On the importance of antimony for temporal evolution of emission from self-assembled (InGa)(AsSb)/GaAs quantum dots on GaP(001)
Petr Steindl, Elisa Maddalena Sala, Benito Alén, Dieter Bimberg, Petr Klenovský
OOn the importance of antimony for temporal evolution of emission fromself-assembled (InGa)(AsSb)/GaAs quantum dots on GaP(001)
Petr Steindl,
1, 2, ∗ Elisa Maddalena Sala,
3, 4, † Benito Al´en, Dieter Bimberg,
6, 7 and Petr Klenovsk´y
1, 8, ‡ Department of Condensed Matter Physics, Faculty of Science,Masaryk University, Kotl´aˇrsk´a 267/2, 61137 Brno, Czech Republic Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, Netherlands Center for Nanophotonics, Institute for Solid State Physics,Technische Universit¨at Berlin, Hardenbergstr. 36, 10623 Berlin, Germany EPSRC National Epitaxy Facility, The University of Sheffield,North Campus, Broad Lane, S3 7HQ Sheffield, United Kingdom Instituto de Micro y Nanotecnolog´ıa, IMN-CNM,CSIC (CEI UAM+CSIC) Isaac Newton, 8, E-28760, Tres Cantos, Madrid, Spain Center for Nanophotonics, Institute for Solid State Physics, Technische Universit¨at Berlin, Germany “Bimberg Chinese-German Center for Green Photonics” of theChinese Academy of Sciences at CIOMP, 13033 Changchun, China Czech Metrology Institute, Okruˇzn´ı 31, 63800 Brno, Czech Republic (Dated: January 19, 2021)Understanding the carrier dynamics of nanostructures is the key for development and opti-mization of novel semiconductor nano-devices. Here, we study the optical properties and carrierdynamics of (InGa)(AsSb)/GaAs/GaP quantum dots (QDs) by means of non-resonant energyand temperature modulated time-resolved photoluminescence. Studying this material system isimportant in view of the ongoing implementation of such QDs for nano memory devices. Our setof structures contains a single QD layer, QDs overgrown by a GaSb capping layer, and solely aGaAs quantum well, respectively. Theoretical analytical models allow us to discern the commonspectral features around the emission energy of 1.8 eV related to GaAs quantum well and GaPsubstrate. We observe type-I emission from QDs with recombination times between 2 ns and 10 ns,increasing towards lower energies. The distribution suggests the coexistence of momentum directand indirect QD transitions. Moreover, based on the considerable tunability of the dots dependingon Sb incorporation, we suggest their utilization as quantum photonic sources embedded incomplementary metal-oxide-semiconductor (CMOS) platforms, since GaP is almost lattice-matchedto Si. Finally, our analysis confirms the nature of the pumping power blue-shift of emissionoriginating from the charged-background induced changes of the wavefunction topology.
PACS numbers: 78.67.Hc, 73.21.La, 85.35.Be, 77.65.Ly
INTRODUCTION
In the last few decades, nano-structures like self-assembled III-V QDs have been investigated due to theirwide range of novel physical properties. Advantages inthis respect led to a number of different applications,such as active media in semiconductor lasers [1–3], asbuilding blocks for quantum information devices, par-ticularly for quantum repeaters [4–6], as efficient singleand entangled photon sources [7–15], including highly-entangled states for quantum computing [16–19], or asnanomemories [20–24]. Among III-V QDs, particularlytype-I indirect (InGa)(AsSb)/GaAs QDs embedded ina GaP(001) matrix [25, 26] have recently attracted at-tention due to their promising use as storage units forthe QD-Flash nanomemory cells [25, 26], as potentiallyeffective entangled photon sources [27], owing to theirsmaller fine-structure splitting (FSS) of the ground stateexciton compared to well-known type-I systems such as(InGa)As/GaAs [13, 14], and as quantum gates [27–30]. The concept of hole storage QD-Flash was ini- tially suggested by Bimberg and coworkers [20–24, 31]following first pioneering studies [31] regarding the mech-anisms of electron escape from InAs/GaAs QDs, byusing the Deep Level Transient Spectroscopy (DLTS).The key feature of the QD-Flash is to combine thefast access times of Dynamic Random Access Memories(DRAM) with the non-volatility of the Flash, which leadsto a universal memory type, potentially simplifying fu-ture computer architectures. Recently, type-I indirect(InGa)(AsSb)/GaAs/GaP QDs showed an improvementof one order of magnitude in the storage time comparedto pure In . Ga . As/GaAs/GaP QDs [32, 33], reaching ∼ a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n was found that these QDs showed concurrently both di-rect and indirect optical transitions for increasing Sb con-tent, finally leading to type-II band alignment [27]. Thatmade such QDs be excellent candidates for quantum in-formation technologies. Increasing the Sb content in theQDs has been previously made possible by overgrow-ing (InGa)(AsSb)/GaAs/GaP QDs with a GaSb cappinglayer, which has effectively modified the QD composi-tion [34]. Moreover, through detailed investigations oftheir optical properties, it was found that such proce-dure led to an energy swapping of the Γ and L states,thereby increasing the wavefunction leakage outside theQDs [27, 34]. This property is indeed very appealing forfurther improvement of storage times since an increasedSb incorporation into the QDs leads to increased hole lo-calization energy [23, 24, 27]. Finally, fabricating QDs onGaP substrates is advantageous in terms of integrationon Silicon