J nanopart res

Defect induced modifications in the optical, dielectric, and transport properties of hydrothermally prepared ZnS nanoparticles and nanorods Anoop Chandran & K. C. George

Journal of Nanoparticle Research An Interdisciplinary Forum for Nanoscale Science and Technology ISSN 1388-0764 Volume 16 Number 3 J Nanopart Res (2014) 16:1-17 DOI 10.1007/s11051-013-2238-5

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Author's personal copy J Nanopart Res (2014) 16:2238 DOI 10.1007/s11051-013-2238-5

RESEARCH PAPER

Defect induced modifications in the optical, dielectric, and transport properties of hydrothermally prepared ZnS nanoparticles and nanorods Anoop Chandran • K. C. George

Received: 28 July 2013 / Accepted: 30 December 2013 Ó Springer Science+Business Media Dordrecht 2014

Abstract Zinc sulfide nanoparticles (particles size range 10–20 nm) and nanorods (particles size range 20–35 nm) were prepared through a hydrothermal method. The influence of surface defects and lattice strain on the optical, dielectric, and electrical transport properties was investigated. The spectral shifts and modification in bandgap are explained based on effective mass approximation model. Photoluminescence and ESR studies clearly showed the presence of large density of surface defects in the samples. The Raman spectra were thoroughly studied using the Gaussian confinement model. Dielectric studies using impedance and electric modulus spectroscopy showed enhanced grain boundary conductivity. Both nanoparticles and nanorods were found to exhibit Cole–Cole type dielectric relaxation. The enhanced ac electrical conductivities observed in both the nanostructures were successfully explained using the correlated barrier hopping model. Parameters like hopping time, barrier width, and defect densities were calculated. Keywords Surface defects  Quantum confinement  Cole–Cole relaxation  Grain boundary effects  Polaron conduction

A. Chandran  K. C. George (&) Department of Physics, SB College, Changanassery 686101, Kerala, India e-mail: [email protected]

Introduction The optical and electrical properties of semiconductor nanoparticles are reported to be significantly different from those of their single crystal and bulk counterparts (George et al. 2006; Xu et al. 2006). The major reasons for such a change in properties are the size-induced quantum confinement of charge carriers and surface effects in nanomaterials. Nanomaterials have high surface to volume ratio which means that the percentage of surface atoms is higher in them compared to their bulk counterparts (Cassina et al. 2009; Wang et al. 2010). The surface marks a sudden termination to the crystal lattice and therefore, is rich in defects like vacancies, interstitials, and dangling bonds. Until recently, tuning of physical properties for advanced applications was mainly done through size modification. Surface defects were considered to be a burden, and they were removed completely to make it easy to predict the properties. However, if the size of a semiconductor nanoparticle is close to its excitonBohr radius, the surface defect density will be very high, and the properties are mainly decided by surface structure. Some semiconductors are predicted to become amorphous in this size regime, and this sets a limit to the tuning of properties by size modification (Junkermeier and Lewis 2009). Hence, selective passivation of surface defects becomes extremely difficult in very small nanomaterials. Recently, the surface defect mediated tuning of properties is gaining much attention as an alternative approach (Bonato

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et al. 2009; Iza et al. 2012). However, the difficulty for this approach comes from the fact that there is no clear picture as to how the nanometric defects influence the physical properties. Hence, it is imperative to get a clear picture of the mechanisms by which surface defects modify the physical properties of nanoscale structures as it would help in tuning the properties more efficiently. Zinc sulfide is an important II–VI semiconductor which is of special interest due to its wide bandgap (Goswami and Sen 2007; Vij and Singh 1998). Nanowires, nanorods, and quantum dots of ZnS exhibit interesting electrical and optical properties, thus, providing numerous opportunities for important applications like UV-nanolasers, UV-detection, and light emitting diodes (Hudlikar et al. 2012; Yang et al. 2010b; Coe et al. 2002). ZnS nanorods show strong field emission and are widely employed in electroluminescence devices (Fang et al. 2011). ZnS nanostructures are reported to have various types of defects like Zn interstitials, S vacancies, and Zn vacancies (Fang et al. 2011). Most of these defects are in the surface layers. Defects introduce energy states within the forbidden gap which alters the optical and transport properties of the materials. Since ZnS is an important optoelectronic material, a detailed investigation of the dielectric and transport properties of ZnS nanostructures is of immense scope. Furthermore, the high density of surface defects can lead to enhancement in dielectric constant and electrical conduction. Recently, colossal dielectric constant due to interfacial polarization is reported in CdS nanoparticles (Ahmad et al. 2013). This is an important finding which predicts the possible application of II–VI semiconductors in capacitive storage devices. Since the topic is controversial more studies on the polarization mechanisms in semiconductor nanostructures are required before arriving at a conclusion. Furthermore, our previous studies based on the correlated barrier hopping (CBH) model gave evidence for polaronic transport in CdS nanostructures with highly distorted surface layers (Chandran et al. 2011a). It would be interesting to find if the same results are obtained in the case of ZnS nanostructures with similar structure. The existence of polaron at or above room temperature in II–VI semiconductors is a topic of great interest. Therefore, the present paper is intended to get an understanding of the defect induced modification of optical, dielectric, and transport properties of ZnS

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nanorods and nanoparticles. A comparison of the properties of nanorods and nanoparticles of ZnS could give us an insight of role of dimensionality and defect density in modifying the physical properties. The validity of CBH model and the nature of polarization mechanism in the samples are also investigated.

