Suppression of phonon-mediated hot carrier relaxation in type-II InAs/AlAs x Sb 1−x quantum wells: a practical route to hot carrier solar cells
H. Esmaielpour, V.R. Whiteside, J. Tang, S. Vijeyaragunathan, T. D. Mishima, S. Cairns, M. B. Santos, B. Wang, I. R. Sellers
SSuppression of phonon-mediated hot carrier relaxation in type-IIInAs/AlAs x Sb − x quantum wells: a practical route to hot carrier solar cells H. Esmaielpour, V. R. Whiteside, J. Tang, S. Vijeyaragunathan, T.D. Mishima, S. Cairns, M.B. Santos, and I.R.Sellers a) and B. Wang Homer L. Dodge Department of Physics & Astronomy, University of Oklahoma, 440 W. Brooks St., Norman,Oklahoma 73019, USA School of Chemical, Biological and Materials Engineering, Sarkeys Energy Center, University of Oklahoma,East Boyd Street-T301, Norman, OK 73019, USA
InAs/AlAs x Sb − x quantum wells are investigated for their potential as hot carrier solar cells. Continuouswave power and temperature dependent photoluminescence indicate a transition in the dominant hot carrierrelaxation process from conventional phonon-mediated carrier relaxation below 90 K to a regime where inhib-ited radiative recombination dominates the hot carrier relaxation at elevated temperatures. At temperaturesbelow 90 K photoluminescence measurements are consistent with type-I quantum wells that exhibit hole lo-calization associated with alloy/interface fluctuations. At elevated temperatures hole delocalization revealsthe true type-II band alignment; where it is observed that inhibited radiative recombination due to the spa-tial separation of the charge carriers dominates hot carrier relaxation. This decoupling of phonon-mediatedrelaxation results in robust hot carriers at higher temperatures even at lower excitation powers. These resultsindicate type-II quantum wells offer potential as practical hot carrier systems.Keywords: Hot carriers, Phonon bottleneck effect, Type-II band alignment I. INTRODUCTION
Hot carrier solar cells (HCSCs) have been proposed asdevices, which can increase the conversion efficiency ofa single junction solar cell above the Shockley-Queisserlimit . Since thermalization of photogenerated carri-ers is a major loss mechanism in conventional solar cells,HCSCs have the potential to produce higher efficiencydevices using simple single gap semiconductor architec-tures by eliminating the thermal losses associated withelectron-phonon interactions .However, before their practical implementation canbe realized, HCSCs must circumvent two mainchallenges : 1. Find an absorber material in whichhot phonons are longer lived than hot carriers such as toprovide the required condition to promote reabsorptionof these hot phonons, a phonon bottleneck, which sig-nificantly reduces hot carrier relaxation through phononchannels ; 2. Implement energy selective contacts inwhich only a narrow range of energy (within the hot car-rier distribution) can be extracted, restricting the energydistributed through carriers cooling, therefore minimiz-ing the entropy heat transfer loss .Here, InAs/AlAs . Sb . quantum-wells are investi-gated as a candidate hot carrier absorber. The use ofquantum wells also offers the potential to facilitate thedevelopment of energy-selective contacts and fast carrierextraction via resonant tunneling from quantum wells(QWs) making them an attractive potential system forHCSCs. a) I. R. [email protected]
II. EXPERIMENTAL RESULTS AND ANALYSIS
A schematic of the sample used in this investiga-tion is shown in Fig. 1(a). The InAs/AlAs . Sb . multi-quantum-well heterostructure was grown by molec-ular beam epitaxy (MBE) at a substrate temperature of465 ◦ C. A 2000 nm InAs buffer layer was grown on a nom-inally undoped GaAs substrate to reduce the density ofcrystalline defects arising from the lattice mismatch ofthe active region (MQWs) and the substrate. The thick-ness of the InAs QWs is 2.4 nm and the AlAs . Sb . barriers are 10 nm.As shown in Fig. 1(b), there is a lower quantum con-finement in the valence band (VB) and much larger con-finement in the conduction band (CB). The lower en-ergy barrier layers in the VB results in the rapid trans-fer of the holes absorbed directly in the InAs QWs tothe AlAsSb