Spectroscopic Properties of Phase-Pure and Polytypic Colloidal Semiconductor Quantum Wires Fudong Wang,* Richard A. Loomis, and William E. Buhro* Department of Chemistry, Washington University, St. Louis, Missouri 63130-4899, United States S Supporting Information *
ABSTRACT: We report ensemble extinction and photoluminesence spectra for colloidal CdTe quantum wires (QWs) with nearly phase-pure, defect-free wurtzite (WZ) structure, having spectral line widths comparable to the best ensemble or single quantum-dot values, to the single polytypic (having WZ and zinc blende (ZB) alternations) QW values, and to those of two-dimensional quantum belts or platelets. The electronic structures determined from the multifeatured extinction spectra are in excellent agreement with the theoretical results of WZ QWs having the same crystallographic orientation. Optical properties of polytypic QWs of like diameter and diameter distribution are provided for comparison, which exhibit smaller bandgaps and broader spectral line widths. The nonperiodic WZ−ZB alternations are found to generate non-negligible shifts of the bandgap to intermediate energies between the quantum-confined WZ and ZB energies. The alternations and variations in the domain sizes result in inhomogeneous spectral line width broadening that may be more significant than that arising from the 12− 13% diameter distributions within the QW ensembles. KEYWORDS: quantum wire, crystal structure, zinc blende, wurtzite, polytypism, extinction spectroscopy, photoluminesence, homogeneous and inhomogeneous broadening
W
dissimilar QW properties. The experimental results are primarily based on studies of colloidal polytypic II−VI and III−V QWs that contain high densities of planar defects, such as twinning boundaries, stacking faults, and WZ−ZB phase alternations.20−25,27,29 This is due to the experimental unavailability, until recently,4 of phase-pure, defect-free, colloidal II−VI and III−V QWs and a lack of spectroscopic data on the few phase-pure systems that had been obtained by VLS growth.30−32 In contrast, the theoretical results are typically based on phase-pure cubic (e.g., diamond or ZB) or hexagonal (e.g., WZ) crystal structures.9−19,26 The WZ−ZB alternations in polytypic QW specimens make theoretical calculations in these random polytypes economically impractical. Consequently, direct comparisons of experimental and theoretical results based on QWs having the same crystal structures, the same stacking sequences, or the same distributions of planar defects are still lacking. Also of interest is how the presence of planar defects alters the optical and electronic structures of QWs. The WZ−ZB phase alternations in QWs can generate staggered, type-II heterojunctions with the bulk band edges of the WZ valence
e report herein that the ensemble extinction and photoluminescence (PL) spectral properties of semiconductor quantum wires (QWs) prepared by the solution−liquid−solid (SLS)1−3 and solution−solid−solid (SSS)4 methods depend on the crystal structures of the QWs. Near phase-pure, defect-free wurtzite (WZ) CdTe QWs show a larger bandgap and narrower spectral line width (defined by the full width at half-maximum or fwhm of the lowest energy absorption or emission features from Gaussian fits) than those exhibited by polytypic QWs (having WZ and zinc blende (ZB) alternations) with like diameter distributions. The existence of randomly distributed stacking faults and the smaller bandgap ZB phase in polytypic QWs lowers the bandgap of the QWs in comparison to the pure WZ QWs. The variations of the ZB and WZ amounts and domain lengths within and between the CdTe QWs generate additional inhomogeneous spectral line width broadening as well as an experimentally significant Stokes shift of the PL from the lowest energy absorption feature. Semiconductor nanowires and QWs, as one-dimensional nanostructures, possess intriguing optical and electronic properties that are fundamentally different from their quantum-dot (QD) and quantum-rod (QR) counterparts, and have been of considerable interest over about two decades.1,5−7 Both experimental and theoretical studies of the optical and electronic structures of semiconductor QWs have appeared,8−29 but direct comparisons between the studies are hindered by © 2016 American Chemical Society
Received: September 8, 2016 Accepted: September 25, 2016 Published: September 25, 2016 9745
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Figure 1. Representative TEM (left panel) and HRTEM (right panel) images of (a, c) WZ and (b, d) polytypic CdTe QWs, designated as QW specimens a, c, b, and d, respectively. The QWs are viewed in the ZB [11̅0] or WZ [112̅0] zone or their equivalents, normal to the growth axis of ZB [111] or WZ [0001]. The ZB (blue) and WZ (gray) segments are labeled as indicated, with red dashed lines denoting twin boundaries or stacking faults. The QWs have an average WZ% of (a) 99.9, (b) 20.9, (c) 96.7, and (d) 18.0% and a mean diameter, d (± one standard deviation in the diameter distribution of the mean diameter), of (a) 6.6 nm (±12.1%), (b) 6.5 nm (±9.2%), (c) 7.7 nm (±13.0%), and (d) 7.8 nm (±10.3%). These QWs have lengths in the range of 1.5−6.0 μm. The scale bars in the HRTEM images are 5 nm.
