Theoretical TEPL model

Based on our previous study14 we first consider the comparison between TEPL and thermal emitters at elevated temperatures. Figure 1a depicts the evolution of the PL spectrum emitted from a 1.1 eV bandgap material. With temperature increase, the rate of emitted photons is conserved and the spectrum is blue-shifted towards higher energies. This process continues as long as the chemical potential is positive (Fig. 1b, dotted line). When the chemical potential vanishes at T>1,200 K, the emission becomes thermal and the number of emitted photons increases (shown by the red spectrum at 1,300 K). Figure 1b also depicts the high-energy photon rate (E photon >1.45 eV) compared with that of thermal emission at the same temperatures. Evidently, the thermal rate is orders of magnitude lower, and, therefore, not useful in the relatively low temperature regime (T<1,000 K).

Figure 1: The TEPL effect. (a) The evolution of PL spectrum emitted from a 1.1 eV bandgap material as a function of temperature. The blue arrow marks the decrease in the low-energy photon rates while the red arrow marks the increase in the high-energy photon rates. This process continues as long as μ>0 (also seen by the dotted line in b). The last spectrum (in red) is thermal emission, which dominates after μ vanishes. (b) A comparison between the rate of energetic photons (E Photon >1.45 eV) in TEPL (blue) and thermal emission (red), as a function of temperature. The chemical potential is shown by the dotted blue line. It decreases monotonically with temperature and vanishes near 1,200 K. Full size image

For the thermodynamic analysis, we consider a theoretical TEPL device consisting of a thermally insulated, low bandgap TEPL absorber that completely absorbs the solar spectrum above its bandgap (E g,Abs ) as depicted in Fig. 2a. Energetic photon absorption increases the absorber’s temperature by electron thermalization, and induces thermal upconversion of cold electron-hole pairs, as indicated by the arrows. The resulting emission spectrum is TEPL, which, according to equation (1), is described by T high and μ TEPL >0

Figure 2: Energy conversion dynamics and ideal efficiency. (a) The TEPL conversion dynamics. Solar spectrum above E g,Abs is absorbed by the luminescent absorber and emitted as TEPL towards the PV. Sub-bandgap photons are recycled back to the absorber (blue arrow) while above E g,PV photons are converted to current. For an ideal PV, its PL is also recycled to the absorber (grey arrow). (b) Ideal system efficiency as a function of the absorber and PV bandgaps. Full size image

While the thermally upconverted portion of the TEPL above the E g,PV bandgap is harvested by a room-temperature PV, sub-bandgap photons are reflected back to the absorber by the PV cell back reflector, as in state-of-the-art GaAs cells15,16 (blue arrow in Fig. 2a), maintaining the high TEPL chemical potential. The emitted PV luminescence, which in the radiative limit has an external quantum efficiency (EQE) of unity, is also recycled back to the absorber (grey arrow). Thus, the otherwise dissipated thermalization energy of the absorber is converted to increased voltage and efficiency at the PV. The ability to generate both high current (due to the absorber low bandgap) and high voltage paves the way to exceeding the SQ limit, inherently set by the single-junction PV current-voltage tradeoff.

The device thermodynamic simulation is achieved by detailed balance of photon fluxes, based on equation (1). The calculation accounts for the different systems variables, such as the two bandgaps, the solar concentration ratio upon the absorber, the absorber’s EQE, the sub-band photons recycling efficiency (PR) and the PL EQE of the PV. The simulation yields the device’s I–V curve at various operating temperatures, from which the system’s efficiency can be deduced (see Supplementary Note 1).

