Helmholtz-Zentrum Dresden-Rossendorf (HZDR)Photoluminescence dynamics in few-layer InSeVenanzi, T.; Arora, H.; Winnerl, S.; Pashkin, O.; Chava, P.; Patanè, A.; Kovalyuk, Z. D.;Kudrynskyi, Z. R.; Watanabe, K.; Taniguchi, T.; Erbe, A.; Helm, M.; Schneider, H.;Originally published:April 2020Physical Review Materials 4(2020)4, 044001DOI: erma-Link to Publication Repository of lease of the secondary publication based on the publisher's specified embargo time.

PHYSICAL REVIEW MATERIALS 4, 044001 (2020)Photoluminescence dynamics in few-layer InSeTommaso Venanzi ,1,2,* Himani Arora,1,2 Stephan Winnerl,1 Alexej Pashkin ,1 Phanish Chava ,1,2 Amalia Patanè,3Zakhar D. Kovalyuk,4 Zakhar R. Kudrynskyi,3 Kenji Watanabe ,5 Takashi Taniguchi,5 Artur Erbe,1Manfred Helm,1,2 and Harald Schneider 11Helmholtz-Zentrum Dresden-Rossendorf, 01314 Dresden, Germany2Technische Universität Dresden, 01062 Dresden, Germany3School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom4Institute for Problems of Materials Science, The National Academy of Sciences of Ukraine, Chernivtsi, Ukraine5National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan(Received 31 January 2020; accepted 25 March 2020; published 14 April 2020)We study the optical properties of thin flakes of InSe encapsulated in hexagonal boron nitride. Morespecifically, we investigate the photoluminescence (PL) emission and its dependence on sample thickness andtemperature. Through the analysis of the PL line shape, we discuss the relative weights of the exciton andelectron-hole contributions. Thereafter we investigate the PL dynamics. Two contributions are distinguishableat low temperature: direct band-gap electron-hole and defect-assisted recombination. The two recombinationprocesses have lifetimes of τ1 8 ns and τ2 100 ns, respectively. The relative weights of the direct bandgap and defect-assisted contributions show a strong layer dependence due to the direct-to-indirect band-gapcrossover. Electron-hole PL lifetime is limited by population transfer to lower-energy states and no dependenceon the number of layers was observed. The lifetime of the defect-assisted recombination gets longer for thinnersamples. Finally, we show that the PL lifetime decreases at high temperatures as a consequence of more efficientnonradiative recombinations.DOI: 10.1103/PhysRevMaterials.4.044001I. INTRODUCTIONVan der Waals (vdW) semiconductors are a very interestingand promising class of materials. By stacking different vdWsemiconductors on top of each other, it is possible to combinetheir properties [1]. While a large number of material combinations is possible, the properties of each do not simply addup. There is a nontrivial interaction between different layers ofthe heterostructures. Already many interesting aspects of thephysics of heterostructures have been discovered; for instance,interlayer excitons [2,3], the interaction between excitons andthe moiré potential [4,5], and exciton condensation at hightemperature [6]. But even without considering the interestrelated to technological applications [7], there is still a lot ofphysics to investigate. In this vast set of vdW heterostructures,we focus here on hexagonal boron nitride (hBN)/InSe/hBNheterostructures and, more specifically, we study their opticalproperties analyzing the photoluminescence (PL) emission.Few-layer InSe has shown promising properties for electronic applications because it features a direct band gap and ahigh electron mobility (low electron effective mass) [8]. Thereare many studies demonstrating the possibility to use thismaterial as an active layer for field-effect transistors [9,10],photodetectors [11,12], and optoelectronic devices for the infrared region [13]. However, one issue that needs to be tackledis the contamination of thin-layer InSe when exposed to air[14,15]. A solution for this issue is to embed the InSe 6)in hBN. This encapsulation procedure protects the materialfrom contamination and assures good optical and electronicproperties, as