Defect Engineering in CdSxSe1–x Nanobelts: An Insight into Carrier

Nov 8, 2012 - Department of Physics, National University of Singapore, 2 Science Drive 3, ... Graduate School of Integrative Sciences and Engineering,...
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Defect Engineering in CdSxSe1−x Nanobelts: An Insight into Carrier Relaxation Dynamics via Optical Pump−Terahertz Probe Spectroscopy Hongwei Liu,†,‡, ∥ Junpeng Lu,†, ∥ Hao Fatt Teoh,§ Dechun Li,⊥ Yuan Ping Feng,† Sing Hai Tang,† Chorng Haur Sow,*,† and Xinhai Zhang*,‡ †

Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 3 Research Link, 117602 Singapore § Graduate School of Integrative Sciences and Engineering, National University of Singapore, 28 Medical Drive, 117456 Singapore ⊥ School of Information Science and Engineering, Shandong University, Jinan, 250100 China ‡

ABSTRACT: Defects in nanomaterials often induce dramatic changes in the photoelectrical properties of semiconducting II−VI compound nanomaterials. The relationship between defects and carrier dynamics is pivotal in material engineering for potential applications. A thorough understanding of the dynamics of defect-related free carrier depletion is particularly important for the fabrication and optimization of nanooptoelectronic devices. In this work, optical pump−terahertz probe spectroscopy was employed to investigate the carrier dynamics in CdS and Se-alloyed CdS nanobelts. The dynamics are dominated by the surface defect trapping in the case of CdS and structural-defect-related recombination for the Sealloyed CdS. The conclusion is also supported by temperature-dependent photoluminescence spectroscopic studies. Our results indicate that congeneric element replacement is an effective approach for defect-distribution restructuring, which modifies the physical properties of nanomaterials through defect engineering.

1. INTRODUCTION II−VI compound semiconductor nanostructures show attractive optical and electrical properties.1,2 They provide versatile platforms not only for the fundamental physical research3,4 but also for the nanoscaled device applications, such as field-effect transistors,5,6 solar cells,7,8 photodetectors,9,10 lasers,11,12 and waveguides.13 Defects in crystals tend to induce dramatic changes in their physical properties. Recent reports indicate that defect distribution is evolving as a favored strategy in material engineering for electronic,14 energy,15,16 and structural17 applications. For nanoscale research, both surface states and stoichiometric defects formed during synthesis are reported as the major types of defects in quantum dots, nanowires, or nanobelts.18 Recently, element doping during nanomaterial growth processes has been used to achieve the desirable defects component and control the defects distribution.19,20 Cadmium chalcogenide, especially CdS nanomaterial, is a typical II−VI compound with attractive properties and offers wide applications in nanoscale devices.11−13 The report of stoichiometric defects in CdS nanobelts further promoted interest in CdS-based nanomaterials.21 Most recently, Sealloyed CdS ternary alloys have attracted great attention due to their tunable optical and electrical properties. 2 2,2 3 CdSxSe1−xnanobelts have been fabricated as nanoscale waveguides,24 lasers,25,26 and field-effect transistors.23 However, there are only a few reports on the study of Se-replacementrelated defects for CdSxSe1−x alloy because the fundamental physics becomes more complicated. Nevertheless, a deep © 2012 American Chemical Society

insight into the complex fundamental properties of these bound complexes could provide a useful guidance for practical applications. In this work, we present an investigation of the competing processes and the progress of carrier dynamics in CdS-based nanomaterials after photoexcitation. A thorough understanding of the mechanism and the defect-related influence in such nanobelts will promote further design, fabrication, and optimization of nanobelt-based optoelectronic devices. Optical pump−terahertz (THz) probe (OPTP) spectroscopy is an important tool to investigate the quasiparticle dynamics in nanostructures on time scales that range from subpicosecond to nanosecond.27 Recent studies of nanomaterials, such as silicon nanocrystals,28 ZnO nanostructures,29 and GaAs nanowires,30 have demonstrated that OPTP spectroscopy possesses a number of advantages compared with other ultrafast techniques. For example, the measurements of time-resolved photoluminescence spectroscopy are often hindered by a large defects density which would reduce the efficiency of the photoluminescence.31 In addition, OPTP spectroscopy is effective in elucidating the defect-related trapping processes due to the high sensitivity of THz probe to the carrier density and mobility.32,33 Received: August 8, 2012 Revised: November 6, 2012 Published: November 8, 2012 26036

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Figure 1. (a) SEM images, (b) EDS spectra, and (c) XRD patterns of CdS and Se-alloyed CdS nanobelts. The top side of (d) is the cross-sectional SEM image of a representative sample. The bottom side of (d) is the HRTEM image of CdS nanobelt.

In this work, the carrier dynamics in CdS and Se-alloyed CdS nanobelts were studied using OPTP spectroscopy. The OPTP results, together with temperature-dependent photoluminescence, reveal a clear picture for the complicated relaxation dynamics of photocarriers. The processes affecting such dynamics include surface-defect-related trapping and structural-defect-related recombination. Specifically, surface defects dominate the carrier relaxation path in CdS while the dominant decay path is structural-defect-related recombination after Se replacement. Therefore, element replacement is an effective approach for defect-distribution restructuring, which would improve the luminous efficiency of nanoscaled light-emitting devices and facilitate high optical conductivity of optoelectronic devices through the reduction of surface defect trapping.

borate (BBO) crystal to generate 400 nm optical pulses for sample excitation. The THz probe beam was generated by using air−plasma technique34 and detected by a THz airbiased-coherent-detection (THz-ABCD) method.35 The samples were excited at 45° incidence with different excitation fluences. The THz probe waves passed through the samples at normal incidence. The spot size of the pump beam was 0.4 cm2, which was about two times larger than the spot size of the THz probe beam. In the OPTP experiment, the transient behavior of the photoexcited carriers was monitored by measuring the differential transmission ΔT/T0 of THz probe waveforms at the peak amplitude as a function of delay time between the THz probe and optical pump pulse. Here ΔT is the time-dependent transmission change of THz wave due to optical excitation, and T0 is the transmitted intensity of THz pulses without optical excitation. Optical pump fluences of 40, 20, 10, and 5 μJ/cm2 were used to excite the samples. All the experiments were carried out under a dry nitrogen purge at room temperature.

2. EXPERIMENTAL SECTION CdS and Se-alloyed CdS nanobelts were grown on C-plane sapphire substrates by a conventional vapor−liquid−solid (VLS) approach. Briefly, CdS powder and the mixture of CdS and CdSe powders were used as the precursor source for CdS and Se-alloyed CdS nanobelts growth, respectively. The samples were grown at 850 °C for 30 min. Purified helium was used as the carrier gas and protection gas. The details of synthesis were described elsewhere.23 The morphology, crystalline structure, and composition of the nanobelts were characterized using a field emission scanning microscope (FESEM, JEOL JSM-6700F), X-ray diffractometer (X’PERT MPD, Cu−Kα (1.5406 Å) radiation), and an energy-dispersive spectrometer (EDS). In optical measurements, ultrafast optical pump was generated by a Ti:sapphire regenerative amplifier laser system, which provides ∼35 fs optical pulses at the center wavelength of 800 nm with a repetition rate of 1 kHz. The fundamental laser output was frequency doubled by a 1 mm thick β-barium

3. RESULTS AND DISCUSSION The SEM images of CdS and Se-alloyed CdS nanobelts are shown in Figure 1a. Both of them exhibit similar beltlike morphologies with a uniform thickness of ∼30 nm, 100−200 nm in width, and an average length of about several tens of micrometers. The corresponding EDS spectra (Figure 1b) indicate the pure CdS phase with a “S/Cd” ratio of 1:1 and Sealloyed CdS sample with the S/Cd ratio equal to 0.65; thus, we defined the sample as CdS0.65Se0.35. The XRD patterns shown in Figure 1c suggest that both CdS and CdS0.65Se0.35 nanobelts have wurtzite structure with a good crystalline quality. As seen from the side-view SEM image (shown in the upper half of Figure 1d), the thickness of the nanobelts films is larger than 10 μm. The penetration depth of light at 400 nm into CdS and CdS0.65Se0.35 is calculated to be about 45 and 33 nm, 26037

