Interfacial thermal and electrical transport properties of pristine and nanometer-scale ZnS modified grain boundary in ZnO polycrystals

Acta Materialia 148 (2018) 100e109

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Interfacial thermal and electrical transport properties of pristine and nanometer-scale ZnS modified grain boundary in ZnO polycrystals Xin Liang*, Lei Shen School of Materials Science and Engineering, Changzhou University, Changzhou, Jiangsu 213164, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 November 2017 Received in revised form 16 January 2018 Accepted 30 January 2018 Available online 3 February 2018

Grain boundary plays an important role in energy carrier transport. By choosing ZnO as a model system of technological importance, and by measuring the thermal and electrical transport properties of ZnO polycrystals with a wide range of grain boundary spacing, we determine the interfacial thermal (Kapitza) resistance of the ZnO grain boundary Rk ¼ 4:0±0:7  109 m2 K W1, which is relatively independent of grain size. The effective electron potential barrier height and the depletion width of the grain boundary generally increase with spacing, but they collapse below ~100 nm and become almost invariant above ~1 mm. When the grain boundary is locally modified by nanometer-thick ZnS thin film, the Kapitza resistance increases by more than three times, up to about 12:9  109 m2 K W1, and the depletion region expands more than twice. The charge carrier concentration is influenced by the effective potential barrier height due to the grain boundary energy filtering effect whereas the electron mobility is related to the depletion width. Our investigations demonstrate the significance of grain boundary characteristics for interfacial and effective bulk transport properties. The findings and the approach are broadly important for polycrystalline materials of which the functional performance can be adjusted via grain boundary engineering. © 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Zinc oxide Grain boundary Interfacial thermal resistance Electron potential barrier Thermal conductivity

1. Introduction Transport properties of heat and charge carriers are crucial to the functional performance of materials and the related devices. The ability to control and tune the electrical and thermal transport behavior is crucial to a large variety of technologically important materials. For instance, simultaneously suppressed phonon thermal conduction and enhanced electrical transport is necessary to boost the thermoelectric performance [1]. Another example is the increasing demand for excellent heat management in microelectronic semiconductor devices where high thermal conductivity is highly desired [2,3]. In contrast, ultralow thermal conductivity is required for thermal barrier coating materials to achieve higher jet engine efficiency [4,5]. Grain boundaries are interfaces naturally present in polycrystalline materials and can play an important role in transport behavior of energy carriers. Knowledge of grain boundary heat and charge transport properties is thus of important significance. Moreover, controlling and tuning the grain boundary characteristics, which can considerably alter the interfacial and

* Corresponding author. E-mail address: [email protected] (X. Liang). https://doi.org/10.1016/j.actamat.2018.01.059 1359-6454/© 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

effective bulk transport properties, can be a robust strategy for optimizing the functional performance of polycrystalline materials and the associated devices. ZnO is one of the most widely used functional materials with applications in the field of electronics [6], optoelectronics [7], piezoelectronics [8e10] and thermoelectrics [11,12] and so on. Grain boundary is known to have prominent effect on effective transport behavior of ZnO polycrystals, related to a number of ZnO based electronic devices like varistors and transistors [13,14]. However, the prior experimental work to quantitatively investigate the interfacial transport properties of ZnO grain boundary is yet insufficient. Particularly, the interfacial thermal (Kapitza) resistance, the effective electron potential barrier height and the depletion width of the ZnO grain boundary all wait to be experimentally determined. It has been shown that the granular structure is related to the work function of the transparent conducting ZnO thin films [15]. Several studies [16e19] also show that the thermal conductivity strongly depends on grain boundary spacing, especially at room temperature and below. It requires systematic work to investigate the change of the ZnO grain boundary interfacial transport properties, and consequently the effective ZnO bulk conductivities, as a function of the grain boundary spacing.

X. Liang, L. Shen / Acta Materialia 148 (2018) 100e109

Additionally, local chemistry and defects at grain boundary can substantially alter the interfacial thermal resistance and the bulk thermal conductivity [20]. Understanding the relation between grain boundary transport properties and grain boundary characteristics in polycrystalline material systems is important for a number of practical applications. In this work, we synthesized a series of polycrystalline ZnO samples with controlled grain boundary spacing and chemistry. We employed solvothermal chemical synthesis, combined with spark plasma sintering (SPS) and controlled post-annealing, to achieve a series of ZnO polycrystals with a wide range of grain boundary spacing. Particularly, we successfully introduce nanometer-thick ZnS thin film at ZnO grain boundaries. We investigated the interfacial thermal and electrical transport properties of the pristine and ZnS-modified ZnO grain boundaries. Our findings reveal the importance of grain boundary characteristics to grain boundary phonon and electron transport properties, and consequently the effective bulk conductivities.