barriers and their enhanced mobility withincreasing temperature. Conversely, due to the large con-finement in the CB, electrons remain strongly confined atall temperatures . The type-II band alignment shownin Fig. 1 (b) (magnified in 1(d) for clarity) and thermaldiffusion of holes results in an excess of electrons (withrespect to holes) in the QWs due to the reduced radiativerecombination rate.In addition, the large energy band offset between theQW and barrier facilitates absorption of a large propor-tion of the solar spectrum directly in the InAs QWs,without significant losses in the barriers. Finally, thenarrow QWs enable a design in which the separation ofthe energy levels in the CB is large ( ∼ a r X i v : . [ c ond - m a t . m t r l - s c i ] O c t FIG. 1. (a) Schematic representation of theInAs/AlAs . Sb . quantum well sample investigated.(b) Simulated energy profiles showing the relative energy ofthe confinement potential at the point in the conduction(high) and valence band (low). (c) 2D Electron density ofstates as a function of the energy for this structure. (d)Shows a magnification of the band offsets displaying thetype II band alignment with large separation of the energysubbands. a range of power densities at 10 K are shown in Fig.2(a).At lower powers, a shift in the PL peak energy is evident,which reflects the effects of alloy fluctuations that havea significant effect at low power and temperature .At intermediate powers, the peak energy stabilizes anda broadening of the high-energy tail becomes evident.Such high-energy broadening is indicative of the presenceof hot carriers generated by non-equilibrium photo-generated carriers in the CB.The observation of the shift in peak energy at lowpower is also evident in Fig.2(b), which shows the de-pendence of the peak PL energy (at increasing tempera-ture) versus absorbed power ( P abs ). At powers below 1-2W/cm a large increase in the peak PL is observed. How-ever, at higher P abs the peak PL energy saturates, par-ticularly at higher temperatures. This behavior has beenshown to be due to the presence of alloy fluctuations atthe InAs-AlAsSb interface and the resulting spatial local-ization of carriers, which is quenched or saturated, withincreasing temperature and/or excited carrier density. The effect of the alloy fluctuations is also illus-trated (somewhat) in Figure 2(c), which shows thepower dependent behavior of the temperature difference(the difference between carrier and lattice temperatures:∆ T = T e − T L ). The carrier temperature, and there-fore, ∆ T , can be quantified by fitting the high-energytail of the PL spectrum, using the generalized Planck relation I ( E ) ∝ ε ( E ) exp (cid:18) − Ek B T e (cid:19) (1) Where I is the energy-dependent PL intensity, ε is theeffective emissivity, which is related to the absorptionprofile, k B is Boltzmann’s constant, and T e representsthe carrier temperature extracted from the slope of thePL at energy greater than the band gap. Although hotcarriers have been predominately investigated using ul-trafast time-resolved spectroscopy , Equation (1)describes a technique to study the behavior of hot car-riers in continuous-wave operation, the mode of opera-tion of solar cells, and therefore presents a more realisticmethod to interpret the hot carrier dynamics in practicalphotovoltaic systems.At low powers, a large shift of the carrier tempera-ture is observed (below 1 W/cm ). The validity of Equa-tion (1) for the extraction of T e assumes that the effec-tive emissivity ( ε ), therefore absorption, is constant at afixed energy. That is, it is independent of the excitationpower. Since the PL energy changes rapidly in the lowpower regime, the initial increase in T e is attributed toan artifact of the increasing absorption rather than thereal carrier temperature. However (as described above)at higher powers ( P abs > ) the energy shift sta-bilizes (Fig.2(b)) and as such, reflects the (true) carriertemperature; independent of fluctuation effects, whichare saturated under these excitation conditions.It is important to emphasize, once more, that sincethere is a large energy difference between the ground-state transition and the higher-order states (Fig.1(d)),the high energy tail represents hot carrier effects relatedsolely to the ground-state of the QW, unperturbed bystate-filling effects. It must be noted, however, that al-though band-to-band recombination in the AlAsSb bar-riers has little effect on the high-energy tail of QW lu-minescence, the effects of impurities in the QW and/orlocalized states at the QW/barrier interface cannot betotally dismissed as contributing to the high-energy tail;the latter of which is discussed in more detail below (seeFig.6).The number of carriers generated ( N c ) with increas-ing intensity is indicated with respect to the absorbedpower on the upper axis of Fig.2(b) and (c). The densi-ties absorbed are the order of, or less than, 3 × cm − for the excitation levels used. If this is compared to thetotal 2D density of states calculated for the ground statefor the InAs QWs, which is shown in Fig.1(c) (1 × cm − ), then it becomes clear that the increased contri-bution of the high energy tail is not the result of signif-icant state-filling, or the saturation of the ground-state,and therefore likely has its origin in inhibited hot car-rier relaxation via the creation of a phonon bottleneck .Similar effects have been observed recently in InAs QDs,where the spatial separation of carriers in impurity statesleads to the observation of inhibited carrier relaxation asa result of reduced carrier-carrier scattering . The type- (c)(b)Carrier Density (cm -2 x10 )(a) P eak E n e r g y ( e V ) T ( K ) P abs (W cm -2 )Power Density N o r m . I n t e n s i t y ( a r b . u . ) Energy (eV) T L = 10 K FIG. 2. (a) Power dependent PL spectrum at 10 K. (b) PeakPL energy at selected various temperatures. (c) Temperaturedifference (∆ T ) versus absorbed power ( P abs ) at 10 K. II nature of InAs/AlAsSb is expected to lead to similarresults here.Equation (1) shows that the PL spectrum can also giveinformation about the absorption and the effective bandgap of the QWs. The pre-exponential term of the Planckdistribution describes an effective emissivity term, whichis an energy dependent parameter. Fig.3(a) shows thenatural logarithm of this effective emissivity ( lnε ) (closedsquares) as a function of photon energy ( E ) at 10 K forlow excitation power, prior to significant hot carrier gen-eration. These data are shown with respect to the powerdependent PL. As the energy increases towards the peakPL energy, and therefore band gap, the effective emissiv-ity increases rapidly. Once the energy gap is reached, theeffective emissivity increases much more slowly, reflecting(somewhat) the lower rate of change of the absorption athigher energy .Fig.3(b) illustrates the effect of the emissivity termwith increasing excitation power obtained by plotting lnεvs. E for the PL spectra of Fig.3(a). These data are com-pared to highest power PL (shown in black). The behav-ior of the effective emissivity data is constant across thespectra with the shift in absolute value related to the in-creasing carrier temperature, as extracted from the slopeof the PL, which is inserted in the Eqn. (1) transposedfor the natural logarithm of the effective emissivity. Theconsistency of lnε confirms that the pre-exponential termin Equation (1) is indeed independent of power (for theconditions used to extract T e ) and demonstrates furtherthat a large separation exists between the ground andthe first excited state in the QWs. Therefore, since thecarrier temperature is extracted in a region with the con-stant effective emissivity over a large energy range, T e isdetermined with relatively low uncertainty.Fig.4(a) and (c) display the dependence of the tem- FIG. 3. (a) Natural logarithm of effective emissivity (bluesquares) and power dependent PL spectrum as a function ofenergy. (b) The comparison of the behavior of the highestpower PL spectrum and natural logarithm of effective emis-sivity for several intensities. perature difference (∆ T ) for temperatures between 10 Kand 90 K, and 90 K and 130 K, respectively. The insetto Fig.4(c) shows the same data at 225 K and 295 K.In Fig.4(a), the carrier temperature, and therefore ∆ T ,tends to increase with increasing excitation power. Thedependence of the hot carriers and their thermalizationrate can be evaluated by studying the rate of the ther-malized energy (which is the same as absorbed power inthe V oc condition) per degree of temperature change as described by: P th = ntE LO τ th exp (cid:18) − E LO k B T e (cid:19) = Q ∆ T exp (cid:18) − E LO k B T e (cid:19) (2) Where P th is the thermalized (absorbed) power, n iscarrier density, t is thickness, τ th is the thermalizationtime, E LO is the phonon energy for InAs, k B is Boltz-manns constant, and T e is the carrier temperature. ∆ T is the difference in temperature between the carriers andthe lattice, and Q is the thermalization coefficient .Equation (2) can be used to extract Q , an empiricalparameter used to assess the contribution of phonon me-diated carrier relaxation in QWs . A high Q is indica-tive of efficient phonon-mediated relaxation of hot carri-ers; therefore, systems with lower Q are desired for prac-tical HCSCs . In Fig.4(b) and (d), the slope of each dataset is used to extract Q for that particular temperature.In Fig.4(b) it can be seen that increasing the temperatureto 90 K results in a Q that is increasing, consistent withthe increasing contribution of LO phonon scattering atelevated temperature . As the temperature is increasedfurther (90 K - 130 K), as shown in Fig.4(d), Q starts tobecome less dependent on T L ; stabilizing between 90 Kand 130 K despite increasing phonon densities at elevatedtemperature. To reveal the mechanism for this unusualbehavior the effect of T e with increasing excitation powerat higher temperatures needs to be considered.Fig.4(a) shows T e versus power between 10 K and 90 K.As excitation power is increased the carrier temperaturealso increases, as the ratio of excited carriers to phonondensity becomes larger. As the lattice temperature is in-creased to 90 K, the absolute increase in T e (with power)begins to slow and reduces. This behavior is expectedsince the phonon density is larger at elevated temper-atures (see Fig.6b), increasing the prevalence of carrierthermalization. This behavior consequently leads to anincreased Q as observed in Fig.4(b). However, for highertemperatures ( >
130 K), we can see the dependence of T e with absorbed power is less than the dependence of T e at lower temperature (Fig.4b). Indeed, although T e is reduced up to 90 K - stabilizing somewhat through130 K rather than producing the expected equilibriumcarrier distribution via strong LO phonon-relaxation, T e actually increases; again, despite an increasing phonondensity at elevated lattice temperatures.In addition to this apparent decoupling of the phonon-relaxation channels above 130 K, the effect of excitationtemperature, also, becomes less pronounced at highertemperature. The inset to Fig.4(b) shows the power de-pendence at 225 K (solid squares) and 295 K (solid cir-cles), respectively. What is evident is: that the absolute T e increases relative to T L above 130 K and from 225 Kto 295 K, the carriers are “hot”, even at lower excitationlevels.This behavior presents an interesting question with re-spect to the validity of using analysis of Q in type-IIsystems. The empirical parameter Q has been used pre-viously to assess, or qualify the contribution of phonon-relaxation channels in type-I QWs and evaluate their po-tential for applications as the absorber in HCSCs .Indeed recently, this analysis has also been extended todetermine the absolute efficiency that may be produced ifsuch systems were applied to HCSCs under concentratedillumination .This analysis, however, is based on two principles:1) that at high temperatures the dominant relaxationchannels are related to LO phonon scattering and 2) aconstant carrier temperature with respect to excitationpower, occurs at (and represents) the equilibrium condi-tion; i.e., the carriers are thermalized at T L . In the caseof the type-II QWs investigated here, the behavior of thesystem is not consistent with these assumptions, partic-ularly at T >
130 K. The high (and increasing) T e , at T >
130 K, along with the relative insensitivity to excita-tion power, suggests the relaxation of hot carriers in thissystem is not dominated by electron-phonon interaction.
This is further illustrated in the inset to Fig.5, whichshows the Q analysis at 225 K (closed circles) and 295K (closed squares). Here, the difficulty in interpreting a (a) P a b s / ex p (- E L O / k T e ) ( W c m - ) T e m p e r a t u r e D i ff e r e n ce ( K ) (b) T= 10KQ= 0.2 W/Kcm T= 40KQ= 0.6 W/Kcm (c) P abs (W/cm ) T ( K ) Absorbed Power (W cm -2 ) T (K)T (K) Absorbed Power (W cm -2 ) (d) T= 130KQ= 1.5 W/Kcm T= 90KQ= 1.8 W/Kcm FIG. 4. (a), (c) ∆ T versus power density for several latticetemperatures. (b), (d) Gradients of P abs /exp(-E LO /(k B T e ))against ∆ T give the thermalization coefficient ( Q ). The insetgraph in (c) displays the independency of ∆ T from powerdensities at temperatures above 200 K. thermalization coefficient becomes clear since the inde-pendence of T e with power at these temperatures resultsin a Q that is large, sometimes infinite, but can also (de-pendent upon fitting methodology) produce a negativevalue!To understand the apparent anomalies in the systemunder investigation with respect to previous systems pre-sented in the literature , the nature of the band align-ment should be considered. The type-II nature of theInAs/AlAs x Sb − x QWs introduces important differencesin the behavior of the samples at high temperature andunder intense illumination. At low excitation and at tem-peratures below 90 K, the PL measured is dominated by aquasi-type-I transition. This is related to recombinationof electrons confined in the QWs and holes localized atthe InAs/AlAsSb interface . At T >
90 K the holeslocalized at the QW/barrier interface are thermally ac-tivated and redistribute into the lower energy AlAsSbbarrier region. This delocalization of trapped charges re-veals the true type-II band alignment of this system, andconsequently the excitons will be spatially separated. Itshould be noted, if the alloy fluctuations were eliminated,or the materials properties improved, the type-II behav-ior would be observed at all temperatures.A consequence of the separation of the electrons andholes is a reduced radiative recombination efficiency, andtherefore a longer radiative lifetime. This behavior willresult in an excess of electrons in the QWs, reducedcarrier-carrier scattering , and (once more) the devel-opment of a phonon bottleneck . As such, the dom-inant relaxation process in the type-II QWs presentedappears related predominantly to the radiative recombi-
130 140 150 160 170 18001020304050
Radiative RecombinationPhonons T ( K ) Th e r m a li z a t i on C o e ff i c i e n t ( W / K c m ) Lattice temperature (K)
T (K) n t E L O / t h FIG. 5. Relation between Q and ∆ T against lattice temper-ature are displayed to T e = 130 K (blue triangles). The insetshows that Q cannot be determined through for these datasets. Also shown (closed stars) is the temperature dependenthot carrier temperature, ∆ T . nation lifetime, rather than phonon mediated processes.Relation between Q and ∆ T against lattice tempera-ture are displayed to T e = 130 K (blue triangles). Theinset shows that Q cannot be determined through forthese data sets. Also shown (closed stars) is the temper-ature dependent hot carrier temperature, ∆ T .This behavior further illustrates that the analysis of athermalization coefficient ( Q ) used for type-I systems appears invalid here. Indeed, since the rapid spatial sep-aration of carriers absorbed directly in the QWs is a gen-eral feature of type-II systems, the decoupling of LO-phonons via inhibited radiative recombination should bea general feature across other type-II QWs investigatedthis way.Fig.5 illustrates further the unique difference betweenthe dominant hot carrier relaxation processes in type-Iand type-II systems. Specifically, Fig.5 shows a compar-ison of the change of Q (open triangles) and ∆ T (closedstars), versus lattice temperature, T L . These data areextracted as in a similar manner to those in Fig.4. At T <
90 K, where the sample displays type-I behavior,T decreases with increasing lattice temperature, i.e., thehot carriers are being thermalized by conventional LO-phonon interaction. In this temperature regime (10 K90 K) Q is shown to increase with temperature from 0.2WK − cm − to 2 WK − cm − , supporting the idea that Q -analysis is valid in this regime, when the system be-haves as a (quasi)-type-I QW .It must be noted, however, that the Q determinedhere should be considered an upper limit since the dif-fusion (and therefore mobility) of the carriers absorbedis temperature dependent. Practically, this will result ina change of the absorbed power density as lateral car- rier diffusion (and luminescence density area) increasesat higher temperatures, before radiative recombinationoccurs.At T >