platforms, since the lattice mismatch betweenGaP and Si amounts to just 0.4%, thus making defect-free MOVPE growth of GaP on Si possible [35].In this work, we take the next step and study thecarrier dynamics of (InGa)(AsSb)/GaAs/GaP QDs, bymeans of time-resolved-photoluminescence (TRPL) forvarying detection energy and sample temperature. Thisallows us to energetically separate the overlapping opticaltransitions previously observed in our recent work [34].First, we provide a brief overview of our sample struc-tures. Afterwards, we discuss the experimental resultson carrier lifetimes for varying measurement conditions.Analytical models, describing the observed physical phe-nomena are provided, leading us to discern the differenttypes of optical transitions involved. We would like topoint out that, to date, there is no such detailed opticalinvestigation of this material system. SAMPLE STRUCTURES
The samples were grown by MOVPE in Stranski-Krastanov (SK) mode on GaP(001) substrates at the TUBerlin [25, 26]. Such samples were also previously inves-tigated by means of steady-state photoluminescence [34].The structures of the samples studied in this work areschematically depicted in all figures as insets.All samples include 5 ML-thick GaAs interlayer (IL),a crucial ingredient for the subsequent QD formation,as pointed out by Sala et al. [25, 36]. The samplehaving the IL only is referred to as S w / o , that labeledS with (S cap ) contains (InGa)(AsSb) QDs, without (with) ∼ ∼
15 nm and heightof ∼ ∼ EXPERIMENTAL SETUP FOR TRPLMEASUREMENTS
In TRPL experiments we used a pulsed laser with thewavelength of 405 nm, focused on 0.06 mm area witha 60 ps pulse-width. The emitted PL spectrum was dis-persed by 1200 grooves/mm ruled grating and detectedby a Si avalanche photodiode (APD). First, we cooledthe samples to 15 K, and detected in 200 ns temporalwindow the energy-resolved TRPL signal for each wave-length. Then, within temperature-resolved TRPL, thesample temperature T was varied in the range 15–130 K.Here, the temporal window was modified to maximizethe resolution from 200 ns for lower T , to 25 ns for higher T . Changing the temporal window is connected withchanges in repetition rate, which was varied between5 MHz (for the temporal window 200 ns; used also forenergy-resolved TRPL) and 80 MHz (for 25 ns). SPECTRAL LINE-SHAPE MODEL
For the description of PL in the time domain (TDPL),we take advantage of the similarity in the grown struc-tures, leading to expected shared spectral features acrosssamples associated with carriers confined in the GaAsIL, i.e., zero-phonon (ZPL) and phonon-replica (rep-ZPL) transitions of electrons from X xy conduction min-ima to Γ valence band maximum [34, 39]. Through anal-ysis of the line-shape in the S w / o sample, we concludethat the convolution of two asymmetrical bands withmaximum emission energy E max concurrently showing asmall high-energy and a prominent low-energy band-tailproduce better results than the purely Gaussian spec-tral deconvolution used in Ref. [34]. The low energy tailshall be related to carrier localization into long-range ILpotential fluctuations [40]. Meanwhile, high energy tailsshall be related to phonon-assisted thermal populationof delocalized states, especially at large excitation pow-ers/temperatures or during the initial stages of the re-laxation process. We follow the work of Almosni et al. to describe the low energy tail long-range fluctuationsthrough the following equation [40] I ∝ exp( (cid:15)/E long ) E long exp( − exp( (cid:15)/E long )) (1) ZPLrep - ZPL ZPL rep - ZPL rep - ZPLZPL QDQD (a) (b) (c)
FIG. 1. Excitation power dependence of emission energies of samples (a) S w / o , (b) S with , and (c) S cap . Symbols representthe emission energies fitted from PL spectra. A typical (normalized) spectrum of each sample measured with D = 3 . together with colored band-reconstruction over spectral range of 1650–1900 meV is shown in insets. The emission energiesevolve in agreement with diffuse interface model for spatial type-I transitions [34, 38] (solid lines). Low-power emission energiesof IL transitions in S with (S cap ) are red-shifted by E w ( E c ) in respect to that in S w / o . where a single parameter E long characterizes the long-range potential disorder energy. Meanwhile, hot carrierpopulation is taken into account through an n phonon-assisted thermalization process by line-shape [41] I n ∝ (cid:15) / − n exp (cid:18) − (cid:15)k B T ca (cid:19) (2)with carrier thermalization energy of k B T ca ; (cid:15) = E − E max . We limit our description of I IL (convolution ofEqs. (1) and (2)) to one-photon process ( n = 1) only.As it can be seen in Fig. 1, two replicas of the abovelineshape model account for most of the PL emissionin these samples, yet not completely. To describe thefull PL spectrum, two additional Gaussian profiles arenecessary. One of them describes a rather broad band(FWHM larger than 35 meV), clearly observable onlyat very low excitation powers, likely originating in thedonor-acceptor pair (DAP) transitions in GaP [42, 43] orother defect induced during GaAs IL and QDs formation(the latter in the case of samples with QDs). We at-tribute the second Gaussian band to the recombinationfrom QDs, being due to non-optimized excitation wave-length, and thus very weak and observable mainly forhigh excitation powers. Before moving to time-resolvedanalysis, we show the validity of the fitting model by ap-plying it to the PL vs. continuous-wave excitation powerdependence D measured at 15 K and published in ourprevious study [34].Similarly as there, the fitted peak energies are usedto analyse the emission blue-shift with increasing D , inorder to determine the type of carrier spatial confine-ment. Although elsewhere in the literature [44–48] thepresence of blue-shift is automatically assigned to indi- rect spatial alignment, the so-called type-II, we examinehere the blue-shift by E = E + U ln( D ) + βD / [34, 38]allowing us to disentangle type-II bend-bending, due tostate squeezing represented by the parameter β , fromthe spatial alignment independent blue-shift caused bycrystalline defects described by the Urbach energy tail U . Having β negligible, the analysis in Fig. 1 suggeststhat the emission bands of our heterostructures are oftype-I, i.e. spatially direct, as also previously reportedbased on Gaussian fits [34] and in agreement with k · p simulations [27]. Moreover, we observe that ZPL andrep-ZPL transitions of samples S with and S cap are red-shifted in respect to their energies observed from PL ofS w / o by E w = 52 meV and E c = 82 meV, respectively.This shift partially reflects the strain-relaxation initial-ized by constituent segregation from QD-layer [37] and,thus, partially induced change in band confinement. Theformer is connected also with the natural spectral broad-ening when additional localized defect states are createdin the heterostructure. These additional states then forman effective background potential increasing with exci-tation power, leading to the energy blue-shift of bandsof samples with QDs, characterized by the Urbach en-ergy. However, the bands of the sample with only GaAsIL do not manifest themselves. A similar shift can bealso observed in the time domain after the non-resonantpulse-excitation when the carriers first thermalize intothe trap states and form the initial background poten-tial. As those recombine, E long decreases, the potentialweakens and, thus, the emission energy is gradually red-shifted, as we will discuss later in more detail. This po-tential weakening is connected also with the spreading ofthe state wavefunctions, effectively observable as an in-crease in recombination times in the excitation resolvedTRPL, see supplemental information [49].Although we attribute the QD band in the emis-sion of samples with dots, we expect in the studiedspectral range even richer spectral response related tomomentum-indirect transitions of QDs [27] and theircompositional variations [37] which are most likely shad-owed by much stronger GaAs IL emission. EMISSION ENERGY DEPENDENT TRPL
In this section, we study the energy-resolved carrier dy-namics in our heterostructures by TRPL. To assign therecombination times to the characteristic bands, we firstfit the signal (see raw experimental data in Fig. 2) in indi-vidual time bins by the spectral shape model discussed inthe previous part, and we refer to this analysis as time-domain PL (TDPL). For the best-fit results presentedin Fig. 3, we use the parameters obtained from steady-state excitation power dependency. Later, we analysethe signal for each wavelength also by the double mono-exponential model (2ME) I ( t ) = A exp( − t/τ ) + A exp( − t/τ ) , (3)characterized by amplitude A ( A ) and decay time τ ( τ ) for the slow (fast) decay process. In the case ofsamples with QDs, we added to the analysis also thethird exponential decay component ( τ ), representing theelectron-hole recombination in QDs. Finally, we analyzethe spectral distribution of the time decay constants τ – τ by an analytical model developed by Gourdon andLavallard [50]: τ = τ r E − E me ) /U ) (4)which is widely used in the literature [52, 53], even thoughin Eq. (4) the hopping processes [50] or temperature de-pendence [54] are not included. The meaning of the pa-rameters in Eq. (4) is as follows: τ r is the exciton radia-tive lifetime, E me the characteristic energy for which theradiative time equals the transfer one, analogously to amobility edge [53, 55], and U is the measured energy oflocalized states, similar to Urbach energy tail, responsi-ble for the observed energy blue-shift [38]. Note, that τ process decays rather slowly and does not completelydisappear in one temporal window, therefore we take intoaccount its repumping from previous pulses in TRPL fits,as discussed in the appendix. This issue is overcomein TDPL by disentangling individual transitions by line-shape model fitting, where the slowest decay is assignedto (mainly non-radiative) pair recombination of DAP inGaP [42, 43]. Moreover, in spectral dependence for theevaluation of τ we need to extend the model (4) by an additional contribution, likely connected with other de-fects created during the epitaxial growth process. Sample without QDs S w / o We start our discussion with the sample S w / o . TDPLdeconvolution allows us to study not only the relaxation-time constants of the considered decay process but alsothe energy changes of the state in the time domain.Specifically, the emptying of the impurity states entailsan exponential-like decrease of the emission energies ofthe total energy ∆ E for both ZPL and rep-ZPL bands,also recently observed for relaxed GaAs/GaP QDs withtype-I band-alignment [56]: E ( t ) = E + ∆ E exp( − t/τ E ) , (5)where E + ∆ E is the energy of the observed state af-ter laser excitation, which exponentially decays propor-tionally to the time constant τ E (an effective time whenimpurities and defects affect the electron state) to elec-tron energy E . That can be equally well understood asdue to defects at the interfaces between segments of theheterostructure, which create a local electric field (non-equilibrium carriers) leading to red-shift ∆ E of the elec-tron state with energy E . The carriers then recombinefor τ E upon which the eigenvalue of electron state returnsto its value without the presence of the local field E .Note, that the shift ∆ E cannot be caused by inter-valleyscattering, which is three orders of magnitude faster thanthe observed τ E [57], nor by the thermalization of higherexcited states (since τ E > radiative recombination times)or thermalization of free-carrier created after excitationwhich is of one order of magnitude faster, see T ca in sup-plemental information [49].Even though both bands are shifted by few units ofmeV, similarly to the total blue-shift observed in steady-state experiments, the integral PL spectrum taken at dif-ferent times of measurement does not show any signifi-cant shift and decays equally in time proportionally tothe decay around 10-15 ns, see inset of Fig. 3 (a) andtable I. These values are in good agreement with cryo-genic radiative lifetimes of InAs/GaAs wetting layer of25 ns [51]. Note, that since for the studied samples theenergy level separations of IL, DAP, and QDs are notclearly distinguishable, we use double mono-exponentialdecay function (with time constants τ TDPL1 and τ TDPL2 )to deconvolute the emission intensity, where the originof the second time constant is assigned according to thefollowing: DAP and other non-radiative defects decayslowly ( τ TDPL2 >
40 ns), whereas quantum dot transitionis fast ( τ TDPL2 <
10 ns).The standard TRPL deconvolution at each wavelengthin Fig. 4 (b) shows two contributions. The faster, being ingood agreement with ZPL and rep-ZPL TDPL band de-cays, with time constants around 13 ns contributes more
TABLE I. Summary of the best-fit parameters of the spectral shape model applied to the excitation power resolved PL andTDPL of all studied samples. Symbol ∗ ( ∗∗ ) refers to a discrepancy of +10 meV ( − E from TDPL in respect to theextracted value from the excitation power-dependent PL. For ZPL and rep-ZPL, we give E long as FWHM.sample transition FWHM (meV) E (meV) U (meV) ∆ E (meV) τ E (ns) τ TDPL1 (ns) τ TDPL2 (ns)S w / o ZPL 10 1858 ± . . ± . . ± . ±
40 10 . ± . ± ± . . ± . . ± . ± ± . ± . with ZPL 19 1796 ∗ ± . ± . . ± . ± . ± . ± ∗ ± . ± . ± ± . ± . ± ∗ ± . ± . . ± . ± . ± . cap ZPL 20 1764 ± . . ± . ± ± . ± . . ± . ± . . ± . . ± . ± ± ∗∗ ± . . ± . ± . ± . . ± τ i r is in ns, E i me and U i are in meV.sample GaAs IL GaAs IL, phonon rep. growth defects DAP in GaP τ ZPLr E ZPLme U ZPL0 τ repr E repme U rep0 τ dr E dme U d0 τ DAPr E DAPme U DAP0 S w / o . ± . ± ± . ± . ± . ± . ± ± . ± . ±
30 1776 ± . ± . with . ± . ± . ± . . ± . ± . ± . ± ± . ± . ± ± . ± . cap . ± . ± ± . ± . ± . ± . ± ± . ± . (a) (b) (c) FIG. 2. False-color plots of PL intensity as a function of time and emission energy for samples (a) S w / o , (b) S with , and (c) S cap . The color scale is identical for all samples. or less constantly by 20 % to the total intensity [panel(c)]. The slower process, related to DAP and crystallinedefects, increases the time-constant up to ∼
200 ns to-wards lower energies where none transition from GaAs ILis expected [27, 39] and is saturated below 1.79 eV as ex-pected from the similarity with the two other samples.Note, that similar behaviour with extremely slow (upto few µ s) low-energy transition were independently re-ported for (In,Ga)As/GaP [58, 59], Ga(As,P)/GaP [60],and GaSb/GaP [61] as momentum-indirect transitionsfrom QDs. Because we observe such transition not only for our QDs with completely different stoichiometry butalso for GaAs/GaP sample clearly without any QDs, wetend to assign the slow transition to defects in GaP sub-strate [62, 63], common for all reported structures. Fur-thermore, we note in Fig. 4(b) a good agreement be-tween TDPL and TRPL time constants, allowing us todeduce, in power and temperature resolved experiments,the character of relaxation based on the results of TRPLmeasurements only. ZPLrep - ZPL ZPL rep - ZPLZPLQDQDrep - ZPLt=0 nst=135 nst=0 nst=135 ns t=0 nst=135 ns (a) (b) (c)
FIG. 3. Fitted TDPL emission energies (symbols) which exhibit exponential-like energy red-shift with temporal evolution (fit,black solid lines). While for S w / o in (a), the shift is timid, for samples S with (b) and S cap (c) it exceeds 10 meV and leads toan observable spectral-shape variation within temporal evolution (see Fig. 2 and insets with color-coded fitted emission bandsover the spectral range of 1.65–1.9 eV). The broken grey vertical lines indicate the moment of the laser pulse excitation. Sample with QDs S with The whole spectrum of S with (Fig. 2), including ZPLand rep-ZPL bands, is also red-shifted in TDPL in re-spect to that of S w / o , approximately by E w , see Fig. 3 andtable II. That is close to the energy shift of E me ( S w / o ) − E me ( S with ) = 47 meV for ZPL (55 meV for rep-ZPL)and together with similar time constants τ TDPL1 , point-ing to similar physics behind the I IL transitions. Thebest fit emission energies of ZPL and rep-ZPL after ex-citation show non-equilibrium carrier background poten-tial, initially squeezing the electron wavefunction [44, 64].Later, as the potential weakens, the wavefunction spa-tially spreads, leading to the gradual red-shift ∆ E of14 meV and 11 meV for ZPL and rep-ZPL bands, respec-tively, to their steady-state energies. This time, in agree-ment with large blue-shift in excitation power-dependentPL, the shifts are more prominent due to significantlyincreased number of defects created within QD layer for-mation and later due to additional atom segregation [37].In addition to the sample S w / o , we observe also ∆ E of14 meV for the TDPL QD band with time constant of ∼
10 ns, suggesting impurity induced dynamics connectedwith the GaAs layer.The TRPL signal, deconvoluted by Eq. (3) by threemono-exponential decay contributions, shows two pat-terns: one similar to that observed for S w / o , and also a much faster one, which we attribute to the emissionfrom QDs. These processes, depicted in panels (d)–(f) ofFig. 4, have different weight across the measured spectralrange. While for energies below 1.75 eV the DAP dynam-ical processes dominate, they lose importance for largerenergies in favor to the processes involving the GaAs IL.The QD contribution is almost negligible in the wholespectral range, except for an increase of w , correspond-ing to QDs, centered around 1.80 eV and 1.83 eV, where w is larger than 10%. The mean values of τ in thesespectral ranges are 9 . ± . . ± . τ , and two contribu-tions for the process τ . The best-fit values (see Tab. II)show the mobility edge of the ZPL transition in IL shiftedwith respect to that of S w / o by 47 meV, which is in theagreement with the shift of the whole spectrum discussedpreviously. On the other hand, the mobility edge of DAPin GaP remains not affected by the heterostructure. Theradiative time of the ZPL (rep-ZPL) band is 31 . ± . . ± . Γ ZPLrep-ZPL QD ZPL1.764 eV τ ZPL ~18.4 ns
QD1.791 eV τ QD :<7.8 ns GaP GaPQD IL
ZPL rep-ZPL τ DAP >300 ns
ZPL rep-ZPL1.826 eV τ rep-ZPL ~ 14.4 ns GaP GaPIL
Xxy
DAP
ZPLrep-ZPL QD τ DAP >300 ns
ZPL1.806 eV τ ZPL ~31.5 ns rep-ZPL1.775 eV τ rep-ZPL: 30.7 ns QD1.787 eV τ QD :<10.4 ns GaP GaP QD IL Xxy m e V
340 meV m e V m e V m e V L DAP (a)(b)
Xxy
DAP
DAP DAP1.687 eV τ DAP >300 ns (c) (d)(e) (f) (g)(h) (i) τ τ τ τ τ τ τ τ I L G a P QD rep - ZPL rep - ZPLrep - ZPL ZPL ZPL ZPL τ ZPL ~13.0 ns Γ rep-ZPL1.733 eV τ rep-ZPL: 18.8 ns DAP
FIG. 4. Band schemes of samples S w / o [panel (a)], S with [panel (d)] and S cap [panel (g)] according to the observed TDPLtransitions E . The insets show the experimentally observed recombination times, transition (taken from fits of TDPL, solidlines) and escape (dashed line) energies. The energy dispersion of (b) time constants and (c) corresponding weights w forsample S w / o obtained by fitting the TRPL signal by the double mono-exponential model using Eq. (3) (symbols) and fittedby the Gourdon-Lavallard’s model 4 (solid lines) [50]. That for samples S with and S cap obtained from fitting of the TRPLsignal by triple mono-exponential model using Eq. (3) is shown in panels (d)–(f) and (g)–(i), respectively. The deconvolutedtime constants show good agreement with TDPL intensity decays (full symbols with arrows representing time-domain ∆ E shift; transitions are assigned by color in agreement with Fig. 3) and are compared to the recombination time of wetting layerin InAs/GaAs QDs system of 25 ns (dashed line), taken from Ref. [51]. Shaded areas of 1 −
10 ns, 10 −
40 ns, and >
100 nscorrespond to different recombination channels. the confinement potentials. On the other hand, disorderenergies U originating from material redistribution – inour case mainly due to the strain relaxation – are higherthan for S w / o , indicating increased disorder of GaAs ILinterface, causing not only creation of trap states, butalso non-radiative rates at higher energies effectively en-larging the time constants. Sample with GaSb-capped QDs S cap As previously shown in [34], overgrowing the QDs witha thin ( ∼ cap using the line-shape model with emissionenergies and FWHM adopted from excitation power de-pendence, we refine the character of the emission bandand assign in Fig. 4 the lifetimes of the observed opticaltransitions, see particularly the fit in inset of Fig. 3 (c).Across the studied spectral range, we again observesimilar signatures as in S w / o , but red-shifted by E c . Thisshift is also apparent from the comparison of mobil-ity edges subtracted from the Gourdon and Lavallardmodel [50], given in Tab. II. In contrast to the previoussamples, we observe also 40 meV shift of DAP mobilityedge which is a rather significant change to be caused bya different character of the DAP process only (i.e. type,or concentration) and possibly causing much longer rep-ZPL transition time as extracted from TDPL. However,we do not observe any change of the mobility edge forsamples S w / o and S with : this might be still connected tothe effect of layer-overgrowth on dynamics. On the otherhand, we observe almost unchanged ZPL radiative timeof 16 . ± . . ± . with , below 1.74 eV the DAP dynamical pro-cesses clearly dominate and their time constant is ∼ µ s.For larger energies, the emission due to DAP loses impor-tance in favor of GaAs IL processes. For energies largerthan 1.76 eV, also the contribution of QDs starts to benoticeable with w ∼