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respectively,36 which indicates that 10 μm thickness is sufficient to absorb the entire incident pump light, and all the probed information reveal the properties of the nanobelts. The typical high-resolution TEM (HRTEM) image of CdS nanobelts is shown in the lower half of Figure 1d, indicating high crystal quality. Parts a and b of Figure 2 show typical time-domain THz pulses through CdS and CdS0.65Se0.35 nanobelts before (black)

Figure 3. (a) Time-dependent differential THz transmission ΔT/T0 of CdS (black) and CdS0.65Se0.35 (blue) nanobelts pumped with 400 nm optical pulses excitation. The excitation fluence is 40 μJ/cm2. The red solid lines are the results of best biexponential fitting as described by eq 1. (b) Photoexcited conductivity σ(t) of CdS and CdS0.65Se0.35 nanobelts are calculated by eq 2.

Table 1. Summary of the Biexponential Fitting Results of CdS and CdS0.65Se0.35 Nanobelts

Figure 2. Time-dependent THz pulses transmitted through (a) CdS and (b) CdS0.65Se0.35 nanobelts samples. The black and blue curves represent the transmitted THz pulses before and after photoexcitation (∼40 μJ/cm2), respectively. Amplitudes of THz waves are normalized to the unexcited pulse amplitude maximum.

and after (blue) optical excitation. Here, the THz pulses transmitted excited CdS and CdS0.65Se0.35 nanobelts were recorded at 3.5 and 3.8 ps after pump excitation, respectively. At these time lapses, the transmitted THz pulses have the biggest drop in intensity. Figure 3a shows the time-dependent differential transmission signals, ΔT/T0, through the CdS nanobelts (black) and CdS0.65Se0.35 nanobelts (blue), where ΔT = T − T0, T and T0 are the transmitted intensity of THz probe through the samples with and without excitation, respectively. Both samples were excited with the excitation fluence of 40 μJ/cm2. The transmitted THz pulses through both samples instantaneously drop upon the arrival of the pump pulses and achieve minimum at 3.5−3.8 ps after optical excitation. The ΔT/T0 of CdS nanobelts quickly recovers to 95% within 55 ps and persists at this value over 500 ps, while that of CdS0.65Se0.35 nanobelts gradually recovers from 62% to 82% within 500 ps. The transient differential transmission, as shown in Figure 3a, can be well fitted with a biexponential function37 ΔT /T0 = A1e−t / τ1 + A 2 e−t / τ2

sample

A1

A1 (%)

τ1 (ps)

A2

A2 (%)

τ2 (ps)

CdS nanobelts CdS0.65Se0.35 nanobelts

−0.27 −0.08

93.1 21.1

21.4 86

−0.02 −0.30

6.9 78.9

1000 895

small penetration depth (45 nm for CdS and 33 nm for CdS0.65Se0.35) for light of 400 nm, the optically excited layer of the samples can be modeled as a highly conductive film on a semi-infinite insulating substrate. From the differential transmission signals, the time-dependent conductivity of such a film can be expressed as38 σ (t ) =

⎤ 1 + n⎡ 1 − 1⎥ ⎢ Z0d ⎣ 1 + ΔT /T0 ⎦

(2)

where Z0 = 377 Ω is the impedance of free space, n = 3.1 is the measured refractive index of sapphire at THz frequencies,39 and d is the optical penetration depth of the pump beam inside the film. Employing eq 2, the calculated σ(t) of CdS and CdS0.65Se0.35 nanobelts as a function of time delay is shown in Figure 3b. The time-dependent conductivity sharply increased due to the increase in carriers concentration caused by photoexcitation and decreased with photocarrier depletion. Careful analysis of the fitting curves reveals more details of the recombination mechanism. Evidently, biexponential decay behaviors of the samples represent two characteristic recombination channels involved in the recombination process. Combining previous studies38,40 and analysis below, the fast decay is mainly attributed to rapid photocarrier capture by the surface traps, and the slow decay is mainly ascribed to nonradiative structural-defect-related recombination. The characteristic time τ1 of fast decay for CdS nanobelts is measured as 21.4 ps; the value is consistent with that of 28 ps for CdS

(1)

where Ai are the weighting factors and τi are relaxation time constants. The best fit parameters are listed in Table 1. The fast relaxation time (τ1) of CdS nanobelts is 21.4 ± 0.8 ps compared with that for CdS0.65Se0.35 nanobelts, which is 86 ± 1.3 ps. The slow relaxation time (τ2) of the CdS0.65Se0.35 nanobelts is 895 ± 3.4 ps, while the τ2 period of CdS nanobelts is much longer, even larger than 1 ns. Because of the 26038

