634 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014

Progress Toward Realizing an Intermediate BandSolar Cell—Sequential Absorption of Photons

in a Quantum Well Solar CellMegumi Yoshida, Hemmel Amrania, Daniel J. Farrell, Ben Browne, Edward Yoxall, N. J. Ekins-Daukes,

and Chris C. Phillips

Abstract—In order to realize an intermediate band solar cell,which promises high photovoltaic energy conversion efficiency,achieving higher photocurrent while maintaining the cell voltage isessential. We report on a transient photocurrent due to the sequen-tial absorption of photons in a single quantum well by continuouslypumping to stimulate interband transitions (from a valence bandto an intermediate band) and showing an intersubband transition(from an intermediate band to a conduction band) with a pulsed in-frared laser. We demonstrate the extent to which multiple-photonabsorption can be achieved in quantum well devices and proposethat a quantum well is a suitable candidate for an intermediateband solar cell. From the combination of this and other sequentialabsorption results, it is clear that enhancing the short lifetime ofa carrier in the intermediate band is the next step toward achiev-ing a working intermediate band solar cell. In light of this, weenhance our previous suggestion, the photon ratchet intermediateband solar cell, as a means of increasing the electron lifetime.

Index Terms—Intermediate band (IB) solar cell, intersubbandtransition, quantum well (QW), sequential photon absorption.

I. INTRODUCTION

A PPLYING the principle of detailed balance, the efficiencyof photovoltaic energy conversion using a single semi-

conductor bandgap solar cell is fundamentally limited to 31.0%at 1 sun, principally because of the broad spectral distributionof solar radiation [1]. Among other third-generation solar cellconcepts [2], the intermediate band solar cell (IBSC) has beenproposed to overcome this limit, by introducing a radiativelyefficient but electrically isolated band between the conductionband (CB) and valence band (VB) [3], as shown in Fig. 1. Theintermediate band (IB) allows additional photocurrent to be gen-erated by the sequential absorption of two subbandgap photons(GVI and GIC ), which would otherwise be unabsorbed, thereby

Manuscript received July 12, 2013; revised December 16, 2013; acceptedDecember 27, 2013. Date of current version February 17, 2014. This work wassupported by Sharp Laboratories of Europe Ltd.

M. Yoshida, H. Amrania, B. Browne, E. Yoxall, N. J. Ekins-Daukes, andC. C. Phillips are with the Experimental Solid State Physics, Imperial CollegeLondon, London SW7 2AZ, U.K. (e-mail: megumi.yoshida06@imperial.ac.uk; hemmel.amrania04@imperial.ac.uk; benbrowne@gmail.com; edward.yoxall05@imperial.ac.uk; n.ekins-daukes@imperial.ac.uk; chris.phillips@imperial.ac.uk).

D. J. Farrell is with the Research Center for Advanced Science and Technol-ogy, University of Tokyo, Tokyo 153–8904, Japan (e-mail: farrell@mbe.rcast.u-tokyo.ac.jp).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JPHOTOV.2014.2301891

Fig. 1. Energy diagram of an IBSC, in which extra photocurrent is produceddue to the sequential absorption of subbandgap photons via the partially filled IB(represented by EF ,IB ) increasing theoretical limit in the conversion efficiency.

reducing below bandgap and thermalization losses. In princi-ple, by introducing the IB, the current can be enhanced withoutsignificantly reducing the voltage (separation of quasi-Fermilevels EF,CB and EF,VB ), hence leading to higher conversionefficiency. Thermodynamical modeling of the IBSC shows thatits limiting efficiency can be increased significantly over theShockley–Queisser limit to 46.8% at 1 sun and 63.2% at fullconcentration [3].

A number of experimental studies on IBSCs have been re-ported, including attempts with quantum dots (QDs) [4], [5].However, even though an increase in a photocurrent has beenobserved in QD IBSCs, they suffer from significant voltage loss,which results in low conversion efficiency [6]. One of the maincauses of the voltage reduction in these IBSCs is the short life-time of electrons in the excited states, which is often caused byfast nonradiative recombination [7], [8]. Furthermore, since theabsorption cross section of QDs is small, the rate of generation(GVI and GIC ) is relatively weak in comparison to the rate of re-combination/relaxation (RVI and RIC ); hence the separation ofthe quasi-Fermi levels (EF,CB , EF,IB , and EF,VB) is relativelysmall [9].

