Degradation of Ge subcells by thermal load during the growth of multijunction solar cells

Germanium solar cells are used as bottom subcells in many multijunction solar cell designs. The question remains whether the thermal load originated by the growth of the upper layers of the multijunction solar cell structure affects the Ge subcell performance. Here, we report and analyze the performance degradation of the Ge subcell due to such thermal load in lattice‐matched GaInP/Ga(In)As/Ge triple‐junction solar cells. Specifically, we have detected a quantum efficiency loss in the wavelength region corresponding to the emitter layer (which accounts for up to 20% loss in equivalent JSC) and up to 55 mV loss in VOC of the Ge subcell as compared with analogous devices grown as single‐junction Ge solar cells on the same type of substrates. We prove experimentally that there is no direct correlation between the loss in VOC and the doping level of the base. Our simulations show that both the JSC and VOC losses are consistent with a degradation of the minority carrier properties at the emitter, in particular at the initial nanometers of the emitter next to the emitter/window heterointerface. In addition, we also rule out the gradual emitter profile shape as the origin of the degradation observed. Our findings underscore the potential to obtain higher efficiencies in Ge‐based multijunction solar cells if strategies to mitigate the impact of the thermal load are taken into consideration.

Multijunction solar cells are generally grown by metal organic vapor phase epitaxy. Unlike all the III-V layers forming the MJSC structure, the Ge BC is created by the in-diffusion of group V elements (n-type dopants in Ge) during the growth of the first III-V layers on the p-type Ge substrate (the so-called nucleation layer 4 ). Thus, the nucleation layer must be optimized not only considering the epi-surface morphology 5,6 but also from the point of view of the Ge subcell emitter formation. Indeed, Friedman and Olson reported that for a Ge solar cell with a base doping of 1 · 10 18 cm −3 , the V OC is limited by the properties of the emitter. 7 In particular, to obtain a high V OC , the emitter should exhibit (i) a low emitter surface-recombination velocity (S E ), (ii) a reduced thickness (X E ), and (iii) a high minority carrier diffusion length (L h,E , where h stands for holes and E for emitter). Krut and coworkers 8 also showed that the performance of Ge subcells is enhanced with reduced emitter thickness. Typical materials for the nucleation layer on Ge(100) include GaAs 9,10 or GaInP, 5,6 yielding in both cases a good template for the subsequent MJSC growth. However, the use of GaInP is preferred as it creates a shallower emitter than GaAs because the solubility and diffusion coefficients of P in Ge are higher and lower, respectively, than that of As. 11,12 In any case, after its formation, the Ge subcell suffers the thermal load associated with the growth of the rest of the subcells forming the MJSC structure (sometimes referred to as "thermal load" for brevity in this text).
In this line, Gudovskikh and coworkers 13 reported the formation of a potential barrier at the n-GaInP/n-Ge heterointerface, due to the simultaneous diffusion of group III elements (Ga and In) into the Ge substrate.
Here, we report on the degradation of the performance at 1 sun of the Ge subcell due to the thermal load suffered in a 3JSC. Although this work is only focused on the GaInP/Ga(In)As/Ge 3JSC, the degradation observed and its mechanisms may also apply to other MJSC configurations such as upright metamorphic MJSCs 14 or other MJSCs with 4 or 5 junctions grown on Ge. 3,15 2 | EXPERIMENTAL AND MODELLING Germanium single-junction solar cell structures were grown in a commercial Aixtron 200/4 metal organic vapor phase epitaxy reactor on p-type gallium doped Ge(100) wafers with 6°misorientation to the [111]. The semiconductor structure of the as-grown devices can be seen in Figure 1.
By as-grown we mean the solar cell that results after growing the semiconductor structure shown in Figure 1. A GaInP nucleation layer on Ge was employed, which also acted as the window layer of the Ge solar cell.
