low - cost solution - processable 
 metal halide perovskite semiconductors have seen encouraging development as inexpensive 
 absorber layers 
 in solar cells , and show high mobility , bright emission , tunable band gap , and photon recycling . while the majority of research has focused on thin - film 
 and bulk materials , perovskite nanocrystals have recently been synthesized . these include 
 hybrid organic  inorganic mapbx3 ( ma = methylammonium , 
 x = cl , br , i ) nanocrystals and nanostructures as well as all - inorganic 
 cesium lead halide cspbx3 ( x = cl , br , i ) and cesium tin 
 halide cssnx3 ( x = cl , br , i ) nanocrystals and nanostructures . the move to colloidal semiconductor quantum dots not only improves 
 solution processability of these materials but also allows band gap 
 tunabilty due to three - dimensional ( 3d ) confinement effects , and creates a material that is readily miscible with other optoelectronic 
 materials , for example , polymers , fullerenes , and other nanomaterials . hybrid organic  inorganic lead halide perovskite nanostructures 
 have been used in detectors for the visible , ultraviolet , and x - ray 
 regions of the electromagnetic spectrum , as gain media for optically pumped lasers , and as emission layers for light - emitting diodes 
 ( leds ) . it has been reported that in perovskites 
 abx3 ( a = ma , 
 cs ; b = pb , sn ; x = cl , br , i ) the ratios of the different halide 
 components have a strong influence on the electronic properties of 
 the material . the ability of the halide 
 ions to migrate within bulk perovskite has been reported both for 
 mapbx3 and for cspbx3 , which has specifically been identified as a halide - ion conductor . the high ion mobility within perovskite crystals 
 has been recognized as a possible source for the hysteresis in the 
 current  voltage curves seen in photovoltaic devices . in cspbx3 nanocrystals , which have 
 a high surface area to volume ratio , halide exchange quickly incorporates 
 new sources of excess halides , resulting in a shift of the optical 
 band gap . this is also the case when crystals with different halide 
 compositions are mixed , resulting in the formation of crystals with 
 an averaged total halide composition . halide exchange 
 has been shown to be possible in both mapbx3 and cspbx3 when moving between periodically adjacent halides , for example , 
 from cspbcl3 to cspbbr3 and cspbbr3 to cspbi3 and vice versa . although 
 recently there has been an increase in the application 
 of cspbx3 nanocrystals , the inability of cspbx3 nanocrystals with different compositions 
 to coexist as discrete semiconductors in one sample without rapid 
 halide exchange significantly limits their use in applications where 
 multiple band gaps are required , such as white - light leds and exciton 
 concentration systems . recently , palazon et al . showed that cross - linking the surface ligands in neat nanocrystal 
 films improves stability , prevents film liftoff , and limits halogen 
 exchange . it has also been shown that wrapping clusters of cspbx3 nanocrystals in polyhedral oligomeric silsesquioxane cages 
 can prevent halogen exchange . however , 
 neither of these methods allows the formation of films where the nanocrystals 
 are mixed on the submicrometer scale . energy transfer from high 
 band gap to low band gap nanocrystals 
 has been demonstrated between cspbbr3 particles of different 
 sizes . interactions between cspbcl3 and cspbi3 nanocrystals have previously been reported 
 to lead to dissolution of the nanocrystals . we find that when the crystals are synthesized and kept in an oxygen- 
 and water - free environment , this is not the case , consistent with 
 a recent report by dastidar et al . we 
 report significantly reduced halide exchange between chloride and 
 iodide in cspbx3 ( x = cl , i ) perovskite nanocrystals because 
 of the unfavorable crystal lattice tolerance factor for iodide this allows us to investigate films and solutions 
 containing nanocrystals of differing compositions , and to study the 
 resulting optical and electronic interactions . efficient excitation 
