We report on a comparative study of narrow-bandgap (∼0.2 eV at 300 K) thermophotovoltaic (TPV) devices with InAs/GaSb type-II superlattice absorbers. By comparing the characteristics of three narrow bandgap TPV structures with a single absorber or multiple discrete absorbers, it is clearly demonstrated that the device performance of a conventional single-absorber TPV cell is limited mainly by the small collection efficiency associated with a relatively short diffusion length (1.5 μm at 300 K). Furthermore, this study revealed that multi-stage interband cascade (IC) TPV structures with thin individual absorbers can circumvent the diffusion length limitation and are capable of achieving a collection efficiency approaching 100% for photo-generated carriers. Additionally, the open-circuit voltage, the fill factor, the output power, and the power conversion efficiency can be significantly increased in IC TPV devices compared to the conventional single-absorber TPV structure. These results have further validated the potential and advantages of narrow bandgap IC structures for TPV cells.
I. INTRODUCTION
Thermophotovoltaic (TPV) systems1,2 convert the radiation of a heat source into electrical power through the photovoltaic process. Among the proposed uses of TPV technology are cogeneration in boiler systems or remote locations,3 heat conversion of concentrated solar energy,4 and radioisotope powered generation in deep-space missions.5 In a TPV system, the heat radiant source is placed close enough to the TPV cells for the radiation intensity to be significantly higher than one sun. In some cases, a filter or selective emitter is incorporated to optimize the spectral match between the radiator and TPV cells. The TPV cell's maximum theoretical conversion efficiency of 85% for full concentration of the incident sunlight6 is much larger than that of the 41% calculated for a single p-n junction solar cell in the detailed balance limit.7 Nanostructured materials and metamaterials have been recently investigated to achieve TPV systems with broadband absorbers and narrowband emitters.8,9
Most previous research on TPV cells focused on diode structures made of III-V semiconductors with bandgaps (Eg) above 0.5 eV, including GaSb (0.7 eV),4,10,11 InGaAs on InP (0.55–0.6 eV),5,12,13 and InGaAsSb on GaSb (0.53 eV).14–16 However, there are many potential applications where a narrow bandgap is required to absorb radiant-heat from lower-temperature sources. For sources with a temperature in the range of 1000–1500 K, the optimum bandgap of TPV cells has been calculated to be 0.2–0.4 eV.17,18 Unfortunately, narrow bandgap materials also have disadvantages, including a relatively small absorption coefficient (α) and a limited diffusion length (L), as well as a very low output voltage. For example, InAs and InSb (intrinsic or lightly doped) in their bulk form have α in the range of 1000–3000 cm−1 near their bandgaps. Their L can be several microns at room temperature, but may be reduced substantially with a high concentration of excess carriers under intensive light illumination. For artificially made type-II (T2) InAs/GaSb superlattices (SLs), α is in the range of 2000–3000 cm−1 near their bandgaps and L is about 1 μm at room temperature for cutoff wavelengths in the range of 4.3–5.2 μm. This value of L is estimated from the temperature dependence and the bias sensitivity of the responsivity observed in infrared detectors based on T2 InAs/GaSb SLs.19–21
The effect of small α and limited L on TPV performance is illustrated in Fig. 1(a), where calculated values of the external quantum efficiency (EQE) (ηe) and the collection efficiency (ηc) of photo-generated carriers are plotted as functions of normalized absorber thickness (d/L). The calculations are based on standard theories for pn junction and barrier photodetector structures22–24 without considering the surface reflection of light. To achieve substantial absorption of radiant photons, the absorber needs to be thick, especially with a small α. However, when the diffusion length is small, ηe will not increase further with the absorber thickness after d ≈ L, as shown in Fig. 1(a). This is because some photo-generated carriers recombine before being collected and the collection efficiency, which is defined as the ratio of collected carriers to the absorbed photons and equals ηe/(1 − exp(−αd)), is reduced with increasing the absorber thickness (d). The reduction with increasing d is more significant when αL < 1, as shown in Fig. 1(a). Also, from Fig. 1(a), one can see that ηe reaches a maximum at a finite absorber thickness when αL > 1 because the collection probability of photo-generated carriers is reduced with increasing the absorber thickness. A high collection efficiency (>90%) can be obtained only when the absorber is thinner than the diffusion length (or less than 0.6 L with αL < 1), as shown in Fig. 1(a). Furthermore, the open-circuit voltage Voc is reduced with a limited efficiency according to eVoc = kbTln{ηeΦ0/[gthL tanh(d/L)]},25 where Φ0 is the photon flux, gth is the thermal generation rate, e is the electron charge, kb is the Boltzmann's constant, and T is the absolute temperature. This is illustrated by the open-circuit voltage factor VF = ln[ηe/tanh(d/L)] in Fig. 1(b), where the dotted curves are calculated by assuming a perfect collection efficiency and solid curves are based on the calculated ηe in Fig. 1(a) with a limited collection efficiency. In comparison, it can be seen that VF is reduced substantially with a limited collection especially when αL < 1 and d > L. For example, when αL = 0.35 and d = 3L, VF is reduced by 0.91, resulting in a reduction of Voc by 24 mV at 300 K. Hence, the efficiency of converting radiant photons into electricity is limited by the finite diffusion length in a conventional single-absorber TPV structure, a restriction that is particularly significant in narrow bandgap semiconductors where αL is typically less than one.
