Band Edge Recombination in CdSe, CdS and CdS x Se 1-x Alloy Nanocrystals Observed by Ultrafast Fluorescence Upconversion: The Effect of Surface Trap States

Please download to get full document.

View again

of 11
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Document Description
Band Edge Recombination in CdSe, CdS and CdS x Se 1-x Alloy Nanocrystals Observed by Ultrafast Fluorescence Upconversion: The Effect of Surface Trap States
Document Share
Document Tags
Document Transcript
  Band Edge Recombination in CdSe, CdS and CdS  x Se 1 -  x  Alloy Nanocrystals Observed byUltrafast Fluorescence Upconversion: The Effect of Surface Trap States Maria Danielle Garrett, † Albert D. Dukes III, † James R. McBride, † Nathanael J. Smith, † Stephen J. Pennycook, ‡ and Sandra J. Rosenthal* ,†,§  Department of Chemistry, Vanderbilt Uni V ersity, 7330 Ste V enson Center, Station B 351822, Nash V ille,Tennessee 37235, Oak Ridge National Laboratory, Condensed Matter Sciences Di V ision, Oak Ridge,Tennessee 37831, and Department of Physics and Astronomy, Vanderbilt Uni V ersity, 6301 Ste V enson Center,1807 Station B, Nash V ille, Tennessee 37235 Recei V ed: April 24, 2008; Re V ised Manuscript Recei V ed: June 12, 2008 The effect of surface trap states on band edge recombination in CdSe, CdS and CdS  x  Se 1 -  x   alloy nanocrystalshas been determined using fluorescence upconversion spectroscopy. These measurements reveal that there isboth a size and composition dependence on the short-lived ( τ  1 ) and long-lived ( τ  2 ) components of fluorescencelifetime at the band edge. An increase in nanocrystal diameter, ranging from 23 to 60 Å, is accompanied byan increase in  τ  1 . This behavior is explained by the decrease in accessible trap sites through a reduction insurface-to-volume ratio. Similarly,  τ  2  is found to increase with increasing nanocrystal size. However, withincreasing sulfur concentration in the alloy nanocrystals, both a reduction in the magnitude of   τ  1  and a reversalin the trend for  τ  2  are observed. These changes in lifetimes associated with the addition of sulfur are explainedby increased trapping on the nanocrystal surface. These results indicate that carrier dynamics may be controllednot only through size, but also through composition of the nanocrystals. Compositional variation has beenshown not only to affect carrier dynamics, but also to affect the optical properties of nanocrystals. An increasein the Stokes shift is observed for CdS  x  Se 1 -  x   alloy nanocrystals as compared to CdSe and CdS nanocrystals.This indicates that the Stokes shift is highly influenced by the nonlinear effects of alloying. Introduction The unique size-dependent optical and electronic properties 1–3 of semiconductor nanocrystals are important from both afundamental and an applied perspective. While size-dependenttunability makes these materials ideal for applications such asphotovoltaics, light-emitting diodes and biological labeling, 4–11 alloy nanocrystals offer the added advantage of composition-dependent tunability. 12 In particular, CdS  x  Se 1 -  x   alloy nanoc-rystals, spanning the compositional range from pure CdS (  x  ) 1) to pure CdSe (  x  ) 0), have band gap energies ranging fromthe UV to the visible. This makes CdS  x  Se 1 -  x   a potentiallyfavorable material for biological imaging applications, wherenanocrystals of the same size but with varying optical propertiesmight be advantageous. Additionally, alloys provide easieraccess to difficult wavelengths. For example, a small red-emitting nanocrystal 13 would be useful for increased lightpenetration through the skin. A more intimate understandingof the dynamics of the CdS  x  Se 1 -  x   nanocrystals is needed in orderfor parameters to be specifically tailored for each individualapplication, making CdS  x  Se 1 -  x   an ideal material with which tostudy the compositional dependence of electron - hole recom-bination at the band edge.Given that the kinetics of the photogenerated electron - holepair in the nanocrystal defines the operational parameters forpractical applications, an understanding of the behavior of theelectron - hole pair is a necessity. As the synthetic methodologiesof the nanocrystals continue to evolve, it is imperative to