 transfer from cspbcl3 to cspbi3 is found to 
 proceed by a radiative process . excitation transfer also occurs in 
 electrically pumped crystals forming the active layer of a bulk heterojunction 
 led . cspbcl3 emission can efficiently be reabsorbed by 
 the cspbi3 nanocrystals and re - emitted in the red region . all chemicals were purchased 
 from sigma - aldrich ( st . louis ) and 
 were used as - received . cs2co3 ( 0.814 g , 99.9% ) was loaded into 100 ml three - neck flask along with 
 octadecene ( ode , 30 ml , 90% ) and oleic acid ( 2.5 ml , oa , 90% ) , and 
 the mixture was dried for 2 h at 120 c under n2 . ode ( 75 
 ml ) , oleylamine ( 7.5 ml , ola , 90% ) , and dried oa ( 7.5 ml ) and pbx2 ( 2.82 mmol ) such as pbi2 ( 1.26 g , 99.99% ) and 
 pbcl2 ( 0.675 g , 99.99% ) , were loaded into a 250 ml three - neck 
 flask and dried under vacuum for 2 h at 120 c . after complete 
 solubilization of the pbx2 salt , the temperature was raised 
 to 170 c and the cs  oleate solution ( 6.0 ml , 0.125 m 
 in ode , prepared as - described above ) was quickly injected . after 10 
 s , the reaction mixture was cooled in an ice  water bath . for 
 cspbcl3 synthesis , 5 ml of trioctylphosphine ( top , 97% ) 
 was added to solubilize pbcl2 . the nanocrystals were transferred 
 to an argon - gloved box ( h2o and o2 < 1 ppm ) 
 and precipitated from solution by the addition of equal volume anhydrous 
 butanol ( buoh , 99% ) ( ode : buoh = 1:1 by volume ) . after centrifugation , 
 the supernatant was discarded and the nanocrystals were redispersed 
 in anhydrous hexane ( 99% ) and precipitated again with the addition 
 of buoh ( hexane : buoh = 1:1 by volume ) . the nanocrystal dispersion was filtered through a 0.2 m polytetrafluoroethylene 
 filter and diluted to 10 mg ml in hexane before 
 use . subsequent mixing was carried out in a nitrogen - filled glove 
 box , and under these conditions the mixed solutions were stable for 
 at least 2 months at 19 c . exposure of mixed solutions 
 to ambient conditions led to rapid dissolution of the cspbi3 particles . absorption 
 spectra of 
 solutions were measured on nanocrystals samples dispersed in hexane 
 at a concentration of ca . 1 mg ml in a 1 cm  
 1 cm cuvette using a hp 8453 spectrometer . the samples were prepared 
 on quartz glass by spin - coating from 10 mg ml solutions 
 at 2000 rpm for 15 s , or for polymer samples a 10 mg ml perovskite nanocrystal dispersion in 10 mg ml poly(9-vinylcarbazole ) ( pvk ) in toluene was spin - coated at 2000 
 rpm for 60 s. photoluminescence was measured on an edinburgh instruments 
 fls980 fluorimeter . solution samples were measured in a 1 cm  
 0.3 cm cuvette excited in the 1 cm direction and imaged in the 0.3 
 cm direction . film samples were excited by front face illumination 
 at 45 to the surface ; detection was at 90 to excitation 
 and also at 45 to the surface . a monte carlo simulation of 
 the expected photoluminescence ( pl ) was constructed , using only the 
 measured emission and absorption spectra of the constituent species . the model is two - dimensional , allowing light to leave the system 
 in either the small or large axis , with dimensions of 0.3 or 3 cm . photon travel lengths are randomly generated , consistent with the 
 concentration- and wavelength - dependent absorption lengths arising 
 from the two species in the mix . if this length takes the photon outside the 
 container , it is counted toward the final spectrum if it leaves via 
 the small axis and ignored if it leaves via the large axis . otherwise , 
 it has a chance equal to the pure substance photoluminescence quantum 
 efficiency ( plqe ) of being re - emitted by the species that absorbed 
 it , in a new random direction and according to that species 
 emission spectrum . all values required can be measured from the single - species 
 solutions , and so the model contains no fitted parameters . the samples were 
 prepared on quartz glass by spin coating from 
 a 10 mg ml perovskite nanocrystal dispersion in 
 10 mg ml pvk in toluene at 2000 rpm for 60 s. 