(a) Calculated quantum efficiency and collection efficiency, (b) open-circuit voltage factor as a function of normalized absorber thickness for several values of αL. VF initially decreases with increasing d/L due to the nearly linear increase in dark current when d/L is small.
(a) Calculated quantum efficiency and collection efficiency, (b) open-circuit voltage factor as a function of normalized absorber thickness for several values of αL. VF initially decreases with increasing d/L due to the nearly linear increase in dark current when d/L is small.
The diffusion length limitation described above can be circumvented in principle by a multi-stage architecture with discrete thin absorbers. An embodiment based on an interband cascade (IC) structure with InAs/Ga(In)Sb T2 SL absorbers is shown in Fig. 2.25–30 In an IC TPV structure, every individual absorber is designed to be thinner than the diffusion length for a high collection efficiency, while the total thickness of all absorbers can be well beyond the diffusion length for high absorption of incident radiant photons. Multi-stage IC structures were originated from IC lasers (ICIs)31,32 that have proven to be efficient mid-infrared light sources with continuous wave operation at room temperature.32–34 They should be suitable for TPV applications based on the relevant discussion on emitters and photovoltaic cells.35 As shown in Fig. 2, the individual absorber in each stage of an IC TPV is sandwiched between an engineered GaSb/AlSb electron barrier (eB) and an AlSb/InAs hole barrier (that serves as the electron relaxation region). The carrier transport between adjacent stages takes place via the type-II broken-gap band alignment between InAs and GaSb layers, rather than Esaki tunnel junctions. As such, the series resistance between stages can be made negligible by careful engineering of the band alignments in different regions of the device structure, and thus more stages do not have a detrimental impact on device performance. In contrast to IC lasers31,32 where one injected electron (in the forward direction) generates multiple photons, an IC TPV device operates under a forward bias with a reverse current (opposite to the direction in an IC laser), where the extraction of one electron requires multiple photons. Hence, in an IC TPV structure, the maximum achievable photocurrent (and ηe) is scaled down by a factor of Nc (the number of cascade stages) in exchange for a higher open-circuit voltage (proportional to Nc). This is advantageous for reducing Ohmic losses due to circuit resistance. For this reason, the EQE is not a complete measure for the performance of multi-stage IC TPV devices. A more appropriate figure of merit is the particle conversion efficiency (PCE),25 which accounts for carrier collection from every individual absorber and the resulting increase in the open-circuit voltage. Our preliminary effort has demonstrated that IC TPV devices are able to achieve a high open-circuit voltage that exceeds the single-bandgap value (Eg/e).25–30 This result reflects the effectiveness of cascade action, which can significantly alleviate the intrinsic difficulty of a low output voltage in narrow bandgap TPV devices.
A schematic illustration of a multi-stage interband cascade photovoltaic device under infrared light illumination. The straight line arrows indicate the transport paths of electrons and holes in the absorbers to collection points. Absorbers in optically deeper stages are designed thicker to achieve current matching.
A schematic illustration of a multi-stage interband cascade photovoltaic device under infrared light illumination. The straight line arrows indicate the transport paths of electrons and holes in the absorbers to collection points. Absorbers in optically deeper stages are designed thicker to achieve current matching.
In this work, we present a comparative study of three TPV devices, one of which has the conventional single-absorber structure, while the others are three- and five-stage IC devices, in order to examine how different configurations affect device performance, including the specific influence of diffusion length on collection efficiency and other characteristics. The absorbers in these TPV devices are made of type-II InAs/GaSb SLs with a bandgap of about 0.2 eV at 300 K, which is the narrowest bandgap reported in TPV cells.