The simulation results of the maximal theoretical efficiency for each absorber and PV bandgap combination, when all the parameters are set to their ideal values are depicted in Fig. 2b. For each E g,Abs, the efficiency initially increases with the increase in E g,PV , but decreases for higher values due to the tradeoff between voltage gain at the PV and loss of photons due to the reduction in the harvested portion of the spectrum. This tradeoff sets a maximal efficiency of 70% for E g,Abs =0.5 eV and E g,PV =1.4 eV, at a temperature of 1,140 K. Since the bandgaps must correspond to available absorber materials and PV technologies, we proceed with a specific absorber and PV combination of E g,Abs =1.1 eV and E g,PV =1.45 eV, which, as will be experimentally shown, correspond to a tailored rare-earth doped absorber matched to GaAs PV cell. Figure 3a shows the efficiency of such bandgap combination as a function of temperature, for several solar concentration levels while the absorber EQE and PR are set to unity. For one-sun irradiance, two cases are plotted. When the PV cell PL EQE is set to unity, efficiencies above 50% are obtained (blue curve). Interestingly, in this regime it is possible to work at low temperatures (500 K) with 50% efficiency, or at moderate temperatures (1,000–1,300 K), which raise the efficiency to above 57%. When setting the PV PL EQE to 24.5% (highest reported value for GaAs cells17) the curve decreases to a maximal efficiency of 48%, which is obtainable at temperatures higher than 600 K (black curve). It may seem odd that such temperatures are achievable with no solar concentration. However, this is a result of the ideal thermal insulation and photon-recycling. Further quantitative analysis of the efficiency dependence on realistic values of the absorber’s EQE and PR values will be presented at the discussion, where we simulate the efficiency of a practical device. For the 24.5% PV PL EQE case at higher solar concentration levels, the curves are shifted towards higher temperatures and efficiencies above 50% at temperature range 1,000–1,500 K can be obtained. For the unity PV PL EQE case, solar concentration enhance efficiency very little (not shown on graph).

Figure 3: TEPL device thermodynamic analysis. (a) Efficiency-temperature dependence, with ideal parameter settings. The different concentration levels are marked by X, which correspond to the different curves by their colour. For one-sun illumination, the blue curve depicts the efficiency when the PV PL EQE is unity, while for the rest it is set to 24.5%. The red curves shows the system efficiency if the absorber is replaced with a thermal emitter; each curve merges with a TEPL curve of the same solar concentration. (b) I–V curves of the two TEPL systems (24.5 and 100% PV PL EQE), at one-sun illumination, in comparison to a SQ limited cell of 1.1 eV bandgap. The inset shows that the voltage enhancement originates from the absorber’s increased chemical potential. Full size image

For all the cases, the resulted efficiency from a thermal emitter (STPV) operating at the same temperatures is shown by the dotted red curves. The TEPL and STPV curves merge at high temperatures, as also shown in Fig. 1b. Although thermal emission achieves equal efficiencies to TEPL in the relatively high temperature regime, it rapidly decreases with temperature whereas the TEPL’s efficiency plateau achieves much greater efficiencies at the moderate temperature regime.

In order to deepen our understanding on the origin of the efficiency increase, we plot the system’s I–V curves for the one-sun irradiation case in Fig. 3b. For comparison, we also plot a 1.1 eV bandgap, SQ limited PV. It is seen that the while the system’s current is identical to the SQ cell, the open-circuit voltage (V oc ) increase is responsible for the efficiency enhancement, in the two TEPL cases. The 100% PV EQE case shows the highest efficiency due to the recycling of the PV luminescence by the absorber, causing its chemical potential to increase relative to the 24.5% PV EQE case. This is shown by the two curves at the inset, depicting the absorber’s chemical-potential temperature dependence.

Towards a TEPL device realization

Next, we investigate the realization of a practical TEPL device based on the above-mentioned bandgap combination of E g,Abs =1.1eV (1,100 nm) and E g,PV =1.45 eV (850 nm). First, the absorber’s EQE is essential for building up the chemical potential14 and hence for the system’s efficiency. Solid state semiconductors, such as GaAs, excel in EQE at room temperature, but the EQE decreases markedly with temperature due to non-radiative recombination mechanisms18. Additionally, EQE requires photon extraction, which creates an additional challenge to semiconductors because of their high refractive index. Conversely, rare-earth ions, such as neodymium and ytterbium, provide excellent performance because their electrons are localized and insulated from interactions19; this results in the conservation of their high quantum yields at extremely high temperatures, as we have recently shown in a silica:Nd3+ system14. Based on these advantages, our experimental demonstration begins with quantitative measurements of the thermal upconversion efficiency of sub bandgap photons at 914nm, which is the TEPL’s key feature. For this monochromatic excitation experiment, we use an off-the-shelf Nd3+ glass. However, because the Nd3+ absorption spectrum is discrete and its absorption coefficients are low (typically 5–10 cm−1), it must be sensitized to operate under white-light excitation. For a practical TEPL converter, we follow with experimental demonstration of broadband sensitization and upconversion at high temperatures.

