A quantum ratchet intermediate band solar cell based on a quantum well superlattice is investigated. The design is similar to that of a previously reported device, but it employs a stronger built-in electric field across the heterojunction; therefore, it works at higher illumination intensities before the photocurrent saturates due to photocarrier accumulation screening out the field and causing leveling of the bands. In this present device, saturation of the two-photon photocurrent occurred at a valence-to-intermediate band pulse energy of ∼4 nJ, approximately ten times greater than the previously reported device, making it more suitable for concentrator applications.

Intermediate band solar cells (IBSCs) are one of the proposed methods to exceed the ∼33% Shockley–Queisser limit on photovoltaic power conversion efficiency.1 The inclusion of an additional set of allowed energy states in between the valence band (VB) and the conduction band (CB) provides electrons with a secondary excitation route via the sequential absorption of two sub-bandgap photons2 [Fig. 1(a)]. Unfortunately this intermediate band (IB) usually introduces additional recombination channels that lead to crippling non-radiative recombination.3–8 

FIG. 1.

(a) Operating principle of an intermediate band solar cell (IBSC) using an additional energy band to provide a secondary route for electrons to go from the valence band (VB) to the conduction band (CB). It also provides additional recombination channels. (b) Operating principle of a quantum ratchet IBSC. The electron scatters, with a small irreversible energy loss, ΔE, into a state that is decoupled from the VB, significantly increasing its lifetime and the probability of absorbing a second below-gap photon. (c) Simulation of the energy levels in the device investigated in this work.

FIG. 1.

(a) Operating principle of an intermediate band solar cell (IBSC) using an additional energy band to provide a secondary route for electrons to go from the valence band (VB) to the conduction band (CB). It also provides additional recombination channels. (b) Operating principle of a quantum ratchet IBSC. The electron scatters, with a small irreversible energy loss, ΔE, into a state that is decoupled from the VB, significantly increasing its lifetime and the probability of absorbing a second below-gap photon. (c) Simulation of the energy levels in the device investigated in this work.

Close modal

The quantum ratchet IBSC (QR-IBSC) involves the deliberate loss of a small amount of energy, ΔE, in the IB, such that electrons scatter into a ratchet band (RB), where they are optically decoupled from the VB9 (Fig. 1). The electron and hole are spatially separated, extending the intermediate state lifetime of the electrons, reducing the non-radiative recombination9 and dramatically improving the sequential photon absorption rates.

Vaquero-Stainer et al. demonstrated the correct operation of a QR-IBSC by implementing a quantum well superlattice to spatially separate electrons and holes10 [Fig. 1(c)]. A similar design was later shown to operate at room temperature.11 However, both the device investigated by Vaquero-Stainer et al.10—which shall hereafter be referred to as the VSD (Vaquero-Stainer device)—and the room temperature device—the HBD (high barrier device)—suffered from the saturation of the two-photon photocurrent (TPP) at low intensities, corresponding to a pulse energy of the VB-to-IB light of just 0.3 nJ10 and 0.15 nJ,11 respectively. Here, we present the results of experiments on another QR-IBSC with a stronger built-in electric field across the heterojunction, which leads to a higher TPP saturation point of ∼4 nJ (equivalent to a photon flux density of 5.26 × 10 13 cm 2 per pulse); we shall refer to this device as the SFD (strong field device).

Since a device such as this would, if implemented in a real-world scenario, likely be part of a solar concentrator system, a high saturation limit is an important feature. While this device was only shown to function at low temperatures, it stands as a successful proof of concept for this particular characteristic.

The real-space band structure of the SFD is shown in Fig. 1(c). The VB-to-IB transition is an interband transition in a 25 nm thick layer of In0.05Ga0.95As at the front of the device; this layer has the narrowest bandgap in the sample, allowing us to excite it selectively by tuning the first of the two sub-gap lasers to its bandgap. The photoelectrons then scatter through the superlattice, ending in a metastable state in the RB, which resides in the final (i.e., the rightmost) well of the superlattice. A second sub-gap photon is then absorbed in an intersubband transition (ISBT), driving the RB-to-CB transition.