A Ga(In)As cap layer was grown on top to facilitate the formation of ohmic contacts. Two different growth temperatures (640 and 675°C) were used to grow these III-V layers, to test their effects on the emitter formation and its performance, and the growth time was around 45 minutes in all cases. Details on the growth can be found elsewhere. 4 Triple junction solar cell solar cells were also grown by using the same nucleation conditions (materials, growth temperature, and Ge wafer resistivity). Table 1 includes information about the growth temperatures and time employed during the growth of the 3JSCs, and more generic details about these 3JSC structures can be found elsewhere. 16 Subsequently, the GaInP top cell (TC), Ga(In)As MC, and tunnel junctions were chemically etched away and the samples were processed into solar cells, using the GaInAs buffer layer as the cap layer. In this way, the assessment of the effect of the thermal load of the growth of the rest of the subcells forming the 3JSC structure on the Ge BC performance is straightforward by comparison with the as-grown solar cells of Figure 1.
Hereafter, these Ge solar cells will be referred to as etched 3JSC devices.
A summary of all the structures analyzed in this work can be found in Table 1, where "#A" and "#E" stand for as-grown and etched 3JSC, respectively. As can be observed in Table 1, a set of Ge wafers with different resistivities were used to study the effect of this variable on the performance of the Ge subcells. Although the reader may be more familiar with carrier concentration values, we prefer to use resistivity values instead because they are generally employed by Ge wafer manufacturers and the resistivity measurement of the epiwafers is straightforward and more reliable than the value extracted from electrochemical capacitancevoltage (C-V) measurements performed from the front of the n on p structures. As a reference to the reader, the carrier concentration value range explored covers approximately from 4 × 10 17 to 4 × 10 18 cm −3 .
Several solar cells were manufactured with an active area of 0.1156 cm 2 by using standard photolithography techniques and gold electroplating for the formation of the metal contacts. In the etched devices, front metal contacts were made on the Ga(In)As cap layer (see Solar cell EQE measurements were taken by using a custom-built, monochromator-based setup with a tungsten lamp as the light source and a monitor detector to compensate for known instabilities in the lamp. A Peltier element with a high-precision controller was used to ensure a constant temperature of 25°C in the solar cell. The system is equipped with a calibrated detector to measure the reflectance (R) in the devices and calculate the internal quantum efficiency (IQE).
Light J-V curves were taken at 25°C by using an X E lamp-based solar simulator, with a temperature controlled chuck. The simulator is adjusted at the equivalent 1-sun AM1.5d solar spectrum for each cell measured, using reference cells and calculating the spectral mismatch factor. For dark J-V measurements, the same setup was used, but with the lamp shutter closed. Ambient light was prevented from reaching the cells by means of an enclosure that totally covers the measurement setup.
Capacitance-voltage etch-depth profiling was employed to measure the electrical doping and thickness of the diffused emitter.
The emitter thickness (X E ) was taken to be equal to the depth of the first p-type point measured with the C-V profile. Secondary-ion mass spectroscopy (SIMS) measurements were also carried out to quantify the concentration of diffused species in the Ge.
Simulations of the device performance and band diagrams were performed with Silvaco Atlas TCAD modeling tool. 17 This type of FIGURE 1 Structure of the Ge solar cells analyzed in this work modeling solves the semiconductor fundamental equations under specified bias conditions. 17 The photogeneration rate has been calculated by using the transfer matrix method, 17  to facilitate the reading of the paper.  A thin tunnel junction was grown at 550°C before each subcell. The solar cell I to V parameters are averaged values from all measured devices. The relative standard deviation is shown inside brackets. In turn, Figure 5 shows the averaged V OC of the as-grown devices plotted (black squares) versus wafer resistivity. Besides, the experimental data are grouped according to the 2 different temperatures employed to grow the nucleation layer (empty and filled symbols for samples grown at 640 and 675°C, respectively). On the one hand, for the group grown at 640°C, there is no clear dependence with the resistivity of the wafer, which confirms that the V OC mostly depends on the emitter properties. 7 On the other hand, the sample grown at 675°C (#A3) shows a reduced V OC as compared with the structure grown at 640°C (around 30 mV less).