Experimental section Materials and preparation of nanostructures ZnS nanoparticles were synthesized using Zinc acetate [Zn(CH3COO)2 2H2O] and Thiourea [SC(NH2)2]. Both the chemicals were of analytical grades. In our experiment, the concentrations of zinc acetate and thiourea were 0.1 and 0.3 M, respectively. Both solutions were mixed vigorously in the presence of 10 ml ethylenediamine using a magnetic stirrer for 30 min. The mixture was then transferred to a stainless steel autoclave and kept in a high accuracy furnace at 180 °C for 10 h. For preparing nanorods, the same solution was heated at 200 °C for 24 h. The resulting products were washed several times using water and ethanol and dried at 100 °C for 4 h. Characterization of nanostructures The XRD patterns of the samples were taken using Bruker AXS D8 Advance X-ray diffractometer. The UV–Vis absorption and Photoluminescence spectra were recorded using PG-instruments T90? UV/Vis spectrometer and Perkin Elmer LS 45 luminescence spectrophotometer, respectively. The SEM observations and EDS spectroscopy were performed using JEOL Model JSM-6390LV scanning electron microscope. Philips CM-200 transmission electron microscope was employed to obtain the TEM micrographs. Electron spin resonance spectra were recorded on Varian E-112 ESR spectrometer. For measuring the capacitance and ac conductivity, the as-prepared samples were converted to pellets of 10-mm diameter and 1.1-mm thickness using a hydraulic press. The pellets were then placed in a tube furnace for taking measurements at various temperatures. The measurements were carried out using HIOKI 3532-50 LCR meter. Silver electrodes were used to connect the instrument to the sample.

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Results and discussion

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2010a). The modified Scherrer’s equation for the plot is given by

Structural and optical studies btotal ¼ 4e tanðhÞ þ Figure 1a shows the XRD patterns of the as-prepared ZnS nanoparticles and nanorods. From the patterns, apparently, the obtained samples are wurtzite (10H) ZnS. The presence of defects at the surface of nanomaterials produces a short range stress field which triggers atomic displacements in crystallites. This acts as a source of lattice strain in nanomaterials (Qin and Szpunar 2005). Recent studies have revealed that nanomaterials experience larger lattice strain compared to their bulk equivalents (Smith et al. 2009; Zhu et al. 2010; Zhao et al. 1997). This is attributed to the excess volume in grain boundaries due to vacancies and vacancy clusters. Since the lattice strain in unpassivated nanoparticles causes error in the calculation of crystallite size using Scherrer’s equation, we have used the Williamson–Hall (W–H) plot to determine the strain and average crystallite size (Yang et al.

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0:9k ; L cosðhÞ

ð1Þ

where btotal is the total broadening, e is the lattice strain, and L is the average crystallite size. Using the least square fitting process, strain and average crystallite size of ZnS nanoparticles are obtained as -0.0031 and 9.5 nm, respectively. For nanorods, the values of the aforementioned parameters are -0.0017 and 13.2 nm, respectively. It is to be noted that the slopes of W–H plots are negative which implies the existence of compressive strain in the samples (Jacob and Khadar 2010; Derlet et al. 2005). Compressive strain is common in nanoparticles with highly defective surface layers. The calculated values of lattice constants ‘a’ and ‘c’ ˚ , respecfor nanoparticles are 3.822 and 6.241 A tively, whereas those for nanorods are 3.841 and ˚ , respectively. 6.253 A

Fig. 1 a Xrd patterns, b, c EDS patterns, d Williamson-Hall plots and e ESR spectra of ZnS nanoparticles and nanorods

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The EDS patterns of the samples presented in Fig. 1b, c show strong peaks corresponding to zinc and sulfur. Impurity peaks are not observed which indicates the high purity of samples. Peaks corresponding to oxygen are also absent which suggests that oxidation of the samples has not occurred. The atomic percentages of zinc and sulfur in ZnS nanoparticles are found to be 54 and 46 %, respectively, whereas those in ZnS nanorods are 52 and 48 %, respectively. These values suggest that both samples possess high density of sulfur vacancies. These vacancies exist mainly on the surface of the nanostructures. To shed further light into the presence of surface defects, electron spin resonance (ESR) technique is used. The ESR spectra shown in Fig. 1e provide evidence for the existence of paramagnetic centers in both the samples. The microwave frequency used is 9.1 GHz, and the resonance peaks are found at 3,267 and 3,258 G for nanoparticles

