Integrated series/parallel connection for photovoltaic laser power converters with optimized current matching

In this paper, we present a stepped architecture optimized for current matching in high‐voltage laser power converter photovoltaic (PV) cells. The integrated series/parallel connection in stepped PV cells combines the advantages of well‐known multijunction and multisegment approaches with respect to current matching, whereas their specific drawbacks are circumvented. The superior misalignment tolerance of stepped PV cells in comparison with multisegment cells is shown by simulations of the maximum acceptable misalignment (MAM) for a range of devices with various output voltages. We present the first realization of stepped PV cells with two stacked GaAs‐based pn‐junctions. Thereby, the unique properties of the lateral current flow in the bottom cell and the assessment of the optical absorption in the subcells are discussed. Moreover, the effects of segmentation and number of stacked junctions on the I‐V characteristics are investigated. Finally, the behavior towards misalignment of a laser spot is studied for stepped and multisegment PV cells. An optimal current matching for misalignment‐prone power‐by‐light systems is found with a six‐segment stepped PV cell.


Abstract
In this paper, we present a stepped architecture optimized for current matching in can be fabricated in very high material quality, and consequently various research groups have published devices with monochromatic light to electricity conversion efficiency above 55%. [2][3][4][5][6][7][8][9][10][11][12] In the radiative limit (external quantum efficiency [EQE] of unity for photon energies above or equal the band gap energy, zero losses because of thermalization, i.e., band gap energy equals photon energy, no shading, no resistive losses, and perfect material with radiative recombination only and an ideal back mirror), the theoretical efficiency potential for PV laser power converters lies beyond 80%. 13 [Correction added on 28 January 2021 after first online publication: Affiliation and corresponding author has been updated in this version.] The output voltage of the PV cell is determined by the PV material and is around 1 V for GaAs. 14 Yet, to power electric circuits, often higher voltages (e.g., 3.3 or 5 V) are desired. A well-known way to increase the output voltage of a PV cell is the division of the cell into several subcells that are connected in series. Thereby, the subcell voltages add up, whereas the current is divided among the subcells. This division of current also reduces resistive losses that scale quadratically with the current, which is especially important in high-power applications.
For such integrated series connection in PV laser power converters, two architectures are state-of-the-art 3,13,14 : the "multijunction" approach where several subcells are stacked by vertical interconnection and the "multisegment" approach where series connection is achieved by lateral segmentation (also known as monolithic interconnected modules, MIMs). 15,16 For efficient operation, the currents in the subcells need to be well matched. Unfortunately, in practice, both architectures suffer from intrinsic nonideal current matching.
In multijunction cells, the absorption of light and thus generation of photocurrent in the subcells generally follow Beer-Lambert's law of exponential absorption. Accordingly, the thicknesses of the individual subcells need to be adjusted to achieve current matching. Because of the temperature dependence of the cell's absorption coefficient, accurate current matching in multijunction cells can only be achieved for a specific operating temperature. 17 In multisegment cells, this layer thickness-dependent current mismatch is avoided. Here, the currents of the subcells are defined by the illuminated segment areas. As a consequence, a misalignment of the laser light spot on the PV cell leads to current mismatch and, thus, a drop in efficiency. As will be elaborated below, this causes significantly severer losses than the pure spillage of light outside the active PV cell area, which represents a fundamental loss mechanism in all device architectures. 18 In this work, we introduce a PV cell architecture with improved misalignment tolerance based on an integrated serial/parallel connection of subcells in a combined lateral/vertical segmentation. With this so-called stepped architecture, the advantages in current matching of both multijunction and multisegment architectures are combined, whereas their specific drawbacks are circumvented. We compare calculations of the misalignment tolerance for the three architectures.   Figure 1 depicts the case of a foursegment two-junction stack of that kind. Here, part of the top cell is removed in a way that the remaining area forms two segments.
The uncovered area of the bottom cell also forms two analogous segments. As illustrated by red arrows in Figure 1A Figure 2B shows the typical connection scheme of multisegment cells, where all segments are connected in series. The fillings of the circles represent the respective photocurrents of the segments. Here, the vulnerability of multisegment cells to misalignment becomes apparent: the overall current of the device is determined by the single least illuminated segment (Segment 1 in our example). The misalignment tolerance is strongly improved in the combined series/parallel connected stepped PV cell ( Figure 2C). Here, the current limitation of the least illuminated segment is partially compensated for the parallel connection of the opposite segment.
In conclusion, with respect to current mismatch tolerance, the stepped approach combines the advantages of the two established  Table 1. Low sensitivity against temperature and layer thickness variation is achieved by current matching via the segment areas, whereas the combined series/parallel connection yields high misalignment tolerances. In the next section, this qualitative finding is examined further by a quantitative assessment of the misalignment tolerance. Table 1  where the segments are separated by isolation trenches. 14

| SIMULATED MISALIGNMENT TOLERANCE
The following assessment of the misalignment tolerance is based on the model introduced in Wagner et al. 19 We consider a circular symmetry for PV cell and light spot, which is the typical geometry for optical fiber-based systems. The misalignment dependence of the cell current is computed by the spatial convolution of the irradiance profile and the subcells' spatial responsivity. For simplicity, the responsivities are assumed constant over the area of the subcell, and