 the nanocrystal films were encapsulated by affixing a glass coverslip 
 on the nanocrystal layer using carbon tape as a spacer unit and epoxy 
 glue as a sealant . the samples were excited by front face illumination 
 at 45 to the surface ; detection was at 90 to excitation 
 and also at 45 to the surface . 40 mg ml perovskite 
 crystals solution in octane on a tem grid ( 200 mesh cu , agar scientific ) 
 in a argon - filled glove box . high - angle annular dark field scanning 
 transmission electron microscopy ( haadf - stem ) and electron energy 
 loss spectroscopy ( eels ) analysis were also conducted on a fei tecnai 
 osiris tem / stem 80 - 200 microscope , operating at 80 kv , using a liquid 
 nitrogen holder , and equipped with a gatan enfinium er 977 spectrometer 
 with dual eels . the convergence and collection angles used were 8.5 
 and 34 mrad , respectively . the eels spectral images were analyzed 
 using principal component analysis and the elemental maps with the 
 absolute quantification were obtained through the use of the integration 
 method proposed by egerton . the eels 
 data analysis and elemental quantification were performed using the 
 open source software package hyperspy toolbox . perovskite nanocrystal films 
 were prepared by drop - casting a 10 mg ml nanocrystals 
 solution in hexane on silicon wafers . xrd experiments were carried 
 out on a bruker x - ray diffractometer using a cu k radiation 
 source (  = 1.5418  ) . the measurements were taken from 
 2 of 1070 with a step size of 0.0102 
 in 2. film thicknesses 
 were measured using 
 a dektak profilometer and a digital instruments / veeco dimension 3100 
 atomic force microscope . nanocrystal films 
 were placed in 
 an integrating sphere and were photoexcited using a 405 nm continuous - wave 
 laser . the laser and the emission signals were measured and quantified 
 using a calibrated andor idus du490a ingaas detector for the determination 
 of pl quantum efficiency . poly(3,4-ethylenedioxythiophene):polystyrenesulfonate 
 ( pedot : pss ) was spin - coated onto an indium  tin oxide ( ito)-coated 
 glass substrate at 6000 rpm for 45 s , followed by annealing at 140 
 c for 30 min in a nitrogen - filled glove box . a 10 mg ml perovskite nanocrystal dispersion in 10 mg ml pvk in toluene was spin - coated at 2000 rpm for 60 
 s in an argon - filled glove box to give a 5060 nm film . the 
 samples were then transferred into a thermal evaporator , and calcium 
 ( ca ; 20 nm ) and silver ( ag ; 80 nm ) were deposited through a shadow 
 mask at 3  10 mbar or better . the leds were 
 encapsulated by affixing a glass slide on top of the contacts using 
 transparent ultraviolet ( uv ) epoxy glue . photon flux 
 was measured simultaneously using a calibrated silicon photodiode 
 centered over the light - emitting pixel . luminance in cd m was calculated based on the emission spectrum of the led , weighted 
 against the standard luminosity function and on the known spectral 
 response of the silicon photodiode . cspbx3 ( x = cl , i ) nanocrystals 
 were prepared as previously 
 reported by protesescu et al . ( details 
 in the methods section ) . all processing and 
 characterization were performed in an inert atmosphere ( oxygen and 
 water < 5 ppm ) . under these conditions we find that cspbcl3 and cspbi3 nanocrystals coexist in solution without undergoing 
 dissolution or significant halogen exchange . to investigate the optical 
 properties of this system , we prepared solutions of cspbcl3 and cspbi3 at an overall crystal concentration of 1 
 mg ml ( figure 1a ) . we find absorbance 
 onsets of 425 and 690 nm for the cspbcl3 and cspbi3 samples , respectively . the cspbcl3 nanocrystals 
 show a sharp peak close to the absorption onset , which likely arises 
 from excitonic effects . mixed solutions show a combination of the 
 characteristic features of the pure nanocrystal solutions without 
 any spectral shifting . by fitting the absorbance spectrum of the mixed 
 solution with a sum of the pure sample spectra , we calculate the ratio 
 of the different crystals in a nominally 1:1 mixed solution sample 
 to be 1:0.957 ( cspbcl3:cspbi3 ) ( figure 1 of the supporting information ) . to investigate 
 the structural and physical properties of the mixed system by powder 
 xrd and tem , neat films of the crystals were drop - cast from a 10 mg 