II. DEVICE DESIGN, GROWTH, AND FABRICATION
Three TPV structures were grown using a GENxplor molecular beam epitaxy (MBE) system and nominally undoped p-type GaSb (001) substrates. In the three structures, each period of the SL absorber consisted of four layers: InSb (1.2 Å), InAs (20.5 Å), InSb (1.2 Å), and GaSb (25.1 Å). The two thin InSb layers were included to balance the tensile strain of the InAs layer.36 The individual absorbers in these structures were p-type doped to 2.6 × 1016 cm−3, and their thicknesses in multi-stage IC structures were varied to achieve current-matching between stages by compensating for light attenuation. The thicknesses were designed based on the absorption coefficient (α ∼ 3000 cm−1) of a monochromatic light source and the assumption of complete collection of photo-generated carriers. The one-stage device had a 2.31-μm thick absorber. The absorber thicknesses in the three-stage device were designed to be 624, 749, and 936 nm from the surface to the substrate (the direction of light propagation) with the total absorber thickness equal to that of the one-stage device. The five-stage device has five discrete absorbers with thicknesses of 360, 408, 480, 576, and 696 nm, respectively, and the total absorber thickness is 2.52 μm, slightly longer than the one- and three-stage devices. The electron barriers in the three devices were composed of four digitally graded multiple GaSb/AlSb quantum wells (QWs) with GaSb well thicknesses (in Angstroms) of 33/43/58/73. The hole barriers (hBs) were composed of eight InAs/AlSb QWs with a digitally graded InAs well thickness sequence of 32/34/36/40/45/52/60/71 Å. After the MBE growth, the wafers were processed into square mesa devices with dimensions from 50 to 1000 μm using standard contact UV photolithography, followed by wet-chemical etching. A RF-sputter deposited two-layer passivation (Si3N4 then SiO2) was used for improving overall stress management and minimizing pin holes, and Ti/Au layers were sputter deposited for top and bottom contacts. Finally, the devices were mounted on heat sinks and wire bonded for characterization.
III. DEVICE CHARACTERIZATIONS AND DISCUSSIONS
A. Quantum efficiency and particle conversion efficiency
The EQE of the devices at zero-bias and temperatures of 300 and 340 K is shown in Fig. 3(a). In contrast to conventional multi-junction solar cells with different bandgaps in each junction, the absorption coefficient and diffusion length are identical in every discrete absorber of these IC TPV devices. The only difference between cascade stages is the absorber thickness. The reported EQE is for the entire multi-stage device, not for any individual stage. Considering that the EQE is limited by the weakest producing stage, this ηe reflects the actual device performance and is more meaningful than knowing the EQE for any individual stage of an IC TPV device. Note that unless expressly stated, hereafter, the size of a device is 0.2 × 0.2 mm2. The EQE was measured using a FTIR spectrometer and a calibrated blackbody radiation source with a temperature of 800 K (aperture radius: 0.76 cm) and a 2π field of view (FOV). At 300 K, the one- and three-stage devices had a 100% cutoff wavelength of 5.5 μm, which corresponds to a bandgap of 225 meV. By comparison, the five-stage device had a slightly longer 100% cutoff wavelength of 5.8 μm with the SL absorber bandgap estimated to be 214 meV. As mentioned in the introduction, the EQE is no longer a good indicator of overall device performance for multi-stage IC structures, but it can be used to characterize carrier collection in individual absorbers. Since the EQE is approximately proportional to the individual absorber thickness, the one-stage device with a 2.31-μm thick absorber had the highest EQE, while the five-stage device with relatively thin individual absorbers had the lowest EQE among the three devices. For instance, at a wavelength λ = 4 μm, the EQEs were 29.5%, 12.0%, and 8.8% for one-, three-, and five-stage devices at 300 K, respectively. At a higher temperature (i.e., 340 K), the EQEs of the one- and three-stage devices decreased, while the EQE was nearly unchanged for the five-stage device. Also, the reduction was more pronounced in the one-stage device with increasing temperature. For example, at λ = 4 μm, the EQE was reduced to 23.6% for the one-stage device compared a small reduction to 11.3% for the three-stage device at 340 K. The EQEs were reduced because the diffusion length was shorter at a higher temperature, resulting in a smaller collection efficiency as illustrated in Fig. 1(a). This is further revealed by the reverse bias dependence of the EQE at λ = 4 μm for the three devices, as shown in Fig. 3(b).
(a) Measured EQE spectra of one-, three-, and five-stage devices at 300 and 340 K. (b) Voltage dependent EQE at 4 μm for the three devices, where different vertical scales are used in the top and bottom portions to better show variations.
(a) Measured EQE spectra of one-, three-, and five-stage devices at 300 and 340 K. (b) Voltage dependent EQE at 4 μm for the three devices, where different vertical scales are used in the top and bottom portions to better show variations.