In this paper, we show that despite fast nonradiative relax-ation, sequential photon absorption can be achieved in a quan-tum well (QW) heterostructure and that this is common to manyother low-dimensional IBSC materials. As a first step towardachieving QW IBSCs, we propose a means by which fast re-laxation can be addressed through the introduction of an energyratchet, designed to promote sequential absorption of photons.

II. QUANTUM WELL AS AN INTERMEDIATE BAND MATERIAL

One of the possible routes to achieving an IBSC is to usequantum mechanically confined structures such as QWs and

2156-3381 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

YOSHIDA et al.: PROGRESS TOWARD REALIZING AN INTERMEDIATE BAND SOLAR CELL–SEQUENTIAL ABSORPTION 635

Fig. 2. Schematic energy diagram of a QW IBSC. Ground states which ariseas a result of quantum mechanical confinement in QW (E1) act as an IB.

QDs [10]. In these materials, the IB would typically arise fromthe confined states of the electrons in the CB potential well. Anelectron can be excited from the VB (H1) to the lowest confinedenergy states in the CB potential well (E1) by absorbing a pho-ton, followed by optical excitation to higher confined states (E2)or continuum states (E3), where the electron can be extracted tothe outer circuit (see Fig. 2).

However, for this two-photon process to be efficient, the longwavelength photon must be absorbed while the electron is stillin the confined state (E1), which is acting as the IB. The shortlifetime (nanoseconds) of the excited electron in the IB meansthat it is necessary either to increase the lifetime of the electronicstate in the IB, or to increase the photon flux by using a highintensity of long wavelength radiation, in order for the secondtransition to occur.

It is well known that confined states in both QDs and QWshave much shorter upper-state lifetimes compared with opticalinterband transitions, because of phonon mediated relaxation.Phonon bottleneck effects have been observed in both QWsand QDs, but under conditions unsuited for solar application[11], [12]. In almost all practical situations, the intersubbandrelaxation in both QW and QD heterostructures is fast, typicallyon a picosecond timescale, relative to the nanosecond timescalefor radiative processes.

To demonstrate sequential absorption, we choose a single QWp-i-n diode, which has the advantage of a larger optical cross sec-tion compared with QDs. Absorption strength can be increasedwith further QW layers, but the use of a single QW avoids com-plexity with transport over multiple QWs. The intersubbandtransition in QWs can only be excited by light polarized normalto the plane of the QWs and thus not by light that is normallyincident [13]. By fabricating a grating on the rear of the solarcell, the light can be scattered inside the structure in such a waythat it has a component of polarization parallel to the QW [14].This has successfully been achieved in quantum infrared pho-todetectors, in which the photocurrent is produced by absorbingscattered infrared light via intersubband excitation. [15].

III. OBSERVATION OF TWO-PHOTON ABSORPTION VIA

INTERSUBBAND TRANSITION IN A QUANTUM WELL

The sample used in this study is a 7-nm In0.2Ga0.8As QWwith GaAs barriers in a p-i-n junction. The sample was fabri-cated using metal-organic chemical vapor deposition. The thick-ness of the intrinsic region is 319 nm, while the p-type region

Fig. 3. Wavelength of the interband transition of the sample predicted by thek.p model, with and without considering the lattice strain. The temperature-dependent electroluminescent peaks from the sample (see Fig. 4) are plotted inred.

Fig. 4. Normalized temperature-dependent electroluminescence of the sam-ple. Peak PL wavelengths are plotted in the Fig. 3.

is doped with 2.0 × 1018 cm−3 carbon and the n-type regionis doped with 1.0 × 1018 cm−3 silicon. Theoretical modeling,using the k.p theory, gives the predictions for the interbandtransition wavelength. The model uses an eight-band Pikus–BirHamiltonian to accurately treat the VB splitting, which occursin strained materials; this results in the four energy bands (CB,HH, LH, and SO). The Schrodinger equation is solved by usingthe finite difference method in real space for each band indi-vidually to give the envelope functions and energy levels of thenanostructures. In Fig. 3, the predicted transition wavelengthfrom the VB to the IB is plotted and is shown to vary between920 and 990 nm depending on its lattice temperature.

