Analysis of subcell open-circuit voltages of InGaP/GaAs dual-junction solar cells fabricated using hydride vapor phase epitaxy

III–V solar cells have attracted much attentions because of their superior performance compared to prevalent materials such as Si solar cells. The conversion efficiency exceeding 40% has been achieved in multijunction solar cells under concentration.^1–5) In addition, InGaP/GaAs dual-junction (DJ) cells and their modules have been widely investigated owing to their excellent bandgap combination in lattice-match systems, exhibiting a conversion efficiency (η) of 32.8%.⁶⁾ Although these devices have shown excellent performances, the use of III–V devices are limited to high-value applications, such as space and high-concentration systems, owing to their high manufacturing cost that arises from the utilization of industry standard metal-organic vapor phase epitaxy and the bulk substrate.^7–9)

Recently, hydride vapor phase epitaxy (HVPE) has gained much attentions as a low-cost alternative for the growth of III–V cells.^10–12) HVPE utilizes cost-effective group-III metals and provides a higher growth rate of several hundred μm h⁻¹, hence decreasing the manufacturing cost. Recently, Young et al. developed a double-chamber vertical HVPE system to fabricate III–V cells.¹³⁾ Schulte et al. successfully demonstrated high performance InGaP/GaAs DJ cells with abrupt-heterointerfaces using HVPE.^7–9) Previously, we developed a triple-chamber vertical HVPE system and successfully demonstrated highly efficient InGaP and GaAs single-junction (SJ) cells^14,15) and an InGaP/GaAs DJ cell.¹⁶⁾ In order to enhance the cell performance of DJ cells, we need to know fundamental characteristics of DJ cells, such as the open-circuit voltage (V_oc) of individual subcell.

Though the photocurrent density generated in each subcell can be estimated by external quantum efficiency (EQE) measurements,^17–19) the V_oc of individual subcell cannot be directly measured in series-connected multijunction devices. On the other hand, it is well known that current–voltage (I–V) characteristics of subcells can be drawn by combining electroluminescence (EL) with EQE measurements under Rau's reciprocity relation (RR).^20–24) Thus, the purpose of this study is to estimate V_oc values of individual subcells of our HVPE-grown InGaP/GaAs DJ cell by using this method.

Thus far, in the evaluation of conventional multijunction cells, the radiative recombination efficiency of each subcell was assumed to be a same degree, because each subcell was sufficiently passivated by window and back surface field (BSF) layers introduced at front and rear sides.²²⁾ However, our HVPE-grown InGaP cells did not have any widegap window and BSF layers because our HVPE system was not equipped with an aluminum source at this time.¹⁵⁾ Therefore, radiative recombination efficiency of the InGaP cell seems to be different with that of the GaAs cell. In this work, we firstly evaluate the radiative recombination efficiencies of InGaP and GaAs SJ cells. Then, we projected I–V curves of subcells in DJ cells by taking the radiative recombination efficiency obtained for each SJ cell into account. Finally, V_oc values of the InGaP top and GaAs bottom cells are estimated. This paper adds experimental data and discussion of results, to the contents of our presentation at solid state devices and materials, 2019.²⁵⁾

Figure 1 shows schematic structures of the InGaP/GaAs DJ cell, the InGaP SJ cell, and the GaAs SJ cell. SJ devices are used to analyze radiative recombination efficiencies. All samples were grown on 2 inch diameter GaAs (001) substrates miscut 4° toward the (111)B direction in a custom-built hot-wall HVPE reactor (Taiyo Nippon Sanso, H260) at atmospheric pressure.^14–16) The source and substrate regions were heated to 850 °C and 660 °C, respectively. Gaseous hydrogen chloride (HCl), gallium (Ga) and indium (In) metals, arsinine (AsH₃), and phosphine (PH₃) were utilized to grow III–V layers. Dimethylzinc (DMZn) and hydrogen sulfide (H₂S) were utilized as the p- and n-type dopants, respectively. For the growth of all cells, growth rates of GaAs and InGaP were 12 and 24 μm h⁻¹, respectively, and the total flow rate of the H₂-carrier gas was 6 SLM. The detailed growth conditions for both GaAs and InGaP cells have been described in Refs. 14 and 15. After the HVPE growth of the device structures, AuGeNi/Au and Ti/Au electrodes were formed as n- and p-type ohmic contacts using electron-beam evaporation. Mesa isolation was performed using a standard photolithography system. SiO₂ (110 nm)/ZnS (50 nm) antireflection coating was deposited onto the cell via radio-frequency magnetron sputtering. The device size is 0.1024 cm².