As one can see from Fig. 3(b), a reverse bias voltage was needed to achieve the maximum (or saturation) value of EQE for full collection of photo-generated carriers in both the one- and three-stage devices at 300 K. This is because the individual absorbers in the one- and three-stage devices are either longer than or comparable to the diffusion length. Hence, some photo-generated carriers recombine during their transport paths when a reverse bias voltage is not applied. At a higher temperature of 340 K, the diffusion length was shorter, and consequently, a larger reverse bias voltage was required to achieve EQE saturation for the one- and three-stage devices. The impact on the five-stage device was much less because its individual absorbers are substantially thinner. Also, the EQE saturation value was higher for all the devices at 340 K because the absorption coefficient was increased due to the bandgap narrowing with rising temperature. Owing to the thickest individual absorber among the three devices, the one-stage device has the highest value of EQE. However, this highest EQE in the one-stage device does not necessarily result in the best performance among the three devices for TPV cell operation with a forward bias voltage. As mentioned in the introduction, a more appropriate figure of merit for multi-stage TPV cells is PCE,29 which is defined as the sum of quantum efficiencies in individual absorbers and equals Nc × EQE for a current-matching configuration. At λ = 4 μm, current-matching is approximately satisfied based on the absorption coefficient (3159 cm−1 for one- and three-stage devices and 3470 cm−1 for the five-stage device) determined from the transmission measurement. PCEs at zero-bias were 29.5%, 36.0%, and 44% for the one-, three-, and five-stage devices at 300 K, respectively. Hence, the five-stage device has the highest PCE among them, which is consistent with the projected high collection efficiency due to thin individual absorbers and the higher power conversion efficiency which will be discussed later. PCE can be further enhanced in IC TPV devices up to a maximum value of 69% (estimated by subtracting the 31% reflection loss from the top surface) by adding more stages to absorb more incident photons. Also, adding an anti-reflection coating onto the surface can raise the PCE beyond 69%.
Theoretically, the quantum efficiency ηN in the Nth stage in a multi-stage IC TPV device can be computed as24
where R is the reflectance of light at the device's top surface, dm is the absorber thickness in the mth stage, and L is the diffusion length. In the current-matched configuration, the quantum efficiency ηN is equal in every stage and is the measured EQE (consequently, PCE=Nc×EQE). From the measured absorption coefficient and EQE, the diffusion length L was extracted from Eq. (1) and found to be about 1.5 μm at 300 K. Apparently, at λ = 4 μm, the product of absorption coefficient and diffusion length (αL) is smaller than unity in the three devices. Consequently, in order to have the collection efficiency higher than 90%, individual absorber thicknesses need to be shorter than 0.6L as indicated in Fig. 1(a). The absorber thickness in the one-stage device is about 1.5 times of the diffusion length, and thus this device had the lowest collection efficiency [∼60% as shown in Fig. 1(a)] at zero-bias voltage. Every individual absorber thickness in the five-stage device is less than 0.6L, resulting in a collection efficiency exceeding 90% and the highest PCE at zero bias voltage as discussed above.
B. Illuminated J-V curves and series resistance
In a TPV system, thermalization and below-bandgap losses can be significantly reduced with selective emitters (or narrow-band filters). Both experimental and theoretical efforts have demonstrated efficient narrow-band emissivity near 4 μm or longer wavelengths by using nanostructured materials for selective emitters,9,37 which supports the applicability and feasibility of narrow bandgap TPV devices. To mimic the characteristics of a selective emitter with a narrow emission spectrum, a type-II IC laser (ICL)32 was employed to illuminate the three TPV devices. This laser was operated at ∼80 K to deliver high output power at an emission wavelength near 4.25 μm [see inset to Fig. 4(b)], corresponding to a photon energy of 291 meV that is 60–80 meV higher than the bandgap of the TPV devices at 300 K. Thus, there is still some thermalization loss (20%–27%) from above-bandgap photons. Nevertheless, at this wavelength, photocurrent matching was almost maintained in the three- and five-stage devices. The performance of the three TPV devices was investigated under different illumination levels from the IC laser by adjusting the injection current of the laser. Figure 4(a) shows the measured current density (J)-voltage (V) characteristics of the three devices at 300 K under a medium level of illumination from the ICL, where the incident power density (Pinc) was about 19 W/cm2. Also, shown in Fig. 4(a) are J-V curves corrected for the series resistance (Rs) loss and the ideal case, which are plotted in a similar manner to what is described in Ref. 38. The determination of the series resistance will be discussed later in this subsection. The ideal J-V curve is the superposition of the dark current density and the maximum photocurrent density Jphmax, where 100% of the photo-generated carriers are collected. Jphmax was evaluated by subtracting the saturation dark current density (J0) from the saturation value Jsat at a reverse bias of the illuminated J-V curve. At 300 K, under this medium illumination level, Jsat (J0) was 25.3 (2.9), 9.1 (1.1), and 5.9 (0.9) A/cm2 for one-, three-, and five-stage devices, respectively. Therefore, the corresponding Jphmax under this illumination level was 22.4 (one-stage), 8.0 (three-stage), and 5.0 (five-stage) A/cm2, proportional to the number of photons absorbed in their individual absorbers. At 300 K, with the same illumination level, the short-circuit current density (Jsc) values of about 9.2 A/cm2, 6.7 A/cm2, and 4.9 A/cm2 for one-, three-, and five-stage devices, are lower than the corresponding value of Jphmax, mainly due to incomplete collection of photo-generated carriers particularly in the one-stage device. Although the highest EQE at zero bias in the one-stage device resulted in the highest short-circuit current among the three devices, its collection efficiency and PCE were the lowest, which lead to the lower power conversion efficiency described in Sec. III D. The higher short-circuit current in the one-stage device also noticeably shifted its Rs-corrected J-V curve from the measured one, while the Rs-corrected J-V curves for the three- and five-stage devices almost coincide with the measured J-V curves because of relatively lower currents compared to the one-stage device.