 ml solution respectively onto silicon and onto 
 carbon - coated copper substrates . the xrd pattern ( figure 1b ) shows peaks at 16 
 and 32.5 corresponding to those found in pure cspbcl3 crystals reported by protesescu et al . and similarly at 14 and 28 in the pure cspbi3 crystals . the xrd pattern of the cspbcl3:cspbi3 ( 1:1 ) sample is a superposition of the cspbcl3 and cspbi3 nanocrystal xrd patterns . the presence of both cspbcl3 and cspbi3 peaks in the blends , without any shifts 
 or additional peaks , indicates that these crystal structures exist 
 in parallel in our nanocrystal blend films . haadf tem imaging ( figure 1c ) shows two distinct 
 types of nanocrystals with slightly different contrasts and sizes , 
 suggesting two different nanocrystal populations . eels and scanning 
 transmission electron microscopy ( stem ) was then used to further assign 
 these crystal populations and obtain an absolute quantification of 
 each element . the individual elemental maps with number of atoms per 
 nm , shown in figure 1c , indicate that the iodide is localized on the larger 
 crystals while the chloride is localized on the smaller crystals . the amount of i and cl in the nanocrystals maintains a 3:1 stoichiometric 
 ratio with cs . the eels spectra measured at the two locations in figure 1c show two distinct 
 traces for different nanocrystal populations and are shown in figure 1d . the blue trace , 
 corresponding to eels measurements at the blue cross , is assigned 
 to a cspbcl3 nanocrystal with edges seen for cs , c , cl , 
 and o , and the red trace , corresponding to eels measurements at the 
 red cross , is assigned to a cspbi3 nanocrystal with edges 
 seen for cs , c , i , and o. the sizes of the cspbcl3 and 
 cspbi3 nanocrystals were measured at 7.0  2.8 and 
 12.0  3.9 nm , respectively . these data confirm that the cspbcl3 and cspbi3 nanocrystals are intimately mixed but 
 remain discrete entities with insignificant halide mixing between 
 them . the data in figure 1 support our conclusion that cspbcl3 and cspbi3 do not undergo significant halogen exchange with each other . the lack of halogen exchange in these systems is assigned to the different 
 tolerance factors of the different crystal lattices acting to inhibit 
 halogen exchange . ( a ) absorption spectra 
 ( left ) of pure cspbcl3 , cspbi3 , and a 1:1 nanocrystal 
 blend and emission spectra ( right ) 
 of pure cspbcl3 and cspbi3 in hexane ( concentration 
 1 mg ml ) . ( b ) powder xrd patterns of cspbcl3 , cspbi3 , and 1:1 nanocrystal blend solid films 
 with distinctive peak highlighted . ( c ) haadf tem images and eels tem 
 maps for cs , i , and cl . ( d ) eels tem spectrum for 
 cspbcl3:cspbi3 ( 1:1 ) samples taken at the positions 
 of the red and blue crosses in ( c ) . the ability of these crystals 
 to exist as discrete entities gives 
 us the unique opportunity to study these crystals and their photophysical 
 interactions with each other . cspbcl3 nanocrystals emit 
 in the near uv at 425 nm , whereas cspbi3 nanocrystals emit 
 in the red at 695 nm ( figure 1a ) . when excited at 365 nm , nanocrystals dispersed in a poly(methyl 
 methacrylate ) ( pmma ) matrix at a total nanocrystal : polymer ratio of 
 1:1 by weight ( film thickness 20 nm ) ( figure 2a ) and neat mixed nanocrystal films spun 
 from toluene ( figure 2b ) clearly show emission from both types of nanocrystals . spectral 
 tuning of the separate crystals was also achievable by incorporating 
 a small ( weight fraction 10% ) amount of cspbbr3 nanocrystals in a solution of cspbcl3 and cspbi3 nanocrystals . as there is not enough cspbbr3 to represent 
 a majority , the cspbbr3 is incorporated into the cspbcl3 and cspbi3 crystals , resulting in a cspbcl(3x)brx and cspbi(3x)brx blend ( figure 2c ) . ( a ) solid - state absorbance and emission spectra of cspbcl3:cspbi3 ( 1:1 ) in pmma , film thickness 20 
 nm ( 10 
 mg ml nanocrystals and 10 mg ml pmma in toluene , spun at 6000 rpm ) . ( b ) solid state absorbance and 
 emission in neat mixed crystal films ( 10 mg ml in toluene , spun at 2000 rpm ) . ( c ) absorbance and emission of 0.1 
 mg ml nanocrystals in toluene ) with different 
 cspbcl3:cspbbr3:cspbi3 ratios . when the crystals were excited 
 directly at 550 nm , the overall 
