1. Introduction

The triple-junction solar cells are considered the de facto standard solar cell design to achieve high conversion efficiencies, exceeding those of single-junction solar cells as calculated by the detailed balance method [1–3]. Although solar-cell fabrication techniques have been continuously improved, the material quality is still an important factor [4, 5]. To further enhance conversion efficiencies, it is necessary to clearly identify the loss mechanisms involved. Optical characterization techniques are very useful for this task.

The standard characterization techniques measure the current–voltage (I–V) curves, external quantum efficiency (EQE), and electroluminescence (EL) of a given solar cell device [6–12]. The electrical conversion efficiency of a tandem solar cell can be evaluated directly, however, information regarding the subcells (i.e., the individual junctions comprising the tandem cell) is difficult to obtain. In this context, an optical method has been proposed to directly extract information regarding the electrical properties of the subcells [13]. This technique uses the photoluminescence (PL) decay time constants to examine charge separation and recombination in the subcells and the upper limit of the carrier-collection efficiency [8, 14] for short circuit has been measured [13].

The excitation-wavelength dependence of the PL spectra and decays is useful to investigate the photocarrier dynamics in different regions of the subcell junction. By clarifying the details of the photocarrier dynamics and their relation with the excitation power, further knowledge of the charge separation in the subcells under different operation conditions can be obtained.

In this work, we investigate the excitation-wavelength and power dependence of PL decays from an InGaP subcell in a triple-junction InGaP/GaAs/Ge solar cell. Three characteristic time constants are obtained in the limit of low and high excitation powers. At low excitation powers, we observe a fast time constant τ₁, and at high excitation powers, we observe two time constants: an initial slow decay τ₂ and a final fast decay τ₃. The excitation wavelength dependence evidences that PL from the top layers provides the information of the charge separation. The time constant τ₃ is identified to be the charge-separation time constant at high junction voltages. Our all-optical method allows to determine the electrical conversion efficiency of the subcell at short circuit condition and close to the point of maximum power. The obtained values are consistent with the previously determined upper limit and results from electrical measurements.

2. Results

2.1. Experimental details and sample characterization

The triple-junction solar cell examined in this study consists of a bottom Ge junction, middle GaAs junction and top InGaP junction [15]. These subcells are connected by tunnel junctions, and further, to reduce surface recombination, a high-Al-content AlInP window layer is grown on top of the InGaP junction. In this work, we used a regenerative-amplifier Yb:KGW laser with an optical parametric amplifier (200kHz) for excitation, and a streak camera with a monochromator and short- and longpass-filter sets for detection. The optical measurements were performed under open-circuit conditions. All measurements were performed for a spot size with full-width at half maximum value of ≈100 μm.

The time-integrated PL for excitation at 360 nm is shown in Fig. 1(a), together with the InGaP and GaAs subcell EQE values, as determined from the standard procedure [16]. The PL peak at 685 nm corresponds to the InGaP layer. The broad peak at 425 nm is attributed to the AlInP donor-acceptor PL of the window-layer [17]. For an excitation photon flux of about 4.8 × 10¹² photons/cm² pulse, the window-layer PL peak intensity is about a thousand times weaker than that of the InGaP layer. The window and InGaP layers determine the EQE drop at short and long wavelengths, respectively. The distinctive EQE peak at about 500 nm is attributed to the increasing absorption loss in the InGaP layer starting from excitation with λ_ex > 500 nm, i.e., the transmission to the middle GaAs subcell. The absorption by GaAs is supported by the onset of the GaAs EQE.

 

Fig. 1 (a) PL from the InGaP subcell and the window layer, compared with the InGaP and GaAs subcell EQEs. (b) PL time decays for low (red) and high (blue) excitation powers. The important PL contributions are indicated.

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The representative InGaP subcell PL decays for two different excitation power densities at λ_ex = 530 nm are shown in Fig. 1(b). The PL decays are integrated over a range of 625–725 nm. For excitation with low powers (red curve), we observe an initial ultrafast decay (τ < 30 ps), followed by a single exponential fast decay with a time constant τ₁ = 55 ps. The initial ultrafast decay cannot be resolved by the streak camera. We consider that this ultrafast decay is due to very fast surface recombination. For high excitation powers (blue), a slow decay (τ₂ = 6.5 ns) is observed, which extends to an interval of about 10 ns. This slow decay is subsequently followed by a final fast decay with a time constant τ₃ = 1 ns. The PL intensity of the transition from decay τ₂ to τ₃ is indicated by the notation I_2→3.