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nanoparticles investigated by the optical-pump IR-probe technique.41 However, the τ1 of CdS0.65Se0.35 nanobelts is measured to be 86 ps, which is much longer than that of CdS. Both the τ1 values in CdS and CdS0.65Se0.35 are measured longer than the previous reports of CdSxSe1−x nanocrystals investigated with time-resolved photoluminescence spectroscopy.42,43 In their studies, the surface trapping decay times are located in the ranges from 0.5 to 1.4 ps and 2 to 5 ps, respectively. The much faster surface trapping is facilitated by the smaller size of the nanocrystals. The diameters of the nanocrystals in both reports are around several nanometers, which is much smaller than the nanobelts studied in this work. Therefore, the nanocrystals possess a larger surface to volume ratio and present more remarkable surface effect, which enable the rapid surface trapping decay. To elucidate the mechanism of the carriers depletion in this fast process, time-dependent differential transmission is measured for the excitation fluence range of 5−40 μJ/cm2 (shown in Figure 4). For the fast decay

Figure 5. (a) Relaxation time (τ1) as a function of photocarrier density. (b) ΔT/T0 of slow recombination process (delay time t = 300 ps) as a function of excitation fluence. The data of CdS0.65Se0.35 can be fitted by an exponential function (green line).

excitation fluence; thus, the fast relaxation process is attributed to surface defect trapping rather than Auger recombination. The increase of fast decay time with pump fluence can be explained by surface trap saturation. At low pump fluence, photocarriers are trapped by the surface defects, while at higher pump fluence the available trapping sites become fully occupied, leading to a longer decay time than lower pump fluence. Similar phenomena were also observed in GaAs nanowires46 and microcrystalline silicon.32 The best fitting parameters suggest that recovery time τ1CdS is indeed shorter than τ1CdSSe. As identified previously, the τ1 process is dominated by surface defect trapping. Therefore, the capture rate of the surface defect states in CdS nanobelts is bigger than that in CdS0.65Se0.35 nanobelts. To verify that CdS has a higher capture rate of surface defects, the temperaturedependent photoluminescence (PL) spectroscopy was carried out for both samples, and the related results are shown in Figure 6. The measurement was carried out at 5 K and fitted by multiple Gaussian functions to identify the peak positions. For CdS nanobelts, the emission peak near 487 nm originates from the near-band-edge excitons while the peak at 498 nm is attributed to surface-defect-related emission. For CdS0.65Se0.35 nanobelts, the corresponding peaks were measured at 586 and 593 nm, respectively. These positions are consistent with our previous report.47 Comparing both PL spectra, CdS nanobelts have a much stronger surface defect peak than CdS0.65Se0.35 nanobelts. These results suggest that carriers can be trapped by surface defects more easily in CdS nanobelts than that in CdS0.65Se0.35 nanobelts. The reason for easier surface trapping in CdS nanobelts can also be considered from the growth aspect, as explained in our previous report.47 In short, during

Figure 4. Excitation fluence dependence of time-dependent differential THz transmission with 400 nm excitation for (a) CdS nanobelts and (b) CdS0.65Se0.35 nanobelts excited at the excitation fluencies of 40 (black), 20 (red), 10 (green), and 5 μJ/cm2 (blue). The solid lines are the results of best exponential fittings.

process, both CdS and CdS0.65Se0.35 nanobelts show observable excitation fluence dependence. Especially, for CdS0.65Se0.35 sample the fast relaxation process disappeared at low excitation fluence, and the solid lines were fittings by monoexponential curves. Since the observed fast relaxation process shows strong excitation-fluence dependence, two possible origins, Auger recombination and surface defect trapping, should be considered.38,44 Figure 5a shows the fast decay time τ1CdS (normalized to the value obtained at 10 μJ/cm2, the lowest excitation fluence at which the fast decay appears) and τ1CdSSe (normalized to the value obtained at 20 μJ/cm2) as a function of photocarrier density, Ne (Ne ∝ [(1 + ΔT/T0)−1 − 1]),44 while Figure 5b illustrates the ΔT/T0 (normalized to the results obtained at 10 μJ/cm2 for CdS and 5 μJ/cm2 for CdS0.65Se0.35, at delay time t = 300 ps) of slow relaxation process as a function of excitation fluence. Auger recombination corresponds to a lifetime following a quadratic dependence τ−1 Auger ∼ N2e ;45 thus, Auger recombination lifetime should decrease with excitation fluences. Contrarily, as shown in Figure 5a, both of the observed τ1CdS and τ1CdSSe increase with increasing 26039