 plqe yield of the cspbi3 crystals decreased with increasing 
 cspbcl3 ratios ( figure 2 of 
 the supporting information ) . despite there being no change in xrd 
 ( figure 3 of the supporting information ) 
 or the emission spectrum , tem images show a small amount of migration 
 of chloride ions into the cspbi3 crystals ( figure 1c ; figure 4 of the supporting information ) . we attribute the decrease 
 in plqe to small amounts of chloride migration which increases the 
 amount of nonradiative decay within the crystals . this is consistent 
 with tcspc measurements ( figure 5 of the 
 supporting information ) , which show the cspbi3 fluorescence 
 decay lifetimes are shortened for ratios greater that 1:1 . we are 
 still able to achieve high plqes in the cspbi3 nanocrystals 
 at a 1:1 ratio . the above spectra ( figure 2a , b ) showed emission from both cspbcl3 and cspbi3 nanocrystals ; however , when cspbcl3 and cspbi3 nanocrystals are mixed in a 1:1 ratio 
 at higher solution 
 concentrations and in thicker polymer matrixes , the emission was found 
 to be predominantly at 695 nm under 405 nm excitation . solutions of 
 cspbcl3 and cspbci3 nanocrystals showed emission 
 solely from the cspbi3 crystals up until a 20-fold excess 
 of cspbcl3 ( figure 6 of the 
 supporting information ) . emission solely from the low - energy particles 
 was also seen for nanocrystals dispersed in a pmma matrix at a total 
 nanocrystal : polymer ratio of 1:1 by weight and film thickness 75 
 nm ( figure 3a ) . these 
 results indicate that there is efficient energy transfer to the low - energy 
 nanocrystals . ( a ) luminescence of cspbcl3 , cspbi3 , and 
 cspbcl3:clpbi3 blends in pmma matrix at a total 
 nanocrystal : polymer ratio of 1:1 by weight and film thickness 75 
 nm . ( b ) transient luminescence decays excited at 405 nm with measurements 
 at 450 or 670 nm . the interaction responsible 
 for this energy transfer in solid films 
 was investigated through transient spectroscopy techniques . for mixed 
 samples with a 1:1 ratio of cspbcl3:cspbi3 by 
 weight , the cspbi3 nanocrystals show an increased lifetime 
 when excited at 405 nm compared to pure cspbi3 samples 
 ( figure 3b ) . consistent 
 with steady state measurements , there was no emission from the cspbcl3 nanocrystals in the mixed samples . an extended luminescence 
 lifetime in the lower - energy particle is consistent with excitation 
 transfer . one possible mechanism for this energy transfer is frster 
 resonance energy transfer ( fret ) . we calculate the frster 
 radius r0 , the distance at which 50% of 
 all excitations lead to energy transfer from the donor to the acceptor , using measured absorption , emission , and plqe 
 data to be 6.8  0.3 nm . this value is comparable to the size 
 of the nanocrystals so the point dipole approximation stipulated in 
 fret calculations is not entirely appropriate . it is also worth noting 
 that the large aliphatic ligands that offer colloidal stability are 
 still attached to these crystals . this combined with the apparent 
 slight phase separation of the two crystals in neat films ( figure 1c ; figure 4 of the supporting information ) and the fact that 
 the crystals are supported in a polymer matrix means that the distance 
 between a cspbcl3 and cspbi3 particle is generally 
 greater than 6.8 nm . we can not completely rule out fret playing a 
 role in energy transfer , but crucially the fact that energy transfer 
 is more complete in thick films , with the same interparticle spacing , 
 suggests that another mechanism is dominating . we therefore ascribe 
 the dominant emission from cspbi3 nanocrystals in cspbcl3:cspbi3 blends to efficient reabsorption of photons 
 emitted from cspbcl3 nanocrystals . a monte carlo algorithm 
 allowing for multiple absorption and re - emission events gives an accurate 
 replication of the measured emission in concentrated solutions and 
 shows the measured down conversion of the blue emission to red ( figure 7 of the supporting information ) . to use the potential of this efficient photon reabsorption between 
 different cspbx3 ( x = cl , i ) nanocrystals , we incorporated 
 them into bulk heterojunction polymer / cspbx3 nanocrystal 
 leds . the leds were made by spin - coating pedot : pss on an ito glass 
 substrate . a toluene solution containing 10 mg ml nanocrystal and 10 mg ml pvk was further spun 