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and nanorods, respectively. The effective g values calculated using the relation geff = hm/(lBBcenter) are 1.985 and 1.991 for nanoparticles and nanorods, respectively. These values are slightly different from the free electron g value which is 2.0023. Kasai and Otomo (1962) have assigned a peak with g value 1.9 to sulfur vacancies. Since the EDS studies suggest that the samples have high density of sulfur vacancies, we assign the aforementioned ESR peaks to sulfur traps. The TEM images of ZnS nanoparticles and nanorods shown in Fig. 2 confirm their spherical and rod like shapes, respectively. From these images, it is found that the diameters of ZnS nanoparticles are in the range 10–20 nm, and those of nanorods lie in the range 20–35 nm. The ZnS nanorods have a length between 80 and 120 nm. The SAED patterns are indexed as shown in the figure confirming the hexagonal structure of the samples.

Fig. 2 TEM images and SAED patterns of a, c ZnS nanoparticles and b, d nanorods

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Figure 3a shows the UV–Vis absorption spectra of ZnS nanoparticles and nanorods. Sharp absorption peaks are observed at 4.6 and 4.2 eV for nanoparticles and nanorods, respectively. The bandgap energies calculated using the Tauc’s plot shown in Fig. 3c are 4.06 and 3.95 eV for nanoparticles and nanorods, respectively. These values are higher than the bandgap energy of bulk ZnS. This shift in bandgap is due to quantum confinement effects. The increment in bandgap energy is 0.26 and 0.15 eV for nanoparticles and nanorods, respectively, which hints at the existence of weak quantum confinement. In the weak quantum confinement regime, the particle size will be higher than the exciton-Bohr radius, and the energy is dominated by the coulomb term. The exciton-Bohr radius of ZnS is 3 nm which is much lower than the obtained particle sizes of the samples confirming our assumptions. The shift in bandgap is influenced by nanometric surface defects and lattice strain. Although the nanoparticles have high surface to volume ratio

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(hence large defect density) compared to nanorods, the bandgap shift is higher in the former, clearly indicating its stronger quantum confinement effects than the latter. It is to be noted that the difference between bandgap and absorption peak energy is 0.64 eV for nanoparticles and 0.25 eV for nanorods. The occurrence of such a huge difference can be explained with the help of energy level diagram shown in Fig. 3b. In Zinc blend materials, the C15 level of the valence band is split into C8 and C7 due to spin orbit interaction. On the other hand, in hexagonal wurtzite ZnS, the combined effect of spin orbit (Dso) and crystal field perturbation (Dcr) splits the valance band into C9, C7, and C70 bands. The spin orbit splitting energies of cubic and wurtzite ZnS are 0.065 and 0.082 eV, respectively. According to the selection rules for optical transitions in wurtzite ZnS, C9–C7 transitions are allowed only for light parallel to the crystallographic axis, while C7–C7 is allowed for light

Fig. 3 a The UV–Vis absorption spectra and b the energy level diagram of zinc blend and wurtzite ZnS c Shows the Tauc’s plots of ZnS nanoparticles and nanorods (inset). and d theoretically calculated variation of bangap energy with particle radius

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perpendicular to the axis (Schroer et al. 1993; Voon and Willatzen 2009). Even if the transition occurs from C70 to conduction band, the total energy of the absorption peak should be Eg ? Eso, which is 4.14 eV for nanoparticles and 4.022 eV for nanorods. Since the absorption peaks are at much higher energy, we can infer that the extra energy of the absorption peaks indicates transition to higher excited states in the conduction band. The influence of quantum confinement on the bandgap of semiconductors can be understood using the effective mass approximation (EMA) technique (Einevoll 1991; Lippens and Lannoo 1989). The simplest three dimensional confinement model based on EMA predicts the bandgap shift, as   2 1 h 1 p2 e2  E¼  0:248ERy þ  1:786 ; 2 me mh R2 eR

ð2Þ

where R is the radius of the particle, me the electron effective mass, mh the hole effective mass, e the dielectric constant, and ERy* the Rydberg energy. The first term in Eq. 2 denotes the confinement energy, the second term is the Coulomb energy and the third term is a result of correlation effects. In the case of nanorods, if the carriers are confined in the y and z directions by an infinite quantum well of width WY and WZ, carriers are free to move in the x direction, i.e., along the length (WL) of the nanorods. Then the confinement energy term can be written as   "    hp 1 1 EconfðRodÞ ¼ þ 4 mL WL2 mT WY2 ð3Þ    # 1 1 þ þ ; mh WZ2 mh WY2 where mL is the longitudinal effective mass and mT the transverse effective mass. The variation of theoretically computed values of bangap energies of ZnS nanoparticles and nanorods as a function of radius is shown in Fig. 3d. The values of me and mh used in the calculation are 0.28 and 0.49, respectively (Vij and Singh 1998). However, instead of the bulk dielectric constant value, we used the measured values of dielectric constants of ZnS nanoparticles (e = 45) and nanorods (e = 25) for the calculation. The values of radius of nanoparticles and nanorods corresponding to bandgap energies of 4.06 and 3.94 eV obtained from the theoretical plots