Calculations by Kipp and co-workers,27,37 however, indicate that the typical WZ and ZB segments in CdSe QWs are too short to effectively confine charge carriers in separate spatial regions along the length of the QW, especially at room temperature, due to the large sizes of the electron and hole wave functions in comparison with the sizes of the crystal domains. As a result, the effective bandgap of these SLS-grown polytypic QWs represent an average of the energies associated with the numerous WZ and ZB segments, and the electron and hole wave functions maintain considerable spatial overlap. The band gap energies in these CdSe QWs can span from the ZB value to the WZ value with the density of states in the VB and CB and the resultant shapes of the absorption and PL features depending on the relative amounts and domain sizes of the two crystal phases within the QWs. Kuno and co-workers38 also proposed that the WZ-ZB alternations shifted the emission energies and broaden the PL spectra, but their proposed mechanism was associated with the localization of the electrons
band (VB) and conduction band (CB) lying energetically above the ZB VB and CB.27,33−38 These type-II heterojunctions can result in the spatial separation of charge carriers, with the electrons localized in ZB domains and holes in WZ domains, especially at low temperatures, where even subtle energy variations can alter the motion of charges. Theoretical calculations by Zunger and co-workers39 showed that at 0 K the absorption spectra for the indirect WZ (hole)−ZB (electron) transitions shifted to lower energy relative to the direct WZ (hole)−WZ (electron) and ZB (hole)−ZB (electron) transitions, with smaller shifts for shorter WZ or ZB segments. The type-II alignment transitioned to type-I alignment at small diameters, d < 7.5 nm, for InP QWs. For these small QWs, the larger quantum-confinement energy in the VB of the WZ domains over that in the ZB domains, which results from a smaller heavy-hole mass for the former phase in the radial [1000] direction, overtakes the bulk VB offset of 45 meV between the WZ and ZB phases. 9746
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specimens b and d (12−13% vs 9−10%). As such, the optical properties for the WZ and polytypic QWs were compared and analyzed on a quantitive basis as described below. Extinction and PL Spectra. The room-temperature extinction spectra for these four sets of QWs are richly structured, having up to six absorption features that can be easily visualized in the range shown (Figure 2). We previously
and holes in the different crystal domain regions, thereby suggesting the separation of photogenerated electrons and holes. Broadening was also observed in the PL spectra of thick semiconductor nanowires grown by the VLS mechanism, and again, the line width broadening was attributed to WZ−ZB alternations.40 In this work, we report the optical properties of nearly phasepure, defect-free WZ CdTe QWs grown by the SSS mechanism.4 Ensembles of such QWs show room-temperature extinction spectra having richly structured absorption features that compare excellently with the calculated spectra of WZ QWs having the same crystallographic orientation.19 Despite their somewhat large (∼13%) diameter distributions, these QWs show absorption and PL spectra with line widths as narrow as ∼50 meV, comparable to those of single, polytypic CdSe QWs (47−64 meV, determined in the present study by nonlinear least-squares fitting of the PL and extinction spectra),24 which are, to our knowledge, the narrowest reported for ensembles of QWs. In contrast, ensembles of polytypic QWs of like diameter and narrower diameter distribution in this work show much broader fwhms of >72 meV and smaller bandgap energies. The major goals of this work are to compare the electronic structure of WZ CdTe QWs obtained from extinction spectra with those from theory19 and to determine quantitatively how the bandgaps and spectral line widths of the QWs are affected by polytypism. The inhomogeneous line width broadening resulting from interwire heterogeneities, such as diameter polydispersity and WZ−ZB variations, and from intra-QW nonperiodic WZ−ZB alternations is analyzed, and the relative contributions of these factors to the spectral line widths are estimated.