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the microstructure was examined on a Zeiss® Supra55 fieldemission scanning electron microscope (FE-SEM). The grain size of the bulk samples was statistically determined from more than 100 grains of each sample. Elemental analysis of ZnS-modified ZnO bulk samples was made on a SHIMADZU® EDX-8000 energydispersive X-ray fluorescence spectrometer. For TEM investigations, the bulk samples were first mechanically thinned and polished down to ~100 mm, followed by ion-beam milling on a Gatan® Model 691 precision ion polishing system (PIPS). The nanoparticle morphology and bulk sample microstructure were examined using high resolution transmission electron microscopy JEOL® JEM 2100 and 2100F. To reveal the details of the ZnS-encapsulated ZnO nanoparticles, high resolution bright field and high-angle annular dark-field (HAADF) imaging were performed under FEI Titan Themis 80-200, a Cs-aberration corrected field emission scanning transmission electron microscope. Energy-dispersive X-ray spectroscopy (EDS) mapping under scanning transmission (STEM) mode was also employed to investigate the nanoscale elemental distribution.

2. Experimental section 2.4. Physical transport measurements 2.1. Polycrystalline ZnO with grain boundary spacing control The ZnO precursor powders were prepared using a wet chemical solvothermal method. Zinc acetate (Sinopharm, 99%) were dissolved in ethanol (Sinopharm, 99.7%) in a series of molar concentration (0.05e0.15 M), which is the first step to adjust the grain size. The solutions were heated at 80  C for complete dissolution and were then transferred into Teflon-lined stainless steel autoclaves of 100 mL capacity. The autoclaves were kept in the oven at 120  C for 12 h and cooled down to room temperature naturally. The assynthesized products were washed in a high-speed centrifuge with distilled water and ethanol for twice, and were then dried at 80  C for 12 h. After being finely ground, the powders were sintered into solid pellets of ~12.7 mm in diameter using spark plasma sintering (Sinter Land®, SPS LABOX-325, Japan). The sintering process was set at 750  C under an axial compressive stress of 70 MPa for a holding time of 5 min under vacuum. Subsequent thermal treatment in air furnace (KSL-1400X, HF-Kejing, China) were applied to the sintered samples to provide further control on grain size.

Thermal conductivity was determined using the standard relation k ¼ arCp , where the thermal diffusivity a was measured on graphite-coated samples using a Netzsch Micro Flash® LFA 457 system, from room temperature to 1073 K in the flowing argon atmosphere. The data presented were averaged from five measurements at room temperature and three measurements at subsequent elevated temperatures. The temperature dependence of heat capacities Cp for pristine ZnO samples were taken from the measured data reported in literature [21] and those for ZnSmodified ZnO samples were obtained by using an Inconel 600 reference sample during the thermal diffusivity measurements. The mass density r was obtained using the Archimedes method. The bulk sample thickness was reduced down below ~200 mm for room temperature Hall measurements, which were conducted on an Ecopia® HMS-5500 instrument using van der Pauw method. The presented Hall measurement results were averaged from ten tests on each sample. Electrical conductivity and Seebeck coefficient at elevated temperature (673 K) were measured on a Netzsch SBA 458 Nemesis® system.

2.2. Modification of ZnO grain boundary with ZnS thin film

3. Results

Sodium sulfide (Aladdin, 99.99%) was used as reactant to form a thin layer of ZnS on the surface of as-synthesized ZnO nanoparticles. A series of molar content of sodium sulfide, which was dissolved in distilled water, was added into the liquid solution of suspended ZnO nanoparticles. The addition of sodium sulfide was designed to form the ZnS with the designated layer thickness of 0.25, 0.5, and 1 nm, respectively, based on the volume of ~20 nm sized ZnO nanoparticle. The mixed solutions were kept at 80  C for 3 h for complete reactions. The reaction products were washed in high-speed centrifuge and then formed into solid pellets using spark plasma sintering, as similar to the pristine ZnO samples. The synthesis process is illustrated in Fig. 1.