explorepossible changes in the kinetics of the carrier dynamics of thenanocrystals resulting from changes in composition. Twoextensive studies on the dynamics of bulk CdS  x  Se 1 -  x   wereconducted by Gadd 14 and Hane. 15,16 Gadd performed timecorrelated single photon counting (TCSPC) and fluorescenceupconversion experiments on bulk CdS  x  Se 1 -  x   (  x  ) 0.00, 0.25,0.50, 0.75 and 1.00 for TCSPC and  x  ) 0.00, 0.25 and 0.50 forfluorescence upconversion). Using TCSPC, the measured life-times were found to be approximately 30 ps for all samplesand, thus, were independent of composition. However, the fluo-rescence upconversion results showed much longer lifetimes,on the order of several hundred ps, that varied with composition.Hane also used TCSPC to study both graded and homogeneousCdS x Se 1-x  alloys. From this study it was found that for gradedalloys, there is a strong dependence of the luminescencelifetimes on detection wavelength. From 500 - 620 nm, forCdSe/S graded alloys, longer lifetimes were exhibited at longerwavelengths. However, from 620 - 720 nm, shorter lifetimeswere seen at longer wavelengths. In contrast, for CdS/Se gradedalloys, the opposite trend was seen for comparable ranges of wavelengths. With homogeneous alloys, a strong lifetimedependence with changing composition was seen. Whileindividual lifetimes were not reported, the lifetimes for thehomogeneous alloys ranged from approximately 100 - 250 ps.The decays for CdSe and CdS were found to be equivalentlyfast. For alloys  x  ) 0.25 and 0.75, the decays were intermediate,while  x   )  0.50 produced the longest decay.While ultrafast studies have been conducted on bulkCdS  x  Se 1 -  x   alloys, 14–16 there has been no major focus on theirnanocrystal counterpart. Most of the ultrafast studies onCdS  x  Se 1 -  x   alloy nanocrystals thus far have focused on nano- * † Department of Chemistry, Vanderbilt University. ‡ Oak Ridge National Laboratory. § Department of Physics and Astronomy, Vanderbilt University.  J. Phys. Chem. C   2008,  112,  12736–12746 12736 10.1021/jp803708r CCC: $40.75  ©  2008 American Chemical SocietyPublished on Web 07/23/2008  crystal doped glasses. 17–21 Zhang et al. studied the multiexcitonrecombination of CdS  x  Se 1 -  x   nanocrystal doped glasses usingfemtosecond transient absorption spectroscopy. 17 Of the twosizes examined, the 2.8 nm sample was found to have a risetimeon the order of 200 fs, corresponding to the pulse width of theexperiment. The second sample (2.6 nm) had a risetime slightlylonger than the pulse width, indicating the excited-state relaxedinto a state with a higher cross section for the probe pulse. Bothsets of rise times were found to be independent of pump power.However, the decay time constants were found to decrease withincreasing pump power as a result of high order excitonrecombination. This behavior was attributed to both second-order exciton - exciton annihilation and Auger recombination,where increasing the pump power increases the concentrationof charge carriers and, thus, the probability of electron - holerecombination. 17 Zhang and Izutsu also observed a relaxationtime of approximately 2 ps for excited carriers in dangling-bond states for CdS  x  Se 1 -  x  -doped glasses, using femtosecondpump - probe experiments. 18 Shen et al. studied the relaxation of photoexcited carriersthrough different channels for CdS  x  Se 1 -  x   nanocrystal dopedglasses using the femtosecond ultrafast transient lensing tech-nique. 19 They fit their data to three decay time constants forthe samples. These three decays were attributed to directrecombination, excited-state trapping and trapping processes atthe nanocrystal-glass interfaces. It was found, in CdS  x  Se 1 -  x  nanocrystals doped in glass, that there is an increase in theradiative decay rate as the nanocrystal sizes decreases. 19 Toyodaand Shen also used photoacoustic spectroscopy to study theCdS  x  Se 1 -  x   (  x   )  0.26) nanocrystals in a glass matrix. 