Improved quantum dot stacking forintermediate band solar cells using straincompensation
Paul J Simmonds1, Meng Sun2, Ramesh Babu Laghumavarapu2,Baolai Liang1, Andrew G Norman3, Jun-Wei Luo3 and Diana L Huffaker1,2
1 California NanoSystems Institute, UCLA, Los Angeles, CA 90095, USA2Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, USA3National Renewable Energy Laboratory, Golden, CO 80401, USA
Received 10 June 2014, revised 31 August 2014Accepted for publication 12 September 2014Published 16 October 2014
AbstractWe use thin tensile-strained AlAs layers to manage compressive strain in stacked layers of InAs/AlAsSb quantum dots (QDs). The AlAs layers allow us to reduce residual strain in the QDstacks, suppressing strain-related defects. AlAs layers 2.4 monolayers thick are sufficient tobalance the strain in the structures studied, in agreement with theory. Strain balancing improvesmaterial quality and helps increase QD uniformity by preventing strain accumulation andensuring that each layer of InAs experiences the same strain. Stacks of 30 layers of strain-balanced QDs exhibit carrier lifetimes as long as 9.7 ns. QD uniformity is further enhanced byvertical ABAB… ordering of the dots in successive layers. Strain compensated InAs/AlAsSb QDstacks show great promise for intermediate band solar cell applications.
Keywords: strain compensation, tensile strain, self-assembled quantum dots, InAs/AlAsSb,intermediate band solar cells
(Some figures may appear in colour only in the online journal)
1. Introduction
Intermediate band solar cells (IBSCs) are expected to be a keytechnology in the drive towards high-efficiency photovoltaics[1, 2]. An IBSC consists of a single-junction solar cellmodified to include an intermediate band (IB) within its bandgap. Sub-band gap photons harvested via the IB increase thephotocurrent. With higher photocurrents, IBSCs are predictedto exceed the efficiency of traditional single-junction devices[2]. IBSCs based on quantum dots (QDs) are of great interest[3, 4], with one of the most attractive candidate systemsconsisting of InAs(Sb) QDs in an AlAsSb matrix [5]. Withvalence band (VB)-to-IB and IB-to-conduction band (CB)transition energies of 0.7 and 1.23 eV respectively, InAs(Sb)/AlAs0.56Sb0.44 QDs form an almost model IBSC system [5–7]. This QD system has strong electron confinement but analmost flat VB and it hence exhibits type-II behavior [8, 9]. Inan IBSC, these characteristics would reduce carrier
recombination, increase carrier lifetime and improve carrierextraction efficiency.
We have already reported the Stranski–Krastanov (S–K)growth of self-assembled InAs/AlAsSb QDs [8, 9]. AddingGaAs(Sb) cladding layers allows the IB position to be tunedand improves QD optical quality [8, 9]. Recently wedemonstrated IB-mediated, two-photon absorption in theseQDs [10]. In general however, photon absorption in type-IIQDs is low. For efficient IBSCs we must increase the totalnumber of photons absorbed. One solution is to stack multiplelayers of InAs/AlAsSb QDs, but to do this we must considerthe effect of strain. The compressive strain that drives the self-assembly of InAs/AlAsSb QDs builds up with each QD layeradded. Above some critical value, the strain energy will bereleased by dislocation formation. Dislocations are undesir-able in IBSCs since they promote carrier recombination andhence reduce efficiency.
Strain balancing can resolve the problem of strain accu-mulation in large QD stacks [11–13]. Inserting thin tensilestrained layers balances the compressive strain of the QDs.Arbitrarily large QD stacks can be engineered with zero totalstrain. In this article we extend this approach to the techno-logically important InAs/AlAsSb QD system. We employthin AlAs strain compensation (SC) layers to create stacks ofup to thirty QD layers with negligible strain. With highstructural and optical quality, these QD stacks show greatpotential for use in IBSCs.
2. Materials and methods
2.1. Nanomaterial synthesis
Using solid source molecular beam epitaxy we grew a series ofInAs/AlAsSb stack structures, each containing five layers of
QDs (figure 1(a)). Samples are grown on on-axis (±0.5°) InP(001) substrates. We remove the InP native oxide at a substratetemperature (Tsub) of 520 °C under As2 flux. Tsub is calibratedusing reflection high-energy electron diffraction to observe theInP surface reconstruction transition from 2×4 to 4×2 at530 °C. We then cool to Tsub = 500 °C for sample growth. First,150 nm AlAsSb is grown lattice-matched to InP, followed byfive repeats of the QD stack, each comprising: a 5ML GaAsbottom cladding layer; 8ML InAs self-assembled QDs; a 5MLGaAs0.95Sb0.05 top cladding layer; a 15 nm AlAs(Sb) spacer.
