Room Temperature Operation of a Quantum Ratchet Intermediate Band Solar Cell

An intermediate band solar cell which generates photocurrent due to sequential absorption of two sub‐bandgap photons at temperatures up to 300 K was realized. The intermediate band is comprised of a “quantum ratchet” semiconductor nanostructure which is designed to store the photoelectron in a long‐lived state that allows for efficient optical re‐absorption; it incorporates a potential barrier designed to both increase the confinement of electrons and reduce thermal escape. This leads to extended electron lifetimes in the ratchet state and room temperature operation. At low temperature (≈12 K), electrons exhibit a ratchet state lifetime of τRB > 100 s, representing an increase by a factor of ≈107 over a device without the barrier.


Introduction
Intermediate band solar cells (IBSCs) have been proposed as a means of exceeding the %31% theoretical Shockley-Queisser limit on single bandgap photovoltaic power conversion efficiency. [1,2] A third set of energy states is introduced between the valence band (VB) and conduction band (CB) often termed "Intermediate Band" (IB), so that electrons can be promoted from the VB to CB by the sequential two-photon absorption (STPA) of photons with energies below the bulk bandgap, in a way that generates additional photocurrent and increases the theoretical efficiency limit to 46.7% under one sun. [2] A number of physical implementations have been trialed, [3][4][5][6][7] however, the presence of the IB often leads to additional non-radiative recombination channels. [8][9][10][11][12] Vaquero-Stainer et al demonstrated the successful operation, albeit at low temperature, of a quantum ratchet IBSC (QR-IBSC) using a quantum well superlattice (QWSL). [13] This approach involved adding a set of "ratchet band" (RB) states, into which the electrons scatter irreversibly, at the cost of a small energy penalty, ΔE. Electrons in the RB are long lived, being optically isolated from photogenerated holes in the VB (Figure 1a) and the irreversible nature of the scattering. The fact that the RB is a 2-dimensional subband with well-defined wavevector, and not a localized state, frustrates non-radiative recombination channels that have historically plagued so-called impurity photovoltaic devices. [14] This leads to a theoretical limiting QR-IBSC efficiency of 48.5% under one sun. [15] In the device of Ref. [13], hereafter referred to as the VSD (Vaquero-Stainer Device)the in-built field in the QWSL spatially separated electrons from holes, (Figure 1b), driving them into the final QW which forms the RB. Here they exist in a long-lived state, the recombination with VB holes being suppressed by the spatial separation.
Here we study an extension of the VSD design, a so-called HBD (High Barrier Device)with a modified (Figure 1b) design that increases the RB state lifetime, τ RB, to the point where room temperature operation becomes possible. The design is similar to the VSD, [13] but with an extra 2 nm thick layer of AlAs inserted between the final quantum well of the QWSL (the RB) and the wide layer of Al 0.3 Ga 0.7 As (the CB). This AlAs barrier increases the confinement of electrons in the RB, reducing thermal escape. As before, we insert an In 0.05 Ga 0.95 As layer in front of the nanostructure, chosen to have the lowest bandgap in the device, so that the VB-IB transition can be excited selectively. Photoelectrons tunnel through the QWSL into the RB, where a second photon can be absorbed in an inter-subband transition (ISBT), which must be driven by p-polarised light due to the dipole selection rules for such transitions. [16,17] Figure 1b shows the band structure and the sub-bandgap optical transitions in the HBD.