These predicted transition wavelengths, when lattice strainis included, match the observed electroluminescence peaks (seeFig. 4). As the temperature of the sample is lowered, the thermaldistribution of the carrier is reduced, resulting in sharper peaks.

In order to minimize the background photocurrent, the sampleis illuminated at 905 nm, a wavelength below the bandgap ofthe bulk GaAs material, so that carrier excitation only takesplace in the QW, and not in the bulk region. However, since thep-n junction device has a built-in voltage, carriers can escapefrom the well by tunneling, and this generates a measurablephotocurrent even at low temperature, as shown in Fig. 5. The

636 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014

Fig. 5. Light and dark current voltage characteristics of the sample. The lightI–V is taken with the sample illuminated at 905 nm at a power of 120 mW.

Fig. 6. Sample is processed with a beveled edge from which intersubbandexcitation can be coupled into the device. The pulsed IR light from the Erbiumlaser will be deflected at the wedge into total internal reflection mode and reachesactive region with component of polarization which can excite intersubbandtransitions. The sample is illuminated with continuous light populating theground state of the QW. Intersubband excitation pulsed radiation is coupledfrom the wedge, while the photocurrent is observed.

temperature variation in the short-circuit current is caused by thedifference in effective density of states in the QW, correspondingto the fixed photoexcitation wavelength of 905 nm, as well asvariation in the carrier escape rate at different temperatures.[16]–[18]

When a forward bias is applied, the tunneling rate of the carri-ers reduces and the photocurrent decreases, eventually reachingzero just below the open-circuit voltage [16]. Near this point,the I–V curve has a flat region (at an applied bias of between1.1 and 1.3 V) as shown in Fig. 5. At this bias, carriers cannotescape via tunneling and become trapped in the well [16]. Thefollowing experiment is performed at this bias condition so thatthere is no dc background current and the only photocurrentdetected is because of the absorption of infrared photons.

The sample was prepared with a wedge structure in order toincrease the optical coupling of IR light into QW intersubbandtransition, as shown in Fig. 6(a). It was illuminated with continu-ous 980-nm light, populating the ground state of the QW. Whilecarriers are continuously excited into the well, a 100-ps pulseof light at 2.79 μm from an Erbium laser [19], with energy 2 mJand 3 Hz repetition rate, was directed at the sample enablingthe carriers that are trapped in the QW to be excited into thecontinuum. Once in this state, the carriers can then be extractedto the external circuit. Fig. 6(b) shows the experimental setupthat has been used in this study.

Fig. 7. Photocurrent from the sample after being illuminated with pulsed100-ps laser of 2.79 μm at t = 0 s. The oscillatory behavior and the delay isbecause of the mismatch in impedance of the electric equipment.

A clear observation of a two-photon photocurrent of 1 mAin a single QW structure has been obtained (see Fig. 7). Theoscillatory behavior is an artifact, called ringing, that is causedby incomplete impedance matching in the detection electronics,and the delay of photocurrent enhancement is because of thecombination of optical and electrical delays in the detectionsystem. The result demonstrates that multiple-photon absorptioncan be achieved in QW devices, which is one of the essentialconditions needed to be satisfied for IBSCs, [9] and the resultindicates that the QW can be in fact a suitable candidate forIBSCs.