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are 8 and 12 nm, respectively. This result is slightly different from the particle sizes calculated from TEM images. This suggests that the experimentally determined values of bandgap of the samples are slightly larger than the EMA predicted values. This is due to the presence of compressive strain. It is reported that the compressive strain can deform the band structure in such a way that it tends to increase the bandgap energy of the material (Khan and Li 2006). It shifts up the BCB (Zn 4s state) at the same time reduces the energy of TVB (S 3p state) thereby increases the bandgap energy (Unlu and Horing 2013). The room temperature photoluminescence spectra of ZnS nanoparticles and nanorods excited at 300 nm are shown in Fig. 4. The best Gaussian fit of the PL bands of both nanoparticles and nanorods has given five peaks. The peaks of ZnS nanoparticles are observed at 3.43 (violet), 3.21(violet), 2.76 (blue), 2.56 (green), and 2.36 (green) eV, whereas those of ZnS nanorods are observed at 3.39 (violet), 3.17 (violet), 2.78 (blue), 2.55 (green), and 2.44 (green) eV. The first three peaks of both the samples are due to interstitial sulfur, interstitial zinc, and sulfur vacancies, respectively (Denzler et al. 1998). The least energetic peak for both the samples arises due to the transition from conduction band to zinc vacancies (Limaye et al. 2008). It is to be noted that the intensity of the peak corresponding to the transition related to zinc vacancies is very weak, while that due to sulfur vacancies is strong. This supports our finding from the EDS studies that the density of sulfur vacancies is high in the as-prepared samples. However, the strongest peak is due to zinc interstitials which are produced at the surface of nanostructures due to the lattice deformation triggered by surface defects. The peaks at 2.56 and 2.55 eV are newly observed, and we assign these to transition from zinc interstitial to sulfur interstitial. Moreover, it should be noticed that the peak corresponding to band-edge/excitonic emission is not obtained in the present spectra. This is common in nanomaterials as the energy levels in bandgap tend to quench the band-edge/excitonic emission (Bhattacharjee et al. 2006; Xiao et al. 2008; Shalish et al. 2004). Thus PL studies have confirmed that both ZnS nanoparticles and nanorods have defects like vacancies and interstitials in their surface layers. Since the defect emission peaks are intense, the density of these defect centers will be high. This will strongly influence the dielectric and transport properties of the samples.

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Fig. 4 PL spectra of ZnS nanoparticles. In the inset is that of nanorods

Raman spectroscopy can give useful information about the nature of defects, quantum confinement effects, and lattice strain in nanomaterials. The Raman spectra of ZnS nanoparticles and nanorods excited with the 488 nm line of argon laser are shown in Fig. 5a. Raman peaks of nanoparticles are observed at 220, 268, 345, 421, 608, and 708 cm-1, while those of nanorods are observed at 222, 273, 349, 423, 601, and 711 cm-1. The modes at 220 and 222 cm-1 correspond to the second order longitudinal acoustic phonon, whereas those at 265 and 273 cm-1 are due to the unresolved A1(TO) and E1(TO) modes (Cheng et al. 2009). The broad peaks around 345 and 349 cm-1 correspond to the unresolved A1(LO) and E1(LO) modes. The last three peaks of both nanoparticles and nanorods are assigned to TA ? LO, 2TO, and 2LO modes, respectively. For wurtzite semiconductors, group theory predicts the following phonon modes: an A1 and two E1 modes which are Raman and infrared active, a doubly degenerate E2 mode which is Raman active and two B1 modes which are silent modes (Arguello et al. 1968). However, it is to be noted that the Raman spectrum obtained for nanorods shows weak TO phonon response. This arises due to the destructive interference of these states with the electronic states of ZnS (Brafman and Mitra 1968; Serrano et al. 2004). This effect is not so evident in nanoparticles due to its dimensionality difference