Figure 2. Room-temperature extinction spectra (a) of CdTe QW specimens a, b, c, and d, corresponding to the QWs shown in Figure 1. The absorption features are labeled 1, 2, 3, 4, 5, and 6 in the order of increasing energies as indicated. The second absorption features (peak 2) for QW specimens a and d are not visually apparent, and thus are not labeled, but were extracted by fitting the extinction spectra with one exponential function for the background and six Gaussian functions for the absorption features (Figure S2). Room-temperature PL spectra (b) for QW specimens c and d, with their extinction spectra provided for comparison. The ensemble PL quantum efficiencies (QEs) are >1% and ∼0.02% for QW specimens c and d, respectively. The high-energy tail associated with scattering is apparent for QW specimen d due to its low PL QE.
RESULTS WZ and Polytypic CdTe QW Specimens. Four sets of CdTe QW specimens that form the basis of these investigations are shown in Figure 1. QW specimens a and c were synthesized by the SSS mechanism at low, non-zero DOP concentrations and low Cd/Te (mol/mol) ratios of 3.0 and 2.0, respectively (see the Methods for details). Under these conditions, the catalyst nanoparticles were converted to BixCdyTez nanoparticles having high Te contents and were consequently solid catalyst nanoparticles. 4 QW specimens b and d were synthesized by the SLS mechanism1−3 using high DOP concentrations and high Cd/Te ratios of 3.5, under which conditions the catalyst nanoparticles contained low Te fractions and remained liquid catalyst nanoparticles.4 Specimens a and c had an average WZ% of 99.9 and 96.7, respectively (see Figure S1 for the WZ-phase distribution histograms for individual wires), and were deemed to be near phase-pure, defect-free WZ QWs. Specimens b and d contained a high density of stacking faults and twinning boundaries, exhibited an average WZ% of 20.9 and 18.0, respectively (see Figure S1 for the WZ-phase distribution histograms for individual wires), and were thus identified as polytypic QWs. The average WZ- and ZB-segment lengths were 0.5 and 1.7 nm for QW specimen b and 0.4 and 1.3 nm for QW specimen d by considering the twinning boundaries in the ZB phase as WZ segments. WZ QW specimen a had a similar mean diameter as the polytypic QW specimen b (d ≈ 6.5 nm) and the WZ QW specimen c had a mean diameter similar to that of the polytypic QW specimen d (d ≈ 7.7 nm). WZ QW specimens a and c exhibited slightly broader diameter distributions than the polytypic QW
reported the absorption spectra for polytypic CdTe QWs, which showed up to five, slightly broader absorption features, consistent with the larger diameter distributions, 14−21% of those CdTe QWs.19 The WZ CdTe QW specimens a and c had much sharper absorption features, especially for the first, lowest energy features (hereafter peak 1), which were comparable to those of monodisperse QDs (see below).41−43 In addition, the peak-1 features were shifted to higher energies relative to those for the polytypic QW specimens b and d of like diameter. We quantitatively analyze these data below. We extracted the individual absorption features by nonlinear least-squares fitting of the extinction spectra,20−23,25 and the resulting peak positions and fwhms are plotted in Figure 3. The absorption features for the polytypic QW specimens b and d were shifted by 23−88 meV (39 and 23 meV for peak 1, respectively) to lower energy than those of the WZ QW specimens a and c. The fwhm values of the features were larger in the polytypic samples in comparison to those of the WZ QW samples, with the peak-1 fwhm values of 84 and 72 meV for b and d, and 66 and 51 meV for a and c, respectively. Similar spectral shifts and fwhms were also evident in the roomtemperature PL spectra of the QWs. For example, the maximum of the PL spectrum of polytypic QW specimen d 9747
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Figure 3. Peak energies (solid lines) and their associated fwhms (dashed lines) of the absorption features of CdTe QW specimens a−d shown in Figure 2. The values were obtained by fitting the extinction spectra by multiple Gaussian functions and extracting the individual absorption features (Figure S2). Fitting uncertainties exist for higher energy features (e.g., peaks 5 and 6) due to their breadth (see Figure 2) and the presence of numerous transitions within the peaks.19
Figure 4. Energies of the absorption features plotted relative to the energies of the lowest, first absorption features. The open symbols are the experimentally observed features for QW specimens a−d. The solid symbols are the calculated absorption features obtained from ref 19. The calculated 3rd, 4th, and 5th features shown here were assigned as 2nd, 3rd, and 4th, respectively, in the previous work,19 because the additional feature (peak 2 shown here and in Figure 2) was not resolved in our previous polytypic QWs. Peak 2 (at ∼1.68 eV) for the 10.2 nm diameter QWs was not resolved in the calculation,19 so the dark cyan, dashed line is the linear fit to the other two points and extrapolated to ∼1.68 eV. The calculated values for peak 6 were not available.
was shifted by 28 meV to lower energy than that of WZ QW specimen c, which exhibited fwhms of 74 and 54 meV, respectively (Figure 2b). Such narrow spectral line widths of nearly 50 meV for WZ QWs are, to our knowledge, the narrowest reported for ensembles of semiconductor QWs. The Stokes shift of the PL spectrum from the lowest energy, peak-1 absorption feature for the polytypic QW specimen d was larger than in the WZ QW specimen c (9.7 ± 0.9 meV vs 5.4 ± 0.5 meV). Comparison of Experimental Spectral Data with the Theoretical Electronic Structure of WZ QWs. Schrier and co-workers19 previously reported theoretical absorption spectra for WZ CdTe QWs having their long axis along the [0001] orientation (as in our experimental WZ QWs). The calculated, well-resolved absorption features are not discrete electronic transitions, but clusters of closely spaced transitions grouped together by the energy spacing of the CB levels. These calculated absorption features agree reasonably well with those of the previously reported experimental polytypic CdTe QWs, with the corresponding features diverging by 35−90 meV.19 Now with the experimental extinction spectra of near singlephase WZ CdTe QWs available, a better comparison between experiment (open symbols) and theory (solid symbols) is possible, as shown in Figure 4. In Figure 4, the experimental and theoretical energies of the higher energy discrete absorption features relative to the lowest energy feature, peak 1, are plotted versus the energy of peak 1. Based on the calculations, peak 1 contains transitions of electrons from the VB2, VB3, and VB4 valence band states to the lowest energy CB1 state in the conduction band, using the notation of ref 19. Peak 2 corresponds to the VB7 and VB8 to CB1 transitions that were not resolved in spectra of the previous polytypic QWs.19 The experimental absorption transition energies for the WZ QW specimens a and c agree well with the dashed, theoretical curves, with discrepancies mainly in the range of 0−10 meV (except for peak 5 for QW specimen a). The discrepancies between the experimental values for the polytypic QW specimens b and d and the theoretical curves are small (10−35 meV) for the low energy features (e.g., peaks 2 and 3) and large (60−80 meV) for high
energy features (peaks 4 and 5) but consistent with the values of 35−90 meV that we previously reported.19 Such large discrepancies in polytypic QWs may reflect many mixed, higher energy, direct, and indirect transitions involved in the polytypic QWs, resulting in averaged absorption features significantly deviating from those of the WZ QWs.
DISCUSSION In the previous section, we showed a systematic shift of the bandgap to lower energy, spectral line width broadening of the absorption features, and larger Stokes shifts of the PL maxima from the first absorption features for ensemble samples of polytypic semiconductor QWs relative to those measured in samples consisting of near phase-pure WZ CdTe QWs. The reported absorption and PL spectral line widths of ∼50 meV in the WZ CdTe QWs are, to our knowledge, the narrowest reported for ensembles of semiconductor QWs. We discuss in this section the origin and significance of the bandgap shifts in polytypic QWs, and what the narrow spectral line widths in ensembles of WZ QWs signify. Origin of the Bandgap Shifts in Polytypic QWs. The experimentally observed shifts of the absorption features in spectra of polytypic QWs to lower energy than those in spectra of pure WZ CdTe QWs are attributed to the presence of high densities of planar defects, including twinning boundaries, stacking faults, and WZ−ZB phase alternations, as suggested by theory.27,37 Bulk WZ CdTe has a bandgap energy of 1.654 eV at 0 K, forming a type-II band alignment with the smaller bandgap (1.607 eV) ZB structure, with CB and VB offsets of 65 and 18 meV, respectively (Figure 5).44,45 The relative energies of the CBs and VBs in the WZ and ZB domains within the CdTe QWs can change due to dissimilar effective masses and quantum confinement effects.39 Thus, the energetics along the lengths of individual QWs will depend on the diameter of the QW and the lengths of the different crystal domains. 9748
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(electron) alignment, with bulk bandgap energies of 1.607 and 1.589 eV, along the QWs will yield transition energies that are lower than expected for pure WZ (hole)−WZ (electron) transition energy of 1.654 eV, and even lower than would be observed for pure ZB (hole)−ZB (electron) transition energy of 1.607 eV. The actual value of the bandgap in these polytypic QWs will depend on the amount of the domains, the domain lengths, and the quantum-confinement energies within each domain.27,37 We expect that the extent of the bandgap shifts to lower energy may be different for each polytypic QW having varying, nonperiodic WZ−ZB alternation and hence will be different for every ensemble specimen of polytypic QWs. Quantitative correlation of such bandgap shifts with the WZ−ZB alternations in these QWs would require substantial modeling and calculations, including the complete stacking sequence of each wire with atomic precision, which is difficult and beyond the scope of this work. Nevertheless, a theoretical study by Wang showed that a single stacking fault in WZ CdSe QR of d × l (length) = 2.8 nm × 7.5 nm decreased the bandgap energy by 10−50 meV,47 clearly showing the broad variation of bandgap shifts that can result from planar defects. Furthermore, we observed a PL shift of 28 meV to lower energy for the polytypic QW specimen d (compared with the WZ QW specimen c having the same diameter), comparable to the 23 meV shift in the extinction spectrum. The slightly larger shift in PL to lower energy may reflect the lower-energy potential minima induced by the WZ−ZB alternations in polytypic QWs that can be sampled by excitons excursing along the wire axis, as evidenced by the larger Stokes shift of 9.7 ± 0.9 meV for the polytypic QW specimen d (vs 5.4 ± 0.5 meV for the WZ QW specimen c). Extent of the Bandgap Shifts Induced by WZ−ZB Alternations. The shifts of the bandgaps to lower energy due to the WZ−ZB alternations in the polytypic QW specimens b and d are 39 and 23 meV, respectively, whereas the confinement energies in phase-pure WZ QW specimens a and c determined from peak 1 (by comparing to the bulk WZ bandgap of 1.50 eV at room temperature48) are 266 and 222 meV, respectively. The bandgap shifts in the QW specimens b and d are thus 15% and 10%, respectively, of the confinement energies for the WZ QW specimens a and c of like diameter. Such a reduction in the bandgap energy due to polytypism is hence substantial. The reduction in bandgap energy is also expected in QDs and QRs, for which stacking faults are often present. The theorectical calculations for WZ CdSe QRs of d × l = 2.8 nm × 7.5 nm noted above showed