90 K, the nature of the system changes:as the holes delocalize from alloy fluctuations, the sys-tem transitions from (quasi)-type-I to type-II. As such, T e begins to increase, increasing linearly with increas-ing lattice temperature, up to 300 K. At temperaturesbetween 130 K and 150 K the behavior, or interpre-tation, of Q becomes ambiguous as the dependence ofthe hot carriers with excitation power becomes less pro-nounced (See Fig.4(c)). In this regime, T e is dominatedby the efficiency of the radiative recombination, whichin type-II systems has been shown to extend for 100s ofnanoseconds . Therefore, the analysis of Q at T > were used to explore the electronicstructure of an analogous InAs/AlSb heterostructurein which the InAs layer is 2.4 nm thick and AlSb isabout 9.4 nm thick. A PBE-GGA exchange-correlationfunctional was used for the structural relaxation; whencalculating the density of states, a hybrid functional wasused . The heterostructure is very similar to thatstudied experimentally and allows a qualitative pictureof its behavior to be determined. In this theoretical sys-tem, AlSb, rather than AlAsSb, is used to simplify theinterpretation.Fig.6(a) shows the 3D density of states (DOS) calcu-lated for the structure, which is magnified about the en-ergy gap. The valence band edges of InAs and AlSbin this heterostructure are almost degenerate, while theconduction bands are well separated between InAs andAlSb. The calculations thus support the type-II bandalignment. It should be noticed that the band gap isnormally underestimated in DFT-PBE calculations andalso hybrid-functional calculations. The first peak above the Fermi level at 0.3 eV is aninterfacial state is mainly located at the InAs/AlSb in-terface, which may account for the carrier localizationand the aforementioned transition from type-I to type-IIin these QWs. This heterostructure displays two distinctinterfaces, i.e. an AlSb-InAs (interface i ) and an Sb-Al/As-In (interface ii ) with the difference arising fromthe varied stacking sequence. A close inspection of the(3D) DOS by projecting it to each atom suggests thatthe interfacial state is more pronounced at the interface i , particularly on the interfacial In, As, and Sb atoms.The origin of these interfacial states is under further in-vestigation but may originate from the interfacial straineffect (Fig.6(a)).The results indicate that reducing the amount of theSb (that is, deposit more Al and As) at the interfacebetween the QWs and the barriers may help to reducethese charge trapping levels. The available (3D) DOSof this interfacial state is in the order of 10 cm − (or10 cm − assuming one-nm-thick 2D-interfaces), similar P honon ( c m × ) -
642 0 20 40 60 80 100 120Temperature (K) -0.2 0.0 0.2 0.4 0.6 0.8 1.0Energy - Ef (eV) D O S ( e V c m × ) - - In As In As In As InAs
Al Sb AlSb Al Sb AlSb Al SbSbAl iii
432 InAsAlSb(a)(b)
FIG. 6. (a) Calculated 3D electron density of states (DOS)for an InAs/AlSb heterostructure, shown inset (upper). TheDOS of InAs and AlSb are plotted by projecting the totalDOS onto each component. (b) Calculated 3D phonon densityof InAs as a function of temperature. The atomic stackingis schematically illustrated in (a) to show the two distinctinterfaces. The size of the atoms is shown based on theircovalent radius. to the InAs conduction band edge. On the other hand,the (3D) phonon density (Fig.6(b)), that is the overallphonon density without distinguishing different types ofphonon, is much higher than the electron density andincreases rapidly as a function of temperature. The in-creased phonon density at higher temperature and theexperimentally observed reduced thermalization suggeststhat phonon-mediated carrier relaxation does not domi-nate at high temperatures, which is consistent with thehypothesis that a phonon bottleneck results in the type-II QWs presented, supporting the conclusion that therelaxation of hot carriers is dominated by the reducedradiative efficiency in these systems.The demonstration of robust hot carriers at elevatedtemperatures (and at reasonable excitation densities),coupled with the relaxation of phonon loss channels, indi-cates that type-II systems offer a viable route to practicalhot-carrier solar cells.The InAs/AlAsSb system, specifically, has several at-tractive features making it a leading candidate: 1) Thelarge QW to barrier energy separation, which is tunableacross the solar spectrum, facilitates efficient absorption of the suns energy; 2) The degeneracy of the valence bandenables efficient hole extraction, while resonant tunnelingstructures are a reasonable route for fast energy selective- hot electron extraction in these systems; and 3) Sincethe photogenerated carriers absorbed directly in the InAsQW are rapidly separated by the type-II band alignment,the loss of photogenerated carriers to photoluminescenceis minimized in the QWs. Work is now underway to de-velop device architectures to further evaluate these sys-tems in practical solar cell devices.
III. ACKNOWLEDGMENTS
The authors would like to acknowledge the contribu-tion of James Dimmock of Sharp Laboratories of EuropeLtd for useful discussions and the critical reading of thismanuscript, and Professor Rui Yang (University of Ok-lahoma) for his insight into the early sample design. Thecomputation was performed at the Extreme Science andEngineering Discovery Environment (XSEDE) and theOU Supercomputing Center for Education & Research(OSCER) at the University of Oklahoma.
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