2.1.

Sample Preparation

Three-terminal tandem solar cells were fabricated through a bonding technique using MNP arrays.¹⁹ To investigate its fundamental properties, we used InGaAsP for the bottom subcells, in which better contact is easily obtained.³² AuGeNi/Au and Ti/Au electrodes were formed in advance on the front and rear sides of the InGaAsP bottom cell using the electron-beam evaporation method [Fig. 1(a)]. An Au electrode was also formed in advance on the GaAs top cell with a thin GaAs contact layer. Figure 1(a) shows the top view of the devices. The centered square shows the top subcell with the top electrode, which is stacked at the center of the bottom subcell with two middle electrodes. The sizes of the top and InGaAsP bottom cells are $\sim 4.0\times 4.0$ and $\sim 4.4\times 8.0{\mathrm{mm}}^2$, respectively.

Fig. 1

(a) Top view of a three-terminal tandem solar cell. Side views of (b) the three-terminal InGaP//InGaAsP tandem solar cell and (c) InGaP/GaAs//InGaAsP tandem solar cells. (d) Digital camera image of a fabricated sample.

Figures 1(b) and 1(c) show a schematic of three-terminal InGaP//InGaAsP and InGaP/GaAs//InGaAsP tandem solar cells, respectively. The p–n junctions are bonded using Pd NP arrays to form a tandem solar cell comprising InGaP and InGaP/GaAs top cells and an InGaAsP bottom cell (1.15 eV) grown on an InP wafer. The fabrication processes follow the methods described in previous papers.^19,20 To form the Pd NP arrays, a diluted solution of polystyrene-block-poly-2-vinylpyridine was spin-coated on the surface of the bottom cell to form a nanometer-scale pattern. The bottom subcell with the middle and bottom electrodes was immersed in an aqueous solution containing Pd ions, and a patterned Pd template is formed on the bottom cell. Next, a plasma treatment was performed to remove the polymer and reduce the Pd ions to form the Pd NP arrays. The typical height of the Pd NPs and period of the arrays are $\sim 10$ and 100 nm, respectively. Next, the InGaP (InGaP/GaAs) top cell, which was grown on a GaAs wafer, was exfoliated using the epitaxial lift-off technique. The thin InGaP (InGaP/GaAs) top cell placed in water was then scooped up and transferred to the InGaAsP bottom cell, which is covered with Pd NP arrays. The stacked sample was pressed down using a weight at room temperature for 2 h. Finally, an ${\mathrm{SiO}}_2$ and ${\mathrm{TiO}}_2$ multistacked layer was formed as an antireflection coating on the front surface.

2.2.

Characterization of the Three-Terminal Tandem Solar Cells

Current–voltage characteristics of the solar cells were measured using a Xe/halogen two-light-source solar simulator. EQE measurements of multijunction solar cells were performed by following the matured procedures for multijunction devices.³⁰ A modulated quasimonochromatic light combined with spectrally adaptable continuous bias light was used. The EQE was measured under a constant photon flux of ${10}^{14}\text{photon}/\mathrm{s}/{\mathrm{cm}}^2$. In addition, the bias dependency of LC was evaluated from the current–voltage measurements conducted using a two-channel source meter (Keithley 2604B).

3.1.

Spectral Response of Subcells in Three-Terminal Tandem Solar Cells

Figure 2(a) shows the EQE curves for the three-terminal InGaP//InGaAsP tandem solar cells. Here, we used a spatial mask to cover the surface of the bottom InGaAsP subcells to ensure equivalence in the illuminated areas of the top InGaP and bottom InGaAsP subcells. Although the InGaP subcell shows high EQE values, the InGaAsP subcell shows lower EQEs; this is partly caused by the interface reflection due to air gap at the bonded interface. Even though the EQE is reduced in the InGaAsP subcell, compared with the InGaP subcell, the InGaAsP subcell shows higher short-circuit current density ($J_{\mathrm{sc}}$) implied by the EQE curve of $15.4\mathrm{mA}/{\mathrm{cm}}^2$.