3.1. Grain boundary characteristics

2.3. Structure characterization and elemental analysis As-synthesized nanoparticles were dispersed on holy carbon films for transmission electron microscope (TEM) observations, and the average particle size was statistically estimated based on more than 100 particles. X-ray diffraction analysis of sintered bulk samples was made on a Rigaku D/Max 2500 PC diffractometer using Cu Ka radiation. The bulk samples were slightly etched using HCl and

In Fig. 2 (a)-(d), we present the transmission electron microscopy (TEM) images of synthesized ZnO nanoparticles with a range of particle sizes. Acetate concentration is a key factor to the growth of ZnO nanoparticles. As shown in Fig. 2 (e), we observe a monotonic dependence of ZnO nanoparticle size with acetate concentration. By adjusting the zinc acetate concentration during synthesis, we are able to tune the nanoparticle size of ZnO precursor within the range of 15e40 nm, which provides the prerequisite for obtaining an appreciable range of nanoscale grain size in sintered bulk polycrystals. By adding sodium sulfide to solutions, nanometer-thick layer of ZnS is uniformly formed on the surface of each ZnO nanoparticle. Fig. 3 (a) provides an overview TEM image for 1 nm ZnSencapsulated ZnO nanoparticles. We clearly observe the nanometer-scale layer with noticeable contrast at the surface of ZnO nanoparticles. In addition, these features are prevailing in almost all ZnO nanoparticles. The layer possesses distinct crystal lattices from ZnO nanoparticles, as seen from the Cs-aberration corrected high resolution TEM (HRTEM) image in Fig. 3 (b). The

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Fig. 1. Schematic illustration of ZnO bulk polycrystals synthesis with controlled grain boundary spacing and chemistry.

Fig. 2. Control of ZnO nanoparticle size through wet chemistry synthesis. (a)e(d) TEM images of ZnO nanoparticles under different synthesis conditions, showing the remarkably varied nanoparticle size within the range of 15e40 nm, as annotated by the red numbers on the top left of each image. (e) The plot of ZnO nanoparticle size with zinc acetate concentration. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) image is shown in Fig. 3 (c), with the corresponding STEM energy-dispersive X-ray spectroscopy (EDS) mappings for the element Zn, O and S presented in Fig. 3 (d), (e) and (f), respectively. The Zn and O distribution is homogeneous over the nanoparticles, whereas the S mapping reveals an apparently hollow nature with higher concentration of S at particle surface and lower inwards, suggesting the encapsulation of ZnO nanoparticle by ZnS thin film. The sintered bulk samples are dense and detailed mass density information can be found in Supplementary Information Table SI. Fig. 4 (a) e (c) are the field emission scanning electron microscopy (FE-SEM) micrographs for the microstructure of three representative pristine ZnO bulk samples. Fast sintering by SPS significantly suppresses the grain growth, which preserves nanograin structure in bulk ZnO polycrystals. The smallest mean grain size we achieved is ~80 nm, as shown in Fig. 4 (c). Subsequent annealing process, with controlled temperature and time, endows the capability of tuning the grain boundary spacing from 80 nm up to 4.6 mm, ranging over the nanoscale and microscale structure. In

Fig. 4 (d) e (f), we show the microstructure of bulk samples sintered from ZnS-encapsulated ZnO nanoparticles with three nominal ZnS layer thickness, 0.25, 0.5 and 1 nm, respectively. By X-ray diffraction analysis, a hexagonal ZnS phase is identified in all ZnS-modified ZnO bulk samples, as shown in Fig. 4 (g). The characteristic X-ray peak intensity for ZnS phase increases with the nominal ZnS layer thickness. The energy-dispersive X-ray fluorescence measurements suggest the global compositions as 3.94, 9.22 and 16.43 mol. % ZnS content in these bulk samples, corresponding to the nominal ZnS encapsulation layer thickness of 0.25, 0.5 and 1 nm, respectively. The measured chemical compositions are used to denote these ZnSmodified ZnO samples in the following content. By extensively examining the sample microstructure, we do not observe any distinct appearance of the second phase, even in the sample with the highest ZnS content. This indicates that ZnS is mostly located at ZnO grain boundaries instead of standing as individual ZnS grains. Such microstructural evolution is expectable considering that the nanometer-scale ZnS thin layer, which originally coats the outer surface of each ZnO nanoparticle, is trapped between the ZnO nano-crystallites during the compacting and

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Fig. 3. Morphology and elemental information of ZnO nanoparticles encapsulated by ZnS with a nominal layer thickness of 1 nm (the measured global content is 16.4 mol. % ZnS). (a) An overview TEM image showing that most of ZnO nanoparticles are encapsulated with nanometer-thick ZnS layer. (b) Cs-aberration corrected HRTEM image providing a close view revealing the crystal lattice contrast across the ZnO/ZnS interface. (c) HAADF-STEM image of several ZnO nanoparticles with the corresponding STEM-EDS mappings, red for Zn (d), yellow for O (e) and green for S (f). Notably, the S mapping shows the hollow features as compared to the uniform distribution of Zn and O ones, revealing the ZnS thin films on the surface of ZnO nanoparticles. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