(a) Current-voltage characteristics of the three devices at 300 K under a medium illumination level where the incident power density was about 19 W/cm2. The solid, dotted, and dashed curves correspond to the measured, Rs corrected, and ideal cases, respectively. (b) Current-voltage characteristics of the three devices at 200 K under the same level of illumination as in (a). The inset shows the emission spectrum of the ICL.
(a) Current-voltage characteristics of the three devices at 300 K under a medium illumination level where the incident power density was about 19 W/cm2. The solid, dotted, and dashed curves correspond to the measured, Rs corrected, and ideal cases, respectively. (b) Current-voltage characteristics of the three devices at 200 K under the same level of illumination as in (a). The inset shows the emission spectrum of the ICL.
The one-stage device had a low collection efficiency because the diffusion length at 300 K was shorter than the absorber thickness as discussed earlier. This can be further understood by examining the behaviors at a low temperature where the diffusion length should be longer. Figure 4(b) shows the J-V curves of the three devices at 200 K under the same illumination level as in Fig. 4(a) from the ICL. Current saturation was reached for the three- and five-stage devices at a certain forward voltage instead of a reverse voltage. This implies that full collection of photo-generated carriers was achieved under a forward voltage and the diffusion length was increased substantially beyond the individual absorber thicknesses in the three- and five-stage devices. The increased diffusion length also enhanced the collection efficiency (∼72% at the zero-bias) of photo-generated carriers in the one-stage device although it remained below 100% because the diffusion length was not longer than the absorber thickness (2.31 μm). Also, the open-circuit voltage was significantly higher for the three devices at 200 K because the dark saturation current density was drastically reduced to orders of magnitude below the photocurrent density. At 200 K, Jphmax under this illumination level dropped to 18.5, 6.9, and 4.4 A/cm2 for the one-, three-, and five-stage devices, respectively. This was due to the decreased number of absorbed photons associated with the increased bandgap at the lower temperatures.
In addition to having a higher collection efficiency compared with the conventional single-stage device, the multistage IC structure can produce an open-circuit voltage (Voc) even above the individual absorber bandgap. For instance, at 300 K, the measured Voc under an illumination level of 19 W/cm2 [Fig. 4(a)] was 72 (one-stage), 223 (three-stage), and 287 meV (five-stage), corresponding to a voltage efficiency (qVoc/NcEg) of 32%, 33%, and 27%, respectively. At 200 K, under the same illumination level, as shown in Fig. 4(b), the Voc was raised to 170 (one-stage), 513 (three-stage), and 745 meV (five-stage) with a corresponding voltage efficiency of 67%, 68%, and 63%, respectively. The slightly lower voltage efficiency in the five-stage device was due to the narrower bandgap and some variations in material quality, which resulted in a substantially higher thermal generation rate (about two times higher at 300 K based on the measured characteristics of dark current density and our calculations) than in the three-stage device. In the ideal case, as shown in Fig. 4(a), the open-circuit voltage was lower in the five-stage device than in the three-stage device. This was attributed to the same factors as mentioned above for the lower voltage efficiency because doubling the thermal generation rate can reduce the open-circuit voltage by ∼90 mV at 300 K (amplified by about 5 times with five cascade stages25). The open-circuit voltage and efficiency increased when the illumination was enhanced. For example, at 300 K, the measured Voc at the highest illumination level (36 W/cm2) from the ICL was 85, 271, and 371 mV for the one-, three-, and five-stage devices, respectively.
In Fig. 4(a), there is another characteristic among the three devices, namely, a shift between the measured and ideal J-V curves, which should merit attention and further discussion. The shift is particularly striking for the one-stage device, substantially reduced for the three-stage device, and almost disappears for the five-stage device. This implies that the illuminated J-V curves are not complying with the usual superposition principle39 and the collection efficiencies and the photocurrents in the three devices are actually voltage-dependent. In other words, the photocurrent should not be treated as a voltage-independent constant as in the commonly used standard model.39 This voltage-dependent characteristic has been reported in solar cells made of Silicon,40–42 CdS/CdTe,38,43,44 CdS/CdInSe2,45,46 and GaAs.41 But, the voltage-dependent collection efficiency in those solar cells mainly stems from the variation of the electrical field in the depletion region when the applied external voltage is changed. In contrast, the diffusion process plays a more important role in IC TPV structures. In some of our previous IC TPV devices,30 the collection efficiency and photocurrent were voltage dependent although the dependences were weaker due to relatively thin individual absorbers. These voltage dependences (even though weak) may have caused an overestimate of the series resistance of IC TPV cells based on a generalized Suns-Voc method.30 Hence, to avoid the complication due to the voltage-dependent photocurrent, we extract the series resistance Rs for the three devices from the dark condition based on the following equation:42,46
The plots of dV/dI under dark conditions, along with the extracted series resistances for the three devices, are presented in Fig. 5, where Rs was obtained by finding the intercept of dV/dI vs. 1/I. The extracted series resistances of the three devices were 4.9 (one-stage), 4.6 (three-stage), and 4.7 Ω (five-stage), which are close to each other. This suggests that the series resistance in the three devices was mainly caused by the contacts and wires, and the resistance between cascade stages can be neglected due to smooth transport with the type-II broken-gap heterostructure.