Bulk Shockley-Read-Hall (SRH) recombination can result in power dependence of PL decays which are qualitatively the same as observed here, [18] but important details cannot be explained: the fast decay at high powers (τ₃) is more than ten times slower than that at low powers (τ₁). Theoretical analysis of charge separation in a pn-junction showed trends very similar to our experimental data. [19] This fact favors the charge-separation model, but there is no experimental evidence against contribution from SRH recombination.

In case of negligible SRH recombination, the time constants could directly provide the charge separation efficiencies at different bias conditions. [13] For optimization of the subcell we thus require clear experimental evidence for or against the SRH model. Since in the SRH model the fast decays at low and high excitation powers are governed by the physics of the minority carrier, their excitation-wavelength dependences have to be similar. The excitation-wavelength dependence can clarify if the time constants are governed by charge separation or not. For the excitation-wavelength dependence we determined the values of τ₂ and τ₃ at a constant photon flux 4.8 × 10¹² photons/cm² pulse and τ₁ for a flux of 1.1 × 10¹² photons/cm² pulse. These values were chosen to obtain the lower and upper limits of the time constants.

2.2. τ₁ – charge-separation time constant for short-circuit condition

The excitation-wavelength dependence of τ₁ is indicated by the red dots in Fig. 2(a). For short wavelengths below 400 nm, the absorption of the window layer strongly affects the PL intensities and decay dynamics. Therefore, we discuss only the PL decays for excitation between 400 and 590 nm. From 400 to 460 nm, τ₁ is almost constant at 120±20 ps. Further, τ₁ is also constant from 510 to 590 nm, but considerably smaller (55 ± 5 ps).

 

Fig. 2 (a) Excitation-wavelength dependence of time constant τ₁ and the corresponding integrated PL intensity of the τ₁-decay component. The red and blue solid lines serve as a visual guide. Inset: PL spectra for excitations at 440 (blue) and 530 nm (red). (b) Wavelength dependence of τ₂ and the corresponding integrated PL intensity of the τ₂-decay component. Inset: PL spectra for excitations at 420 (blue) and 530 nm (red).

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The above behavior of τ₁ is further characterized with the integrated PL intensity data of the τ₁-decay component, indicated in Fig. 2(a) by means of the the blue open circles. Note that the PL intensity scale is logarithmic. We observe small intensities for excitation with λ_exc < 480 nm, and considerably larger intensities for λ_exc > 480 nm. From the inset, we note that at the same time, the time-integrated PL spectra of the τ₁-decay component for excitation with λ_exc <480 nm exhibit a PL peak at 685 nm, but this peak locates at 655 nm for λ_exc > 480 nm. This trend indicates that for short wavelengths, the thin top n- or i-layer is excited, and PL from this region is observed. For long-wavelength excitation, the thick p-layer is mainly excited, and PL from this region is observed. It is well-known that a strong shift in the PL spectrum occurs for the p-doped layer, which is a result of disordering [20].

Two distinct τ₁ values have been observed, accompanied with a shift in the PL spectrum and PL intensities. This is a distinct feature of PL that occurs during charge separation, i.e., PL from the region with dominant absorption. For excitation with λ_exc < 480 nm, the PL corresponding to the τ₁-decay component is mainly from the n- or i-layer. The considerably faster decay for λ_exc > 480 nm can be either due to faster carrier recombination in the p-layer, or due to faster charge separation. Since the onset of the direct excitation of GaAs in Fig. 1(a) (EQE onset at about 480 nm) coincides with the change in τ₁, the latter explanation appears plausible.

2.3. τ₂ – carrier recombination time constant at flat-band condition

The red dots in Fig. 2(b) indicate the wavelength dependence of τ₂. The decay time is almost constant at 7±0.5 ns with a slight decrease towards λ_exc = 590 nm. The blue open circles in Fig. 2(b) indicate that the total PL intensity of the τ₂-decay component is also nearly constant. The inset shows that the corresponding PL spectra are independent of the excitation wavelength. This data confirms that PL for high photon fluxes is from the top n- or i-layer.

The nearly unchanged PL spectra and τ₂-decay indicate that this process is not influenced by the initial carrier distribution determined by the absorption coefficient. This means that the PL of the decay τ₂ is emitted after the carrier redistribution, i.e., after change in the junction voltage. Since τ₂ remains almost constant for even higher excitation powers, a so-called flat-band condition is reached. Flat band is defined with carrier densities where the electric field is so small that drift is negligible and the intrinsic recombination dominates the decay.

2.4. τ₃ – charge-separation time constant near operating point

The wavelength dependence of τ₃ is shown by means of red dots in Fig. 3. The data indicate an almost-constant τ₃ value of 1 ns with slightly increased values for excitation above λ_exc = 430 nm. τ₃ is almost ten times faster than τ₂, and thus, in the framework of the SRH model, τ₃ should be governed by the minority carrier recombination. Nevertheless, the τ₃ wavelength dependence is completely different from that of τ₁. This evidences that the fast decay τ₁ is governed by charge separation rather than minority carrier recombination. Furthermore, the step at 430 nm reveals that τ₃ is significantly influenced by charge separation, since no such features are observed for the intrinsic recombination time constant τ₂.

 

Fig. 3 Excitation-wavelength dependence of τ₃ (red dots) and PL intensity at crossover between τ₂ and τ₃ decays (blue open circles).

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Due to the recombination during flat-band condition, the carrier density gradually decreases until the flat-band cannot be maintained anymore (Fig. 3, constant I_2→3). Starting from here τ₃ is observed, and the junction transits to the short-circuit condition, through further recombination. However, in high-mobility materials the short-circuit condition can be only reached while charge separation occurs. The τ₃-decay has therefore contributions from both recombination and separation. We consider that the charge separation significantly contributes to the PL decay between reduced and maximum built-in potentials.

The voltage governing the τ₃-decay is estimated from the PL intensities. The quasi-Fermi level splitting in the flat-band region in Fig. 1(b) (blue curve, t = 0) is μ(0ns) = k_BT/q ln I_PL(t = 0) ≤ E_g − 2k_BT. Since the PL intensity at 17 ns is about 300 times smaller, we have μ(17ns) = k_BT/q ln I_PL(t = 0)/300 ≤1.6 V, which is sufficiently close to the operating point of the solar cell. Therefore, τ₃ is the important time constant for evaluating the performance near the operating point.

3. Charge collection efficiencies

Together, τ₁ and τ₂ can be used to determine the intrinsic recombination losses in the junction due to the finite carrier mobility [13]. The carrier-collection efficiency is defined as the fraction of carriers that can be extracted without intrinsic recombination. By using ${\tau }_1^{-1}$ for the charge-separation rate, the carrier-collection efficiency for 0 V (upper limit of EQE) is given as η_c(0) = 1/(1 + τ₁/τ₂). For the present excitation spot size, we estimate a carrier-collection efficiency of 98% at short circuit. Since ${\tau }_1^{-1}$ reflects the drift-limited separation rate, this value represents an upper limit for η_c at the operating point. Under illumination by sunlight the bands are flatter, and diffusion reduces the charge-separation rate. The influence of diffusion on η_c can be predicted using the uniform field approximation [13], as long as recombination by diffusion is not dominant. For all other cases, the diffusion-reduced η_c has to be obtained experimentally using τ₃.

To obtain the diffusion-reduced η_c, it is required to relate the separation rate at high voltages ( ${\tau }_3^{-1}$) with the recombination rate ( ${\tau }_2^{-1}$). Close to the voltage V_m for maximum power we expect η_c(V_m) = 1/(1 + τ₃/τ₂). For the present subcell, this works out to ≈ 1/(1 + 1/7.5) = 88.2%. This value provides the subcell EQE under sun light at V_m, excluding interface recombination, i.e., maximum of EQE in Fig. 1(a). The subcells Shockley-Queisser limit (17%) [12] multiplied by η_c is then the electrical conversion efficiency of the subcell, in excellent agreement with the 15.2% obtained from EL [12]. The value 88.2% is also consistent with that predicted for the point of maximum power using the uniform field approximation [13], indicating negligible recombination by diffusion at V_m.

4. Conclusion

We measured time-resolved PL from the top InGaP subcell of a triple-junction solar cell. Depending on the excitation power, three different time constants were observed. The wavelength dependence revealed that the fast time constants are governed by charge separation rather than minority carrier recombination. The value of τ₁ for short wavelengths reflects the sweep-out of carriers from the i-layer. The slow decay τ₂ represents the dominant non-radiative recombination rate under the flat-band condition. The time constant τ₃ is determined by the charge separation for reduced built-in fields. We propose that τ₃ is of high practical value, since it governs the electrical performance of the subcells at high operating voltages, close to the operating point.