sintering process. This is further evidenced by our HRTEM investigations. Fig. 5 (a) is the TEM micrograph of the typical microstructure for pristine ZnO bulk sample with the average grain boundary spacing of 290 nm, and Fig. 5 (b) is for the bulk sample sintered from ZnSencapsulated ZnO nanoparticles, which has a global content of 16.4 mol. % ZnS. At the first glance, the two samples appear to have rather similar microstructure; however, a closer view reveals remarkably different local grain boundary structure. The grain boundaries in pristine ZnO bulk samples are clean and free out of the second phases, as is shown in Fig. 5 (c). In contrast, along the grain boundaries of ZnS-modified ZnO sample, there is ~2 nm thick layer with the crystal lattice differing from the grains on both sides of the grain boundary, as indicated by the yellow dashed lines in Fig. 5 (d). In combination with the above characterization results, we can conclude that the nanometer-thick layer at grain boundary is ZnS thin film that is retained from the ZnS encapsulation. We thus demonstrate that polycrystal grain boundary can be modified at the nanoscale via the surface chemical reaction of nanoparticle precursors. This provides a useful approach to examine the relation between interfacial transport properties and interfacial characteristics. 3.2. Transport properties: phonons and electrons It is well-known that ZnO is a wide bandgap semiconductor with Eg ¼ 3:3 eV [22], where electrical and thermal energy are mainly carried by electrons and phonons, respectively. The electronic contribution to thermal conductivity, according to the Wiedemann-Franz law, is negligibly small as compared to the phonon contribution in these low electronically conducting samples; the measured thermal conductivity is thus representative of the phonon or lattice thermal conduction. Thermal conductivity measured from room temperature (RT) up to 1073 K is presented in Fig. 6 (a). Corresponding to fully dense samples, thermal conductivity has been corrected for porosity P according to the formula kdense ¼ kmeasure =ð1  4P=3Þ [23]. The thermal conductivity of pristine ZnO notably varies with grain boundary spacing at room

temperature. For instances, it decreases from 40.5 W m1 K1 for grain size dz4:63 mm down to 16.4 W m1 K1 for dz80 nm, by more than two-fold reduction. However, the thermal conductivity becomes less dependent on grain boundary spacing as temperature increases, and eventually converges to a value of ~6 W m1 K1 at 1073 K. Thermal conductivity is dramatically reduced in ZnS-modified ZnO samples where there are nanometer-scale ZnS thin films at grain boundaries. For example, for the same level of grain boundary spacing 200e300 nm, the RT thermal conductivity decreases from 24.2 W m1 K1 for pristine ZnO down to 17.0 W m1 K1 for the sample with 3.94 mol. % ZnS. Nevertheless, high temperature thermal conductivity limit is virtually unchanged with the addition of ZnS. This result indicates that these ZnS-modified ZnO samples remain the ZnO crystal bonding nature and the intrinsic phononphonon scattering processes in ZnO are not considerably altered. Electrical conductivity data for pristine ZnO polycrystals measured at RT and 673 K are plotted as a function of grain boundary spacing, as shown in Fig. 6 (b). Data for ZnS-modified ZnO are superimposed on the figure, as represented by the closed symbols. For pristine ZnO, the electrical conductivity varies by orders of magnitude as grain boundary spacing changes from nanometer to micrometer length scale. For instance, RT electrical conductivity decreases from 189 S cm1 for dz80:6 nm down to 0.27 S cm1 for dz4:6 mm. However, electrical conductivity remains almost invariant with grain boundary spacing as reaching above the micrometer length scale. Electrical conductivity of pristine ZnO, and its dependence on grain boundary spacing, are generally the same at RT and 673 K. The improved electrical conductivity at elevated temperature can be attributed to the thermal excitation of charge carriers. The electrical conductivity does not notably vary for small extent of ZnS encapsulation, but significantly drops with higher ZnS content. The electrical transport can be further understood from the electron concentration and mobility obtained from Hall measurements. As shown in Fig. 6 (c), the carrier concentration generally decreases with grain boundary spacing until ~1 mm, and then becomes generally invariant with larger spacing. The higher carrier