While room temperature two-photon photocurrent (TPP) results have been reported previously, [4][5][6][7][18][19][20][21] they were measured with steady state illumination schemes whose validity has come into question due to the likelihood of thermal artefacts. [22] Here we developed a high-speed double-demodulation two-photon spectroscopy setup (see Experimental Section) to measure the TPP, and to verify that its dynamical characteristics evidenced an electronic and not a thermal origin. We measured an RB state lifetime in the HBD of τ RB > 100 s at 12 K. This is an DOI: 10.1002/solr.202200897 An intermediate band solar cell which generates photocurrent due to sequential absorption of two sub-bandgap photons at temperatures up to 300 K was realized. The intermediate band is comprised of a "quantum ratchet" semiconductor nanostructure which is designed to store the photoelectron in a longlived state that allows for efficient optical re-absorption; it incorporates a potential barrier designed to both increase the confinement of electrons and reduce thermal escape. This leads to extended electron lifetimes in the ratchet state and room temperature operation. At low temperature (%12 K), electrons exhibit a ratchet state lifetime of τ RB > 100 s, representing an increase by a factor of %10 7 over a device without the barrier.
increase by seven orders of magnitude over that measured by Vaquero-Stainer et al. in the VSD, [13] and the lifetime enhancement meant that we were able to measure a TPP in the HBD at temperatures up to 300 K. Figure 2a shows the 12 K photoluminescence spectrum of the HBD when illuminated with 600 nm light. The peak at %850 nm corresponds to emission from the In 0.05 Ga 0.95 As absorption layer; there are no features at longer wavelengths, confirming that the In 0.05 Ga 0.95 As layer has the smallest bandgap in the device. The signal at shorter wavelengths corresponds to transitions in the QWSL layers. Figure 2b then shows the photocurrent-voltage curve of the device under illumination by a single beam of 850 nm lightmodulated at 22 kHz and detected with a lock-in detection schemefor a range of temperatures from 20-300 K. There is a zero-photocurrent plateau at every temperature, indicating that the barrier is successfully keeping electrons trapped in the RB, even at 300 K.

Results
The zero-photocurrent plateau that occurs at about 0.7 V bias corresponds to a regime where there is enough field in the structure to drive the photoelectrons from the IB to the RB, but not enough to cause them to be extracted from the RB to the CB. The RB fills with a population of Figure 1. Operating principles of a QR-IBSC and band structure of the "high barrier device" (HBD). a) Band structure schematic. Photoexcitation is possible directly between valence band (VB) and conduction band (CB), as well as between VB and intermediate band (IB) or between ratchet band (RB) and CB by absorption of a sub-bandgap energy photon. Electrons in the IB irreversibly relax into the RB due to a deliberate energy loss ΔE. Recombination between RB and VB can be suppressed by design, dramatically extending the ratchet band state lifetime, τ RB . b) Band structure simulation of the High Barrier Device (HBD) investigated here. A layer of In 0.05 Ga 0.95 As serves as a dedicated VB-to-IB absorption layer. An electron in the IB is scattered through a GaAs-Al x Ga 1Àx As quantum well superlattice (QWSL) by the in-built electric field across the junction, spatially separating the electron and hole. Once trapped in the final well of the QWSL (our RB), a second photon excites the electron in an inter-subband transition (ISBT). When this ISBT is driven by lower energy photons (λ = 8.20 μm in this work), the electron then tunnels through the high AlAs barrier into the CB. When the ISBT is driven by highenergy photons (λ = 2 μm in this work), the electron is excited to an energy above the top of the barrier and is able to pass directly into the CB. Single-photon characterization of the HBD. a) Photoluminescence spectrum at 11 K and zero bias, under 600 nm illumination. The peak at %850 nm corresponds to the In 0.05 Ga 0.95 As absorption layer, with no features at longer wavelengths. The emission at shorter wavelengths originates in the layers in the QWSL. b) Photocurrent-voltage curves for the HBD under illumination by 850 nm light for temperatures of 20-300 K. A zero-photocurrent plateau can be seen when the applied bias levels out the in-built electric field by just enough to trap electrons in the RB. In the Vaquero-Stainer Device (VSD), two-photon photocurrent (TPP) was only observed in the temperature-and bias-ranges in which this plateau occurs. In this HBD, the plateau persists right up to 300 K.