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e−I/I0)) with the excitation fluence at the slow relaxation process, as shown in Figure 5b. On the other hand, ΔT/T0 (delay time t = 300 ps) of CdS nanobelts (red dots in Figure 5b) does not show any significant dependence on the excitation fluence. This observation can be explained by its low concentration of structural defects, in which case the high photoexcited carrier density exceeds the density of available sturctural trap states. In CdS nanobelts, when structural defects are saturated, carriers are forced to move to the surface, and these carriers can be easily trapped by surface defects. The trend of τ1 shows that the density of surface trap states is higher than the photocarrier density, as we demonstrate above, and more carriers can be trapped by surface defects with increasing excitation fluences, accompanied with fewer carriers localized in the structural defects. Since structural defects are limited in CdS nanobelts, the amount of localized carriers by structural defects is independent of excitation fluences. However, the structuraldefects-related traps induced by composition disorder in CdS0.65Se0.35 nanobelts can prevent free carriers from moving to the surface through localization or scattering of the carriers. In addition, the formation of type-I core−shell-like structure near the surface in Se-replacement samples also prevents carrier migration to the surface. Thus, more carriers localized in the interior of the CdS0.65Se0.35 nanobelts with excitation fluences so that subsequently ΔT(t) increased exponentially with excitation fluence during the slow recombination process. Therefore, the dependence of ΔT/T0 with excitation fluence in the slow recombination process of CdS0.65Se0.35 nanobelts indicates that the relative density of bulk defect in CdS0.65Se0.35 nanobelts is expected to be much higher than that in CdS nanobelts. The origin of this kind of defects is attributed to the compositional disorder in ternary compound, which could lead to statistically distributed fluctuations of an average potential.48 During the synthesis of Se-alloyed CdS nanobelts, stoichiometric defects will be unavoidably formed because vapor pressures for II−VI compound elements are quite different at certain temperatures.21 The ionic binding configuration of CdSxSe1−x is considered from the semiconductor band model as follows: Cd(3d 10 4s 2 ) + S(3s 2 3p 4 )/Se(4s 2 4p 4 ) → Cd2+(3d104s0) + S2−(3s23p6)/Se2−(4s24p6). Free electrons usually occupy the lowest empty s-level of cations in the conduction band, and free holes frequently originated from the highest occupied p-level in the valence band of anions.49−51 As known, the energy level of the conduction band in CdSe is lower than that in CdS.52,53 Therefore, the Se replacement and its induced lattice distortion can localize considerable amount of free carriers. This kind of defect is formed due to random composition disorder, and they are mainly located in the interior of the nanobelts, so these defects are denoted as “structural defects” or “bulk defects”, distinguished from surface defects. Evidently, the replacement causes structural defect that gives rise to the slow relaxation process for CdS0.65Se0.35 nanobelts. However, the dopant-induced structural defects are absent in CdS nanobelts. The origin of the slow recombination process in CdS nanobelts may be attributed to the defect resulting from other kinds of bulk defects, such as intrinsic defects of Cd vacancies or S vacancies. These defects can also trap free carriers and act as the radiative or nonradiative recombination centers. However, the concentration of such defects is very low since our CdS nanobelts sample shows a good crystalline quality by XRD pattern (Figure 1c) and HRTEM image (Figure 1d).These results further verified the inference that structural defect is the main contributing factor

Figure 6. PL spectra of CdS and CdS0.65Se0.35 nanobelts at 5 K excited with a 405 nm diode laser. The red and blue curves are Gaussian line shape decompositions with surface emission peaks (labeled by red dots) and near-band-edge emission peaks (labeled by blue dots).