IV. DISCUSSION OF THE RESULTS AND REALIZING

INTERMEDIATE BAND SOLAR CELLS

Our observation of an increase in photocurrent in QW IBSCsvia a transient electrical measurement adds to the growing bodyof the literature from QD IBSCs in the forms of both quasi-continuous-wave electrical and transient optical measurements.Martı et al. reported an increase in the photocurrent in a δ-dopedInAs/(Al,Ga)As QD system with continuous infrared light ex-citing carriers from the IB to the CB [5], which is an essentialprocess in IBSCs. However, the photocurrent increase observedwas as small as 10–12% of the initial value. A recent reportby Okada et al. also shows an increase in quantum efficiencyof 0.3% in a δ-doped InAs/GaNAs QD solar cell [4], whileSugiyama et al. achieved 0.5% in an InGaAs/GaAsP strain-balanced QW superlattice cell [20]. Kita et al. reported proof ofsequential absorption of photons via the IB in the form of bleach-ing and recovery of photoluminescence (PL) in InAs/GaAs QDsin an optical cavity [21]. As an IR radiation pulse excites carriersfrom the IB to the continuum, Kita et al. observed a reduction inthe carrier density in the IB, causing a transient suppression ofthe PL. To achieve sufficient absorption, the quantum dots werelocated in a photonic cavity and short, high-power pulses wereused.

As demonstrated in this paper as well as in the literature,the short excited-state lifetime of the carriers remains a criticalproblem in realizing efficient IBSCs. In fact, all experimentalreports on IBSCs show only a very weak sequential absorption

YOSHIDA et al.: PROGRESS TOWARD REALIZING AN INTERMEDIATE BAND SOLAR CELL–SEQUENTIAL ABSORPTION 637

Fig. 8. Energy diagram of a “photon ratchet” IBSC. The photon RB ERB islocated at an energy interval ΔE below the IB EIB and the occupation of bothIB and RB can be described by a single quasi-Fermi level EF ,IB . The chargecarriers in the IB will quickly scatter to the RB where they may have a longlifetime since the RB is optically isolated from the VB. [23].

of photons, resulting in a negligible gain in energy conversionefficiency. The short lifetime of electrons in the intermediatestates is mainly caused by fast nonradiative recombination thatproceeds faster than all radiative processes. In most of the solarcells described previously, radiative and nonradiative recombi-nation of carriers of the IB occurs before significant sequentialabsorption can take place. Thus, as with a conventional two-band solar cell, the product of carrier lifetime and mobility iscritical for an efficient operation [22].

One means to extending the IB carrier lifetime is to allowsome energy relaxation to take place, forming a so-called “pho-ton ratchet.” The photon ratchet IBSC has been proposed toincrease the lifetime of the carriers in the IB and CB by intro-ducing an extra energy band called the “ratchet band” (RB), i.e.,some energy ΔE below the IB, which is optically decoupledfrom the VB but thermally coupled to IB [23] (see Fig. 8). Insuch systems, the photoexcited electrons in the IB rapidly relaxinto the RB, and when the energy loss ΔE is sufficiently large,their lifetime can become very long. The increase in the carrierlifetime enhances the probability of the second optical excita-tion process from the RB to the CB (GIC ). The enhancementin carrier lifetime is a key to high efficiency PV [24]. To in-crease the generation rate GIC , the photon ratchet also reducesthe population of the IB (as suggested by the quasi-Fermi levelEF,IB ), which, in turn, reduces the recombination rate of theelectrons from the IB to the VB (GVI). Both effects increasethe photocurrent of the solar cell, leading to higher efficiency.The limiting efficiency of such a system shows an efficiencyenhancement from 46.8% to 48.5% when an RB is introducedat ΔE of 270 meV with the globally optimized bandgaps [23].

In practice, introducing the RB to a conventional IBSC addsthe very important advantage that it combats the extremely fastnonradiative recombination rates that are typically caused by theintroduction of the IB. The RB extends the lifetime of the carri-ers in the IB and ensures that the two transitions GVI and GICpump electrons from occupied ground states into vacant excitedstates. Hence, we propose that the RB is an important com-ponent to realizing efficient operation of an IBSC, especiallyin systems where the ideal situation of achieving degeneratedoping, high mobility, and long carrier lifetime in the IB isdifficult. The photon ratchet IBSC can be implemented in QWand quantum dot systems by spatially separating the carriers

using type-II structures. In such systems, the photo-generatedelectrons and holes rapidly separate into positions in the lat-tice, reducing the strength of both radiative and nonradiativerecombination processes; hence, the lifetime of the carriers canbe extended [25]–[27]. We note that theoretical calculation ofthe type-II “ratchet” quantum dots IBSC predicts the enhance-ment in efficiency [28] and the same would apply to the type-II“ratchet” QW IBSC. The next challenge is to implement a pro-totype structure and to enhance the conversion efficiencies byextending the carrier lifetime in an IBSC.