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from nanorods. As we know, the LO mode usually consists of A1(LO) and E1(LO) modes from polarization fields parallel and perpendicular to the c-axis, respectively. However, they are not resolved in the spectra we obtained. Therefore, we have employed the Gaussian fitting to resolve the peaks corresponding to the aforementioned modes as shown in Fig. 4b. Since the 2LA mode is weak in the Raman spectrum of ZnS nanoparticles, they are also baseline corrected and Gaussian fitted as shown in Fig. 4c. The TO mode is also fitted, since it is very weak in the obtained spectrum of ZnS nanorods. From the fits, the peak positions of 2LA, A1(LO), and E1(LO) modes of ZnS nanoparticles are obtained at 221, 338, and 348 cm-1, respectively, while those of nanorods are found at 224, 342, and 350 cm-1, respectively. However, we couldn’t resolve the mixed E1(TO) and A1(TO) modes which may be an indicative of both modes occurring at the same wavenumber and having very close intensity values. It is clear that the modes A1(LO), E1(LO), A1(TO), and E1(TO) for which the peak positions in bulk ZnS are 274, 274, 352, and 352 cm-1, respectively, red shifts in the case of ZnS nanoparticles and nanorods (Brafman and Mitra 1968). The red shift arises due to the quantum confinement of phonons in nanostructures (Prabhu and Khadar 2008). However, the compressive strain present in nanomaterials tends to blue shift the Raman peaks (Balandin et al. 2000). The red shift of peaks in the spectra of both samples show that the effect of phonon confinement dominates over the blue shift produced by lattice strain. We employed the renowned Gaussian confinement model proposed by Ritcher to analyze the de-convoluted A1(LO) mode (Ritcher et al. 1981). This model predicts the first order Raman spectrum as Z jCðqÞj2 d 3 q IðxÞ ¼ ð4Þ  2 ; ½x  xðqÞ2 þ C0=2 where IC x(q) I is the phonon dispersion curve, C0 is the natural line width of the zone center optical phonon in the bulk, IC(q)I2 is the Gaussian confinement function  2 qd which can be written as exp 2a for nanoparticles  2 2  2 2   2 q d q d  2 d2ffi  and exp 2a1 1 exp 2a2 2 1  erf piqffiffiffiffiffi  for nano32p rods. This equation is used to fit the experimental

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Fig. 5 a Micro Raman spectra of ZnS nanoparticles and nanorods and the Gaussian resolved Raman peaks corresponding to b 1TO and c 1LO modes. The solid curves show the theoretical modes

values of A1(LO). The parameters obtained are given in Table 1. The data presented in Table 1 show that there is a large shift in the A1(LO) peaks of both ZnS nanoparticles and nanorods compared to that of their bulk equivalent. The full widths at half maximum of the experimentally obtained peaks are much higher than that of bulk ZnS. This widening can be assigned to the shortening of phonon lifetime due to the quick transfer

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of vibrational energy to the surrounding which is a commonly observed phenomenon in nanomaterials. Dielectric properties using impedance and electric modulus spectroscopy Dielectric spectroscopic investigations can give detailed information about the structure, charge storage capabilities, and transport properties of a dielectric

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material. Although a few papers have reported the dielectric properties of ZnS nanoparticles, a detailed and systematic study is still lacking (Suresh 2013; Shevarenkov and Shchurov 2006). Moreover, there are no reports till today on the dependence of the dielectric properties on the morphology and surface defects of nanomaterials. The dielectric dispersions of ZnS nanorods and nanoparticles are shown in Fig. 6. The complex dielectric constant (e*) of the samples shows a significant increase compared to that of bulk ZnS (8.76 at RT) and reported values of e* of ZnS nanoparticles (Suresh 2013; Chihara et al. 1987). In nanomaterials, along with electronic and orientational

Table 1 Parameters obtained by fitting the A1(LO) mode peak using the Gaussian equation C (experimental)

C0

dx

Nanoparticles

30.77

13

13.66

Nanorods

30.56

14

8.59

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polarizations, space charge polarization also plays a significant role. Space charge polarization is associated with mobile and trapped charges, mostly, occurring at the grain boundaries of nanomaterials. The real part of dielectric constant shown in Fig. 6a, b becomes negligible at very high frequencies due to the incapability of dipoles to align themselves in a rapidly varying field. Only those polarization mechanisms with a polarization time greater than the field switching time will contribute to the dielectric constant. Most II–VI semiconductors are polydispersive, and they do not satisfy the Debye equations. To take into account the distribution of relaxation times, we use Cole–Cole equation according to which the imaginary part of dielectric constant is give by )  p  0 ( sin b De 2  ; e00 ðxÞ ¼ ð5Þ 2 coshðbkÞ þ cos b p2 where k = ln(xs), De0 = es - e?, e? is the dielectric permittivity at high frequency, es is the static dielectric

Fig. 6 The dispersion of the real parts of dielectric constant of a ZnS nanoparticles and b nanorods. The imaginary parts of nanoparticles and rods are show in (c) and (d), respectively