20 Theyfound this material exhibited triexponential behavior corre-sponding to direct recombination processes with possible trap-ping, and radiative and nonradiative recombination processes.In this paper, we use femtosecond fluorescence upconversionto directly probe the depopulation of the excited-state in CdSe,CdS and CdS  x  Se 1 -  x   alloy nanocrystals. Although upconversionobserves only the radiative recombination, a nonradiative processis also reflected in the decay. By varying the amount of sulfurand selenium in the alloy nanocrystals, we explore the composi-tion dependence of electron - hole recombination at the bandedge for CdS  x  Se 1 -  x   alloy nanocrystals in solution. These resultsreveal both a size and composition dependence on the short-lived ( τ  1 ) and long-lived ( τ  2 ) lifetime components and arecompared to previously published fluorescence upconversiondata on the dynamics of CdS  x  Se 1 -  x   bulk alloys. This work iscritical in developing a better understanding of the strong effectthat compositional variations have on surface trapping and bandedge recombination. Experimental MethodsCdSe, CdS and CdS  x Se 1 -  x  Synthesis.  Homogeneous alloynanocrystals were synthesized as previously described bySwafford et al. 12 The synthesis was carried out in a single three-neck flask. The Cd precursor was prepared by combining 0.256g of CdO (Puratrem, 99.999%), 2.4 mL of oleic acid (OA,Aldrich, 90%) and 10 mL of 1-octadecene (ODE, Aldrich, 90%).This solution was heated to 310  ° C. The system was purgedwith argon until 140  ° C. When the temperature reached 310 ° C, a selenium:tributylphosphine (Strem, Se, 200 mesh and TBP,97%) injection solution [15 mL of 0.1 M Se:TBP:ODE (dilutedwith ODE from a 4 M Se:TBP stock solution) for CdSenanocrystals, 10 mL of 0.1 M S:ODE for CdS nanocrystals, or10  x   mL of 0.1 M S:ODE with 10(1-  x  ) mL of 0.1 M Se:TBP:ODE for CdS  x  Se 1 -  x   alloy nanocrystals] was swiftly injected andthe temperature was reduced to 275  ° C.To grow nanocrystals larger than approximately 36 Å indiameter, it was necessary to add growth solution to the reactionflask. The growth solution was prepared by stirring 0.76 g of CdO, 6 mL of OA and 25 mL of ODE while heating to 290 ° C. Once the solution reached temperature and turned clear, itwas cooled to 50 - 100  ° C while stirring. After reaching thistemperature, 0.16  x   g of S powder was added and dissolvedwhile stirring. This solution was then allowed to cool to roomtemperature. Upon reaching room temperature, 1.25(1-  x  ) mLof a 4 M Se:TBP solution was added to the solution. The growthsolution was then stirred until use. Growth solution was addedto the initial reaction solution, immediately after the injectionsolution, at a rate of approximately 0.45 mL/min, until thenanocrystals reached the desired size.Isolation of the nanocrystals was carried out by precipitationin a butanol:ethanol (1:4) mix, followed by centrifugation. Thesupernate was discarded, and the resulting solid was slurried in5 mL of chloroform. The nanocrystals were then precipitatedout of the chloroform by the addition of acetone and isolatedby centrifugation. 22 The supernate was decanted from thepelleted solid and the nanocrystals were once again precipitatedwith the chloroform:acetone mix, followed by centrifugation.After disposing of the supernate, the solid nanocrystals weresolvated in toluene or in hexanes. Femtosecond Fluorescence Upconversion.  Fluorescenceupconversion spectroscopy was performed with a CoherentVerdi V18 (CW, 532 nm, 18W) that was used to pump a mode-locked Ti:Sapphire oscillator (Mira 900 Basic, Coherent). Theoutput from the Mira was used to seed a regenerative amplifier(RegA 9000, Coherent), which in turn powered an opticalparametric amplifier (OPA 9400, Coherent), from which theexcitation and gate sources were obtained. Operating at arepetition rate of 250 kHz, the system produced pulses typicallyranging from 150 - 200 fs (fwhm) leading to instrument responsefunctions spanning approximately 200 - 280 fs (fwhm). ForCdSe, the tunable, visible OPA output (480 - 750 nm) was usedas the sample excitation source. In order to minimize the effectof the instrument response function on the spectrum, the OPAwas tuned 20 nm above the band edge absorption of the CdSenanocrystals. The frequency-doubled fundamental (400 nm) wasselected as the pump source for the CdS and CdS  x  Se 1 -  x  nanocrystals due to their lower wavelength band edge absorptionand the limitations of the tunable OPA output. Additionalsamples of OA synthesized