also completely missing thus increasing the concentration of generated carriers. The carrier drift lengths become higher with increasing bias and hence more generated electrons can reach the surrounding cap layer before they recombine.
In Fig. 6, the normalized SRPS map of the upper left-hand quarter of the undamaged solar cell measured at a reverse bias of 0.5 V and a laser intensity of 812 W/cm2 is depicted. The experimental uncertainty is below 1.0%. The photocurrent distribution is much more homogeneous compared to the damaged cell, although the intensity of the incident laser beam is comparatively high. This shows that a homogeneous material quality leads to a homogeneous photocurrent distribution.
Altogether, the results of the experimental evaluation prove the ability of the SRPS method to analyze the material quality of a processed solar cell with a high spatial resolution and reliability. Structural problems, like the mechanical surface defect of the damaged solar cell, are also clearly visible in the obtained SRPS maps. Even some of the broken contacts are spotted for special experimental conditions. The material quality appears more inhomogeneous than it really is if the applied laser intensity is too high, which is due to a relatively high voltage drop in the cap layer caused by the large induced photocurrent. However, the applied bias has also a large influence on the obtained SRPS maps, which may become more homogeneous with increasing bias due to the stronger contribution of optically induced shunt resistances to the measured photocurrent. This effect may also lead to more inhomogeneous SRPS maps, as it depends on the particular distribution of the optically induced shunt resistances. Therefore, one should always keep in mind that the bias voltage as well as the applied laser intensity must not be too high to avoid artificial inhomogeneities. Equation (1) allows a simple correction of SRPS maps for series resistances in the experimental setup. Such a corrected map quantitatively shows the local photocurrent and can be used to determine the local bias dependent external quantum efficiencies (EQE) of the sample. The corresponding internal quantum efficiencies (IQE) are accessible when the reflectance is additionally measured. A comparison of two corrected SRPS maps measured at the same laser intensity but different reverse biases can be used to determine the local values of the optically induced shunt resistance. In subsection 3.2 below the series resistance in the solar cells contact grid is shown to only have small influence on the measured photocurrent. Therefore the uncertainty due to this source of error is small.
3.2 Theoretical evaluation of the SRPS method
In the lower half of Fig. 5 a simulated SRPS map of the damaged solar cell is compared to the corresponding experimental SRPS map. A laser intensity of 8.9 W/cm2 was chosen. The material quality of the cell was assumed to be homogeneous for the simulation, with completely missing fingers in the upper left-hand corner, corresponding to the observed cracks in Fig. 1. Both maps are normalized a correction for series resistances in the experimental setup is unnecessary. The simulation predicts a comparatively homogeneous photocurrent distribution showing that the SRPS method is relatively insensitive even to heavy damages in the contact grid. It also proves the statement made in subsection 3.1 above that the photocurrent basically depends on the material quality. This particularly applies to the large voltage drop in the upper left-hand corner of the cell.
3.3 Experimental evaluation of the SRIV method
Four SRIVs measured in the center, in the upper left-hand corner, and at the mechanical defect site of the damaged cell are depicted in the upper right-hand corner of Fig. 5. The laser intensity was set to 8.9 W/cm2. The experimental uncertainty is below 2% for all measurements. Each site shows a p-n-like behavior, with varying magnitudes of the photocurrent and the optically induced shunt resistance. The latter is given by the reciprocal slope of the linear part of a SRIV, as constant shunt resistances do not contribute to the signal. This reveals that the p-n junction itself is not damaged neither in the upper left-hand corner nor at the mechanical defect site. Hence, this defect only affects the layers above the p-n junction. All measurements were performed with a series resistance of 76.6 Ω for reasons of noise reduction. This is much higher than the total shunt resistance of the dark cell being 9.5 Ω. The series resistance in the experimental setup is shown to have a large influence on the obtained SRIV in subsection 3.4 below. Therefore, the local characteristic parameters of the p-n junction, especially the saturation current and the ideality factor, can only be extracted with high numerical effort from the shown SRIVs. If possible, it is useful to have a series resistance which is low in comparison to the total shunt resistance of the dark cell. In this case a correction of the data is not necessary and the characteristic parameters can be extracted directly by fitting the obtained I-V curve. Again the uncertainty due to the series resistance in the solar cells contact grid is small.
3.4 Theoretical evaluation of the SRIV method
Figure 7 shows two simulated SRIVs of the damaged solar cell together with the corresponding experimental SRIVs from site four in Fig. 5. Furthermore the assumed I-V characteristic of the p-n junction without the illumination independent part of its shunt resistance is depicted. It is obtained by plotting an I-V curve based on the parameters used for the simulation. The laser intensity is 8.9 W/cm2 and the series resistances in the experimental setup are 2.6 Ω and 76.6 Ω, respectively. All curves are normalized to their magnitude at zero bias for reasons of a better comparability, thus revealing a good agreement between measurement and simulation. The simulation clearly shows that a large series resistance strongly distorts the SRIV whereas a SRIV obtained for a low series resistance matches the assumed I-V characteristic very well. Furthermore, the matching slopes of the linear parts of the curves show that the illumination independent part of the shunt resistance which is also considered in the simulation does not contribute to the obtained SRIV.
4. Summary and discussion
A combination of the SRPS and SRIV method was shown to be a reliable and powerful tool to characterize solar cells. The material quality as well as structural defects can be examined with a high spatial resolution and comparably low experimental effort. The local EQE as well as the local characteristic parameters of the p-n junction are quantitatively accessible. In combination with a reflectance measurement the corresponding IQE can also be determined. The numerical simulations show in combination with the presented experimental data that quantitative results can easily be extracted from the raw experimental data if adequate experimental conditions are applied. For SRPS experiments especially the correct choice of the bias is important such that the current due to optically induced shunt resistances is small in comparison with the local short circuit current. The laser intensity must not be too high as well and should not exceed a few ten W/cm2. For SRIV experiments the series resistance has to be small in comparison to the total shunt resistance of the dark cell. If these conditions are met no additional computational effort is necessary to evaluate the raw data within a few percent of accuracy. The difference to existing techniques like the LBIC method is the applied bias, which offers the following key advantages: i) the signal to noise ratio is improved, ii) the lateral diffusion of photoexcited carriers is reduced, and iii) the local characteristic parameters of the p-n junction can be measured. The points i) and ii) allow a higher spatial resolution and point i) additionally allows faster measurements. Concerning point iii) the short circuit current, the saturation current, the ideality factor, and the optically induced shunt resistance become accessible.
A further improvement of the experiment will be a combination of a photocurrent and a reflectance measurement by placing the sample into an integrating sphere. A transfer of the complex numerical calculation of a solar cells voltage distribution to fast graphic boards is expected to significantly accelerate the simulations. Furthermore, new methods of extracting the local characteristic parameters of the p-n junction from SRIVs measured at high series resistances in the experimental setup will be evaluated. In addition with the graphic board calculation, the letter will significantly facilitate the interpretation of SRIV data.
The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG) in the framework of the Topical Research Group on Metastable Compound Semiconductor Systems and Heterostructures as well as in the framework of the Heisenberg-Program (KV). We also thank the “III-V-Epitaxy and Solar Cells” group of the Fraunhofer ISE in Freiburg, Germany, for their expert support in processing the solar cell test structures and Swantje Horst from the Philipps-Universität Marburg for the time-resolved photoluminescence measurements.
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