www.advancedsciencenews.com www.solar-rrl.com trapped electrons. These can be photoexcited out of the RB by the subsequent absorption of a mid-IR photon in a STPA process. As the temperature is raised thermal escape from the RB increases, and this has the effect of narrowing the voltage range over which the RB trapping is effective, as evidenced by the fact that the voltage width of the photocurrent plateau shrinks; it starts at higher forward biases, and returns to non-zero values at lower bias values. In previous experiments by Vaquero-Stainer et al., TPP was only observed when the device was biased at a voltage within the plateau range. [13] 2.1. Two-Photon Photocurrent at 12 K The device was illuminated with two lasers simultaneously: one beam incident on the front of the device, driving the interband VB-to-IB transition, the other incident on the back of the device, driving the intraband RB-to-CB transition. See Experimental Section for details of the setup and the various laser modulation schemes. Figure 3a,b show the TPP as a function of the bias voltage, with the device held at %12 K. The interband transition was driven by λ 1 = 850 nm light, with a pulse energy of %0.4nJ, while the intraband transition was driven by λ 2 = 8.20 μm light. The TPP was first measured (Figure 3a) at the 5 kHz differencefrequency of the laser pulse rates (30 kHz/25 kHz for the 8.20 μm/850 nm beams respectively)), then at the 30 kHz pulse rate of the λ 2 = 8.20 μm intraband beam ( Figure 3b). The results in Figure 3a,b show that, at this temperature, the TPP in the HBD peaks at a bias of %0.65 V, similar to the VSD (0.64 V). [13] Henceforth, unless otherwise specified, all HBD measurements were made at this optimum 0.65 V bias.
With the intraband beam still fixed at λ 2 = 8.20 μm, the red trace in Figure 3c shows the TPP in the HBD as a function of the interband wavelength at 12 K, normalized with respect to both photon energy and spectral power variation of the laser. There is some photocurrent generation at high photon energies, with a peak at λ = 840 nm, before steeply falling off at wavelengths beyond the In 0.05 Ga 0.95 As bandgap. With the interband beam then fixed at λ 1 = 850 nm, the black trace in Figure 3c shows the normalized TPP as a function of the wavelength of the intraband beam, peaking at λ = 8.20 μm. The data in both traces in Figure 3c were measured with a lock-in working at 50 kHz pulse rate of the λ 2 = 8.20 μm intraband beam as the extremely long RB lifetimes meant that the electron density could not follow the λ 1 = 850 nm interband excitation under these experimental conditions. From a PV device point of view, a key shortcoming of the VSD was the saturation of the TPP as the interband pulse energy was increased. [13] Figure 3d shows the TPP as a function of interband pulse energy at %12 K in the HBD. Both the lasers were driven with signals originating from the same 25 kHz source but the pulse trains were subsequently divided down to give modulation envelopes of 5 and 6.25 kHz, and the TPP was measured with a lock-in at the 1.25 kHz difference-frequency. An electronic delay was imposed between the trigger signals to ensure the pulses from each laser arrived at the device in synchrony. In this case, the saturation of the TPP begins at a pulse energy of %0.15 nJ (vs %0.25 nJ in the VSD [13] ), and decreases as the pulse energy is increased beyond %0.5 nJ. This is consistent with the idea that a large electron population is built up in the RB as the electrons live for very much longer than the 40 μs laser pulse repetition period.
The low temperature RB intermediate state lifetimes, τ RB , proved to be much longer than the longest pulse separation available. To study their temperature dependence, the device was biased at a value, 1.10 V, that was within the single-photon photocurrent plateau at all temperatures (Figure 2b), and both laser pulses were synchronized to arrive at the sample simultaneously at a 22 kHz rep. rate. The intraband beam wavelength was decreased to λ 2 = 2 μm to excite electrons above the top of the barrier. This λ 2 = 2 μm beam was mechanically chopped at 510 Hz, and the sample was illuminated with the λ 1 = 850 nm beam for 20 s, after which the TPP was logged (with a lock-in detecting at 510 Hz), once a second for 10 min (Figure 4).