shown recently for InSe itself and other vdWmaterials [16–18].Here, we present an investigation of the photoluminescence emission from thin flakes of InSe of different thicknesses encapsulated in hBN. In particular, we investigatethe temperature dependence of the PL emission analyzingthe data using a modified version of Katahara’s model [19].Through this analysis we show that for thin-layer InSe theexciton interaction is observable only at low temperature.Moreover, we present layer-dependent time-resolved PL ofInSe encapsulated in hBN and we determine the time constants of the radiative recombination. The PL decay showstwo components that are the electron-hole and defect-assistedradiative recombination. The ratio of the weights of the twoPL components varies with the number of layers, in agreementwith the crossover from the direct band gap in the bulk tothe indirect band gap in few-layer crystals. Finally, a decreaseof the PL lifetime is observed at higher temperature due tononradiative scattering.II. SAMPLE AND METHODSFigure 1(a) shows an optical image of a hBN-encapsulatedInSe on SiO2 (285 nm)/Si substrate. The hBN-encapsulatedInSe samples were fabricated using the dry transfer techniqueunder ambient condition in an ISO 4 cleanroom environment, as described previously by Wang et al. [20]. By usingthis polymer-assisted fabrication technique, we ensured clean044001-1 2020 American Physical Society

TOMMASO VENANZI et al.PHYSICAL REVIEW MATERIALS 4, 044001 (2020)FIG. 1. (a) Optical image of an InSe flake fully encapsulatedin hBN. The black dashed line highlights the InSe flake. (b) AFMprofile along the dashed red line in the optical image of the sample.interfaces between InSe and hBN. This technique allows us toobtain samples with good crystal quality and low contamination.After the fabrication, the samples were kept in vacuum(10 6 mbar at T 300 K) in order to prevent any degradation. For the time-integrated PL measurements we used acw frequency-doubled Nd:YAG laser as an excitation pumpat a wavelength of λ 532 nm. The spot diameter on thesample was approximately 3 μm, i.e., smaller than theheterostructure size. A nitrogen-cooled Si-CCD deepdepletion camera was used to detect the PL emission, whichis dispersed in a spectrometer. For the time-resolved measurements, we used a single-photon avalanche diode as adetector coupled to a spectrometer. With this system 60 pstime resolution and 1 meV spectral resolution were obtained.A mode-locked Ti:Sa oscillator with a pulse length of 3 ps incombination with a Barium borate (BBO) frequency doublerwas used as an excitation source at λ 405 nm. The repetition rate was reduced from 78 to 6.5 MHz by pulse pickingin a Pockels cell: this was done because of the relatively longPL lifetime of the sample. For time-resolved measurementswe used a larger spot diameter ( 10 μm) in order to collectmore PL emission, while keeping the excitation power densityas low as possible.The thicknesses of the encapsulated InSe flakes range from20 to 2.4 nm, corresponding to around 24 atomic layers to 3layers [8]. The thickness was measured using atomic forcemicroscopy, as shown in Fig. 1(b). We note that the hump inthe AFM profile is due to a bubble at the edge between theInSe flake and the top-encapsulating hBN layer.As shown recently [8,21–24], the band structure of InSe isstrongly dependent on the number of layers. Bulk InSe hasa direct band gap while monolayer and few-layer InSe haveFIG. 2. (a) and (b) Temperature dependence of the PL spectra of a 24-layer and a 9-layer InSe sample, respectively. The excitation poweris 10 μW. For the 24-layer-thick sample a redshift of the PL emission is observed due to the reduction of the band-gap energy. The 9-layersample shows an s shape due to the large contribution of the defect-assisted recombination. The temperatures of the PL spectra are the sameas for the data points in (d). (c) Absorption spectra as extracted from the fitting of the PL spectra for the 24-layer-thick sample. An excitonfeature is observable at low temperature. (d) Effective PL temperature obtained from the model with respect to the actual lattice temperature.044001-2