that even a single stacking fault caused 2−9% reduction of the confinement energy relative to pure WZ QRs.47 The results above thus indicate that the polytypism-induced bandgap changes depend to a large degree on the extent and randomness of the WZ−ZB alternations and cannot simply be neglected. Despite this, experimental comparisons with theoretical results of either pure WZ or ZB QW structures are often made using polytypic structures without considering the effects of planar defects, and discrepancies are thus expected (see above and Figure 4).19−25,27,29 Role of Crystal-Phase Purity on Line Width. An ensemble spectrum is the sum of single-nanocrystal spectra having properties that depend on the size, shape, and crystalphase purity of the nanocrystals. Thus, sample heterogeneities such as size polydispersity, shape nonuniformity, and crystalphase defects that commonly coexist in colloidal semiconductor nanocrystals are the primary origins of inhomogeneous line
Figure 5. Schematic depiction of the band alignment of the axial heterojunction WZ/ZB CdTe QWs at ∼0 K. Bandgaps or band offsets are not quantitatively scaled. The bandgaps for bulk WZ and ZB, as shown, are 1.654 and 1.607 eV, respectively, with a bandgap offset of 65 meV for the conduction band (CB) and 18 meV for the valence band (VB).44,45 Both type-I and type-II band alignments are possible in the QW (see text for details). The scale bar is provided to indicate the length scale of the typical WZ and ZB segments. Most of the WZ and ZB segments are too short to effectively confine charge carriers in separate spatial regions along the length of the QW, and hence, the electron and hole wave functions are spatially considerablely overlapped, especially at room temperature.27,37 The effective bandgap of the polytypic QW thus represents an average of the energies associated with the numerous WZ and ZB segments.
As demonstrated by Zunger and co-workers, for III−V QWs,39 the situation can become complicated because the band alignment may change from type-II to type-I as the diameter of the QW is descreased. A type-II band alignment is likely expected for thick CdTe nanowires (i.e., d > exciton Bohr radius of ZB CdTe, 7.5 nm46), for which the quantum confinement is weak and any differences in the confinement in the WZ and ZB domains are likely not large enough to overcome the 18 meV WZ−ZB VB offset. The type-II band alignment may transition to type-I band alignment below a critical diameter, which is predicted to be 7.5 nm for InP QWs,39 as the QW falls into a stronger quantum-confinement regime. The diameters of the CdTe QW samples investigated here are close to this critical diameter, and both band alignments may exist within the sample (Figure 5). The WZ and ZB domain lengths are also a consideration in determing the band alignment. Type-II alignment, with holes in the WZ domains and electrons in the ZB domains, may be expected for long domain lengths in the QWs, based on bulk energies. In the polytypic QW specimens b and d, the average lengths of the WZ domains are shorter than the ZB domains (0.5 versus 1.7 nm for b, and 0.4 versus 1.3 nm for d), and the domain lengths are quite short relative to the sizes of the electron and hole wave functions. Consequently, even though both type-II and type-I band alignments could be present in our 6−7 nm-diameter polytypic CdTe QW specimens b and d (Figure 5),39 the sizes of the electron and hole wave functions in the CB and VB are larger than most of the domain lengths, and smoothly varying CB and VB energies that are dictated by the amount and lengths of the crystal domains are sampled by the charge carriers, as recently shown in calculations by Kipp and co-workers.37 As a result, the presence of both type-I ZB(hole)−ZB(electron) alignment and type-II WZ (hole)−ZB 9749
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Table 1. Narrowest PL and Absorption (abs) Spectral Line Widths Reported for Selected Colloidal Semiconductor Quantum Nanostructures nanostructure
crystal phase
single or ensemble
d or thickness distribution (%)
ref
5.4 ± 0.5
this work
9.7 ± 0.9
this work
40−60
51
57−61/47−64
11−33
24
7−19 25−85 31−56
∼5 (d) and 10 (l)
56−70/− 65−80/− 67−96/− 53/− 45−60/− 90−110/−
40−55
42 41 43 42 42 52, 53
0 0 0 0 0
50/45−64