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Fig. 4. Microstructure and phase compositions of sintered ZnO bulk samples. FE-SEM micrographs: (a)e(c) selected pristine ZnO samples with representative grain boundary spacing, and (d)e(f) samples sintered from the ZnS-encapsulated ZnO nanoparticles with different ZnS content: 3.94, 9.22 and 16.43 mol. %, corresponding to the samples with the nominal ZnS encapsulation layer thickness of 0.25, 0.5 and 1 nm, respectively. The red number on the top left of each image indicates the averaged grain size. (g) X-ray diffraction patterns of bulk polycrystalline samples sintered from pristine and ZnS-encapsulated ZnO nanoparticles; the global compositions obtained from the energy-dispersive X-ray fluorescence measurements are also indicated on the X-ray spectra. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

concentration in nanograin ZnO samples is partially attributed to the intrinsic defects that come from the SPS sintering process. Intriguingly, the carrier mobility of pristine ZnO also decreases with grain size, from 58.1 cm2 V1 S1 for dz80:6 nm down to 5.1 cm2 V1 S1 for dz4:63 mm. The carrier concentration somewhat increases by small extent of ZnS encapsulation (3.94 and 0.22 mol. % ZnS) but is considerably reduced at larger ZnS addition (16.43 mol. % ZnS); the carrier mobility is lowered in all ZnSmodified ZnO samples. The Seebeck coefficient measured at 673 K is plotted as a function of grain boundary spacing, as shown in Fig. 6 (d). Both the pristine and ZnS-modified ZnO exhibit negative Seebeck coefficient implying the n-type semiconductor conduction. Seebeck coefficient for the pristine ZnO increases with grain boundary spacing, from 157 mV K1 for dz80:6 nm up to 399 mV K1 for dz671 nm, by a factor of more than 2.5, and it then becomes almost constant with further increasing d. The dependence of Seebeck coefficient on grain boundary spacing is opposite to electrical

conductivity, implying a free electron conduction behavior. However, the Seebeck coefficient for all ZnS-modified ZnO samples is reduced to some extent, as compared to the pristine ZnO of similar grain size. 4. Discussion 4.1. Grain boundary electron potential barrier and depletion region The strong dependence of electron mobility on grain boundary spacing, as shown in Fig. 6 (c), implies that grain boundary dominates electron scattering process in these ZnO polycrystals. Our observations also indicate that the grain boundary electron scattering strength is not constant but varies with grain boundary spacing. As is known, the Fermi level is pinned to the localized states at grain boundary and there is an electron potential barrier of height EB formed there [24]. When electronic charge carriers with an energy distribution pass through the grain boundary, carriers

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Fig. 5. TEM micrographs of microstructure in sintered bulk samples. (a) Pristine bulk ZnO with an average grain size of 290 nm. (b) ZnS-modified ZnO with a global content of 16.43 mol. % ZnS (b). (c), (d) are HRTEM images of grain boundary in (a) and (b), respectively. The grain boundary in pristine ZnO is clean (c), whereas there is nanometer-scale ZnS thin film along the grain boundary of ZnS-modified ZnO (d), as indicated by the yellow dashed lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

with energy lower than the barrier height EB are strongly scattered and filtered out [25,26]. The barrier height apparently affects the fraction of electrons that participate in the conduction process. In addition, the depletion region, also known as space charge region, with the width of 2W centered at the grain boundary, is expected to influence electron mobility. Accordingly, the role of grain boundary in electronic transport behavior for these polycrystals can be investigated and understood from these two characteristic parameters. Seebeck coefficient, which characterizes the thermoelectric voltage in response to a thermal gradient, can provide some insights into the electrical transport behavior. For the material with grain boundary potential barriers of height EB , the Seebeck coefficient S is given by Ref. [24],

2

  6 Z ∞ vf ðEÞ 2 6 dE  t ðEÞgðEÞE vE 1 6 6 EB    EF S¼ 6 Z ∞ vf ðEÞ eT 6 6 dE t ðEÞgðEÞE  4 E vE B

3 7 7 7 7 7 7 7 5

(1)

where e is the electronic charge, T is the absolute temperature, E is the electron energy, tðEÞ is the electron relaxation time, gðEÞ is the density of states, f ðEÞ is the Fermi distribution function and EF is the Fermi energy. In the limit of EF =kB T[1, Equation (1) can be approximated to a practical form,

S¼

      kB  *  h þ 1 þ exp h* ln  1 þ exp h* e

(2)

where h* ¼ ðEB  EF Þ=kB T, and ðEB  EF Þ is the effective electron potential barrier height. Using Equation (2), ðEB  EF Þ is estimated