 on top , giving a 5060 nm film , and a calcium and silver electrode 
 was deposited by thermal evaporation ( figure 4a ) . devices of cspbcl3 , cspbi3 , cspbcl3:cspbi3 ( 1:1 ) ( all in pvk matrixes ) , 
 and pure pvk were produced . ( c ) electroluminescence spectra of cspbi3:pvk , cspbcl3:cspbi3:pvk , and cspbcl3:pvk at different 
 voltages . the electroluminescence spectra of the cspbi3:pvk and cspbcl3:cspbi3:pvk remain constant 
 with voltage ( not shown ) . all devices were inefficient , with quantum efficiencies less 
 than 
 0.04% ( figure 8a of the supporting information ) , 
 and relatively high voltages were required to achieve significant 
 luminances ( figure 4b ) . devices containing pvk showed broad emission , consistent with 
 previous reports , and had the highest current densities 
 ( figure 8b ) . adding cspbcl3 particles 
 had only a minor effect on the current density ( figure 8b ) , but at high voltages led to a clear emission peak 
 around 400 nm ( figure 4c ) , consistent with charge capture and recombination occurring on 
 the particles . with cspbi3 particles , the emission was 
 solely from the particles , centered around 695 nm ( figure 4c ) , but the current density 
 was reduced by an order of magnitude ( figure 8b ) , consistent with trapping of one or both carriers on the particles . mixed cspbcl3:cspbi3/pvk devices maintain the 
 high current densities comparable to those of the pvk and cspbcl3/pvk devices but show emission solely from the cspbi3 nanocrystals ( figure 4c ; figure 8b of the supporting information ) . this suggests that transport is dominated by the cspbcl3 particles but that any emission occurring from the cspbcl3 particles is converted to cspbi3 emission through photon 
 reabsorption as demonstrated in the optical measurements described 
 above . devices containing mixed nanoparticles therefore show the best 
 device performance . it would be attractive to obtain a mixture of 
 blue and red emission in leds , which would require thinner films of 
 mixed nanoparticles to avoid complete reabsorption of the blue emission 
 as demonstrated optically in figure 2 . unfortunately , though , we have not yet been able 
 to fabricate working leds with active layer thicknesses below 40 nm . in conclusion , we present the study of interactions in blends films 
 with mixtures of different cspbx3 ( x = cl , i ) perovskite 
 nanocrystals . we find that cspbcl3 and cspbi3 nanocrystals can exist as discrete entities in solution , embedded 
 in a polymer matrix and as neat films . the cspbcl3 emission 
 can be reabsorbed by the cspbi3 nanocrystals due to the 
 large absorption coefficient of the cspbi3 nanocrystals 
 in the range of the cspbcl3 emission . this phenomenon can 
 be utilized in bulk heterojunction leds where the luminance of devices 
 emitting in the 695 nm region can be improved by the incorporation 
 of cspbcl3 nanocrystals . this causes the devices to operate 
 at a higher current density with photon reabsorption transfer occurring 
 from the cspbcl3 nanocrystals to the cspbi3 crystal 
 for efficient re - emission .
cesium lead halide 
 nanocrystals , cspbx3 ( x = cl , br , 
 i ) , exhibit photoluminescence quantum efficiencies approaching 100% 
 without the core 
 shell structures usually used in conventional 
 semiconductor nanocrystals . 
 these high photoluminescence efficiencies 
 make these crystals ideal candidates for light - emitting diodes ( leds ) . 
 however , because of the large surface area to volume ratio , halogen 
 exchange between perovskite nanocrystals of different compositions 
 occurs rapidly , which is one of the limiting factors for white - light 
 applications requiring a mixture of different crystal compositions 
 to achieve a broad emission spectrum . here , we use mixtures of chloride 
 and iodide cspbx3 ( x = cl , i ) perovskite nanocrystals where 
 anion exchange is significantly reduced . we investigate samples containing 
 mixtures of perovskite nanocrystals with different compositions and 
 study the resulting optical and electrical interactions . 
 we report 
 excitation transfer from cspbcl3 to cspbi3 in 
 solution and within a poly(methyl methacrylate ) matrix via photon 
 reabsorption , which also occurs in electrically excited crystals in 
 bulk heterojunction leds .