V. CONCLUSION

Clear observation of a photocurrent of∼1 mA arising from thesequential absorption of photons has been obtained by illumi-nating the sample with a continuum laser to populate the groundstate of a QW, followed by a pulsed laser to pump the intersub-band transition. The result adds to other published observationsthat sequential absorption of the photons is possible in bothQW and quantum dot systems but the short lifetime of carriersprevents efficiency gains that the IBSC concept promises. Intro-ducing a relaxation step into a nonradiative state, the so-called“ratchet band,” can be used to lock carriers into long-lived statesthereby promoting sequential absorption. In a low-dimensionalmaterial system, the RB could arise from type-II structures.

REFERENCES

[1] W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency ofp-n junction solar cells,” J. Appl. Phys., vol. 32, pp. 510–519, 1961.

[2] M. A. Green, “Third generation photovoltaics: Ultra-high conversion effi-ciency at low cost,” Prog. Photovoltaics: Res. Appl., vol. 9, pp. 123–135,2001.

[3] A. Luque and A. Martı, “Increasing the efficiency of ideal solar cells byphoton induced transitions at intermediate levels,” Phys. Rev. Lett., vol. 78,no. 26, pp. 5014–5017, 1997.

[4] Y. Okada, T. Morioka, K. Yoshida, R. Oshima, Y. Shoji, T. Inoue, andT. Kita, “Increase in photocurrent by optical transitions via intermediatequantum states in direct-doped InAs/GaNAs strain-compensated quantumdot solar cell,” J. Appl. Phys., vol. 109, p. 024301, 2011.

[5] A. Martı, E. Antolın, C. R. Stanley, C. D. Farmer, N. Lopez, P. Dıaz,E. Canovas, P. G. Linares, and A. Luque, “Production of photocurrent dueto intermediate-to-conduction-band transitions: A demonstration of a keyoperating principle of the intermediate-band solar cell,” Phys. Rev. Lett.,vol. 97, p. 247701, 2006.

[6] A. Luque, A. Martı, N. Lopez, E. Antolın, and E. Canovas, “Operationof the intermediate band solar cell under nonideal space charge regionconditions and half filling of the intermediate band,” J. Appl. Phys., vol. 99,p. 094503, 2006.

[7] W. Shockley and W. T. Read, Jr., “Statistics of the recombinations of holesand electrons,” Phys. Rev., vol. 87, pp. 835–842, 1952.

[8] R. N. Hall, “Electron–hole recombination in germanium,” Phys. Rev.,vol. 87, p. 387, 1952.

[9] N. J. Ekins-Daukes, C. B. Honsberg, and M. Yamaguchi, “Signature ofintermediate band materials from luminescence measurements,” in Proc.31st IEEE Photovoltaic Spec. Conf., 2005, pp. 49–54.

[10] A. Marti, L. Cuadra, and A. Luque, “Quantum dot intermediate band solarcell,” in Proc. Conf. Record 28th IEEE Photovoltaic Spec. Conf., 2000,pp. 940–943.

[11] E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira,G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick,and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transi-tions in the terahertz range,” Nat. Mater., vol. 8, pp. 803–809, 2009.

[12] B. Murdin, W. Heiss, C. Langerak, S. Lee, I. Galbraith, G. Strasser,E. Gornik, M. Helm, and C. Pidgeon, “Direct observation of the LOphonon bottleneck in wide GaAs/AlxGa1-xAs quantum wells,” Phys. Rev.B, vol. 55, pp. 5171–5176, 1997.

638 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014

[13] D. D. Coon and R. P. G Karunasiri, “New mode of IR detection usingquantum wells,” Appl. Phys. Lett., vol. 45, no. 6, pp. 649–651, 1984.