| As-grown solar cell characterization
As emitter thickness (X E ) may have a big influence on the V OC of the Ge subcell, 7 C-V electrochemical profiling measurements were performed on the Ge solar cells to estimate the electrical carrier concentration profile and X E . Figure 6 shows the carrier concentration profiles of representative samples #A2 and #A3 (ie, similar wafer resistivity and different nucleation temperature). The sample grown at 675°C (ie, sample #A3) shows a deep emitter, of around 250 nm, whereas the sample grown at 640°C (#A2) has a shallower emitter with a thickness between 160 and 190 nm. We also performed SIMS measurements on sample #A2 to check for P, Ga, and In contents and therefore shed some light on the diffusion processes taking place ( Figure 7). On the one hand, P diffuses deep into the substrate creating the emitter. On the other hand, Ga and In diffusion is less pronounced but it will be taken into account later when discussing the particular shape of the CV profile.

| Etched triple junction solar cell solar cell characterization
The thermal load caused by the growth of the other subcells that constitute the MJSC structure significantly affects the performance of   Table 1 summarizes the averaged J SC , V OC , and FF values. In some cases, a higher variability in these values is obtained due to the final morphology of the remaining layers (where the electrical contacts are made) after the wet etching. Figure 2B shows the IQE of the Ge solar cells after the growth of the 3JSC for a variety of wafer resistivity values as indicated in Table 1.
Again, the absence of response in the range from 300 to 800 nm is due to the absorption that takes place in the GaInP nucleation and Ga(In)As layers that were not chemically etched away. In comparison with the IQE of the as-grown solar cells in Figure 2A, the IQE in the wavelength range between 900 and 1300 nm has decreased. As it will be shown later in the simulation section, a reasonably good fit of the curves can be obtained by assuming no contribution from the emitter region to the IQE, thus pointing out a significant degradation of the minority carrier properties in the emitter. This fact accounts for the significant drop in the IQE from 600 to 1200 nm, where the emitter response is the largest contributor to the device IQE. Besides, the IQE in the base region (that mostly shows from 1400 to 1700 nm) exhibits a slight dependence on the substrate resistivity, unlike the as-grown devices. The combination of these facts yields a reduction of the average 1-sun J SC as observed in Table 1 The increase in the dark saturation current density observed will determine the V OC of the device. Figure 5 shows with red circles the V OC of the Ge devices after the growth of the TC and MC. Again, the data are split in samples with the GaInP nucleation layer grown at 675 and 640°C with filled and empty symbols, respectively. Each structure suffered a slightly different thermal load, as summarized in Table 1. Figure 5 shows that the V OC of etched solar cells lie around 175 ± 15 mV, which represents an average ≈55 mV loss as compared with as-grown devices. As occurred with the as-grown samples, the V OC seem largely unaffected by substrate resistivity.
To check the emitter properties and their eventual modification, C-V and SIMS profiles were also measured on etched 3JSC devices.

| Germanium emitter formation and evolution
Germanium emitter shows a characteristic, mesa-shape carrier concentration profile due to its formation by in-diffusion of P, Ga, and In during the GaInP layer growth (see Figures 6 and 7). Although Ga and In diffusion in Ge is, in principle, less intense than the diffusion of group V elements (their diffusion coefficients are 2 to 3 orders of magnitude lower than those of group V elements 12 ), they affect the emitter free carrier concentration profile. Besides, results in Figures 6 and 7 show that the thermal load acts as a drive-in process that favors further P and In penetration into the substrate. P atoms diffuse and create the n-type emitter by compensation of the p-type dopant of the substrate (Ga in the wafers used in this work), which explains the gradual transition from the uniform p-type doped substrate to the n-type plateau region in the C-V profile of Figure 6. Going from right to left in Figure 6, as P concentration increases, the effective p-type carrier concentration level is reduced until it switches to n-type and then smoothly increases until an uniform level is reached (ie, the n-type plateau we see in Figure 6). At this point, the emitter C-V carrier concentration profile approximately reproduces the SIMS P concentration profile, meaning that the ionization of P atoms is almost complete at room temperature. In addition, group III elements (such as Ga and In) also diffuse into the Ge substrate, acting as p-type dopants. Although a quantitative analysis was not possible because In was only given in counts/second in the SIMS measurement, it can be deduced that (i) In has a higher diffusion coefficient than Ga and (ii) group III diffusion coefficients are significantly lower than those of group V elements, in agreement with Dunlap. 12 The shallow diffusion of In and Ga creates an additional p-type doping close to the heterointerface that partially compensates the n-type P profile. However, as P diffusion in Ge shows a characteristic kink-and-tail profile, 21 Ga and In compensations are not strong enough to revert to p-polarity, and they simply reduce the n-type concentration level obtained in the shallower region of the emitter. Hereafter, this region will be referred to as the gradual emitter. Finally, as shown in Figure 7, only P and In seem to diffuse further in Ge due to the extra thermal load. As a consequence, X E is increased and the profile of the gradual emitter extends slightly deeper, as observed in The degradation in the IQE is mainly observed in the emitter region. Figure 8 shows the simulated IQE of devices #A2 and #E3 (same devices as in Figure 4), together with the contributions of each part of the device. In both cases, the main contribution to the IQE comes from the base, and a slight degradation from that region can be seen in sample #E3. For as-grown devices, the emitter contributes little to the IQE (around 5% relative), whereas for etched devices, assuming there is no contribution at all from the emitter, the emitter yields the best fit to the experimental data. In connection with this, for as-grown devices, X E is increased and the change in the shape  Table 1. In the following section, we will use simulations to identify the different phenomena that could explain the observed increase in J 0 .  Table 2. The highest deviation (4%) occurs for the J SC values of device #E3, which is explained by the worse fitting of the IQE from 440 to 700 nm (see Figure 8).