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from the measured Seebeck coefficient, and is plotted as a function of grain boundary spacing, as shown in Fig. 7 (a). We find that ðEB  EF Þ for pristine ZnO grain boundary collapses for nanograin sized samples, which is probably due to the presence of intrinsic point defects that improves the electrical conductivity. With increasing grain boundary spacing, ðEB  EF Þ dramatically increases to the level well above the thermal energy at RT or 673 K (kB Tz0:026 eV at RT and 0:058 eV at 673 K), suggesting that grain boundary plays a non-negligible role in electron conduction process. This observed behavior of grain boundary potential barrier height with grain size qualitatively agrees with the trend EB  d2 that is predicted by a grain boundary model for polycrystalline Si films [27]. As the spacing approaches ~1 mm and above, the effective potential barrier height becomes almost constant. Referring back to grain boundary spacing dependence of carrier concentration shown in Fig. 6 (c), we immediately find that carrier concentration n monotonically depends on grain boundary potential barrier height ðEB  EF Þ. For instance, n decreases as ðEB  EF Þ increases; as ðEB  EF Þ no longer changes for larger grain boundary spacing, n becomes almost invariant as well. These results strikingly confirm that grain boundary selectively filters out electrons and the number of conducting electrons is related to the effective barrier height. Here we show that electrical conductivity, Seebeck coefficient and Hall measurement results can help understand the electronic transport behavior from complementary perspectives. In comparison with the pristine ZnO samples that have similar grain boundary spacing, the potential barrier heights of ZnS-encapsulated ones are lowered to some extent, which is due to the modification of density of grain boundary states. By solving the Poisson equation for charge distribution near the grain boundary, the grain boundary potential barrier height EB is given by [27,28].

EB ¼

eNT2 2εε0 n

(3)

where e is the electronic charge, n is the carrier concentration, ε0 is the vacuum dielectric constant (permittivity of free space), ε is the relative dielectric constant of the ZnO grains. NT is the density of charges trapped at grain boundary, which relates to W, the width of the depletion region on one side of the grain boundary. According to the charge neutrality condition, we have

NT ¼ 2nW

(4)

As has been discussed previously, the width of the grain boundary depletion region is expected to be an influential factor in charge carrier mobility. The larger the grain boundary depletion width, the stronger electron scatterings and consequently the lower carrier mobility. The foregoing model provides a way of estimating the depleting width of the grain boundary. Mathematical rearrangement of Equations (3)e(4) readily gives

 W¼

2εε0 EB en

1 2

(5)

Inputting the measured carrier concentration and the derived potential barrier height, taking ε ¼ 8:12 for bulk ZnO [29], we estimate the grain boundary depletion width W for these bulk polycrystals, as presented in Fig. 7 (b). For grain boundary spacing d less than ~200 nm, the depletion width W is generally invariant and is less than 1 nm. As d increases to the micrometer length scale, W dramatically increases up to ~20 nm. However, W becomes almost constant with further increase in d. The dependence of grain

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Fig. 6. Physical transport properties of ZnO bulk polycrystals sintered from pristine and ZnS-encapsulated ZnO nanoparticles. Thermal conductivity (a) as a function of temperature from RT to 1073 K; electrical conductivity (b) measured at RT and 673 K, RT Hall carrier concentration and mobility (c), Seebeck coefficient (d) at 673 K, plotted against grain boundary spacing. Open and filled symbols represent the data for pristine and ZnS-modified ZnO samples, respectively. The dashed lines in thermal conductivity plots (a) are the best fitting of measured data according to a modified Klemens-Callaway model, with the consideration of grain boundary thermal resistance, i.e. Equations (6)e(7); the solid lines in plots (b)e(d) are guides to the eye.

Fig. 7. (a) Effective electron potential barrier height ðEB  EF Þ for pristine and ZnS-modified ZnO grain boundaries, as derived from the Seebeck coefficient measured at 673 K, plotted as a function of grain boundary spacing. (b) Estimated grain boundary depletion width W as a function of grain boundary spacing. The solid lines are connecting the data for pristine ZnO polycrytals.

boundary depletion region width on grain boundary spacing well interprets the observed trend of electron mobility that is shown in Fig. 6 (c). Combining the two data plots, it is clearly found that electron mobility m inversely depends on grain boundary depletion width W, suggesting that the extent of grain boundary depletion

region influences the electron mobility in these ZnO polycrystals. The other important results shown in Fig. 7 (b) are the depletion width of the ZnS-modified ZnO grain boundary. Small amount of ZnS-encapsulation makes little change in W. Strikingly, the grain boundary depletion width W reaches about 30.0 nm for the