PHOTOLUMINESCENCE DYNAMICS IN FEW-LAYER InSePHYSICAL REVIEW MATERIALS 4, 044001 (2020)an indirect band gap. The difference in energy between thedirect and the indirect band gap is 70 meV for monolayerInSe and it decreases rapidly upon increasing the number oflayers. The direct band gap is at the point. Upon decreasingthe number of layers, the conduction band does not changequalitatively but the valence band forms a Mexican-hat-likedispersion centered at the point so that thin layers of InSehave an indirect band gap. The samples presented in this studycover the range of the direct-to-indirect band-gap crossover.III. STEADY-STATE PHOTOLUMINESCENCEFigures 2(a) and 2(b) show temperature-dependent PLspectra for 24- and 9-layer InSe crystals, respectively. Theenergy position of the PL band of the two samples at 4 K is inagreement with previous reports on thin layers of InSe [25].At T 4 K both samples show a single broad PL emissionband mostly due to defect-assisted radiative recombination.As noted in [21], the large broadening of the PL lines isdue to the low electron mass that makes the emission verysensitive to any surface effect and to any disordered potential.The broadening of the PL lines increases while decreasing thenumber of layers, as becomes clear from the broad emissionof the 9-layer sample.While increasing the temperature, the 24-layer sampleshows a monotonic redshift that is a consequence of the reduction of the band-gap energy due to the lattice expansion andto the interaction with phonons. Further details are given inthe Supplemental Material (SM) [26]. The temperature dependence of the PL energy position of the nine-layer flake showsan s shape. This is a consequence of the defect-state emissionthat dominates the PL at low temperature, as discussed inprevious studies and observed in other semiconductor systems[25,27]. The PL energy position of the nine-layer sampleshows an overall blueshift in comparison with the thicker InSesample. This is due to quantum confinement and is extensivelyreported in the literature [21,22].To get more information on the PL emission mechanisms,we looked at the PL line shape of the 24-layer sample. Weconsider the model proposed by Katahara and Hillhouse [19]for PL emission and we adapt it to our case. This model is ageneralized version of the van Roosbroeck–Shockley equationthat connects absorption and interband PL in semiconductors[28,29]. This means that we can extract absorption from PLdata. Moreover we consider both band-to-band and excitonabsorption. In this way we can evaluate the relative weight ofthese two contributions. The expression used for modeling thePL line shape is 2E 2 a(E )1 , (1)IPL (E ) μ E μ 1 1exp EkTexp2kTPLPLwhere the first part is the connection between Planck’s law andthe absorption, and the second part in parentheses is a smallcorrection that takes into account the occupation of the bands(Pauli blocking). Here, a(E ) aB (E ) paX (E ) is the totalabsorption given by a linear combination of band-to-band andexciton contribution, μ is the quasi-Fermi energy, and TPL isthe effective photoluminescence temperature. We note that inmany cases the part of the expression containing the tempera-ture can be simplified assuming a Boltzmann distribution. Thequasi-Fermi energy is an effective Fermi energy introduced byLasher and Stern in order to consider the occupation of theconduction and valence bands, and it assumes values close tothe band-gap energy [29]. The model is reported in detail inthe SM [26].Figure 2(c) shows the absorption spectra deduced fromEq. (1). At low temperatures the exciton resonance is clearlyobservable in the absorption spectra and it smears out at highertemperature as expected. In fact, the exciton binding energy is 14 meV [30–32] that corresponds to about 160 K.We want to highlight another