The microscopic structure for the SFD is identical to that of the VSD (see Ref. 10), except that two end layers are shorter in the former—a GaAs buffer layer at the front of the device [layer 2 in Fig. 1(c)] has been thinned from 50 to 20 nm, and the Al0.3Ga0.7As CB layer [layer 5 in Fig. 1(c)] has been thinned from 100 to 20 nm. The built in junction potential is the same in both devices, so the thinner depletion zone in the SFD results in a proportionately higher field.

Details on the fabrication and macroscopic layout of the device are the same as for the VSD and the HBD, as previously described in Refs. 10 and 11.

A schematic of the setup used is shown in Fig. 2. The device was mounted in a cryostat and cooled to ∼13 K for all experiments presented here. The interband transition is excited by front-side illumination using a fiber supercontinuum source (NKT SuperK Compact), triggered at 25 kHz, with a pulse width of ∼1 ns. The wavelength is selectable in the range 600–2000 nm with a bandwidth of ∼4 nm using an acousto-optic tunable filter. The ISBT is excited by back-side illumination using a quantum cascade laser (QCL) (Block Engineering LaserTune), triggered at 30 kHz with a pulse width of 496 ns; its wavelength range is 6.25–10 μm.

FIG. 2.

Schematic diagram of the experimental setup used in this work. The device was held in a cryostat and illuminated with independently pulse-modulated beams of light from the front (VB-to-IB interband) and the back (RB-to-CB intraband). The modulation trigger signals are passed through a digital mixer with low-pass filter, and the signal is recovered at a lock-in amplifier (LIA).

FIG. 2.

Schematic diagram of the experimental setup used in this work. The device was held in a cryostat and illuminated with independently pulse-modulated beams of light from the front (VB-to-IB interband) and the back (RB-to-CB intraband). The modulation trigger signals are passed through a digital mixer with low-pass filter, and the signal is recovered at a lock-in amplifier (LIA).

Close modal

We detected the TPP with a lock-in amplifier (LIA) via a transimpedance amplifier (Femto DHPCA-100S), using the difference-frequency of the pulses as a reference. This 5 kHz signal was isolated using a digital frequency mixer and a low-pass filter. This ensures the signal measured is only present when both beams are incident on the device, and thus is a result of sequential absorption of two photons. As described in Ref. 11, this frequency mixing double demodulation method allows us to exclude the possibility of thermal artifacts, which can otherwise distort measurements made at low modulation rates or with DC illumination.12 

Photoluminescence spectroscopy was performed by using only frontside illumination by the NKT. The luminescence was focused into a scannable monochromator, with a photodetector at the output. This detector was connected to a second LIA, the reference frequency provided by the NKT trigger pulse train.

The device was illuminated with 600 nm light to excite carriers in every layer of the nanostructure. The resulting photoluminescence spectrum is shown in Fig. 3(a). The key feature of this curve is the sharp peak at ∼850 nm, corresponding to the In0.05Ga0.95As absorption layer, with no features at longer wavelengths. This confirms the lowest energy gap in the device. The smaller, broad peak over the range of ∼780–810 nm results from luminescence by the various layers of the superlattice.

FIG. 3.

(a) Photoluminescence spectrum for the SFD under illumination with 600 nm light with no external bias. (b) Photocurrent–voltage response of the SFD, using a LIA to detect the photocurrent, with 850 nm (red), 650 nm (blue), and no illumination (black); values are normalized for photon energy/laser power.

FIG. 3.

(a) Photoluminescence spectrum for the SFD under illumination with 600 nm light with no external bias. (b) Photocurrent–voltage response of the SFD, using a LIA to detect the photocurrent, with 850 nm (red), 650 nm (blue), and no illumination (black); values are normalized for photon energy/laser power.