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16.43 mol. % ZnS sample with d ¼ 450 nm; this is more than twice that of the pristine ZnO grain boundary (W ¼ 13:2 nm for d ¼ 474 nm). This substantial change of grain boundary depletion region is unambiguously related to the grain boundary ZnS thin films, as previously shown in Fig. 5 (d). It is yet challenging to quantitatively predict how the grain boundary ZnS thin film affects the depletion width. Nevertheless, our results undoubtedly show that the depletion region can be effectively modified by grain boundary chemistry and structure, which dramatically changes the interfacial electron transport properties. 4.2. Grain boundary phonon scattering strength With decreasing grain boundary spacing, the measured thermal conductivity for pristine ZnO decreases and also becomes less dependent on temperature, as previously shown in Fig. 6 (a). This suggests that grain boundary phonon scatterings are more dominant as grain boundary spacing decreases, due to the comparative length scale of grain boundary spacing to phonon mean free path. Apparently, for similar level of grain size, ZnS-modified samples demonstrate notably lower thermal conductivity than pristine ZnO. Similar to electron transport, this significant change is mostly ascribed to the grain boundary modification by nanometer-scale ZnS thin film, which remarkably alters the grain boundary thermal transport properties. Interfacial thermal (Kapitza) resistance Rk is the parameter that measures the interface's resistance to thermal flow and characterizes the scattering strength of heat carriers across the interface, and it is a useful value to evaluate and compare the interfacial phonon transport properties for different types of grain boundary and interface. To exact the grain boundary thermal resistance Rk , we apply the effective medium theory and assume that grains and grain boundaries are connected in series as conductors and resistors, respectively. For polycrystals with isotropic crystallites, we have

1

k*

¼

1

ki

þ

Rk d

(6)

where k* is the effective bulk thermal conductivity that is obtained from measurements, d is the grain boundary spacing, and Rk is the Kapitza resistance of the grain boundary. ki is the intrinsic thermal conductivity of the pristine ZnO without defects and grain boundaries, which is characteristic of phonon-phonon scatterings. Here we employ the modified Klemens-Callaway model for ki, which is based on the analytical solution to the Boltzmann transport equation under relaxation time approximation assuming a Debye dispersion relation [30,31]. In this model, we introduce a phonon mean free path cut-off so that the mean free path cannot be smaller than the interatomic spacing. This gives ki as [32,33].

ki ¼

107

thermal conductivity for both pristine and ZnS-modified ZnO samples, we obtain excellent fitting results, which are represented by the dashed curves in thermal conductivity plots shown in Fig. 6 (a). The R2 values for fitting the pristine ZnO data are all above 0.98, suggesting a good description of the experimental results by the model. The Kapitza resistance of the pristine ZnO grain boundary is derived to be Rk ¼ 4:0±0:7  109 m2 K W1 in the temperature range of RT to 1073 K and is relatively independent on grain size d within the range of 80 nm to 4:6 mm. This experimentally determined Rk value agrees well with the theoretically calculated value for the ZnO grain boundary that has a misorientation angle of 30 [20]. We find that the grain boundary thermal resistance of ZnO is similar to that of yttria-stabilized zirconia (YSZ) [17] and SrTiO3 [37]. For comparison, we summarize a number of reported Rk values which can fall into two categories: grain boundaries and superlattice/nanolaminate interfaces, as shown in Fig. 8. As a general observation, superlattice or nanolaminate interfaces have less resistance to heat transport than grain boundaries. This can be partially attributed to the epitaxial nature of some interfaces. In contrast, heat carriers encounter considerable crystallographic mismatch across the grain boundary. At the first glance, it is interesting to see that the grain boundary Rk of well-known low thermal conductivity materials like YSZ and SrTiO3 is significantly smaller than that of some relatively high thermal conductivity materials such as Al2O3 and SnO2. The suppressed phonon transport in materials like YSZ and SrTiO3 largely arises from the intrinsic thermal conductivity ki due to their large molecular weight and complex crystal structure [39,40]. When ZnO grain boundary is coated by nanometer-thick ZnS thin film, there is a substantial increase in Kapitza resistance, as seen from the inset in Fig. 8. For the 16.43 mol. % ZnS-modified sample where the grain boundary is modified by ~2 nm thick ZnS thin film, Rk is determined to be 12:9  109 m2 K W1, which is more than three times that of the pristine ZnO grain boundary. This significant increase in Rk suggests the increase of grain boundary phonon scattering strength. Besides the intrinsically present crystallographic misfit at the grain boundary, the mismatch of phonon

3

1 kB 1 q kB 4 lmin T 3=2 þ 2 2 1=2 3p C 3=2 ðlmin vs Þ 6p Z3 v2s

(7)

where kB is the Boltzmann constant, C ¼ 1:62  1018 s K1 is the inverse phonon lifetime coefficient for phonon-phonon scatterings [20], vs ¼ 3090 m/s is the sound velocity in ZnO that is calculated based on the longitudinal (vL ) and transverse (vT ) wave velocities, lmin is the minimum phonon mean free path, q ¼ 370 K is the Debye temperature for ZnO [34] and Z is the reduced Planck constant. This model assumes that the Kapitza resistance Rk is relatively independent of temperature, which is generally true for oxide materials above room temperature [17,35e38]. The present work meets well this condition since the thermal transport properties were all measured at room temperature and above. Applying Equations (6) and (7) to the measured temperature dependent