The 12 K τ RB values of several minutes were %7 decades longer than the %10 μs figure found in the VSD. [13] At higher temperatures the HBD τ RB values decrease monotonically, until, by %250 K they are too short to be measurable with this simple technique. However, we see a non-zero TPP, even at room temperature.

Two-Photon Photocurrent at 300 K
In contrast to the low temperature data, at 300 K the TPP signal was present at a wide range of sample biases outside the singlephoton plateau, as shown in Figure 5a. Moreover, blocking the λ 1 = 850 nm interband beam only reduced the TPP signal by %50% at 300 K, whereas it is virtually eliminated it at low temperatures with the λ 2 = 8.20 μm laser setup. This is because the 300 K experiment is sensitive to the fact that the 2 μm beam comes from a filtered supercontinuum source and sits on top of an incompletely rejected visible background that can be readily absorbed throughout the whole device structure to partly populate the RB. We surmise that the energy received by the trapped electrons from the λ 2 = 2 μm photons in the 300 K experiment is great enough that any small electric field that acts to drive the electrons into the CB for extraction is sufficient, even at high biases, where the bands are nearly flat. Meanwhile, at low biases (strong fields across the junction), the barrier prevents some escape, so the two-photon channel still generates enough of an additional current that it is comparable to that generated at plateau biases, and so is still visible under this measurement setup. Figure 5b shows the room temperature TPP as the pulse energy (and average power) of the 2 μm intraband beam was varied. The interband wavelength was fixed at 850 nm, and the device was biased at 0.85 V (so chosen because it is at the low-bias edge of the single-photon plateau at 300 K, and the 12 K TPP was found to be maximal at such a bias in both the HBD and VSD [13] ). In this case, the TPP grows superlinearly www.advancedsciencenews.com www.solar-rrl.com with the intraband pulse energy over all the intensity range that was accessible to us. This suggests that the TPP at room temperature could be increased further if the setup were modified to produce more energetic 2 μm pulses. The polarisation dependence of the TPP measured with this single-demodulation method (i.e., with both lasers pulsed at 22 kHz, and the λ 2 = 2 μm beam mechanically chopped at 510 Hz) showed a > 20:1 extinction ratio, falling from %26 pA (p-polarised) to %1.2 pA (s-polarised). This was also checked in separate double-demodulation experiments with both beams chopped, the λ 1 = 850 nm interband beam at 480 Hz, and the λ 2 = 2 μm intraband beam at 510 Hz, with the TPP signal detected at the 30 Hz difference-frequency. In this case the TPP dropped from %0.7 pA using p-polarisation to below the %0.1 pA noise floor using s-polarisation. This demonstrates that the measured signal at 300 K is strongly reliant on an ISBT, and is therefore a result of STPA.

Numerical Analysis of Device Operation at 12 K
At 12 K, the TPP peaked at a value of %140 pA, while the singlephoton photocurrent, under the same conditions, was %14 nA. This corresponds to a raw increase of %1% from STPA in the HBD. This compares with the %0.50% for the VSD. [13] Figure 1 as a function of applied bias voltage, laser wavelengths, and interband pulse energy. As measured using a double-demodulation technique (see Experimental Section) the λ 2 = 8.20 μm intraband laser was modulated at 30 kHz, and the λ 1 = 850 nm interband laser modulated at 25 kHz, with the TPP signal lock-in detected at the 5 kHz difference-frequency. b) A single-demodulation measurement, detecting at the 30 kHz modulation rate of the λ 2 = 8.20 μm intraband beam. c) The dependence of the 12 K TPP on the wavelength of the interband (red) and intraband (black) beams under a bias of 0.65 V; there are peaks at λ = 840 nm and λ = 8.20 μm in the interband and intraband spectra, respectively. In both cases the wavelength of the fixed laser was held at the TPP peak whilst the other was scanned, and both datasets have been normalized with respect to variation in both photon energy and power output. d) 12 K TPP against interband pulse energy; the TPP saturates at very low pulse energies, %0.15 nJ, of the λ 1 = 850 nm beam. The RB lifetime, τ RB , was separately measured to be many decades longer than the pulse separation in these experiments, with the result that the RB level could be readily filled, with electrons remaining in the RB between successive pulses in a way that would reduce the modulation of the RB electron population and lead to an underestimate of the TPP efficiency. The device was biased at 0.65 V.
www.advancedsciencenews.com www.solar-rrl.com However, taking the %2.5% duty cycle of the λ 2 = 8.20 μm intraband beam into account, we find that the STPA channel results in a %40% increase in photocurrent, (compared with %50% in the VSD). [13] Turning our attention to the 12 K double-demodulation experiments, the TPP peaked at %9 pA, a raw increase of %0.28% by STPA. In this case the λ 2 = 8.20 μm intraband beam was pulsed at 6.25 kHz, with a duty cycle of 3.1 Â 10 À3 , and when this is factored in we see that the STPA channel results in a %91% increase in the photocurrent, i.e., somewhat larger than the %50% VSD value, [13] and allowing practically a doubling of the low temperature photocurrent.
A numerical analysis of the various photocurrents (see Supplementary Note 1, Supporting Information) implies that, at 12 K, %28% of the electrons created in the absorber layer (i.e., by VB-to-IB transitions) get scattered from the IB into . Intermediate RB state lifetime, τ RB, measurements from 50-300 K. Data were acquired with the device biased at 1.10 V, while using a λ 1 = 850 nm and a λ 2 = 2 μm beam to drive the interband and intraband transitions, respectively. Both beams were output by the same laser, pulsed at 22 kHz, with the TPP signal measured at the 510 Hz mechanical chopping frequency of the λ 2 = 2 μm beam. After 20 s, the 850 nm beam was blocked, and the TPP measured as it decreased over ten minutes. For 250 and 300 K, only the first 100 s are shown to highlight the presence of TPP despite the short lifetimes.
www.advancedsciencenews.com www.solar-rrl.com the RB. This is significantly lower than the %57% seen in the VSD. [13] This may be a result of a large electron population being built up in the RB, on account of the extremely long τ RB lifetimes, which is large enough to screen out the built-in fields in the HBD that drive the irreversible IB-RB scattering process. In a similar vein, at 12 K, at the intensity at which the TPP starts to saturate, the nominal electron density created by each λ 1 = 850 nm interband laser pulse in the RB is estimated to be %9.58 Â 10 9 cm À2 (Supplementary Note 2, Supporting Information). This is more than a decade smaller than the nominal density at which TPP saturation began in the VSD. [13] Again, we surmise that adding the barrier in the HBD has increased the effective τ RB values to much larger than the pulse separation in the experiment, so that electrons accumulate in the RB from successive interband pulses and end up in much higher concentrations than this calculation assumes. In view of the fact that τ RB values up to several minutes were measured in the separate timeresolved measurements this effect could very easily account for the order of magnitude discrepancy with the VSD.
Comparing to a calculation in Ref. [23], the optical coupling efficiency of the ISBT in the HBD is estimated as %5.47 Â 10 À6 (Supplementary Note 3, Supporting Information). Being, as it is, directly proportional to the RB carrier concentration, this is also approximately a decade smaller than the corresponding %7.4 Â 10 À5 value for the VSD, [13] but is again likely to be an underestimate due to the assumption that the RB depopulates entirely between pulses.
The %9 pA TPP measured with double-demodulation was obtained using a λ 2 = 8.20 μm intraband beam with an average power of %150 μW. The RB-to-CB scattering efficiency is then %9.07 Â 10 À9 . Accounting for the optical coupling efficiency calculated above, the extraction efficiency of photoexcited carriers is %1.66 Â 10 À3 . This is approximately two orders of magnitude greater than the value calculated for the VSD. [13] However, since the optical coupling of the ISBT has likely been underestimated by at least an order of magnitude, this extraction efficiency is likely to be an overestimate by the same factor. We estimate that when the TPP is maximized at 12 K, only %0.5% of electrons entering the RB are extracted at the CB (see Supplementary Note 4, Supporting Information).