dV/dI data to acquire series resistance, which was found from the intercept of dV/dI.
dV/dI data to acquire series resistance, which was found from the intercept of dV/dI.
C. Characterization of collection efficiency
The voltage-dependent collection efficiency ηc(V) can be obtained through an approach described in Refs. 38, 42, and 46. The voltage-dependent photocurrent density Jph(V) is expressed as the maximum photocurrent density times ηc(V): Jph(V) = Jphmax · ηc(V). The dark current density is assumed to be constant and does not change with the illumination level.38,42,46 Applying this approach to IC TPV structures, the voltage-dependent collection efficiency in the three devices can be expressed as
where J1(V) and J2(V) denote the current densities at two different illumination levels, and J1phmax and J2phmax are the corresponding maximum photocurrent densities. For each device at 300 K, four J-V curves were chosen at relatively low incident power densities of 19, 13, 7 W/cm2 and the dark condition to extract ηc(V), as shown in Fig. 6(a). As can be seen, the curves for ηc(V) extracted from different pairs of J-V data are not exactly coincident for the one- and three-stage devices, which implies that the dark current might vary with the illumination level. This may be partially explained by a large number of photo-generated excess carriers shortening the carrier lifetime and possible small variations of device temperature (<1 K based on the estimated thermal resistance for IC structures47 and illumination power), which would change the dark injection current contribution, especially at high illumination levels. For this reason, the J-V data under relatively low illumination levels were used for extracting ηc(V) [Fig. 6(a)]. This is consistent with the measured and ideal J-V curves in Fig. 4(a), which were also obtained at a relatively low incident power density (19 W/cm2) for a fair comparison without the influence of a possible variation of dark current. However, this effect somehow becomes negligible when the individual absorbers are thin, as evidenced by the nearly overlapping ηc(V) profiles with different pairs of illumination levels for the five-stage device. Another factor is the surface leakage current due to imperfect passivation of the etched sidewalls, which will be discussed later. We note that possible variations of the diffusion length due to a small change of temperature (<1 K) under different illumination levels should be insignificant because the EQE would only differ by at most 0.15% with a 1 K deviation at 4.25 μm, as shown in Fig. 3(a). The temperature variation for a larger device size could be somewhat larger under light illumination but should be manageable with effective thermal dissipation through a heat sink. For example, the specific thermal resistance (Rsth) for a device with a side dimension of 1 mm is not higher than 100 K⋅cm2/kW, based on previously extracted data for IC structures.47 Illumination at a power density of 36 W/cm2 would increase the device's temperature by less than 3.6 K (with effective thermal conduction through the substrate to a heat sink) compared to its temperature in the dark.
(a) Voltage dependence of collection efficiency derived from Eq. (3) using four different pairs of J-V data at 300 K for the three devices. The numbers in the legend indicate the incident power densities under different illumination levels. (b) Average collection efficiency over the four pairs in (a).
(a) Voltage dependence of collection efficiency derived from Eq. (3) using four different pairs of J-V data at 300 K for the three devices. The numbers in the legend indicate the incident power densities under different illumination levels. (b) Average collection efficiency over the four pairs in (a).
For convenience of comparison, the average of the four ηc(V) profiles (with different illumination pairs) in Fig. 6(a) is plotted in Fig. 6(b). As can be seen, the average ηc(V) of the five-stage device was the highest among the three devices and ηc(V) was the lowest in the one-stage device. The zero-bias collection efficiency ηc(0) was 40%, 76%, and 95% for the one-, three-, and five-stage devices, respectively. For the one-stage device at a forward bias (>0.1 V), more than 80% of the photo-generated carriers were not collected as indicated by the small ηc(V) (<0.2). This small ηc(V) will reduce the fill factor (FF), consequently penalizing the conversion efficiency, which will be discussed in Sec. III D. Compared with the zero-bias collection efficiency (∼60% for the one-stage device) derived in Fig. 1, ηc(0) shown in Fig. 6(b), was substantially smaller, especially for the one-stage device. This may likely be caused by the surface leakage of photocurrent as mentioned earlier. As shown in the Appendix, there is significant leakage in the dark current especially in the one-stage device. Likewise, under illuminated condition, a substantial number of photo-generated carriers could leak through the sidewalls and thus reduce the collection efficiency, particularly for the one-stage device, as shown in Fig. 6(b). The reason why the most notable surface leakage was in the one-stage device with a thick absorber is not fully understood and deserves further study in the future.
