3.1.

Fundamental Solar Cell Characteristics

Figure 1(a) shows the current–voltage curves of the InGaP/GaAs tandem solar cell and the reference InGaP solar cell. Current–voltage characteristics of the solar cells were measured using a Xe/halogen dual-light-source solar simulator. The InGaP/GaAs tandem solar cell used in this work had a $J_{\mathrm{sc}}$ of $11.6\mathrm{mA}/{\mathrm{cm}}^2$, $V_{\mathrm{oc}}$ of 2.30 V, fill factor of 0.81, and efficiency of 21.7% at 1 sun. The reference InGaP solar cell had a slightly reduced $J_{\mathrm{sc}}$ compared with the tandem device.

Fig. 1

(a) Current–voltage curves of InGaP/GaAs tandem solar cell and reference InGaP solar cell. (b) EQE curves of the InGaP and GaAs subcells of the InGaP/GaAs tandem solar cell and the reference InGaP solar cell.

Figure 1(b) shows the EQE curves for the InGaP and GaAs subcells of the InGaP/GaAs tandem solar cell and the reference InGaP solar cell. The subcell $J_{\mathrm{sc}}$, as implied by the EQE spectra, was 11.2 and $11.5\mathrm{mA}/{\mathrm{cm}}^2$, in the InGaP top and GaAs bottom subcells, respectively; this meets the current matching requirements of tandem solar cells. The reference InGaP solar cell had a slightly reduced EQE value at shorter wavelengths (below 500 nm) compared with the InGaP subcell. This is probably why the two curves differ in Fig. 1(a).

3.2.

Analysis of Luminescent Coupling Efficiency

First, we analyze the LC efficiency from the top to the bottom subcell. To estimate the LC, photocurrent was generated only in the top InGaP subcell using monochromatic 405-nm laser illumination. The current in the top subcell was evaluated using the reference InGaP single-junction device under the same conditions. Figure 2(a) shows the current–voltage curves of the reference InGaP solar cell measured at different 405-nm laser intensities. Thus, the reference InGaP solar cell generated a photovoltage of $\sim 1.3\mathrm{V}$ at a photocurrent of 5 to $20{\mathrm{mA}/\mathrm{cm}}^2$. InGaP/GaAs tandem devices consist of a fully absorbing InGaP subcell stacked on a GaAs subcell, with the bottom GaAs subcell generating current from the top InGaP subcell via LC only. The LC current generated by the bottom GaAs subcell limits the current in a series-connected InGaP/GaAs tandem device because it is smaller than the current generated directly by laser illumination of the top InGaP subcell.

Fig. 2

(a) Current–voltage curves of reference InGaP solar cell and (b) InGaP/GaAs tandem solar cell measured at different 405-nm laser intensities. Inset: Schematic diagram of the equivalent circuit. (c) Photocurrent generated in reference InGaP solar cell and current generated through LC in the InGaP/GaAs tandem solar cell. (d) LC efficiency calculated from (c) as a function of light intensity. Inset: Schematic of LC from InGaP top subcell to GaAs bottom subcell.

Figure 2(b) shows the current–voltage curves of an InGaP/GaAs tandem solar cell measured at different 405-nm laser intensities. The current in the figure is the photocurrent into the GaAs subcell of the InGaP/GaAs tandem solar cell generated via LC. The obtained $V_{\mathrm{oc}}$ of $\sim 2\mathrm{V}$ indicates that the GaAs subcell shows $V_{\mathrm{oc}}$ of $\sim 0.7\mathrm{V}$ due to photocurrent generation via LC because $V_{\mathrm{oc}}$ of 1.3 V is obtained in the reference InGaP solar cell under the same 405-nm laser illumination and the $V_{\mathrm{oc}}$ of the tandem device is determined by the sum of the subcell $V_{\mathrm{oc}}$. Here, we assume that the photocurrent measured at 1.3 V is the short-circuit current of the GaAs subcell because the photovoltage of 1.3 V is generated in the InGaP subcell and the photocurrent of the tandem device is limited by the GaAs subcell. The increase in current with decreasing voltage below 1.3 V is probably related to an increase in dark current in the GaAs subcell toward GaAs diode breakdown.

Figure 2(c) shows the current generated by the GaAs subcell of the InGaP/GaAs tandem solar cell and the reference InGaP solar cell. In the reference single-junction InGaP device, the current increases in proportion to the illumination. Figure 2(d) shows $J_{\mathrm{LC}}/J_{\mathrm{ph}}$, the ratio between the current densities in the InGaP/GaAs tandem device and the reference InGaP device, obtained from Fig. 2(c). The current ratio $J_{\mathrm{LC}}/J_{\mathrm{ph}}$ reflects the LC efficiency of the InGaP/GaAs tandem solar cell from the top subcell to the bottom subcell. LC efficiency increases slightly with the light intensity of the illumination. This increase has been interpreted as meaning that the top subcell becomes more radiative with increasing illumination intensity. This increase in radiative efficiency is explained by the fact that the Shockley–Read–Hall lifetimes of electron and hole increase with illumination intensity.⁵ The measured current ratio was of 0.4% to 0.6% and remained almost unchanged above $100\mathrm{mW}/{\mathrm{cm}}^2$, showing that the LC occurs in the tandem device fabricated using HVPE.

Even though the luminescent effect is a small contributor to the efficiency of the bottom subcell, it would be able to design a device to increase LC efficiency by enhancing the EQE of the GaAs subcell around the peak wavelength of EL of the InGaP layer around 650 nm. This can be achieved by the thinning InGaP layer, which increases the EQE of the GaAs subcell around 650 nm because the EQE of the GaAs subcell is determined by the transmittance of the incident light through the InGaP subcell. In Fig. 1(b), the wavelength light shorter than 650 nm is absorbed by the front InGaP layer and is not transmitted to the GaAs layer, resulting in a reduced EQE of the GaAs subcell below 650 nm. The modification of the InGaP subcell thickness would probably increase in LC efficiency from the InGaP subcell to the GaAs subcell.

3.3.

Current–Voltage Analysis Using Electroluminescence Measurements

Next, we perform an analysis of the subcell $V_{\mathrm{oc}}$ and investigate the effect of LC on the analysis. Subcell $V_{\mathrm{oc}}$ was calculated from the EL intensity at a given current according to the procedure reported in previous papers.^20,21 Figure 3(a) shows the dark current–voltage curves of the InGaP/GaAs tandem and reference InGaP solar cells. The markers in Fig. 3(a) indicate the injection currents used for the EL measurements. Figure 3(b) shows the EL spectra of the InGaP/GaAs tandem solar cell measured at different injection currents. The luminescence signals at 660 and 870 nm correspond to InGaP and GaAs, respectively. Figure 3(c) summarizes the EL intensity of the InGaP and GaAs subcells of the tandem and reference InGaP solar cells. The luminescence intensity of both subcells increased with the injection current.

Fig. 3

(a) Dark current–voltage curves of InGaP/GaAs tandem and reference InGaP solar cells. (b) EL spectra of InGaP/GaAs tandem measured at different injection currents. (c) EL intensity of InGaP (blue solid circle) and GaAs (red solid circle) subcells of tandem and reference InGaP solar cells (blue open square). Inset: $V_i^{*}$ of the InGaP and GaAs subcells of the tandem and the reference InGaP devices calculated using Eq. (2). (d) Calculated offset voltage of reference InGaP (blue triangle) and tandem solar cells (green triangle) at different injection currents. (e) Current–voltage curves of GaAs (red diamond) and InGaP (blue diamond) subcells and the tandem solar cells (green diamond) obtained by EL intensity analysis. (f) Schematic diagram of LC effect of InGaP/GaAs tandem solar cell.

The current–voltage curves of the individual subcells are evaluated from EL and EQE measurements using the spectral reciprocity relation between the solar cell and light-emitting diode²¹