Close modal

Figure 3(b) shows the photocurrent–voltage behavior of the SFD under illumination by 850 and 650 nm light, and no light. With 850 nm light—tuned to the In0.05Ga0.95As bandgap—there is a zero-photocurrent plateau in a narrow bias range of ∼1.3–1.5 V. For these biases, the built-in field is reduced to just the right amount for electrons to continue to scatter efficiently through the superlattice, but not to tunnel out of the RB into the CB.

In the VSD, a similar plateau was found to exist at ∼0.4–0.8 V, and TPP was only measured within this bias range,10 while an equivalent feature was also found in the HBD at voltages above ∼0.6 V.11 The stronger built-in electric field across the junction of the SFD means a higher applied bias is required to reduce the field in the junction to the “plateau” region where the TPP generation mechanism works most efficiently.

The experiment was repeated while illuminating the device with 650 nm light, i.e., with photons that are energetic enough to excite electrons throughout the nanostructure. The results are shown in blue in Fig. 3(b). These higher-energy photons generate some photocurrent for all biases, including within the 850 nm plateau region. The magnitude of the photocurrent is decreased by a factor of ∼4 when changing the illumination wavelength from 850 to 650 nm. This is likely to be due to the faster recombination between electrons and holes before being spatially separated, as they exist throughout the nanostructure. Absorption of the high-energy photons in the GaAs layer in front of the nanostructure might also contribute to this observed reduction in photocurrent.

Figure 4(a) shows the variation of the TPP with interband wavelength, with a fixed 8.26 μm intraband beam. The signal is greatest when using a wavelength of 820 nm, rather than 850 nm. This is probably a result of the increased absorption coefficient in the In0.05Ga0.95As layer at the shorter wavelength, which depends on the wavelength, λ, as α ( λ ) ( h c / λ E g ) 1 / 2, for Eg the bandgap.13 It was confirmed that the single-wavelength photocurrent still exhibited a plateau under illumination by 820 nm light (supplementary material, Note 1).

FIG. 4.

(a) Two-photon photocurrent (TPP) as a function of the wavelength of light used to drive the VB-to-IB transition. The ISBT was driven at 8.26 μm. (b) TPP against wavelength of the light used to drive the ISBT, with the interband beam fixed at 820 nm. Data in both graphs were taken with the device biased at 1.36 V and are normalized for spectral variation in laser power/photon energy. (c) Bias-dependence of the TPP in the region of the single-wavelength zero-photocurrent plateau. (d) The TPP as a function of pulse energy/average power of the interband VB-to-IB light, showing the saturation of the signal at a pulse energy of 4 nJ; the device bias was fixed at 1.36 V. In both graphs, the transitions were driven at wavelengths of 820 nm and 8.26 μm.

FIG. 4.

(a) Two-photon photocurrent (TPP) as a function of the wavelength of light used to drive the VB-to-IB transition. The ISBT was driven at 8.26 μm. (b) TPP against wavelength of the light used to drive the ISBT, with the interband beam fixed at 820 nm. Data in both graphs were taken with the device biased at 1.36 V and are normalized for spectral variation in laser power/photon energy. (c) Bias-dependence of the TPP in the region of the single-wavelength zero-photocurrent plateau. (d) The TPP as a function of pulse energy/average power of the interband VB-to-IB light, showing the saturation of the signal at a pulse energy of 4 nJ; the device bias was fixed at 1.36 V. In both graphs, the transitions were driven at wavelengths of 820 nm and 8.26 μm.

Close modal

While there is also TPP at lower wavelengths, there is importantly a sharp drop-off in signal for photon energies below the In0.05Ga0.95As bandgap. High-energy interband photons excite electrons across the bandgap, which scatter into the RB and are excited by the intraband beam. With low-energy interband photons, the VB-to-IB transition cannot be excited, so no TPP is seen. The valley in the TPP at interband photon energies just above the In0.05Ga0.95As bandgap may be associated with optical interference resonances in the device resulting from etaloning in the narrow layers, as well as the competition between increasing fractional absorption in the In0.05Ga0.95As and decreasing amounts of light reaching it through the GaAs capping layer as the wavelength is shortened. All other experiments performed on the SFD were done with an 820 nm interband beam, because significantly larger photocurrents were measured relative to those seen using an 850 nm beam, which had poorer signal-to-noise ratios.

Figure 4(b) shows the TPP in the SFD as a function of intraband wavelength, with a fixed interband wavelength of 820 nm. Scanning over the full range of wavelengths available showed a sharp peak at ∼8.2 μm (supplementary material, Note 2). Figure 4(b) shows the TPP measured only within the region of this peak. The TPP is maximized using a wavelength of 8.26 μm. Importantly, this signal also drops sharply at longer wavelengths. Photons with λ > 8.26 μ m are not energetic enough to excite the ISBT at all. Non-zero TPP at shorter wavelengths results from higher-energy photons exciting the transition non-resonantly.

The wavelength of 8.26 μm was thus used to excite the ISBT in the SFD for all other experiments. It is worth noting that, despite the nanostructure in this device being identical to that in the VSD, the energy of the ISBT is not expected to be the same in the two devices, as the electric field across the junction is different (the quantum-confined Stark effect14).

Figure 4(c) shows the TPP as a function of the applied bias voltage. There is a sharp increase from zero TPP at biases near the start of the single-wavelength photocurrent plateau, before which electrons are scattered through to the CB without optical excitation. The TPP peaks at a bias of 1.36 V, and as the bias is increased further, the net electric field across the junction drops to a point where the scattering efficiency of electrons through the superlattice starts to be significantly reduced, and the TPP drops off. This is consistent with the results of the same experiment on the VSD, which was also found to have a maximum TPP near the low-bias edge of the zero-photocurrent plateau.10 

Figure 4(d) shows the TPP as a function of the pulse energy/average power of the interband beam. The area of the laser spot incident on the device, and of the mesa on which the light was incident, was the same for both devices. While the signal clearly still saturates at the lower end of the range of pulse energies used, the key element is the value at which this occurs. The TPP in the SFD saturates at an interband pulse energy of ∼4 nJ. This is a tenfold increase over the ∼0.3 nJ at which the VSD saturated,10 and 20 times that found in the HBD.11 This is a significant improvement and demonstrates that increasing the strength of the built-in field across the junction successfully raised the saturation limit. Other experiments on the SFD were done using a pulse energy of 4.2 nJ, right on the cusp of the saturation, giving the largest photocurrent without over-filling the RB.

Measuring the TPP at different device temperatures, it was found to vanish for temperatures above ∼50 K, and to be maximized for temperatures below ∼20 K, as was the case for the VSD10 (supplementary material, Note 3).

The maximum TPP measured in the SFD was ∼10 pA at a bias of 1.36 V, at which the single-wavelength photocurrent was ∼1.42 nA. This corresponds to a time-averaged fractional increase in photocurrent of ∼0.70% (vs ∼0.50% for the VSD10 and ∼1% for the HBD11). We expect all the TPP to be produced during the intraband pulses due to the short timescales of ISBTs.15 The intraband beam had a duty cycle of ∼1.5%, meaning the two-photon channel increases the photocurrent by ∼48%. This is very similar to the ∼50% for the VSD,10 but less than the 91% observed at this temperature in the HBD.11 

Illuminating the device with ∼101 μW of 820 nm light led to an estimated maximum single-wavelength photocurrent of ∼2 μA (supplementary material, Note 4). This indicates an external quantum efficiency (EQE) of ∼2.99%. This is significantly greater than the ∼0.98% found for the VSD10 and the 0.47% for the HBD.11 The use of 820 nm light, compared to the 850 nm used in Refs. 10 and 11, accounts for this.

We estimate that ∼5% of incident 820 nm photons excite electrons in the In0.05Ga0.95As layer, of which ∼66% are scattered into the RB (supplementary material, Note 5). This value excludes electrons, which might be excited in the p-doped contact layer of GaAs, as these electrons have a large amount of material through which to scatter to even reach the nanostructure. This cannot be directly compared to the ∼50% scattering efficiency in the VSD10 due the different excitation wavelengths. We simply conclude that the stronger built-in electric field does not significantly impede the IB-to-RB scattering. This is because the built-in field is largely screened out by the applied voltage in both devices at their operating points, so the net field across the junction is much the same in each case (supplementary material, Note 6).

The TPP in the SFD saturated at a pulse energy of ∼4 nJ of 820 nm light. This would correspond to an electron concentration in the RB of n RB 1.57 × 10 12 cm 2 (supplementary material, Note 7), compared to an equivalent value of ∼ 1.3 × 10 11 cm 2 in the VSD.10 This would appear to confirm the tenfold increase found earlier by looking at pulse energies; however, we believe the true steady state value of n RB is lower than this, because this would be enough charge density to more than completely screen out the electric field driving the IB-to-RB scattering.

Indeed, the electric field across the SFD junction at its operating point is estimated as 6.2 × 10 6 Vm 1, within 3% of that in the VSD at its own operating point (supplementary material, Note 6). This would be fully screened out by an RB electron concentration of n flat 4 × 10 11 cm 2. The apparent concentration at which saturation is observed is therefore ∼4 times that needed to level the bands completely (supplementary material, Note 8). We thus suppose that, in reality, n RB n flat. This discrepancy, and the observed tenfold increase in the saturation limit, could be a result of rapid extraction of these trapped electrons, or of some electrons quickly leaking out of the RB. We also believe that this flattening of the bands is the main cause of the saturation, as state filling in the RB is not significant (supplementary material, Note 9).

We therefore take n RB = n flat 4 × 10 11 cm 2, which leads to an estimated optical coupling efficiency of the ISBT of 0.02% (supplementary material, Note 8). This is of the same order as the ∼ 7.4 × 10 5 for the VSD,10 slightly lower as a result of the increased RB occupancy. The efficiency with which electrons excited in an ISBT are extracted to the CB is estimated as 2.25 × 10 5 (supplementary material, Note 10). This is again very similar to—but slightly lower than—that in the VSD ( 3.9 × 10 5),10 despite the stronger built-in electric field. This is because, at their operating points, both the SFD and the VSD have very similar fields across their junctions.

We have shown that by increasing the strength of the built-in electric field of a QR-IBSC, the interband pulse energy at which the two-photon photocurrent saturates is increased by a factor of ∼10. Calculations show that the probable cause of the saturation remains the screening of the field due to charge accumulation in the RB, despite the built-in field being more than twice the strength of the previous device.

Extraction of electrons from the RB to the CB was estimated to be of the same order as in the first prototype, and remains a limiting factor of these devices. Operation only at low temperatures also persists as a shortcoming; however, this has been shown to be mitigated using another structural design change.11 Combining this with the increased built-in field should be investigated in future.

See the supplementary material for graphs that are useful to support the data presented in the main text, while not necessary to communicate the key results of our findings. Also, the details of the calculations done in the analysis are presented.

The work was funded by the UK Engineering and Physical Sciences Research Council, Grant No. EP/K029398/1. Devices were fabricated at the National Epitaxy Facility by Rob Airey, Saurabh Kumar, Edmund Clarke, and Ken Kennedy.

The authors have no conflicts to disclose.

Kenneth M. Hughes: Data curation (lead); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (lead); Writing – original draft (lead); Writing – review & editing (equal). Megumi Ito: Conceptualization (supporting); Methodology (equal); Software (supporting). Anthony Vaquero-Stainer: Conceptualization (supporting); Methodology (equal); Software (supporting). Nicholas J. Ekins-Daukes: Conceptualization (equal); Methodology (equal); Supervision (supporting). Chris C. Phillips: Conceptualization (lead); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material