| Impact of gradual emitter profile and emitter thickness
The electric field in a heterojunction between 2 different semiconductors results mainly from their band alignment, which can be modified by the doping level in each semiconductor. In the GaInP/Ge heterojunction that applies to this work, the particular doping profile created by the simultaneous diffusion of group V and III elements (ie, the so called gradual emitter) modifies the conduction and valence band in the vicinity of the heterointerface, as depicted in the simulation shown in Figure 9. This figure presents the conduction and valence band diagrams of an n-GaInP/n-Ge isotype heterojunction-calculated with ATLAS from Silvaco-for 3 cases, namely, the 2 doping profiles presented in Figure 6 and the ideal case of uniform doping. In other words, the band diagrams of Figure 9 represent To quantify the impact of these different band diagrams (structures #A2 and #E3) on the electrical performance of the Ge subcells, the corresponding J-V curves were simulated. As a first approach, the emitter minority carrier diffusion length and S E values of structure #A2 (0.6 μm and 1.5·10 4 cm/s, respectively) were assumed for both structures. In this respect, this first simulation allowed us to assess the sole influence of the emitter characteristics (ie, doping gradient and thickness) in the V OC of the devices. Under these assumptions, the difference in the calculated V OC between profiles #A2 and #E3 was only 10 mV (247 and 237 mV, respectively), much less than observed experimentally (seeTable 2). If the simulation is repeated with the same X E (280 nm) in both cases, but keeping their corresponding  The same equations were used for holes as majority (p-type base) and minority carriers (n-type emitter #2) because to our knowledge, no empirical data for hole properties in highly doped n-type germanium can be found in the literature. Noticeably, hole properties in emitter #2 will vary with depth due to the gradient in dopant concentration, whereas electron properties in the p-type base will be constant throughout. Finally, bandgap narrowing in the highly doped n-type emitter was also accounted for using the analytical expression obtained in Jain and Roulston. 24 Despite that this expression was derived for uniformly doped materials and thus its accuracy may be limited when working with varying doping profiles, 25 Figure 10A and B represent the iso-J SC and iso-V OC curves that match the experimental values measured for structure #A2 (see Table 2). Focusing on the current, in the iso-J SC contour for 20.7 mA/cm 2 that applies to sample #A2,  Figure 10B.
According to the latter explanation, an upper bound for S E and a lower threshold for the L h,E can be established for sample #A2. Even more so, because the maps for J SC and V OC are calculated independently, the combinations of L h,E and S E that fit the experimental J SC and V OC do not need to be exactly the same; ie, the thick dashed curves in Figure 10A and B do not exactly overlap. Therefore, the intersection between those curves represents the set of possible (L h,E and S E ) that have physical meaning for structure #A2. The overlap for the best fit occurs at the points marked with a yellow star in Figure 10A and B and allows to further reduce the range of S E and L h,E ranges that fit the results of sample #A2.
Analogously, Figure 10C and D contains contour plots of J SC and V OC for the etched 3JSC device #E3, again as a function of L h,E and S E . In this case, the additional thermal load produces an increase in X E of about 100 nm, being the gradual emitter zone 90 nm deep, whereas the plateau-tail zone was of about 190 nm. Again, the thick dashed lines represent the iso-J SC and iso-V OC that match the experimental values measured for structure #E3 (see Table 2), and their overlapping corresponding to the best fit has been also marked with a yellow star.
In this case, the iso-J SC contour of 16.3 mA/cm 2 and the iso-V OC curve of 180 mV that fit the experimental result do not look anymore as rounded corners but almost as flattened s-shaped curves or almost straight lines running parallel to the x-axis. This reveals an (almost) total insensitivity to S E and a sole dependence on a very small diffusion length of L h,E~0 .14 μm. In this way, the interpretation of the degradation process behind the thermal load is straightforward: a severe degradation of the minority carrier collection properties occurs in emitter #1.
All in all, the simulations show that hole properties of the n-type Ge emitter in the vicinity of the GaInP/Ge heterointerface are the main responsible for the recombination losses within the structure and are limiting the V OC of the devices. In fact, according to the simulations, the base accounts for just 16% of the total recombination losses for the as-grown case, whereas it drops to about only 3% for etched devices.

| SUMMARY AND CONCLUSIONS
During the growth of Ge-based MJSCs, the Ge subcell suffers performance degradation. To quantify this effect, we have grown and characterized single Ge solar cell test structures in the first place.
These devices showed reasonably good V OC (around 240 mV) and J SC (around 19 mA/cm 2 without ARC) values, and there was no dependence of their IQE and V OC with base doping.