The last term, $\delta V_i$, reflects luminescence collection factors, such as geometrical factors that reflect the shape of the optics setup and luminescence extraction efficiency. Previous papers assumed that the voltage offsets are the same for all subcells of the device under test.²¹ Here, we estimate the voltage offset using the dark current–voltage curves of the tandem and reference devices. Figure 3(d) shows the voltage offsets of the reference InGaP and tandem solar cells from the results in Fig. 3(a) and the inset of Fig. 3(c) for various injection currents. The voltage offset is slightly dependent on the injection currents. This is probably due to series resistance that influences only current–voltage curve measurements, while it does not affect the curves obtained from the EL intensity. The current–voltage characteristic of each subcell, derived from the EL intensity, represents $J_{\mathrm{sc}}-V_{\mathrm{oc}}$ pairs and therefore is free of influences of series resistance.²⁶ By fitting the relation in Fig. 3(d) using a linear function, we obtained the voltage offset $\delta V_{\mathrm{InGaP}}$ of 2978 mV at zero current limit. Similarly, as shown in Fig. 3(d), we analyzed the current–voltage characteristics of the InGaP/GaAs tandem solar cell and obtained the voltage offset for the tandem. Here, the voltage of the tandem is the sum of the subcell voltages: $V_{\text{tandem}}(J_{\mathrm{EL}})=V_{\mathrm{InGaP}\text{sub}}^{*}(J_{\mathrm{EL}})-\delta V_{\mathrm{InGaP}\text{sub}}+V_{\mathrm{GaAs}\text{sub}}^{*}(J_{\mathrm{EL}})-\delta V_{\mathrm{GaAs}\text{sub}}$. The voltage offset of the tandem was obtained from the calculated voltage in Fig. 3(c) and the dark current–voltage curve of the tandem device in Fig. 3(a): $\delta V_{\mathrm{InGaaP}\text{sub}}+\delta V_{\mathrm{GaAs}\text{sub}}$. Fitting the voltage offset using a linear function gave a voltage offset of 5936 mV at zero current limit. By assuming that the voltage offset of the InGaP subcell was the same as the voltage offset of the reference InGaP solar cell, $\delta V_{\mathrm{InGaP}\text{sub}}=\delta V_{\mathrm{InGaP}}$, the voltage offset $\delta V_{\mathrm{GaAs}\text{sub}}$ was determined to be 2958 mV. Note that the voltage offset of the InGaP subcell was larger by 20 mV than the voltage offset of the GaAs subcell. This indicates that the luminescence collection efficiency of the InGaP subcell was low, as will be described later.

Equation (2) gives the current–voltage curves for GaAs and InGaP subcells, shown in Fig. 3(e). Combined with a subcell photocurrent of $11.6\mathrm{mA}/{\mathrm{cm}}^2$, a subcell $V_{\mathrm{oc}}$ of 1357 mV was estimated for the top InGaP subcell and 983 mV for the bottom GaAs subcell. Therefore, as shown in Fig. 1(a), the $V_{\mathrm{oc}}$ of the tandem device generated from the internal voltage of the InGaP and GaAs subcells was 2300 mV.

Conventional procedures^21,22 assume that the voltage offsets for all subcells are the same, $\delta V_{\mathrm{InGaP}\text{sub}}=\delta V_{\mathrm{GaAs}\text{sub}}$. Without considering the voltage offset of each subcell, the individual subcell $V_{\mathrm{oc}}s$ were extracted as 1376 and 962 mV for InGaP and GaAs subcells, respectively. The value of the InGaP subcell was slightly larger than 1350 mV, the value of the reference InGaP solar cells reported in a previous paper.¹⁸ This also means that the luminescence extraction efficiency of the InGaP subcell is lower than that of the GaAs subcell. For multijunction devices with three or more junctions, the effect of the voltage offset difference may be negligible because the voltage offset is averaged between the subcells. However, for double junction devices, these results indicate that the luminescence collection coefficients, such as the luminescence extraction efficiency and geometric factors that reflect the shape of the optical setup, need to be different for each subcell. We carefully checked that the geometric factors caused by the optics setup do not change to obtain exactly the same result for each subcell. Therefore, the discrepancy is probably caused by the luminescence extraction efficiency of the device. A difference in voltage offset of $\sim 20\mathrm{mV}$ corresponds to a luminescence extraction coefficient of the InGaP subcell that is about half of the GaAs subcell. This cannot be explained by the internal radiative efficiency of the InGaP subcell alone because it is unlikely to be $<50\%$ even if we assume the radiative efficiency of GaAs to be 100%. A possible cause is luminescence reabsorption or an LC effect in the GaAs layer behind the InGaP subcell, as shown in Fig. 3(f). Luminescence extraction efficiency is related to the device structures and depends on each device. Thus, our findings indicate that a more detailed analysis can be performed with the help of a reference device and we can evaluate more accurately the efficiency of luminescence extraction.