The tensile GaAs(Sb) QD cladding layers [8, 9] alreadycompensate the compressive strain in the InAs QDs to someextent. Even so, additional tensile strain is required to com-pletely balance the net compressive strain. A straightforwardway to add tensile strain is to modulate the composition of theAlAsSb spacer between each QD layer (figure 1(a)). We cancreate a thin layer of tensile strained AlAs in the AlAsSb bybriefly closing the antimony shutter. Each spacer thus consistsof two AlAsSb layers of equal thickness t2 surrounding anAlAs SC layer, thickness t1. As we vary t1 from 0–6ML, weadjust t2 to maintain a constant total spacer thickness,t1 + 2t2 = 15 nm. A final layer of InAs QDs completes thestructure. We grow the AlAs(Sb), and GaAs(Sb) layers withV/III beam equivalent pressure (BEP) ratios of ∼17 and ∼11,respectively. The InAs QDs are grown with a V/III BEP ratioof ∼60.
2.2. Nanomaterial characterization
We study the surface InAs QDs with atomic force microscopy(AFM), and use the watershed algorithm included withGwyddion software [14], to analyze dot size and areal den-sity. We fit the QD size distributions with Gaussian–Lor-entzian functions to extract peak and full-width-at-half-maximum (FHWM) values. X-ray diffraction (XRD) allowsus to extract the total residual strain in each sample. Weinvestigate the buried QD layers with (scanning) transmissionelectron microscopy ((S)TEM) and use STEM high-angleannular dark-field (HAADF) imaging to view contrast inatomic number. For photoluminescence (PL) spectroscopy weuse a 532 nm pump laser at 300 K and 77 K. Time-resolvedphotoluminescence (TRPL) is conducted at 77 K with a650 nm laser (pulse width 10 ps), using time-correlated sin-gle-photon counting to record the decay traces.
2.3. Modeling SC and band structure
To decide how thick the AlAs SC layers need to be we cal-culate the strain in each six-layer period of the stacked QDstructure in figure 1(a). We adopt the simple model used byTatebayashi et al [15]. The average perpendicular strain ε⊥ isgiven by
∑
∑ε
ε=
⋅
⊥
⊥ t
t
( )
,ii i
ii
where the strain of the ith layer ε = −⊥ a a a( ) ( ) /i i InP InP, and ti
Figure 1. (a) Schematic of the stacked structures studied, showingthe repeated sections of buried QDs separated by spacers, theposition of the AlAs SC layer and the surface layer of QDs formicroscopy. (b) The band structure calculated for one repeat of theQD stack (AlAs, t1 = 2.5 ML) at 300 K.
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and ai are the thickness and lattice constant of the ith layer,respectively. Due to the 3D nature of the InAs QD layer, itsthickness is not uniform. However, we approximate the InAsQD layer thickness by using an rms height value of 3.29 nmmeasured by AFM for these surfaces (see figure 3(c)). Puttingin values for the GaAs, InAs, GaAsSb, AlAsSb and AlAslayers, we can calculate the thickness of AlAs needed in eachrepeat for strain balancing, which we define to be ε⊥⩽ 1 × 10−5. We calculate that each AlAs SC layer should be0.698–0.709 nm thick (2.47–2.50ML) to compensate the totalstrain completely.
Simulating the band structure of each repeat of the QDstack structure using Sentaurus software shows that the AlAsSC layers form barriers in both the CB and VB with heights47 meV and 219 meV respectively (figure 1(b)). However, weshow below (figure 5(d)) that these extremely thin AlAslayers do not increase carrier recombination and so areexpected to have minimal effect on IBSC performance.
3. Results and discussion
3.1. Experimental conditions for strain balancing
By fitting models to XRD spectra we can calculate the layerthicknesses and compositions in each QD stack (figure 2(a)).Diffraction peaks from the InP substrate and slightly com-pressive AlAsSb buffer occur at 0″ and −300″, respectively.We also see superlattice (SL)-type fringes due to the fiveperiodic repeats of the QD stack. These SL fringes are broadand low in intensity for two reasons. The first is the finite QDsize distribution in each array, which leads to local variationsin strain. The second is the undulating nature of the InAs QD/GaAsSb cladding interfaces.