CdSe were also excited at 400 nmto check the effect of excitation wavelength on the dynamics.The residual 800 nm light remaining from the doubling processin the OPA was used as the gate beam.For excitation 20 nm above the band gap, samples wereallowed to flow in anhydrous toluene through a 2 mm quartzcell under argon or nitrogen and excited by the focused tunablebeam. However, because of interference with the upconvertedsignal due to the UV cutoff for toluene, hexanes were used forsamples excited at 400 nm. A rhodium coated elliptical reflectorfocused the sample emission onto a nonlinear mixing crystal(1 mm XC8-LiIO 3 -Type I SFM-800/500 - 1000//308 - 444 nm,Cleveland Crystals, Inc.). The upconverted signal was maxi-mized by a suitable choice of the angle of the nonlinear mixingcrystal. For excitation at 400 nm, a color glass filter (03FCG579,Melles Griot) was used to filter out residual excitation light.A UV-dispersing prism (STS#37261, CVI Laser Corp.) wasused to separate the upconverted signal from any residual light.The upconverted signal was then directed into a UV-optimizedBand Edge Recombination in Alloy Nanocrystals  J. Phys. Chem. C, Vol. 112, No. 33, 2008  12737  monochromator (McPherson), detected by a photon-countingphotomultiplier tube (R1527P, Hamamatsu) and digitized witha photon counter (SR400, Stanford Research Systems). Thefitting function used to analyze the data was derived from theconvolution of the Gaussian laser pulse with a decayingexponential: 23 F  ( t  ,  A , τ  , W  ) )  A 2 [ 1 + erf  ( 14 ) [ 8 t  ln 2 - W  2 τ  W  √ ln 2  ]] × exp [ - ((16 t  ln 2) τ   - W  2 τ  2  )16ln 2  ]  (1) where  A  is amplitude of the decay,  W   is the fwhm of theGaussian, and  τ   is the decay time constant. To allow the positionof the Gaussian to “float” relative to the exponentials, a timeshift ( t  0 ) was added to the fitting function. Additionally, an offsetwas added so that the exponential decays back to the baselinerather than to zero. In order to account for multiple electron - holerecombination pathways, conventionally, several decays are usedfor fitting ultrafast data. 1,23–26 The fitting function is thesummation of as many convolved functions as observed decayprocesses ∑ i ) 0 n  A i 2  [ 1 + erf  ( 14 ) [ 8( t  - t  0 )ln 2 - W  2 τ  i W  √ ln 2  ]] × exp [ - ((16( t  - t  0 )ln 2) τ  i - W  2 τ  i 2  )16ln 2  ] + offset   (2) For the data presented here, two lifetimes were observed: a short-lived ( τ  1 ) and long-lived ( τ  2 ) decay. Additionally, for severalsamples, a risetime ( τ  3 ) was observed. Results and DiscussionCharacterization.  The band edge absorption wavelength(Figure 1a - e) of each sample was measured using a VarianCary 50 UV - vis spectrophotometer. The typical nanocrystalsize dependence of the band gap is apparent in Figure 1a - d;while Figure 1e reveals the composition dependence of the bandgap. Each sample was excited at either 20 nm above the bandedge absorption or at 400 nm, and the fluorescence upconversiondata was collected at the peak wavelength of the static emissionspectrum (Figure 1f). A compositional dependence of the Stokesshift is observed for CdSe, CdS and CdS  x  Se 1 -  x   alloy nanoc-rystals. Although the nonresonant Stokes shift is known todecrease with increasing nanocrystal size, 27 based on suchprevious reports in literature, the Stokes shift for the size rangeexamined in this work is relatively constant.The nonresonant Stokes shift is tied to the band-edge excitonfine structure, where the nonresonant Stokes shift is the energydifference between the two upper states of the band-edge excitonfine structure and the dark exciton ground state. 27,28 Thenonresonant Stokes shift may also be influenced by dispersionsin shape, inhomogeneity in structure, and phonon effects. 27,28 While only a small Stokes shift 1,29 is observed for CdSe andCdS, the Stokes shift almost doubles for CdS  x  Se 1 -  x   alloynanocrystals (Figure 2a). Similarly, increases in Stokes shift withchanging alloy composition have previously been seen inIn  x  Ga 1 -  x  N 30 and Zn 1 -  x  Cd  x  O 31 alloy films, and, most notably,in CdSe 1 -  x  Te  x   alloy nanocrystals. 32 Bailey and Nie 32 observe a nonlinear relationship betweenalloy composition and the band gap peak absorption andemission for CdSe 1 -  x  Te  x   alloy nanocrystals. They attribute the Figure 1.  