detail of our fitting procedure. We introduced an effective PL temperature to reproduceaccurately the PL spectra especially at low temperature. Thisis strictly connected to the inhomogeneous broadening ofthe PL line. In fact, the effective PL emission temperatureis determined by the high-energy side of the PL emission,where the excited carriers can thermalize. More specifically,the effective PL temperature is proportional to the slope ofthe exponential high-energy tail of the PL emission [33,34].The high-energy tail is due to the thermal population of thebands that is in very good approximation due to a Boltzmanndistribution. The higher the PL temperature, the less steep isthe exponential decay of the PL high-energy tail. This effectcan be observed in Fig. 2(a). At 4 K one would expect a verysharp decay, but we observe a smoother decay due to inhomogeneous broadening. Figure 2(d) shows the PL temperatureversus the lattice temperature. The PL temperature does notapproach 0 K but it saturates around a certain value muchlarger than zero.We can model this behavior with this formula: (2)TPL T 2 T02 ,in analogy with the model proposed by Marianer et al. fordisordered semiconductors [35,36]. The idea is to incorporatethe disorder, that in our case shows up as inhomogeneousbroadening of the PL line, in the effective temperature. Thissimple model reproduces the observed electron-hole temperature reasonably well. Therefore, T0 44 K 4 meV is ameasurement of the disorder in the material and it can beintuitively interpreted as the standard deviation of the disorderpotential in the sample due to lattice defects and sampleinhomogeneity. The PL temperature at 0 K T0 increases upondecreasing the number of layers (see SM [26]). This behaviorindicates that the disorder is more pronounced for thinnersamples, as expected. This treatment has a general validity forsemiconductors with direct band gap and parabolic dispersion.We finally note that a nonvanishing T0 could be due tohigher electron-hole temperature induced by laser excitation.However, in our case this effect is negligible because we donot observe a dependence of the parameter T0 on excitationpower (see SM [26]).IV. TIME-RESOLVED PHOTOLUMINESCENCEFigure 3(a) shows the PL intensity as a function of time andphoton energy for a 24-layer InSe crystal. The PL emissionshows a spectral-dependent biexponential decay. In order toget the time constants, we average the PL emission overthe photon energy and we fit the data with a biexponential044001-3

TOMMASO VENANZI et al.PHYSICAL REVIEW MATERIALS 4, 044001 (2020)FIG. 3. (a) and (d) 2D false-color maps of normalized PL intensity as a function of time and photon energy at T 4 K and 10 μJ cm 2excitation fluence. The two maps are of a 24- and 9-layer sample, respectively. (b) PL decays integrated in the photon energy of sampleswith different thicknesses. The decays are biexponential. (c) Spectra of the extracted fast (electron-hole) and slow (defect) components for the24-layer-thick sample. (e) Lifetimes of the fast and slow components of the PL decay as a function of sample thickness. (f) Dependence of theratio between PL contributions associated with the fast and the slow component on the number of layers.decay convoluted with the instrument response function. Theenergy-integrated PL decay is shown in Fig. 3(b). The fast andslow PL components have lifetimes of τ1 7.7 0.2 ns andτ1 49 6 ns, respectively. In order to visualize the two PLcomponents independently, two-dimensional (2D) false-colorplots of the extracted fast and slow decays are shown in theSupplemental Material [26].The slow PL decay is a fingerprint of a defect-assistedelectron-hole recombination. Therefore we associate the slowcomponent with this radiative channel. The fast component isassociated with the direct band-gap electron-hole recombination.Integrating in time the fast and the slow components asobtained from the fit, it is possible to separate the spectraof the two contributions [shown