Fig. 8. Interfacial thermal (Kapitza) resistance Rk of grain boundaries in pristine ZnO and ZnS-modified ZnO polycrystals, in comparison with literature reported data on grain boundaries (SnO2 [38], CeO2 [16], Al2O3 [41], SrTiO3 [37], YSZ [17] and Si [42]) and superlattice or nanolaminate interfaces (Al/Si [43], W/Al2O3 [44], Ni/Ti [45], TiN/MgO [46], AlN/GaN [47], In2O3(ZnO)k [48], Al2O3/TiO2 [49] and Si/Ge [50]). The subscript for each data symbol denotes the temperature range from which the Rk value is determined. The inset plot shows the Rk for ZnO grain boundary as a function of ZnS modification.

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dispersion relation across the boundary and the complex interfacial bonding introduced by nanometer-scale ZnS thin film further reduce the phonon transmission. Our observations thus reveal the marked impact of local grain boundary chemistry and structure on the interfacial phonon transport properties. 5. Conclusions In summary, by analyzing the measured physical transport properties of ZnO polycrystals with a wide range of grain boundary spacing, we investigate the interfacial thermal and electrical transport properties of ZnO grain boundary. We determine the interfacial thermal resistance for pristine ZnO grain boundary as Rk ¼ 4:0±0:7  109 m2 K W1 in the temperature range of RT to 1073 K, which is relatively independent of grain size. However, both grain boundary effective electron potential barrier height ðEB  EF Þ and depletion width W vary with grain boundary spacing d. When grain boundary spacing is below ~100 nm, the potential barrier collapses and the depletion region is negligibly small. The effective potential barrier height and depletion width monotonically increase with grain boundary spacing until ~1 mm, and become virtually invariant for larger spacing. By tuning the surface chemistry of nanoparticle precursors, we successfully modified the grain boundary in ZnO polycrystals. Strikingly, when ZnO grain boundary is modified by ~2 nm thick ZnS thin film, the interfacial thermal resistance Rk increases by more than three times, up to 12:9  109 m2 K W1, and the grain boundary depletion region enlarges by a factor of more than two. The alteration of interfacial transport properties consistently affects the effective bulk conductivities. The correlation between effective potential barrier height and carrier concentration implies the grain boundary energy filtering effect, and variation of electron mobility with depletion width suggests the role of depletion region in electron scatterings. These findings not only provide intrinsic grain boundary phonon and electron transport properties for ZnO, but also demonstrate the importance of grain boundary characteristics for energy carrier transport behavior in polycrystalline materials. Acknowledgements This work was supported by National Natural Science Foundation of China (Grant No. 51502024), Jiangsu Province Distinguished Professorship Endowment and Six Talent Summit Plan of Jiangsu Province (No. 2015XCL037). Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.actamat.2018.01.059 References [1] G.A. Slack, in: D.M. Rowe (Ed.), CRC Handbook of Thermoelectrics, CRC Press, Boca Raton, FL, USA, 1995. [2] J. Chen, X. Huang, Y. Zhu, P. Jiang, Cellulose nanofiber supported 3D interconnected BN nanosheets for epoxy nanocomposites with ultrahigh thermal management capability, Adv. Funct. Mater. 27 (2017) 1604754. [3] D. Suh, C.M. Moon, D. Kim, S. Baik, Ultrahigh thermal conductivity of interface materials by silver-functionalized carbon nanotube phonon conduits, Adv. Mater. 28 (2016) 7220e7227. [4] N.P. Padture, M. Gell, E.H. Jordan, Thermal barrier coatings for gas-turbine engine applications, Science 296 (2002) 280e284. [5] J.H. Perepezko, The hotter the engine, the better, Science 326 (2009) 1068e1069. [6] J. Shi, M.B. Starr, H. Xiang, Y. Hara, M.A. Anderson, J.-H. Seo, Z. Ma, X. Wang, Interface engineering by piezoelectric potential in ZnO-based photoelectrochemical anode, Nano Lett. 11 (2011) 5587e5593. [7] X.D. Wang, C.J. Summers, Z.L. Wang, Large-scale hexagonal-patterned growth of aligned ZnO nanorods for nano-optoelectronics and nanosensor arrays,

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