Fig. 2

EQE curves of the three-terminal (a) InGaP//InGaAsP and (b) InGaP/GaAs//InGaAsP tandem solar cells.

Figure 2(b) shows the EQE curves for the three-terminal InGaP/GaAs//InGaAsP tandem solar cell. The device size is defined by the bottom subcell size ($\sim 0.35{\mathrm{cm}}^2$) and a spatial mask is not used. Note that the device area even for the top subcell is defined by the bottom subcell size for EQE measurements. Owing to the smaller subcell sizes ($\sim 0.16{\mathrm{cm}}^2$), lower implied $J_{\mathrm{sc}}$ of 4.6 and $4.1\mathrm{mA}/{\mathrm{cm}}^2$ are obtained for the InGaP and GaAs subcells, respectively, compared with the InGaAsP subcells of $14.8\mathrm{mA}/{\mathrm{cm}}^2$.

3.2.

Power Extraction in Three-Terminal Tandem Solar Cells

The power extraction in the proposed three-terminal tandem solar cells was analyzed using a simple model calculation method. Figure 3 shows a schematic of the optoelectronic equivalent circuit of the three-terminal tandem solar cells. Here, we used a dual-junction solar cell with three-terminal electrodes. In the device used in this work, the EQE measurements show that the photocurrent generated in the bottom subcell is higher than that in the top subcell as shown in Fig. 2. Therefore, as an example, we considered the case where the photocurrent generated in the bottom subcell (subcell #2) is higher than that in the top subcell (subcell #1). While the power is primarily extracted using top (t) and bottom (b) electrodes as in conventional two-terminal tandem solar cells, the additional power generated in bottom subcell #2 due to the current mismatch can be extracted using the middle (m) and bottom electrodes. The power extraction is determined by the product of voltage $V_{\mathrm{t}-\mathrm{b}}$ ($V_{\mathrm{m}-\mathrm{b}}$) and current $J_{\mathrm{t}-\mathrm{b}}$ ($J_{\mathrm{m}-\mathrm{b}}$) between the top (middle) and bottom electrodes as

Fig. 3

Schematic of optoelectronic equivalent circuit of the three-terminal tandem solar cells.

Next, we evaluated the power extraction in the fabricated devices. The current–voltage curves were measured with varying terminal conditions. Figure 4(a) shows the current–voltage curves of the three-terminal InGaP/InGaAsP tandem solar cells. First, the current–voltage curve for the bottom subcell was measured using middle–bottom electrodes, while the top electrode was set at an open-circuit condition. Then, the voltage of the maximum power condition, $V_{\mathrm{m}-\mathrm{b},\mathrm{mpp}}$, was determined from the current–voltage curve. Second, the current–voltage curve for the tandem solar cells was measured using the top–bottom electrodes, where the voltage between the middle and bottom electrodes was set at the maximum power condition $V_{\mathrm{m}-\mathrm{b}}=V_{\mathrm{bot},\mathrm{mpp}}$. Then, the maximum power extraction and condition were determined from this curve as $P_{\mathrm{t}-\mathrm{b},\mathrm{mpp}}$, $V_{\mathrm{t}-\mathrm{b},\mathrm{mpp}}$, and $J_{\mathrm{t}-\mathrm{b},\mathrm{mpp}}$. Finally, the current of the middle–bottom electrodes at the maximum power condition of $J_{\mathrm{m}-\mathrm{b},\mathrm{mpp}}$ was measured under the condition that both the top–bottom and middle–bottom electrodes were set at voltages for the maximum power condition, i.e., $V_{\mathrm{m}-\mathrm{b},\mathrm{mpp}}$ and $V_{\mathrm{t}-\mathrm{b},\mathrm{mpp}}$, respectively. Based on the obtained voltages and currents for the maximum power condition, we determined the power extraction as $P_{3\mathrm{T}}=P_{\mathrm{t}-\mathrm{b},\mathrm{mpp}}+P_{\mathrm{m}-\mathrm{b},\mathrm{mpp}}=16.86+0.39=17.25\%$ for the InGaP//InGaAsP tandem solar cells. Note that the current difference between the top and bottom subcells is low, and thus the additional power extraction using the middle–bottom electrodes is low. For comparison, we determined the total power extraction using the maximum power extraction of each subcell, which in turn was determined by measuring the current–voltage curves when the unmeasured subcells were set at the open-circuit condition. The value was obtained as $P_{4\mathrm{T}}=P_{\text{top}}+P_{\mathrm{bot}}=12.20+5.09=17.29\%$, which is comparable to the aforementioned value obtained by the three-terminal electrodes (17.25%).