in Fig. 3(c)]. The centralemission energy of the fast component is 1.312 0.001 eVwith full width at half maximum (FWHM) of 6.8 0.5 meV,while the slow component is centered at 1.300 0.001 eVwith FWHM of 15 1 meV. The slow component lies atlower energy and with a broader spectrum, as expected fora defect-assisted emission. The two components were notspectrally distinguishable in steady-state PL.Now we look at the layer dependence of the time-resolvedPL. Figure 3(d) shows the PL data for a 9-layer thick InSecrystal measured under the same condition as the 24-layerthick sample. Qualitatively, it is evident that the PL decaytakes place on a longer timescale. In addition, the weightsof the two PL components change significantly. The defectassisted recombination appears to be more dominant with respect to the electron-hole recombination for thinner samples,as expected from the direct-to-indirect band-gap crossoverdriven by the sample thickness [21]. Conversely, electrons andholes in the 24-layer sample can recombine easily becauseof the direct band gap, while in thin samples they need theassistance of a scattering process.To further corroborate this observation and to perform aquantitative analysis, we fabricated and measured a seriesof encapsulated InSe crystals with different thicknesses. Figure 3(b) shows the PL decays integrated in photon energy fordifferent layer thicknesses.We fitted the PL decay with a biexponential decay andwe extracted the fast and slow lifetimes (τ1 and τ2 ) for eachsample. The lifetimes are shown in Fig. 3(e). We do notobserve a clear layer dependence of the fast component, i.e.,044001-4

PHOTOLUMINESCENCE DYNAMICS IN FEW-LAYER InSePHYSICAL REVIEW MATERIALS 4, 044001 (2020)FIG. 4. (a) PL decays as a function of temperature. The PL decay gets faster at higher temperature due to the more efficient nonradiativescattering. The sample is 24 layers thick and fully encapsulated in hBN. (b) PL lifetime τ1 as a function of temperature. The red curve isobtained from Eq. (3).electron-hole recombination. On the other hand, the lifetimeof the slow component increases with decreasing the flakethickness. The dynamics of the electron-hole recombination islimited at low temperature mainly by the population transferto lower-energy states, i.e., bound states below the band gap.This could explain why we do not observe a layer dependencefor the fast component of the decay.(τ1 )The ratio II (τfor each sample is shown in Fig. 3(f).2)The fast component becomes more and more dominant withincreasing the number of layers. The increase of the ratio takesplace between five and ten layers, i.e., in good agreement withthe number of layers where the direct-to-indirect band-gapcrossover is expected [8]. The error bars were obtained fromthe standard errors of the least-square fitting procedure andthe propagation of errors.Finally, we consider the temperature dependence of thePL dynamics. Figure 4(a) shows the electron-hole PL decays as a function of temperature. The PL lifetime decreasesmonotonically with increasing the temperature due to highernonradiative scattering, i.e., phonon scattering. We note thatthe PL decays at temperatures higher than 70 K show a singleexponential decay. This is because the defect states responsible for the slow component are not stable anymore and theonly radiative channel is the fast electron-hole recombination.Figure 4(b) shows the extracted PL lifetime as a function oftemperature. We use an empirical model in order to fit the dataconsidering the radiative and nonradiative decay. Assuming anexponential decay, the lifetime is inversely proportional to thesum of the radiative and nonradiative decay rates:τ 11, βr βnrβ0 αnr T(3)where βr and βnr are, respectively, the radiative and nonradiative decay rates, β0 is the decay coefficient at 0 K, and alinear approximation was done to model the dependence ofthe nonradiative scattering on temperature.This simple approximation shows a good agreement withthe experimental data and gives two quantitative pieces ofinformation: (1) the lifetime at 0 K ( β10 τ0 6 ns) and(2) the temperature T at which the nonradiative scatteringovercomes the radiative scattering. The latter is T αβnr0 50 K.Finally, we note that if we use a square root temperaturedependence in Eq. (3) instead of a linear one, the modellooks like the Schockley-Read-Hall model for nonradiativescattering [37,38]. However, this gives a worse agreementwith the experimental data and no significant parameters canbe extracted. We also note that, according to the data, thebest-fitting exponent for the temperature would be 1.34 0.06 43 instead of 1, but no physical explanation could befound.V. CONCLUSIONWe investigated the PL and time-resolved PL emissionfrom few-layer InSe fully encapsulated in hBN. A lineshape analysis of the time-integrated emission reveals thecontribution of exciton and electron-hole recombination. Theexcitonic emission was observed only at low temperatures.The role of disorder in the material can be modeled very wellby introducing an effective temperature.The analysis of the time-resolved PL signals allows us todisentangle the contribution from direct band-gap electronhole recombination (τ1 8 ns) and to defect-assisted recombination (τ2 100 ns). These contributions are not spectrallydistinguishable without resolving the dynamics. The defectassisted contribution becomes increasingly important as thenumber of layers is decreased. Remarkably, the electron-holePL lifetime basically is independent of the number of layers,while the lifetime of the defect-assisted recombination increases for thinner samples. Furthermore, shorter PL lifetimeswere found with increasing temperature, which is caused bymore efficient nonradiative recombination.In summary, the analysis of a comprehensive set of experimental data on the PL emission dynamics of few-layerInSe encapsulated in hBN allows us to distinguish the involved microscopic physical mechanisms. These results areimportant for technological applications based on few-layerInSe.044001-5

TOMMASO VENANZI et al.PHYSICAL REVIEW MATERIALS 4, 044001 (2020)ACKNOWLEDGMENTSThe authors cordially thank Pedro Pereira for givingfriendly help during the course of this work. This workhas been partially funded by the Initiative and Networking Fund of the German Helmholtz Association, HelmholtzInternational Research School for Nanoelectronic Networks[1] A. K. Geim and I. V. Grigorieva, Nature (London) 499, 419(2013).[2] P. Rivera, H. Yu, K. L. Seyler, N. P. Wilson, W. Yao, and X. Xu,Nat. Nanotechnol. 13, 1004 (2018).[3] P. Merkl, F. Mooshammer, P. Steinleitner, A. Girnghuber, K.-Q.Lin, P. Nagler, J. Holler, C. Schüller, J. M. Lupton, T. Korn, S.Ovesen, S. Brem, E. Malic, and R. Huber, Nat. Mater. 18, 691(2019).[4] K. L. Seyler, P. Rivera, H. Yu, P. Nathan, E. L. Ray, D. G.Mandrus, J. Yan, W. Yao, and X. Xu, Nature (London) 567, 66(2019).[5] K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai,D. A. Sanchez, J. Quan, A. Singh, J. Embley, A. Zepeda, M.Campbell, T. Autry, T. Taniguchi, K. Watanabe, N. Lu, S. K.Banerjee, K. L. Silverman, S. Kim, E. Tutuc, L. Yang, A. H.Macdonald, and X. Li, Nature (London) 567, 71 (2019).[6] Z. Wang, D. A. Rhodes, K. Watanabe, T. Taniguchi, J. C. Hone,J. Shan, and K. F. Mak, Nature (London) 574, 76 (2019).[7] S.-J. Liang, B. Cheng, X. Cui, and F. Miao, Adv. Mater.,1903800 (2019).[8] G. W. Mudd, M. R. Molas, X. Chen, V. Zólyomi, K.Nogajewski, Z. R. Kudrynskyi, Z. D. Kovalyuk, G. Yusa, O.Makarovsky, L. Eaves, M. Potemski, V. I. Fal’Ko, and A.Patanè, Sci. Rep. 6, 39619 (2016).[9] W. Feng, W. Zheng, W. Cao, and P. Hu, Adv. Mater. 26, 6587(2014).[10] S. Sucharitakul, N. J. Goble, U. R. Kumar, R. Sankar, Z. A.Bogorad, F.-c. Chou, Y.-t. Chen, and X. P. A. Gao, Nano Lett.15, 3815 (2015).[11] S. R. Tamalampudi, Y.-Y. Lu, R. Kumar U., R. Sankar, C.-D.Liao, K. Moorthy B., C.-H. Cheng, F. C. Chou, and Y.-T. Chen,Nano Lett. 14, 2800 (2014).[12] S. Lei, L. Ge, S. Najmaei, A. George, R. Kappera, J. Lou, M.Chhowalla, H. Yamaguchi, G. Gupta, R. Vajtai, A. D. Mohite,and P. M. Ajayan, ACS Nano 8, 1263 (2014).[13] S. J. Magorrian, A. Ceferino, V. Zólyomi, and V. I. Fal’ko, Phys.Rev. B 97, 165304 (2018).[14] X. Wei and C. Dong, Phys. Chem. Chem. Phys. 20, 2238(2018).[15] H. Arora, T. Schönherr, and A. Erbe, IOP Conf. Ser.: Mater. Sci.Eng. 198, 012002 (2017).[16] D. A. Bandurin, A. V. Tyurnina, G. L. Yu, A. Mishchenko,V. Zólyomi, S. V. Morozov, R. K. Kumar, R. V. Gorbachev,Z. R. Kudrynskyi, S. Pezzini, Z. D. Kovalyuk, U. Zeitler,K. S. Novoselov, A. Patanè, L. Eaves, I. V. Grigorieva, V. I.Fal’Ko, A. K. Geim, and Y. Cao, Nat. Nanotechnol. 12, 223(2017).[17] G.-h. Lee, X. Cui, D. Kim, G. Arefe, X. Zhang, C.-h. Lee, F.Ye, K. Watanabe, T. Taniguchi, P. Kim, and J. Hone, ACS Nano9, 7019 (2015).NanoNet (VH-KO-606). We acknowledge the EuropeanUnion’s Horizon 2020 research and innovation programGraphene Flagship Core 2 under Grant Agreement No.785219. We acknowledge also the National Academy of Sciences of Ukraine. Growth of hexagonal boron nitride crystalswas supported by the Elemental Strategy Initiative conductedby the MEXT, Japan and the CREST (JPMJCR15F3), JST.[18] H. Arora, Y. Jung, T. Venanzi, K. Watanabe, T. Taniguchi, R.Hübner, H. Schneider, M. Helm, J. C. Hone, and A. Erbe, ACSAppl. Mater. Interfaces 11, 43480 (2019).[19] J. K. Katahara and H. W. Hillhouse, J. Appl. Phys. 116, 173504(2014).[20] L. Wang, C. R. Dean, I. Meric, K. L. Shepard, J. Hone, P. Kim,K. Watanabe, T. Taniguchi, L. M. Campos, D. A. Muller, J.Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, Science342, 614 (2013).[21] G. W. Mudd, S. A. Svatek, T. Ren, A. Patanè, O. Makarovsky,L. Eaves, P. H. Beton, Z. D. Kovalyuk, G. V. Lashkarev, Z. R.Kudrynskyi, and A. I. Dmitriev, Adv. Mater. 25, 5714 (2013).[22] T. Zheng, Z. T. Wu, H. Y. Nan, Y. F. Yu, A. Zafar, Z. Z. Yan,J. P. Lu, and Z. H. Ni, RSC Adv. 7, 54964 (2017).[23] Y. Guo and J. Robertson, Phys. Rev. Mater. 1, 044004 (2017).[24] M. J. Hamer, J. Zultak, A. V. Tyurnina, V. Zólyomi, D. Terry, A.Barinov, A. Garner, J. Donoghue, A. P. Rooney, V. Kandyba, A.Giampietri, A. Graham, N. Teutsch, X. Xia, M. Koperski, S. J.Haigh, V. I. Fal’ko, R. V. Gorbachev, and N. R. Wilson, ACSNano 13, 2136 (2019).[25] G. W. Mudd, A. Patane, Z. R. Kudryinskyi, M. W. Fay, O.Makarowsky, L. Eaves, Z. D. Kovalyuk, and V. Falko, Appl.Phys. Lett. 105, 221909 (2014).[26] See Supplemental Material at terials.4.044001 for more detailed discussion on this topic.[27] Y.-H. Cho, G. H. Gainer, A. J. Fischer, J. J. Song, S. Keller,U. K. Mishra, and S. P. DenBaars, Appl. Phys. Lett. 73, 1370(1998).[28] W. van Roosbroeck and W. Shockley, Phys. Rev. 94, 1558(1954).[29] G. Lasher and F. Stern, Phys. Rev. 133, A553 (1964).[30] J. Merle, R. Bartiromo, E. Borsella, M. Piacentini, and A.Savoia, Solid State Commun. 28, 251 (1978).[31] J. Camassel, P. Merle, H. Mathieu, and A. Chevy, Phys. Rev. B17, 4718 (1978).[32] T. V. Shubina, W. Desrat, M. Moret, A. Tiberj, O. Briot, V. Y.Davydov, M. A. Semina, and B. Gil, Nat. Commun. 10, 3479(2019).[33] H. W. Yoon, D. R. Wake, and J. P. Wolfe, Phys. Rev. B 54, 2763(1996).[34] R. F. Schnabel, R. Zimmermann, D. Bimberg, H. Nickel, R.Lösch, and W. Schlapp, Phys. Rev. B 46, 9873 (1992).[35] S. Marianer and B. I. Shklovskii, Phys. Rev. B 46, 13100(1992).[36] T. Venanzi, H. Arora, A. Erbe, A. Pashkin, S. Winnerl, M.Helm, and H. Schneider, Appl. Phys. Lett. 114, 172106 (2019).[37] W. Shockley and W. T. Read, Phys. Rev. 87, 835 (1952).[38] B. C. Connelly, G. D. Metcalfe, H. Shen, and M. Wraback,Appl. Phys. Lett. 97, 251117 (2010).044001-6

PHYSICAL REVIEW MATERIALS4, 044001 (2020) Photoluminescence dynamics in few-layer InSe Tommaso Venanzi , 1,2 * Himani Arora, 1,2Stephan Winnerl, Alexej Pashkin , Phanish Chava , Amalia Patanè,3 Zakhar D. Kovalyuk,4 Zakhar R. Kudrynskyi,3 Kenji Watanabe ,5 Takashi Taniguchi,5 Artur Erbe,1 Manfred Helm, 1,2 and Harald Schneider 1Helmholtz-Zentrum Dresden-Rossendorf, 01314 Dresden, Germany