[14] M. Helm, “The basic physics of intersubband transitions,” SemiconductorsSemimetals, vol. 62, pp. 1–99, 1999.

[15] B. F. Levine, “Quantum-well infrared photodetectors,” J. Appl. Phys.,vol. 74, pp. R1–R81, 1993.

[16] J. Nelson, M. Paxman, K. W. J. Barnham, J. S. Roberts, and C. C. Button,“Steady-state carrier escape from single quantum wells,” IEEE J. Quan-tum. Electron., vol. 29, no. 6, pp. 1460–1468, Jun. 1993.

[17] A. Zachariou, J. Barnes, K. W. J. Barnham, J. Nelson, E. S. M. Tsui,J. Epler, and M. Pate, “A carrier escape study from InP/InGaAs singlequantum well solar cells,” J. Appl. Phys., vol. 83, pp. 877–881, 1998.

[18] M. Paxman, J. Nelson, B. Braun, J. Connolly, K. W. J. Barnham,C. T. Foxon, and J. S. Roberts, “Modeling the spectral response of thequantum-well solar-cell,” J. Appl. Phys., vol. 74, pp. 614–621, 1993.

[19] K. L. Vodopyanov and V. G. Voevodin, “Parametric generation of tunableinfrared radiation in ZnGeP2 and GaSe pumped at 3 μm,” J. Opt. Soc.Amer. B, vol. 10, no. 9, pp. 1723–1729, 1995.

[20] M. Sugiyama, Y. Wang, K. Watanabe, T. Morioka, and Y. Okada, “Pho-tocurrent generation by two-step photon absorption with quantum-wellsuperlattice cell,” IEEE J. Photovoltaics, vol. 2, no. 3, pp. 298–302, Jul.2012.

[21] T. Kita, T. Maeda, and Y. Harada, “Carrier dynamics of the intermediatestate in InAs/GaAs quantum dots coupled in a photonic cavity under two-photon excitation,” Phys. Rev. B, vol. 86, p. 035301, 2012.

[22] J. J. Krich, B. I. Halperin, and A. Aspuru-Guzik, “Nonradiative lifetimesin intermediate band photovoltaics—Absence of lifetime recovery,” J.Appl. Phys., vol. 112, p. 013707, 2012.

[23] M. Yoshida, N. J. Ekins-Daukes, D. J. Farrell, and C. C. Phillips, “Photonratchet intermediate band solar cells,” Appl. Phys. Lett., vol. 100, no. 26,pp. 263902–263902, 2012.

[24] M. J. Y. Tayebjee, A. A. Gray-Weale, and T. W. Schmidt, “Thermody-namic limit of exciton fission solar cell efficiency,” J. Phys. Chem. Lett.,vol. 3, pp. 2749–2754, 2012.

[25] G. Ru, F.-S. Choa, X. Wei, G. Chen, and J. B. Khurgin, “Measurement ofthe lifetimes of photo-excited carriers in type-I and type-II quantum wellmaterials,” in Proc. Conf. Lasers Electro-Opt., 2006, pp. 1–2.

[26] S. Fukatsu, H. Sunamura, Y. Shiraki, and S. Komiyama, “Phononlessradiative recombination of indirect excitons in a Si/Ge type-II quantumdot,” Appl. Phys. Lett., vol. 71, pp. 258–260, 1997.

[27] F. Hatami, M. Grundmann, N. N. Ledentsov, F. Heinrichsdorff, R. Heitz,J. Bohrer, D. Bimberg, S. S. Ruvimov, P. Werner, V. M. Ustinof,P. S. Kop’ev, and Z. I. Alferov, “Carrier dynamics in type-II GaSb/GaAsquantum dots,” Phys. Rev. B, vol. 57, pp. 4635–4641, 1998.

[28] A. M. Kechiantz, L. M. Kocharyan, and H. M. Kechiyants, “Band align-ment and conversion efficiency in Si/Ge type-II quantum dot intermediateband solar cells,” Nanotechnology, vol. 18, p. 405401, 2007.

Authors’ photographs and biographies not available at the time of publication.