Technological requirements
Photolithography steps Area loss by segmentation 0 n Á isolation trench Flank steepness Note: Comparison of multijunction, multisegment, and stepped PV cells with respect to the sensitivity towards three mechanisms of current matching. A low sensitivity is marked with a (+) and high sensitivity with (−). The letter in brackets signifies the parameter that influences the vulnerability, where j represents the number of junctions and n the number of segments. In the case of Beer-Lambert-type absorption, the absorber thickness follows the equa- where Abs is the desired absorptance, for example, 0.98, and α the absorption coefficient.
the irradiance is simplified to a constant flat-top profile. There are two characteristic axes for a displacement of the light spot that we call the "best case" and the "worst case" axis, as depicted in Figure 2A. In the worst case (Axis 1), the light spot is displaced along the center of one segment, which will lead to the highest power loss, whereas in the best case (Axis 2), it is displaced along the edge of two segments edge, yielding the lowest power loss. Figure 3 illustrates the behavior of current limitation for a two-junction, four-segment stepped PV cell with an electrical interconnection as depicted in Figure 2C. Figure 3 shows simulations of the normalized photocurrents in each subcell as a function of a displacement of the light spot along the "worst case" axis. The plot shows that for small displacements, the current is limited by Subcell 1, which comprises of the poorly illuminated Segment 1 and the fully illuminated Segment 3. The superior misalignment tolerance of the stepped geometry is most evident at an extreme displacement of one cell radius, where the current in the multisegment cell, which is currently limited in Segment 1, is zero, whereas in the stepped PV cell, Subcell 1 still provides 50% of the initial current.
The thin black line depicts the reference case of current loss because of misalignment for one segment n = 1 as in a multijunction cell. It is noteworthy that as a result of symmetry for a displacement along the "best case" axis, the combined serial/parallel geometry always behaves as this ideal (n = 1) case; since then, the photocurrents of both subcells are equally affected from spillage.
A quantitative comparison of the different architectures can be assessed by the maximum acceptable misalignment, MAM 90 , for which 90% of the maximum photocurrent (i.e., the current at optimal alignment) can be ensured. 19 This critical displacement is illustrated by a horizontal arrow in Figure 3.  Figure 4A shows that in multisegment PV cells, for both axes, the MAM 90 drops with increasing segment numbers and converges to a lower limit of 5.13% of the cell radius, 19 as marked by the lower horizontal line. Figure 4B shows a converse trend for the stepped geometry. As  Figure 4B is the discontinuities in the worst case behavior. These are due to a toggling between top and bottom cell as limiting subcell for different segment numbers.
Yet one has to keep in mind that Figure 4B only considers twojunction stepped PV cell, that is, GaAs cells with about 2-V output voltage, whereas for the multisegment case in Figure 4A, the voltage increases proportionally with the number of segments. In the 2-V case, compared with multisegment cells, the stepped geometry has a two times higher misalignment tolerance for high segment numbers (n ! ∞). For an n = 6 segment cell, already 94.4% of this limit is reached.

| Optical absorption in top and bottom cell
To obtain high efficiencies in stepped PV cells, the subcells need to be sufficiently thick that practically all light is absorbed. Because of the series connection with the bottom cell, the absorption in the top cell cannot be directly measured, and two approaches have been followed to access the top cell current. In a first approach, unstructured twojunction ( j = 2, n = 1) cells were processed. Because of shadowed bottom cell connected in series with the fully absorbing top cell, a device current close to zero would be expected in the first place. Yet, in contrast, we found a remarkably high current which we could attribute to luminescence coupling between the two junctions, as further discussed in Walker et al. 21 In a second approach, two test structures were fabricated for which the EQE was measured with a diffraction grating monochromator. The EQE of the bottom cell could be easily accessed with a test structure from which the top cell was completely removed. To access the top cell current, segmented structures were processed with a mismatch of the areas such that the bottom cell current was much larger than the top cell current. The area mismatch was determined with an optical microscope to 0.52:1. Therefore, the limiting current of the top cell determined the current of the overall cell. Figure 6 shows the corresponding EQE of the single bottom cell

| CONCLUSION
In this paper, we introduced a novel architecture for PV laser power converters. The integrated series/parallel connection in stepped PV cells combines the advantages in current matching of common PV cell designs, namely, high tolerance against temperature changes and misalignment.
We presented a quantitative assessment of the misalignment tolerance by the comparison of the maximum acceptable misalignment, MAM 90 , of stepped, multijunction and multisegment PV cells. For an increasing number of segments, the stepped architecture approaches the performance of the ideal one-segment multijunction PV cell, whereas the MAM 90 for multisegment cells converges to less than one third of this value. Calculations of the MAM 90 for 2-, 3-, and 4-V GaAs-based stepped and multisegment PV cells revealed that for realistic numbers of segments (6, 9, and 12, respectively), high misalignment tolerances can be achieved with stepped PV cells.
Finally, we demonstrated the first realization of such devices by two-junction circular PV cells. Based on this example, the unique features such as the azimuthal path of the current in the bottom cell and the optical absorption in the subcells were discussed, and means to simulate and measure these features were presented. We studied the effect of segmentation and identified the six-segment device to be the optimal candidate for power-by-light systems.
In conclusion, it was demonstrated that the presented stepped approach combines the advantages regarding current matching from both multisegment and multijunction PV architectures. However, the epitaxial thickness and processing efforts increase with the desired photovoltage because more and more fully absorbing junctions are stacked. For practical applications that justify higher effort in fabrication, the presented approach has shown significant reduction of misalignment losses and can therefore increase performance.