the synthesis process of CdS0.65Se0.35, CdS precursor has a lower growth temperature than CdSe; therefore, the composition in the surface region of the CdS0.65Se0.35 nanobelts might be different from that of the interior. For example, in the cooling stage, when temperature is lower than CdSe growth point, CdS vapor could be maintained at this temperature, consequently leading to slightly higher S concentration near the CdS0.65Se0.35 nanobelt surface layer than that in the interior. The following diffusion process may not be able to completely make the whole nanobelt uniform; thus, a very thin layer near the surface may be formed with slightly higher S content. The formation of type-I core−shell-like structure near the surface may prevent carrier migration to surface, thus reducing the carrier capture possibility caused by surface defects. From the above, the shorter relaxation time, τ1CdS, indicates an easier surface trapping in CdS nanobelts than that in CdS0.65Se0.35 nanobelts. On the other hand, revealed in parts a and b of Figure 4, the slow process does not show observable excitation intensity dependence, suggesting that the carrier recombination is mainly due to structural-defect-related nonradiative recombination and/or band-to-band recombination.40 In this work, the origin of structural defects is attributed to the compositional disorder in ternary compound. The characteristic lifetime of slow process is 1000 ps for CdS nanobelts, while it is 894 ps for CdS0.65Se0.35 nanobelts. Shorter characteristic time for Sereplacement sample suggests that the carrier recombination is dominated by defect-related nonradiative recombination, since alloyed samples are expected to have higher defect concentrations. However, our measurements were conducted in a limited time window; consequently, the band-to-band recombination could not be clearly distinguished from the defect-related one in our data. It should be noted that the curves of CdS nanobelts sample coincide in the delay time range from 90 to 500 ps (in Figure 4a), which means that ΔT/ T0 reaches saturation readily even at low excitation during the slow process, while ΔT/T 0 of CdS 0.65 Se0.35 nanobelts demonstrates an exponential relationship (ΔT/T0 ∝ (1 − 26040

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to the slow relaxation process and CdS0.65Se0.35 possesses higher structure defect density than pure CdS nanobelts. Above all, the origins of two recombination processes are ascribed to surface defect trapping and structural-defect related recombination, respectively. However, the contributions of each process to the entire relaxation can be further identified by the weighting factor Ai shown in eq 2. The weighting factor percentages, A1% = A1/(A1 + A2) and A2% = A2/(A1 + A2), imply the contributions of each component (fast component and slow component) to the maximum differential transmission (ΔT/T0)max, respectively. The value of A% could be considered as the proportion of depleted free carriers in a complete recombination process. For CdS nanobelts, A1CdS% is 93.1% and A2CdS% is 6.9%, suggesting that the fast relaxation process is the dominant channel in the recombination process and surface defects make more contribution than structural defects for carriers depletion inside CdS nanobelts. On the other hand, for CdS0.65Se0.35 nanobelts, A1CdSSe% is 21.1% and A2CdSSe% is 78.9%, which demonstrated that the slow relaxation process is the dominant part and the Se-replacement-induced structural defects contribute more for photocarriers trapping in the complete recombination process. The results above demonstrate that the replacement effect could cause a significant impact on the defect type, which would influence the approaches of photocarrier recombination and then modify the photoelectrical properties of the semiconductor materials.

4. CONCLUSION We have investigated the carrier relaxation dynamics in CdS and Se-alloyed CdS nanobelts using optical pump−THz probe spectroscopy. Biexponetial relaxation fit to the time-dependent differential transmission signals shows that the carrier dynamics of CdS and CdS0.65Se0.35 nanobelts are due to the fast photocarrier captures by the surface defects and structuraldefect-related recombination. The origins of bulk defects in CdS and CdS0.65Se0.35 nanobelts are intrinsic defects (such as Cd vacancies and S vacancies) and Se-replacement-induced structural defects, respectively. The excitation-fluence-independent relaxation dynamics rules out nonlinear recombination process such as Auger recombination. Our results demonstrate that replacement effect can result in a significant modification for the optoelectrical property of semiconductors. These results are helpful for improving the luminous efficiency of nanoscaled light-emission devices and enhancing the photoconductivity in nanobelt-based optoelectronic devices through the reduction of the decay of free carriers concentration in surface defect trapping.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (C.H.S.), [email protected] (X.Z.). Author Contributions ∥

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.



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