10 % and τ of 2–6 ns.The time-evolution of the best-fit emission energiesof individual transitions from the TDPL fit given inFig. 3(c) shows that ZPL and rep-ZPL bands are expo-nentially red-shifted by 17 meV and 5 meV, respectively,with time constant τ E being 19–44 ns.The previous analysis showed an increase of QD re-combination times with decreasing energy from 6 ns to9 ns for S with , of 1.83 eV and 1.80 eV, respectively, andfrom 2 ns to 6 ns for S cap of energies close to 1.79 eVand 1.73 eV. The slower recombination times might beassigned to indirect momentum transitions, even though,without detailed single dot spectroscopic study [65], thisis rather speculative because it could be as well causedby ensemble averaging [66]. TEMPERATURE DEPENDENT TRPL
In this section, we separated radiative and non-radiative contributions of the observed decay times andcomplete the band schemes in Fig. 4 of the non-radiativeprocesses. Individual recombination channels as a func-tion of T were extracted again using the 3ME (2ME)model for deconvolution of TRPL signal of S with andS cap (S w / o ). Contrary to the sample S w / o , the lifetime of ZPL ( τ ) for samples with QDs (S with and S cap ) increaseswith T between 30 and 50 K and thereafter progres-sively reduces, which is characteristic for the activation ofthermally activated escape paths of shallow defects [67].Those are most likely generated at the IL/QDs inter-face during the strain-relaxation caused by QDs over-growth [34].To separate the radiative ( τ R ) and non-radiative ( τ NR )lifetimes from individual transition channels, we assume,in accordance with Ref. [68], that for 15 K the only lossmechanism is the radiative recombination. Thereafter, τ R and τ NR decay times can be extracted from the slowdecay time τ by τ R = I I PL ( T ) τ , (6)and 1 τ = 1 τ R + 1 τ NR , (7)where I and I PL are the PL intensities at 15 K and atlarger T , respectively. As can be seen in Fig. 5, ther-mally activated scattering processes cause an exponentialdecrease characterized by τ NR of localized carriers with T . That process can be quantitatively interpreted by themodel involving two non-radiative processes1 τ NR = 1 τ exp (cid:18) − E k B T (cid:19) + 1 τ exp (cid:18) − E k B T (cid:19) , (8)characterised by the activation energies E and E andtime constants τ and τ , respectively. Conversely, τ R of exciton increases exponentially with Tτ R = τ + τ T R (cid:20) exp (cid:18) TT C (cid:19) − (cid:21) , (9)where τ ( τ T R ) describes the T independent (dependent)part of the radiative lifetime, and T C is the character-istic value of T corresponding to the energy of the lo-calised states. On the other hand, the behaviour of thedecay time with T of the fast component τ suggeststhat there is a non-radiative contribution even at low-est T , which prevents us to use Eq. (6). To overcomethis limitation, we assume that the radiative lifetime at15 K is the same as that for the slow component τ , i.e., τ R2 (15 K ) = τ R1 (15 K ), and a T independent non-radiativedecay τ C is also present and given by1 τ C = 1 τ (15 K ) − τ R2 (15 K ) . (10)Since τ C is not dependent on T , we can now calculatethe radiative lifetime τ R2 of the fast component at any T using Eq. (6), replacing τ with τ and 1 /τ NR with1 /τ C + 1 /τ NR2 . The overall decay time as a function of T is then given by1 τ ( T ) = 1 τ C + 1 τ R2 ( T ) + 1 τ NR2 ( T ) . (11) (a)(b) (c)(d)(e) (h)(f)(g) FIG. 5. Individual TRPL decay times τ – τ (black stars) shown as a function of temperature with the radiative (blue) andnon-radiative (red) components for all three samples - panels (a) and (b) show decay times for sample S w / o , (c)–(e) that forS with and (f)–(h) for S cap . The radiative and non-radiative component (circles and squares) are fitted by Eq. (9) and Eq. (8)(broken curves), respectively. The best-fit parameters from the models, including τ C (horizontal dash-dot lines), are added foreasier comparison. τ R2 and τ NR2 . A similar approach can be used also for τ ofsamples S with and S cap , with the assumption that thesame radiative lifetime is used for τ as that for τ , i.e., τ R3 (15 K ) = τ R2 (15 K ), and T independent non-radiativelifetime τ C is similar to Eq. (10) as 1 /τ C = 1 /τ (15 K ) − /τ R3 (15 K ). The numerical results of the described de-convolution are summarised in Tab. III for individual de-cay times taken at the maximum of the PL intensity foreach sample. Based on the previous analysis, we workedout the Arrhenius-like equation with explicit dependenceof PL on all parameters derived from the TRPL results: I I PL ( T ) = 1 + (cid:88) i =1 (cid:20) τ i R + τ Ti R exp (cid:18) TT i C (cid:19)(cid:21) × (cid:20) τ i NR exp (cid:18) − E i k B T (cid:19) + 1 τ i NR exp (cid:18) − E i k B T (cid:19)(cid:21) , (12)where the upper limit of the sum depends on a numberof mono-exponential decays in the fitting model used fordeconvolution of the TRPL signal.We attributed the slowest process τ to the recombina-tion of DAP and other crystalline defects, which followsthe same trend with increasing T for S w / o and S cap , i.e., itdecreases over 2 orders of magnitude from 100 ns to 1 ns.Due to larger amount of defects, τ of S with decreases onlyby one order of magnitude to 20 ns, which significantlychanges the character of the radiative lifetime, increasingexponentially with T from τ = 96 .
45 ns at 15 K due tothermalization of the defects. In comparison with thatfor S w / o and S cap , we find that to be constant at 64.62 nsand 82.62 ns, respectively.The radiative time constant τ R of the faster process τ increases exponentially across the samples with T from τ =14 ns. This increase is most likely caused by impu-rity thermalization via T C ( T C ≈
50 K is close to disorderenergy determined for these samples in [34]). While nomaterial exchange with QD constituents in GaAs IL forsample S w / o occurs by design, confirmed by the fact thatthe amplitude τ T R of thermalization change of τ R is almostzero, after QD formation, In-Ga redistribution occurs aspreviously reported in Refs. [34, 37], leading to almostthirty-fold increase of τ T R (sample S with ). The redistri-bution can be prevented by overgrowing the structureby a thin GaSb capping layer (see the similarity in pan-els of S cap and S w / o in Fig. 5), which for a thickness of ∼ τ T R thanthat for sample S cap , and an As-Sb intermixing betweenQDs and capping takes place, resulting in an increase ofthe Sb content in QDs [34].It can be assumed that the importance of this effectcan be reduced if the Sb layer is thicker because then thecapping might be more robust, yet that can also resultin pushing the wavefunctions out of the QD body, andthe corresponding change of the type of spatial band-alignment, previously reported for similar dots grown onGaAs substrate in Refs. [69–71]. The fastest process τ was considered only for QD sam-ples S with and S cap . The parameter τ of the sample S with decreases from ∼
10 ns (at 15 K) to 6 ns (at 70 K). Sincethe value of the lifetime is close to τ , we assume that theelectrons are localized preferably at the QD/IL interface.The radiative part τ R is quenched with T C = 56 . et al. in Refs. [25, 36]. This process could have, thus, led to abetter electron-wavefunction localization in the QD body,resulting in a shorter decay time τ of ≈ cap . This is in agreementwith the 2.5 ns observed for (InGa)(AsSb)/GaAs/GaPQDs grown with higher Sb flow [36]. This points to thefact that both growing a thin GaSb cap above the QDsand using a higher Sb flow before QD formation are bothefficient ways to affect the QD structural properties andpossibly increase the Sb content in the QDs [37].The transition is thermally quenched with T C = 14 . T -resolved PL experiments [34]) of τ R intodisordered centers most likely at the QD/IL interface.The analysis in panels (a) and (b) of Fig. 5 shows thatPL of the sample S w / o is thermally quenched via phonon-excitation from X -valley in GaAs, with activation energy E = 16 . T via unipolar escape of electrons from X -valley of GaAslayer and GaP to L -valley in GaP, with activation ener-gies of E = 441 . k · p ) and E = 339 . k · p ) [34], respectively.From the analysis of non-radiative lifetime in panels(c)–(e) in Fig. 5, we identify that the emission from sam-1 TABLE III. Summary of the TRPL Arrhenius-like fits using Eq. (12). The displayed values are obtained with accuracy betterthan 10 − %.sample process E [meV] τ [ns] E [meV] τ [ns] τ [ns] τ T R [ns] T C [K]S w / o τ τ with τ τ – – 57.3 0.050 14.61 8.18 62.2 τ cap τ τ τ ple S with at low T is thermally quenched via electron-thermalization from X xy in IL to, most likely, nitrogencomplexes present in the structure from GaP growth [73],having escape energies of 8 ± ∼
60 meVis most likely the escape of electron from X xy -valley inIL to X -valley in bulk (41 meV determined from 8-band k · p , 43 ± X xy -valley in IL to L -valley in IL (87 meV)and the escape of L -electron in QDs to the bulk GaP(46 meV).Also, for the sample S cap we identify, using the sameanalysis as in panels (f)–(h) of Fig. 5, a shallow impu-rity (8 . ≈
25 meV), escape ofelectron from IL to GaP substrate (284.7 meV, from PL245 meV [34], 288 meV from 8-band k · p ), and hole-escape from IL to bulk ( ≈
590 meV, 670 meV from 8-band k · p ), see Fig. 15 in [34]. Note that we attributethe increase in E to correspond to the phonon emis-sion to As-Sb intermixing between GaAs IL and GaSbcapping layer, reported already above. Calculating theactivation energies by k · p model, i.e., without atomisticresolution, cannot explain the observed changes, such asintermixing or material redistribution on the surface ofQDs, which creates a concentration gradient leading tolocal strain and potential changes affecting the escapeof carriers and, therefore, a slight discrepancy betweenexperiment and simulation is expected. CONCLUSIONS AND OUTLOOK
We performed the first detailed analysis of the car-rier dynamics of (InGa)(AsSb)/GaAs/GaP QDs to date,by means of energy and temperature modulated time-resolved-photoluminescence. Based on steady-state PLmeasurements carried out in our previous work [34] as areference, we develop spectral shape model taking into account phononic, impurity-related, and thermalizationeffects to address the four emission bands expected from k · p calculations [27]. The application of analytical mod-els shows similarities across the samples studied here,originating from GaAs interlayer and defects in the GaPsubstrate. Specifically, the transitions are zero-phononand phonon-assisted transitions of electrons in the GaAsinterlayer from the X xy valley to the Γ valence band,with decay times around 15 ns, and donor-acceptor pairrecombination in GaP decaying extremely slowly (up tofew µ s). Moreover, we observe type-I emission from QDs,which is faster than 10 ns and its recombination timesvaries across the studied range, most likely due to co-existence of momentum direct and indirect transitionsand compositional changes of individual dots. Finally,we want to point out the spectral shift of the type-Iemission from GaAs interlayer and QDs bands caused bycharge potentials from defects created during QD forma-tion. This shift is evident in both pump-power resolvedphotoluminescence, as well as in the time domain studyof the emission.Our data suggest that epitaxial growth strategies canbe employed to efficiently increase the Sb content in theQDs by a thin GaSb cap overgrowth. Such Sb con-centration increase in QDs increases the carrier confine-ment and will subsequently lead to an increase of theQD storage time, which is of utmost importance forthe implementation of such QDs into nano-memory de-vices [23, 76]. However, the use of Sb, and its potentialpartial segregation [37, 77], may lead to the formation ofadditional point defects, which could affect the storagetime by increasing capture cross-section [78]. Therefore,the development of the truly defect-free Sb-rich QDs ontop of GaP is the key for further improvement of QD-Flash nano-memories. In this respect, further epitaxialengineering techniques are demanded. However, consid-ering the present study and our previous work [34], wehave demonstrated that overgrowing such QDs with aGaSb capping layer is a promising epitaxial method toincrease the Sb content in (InGa)(AsSb) QDs and to ma-nipulate their carrier dynamics.Furthermore, for their naturally small FSS [14], such2Sb-rich dots are promising candidates for entangled-photon sources, potentially operating not only at cryo-genic temperatures due to Sb-increased electron confine-ment. The use as entangled-photon, as well as single-photon, sources will require future effort in the optimiza-tion of optical efficiency by both sample quality and cav-ity enhancement [79]. Even though the growth may bechallenging, these structures have benefits, such as smallsize and improved compositional homogeneity comparedto conventional SK QDs [25, 26, 37]. Moreover, consider-ing the negligible lattice mismatch between GaP and Si,they can serve as a CMOS compatible quantum platform.Finally, since the incorporation of Sb during growth leadsto (i) tunable quantum confinement of the dots [27] and(ii) the possibility to reduce the amount of charge trapstates originating from crystal structure imperfections,we suppose our dots might be superior to those recentlyproposed on SiGe quantum dots [80, 81]. ACKNOWLEDGEMENTS
P.S. is Brno Ph.D. Talent Scholarship Holder–Fundedby the Brno City Municipality. E.M.S. and D.B. thankthe DFG (Contract No. BI284/29-2). A part ofthe work was carried out under the project CEITEC2020 (LQ1601) with financial support from the Min-istry of Education, Youth and Sports of the Czech Re-public under the National Sustainability Programme II.Project CUSPIDOR has received funding from the Quan-tERA ERA-NET Cofund in Quantum Technologies im-plemented within the European Union’s Horizon 2020Programme. In addition, this project has received na-tional funding from the MEYS and funding from Eu-ropean Union’s Horizon 2020 (2014-2020) research andinnovation framework programme under grant agree-ment No 731473. The work reported in this paper was(partially) funded by project EMPIR 17FUN06 Siqust.This project has received funding from the EMPIR pro-gramme co-financed by the Participating States and fromthe European Union’s Horizon 2020 research and inno-vation programme. This works was also partially fundedby Spanish MICINN under grant PID2019-106088RB-C3and by the MSCA-ITN-2020 Funding Scheme from theEuropean Union’s Horizon 2020 programme under Grantagreement ID: 956548.
APPENDIXRepumping T R P L s i g n a l st window 2 nd window, measureddark signalbackground r e pu m p e d s i g n a l f r o m s t w . s i g n a l f r o m nd w . m e a s u r e d s i g n a l FIG. A1. TRPL decay signal with τ = 350 ns (blue for 1 st window, red for 2 nd ) after excitation (black) shown in two con-secutive temporal windows (200 ns). Gray symbols representscompound signal from two temporal windows. The arrowpoints to re-pumped signal from background level (includingdark counts) due to contribution to the measured signal fromthe previous temporal window. Because some of the observed transitions decay ratherslowly and do not completely disappear in one tempo-ral window, we take into account re-pumping of the slowTRPL component τ from previous pulses, which leadsto a “background” increase as can be seen in Fig. A1,complicating a proper extraction of the background sig-nal for individual wavelengths and correct time-constantextraction. 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