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permittivity, x is the angular frequency, s is the mean relaxation time, and b = (1 - a), where a is a measure of the distribution of relaxation times (Cole and Cole 1941). This equation is used to obtain theoretical fits to the experimental values of e00 which are shown in Fig. 6c and d. The parameters obtained are listed in Table 2. Since the values obtained for a are greater than zero, the relaxation process is Cole–Cole type. Moreover, the values of a decrease with increase in temperature which means that the dielectric relaxation behavior approaches the Debye nature at high temperatures. The dielectric relaxation time obtained is between 10-3 and 10-5 s. This is the time regime of orientational and space charge polarizations (Kao 2004). Both hopping and interfacial type space charge polarizations exist in the samples due to their highly distorted surface layers. However, a distinction of these mechanisms cannot be seen, since they have very close relaxation times. The impedance spectra of the samples presented in Fig. 7 show only one depressed semicircle at temperatures up to 523 K. This arises due to the overlapping of grain and grain boundary responses at low temperatures (Chiang et al. 1996). A depressed semicircle typically indicates a process with a distribution of relaxation times (Chandran et al. 2011b). Figure 7a reveals that the grain boundary resistance on ZnS nanoparticles is very much lower than its grain resistance. This is due to the large density of trapped states in the surface layers of nanoparticles which can lead to space charge polarization. Interestingly, the grain boundary resistance of nanorods has a higher value than its grain resistance. Such a nature is observed due to the relatively lower surface to volume ratio of nanorods compared to nanoparticles. The large surface to volume ratio is a consequence of structural

Table 2 The parameters obtained by fitting the experimental data to Cole–Cole equation at different temperatures T (K) Nanoparticles

Nanorods

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a

s (s)

373

0.374

0.001411

473

0.252

0.000192

573

0.223

0.000081

373

0.472

0.000663

473

0.333

0.000019

573

0.292

0.000010

peculiarity and small particles size. Once the surface to volume ratio is reduced, the densities of dangling bonds and other grain boundary defects diminish. In order to deconvolute the contributions from grains and grain boundaries to impedance, we employed the brick layer model (Raymond et al. 2005). According to this model, the expression for the complex impedance (Z* = Z0 - jZ00 ) can be written as Rg Rgb þ 1þðxRg Cg Þ2 1þðxRgb Cgb Þ2 ( " # " #) xRg Cg xRgb Cgb j Rg þRgb ; 1þðxRg Cg Þ2 1þðxRgb Cgb Þ2

Z  ¼ Rþ

ð6Þ where Rs denotes the grain resistance, Cg is the capacitance related to domain and dipole reorientation in grain, Rg denotes the resistance associated with grain, Cgb is the capacitance related to grain boundary layer, and Rgb denotes the resistance across the grain boundary layer. Fitting the experimental values with Eq. 6, the grain and grain boundary resistances are obtained. It is found that the grain boundary resistance of ZnS nanorods is higher than that of nanoparticles, which indicates the presence of large density of grain boundary defects. The variation of Rgb with the inverse of temperature is shown in Fig. 8. The grain boundary resistance of semiconductors follows the Arrhenius law given by  Rgb ¼ R0 exp

 Ea ; kB T

ð7Þ

where R0 is the pre-exponential factor, and Ea is the activation energy for conduction through grain boundaries. The best fits to the experimental values using Eq. 7 have given Ea as 0.198 eV and 0.316 eV for ZnS nanoparticles and nanorods, respectively. From the values of Ea, it is clear that grain boundary conduction in nanoparticles occurs much easier than that in nanorods which is, once again, due to the large density of trapped and mobile charges in the surface layers of the former compared to that in the latter. The preexponential factors for nanoparticles and nanorods are found to be 568.4 and 3076.2 X, respectively. The complex electric modulus formalism proposed by Moynihan is an alternative approach to study the electrical behavior of dielectric materials. It is mainly

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Fig. 7 Impedance spectra of a ZnS nanoparticles and b nanorods at different temperatures 00 M  ðx Þ ¼ M 0 þ 8iM 1 9  Z  < = d/ðtÞ ¼ M1 1  expðixtÞdt ; : ; dt 0

ð8Þ

Fig. 8 The grain boundary resistance is plotted against T-1 for CdS nanorods and nanoparticles (inset)

useful in interpreting the low frequency data which are difficult to perform using dielectric dispersion analysis due to the absence of well-defined dielectric loss peak. It can also be used for the detection of electrode polarization, conductivity relaxation times, and charge transport mechanisms. The electric modulus can be expressed as

where M0 and M00 are the real and imaginary parts of the complex modulus function, M? is the asymptotic value of M0 (x), x is the angular frequency, and u(t) = exp[-(t/sM)n] is the time evolution of the electric field within the material, where n is the exponent, and sM is the conductivity relaxation time (Savitha et al. 2007). Figures 9a and c shows the variation in the real part of M* of the samples as a function of frequency. It clearly implies that, at all temperatures, the M0 (x) values approach zero at low frequencies and reach the asymptotic value at high frequencies. This suggests that electrode polarization is negligible (Sural and Ghosh 1998). We have also plotted the imaginary part of M*(x) as a function of angular frequency as shown in Fig. 9b, d. Peaks are observed in the frequency dispersion of M00 data which confirms the existence of conductivity relaxation process. In the frequency region below the peak, long range transport of charge carriers takes place. At frequencies above xmax, the carriers are confined to potential wells, undergoing short range hopping type transport. The peaks of M00 of