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The EQE was measured using spectral response measurement system (Model CEP-25C1, Bunkoukeiki Corporation) with a chopped, monochromatic light with a constant photon flux of 1 × 10¹⁴ cm⁻². The EQE measurements for DJ solar cells were performed by conventional procedures to minimize the artifacts caused by tuning bias light and voltage.^26–29) The I–V characteristics were measured under an air mass of 1.5 global (AM1.5G) with illumination of 1 sun. For the EL measurements, the current was injected by applying the constant voltage to devices using the source measure unit (Keithley 2604B). The luminescence was collected by using optical fiber probe with similar configuration for all the measurements in this work. Luminescence signals were detected by a charge-coupled device.

Figure 2 (a) shows light I–V curves for the InGaP/GaAs DJ cell, the InGaP SJ cell, and the GaAs SJ cell. The solar cell properties are summarized in Table I. The InGaP/GaAs DJ cell yielded an η value of 21.89% at 1 sun with J_SC = 11.37 mA cm⁻², V_OC = 2.318 V, and fill factor = 0.83. The V_oc of the DJ solar cell was roughly equal to the sum of the V_oc values of the InGaP and GaAs SJ cells, suggesting a low resistance interconnection by a GaAs tunnel junction with a minimal V_oc drop.

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Figure 2(b) shows EQE spectra for InGaP top and GaAs bottom cells of the InGaP/GaAs DJ cell and those for the InGaP SJ cell and the GaAs SJ cell. The EQE spectra of the InGaP top subcell matched well to that of the InGaP SJ cell. On the other hand, the EQE of the GaAs bottom cell is lower than that of the GaAs SJ cell, which was caused by the parasitic absorption of the GaAs tunnel junction used in the DJ cell [Fig. 1(a)]. As a result, the photocurrent density generated in the GaAs bottom cell was projected to 11.3 mA cm⁻², which was unexpectedly similar with that of the InGaP bottom cell, fulfilling a current matched condition in the DJ cell.

Figure 3(a) shows the dark I–V curves for the InGaP/GaAs DJ solar cell, the InGaP SJ cell, and the GaAs SJ cell. The markers in Fig. 3(a) show the injection currents for EL measurements for the InGaP/GaAs DJ cell, the InGaP SJ cell, and the GaAs SJ cell. Figure 3(b) shows EL spectra measured with varying injection current for the InGaP/GaAs DJ cell. The luminescence signals at 1.4 and 1.9 eV correspond to the GaAs and InGaP, respectively. The luminescence intensities increase with injection current for both subcells. Figure 3(c) shows the EL peak intensity as a function of the injection current for the InGaP top and GaAs bottom cells of the InGaP/GaAs DJ cell. We also performed similar EL measurements for SJ cells to analyze the radiative recombination efficiency as shown in Fig. 3(d).

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We analyzed I–V characteristics of each subcell in the DJ cell from the EL intensity at a given current by following procedures reported in previous papers.^21,22) I–V curves of individual subcells can be projected from EL and EQE measurements using the spectral RR between solar cell and light emitting diode. The spectral RR is given by²¹⁾

$$\begin{eqnarray}&&{\varphi }_{{\rm{E}}{\rm{L}},i}\left({J}_{{\rm{E}}{\rm{L}}}\right)={\varphi }_{{\rm{E}}{\rm{Q}}{\rm{E}},i}\cdot {\varphi }_{{\rm{B}}{\rm{B}}}\left[\exp \left(\displaystyle \frac{q{V}_{i}\left({J}_{{\rm{E}}{\rm{L}}}\right)}{kT}\right)-1\right],\end{eqnarray} \tag{ 1 }$$

where ${\varphi }_{{\rm{E}}{\rm{L}},i}\left({J}_{{\rm{E}}{\rm{L}}}\right)$ is the intensity of the EL peak signal depending on the EL injection current density J_EL. ${\varphi }_{{\rm{E}}{\rm{Q}}{\rm{E}},i}$ and ${\varphi }_{{\rm{B}}{\rm{B}}}$ describe the EQE and the black body photon flux with respect to the photon energy E of the EL peak of the subcell i. q and V_i are the elementary charge and the voltage of the subcell i depending on the J_EL. Using the Boltzmann approximation, Eq. (1) is rearranged to²¹⁾

$$\begin{eqnarray}\begin{array}{r}\begin{array}{rcl}{V}_{i}\left({J}_{{\rm{E}}{\rm{L}}}\right) & = & \displaystyle \frac{kT}{q}\,{\rm{l}}{\rm{n}}\left[{\varphi }_{{\rm{E}}{\rm{L}},i}\left({J}_{{\rm{E}}{\rm{L}}}\right)\right]+\displaystyle \frac{E}{q}-\displaystyle \frac{kT}{q}\,{\rm{l}}{\rm{n}}\left(E\right)\\ & & -\,2\displaystyle \frac{kT}{q}\,{\rm{l}}{\rm{n}}\left({\varphi }_{{\rm{E}}{\rm{Q}}{\rm{E}},i}\right)-\delta {V}_{i}.\end{array}\end{array}\end{eqnarray} \tag{ 2 }$$

Equation (2) allows to determine V_i, as a function of J_EL, except for the voltage offset δV_i.²¹⁾ The first, second, and third terms are obtained from EL measurements, while the fourth term is obtained from EQE measurement. The last term, δV, is determined by the luminescence collection factors. The δV is dominantly related to both a geometrical factor reflecting the optics setup and radiative recombination efficiency.