Fig. 4

Current–voltage curves of the three-terminal (a) InGaP//InGaAsP and (b) InGaP/GaAs//InGaAsP tandem solar cells.

Next, we investigated the three-terminal InGaP/GaAs//InGaAsP tandem solar cells, which showed significant current mismatch between the InGaP/GaAs top cell and the InGaAsP bottom subcell owing to different cell sizes. Figure 4(b) shows the current–voltage curves of the three-terminal InGaP/GaAs//InGaAsP tandem solar cells. Here, a spatial mask is not used and the device size ($\sim 0.35{\mathrm{cm}}^2$) differs from the area of the InGaP/GaAs top subcell ($\sim 0.16{\mathrm{cm}}^2$). Therefore, the $y$ axis represents the current. According to the same procedure as that used for the InGaP//InGaAsP tandem solar cell, the power extraction in the three-terminal InGaP/GaAs//InGaAsP tandem solar cells was determined as $P_{3\mathrm{T}}=P_{\mathrm{t}-\mathrm{b}}+P_{\mathrm{m}-\mathrm{b}}=2.134+1.013=3.147\mathrm{mW}$. The additional photocurrent in the bottom InGaAsP subcell was extracted through the middle–bottom electrode. The value is consistent with the value obtained in the four-terminal configuration: $P_{4\mathrm{T}}=P_{\text{top}}+P_{\mathrm{bot}}=1.717+1.325=3.042\mathrm{mW}$.

3.3.

Luminescence Coupling in Three-Terminal Tandem Solar Cells

Next, we investigated the properties of LC using the three-terminal tandem solar cell. First, we used InGaP//InGaAsP tandem solar cells. To avoid a direct illumination into the bottom InGaAsP subcell, a spatial mask covering the surface of the bottom InGaAsP subcells was used. The illuminated 405-nm laser was absorbed only by the top InGaP subcell. Then, a photocurrent was generated in the InGaAsP bottom cell because of the reabsorption of the luminescent originated from the InGaP top cell. We measured the current–voltage curves for the InGaAsP subcell using the middle–bottom electrodes. Figure 5(a) shows $J_{\mathrm{sc}}$ of the InGaAsP subcell as a function of 405-nm laser intensity. In addition, according to the ratio of the LC current to the photocurrent generated through illumination in the top InGaP subcell, the LC efficiency is defined as $J_{\mathrm{sc},\mathrm{bot}}/J_{\mathrm{sc},\text{top}}$. The LC efficiency in the InGaP//InGaAsP tandem solar cell was evaluated as $\sim {10}^{-4}$, as shown in Fig. 5(a). The low LC efficiency is probably caused by low radiative recombination rate in the InGaP top cell because the LC efficiency reflects the external radiative efficiency of InGaP top cell ${\eta }_{\mathrm{rad}}$ and the transmittance of the luminescence at the top subcell into the bottom subcell, $t_{\text{top}\to \mathrm{bot}}$, which is calculated to be an order of ${10}^{-1}$.³³ Note that the LC efficiency depends on the properties of MNP arrays, such as the NP size. Compared with the adhesive bonding, the bonding technique using MNP forms a narrower gap between the subcells, which can provide a better LC efficiency.³³

Fig. 5

(a) $J_{\mathrm{sc}}$ measured under the open-circuit (open circles) and short-circuit condition of the top–middle electrodes, as a function of the illumination intensity. (b) $J_{\mathrm{sc}}$ measured under light intensity of $140\mathrm{mW}/{\mathrm{cm}}^2$, as a function of the voltage applied to the top–middle electrodes.

Here, the values of $J_{\mathrm{sc}}$ for the top electrode under the conditions of open- and short-circuit to the middle subcell were compared. Under the open-circuit condition, $J_{\mathrm{sc}}$ was determined to increase more with light intensity, compared with $J_{\mathrm{sc}}$ under the short-circuit condition. This indicates that the luminescence intensity at the InGaP top cell increases under the open-circuit condition. To understand this tendency, we measured the LC current for different bias voltages. Figure 5(b) shows $J_{\mathrm{sc}}$ as a function of the bias voltage. The current increases above 1.2 V, indicating enhanced luminescence in the InGaP subcells. Under a low bias-voltage condition, the photocarriers are partly recombined and emit light in the absorber before reaching the p–n junction owing to finite mobility. With increasing bias voltage, the photocarriers start to recombine at the p–n junction, and thus the radiative recombination at the junction leads to enhanced luminescence. This result is explained by the bias-voltage dependency of LC.²⁷

Next, we measured the LC currents for 660- and 780-nm laser illuminations in the three-terminal InGaP/GaAs//InGaAsP tandem solar cells. Here, we used a spatial mask to cover the surface of the bottom InGaAsP subcells and investigated the coupling of the luminescence emitted from the GaAs subcell and reabsorbed by InGaAsP subcells. While the 750-nm laser was absorbed only by the GaAs subcell, the 660-nm laser was absorbed by both InGaP and GaAs subcells. Figure 6(a) shows the current–voltage curves for different 780-nm laser intensities under open- and short-circuit conditions of the illuminated top InGaP/GaAs subcell. Figure 6(b) shows $J_{\mathrm{sc}}$ as a function of light intensity under open- and short-circuit conditions. While the current increases with the laser intensity, a negligible difference was observed between the open- and short-circuit conditions. This can be understood by the unilluminated InGaP subcell, which prevents the current flow through the InGaP/GaAs subcell even under the short-circuit condition. In addition, the LC efficiency of the InGaP/GaAs//InGaAsP tandem solar cells was estimated as $\sim {10}^3$ for the luminescence from the GaAs to InGaAsP subcells.

Fig. 6

(a) Current–voltage curves for different 780-nm laser intensities under open- and short-circuit conditions and (b) $J_{\mathrm{sc}}$ as a function of light intensity. (c) Current–voltage curves for different 660-nm laser intensities under open- and short-circuit conditions and (d) $J_{\mathrm{sc}}$ as a function of light intensity.

Figure 6(c) shows the current–voltage curves for different 660-nm laser intensities under the open- and short-circuit conditions of the illuminated top GaInP/GaAs subcell. Figure 6(d) shows $J_{\mathrm{sc}}$ as a function of light intensity. While the LC current increases with the laser intensity, the current under the open-circuit condition shows higher current density than that under the short-circuit condition. This could be because both InGaP and GaAs subcells are illuminated by the 660-nm laser, thus enabling the current flow through the InGaP/GaAs subcell under the short-circuit condition. As a result, the photocarriers extracted as current increases, whereas the radiative carrier recombination decreases, resulting in reduced LC current under the short-circuit condition. This is consistent with the results that the LC current depends on the bias voltage applied to the subcell emitting luminescence, as shown in Fig. 5.

3.4.

Impact of the Coupling Between the Subcells to Power Extraction

Finally, we discuss the impact of LC between the subcells on the power extraction in the three-terminal tandem solar cells. Although the LC of the devices used in this work is negligible, some devices show a significantly high LC efficiency.²⁶ The higher LC can modify the maximum power condition in the three-terminal tandem solar cells. As an example, we consider the power extraction of the three-terminal tandem solar cells with high LC efficiency. We used LC efficiency $\alpha$ defined as $J_{\mathrm{LC}}=\alpha J_{0,\text{top}}\exp (q{V}_{\text{top}}/k_{\mathrm{B}}T)$, where $J_{\mathrm{LC}}$ and $J_{0,\text{top}}$ are the LC current generated in the bottom subcell and the saturation current determining the dark current of the top subcell, respectively. The currents for the top and bottom subcells are given as