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Fig. 9 Frequency dependance of the real part of electric modulus (M0 ) of a ZnS nanoparticles and c ZnS nanorods. b, d Shows the imaginary parts of electric modulus (M00 ) of nanoparticles and nanorods, respectively

both nanoparticles and nanorods shift to higher frequency side with increasing temperature. This may be due to the formation of broken bonds at high temperatures, which favors the long range transport. It is typically observed that the conductivity relaxation time sM follows the Arrhenius law given by   EMa sM ¼ s0 exp ; ð9Þ kB T where s0 is the pre-exponential factor, and EMa is the activation energy. We have fitted the variation in sM with the inverse of temperature according to the Arrhenius law given by Eq. 9 as shown in Fig. 10. The values of EMa and s0 obtained from the Arrhenius fit for ZnS nanoparticles are 0.537 eV and 2.787 9 10-11 s, respectively, whereas those for nanorods are 0.592 and 3.735 9 10-11 s, respectively. The values of activation energy and time period indicate that the conduction mechanism may be polaron hopping based on electron carriers (Dutta and

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Sinha 2007; Veena et al. 2009). It can be noted that the energy needed to activate hopping conduction is higher for nanorods compared to nanoparticles. This is due to the large surface to volume ratio of the former due to which broken bonds are easily produced when the temperature is raised. Also, since the electrical modulus formalism takes into account both the grain and grain boundary charge transport, the values of activation energy obtained here are different from that obtained for grain boundary conductivity. In fact, the increased activation energy obtained from the electric modulus formalism is a suggestive of the crystalline nature of the interior where the densities of trapped and free charge carriers are considerably low. AC electrical transport The dielectric studies have shown that polaron-based hopping conduction may be the charge transport mechanism in ZnS nanoparticles and nanorods. To get

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Fig. 10 The temperature dependance of conductivity relaxation time of ZnS nanoparticles and rods

a detailed picture of the ac electrical transport properties, we invoke the CBH model proposed by Elliot and later modified by Shimakawa (Elliott 1977; Shimakawa 1982). There are already a few reports on this model being used to explain the polaron-based transport in certain amorphous and nano materials (Lunkenheimer et al. 1991; Sayer et al. 1978; Biju and Abdulkhadar 2001). Our previous studies on CdS nanostructures have proved that CBH model can be successfully used to explain the ac transport mechanism in low-dimensional semiconductor nanostructures(Chandran et al. 2011a). CBH model predicts that the charge transport in disordered materials takes place via bipolaron hopping between the D? (positively charged dangling bond) and D- (negatively charged dangling bond) centers at low temperatures. At high temperatures, some of the charged defects are converted into neutral defects (D0), and single polaron hopping between D0 and charged defects becomes dominant. Unlike in bulk ZnS, the Zn and S atoms on the surface of nanostructured ZnS have two fold/or threefold coordination. This is due to the highly distorted surface layers of nanomaterials. Therefore, bipolaron transport takes place between negatively charged twofold coordinated C1- and positively charged threefold coordinated C3?, where C stands for sulfur. Since the samples are rich in S vacancies, we believe that the single polaron hopping occurs between neutral tetrahedrally coordinated T03 state and C? 3 . Here, T stands for the tetrahedrally coordinated Zn atom (Chandran et al. 2011a).

Fig. 11 The temperature dependance of ac conductivity of ZnS nanorods and nanoparticles

The variation in the ac electrical conductivities of ZnS nanoparticles and nanorods with temperature is shown in Fig. 11. Both nanorods and nanoparticles show enhanced conductivity as compared to bulk ZnS (Brada 1989). This effect arises due to the formation of excess charge carriers at the grain boundaries of nanomaterials. The density of charge carriers will be less in bulk material compared to its nano-counterpart. Also, the conductivity is found to be higher for nanoparticles than nanorods. This result supports our earlier findings that the grain boundary resistance is higher in nanorods. Hence, these results together reveals that the main contribution to ac conductivity of nanostructures comes from the surface layers. The reason for this enhancement in conductivity is the presence of almost free (trapped) charge carriers at the surface which can be excited by applying electric field or temperature. It is imperative to note that from around 480 K, the conductivity increases sharply with temperature. This is the critical temperature at or above which the single polaron hopping becomes dominant. The general equation used to relate the ac conductivity of materials with frequency is rac ¼ Axs ;

ð10Þ

where x is the circular frequency and s is the frequency exponent, generally less than, or equal to