Monochromatic TEPL upconversion

The upconverting experiment is described in Fig. 4a. We use a sub-bandgap photon source of 914 nm (1.35 eV), which is absorbed by the Nd3+ 4F 3/2 level, for the photo-excitation and generation of the chemical potential of this level. This light source cannot contribute to the GaAs cell photocurrent, thus making any observed photocurrent induced only by the thermal effect. The heat source is a 532-nm laser pump, which is absorbed by the 4G 5/2 and 2G 7/2 levels. Photon absorption is followed by fast thermalization of electrons to lower energy levels, leading to the sample heating and subsequent thermal upconversion of electrons from the 4F 3/2 level to the 4F 5/2 level, followed by emission of upconverted photons above the GaAs cell bandgap. Figure 4b depicts the experimental set-up. The sample is vacuum-insulated, in an integration sphere. The sample’s emission is shone on the GaAs PV cell and is measured by a calibrated spectrometer (see Methods section).

Figure 4: Experimental TEPL demonstration. (a) TEPL upconversion energy diagram. The Nd3+ system is pumped by a sub-bandgap source of λ=914 nm (relative to the GaAs cell, orange arrow) for PL generation at the 4F 3/2 level. The system is also pumped by 532 nm photons that are absorbed by the 4G 5/2 level, followed by fast thermalization heating the sample. Thermally upconverted photons emitted from the 4F 5/2 level are marked as TEPL, and are harvested by the GaAs cell. (b) Experimental set-up of the Nd3+: glass sample in an integration sphere in vacuum, co-pumped by the 532 and 914 nm lasers. (c) Temperature dependence of the PL spectrum. The 914 nm pump is shown on the right (blue arrow), and the GaAs bandgap is shown by the dotted line. Upon temperature rise, the TEPL spectrum is enhanced. Full size image

First, we turn on the 532-nm laser until the sample’s temperature reaches a steady state. Then, the laser is switched off, and we monitored a negligible current at the PV, which indicates on the sample’s negligible thermal emission. This step is critical because the 532-nm pump induces PL at the probed 4F 3/2 level in addition to the heating effect. Before switching on the 914-nm pump we wait for 1 s, much longer than the PL lifetime of ∼300 μsec (http://www.schott.com/advanced_optics). This ensures that the 532 nm induced PL vanishes. Due to the vacuum thermal insulation, the sample maintains its high temperature upon the introduction of the 914 nm pump. Figure 4c shows the resulting TEPL power spectrum, which is enhanced upon temperature increase. Figure 5a shows the corresponding evolution in the PV I–V curves (produced only by the thermally induced blue-shifted 914-nm pump). Figure 5b shows the upconversion efficiency versus temperature. The red curve shows the upconversion efficiency of the photons from the 914 nm pump to energies above the GaAs bandgap of 1.45 eV (λ<850 nm), as extracted from the power spectrum. Although it peaks at ∼6%, the real PV conversion efficiencies are lower because of the limited PV efficiency. The green plot shows the conversion efficiency of the 1-mm2 cell (which was measured to have η=17% under 1 Sun illumination). Because this cell is far from ideal, the blue line in Fig. 5b shows the calculated efficiency of a state-of-the-art GaAs cell15 (η=28.8% under 1 Sun illumination). Noticeably, even at room temperature a relatively small blue shift is detected, resulting in a 0.3–0.5% efficiency for the tested and state-of-the-art cells. The efficiency peaks at 600 K, with values of 1.4% and 2.5% for the tested and state-of-the-art cell, respectively. As shown, efficiencies deteriorated above 600 K. Such a limit was not observed when rare-earth materials were doped in pure silica, in which temperatures above 1,300 K have been reported14. We thus hypothesize that the silicate glass used for this experiment exhibits thermal degradation of the PL at high temperatures. Extrapolating the experimental results for an Nd:SiO 2 system up to 1,000 K would reach ∼6.7% (see Supplementary Note 2 and Supplementary Fig. 1). In addition, we have measured the sample’s EQE to be ∼30%, whereas Nd3+ doped glasses are reported to achieve PL EQE’s of almost 100% (refs 20, 21, 22) at relatively low Nd3+ concentration levels of 1 wt%.