Absorbance spectra for (a) CdS nanocrystals ranging in sizefrom 45 to 55 Å, (b) CdS 0.59 Se 0.41  alloy nanocrystals ranging in size from26 to 49 Å, (c) CdS 0.39 Se 0.61  alloy nanocrystals ranging in size from 23 - 58 Å, (d) CdSe nanocrystals ranging in size from 24 to 60 Å, (e) 44 Å( ( 5%) nanocrystals spanning the compositional range from pure CdS(  x   )  1) to pure CdSe (  x   )  0), and (f) representative absorption andemission spectra for CdSe nanocrystals. To run the fluorescenceupconversion experiment, CdSe samples were typically excited 20 nmabove the band edge, while CdS and CdS  x  Se 1 -  x   samples were excitedat 400 nm. Additional samples of CdSe were excited at 400 nm tocheck the effect of excitation wavelength on electron - hole recombina-tion at the band edge. 12738  J. Phys. Chem. C, Vol. 112, No. 33, 2008  Garrett et al.  exceptionally large Stokes shift to nonlinear effects, such asoptical bowing. Although the bowing parameter, a measure of the degree of nonlinearity, for CdS  x  Se 1 -  x   is smaller than forCdSe 1 -  x  Te  x  ,  12,33 the change in Stokes shift with compositionis clearly nonlinear (Figure 2b) for CdS  x  Se 1 -  x   alloy nanocrystals.Such nonlinear effects can be attributed to changes in the bandstructure due to variations in the lattice constant, deformationof the electron distribution due to different electronegativityvalues of the ions in the alloy, and structural ordering of differentsized ions due to relaxation of anion - cation bonds. 12,32 Not onlydoes the Stokes shift increase significantly for CdS  x  Se 1 -  x   alloynanocrystals, but it also appears to reach a maximum value nearthe middle of the compositional range (inset Figure 2b). Similarbehavior has been reported for In 1 -  x  Ga  x  N alloys. 34 Wu et al.attribute this behavior to a nonuniform distribution of the cations,implying that compositional variation or structural disorder ismaximized near the middle of the compositional range. Theirreasoning also coincides with Hane’s work on CdS  x  Se 1 -  x   bulkalloys, which states that maximized localization may well benear  x   )  0.50, where the material is most disordered. 16 The synthesized nanocrystals were found to be highly cry-stalline and have a zinc-blende structure. 12 High resolutiontransmission electron microscopy (HRTEM) images were takento check the size and to ensure each alloy sample consisted of monodisperse nanocrystals (Figure 3). Atomic number contrastscanning transmission electron microscopy (Z-STEM) was usedto obtain spatially resolved chemical information about thenanocrystals. 35,36 As heavier elements scatter electrons moreeffectively, they appear brighter in Z-STEM images. Thus, core/ shell structures exhibit a distinct difference in intensity betweenthe core and shell materials. In contrast, homogeneous alloynanocrystals should appear uniformly bright. As seen in Figure4, our materials are uniform in intensity, confirming that wehave synthesized homogeneous alloy nanocrystals.Homogeneity of the CdS  x  Se 1 -  x   alloy nanocrystals has beenpreviously verified in the literature. Swafford et al. conductedan extensive Rutherford backscattering spectroscopy (RBS)study where it was found that the composition of CdS  x  Se 1 -  x  was nearly constant over the entire growth period, indicating ahomogeneous alloy rather than a core/shell structure. 12 In orderto verify the composition of the material being used for thefluorescence upconversion experiments presented in this work,RBS was used to determine the compositional ratio of eachsample (Figure 5a). For a given composition series, thecomposition distribution of each alloy nanocrystal sample fallswithin  (  5% (Figure 5b). Carrier Dynamics.  The fluorescence lifetime data for CdSe,CdS and CdS x Se 1-x  alloy nanocrystals ranging in size from 23to 60 Å, collected using ultrafast fluorescence upconversion,are shown in Figure 6. For most of these samples, three lifetimeswere observed: a short-lived ( τ  1 ) and long-lived ( τ  2 ) decay anda risetime ( τ  3 ). The corresponding amplitude percentagesextracted from the fits for each decay lifetime are given in Tables Figure 2.  