D. Fill factor and conversion efficiency
The dependences of Voc, FF, maximum output power density (Pmax), and conversion efficiency (η) on incident power density at 300 K for the three devices are shown in Fig. 7. At the maximum incident power density available from the ICL, the extracted FF was 25%, 28%, and 38% for the one-, three-, and five-stage devices, respectively. At almost all illumination levels, the five-stage device has the highest FF because it has the highest collection efficiency, while the one-stage device has the lowest FF mainly because it has the lowest collection efficiency [Fig. 6(b)] and a larger series resistance loss [Fig. 4(a)]. Under the highest illumination level, the maximum output power was harvested at a voltage (Vmax) of 43, 136, and 226 meV for the one-, three-, and five-stage devices, respectively. At this voltage, according to Fig. 6(b), the corresponding collection efficiencies were about 29% (one-stage), 53% (three-stage), and 87% (five-stage). If the photo-generated carriers were completely collected as in the ideal case, the FF would reach to 32%, 36%, and 39% for the one-, three-, and five-stage devices, respectively. From this perspective, the five-stage device with thin individual absorbers is closest to the ideal case for maximum output power. It was also observed that FFs of the one- and three-stage devices peaked at a certain incident power density and then decreased with further increasing of the incident optical power. This could be related to the larger Jsc (proportional to the incident power) and the resulting higher Ohmic losses. Nevertheless, the FF of the five-stage device exhibited a consistent rise with increasing incident power. The FFs of the three devices were fairly small compared with typical values (∼60%–70%) of TPV cells with absorbers having bandgaps of 0.5–0.6 eV2 but were reasonable for un-optimized structures with a narrow bandgap (∼0.2 eV).
(a) Open-circuit voltage, (b) fill factor, (c) maximum output power density, and (d) conversion efficiency as a function of incident power density for the three devices at 300 K.
(a) Open-circuit voltage, (b) fill factor, (c) maximum output power density, and (d) conversion efficiency as a function of incident power density for the three devices at 300 K.
Owing to the efficient collection of photo-generated carriers, the five-stage device achieved the highest power conversion efficiency. For the three devices at 300 K, the maximum conversion efficiencies were 0.9% (one-stage), 2.5% (three-stage), and 3.6% (five-stage), as shown in Fig. 7(d). This clearly validates the benefits of a multistage IC structure with thin discrete absorbers for narrow-bandgap TPV cells. The relatively low conversion efficiency in the three devices was mainly due to the significant dark current from a high thermally generated carrier concentration in such a narrow band gap (∼0.2 eV) structure. Other factors include some thermalization loss (20%–27%), the contact resistances, surface reflection (31%), and incomplete absorption (∼50%) due to an insufficient thick total absorber (≤2.52 μm). At relatively low illumination levels (Pinc<5 W/cm2), the five-stage device had a conversion efficiency that was slightly lower than that of the three-stage device due to the narrower bandgap and the higher thermal generation rate mentioned early. For example, under illumination at an input power density of 3.5 W/cm2, the power conversion efficiency was 0.94% and 0.88% for the three- and five-stage devices, respectively, although the five-stage device had a somewhat higher open-circuit voltage (103 vs. 95 mV). In fact, the conversion efficiencies of the three- and five-stage devices can be further enhanced by increasing the incident power. This can be achieved with built-in lenses on the semiconductor surface when the radiation source is far from the device or by exploring a photonic structure and metamaterial to modify the emission pattern of a radiation source to be favorable for concentration. The conversion efficiencies have not yet saturated for the three- and five-stage devices, while the one-stage device approached a saturation at a relatively low input power density. Also, the conversion efficiency of the one-stage device exhibited a drop (16%) after saturation, which coincides with the trend of FF with incident power [Fig. 7(b)]. Similar to FF, the increased ohmic losses at higher illumination levels in the one-stage device provided another mechanism for reducing the conversion efficiency after saturation. In contrast, for the three-stage device, the rapid increase in Voc [Fig. 7(a)] overwhelmed the decrease in FF with increasing incident power, and the photocurrent density (e.g., Jphmax) and the resulting ohmic loss in the three-stage device are smaller compared to that in the one-stage device. Hence the conversion efficiency in the three-stage device exhibited a similar trend to its Voc. Table I summarizes the photovoltaic performance characteristics and related parameters of the representative devices from the three wafers. These data collectively show the limitation of the single-stage TPV devices, and the potential and advantages of multi-stage IC TPV devices.
Summary of the photovoltaic performance and the related parameters of representative devices (0.2 × 0.2 mm2) from the three IC TPV wafers at 300 K. The maximum efficiencies shown in the table for the three- and five-stage devices were obtained at a maximum incident power density of 36 W/cm2.
Device . | ηc (0) (%) . | Jsc (A/cm2) . | Jphmax (A/cm2) . | Voc (mV) . | FF (%) . | Pmax (W/cm2) . | Maximum efficiency (%) . | Rs (Ω) . |
---|---|---|---|---|---|---|---|---|
One-stage | 40 | 12.9 | 40.8 | 85 | 25 | 0.27 | 0.9 | 4.9 |
Three-stage | 76 | 12.2 | 15.7 | 271 | 28 | 0.91 | 2.5 | 4.6 |
Five-stage | 95 | 9.3 | 9.7 | 371 | 38 | 1.29 | 3.6 | 4.7 |
Device . | ηc (0) (%) . | Jsc (A/cm2) . | Jphmax (A/cm2) . | Voc (mV) . | FF (%) . | Pmax (W/cm2) . | Maximum efficiency (%) . | Rs (Ω) . |
---|---|---|---|---|---|---|---|---|
One-stage | 40 | 12.9 | 40.8 | 85 | 25 | 0.27 | 0.9 | 4.9 |
Three-stage | 76 | 12.2 | 15.7 | 271 | 28 | 0.91 | 2.5 | 4.6 |
Five-stage | 95 | 9.3 | 9.7 | 371 | 38 | 1.29 | 3.6 | 4.7 |
IV. CONCLUSION
Through a comparative study of three narrow bandgap (∼0.2 eV) TPV structures with a single-absorber and multiple discrete absorbers, it is demonstrated that the device performance of a conventional one-stage TPV cell based on a T2SL absorber is limited mainly by the small collection efficiency associated with a relatively short diffusion length (1.5 μm at 300 K). Also, this study showed that multi-stage IC TPV structures with thin individual absorbers can circumvent the diffusion length limitation and are capable of achieving a collection efficiency approaching 100% for photo-generated carriers. As such, the open-circuit voltage, FF, output power, and conversion efficiency can be significantly increased compared to the conventional single-absorber TPV structure. The demonstrated room-temperature power conversion efficiency (3.6%), although very low compared to well-developed solar cells, can be further enhanced significantly. For example, adding an anti-reflection coating onto the surface and increasing the total absorber thickness (or insertion of a back reflector), as well as reducing the contact resistance, would make η of IC TPV devices approach or exceed 10%. To overcome the fundamental limitation of a high dark current density in narrow bandgap materials, an even stronger optical illumination can be applied. This will increase the power conversion efficiency because the collection efficiency in IC TPV structures is high and η has not yet saturated, as shown in Fig. 7(d). Alternatively, these narrow bandgap TPV devices can be operated at low temperatures with significantly reduced dark current density and increased power efficiency for applications such as in space (e.g., Jupiter and Saturn missions) where the ambient temperature is well below 300 K. Considering that interband cascade structures are in an early phase of development for TPV applications, a focused effort on exploring and understanding the relevant physics is needed. With improved understanding, further development, and optimization, IC TPV devices may provide a promising solution for useful applications such as space exploration, waste-heat recovery, and portable power sources.
ACKNOWLEDGMENTS
This work was supported, in part, by the National Science Foundation (NSF) under Grant No. DMR-1608224. The GENxplor MBE system was acquired with support from the NSF through Grant No. DMR-1229678.
APPENDIX: ANALYSIS OF SURFACE LEAKAGE
In principle, the effect of surface leakage under dark conditions can be quantified by fitting the device's zero-bias resistance-area product (R0A) to the equation48
where ρsw is the device sidewall resistivity, and P and A are the device area and perimeter. The size dependent R0A, along with the ρsw obtained through the above fitting for the three devices at 300 K, is shown in Fig. 8. At 300 K, the R0A values were 0.02 (one-stage), 0.11 (three-stage), and 0.18 Ω cm2 (five-stage) for the devices with a side dimension of 0.2 mm. Hence, surface leakage is responsible for 74%, 62%, and 48% of the total dark current for the one-, three-, and five-stage devices, respectively. Devices with larger sizes have smaller percentages of leakage current in the total current. However, the larger size device has a relatively low zero-bias resistance R0 (e.g., only 26 Ω for the 0.5 × 0.5 mm2 device from the one-stage wafer at 300 K), which makes it difficult to accurately extract the device EQE. Hence, to optimize the tradeoff, the 0.2 × 0.2 mm2 devices with comparatively high R0 in the three wafers were chosen for device analysis.
Size dependent R0A for the three devices at 300 K. The sidewall resistivity was smallest for the one-stage device.
Size dependent R0A for the three devices at 300 K. The sidewall resistivity was smallest for the one-stage device.