Numerical Analysis of Device Operation at 300 K
At 300 K, the raw fractional increase in photocurrent due to STPA was %0.81%. However, when the 2.2 Â 10 À5 duty cycle of the λ 2 = 2 μm intraband beam is factored in, we find the STPA two-photon channel has increased the photocurrent by a factor of >10 4 . This shows that the two-photon channel vastly increases the photocurrent in the HBD at room temperature.
Approximate calculations indicate an IB-to-RB scattering efficiency of >100%, which, while obviously not the true value, indicates highly efficient scattering through the QWSL in the HBD at room temperature, much more so than at low temperatures. Again this is likely to be due to the fact the at 300 K the τ RB values have fallen to less than the 22 kHz À1 pulse separation so that, unlike at 12 K, electrons are completely swept out of the device between pulses, allowing the built-in fields to be preserved that drive the irreversible IB-RB scattering.
Assuming that the electrons are swept out of the device between pulses, we estimate that, at the point of maximum 300 K TPP, the electron concentration in the RB is just over half the value required to screen out the in-built field, and that RB state-filling is not likely to be having any noticeable effect (see Supplementary Note 5, Supporting Information). Future work should involve measuring the room temperature TPP as a function of interband pulse energy, to further investigate this Figure 5. TPP at 300 K against bias voltage and 2 μm intraband pulse energy. a) 300 K TPP as a function of bias, measured at the 510 Hz chopping frequency of the 2 μm intraband beam. Signal measurements were made with both lasers incident on the device, as well as with each laser blocked in turn, and with both lasers blocked. b) The TPP increases superlinearly with intraband pulse energy, suggesting that even at the maximum pulse energy of the system at this wavelength (1.0 nJ), the RB is not fully emptied by each such pulse. A more intense beam of 2 μm photons should thus produce even more TPP at room temperature. The bias voltage was 0.85 V.
www.advancedsciencenews.com www.solar-rrl.com saturation, especially as the RB electron density approaches that which would screen out the in-built field.
The optical coupling efficiency of the ISBT at 300 K is estimated to be %7.74 Â 10 À5 , similar to the value calculated for the VSD (7.4 Â 10 À5 ). [13] The extraction efficiency of electrons excited in an ISBT is estimated as %9.46 Â 10 À3 . This is slightly higher than that calculated for the same device at 12 K, suggesting the increased temperature, in combination with the more energetic intraband photons (2 μm vs 8.20 μm), allows photoexcited electrons to more easily be extracted into the CB. The 2 μm photons may be so energetic that the transition excites electrons above top of the barrier, allowing them to bypass it during extraction.

Conclusions
We have shown that inclusion of a barrier between the ratchet band (RB) and the CB of a QWSL QR-IBSC can lead to an increase in the RB intermediate state lifetime, τ RB , by a factor of %10 7 at low temperatures, relative to the same device without the barrier. This led to the successful operation of the device at 300 K, representing significant progress in the field of IBSCs.
We estimate that the two-photon channel increases the photocurrent at room temperature by a factor of %10 4 . At both 12 and 300 K, the IB-to-RB scattering was calculated to be extremely efficient, and the extraction efficiency from RB-to-CB of electrons photoexcited in an ISBT was calculated to be two orders of magnitude better than in a device without the barrier.
Future generations of the device should now be developed, whose bandgaps better match the solar spectrum, and with designs which improve the efficiency of photon capture and RB-to-CB extraction.