With thicker AlAs the SL fringes move to larger Braggangles due to increasing tensile strain. We plot the SL peakpositions for each sample (figure 2(b)). Linear interpolationallows us to locate the positions of the 0th order SL peakssince the InP and AlAsSb buffer peaks otherwise obscurethem. In a perfectly strain-balanced sample, the 0th order SLpeak would be at 0″ (i.e. superimposed on the InP). We defineΔ″ to be the angular separation between the InP and 0th orderSL peaks. Δ″ is negative for the sample with 2ML AlAs SClayers and positive for the 4–6ML AlAs samples (inset tofigure 2(b)). This means we can tune the net strain betweencompression and tension, and hence careful control of theAlAs thickness will result in QD stacks with no residualstrain. A linear fit to the positions of the 0th order peaksshows that for this series of samples, AlAs SC layers2.4 ± 0.4ML thick would have given us zero net strain (insetto figure 2(b)). This experimental result is in good agreementwith our theoretical prediction of ∼2.5 ML AlAs, despite theapproximation we made regarding the InAs thickness in oursimple model.
3.2. Nanomaterial quality and SC
The optical quality of these InAs/AlAsSb QD stacks ishighest when strain is lowest. We see bright PL emissionfrom the InAs QDs, consistent with our previous studies ofthis material system (figure 3(a)) [8, 9]. For AlAs SC layerthicknesses in the range 0–6ML, we obtain highest intensityPL from the 2ML sample, which has lowest residual strain(i.e. smallest |Δ″|). Brighter PL in the strain-balanced sampleindicates the suppression of strain-related defects, such asdislocations, that cause non-radiative recombination. Redu-cing the residual strain almost to zero hence results in ameasurable improvement in material quality.
The FWHM of the PL peaks is correlated with the sizedistribution of the QDs in each structure (figure 3(b)). A moreuniform QD array will have a smaller range of ground stateenergies and hence a sharper PL peak. Of the four PL spectrathe 0ML sample (i.e. no AlAs SC layers) has the largest
Figure 2. (a) XRD spectra for 5× QD stack samples containingtensile AlAs SC layers of various thicknesses. The dashed lineemphasizes the change in +1st order QD SL peak position withincreasing AlAs thickness. (b) Plot showing the angular position ofeach SL peak for the three XRD spectra in (a). Linear fittingidentifies the angular position of the 0th order SL for each sample.(Inset) Δ″ (splitting between the InP substrate and 0th order SLpeaks) as a function of AlAs SC layer thickness, shown with alinear fit.
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FWHM of 59.5 meV. Adding SC layers reduces the PLFWHM, with the lowest value of 51.6 meV measured in thealmost perfectly strain balanced 2ML sample. Strain balan-cing ensures that the compressive strain in each layer of InAswill be identical, rather than increasing with the number ofstacked layers. This means that average dot size in the firstand nth stacked QD layers should remain constant, leading toa narrower distribution throughout the structure as a whole.
We analyze AFM images from each QD array(figure 3(c)) to measure the QD size uniformity. The surfaceQD size distributions on each sample are summarized intable 1. The narrow distributions of both QD radius andheight in the strain-balanced, 2 ML AlAs sample are con-sistent with its low PL emission linewidth (figure 3(b)).Uniform QDs are desirable for IBSC devices since theirreduced distribution of ground state energies, increases theprobability of IB formation.
Figure 3(a) also shows that raising the AlAs SC layerthickness from 0 to 6ML increases the PL emission energyby 24 meV. The AFM data in table 1 suggest that this smallblue shift is caused by a reduction in average QD size(figure 3(c)). We deposit the same amount of InAs on eachsample, which in S–K growth is divided between the 2Dwetting layer and the 3D QDs. Increasing the AlAs thicknessadds tensile strain to the stack so that thicker compressiveInAs wetting layers are needed to trigger the transition to 3Dgrowth [16, 17]. Thicker wetting layers mean that less InAs isleft over to form QDs and so average QD size decreases.Decreasing QD size increases the ground state energy and thiscauses the blue-shift observed in the PL (figure 3(a)). QDareal density undergoes a simultaneous increase, as requiredfor conservation of mass.
3.3. Synthesis of thick QD stacks for IBSCs
Since a useful IBSC device will need to contain a significantnumber of QD layers, we grew another structure as perfigure 1(a) but with thirty repeats of the QD stack (plus asurface QD layer for AFM). We set the AlAs SC layerthickness, t1 = 3ML (i.e. close to optimum for strain balan-cing) with again 15 nm total spacer thickness. In agreementwith our calculations, the 3ML AlAs SC layers result inalmost complete strain balancing. After growing thirty layersof QDs (figure 4(a)) we calculate Δ″ = +140″ from XRD.High-resolution STEM images (not shown) indicate that,even at the top of the 30× stack, the InAs QDs do not nucleatedislocations. The 3ML AlAs SC layers appear as thin darkbands in the center of the AlAsSb spacers (figure 4(b)). Wenote an interesting alignment of the InAs QDs at 45° to the(100) plane (figures 4(b) and (c)). Compared to the well-known stacking of QDs parallel to the growth direction[17, 18], this staggered 45° alignment is a little more unusual[19–22]. Springholz and Holy discuss three mechanismsgiving rise to vertical ordering in QD stacks: non-planarsurface morphology; elastic anisotropy of the spacers; andalloy decomposition in the spacers [23]. Alloy decompositionoften results in QDs located at the interstices of those in thepreceding layer, i.e. 45° alignment, or ABAB… stacking[19, 24]. AlAsSb has a wide miscibility gap and so alloydecomposition is perhaps the most likely candidate[8, 25, 26]. However, figure 4(b) also shows the presence ofnon-planar interfaces, and we cannot rule out elastic aniso-tropy effects. Additional investigation is needed to decon-volve the mechanism(s) responsible for the staggered QDalignment.
Figure 3. (a) 77 K PL emission from 5× QD stack samplescontaining different AlAs SC layer thicknesses. (b) FWHM of thePL spectra in (a) as a function of AlAs SC layer thickness. (c) AFMimages of the surface layer of InAs dots on each 5× QD stack sampleshowing the evolution of morphology with increasing AlAs SC layerthickness.
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The ABAB… stacking means the separation betweenadjacent QD layers is effectively larger than the spacerthickness of 15 nm. The distance between the center of a QDand its nearest neighbors in the layers above and below is∼21 nm. The increased separation will reduce couplingbetween successive layers of QDs. To compensate for thiseffect, it may therefore be useful to decrease the spacerthickness slightly in future stacks with this 45° QD alignment.The staggered alignment of the InAs/AlAsSb QDs may in factbenefit future IBSCs by maintaining QD uniformity as thenumber of layers increases [20, 24].
Raising the number of strain compensated QD layersfrom five to thirty (figures 3(b) and 5(a)) increases lateralordering. AFM of the 30× stack sample shows organization ofthe QDs into chains, 5–10 dots long. This is likely the resultof the in-plane ordering that ABAB… QD stacking introduces.We also compared surface QDs on the 30× stack with thoseon an identical control sample grown without SC layers(figures 5(a) and (b)). The QD size distribution is relativelynarrow for both, although the dots on the 0ML controlsample are elongated and less uniformly shaped. The
accumulation of compressive strain in the 0ML control maydisrupt the vertical ordering towards the top of the QD stack.
PL spectra from the 30× QD stacks with and without SCare shown in figure 5(c). It is interesting that the trendsobserved for the series of 5× QD stacks are not evident inthese two thicker samples. There is a small blue shift of7 meV between the two samples but here it is the 0MLcontrol sample that is at higher energy. The 3ML sample hasa negligibly smaller PL linewidth than the 0ML sample(107 meV versus 109 meV) rather than the dramaticimprovement we saw from strain balancing in the 5× QDstack series. Analysis of the AFM data in figures 5(a) and (b)shows that QD height is essentially identical in the twosamples, while QD radius is slightly lower in the 3MLsample (29.5 nm versus 31.4 nm). QD quantum confinementstrength is typically stronger in the z-direction than in-plane.Constant QD height (rather than decreasing, as in the 5×samples) with increasing AlAs thickness is the most likelyreason we don’t see the same blue shift in the PL. The causeof this difference between the 5× and 30× stacks could stemfrom the relative lengths of the growths. Due to the mis-cibility issues we mention above, AlAsSb composition is
Table 1. Summary of QD size and areal density variation among the four 5× QD stack samples with different AlAs SC layer thicknesses.
Figure 4. (a) STEM HAADF images showing the full 30× QD stackstructure. The InAs QDs with their 5 ML GaAs(Sb) cladding layersshow up as bright horizontal lines. (b) A higher magnification STEMHAADF image of the InAs QD layers. Scale bar indicates 25 nm. (c)Schematic of (b) highlighting the InAs QDs (white) and the AlAs SClayers (black lines). The dashed line emphasizes the staggeredalignment of the InAs QDs at 45° to the growth direction.
Figure 5. AFM images of surface dots on (a) a stack of 30 QD layerswith 3 ML AlAs SC layers and (b) a control sample consisting of 30QD layers without SC layers (i.e. 0 ML AlAs). (c) 300 K PL spectraand (d) 77 K TRPL spectra from these two 30-layer QD stacksamples.
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known to be extremely sensitive to growth conditions[8, 25, 26]. It is therefore possible that the AlAsSb alloyfluctuates during growth but at a sufficiently low rate that itseffect only becomes apparent in these long 30× QD stackgrowths. Small changes in composition could throw off thedelicate balance of strain and obscure the effects of the AlAsSC layers on QD size. However, owing to the already broadSL XRD peaks and the overlap between the peaks of theAlAsSb buffer and the InP substrate we cannot see if theseminor variations in AlAsSb composition are present or not.Further work will be needed to understand how the structureevolves as we increase the number of QD layers.
Despite this, brighter PL from the 3ML AlAs sample(figure 5(c)) still shows that strain balancing improves thematerial quality of the stacked structure. The benefits ofadding SC are further confirmed in carrier lifetime measure-ments. We observe a biexponential decay of the TRPL signal(figure 5(d)), consistent with previous measurements in thistype-II QD system [9]. Immediately after pumping, a highconcentration of carriers in and around the QDs leads to bandbending. Band bending increases electron and hole wave-function overlap and results in an initially fast decay process(time constant τ1). As nonequilibrium carriers recombine,band bending is reduced. This lowers wavefunction overlapand a slower decay process takes over (time constant τ2). Weextract τ1 and τ2 by fitting the decay curve with a biexpo-nential function [9]. For the strain-balanced sample (3 MLAlAs) we calculate τ1 = 0.98 ± 0.15 ns and τ2 = 9.65 ± 0.25 ns.For the control sample (0 ML AlAs) without SC layers wefind τ1 = 0.93 ± 0.09 ns and τ2 = 5.39 ± 0.27 ns. The fasterdecay process seems to be identical in the two samples, andits time constant of ∼1 ns is consistent with radiative lifetimesin other QD systems [27]. In contrast, τ2 is almost twice aslong in the strain compensated sample than in the controlsample. We attribute this increase in carrier lifetime to areduction in defects due to the successful elimination ofresidual strain in the QD stack. Longer carrier lifetimes as aresult of effective strain balancing will help increase theefficiency of future IBSC devices built from this QD system.
4. Conclusion
We have demonstrated the ability to manage compressivestrain in stacked InAs/AlAsSb QD structures by adding thin,tensile strained AlAs layers. Controlling the AlAs thicknessallows us to tune the net strain from compression to tension.We identify the AlAs thickness required for perfect strainbalancing with a combination of modeling and experiment.We show that material quality and QD size uniformity bothimprove as the magnitude of the strain is reduced. Usingoptimized AlAs SC layers we demonstrate stacks of thirty QDlayers with almost zero residual strain. The dislocation-freeQDs adopt a 45° alignment between adjacent layers, whichmay help increase dot uniformity throughout the structure.Overall, strain balancing enhances QD optical quality andcarrier lifetime both of which are critical for IBSC applica-tions. The next step for this research is to build IBSC devices
from these strain-balanced nanomaterials. We anticipate thatthe improved properties of strain compensated QDs will leadto InAs/AlAsSb IBSCs with increased efficiency.
Acknowledgments
This material is based upon work supported by the Depart-ment of Energy under Award Number DE-EE0005325. Theauthors at UCLA gratefully acknowledge the use of the Nanoand Pico Characterization Lab in the California NanoSystemsInstitute, and the XRD resources made available by MarkGoorsky. We thank Seth Hubbard for useful discussions.
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