Figure 5: TEPL upconversion. (a) The GaAs PV cell I–V curves evolution with temperature. (b) Total energy upconversion efficiency (red), ideal cell projected upconversion efficiency (blue) and tested PV efficiency (green) dependence on temperature. Full size image

Broadband TEPL upconversion

We now proceed from monochromatic upconversion to broadband excitation of TEPL. Since an Nd3+ doped absorber is not suitable for white-light harvesting, we fabricated a tailored Cr:Nd:Yb glass absorber (doping concentrations: 0.1:1:0.4 wt%, see preparation details at the methods section), which continuously absorbs sunlight in the visible–near-infrared (NIR) part of the spectrum (400–1,100 nm; see Supplementary Fig. 2 with the association of different spectral bands to the absorbing dopant). The Cr3+ dopant serves as an efficient sensitizer of Nd3+ in the 300–600 nm regime23,24, and the Yb3+ completes the lacking Nd3+ absorption near 1,000 nm, in order to form a continuous NIR band. The room temperature emission of this at 850–1,100 nm will be shifted by the TEPL towards λ<850 nm. At room temperature, the Nd3+ 1,064 nm line does not absorb light, due to its 4-level characteristics. However, at high temperatures the lower level of this transition (4I 11/2 ) is thermally populated by the ground level. At 1,500 K, about 20% of the electrons occupy this level, giving rise to light absorption. Before full white-light excitation, we verify TEPL conversion of this material composition at the 900 nm (Nd3+), 980 nm (Yb3+), and 1,064 nm (Nd3+) bands composing the sub-band regime (850 nm<λ<1,000 nm). Here, in addition to the pumps, which do not heat the sample due to lack of thermalization, we use a CO 2 laser to raise the temperature. Figure 6a depicts this upconversion experiment. The three monochromatic pumps are shown both on the spectrum and at the energy diagram below. The green arrows indicate the TEPL conversion from each of the bands. We qualitatively validate the TEPL conversion by monitoring the spectral evolution with the rise in temperature. The spectral data for the 1,064 nm pump is presented in Fig. 6b, showing the rise in TEPL emission upon the sample’s heating, further validating our claim regarding the 1,064 nm light absorption. We verify that the signal is not thermal emission by switching off the NIR pump and monitoring negligible signal under CO 2 excitation. Similar conversion was observed under the 900 nm excitation as previously shown for Nd3+ alone. The TEPL conversion was also observed for the 980 nm pump, indicating sensitization from the Yb3+ 2F 5/2 level to the Nd3+ 4F 3/2 level, as shown at the energy diagram (please refer to the Supplementary Note 3 and Supplementary Figs 3 and 4 for the 900 and 980 nm pump spectral data and for the quantitative assessment of the 1,064 nm line absorption coefficient).

Figure 6: Broad-band TEPL upconversion. (a) The Cr:Nd:Yb glass sample lineshape in the NIR. The three pumps used are indicated with their corresponding electronic transitions in blue arrows (two for the Nd3+ and one for the Yb3+). The purple arrow indicates energy transfer between the Yb3+ and the Nd3+. The red dotted line indicates the thermal upconversion process, resulting in TEPL emission. (b) The rise of TEPL emission (marked by an orange arrow) for the 1,064 nm pump (blue arrow), upon heating. (c) The PL spectrum evolution showing the reduction of sub-bandgap photon rate (blue arrow, λ>850 nm) and the rise in the rate of photons of λ<850 nm (orange arrow) under white-light excitation. (d) Temperature dependence of the ratio of energetic photon (λ<850 nm) to total photon rates, for white-light pumping (supercontinuum laser). The dotted line marks the temperature where a CO 2 laser was used as an additional heat source. Full size image