First, I–V curves of InGaP and GaAs SJ solar cells were projected as shown in Fig. 4(a). By fitting with experimental dark I–V curves of the InGaP and GaAs SJ cells in Fig. 3(a), we determined the δV to be δV_InGaP = 383.2 meV and δV_GaAs = 287.5 meV, respectively. Here, we can evaluate the difference in the luminescence collection factor using the obtained δV

$$\begin{eqnarray}&&\delta {V}_{{\rm{InGaP}}}-\delta {V}_{{\rm{GaAs}}}=\displaystyle \frac{kT}{q}\,\mathrm{ln}\left(R\right),\end{eqnarray} \tag{ 3 }$$

where R is luminescence collection factor ratio. However, the obtained R is dominantly related to the radiative recombination efficiency because the configuration of the optical fiber probe was similar for all the measurements in this work. By substituting each obtained δV for Eq. (3), we found that radiative recombination efficiency of the InGaP SJ cell is lower by a factor of 40 than that of the GaAs SJ cell. The lower radiative recombination efficiency might be due to the fact that we used highly doped InGaP layers as passivation layers of the InGaP cells, which accelerate non-radiative recombination.¹⁵⁾ From the result, we treated the radiative recombination efficiency for the GaAs bottom cell is 40 times higher than that for the InGaP top cell in the characterization of the InGaP/GaAs DJ solar cell, which is same as the situation of SJ devices.

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Then, we projected the I–V curves of the InGaP top and GaAs bottom cells of the InGaP/GaAs DJ cell. Here, in addition to δV_InGaP and δV_GaAs, the voltage offset δV_DJ is considered by rearranging of Eq. (2) as shown in Fig. 4(b)

$$\begin{eqnarray}&&{V}_{{\rm{D}}{\rm{J}}}\left({J}_{{\rm{E}}{\rm{L}}}\right)={V}_{{\rm{I}}{\rm{n}}{\rm{G}}{\rm{a}}{\rm{P}}{\rm{t}}{\rm{o}}{\rm{p}}}\left({J}_{{\rm{E}}{\rm{L}}}\right)+{V}_{{\rm{G}}{\rm{a}}{\rm{A}}{\rm{s}}{\rm{b}}{\rm{o}}{\rm{t}}{\rm{t}}{\rm{o}}{\rm{m}}}\left({J}_{{\rm{E}}{\rm{L}}}\right)-2\delta {V}_{{\rm{D}}{\rm{J}}},\end{eqnarray} \tag{ 4 }$$

where δV_DJ of 3 mV is determined by fitting of the experimental dark I–V curve of the InGaP/GaAs DJ cells as shown in Fig. 3(a). Figure 4(c) shows projected I–V curves of the top and bottom cells and of the DJ solar cell. Finally, we extracted the subcell V_oc. By combining the projected I–V curves of subcells with the experimentally obtained J_sc of 11.37 mA cm⁻², we estimated individual cell V_oc values to be 1.339 for the InGaP top cell and 0.978 V for the GaAs bottom cell, respectively. The projected V_oc value of 1.339 V for the InGaP top cell was matched well with the experimentally obtained V_oc of 1.350 V. Contrary, the calculated V_oc value of 0.978 V for the GaAs bottom cell was slightly smaller than the experimentally obtained V_oc of 1.018 V, which can be explained by lower J_sc for the InGaP/GaAs DJ cell compared to that of the GaAs SJ cell. On the other hand, the estimated V_oc values of top and bottom cells were 1.412 V and 0.948 V, respectively, when the luminescence collection factor is assumed to be same degree for both subcells. These results indicate that radiative recombination efficiency of individual subcells are critical for accurate analysis, though another studies using the absolute EL intensity measurements³⁰⁾ are required to determine the precise V_oc values in multijunction devices.

We analyzed individual V_oc values of subcells in InGaP/GaAs DJ cells fabricated using HVPE. The I–V characteristics of the DJ cells and individual subcells were projected by EL and EQE measurements. We accurately estimated I–V curves of subcells by determining the radiative recombination efficiencies of InGaP and GaAs SJ cells. By combining estimated I–V curves with the experimentally obtained J_sc, the V_oc values of 1.339 V and 0.978 V were obtained for the InGaP top and GaAs bottom cells, respectively, which were consistent with the experimentally obtained V_oc values of the SJ cells.

This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) under the Ministry of Economy, Trade and Industry (METI).