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Fig. 12 a Variation of frequency exponent with temperature for a fixed frequency w = 100,000 Hz. The solid line shows the theoretical fits to the experimental values and b the frequency dependence of AC conductivity of ZnS nanorods and nanoparticles. Solid lines are the theoretical fits to the experimental values

unity. CBH model predicts the frequency exponent to follow the relation S¼1

6kB T ; WM þ kB T lnðxs0 Þ

ð11Þ

where WM is the maximum barrier energy, s0 is the characteristic relaxation time, and kB is the Boltzmanns constant. From the plots between temperature and s given in Fig. 12a, it is obvious that the s values initially decrease and eventually increase after 523 K for both the samples. This is a clear evidence of the switching of transport mechanism from CBH to small polaron tunneling. A similar trend was observed in the case of many amorphous and low-dimensional materials. Our own previous studies have established such a switching of mechanism in CdS nanowires (Chandran et al. 2011a). A change in mechanism indicates an abrupt

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Table 3 The parameters obtained by fitting the experimental data to CBH model for a frequency x = 100000 s-1 and a temperature of 373 K WM (eV)

s0 (ps)

˚) Rx (A

Nanoparticles

1.14

8.14

7.05

Nanorods

1.08

8.34

7.9

increase in the defect density or a structural change due to temperature effects. Hence, a detailed discussion of the SPT model and its application at very high temperatures are beyond the scope of this work. The theoretically calculated parameters for a frequency x = 100,000 S-1 and a temperature of T = 373 K are given in Table 3. For bipolaron hopping, the ac conductivity follows the relation

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Table 4 Variation in the density of defect states in ZnS nanoparticles and nanorods with temperature

Nanoparticles

Nanorods

T (K)

N (cm3)

NT (cm3)

323

1.77 9 1020

423

1.75 9 1020

513 323

1.09 9 10

423

1.13 9 1020

p3 2 N ee0 xR6x ; 12

ð12Þ

where e is the dielectric constant of the material, e0 is that of the free space, and Rx is the hopping distance. For single polaron hopping, the equation for conductivity is given by rðxÞ ¼

p2 NT NP KxR6x ; 24

Rx (A0) 7.05 7.10

1.02 9 1018

2.11 9 1016

2.41 9 1018

1.20 9 1016

20

513

rðxÞ ¼

Np (cm3)

2.12 7.02 7.21 2.10

electrical transport. Although, the defect densities calculated for single polaronic transport are less than that of bipolaronic transport, the hopping distance is very small for the latter which enhances its conductivity.

Conclusions ð13Þ

where NT is the total density of levels participating, Np is the number of carriers that hops, and K is the effective dielectric constant. Equations 12 and 13 are used to fit the experimental data as shown in Fig. 12b. We have used the equation for bipolaron hopping to fit data up to 473 K and the equation for single polaron hopping to fit data measured at higher temperatures. From the figure, it is clear that up to 473 K good fits are obtained. The fit at 513 K is not so good, because mixed single polaron hopping and small polaron tunneling exist at this temperature regime. The formation of both small and large polarons makes the transport properties at very high temperatures complicated. A general theory of polaron transport is required to explain the properties above 513 K which is beyond the scope of this paper. Various parameters calculated from the fits are given in Table 4. The results clearly show that bipolaron centers decrease in number as the temperature increases indicating their conversion to neutral single polaron centers (Shimakawa 1982). Also the densities of various defect centers are very high which indicates that the samples have highly defective surface layers. The hopping distance increases slightly with temperature which is also an indicative of the decrease in the density of charged defects. At very high temperatures, the single polaron hopping decides the nature of

The influences of size and surface effects on the optical, dielectric, and electrical transport properties of ZnS nanoparticles and nanorods were probed. The presence of compressive strain was confirmed with the help of W–H plots. The bandgap energies obtained experimentally were found to be consistent with the EMA model. ESR and EDS studies indicated the existence of sulfur vacancies in the samples. PL spectra showed that the band-edge emission is quenched due to the large density of defects in the samples. The A1(LO) mode of spectra is analyzed with the Gaussian confinement model, and natural line width of bulk ZnS is calculated. Raman peaks were red shifted as a result of the joined effect of reduced dimensionality and lattice strain. Impedance spectroscopic studies of these materials showed that the dielectric constant of the samples has higher values than that of bulk ZnS due to the high density of trapped and free charges at the surface of the former. The dielectric relaxation process was found to be Cole– Cole type which transforms to Debye type at high temperatures. Electric modulus spectroscopic investigations confirmed that polaronic short range and long range transport occur in the samples. The electrical conductivity values of both nanostructures were found to be higher than their bulk counterparts owing to the excess charge carriers at the distorted surface layers. The CBH model successfully explained the ac transport mechanism in ZnS nanorods and nanoparticles

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and proved the existence of polarons and bipolarons in them even at high temperatures. The defect densities of both nanoparticles and nanorods were calculated. Acknowledgments The authors wish to thank STIC (Cochin), IUC-DAE consortium for scientific research (INDORE), and the central instrumentation facility (SB College) for the analyses carried out.

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