Experimental Section
Device Design and Fabrication: The device was grown on an undoped GaAs substrate by molecular beam epitaxy. The in-built electric field across the junction was generated by doped layers of GaAs at either end of the nanostructure; these had doping concentrations of 10 18 cm À3 (p-type at front of device) and 2 Â 10 À18 cm À3 (n-type at back of device). After the p-doped region there is a 50 nm buffer layer of undoped GaAs, before the 25 nm thick layer of In 0.05 Ga 0.95 As, which acts as the designated absorption layer for the VB-to-IB interband transition. The nanostructure part of the device consists of six undoped GaAs QWs, with the first four barriers between these QWs being made of Al 0.3 Ga 0.7 As, and the two barriers nearest the CB being made of Al 0.7 Ga 0.3 As. There was then a 2 nm thick layer of AlAs between the last QW (the RB) and the CB forming the high barrier. The CB was formed by a 100 nm thick layer of Al 0.3 Ga 0.7 As. The width of the QWs and the barriers in the QWSL were optimized for electron transport by an annealing genetic optimization algorithm (for details see Ref. [24]).
The wafer was processed into a device with four pairs of mesas in which the p-doped GaAs layer was etched away for front-side optical illumination ( Figure 6a); the measurements presented here involved illumination of a mesa with a 200 μm diameter. Rings of gold (200 nm thick) on titanium (20 nm thick) around the mesa edges formed the front-side electrical contact, with the front of the device metallized with layers of Au/Zn/Au (5/10/ 200 nm thick respectively). The back-side electrical contact was made using a partial etch through to the n-doped region which was then metallized with In-Ge (20 nm) and Au (200 nm), and was then connected to a gold strip.
The back-side of the device was polished to a 45°chamfer ( Figure 6b) in order to refract the intraband beam which was incident on the back of the device. One undesirable consequence of this approach was that optical resonances in the layered sample could distort the mid-IR spectral responses as the mid-IR wavelength was scanned ( Figure 3c in the main text). This direction change meant that the linearly polarised light had some component of its polarisation perpendicular to the plane of the QWs, and could therefore excite the ISBT according to the polarisation selection rules (see Ref. [16,17]).
Experimental Setup: The setup is shown in Figure 7. The front-side of the device was illuminated using a pulsed supercontinuum laser (NKT SuperK COMPACT) with a wavelength range of 400-2000 nm, connected to an acousto-optic tunable filter (AOTF) unit. The AOTF allows the wavelength to be selected to nm precision with a bandwidth of %4 nm. The pulse frequency is tunable in the range 1-28000 Hz, with a fixed pulse width of %1 ns. When illuminating the back of the device with mid-IR photons, a quantum cascade laser (QCL, a Block Engineering LaserTune) was used. The QCL can output a wavelength in the range 6.25-10 μm, with a pulse www.advancedsciencenews.com www.solar-rrl.com frequency of up to 1.5 MHz and a pulse width of 32-496 ns; a pulse width of 496 ns was used for all measurements presented here. The pulse rates of the lasers were often used as the modulation frequency in signal recovery, though optical chopper wheels placed in the beams provided another source of modulation. The beams were independently aligned with the connected mesa, and the TPP signal then maximized with fine alignment. Many of the 12 K data were measured at the 50 kHz pulse frequency of the QCL beam. Although the NKT interband beam was actually pulsed at 22 kHz, at low temperatures the extremely long τ RB RB lifetimes meant that the interband excitation was effectively continuous -wave (CW). At 300 K, the pulses from the NKT supercontinuum were being used to drive both transitions, since the QCL output power was insufficient at the low rep. rates required. The nature of the source meant that both pulses were generated simultaneously, so they could not be triggered at different rates for the difference-frequency double-demodulation experiments (see below). They were both pulsed at 22 kHz, with the 2 μm intraband beam mechanically modulated at 510 Hz using a 50/50 optical chopper; the signal was then detected at this 510 Hz chopping frequency. In these experiments the limited wavelength rejection efficiency of the AOTF unfortunately meant that enough visible light got through to generate a TPP even when the 850 nm beam was blocked (see Figure 5a). In these cases, in order to confirm that sample heating was not influencing the results, additional measurements were made with one or both laser beams blocked and signal amplitudes were carefully checked to be independent of modulation frequency to rule out the possibility of any thermal artefacts.
Further measurements were made using one of a trio of doubledemodulation techniques, whereby the two beams were independently modulated at different modulation frequencies, and the photocurrent was measured at the difference-frequency of the two modulation signals. If one thinks of each beam as being square wave modulated, then the TPP signal we want is that component which is there only when both beams are present. Its temporal profile will be a logical AND of the two individual modulating waveforms and corresponds to simply multiplying the two digital waveforms together. In frequency terms this multiplication of signals varying as ω 1 and ω 2 generates sum (ω 1 þ ω 2 ) and difference (ω 1 À ω 2 ) frequency components, and demodulating the photocurrent signal at either of these with a lock-in amplifier will isolate the TPP. In practice, blocking either or both the beams was always found to make the difference-frequency lock-in output vanish.
This approach also pushes the bandwidth of the measurement up into a frequency regime that can be varied, and also made fast enough to exclude the possibility that the observed TPP signals have a thermal origin. However, due to the extremely long τ RB lifetimes we found, especially at low temperature, electrons persist in the RB even between interband pulses, and the laser pulses only alter the RB population by a small fraction. In this case, detection at the difference-frequency leads to an artificially low signal (similar to the current-matching condition of tandem cells). [25] The first approach had the supercontinuum source pulsed at 25 kHz, with the clock signals sent through 2 digital divider circuits, one dividing by 5, down to 5 kHz, the other by 4, down to 6.25 kHz. Figure 7. Schematic diagram of the experimental setup. The NKT fibre supercontinuum source was used to generate both the λ 1 = 850 nm beam that drives the VB-IB interband transition, and the λ 2 = 2 μm beam that was used to drive the intraband RB-CB transition in the higher temperature experiments. The quantum cascade laser (QCL) was used to generate the λ 2 = 8.20 μm beam driving the RB-CB transition at 12 K. The temperature was maintained using a closed cycle helium cryostat, with resistive wire and a temperature controller. Mechanical chopper wheels in each beam allowed for independent low frequency modulation of the beams. The device was electrically connected to a pre-amplifier, with the signal then passing to a lock-in amplifier (LIA). The reference frequency at the LIA here is shown as the difference-frequency in the modulation signals. Photoluminescence of the device is focused into a monochromator, the output of which hits a photodetector, and this then passes the signal to another LIA.
www.advancedsciencenews.com www.solar-rrl.com These then triggering the two lasers, and the photocurrent was measured at the difference frequency of 1.25 kHz. The second approach, only possible at 12 K when the QCL could be employed, involved the lasers being pulsed at 25 and 30 kHz, with lock-in amplifier (LIA) detection at 5 kHz. A final low-frequency setup involved optical choppers being placed in the two beams, at 480 and 510 Hz, with LIA detection at 30 Hz. When using double-demodulation, the two modulation signals were passed through a digital frequency mixer with a 3rd order Butterworth low pass filter (LPF). The signals were mixed with a Boolean AND, with the output passed through the LPF, which had a cut-off frequency marginally above the difference-frequency of the modulation signals (the cut-off was selected using a switch depending on the modulation frequencies being used). Wherever possible it was verified that the magnitudes of the TPP signals were independent of the modulation frequencies.
The device was mounted on a custom TO-8 header with a hole drilled through the centre for back-side illumination, and secured in a cryostat that allowed for temperatures as low as 12 K, with resistive wire and a temperature controller (LakeShore 331) used to hold the device at intermediate temperatures.
The device photocurrent was monitored with a pre-amplifier (a custom Femto DHPCA-100S) which allowed gains of up to 10 7 V A À1 . Its gain frequency characteristics were switchable and had to be factored in when comparing TPP signals taken at the various modulation frequencies. This output was then sent to a lock-in amplifier (EG&G Ametek 5209), where the signal was recovered at either the difference-frequency or the single modulation frequency of the intraband beam. Photoluminescence from the device was focused into a monochromator (Bentham M300), with a photodetector (Hamamatsu H7422) at its output, which connects to another LIA (Stanford Research Systems SR844).

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.