Graph of (a) Stokes shift (meV) versus nanocrystal size fordifferent alloy compositions and (b) peak absorption and emission (eV)for 44 Å ( ( 5%) nanocrystals spanning the compositional range frompure CdS (  x   )  1) to pure CdSe (  x   )  0), where the change in Stokesshift with composition is nonlinear. The inset depicts the Stokes shift(eV) for the 44 Å alloy nanocrystal series. Figure 3.  (a) HRTEM images of CdS 0.38 Se 0.62  52 Å alloy nanocrystalsand (b) CdS 0.58 Se 0.42  49 Å alloy nanocrystals. Band Edge Recombination in Alloy Nanocrystals  J. Phys. Chem. C, Vol. 112, No. 33, 2008  12739  1 and 2. It should be mentioned again that although theexcitation source was tuned to 20 nm above the band edgeabsorption of the OA synthesized CdSe nanocrystals, a 400 nmexcitation source was used for the CdS and CdS  x  Se 1 -  x  nanocrystals.Pumping the system at energies greater than twice the bandgap of the semiconductor nanocrystal results in the generationof multiexcitons. 37 By probing the intraband transitions in themid-IR, Ellingson et al. found that the exciton decay observedwith an increase in photon energy is related to nonradiativerecombination of multiexcitons through Auger recombination. 37 While initial measurements of the risetime of the transientabsorption data did not indicate any sign of carrier multiplica-tion, analysis of the decay data for inter- and intraband transientabsorption indicated that the biexciton effect, while importantin the first few ps, does not influence the long-term decaydynamics.Seeing that the excitation source was never double the bandgap of any sample presented in this work, carrier multiplicationwas not a concern. However, additional samples of CdSe werealso excited at 400 nm to verify that there was no significanteffect of excitation wavelength on the dynamics. Although ithas been reported that increasing the excitation energy mayproduce more relaxation pathways, involving surface or externalenergy states, that reduce the efficiency of charge carrierrelaxation to the band edge, 38 this does not appear to have acritical effect on the trends we report here. As seen in Figure 7,there is no appreciable dependence of the short-lived lifetimecomponent on excitation wavelength.To further verify the omission of multiexciton effects, theaverage number of photons absorbed per nanocrystal (  N  j ) wascalculated 39  N  ) σλ  E hc  (3) where  σ   is the absorption cross section,  λ  is the excitationwavelength,  E   is the laser energy per cm 2 ,  h  is Planck’s constantand  c  is the speed of light. From these calculations, it was foundthat the average number of photons absorbed per nanocrystalwas less than 1 for excitation at both 20 nm above the bandgap and at 400 nm. 40 Figure 8a - d shows that there is both a size and compositionaldependence on the electron - hole recombination of the nanoc-rystals. Focusing first on the size dependence, an increase inthe nanocrystal diameter is accompanied by an increase in theshort-lived component for band edge emission,  τ  1 . The short-lived component,  τ  1 , representing the lifetime of fluorescencedecay at the band edge, is comprised of both a radiative decayfrom electron - hole recombination and a nonradiative decay viatrap states. Upconversion observes only the radiative recombina-tion, but the nonradiative process depletes the radiative state.We attribute the changes observed in the measured decaylifetime to the effect surface trapping has on electron - hole Figure 4.  (a) Z-STEM image of CdS 0.50 Se 0.50  51 Å alloy nanocrystalstaken on a VG Microscopes’ model HB603U, operating at 300 kVand fitted with a Cs corrector from Nion, located at Oak Ridge NationalLaboratory. The operation and data collection were done with DigitalMicrograph. (b) It can be seen that there is no core/shell structure, asthe nanocrystal is uniform in intensity. Figure 5.  (a) Representative RBS spectrum of CdS  x  Se 1 -  x   alloynanocrystals and (b) compositional ratios, S/(S + Se), determined fromRBS measurements. For a given composition series, the compositiondistribution of each alloy nanocrystal sample falls within  ( 5%. 12740  J. Phys. Chem. C, Vol. 112, No. 33, 2008  Garrett et al.
Similar documents
View more...
Search Related
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks