Grain size dependence of dielectric relaxation in cerium oxide as high-k layer
© Zhao et al.; licensee Springer. 2013
Received: 24 January 2013
Accepted: 27 March 2013
Published: 15 April 2013
Cerium oxide (CeO2) thin films used liquid injection atomic layer deposition (ALD) for deposition and ALD procedures were run at substrate temperatures of 150°C, 200°C, 250°C, 300°C, and 350°C, respectively. CeO2 were grown on n-Si(100) wafers. Variations in the grain sizes of the samples are governed by the deposition temperature and have been estimated using Scherrer analysis of the X-ray diffraction patterns. The changing grain size correlates with the changes seen in the Raman spectrum. Strong frequency dispersion is found in the capacitance-voltage measurement. Normalized dielectric constant measurement is quantitatively utilized to characterize the dielectric constant variation. The relationship extracted between grain size and dielectric relaxation for CeO2 suggests that tuning properties for improved frequency dispersion can be achieved by controlling the grain size, hence the strain at the nanoscale dimensions.
KeywordsCerium oxide High-k Grain size Dielectric relaxation
It is well known that the optical and electrical properties of CeO2 are highly dependent on the surface and interface structure, morphology, and chemistry , which in turn is controlled by the fabrication technique and growth conditions . The ability to tailor the properties so as to optimize performance requires a detailed understanding of the relationship between electronic and geometric structures, particularly at nanoscale dimensions, of CeO2. CeO2 readily crystallizes in the fluorite form, but control over the grain size formed is important due to the effect of grain boundary density on properties like ionic conductivity and dielectric response . Moreover, the intrinsic frequency dispersion (dielectric relaxation) studies [13, 14] have also been found to be relevant to grain size of the samples, especially those dealing with nanostructured materials.
In this paper, CeO2 is prepared by ALD under different deposition temperatures. The grain size of the samples is determined respectively by the fabrication technique and growth conditions. The focus of the present work is, therefore, on elucidating grain size effects on the electrical properties of CeO2. An interesting correlation between grain size and dielectric relaxation, which provides a reference to tailor the properties and performance of CeO2 as a high-k thin film, has been presented and discussed in the paper.
The CeO2 thin films were deposited by liquid injection ALD via a modified Aixtron AIX 200FE AVD reactor (Herzogenrath, Germany) fitted with a liquid injector system. The precursor was a 0.05-M solution of [Ce(mmp)4] (SAFC Hitech Ltd, Dorset, England, UK) in toluene , and the source of oxygen was deionized water. ALD procedures were run at substrate temperatures of 150°C, 200°C, 250°C, 300°C, and 350°C, respectively. The evaporator temperature was 100°C, and the reactor pressure was 1 mbar. The CeO2 thin films were grown on n-Si(100) wafers. Argon carrier gas flow was performed with 100 cm3/min. The flow of [Ce(mmp)4]/purge/H2O/purge was 2:2:0.5:3.5 s, and the number of growth cycles was 300.
For physical characterization, X-ray diffraction (XRD) was achieved using a Rigaku miniflex diffractometer (Shibuya-ku, Japan) with CuKα radiation (0.154051 nm, 40 kV, 50 mA), spanning a 2θ range of 20° to 50° at a scan rate of 0.01°/min. Raman spectra were obtained with a Jobin-Yvon LabRam HR consisting of a confocal microscope coupled to a single grating spectrometer equipped with a notch filter and a charge-coupled device camera detector. Raman measurements were performed using a confocal aperture of 300 μm to limit the light to improve the quality of signal. The measurements were spanned with 150 to 1,500/cm of four accumulations, and the exposure time was 30 s. All of the spectra were observed using an incident wavelength of 325 nm from a He-Cd laser. To determine the electrical characteristics of the CeO2 samples, capacitance-voltage (C-V) measurements were implemented using an Agilent E4980A precision LCR meter (Santa Clara, CA, USA). Gold contacts were deposited with an area of 4.5 × 10-4 cm2, and aluminum was deposited onto the backside of the silicon substrate.
Results and discussion
XRD diffraction patterns for the as-deposited CeO2 thin films at 150°C, 200°C, 250°C, 300°C, and 350°C, respectively, are shown in the inset of Figure 1. Diffraction scans with a slower scan speed were performed in the region of the peak to obtain full width at half-maximum data (the most distinct diffraction peak). XRD results show crystalline diffraction features for all deposition temperatures. The grain size value is obtained using the Scherrer formula  based on the XRD data (Figure 1). The measurements performed have the grain size changing from 6.14 nm for the 150°C sample to 23.62 nm for the 350°C sample. For the 200°C, 250°C, and 300°C samples, the grain sizes are 6.69, 8.83, and 15.86 nm, respectively. There is a clear trend that the grain size increases with increasing deposition temperatures. The proposed explanation is most likely due to the high deposition temperature contributing to the settling of the atoms to their lattice sites. Post-deposition annealing (PDA) was operated on the 250°C as-deposited samples in vacuum at 800°C for 5 min. Figure 2 shows the XRD diffraction patterns for the as-deposited and annealed samples, respectively. The grain size of the annealed sample (9.55 nm) is bigger than the original sample (8.83 nm), which suggested that PDA in vacuum causes an increase in the size of the crystalline grains. The same phenomenon is also observed in the 150°C as-deposited samples after PDA.
Raman spectra of the same CeO2 thin films deposited at five substrate temperatures (150°C, 200°C, 250°C, 300°C, and 350°C) are shown in Figure 3. The data show a distinct shift on the intensity axis following the increased deposition temperature. The first-order triply degenerate mode is the mode at approximately 465/cm associated with the fluorite crystal structure. The measurement presented confirms that the crystalline phase is cubic. A clear shift to a higher wave number together with a broadening of the band with decreasing temperature is observed. Decreased phonon lifetime with smaller grain size is the main reason for the broadening effect. The peak shift to a higher wave number is due to a releasing of the chemical bonds for smaller grain size at the lower deposition temperature. Comparing the five Raman spectra, their intensities relatively decrease as the grain size decreases . Consequently, Raman results are correlated to XRD data: Raman spectral data and XRD results share the same trend that larger grain sizes are formed as the deposition temperature increases.
C-V measurements are used to characterize frequency dispersion  and to obtain permittivity of the CeO2 thin films. A typical set of C-V characteristics of the as-deposited (dashed line) under different frequencies (100 Hz, 1 kHz, 10 kHz, 100 kHz, and 1 MHz) is shown in Figure 4 for the sample deposited at 250°C. C-V measurements are carried out from strong inversion (-1 V) toward strong accumulation (2 V). Noticeable frequency dispersion on C-V curves is observed. Frequency dispersion in C-V or capacitance-frequency measurements are categorized into two parts: extrinsic and intrinsic. Extrinsic frequency dispersion includes (1) parasitic effect, (2) lossy interfacial layer effect, (3) surface roughness effect, (4) polysilicon depletion effect, and (5) quantum mechanical effect. For part 1 of the extrinsic frequency dispersion, parasitic effects in MOS devices contain parasitic resistances and capacitances such as bulk series resistances, contacts (including contact between the MOS capacitor and probe station), cables, and many other parasitic effects. The parasitic effects can simply be minimized by using suitable cables and also by depositing an aluminum thin film at the back of a large-area silicon substrate. For the cerium oxide samples, the aluminum back contact and substrate area is approximately 2 × 2 cm2. Concerning part 2, the existence of extrinsic frequency dispersion in some high-k materials (LaAlO3) is mainly due to the effect of the lossy interfacial layer between the high-k thin film and silicon substrate on the MOS capacitor. Relative thicker thickness of the high-k thin film than the interfacial layer significantly prevented frequency dispersion. For the cerium oxide samples, the high-k thin film thicknesses for 150°C, 200°C, 250°C, 300°C, and 350°C are 51, 43, 50, 31, and 44 nm, respectively, from spectroscopic ellipsometry. The SiO2 interfacial layer thickness is approximately 1.6 nm, which leads to much larger capacitance than the high-k thin film. Thus, lossy interfacial layer effect is excluded for the cerium oxide samples. In terms of part 3, the surface roughness is not responsible for the observed extrinsic frequency dispersion of the high-k thin films used in the paper. With respect to part 4, the poly depletion effect will become more significant leading to reduced surface potential, channel current, and gate capacitance. However, the polysilicon depletion effect is not under consideration for the samples here because the gates of the MOS capacitor samples were Au-fabricated by thermal evaporation through a shadow mask. Finally, as regards part 5, for oxide thickness down towards 1 to 3 nm, the quantum mechanical effect should be taken into account. The cerium oxide samples are not suitable for the domain (greater than 30 nm at least). All in all, after taking into account all extrinsic causes of the frequency dispersion mentioned above, the intrinsic effect (dielectric relaxation) of the high-k dielectric thin films is proved to be the main impact factor for the C-V frequency dispersion observed in Figure 4. Similar observations are also seen in the rest of the as-deposited samples (deposition temperatures from 150°C to 350°C). At the frequency of 1 MHz, the capacitance is 300 pF in strong accumulation. Enhanced capacitance (1,420 pF) in strong accumulation at a frequency of 100 Hz is observed, which is more than four times the capacitance measured at 1 MHz. Moreover, it is found that the value of accumulation capacitance is inversely proportional to the frequency. The C-V measurements of the annealed samples (solid lines) are also shown in Figure 4. In contrast to the as-deposited high-k thin films, the annealed samples show a pronounced accumulation capacitance reduction, which is mainly due to the increased interfacial layer (IL). One kind of high-k materials were researched by our group before: La-doped ZrO2 films, with a thickness of 35 nm deposited on n-type Si(100) substrates by liquid injection ALD at 300°C . The 35-nm-thick La0.35Zr0.65O2 layers retained their thickness after PDA, but the IL (SiO x ) increased from 1.5 nm on the as-deposited samples to 4.5 nm after PDA at 900°C in N2, respectively, which is attributed to either an internal or external oxidation mechanism. As high-k layer is on the top of the IL, the capacitance of high-k layer is in series of the IL capacitance. When the thickness of the IL is increased, the capacitance of the IL is decreased, and it is no longer much larger than the high-k layer capacitance. Therefore, the total capacitance (including the capacitance of the high-k layer and the IL capacitance) is decreased significantly. Generally speaking, the most obvious effect of annealing is therefore to weaken the accumulation capacitance and hence reduce the k-value. Insignificant frequency dispersion is observed from 100 Hz to 1 MHz. The annealed capacitance of 100 Hz decreases by approximately 70% of the as-deposited sample. The accumulation capacitance value is 410 pF below 100 Hz. The capacitances from 1 kHz to 1 MHz are in the range of 180 to 240 pF.
In order to further investigate the frequency dispersion for CeO2, a normalized dielectric constant (to the dielectric constant at 100 Hz) is utilized to quantitatively characterize the dielectric constant variation. At the start, both as-deposited and annealed samples are used. Concerning the 250°C samples, the comparison between the as-deposited and annealed is given in Figure 5. It is observed that the dielectric relaxation for the as-deposited sample (triangle symbol) is much pronounced than that of the annealed one (square symbol). Within the range of various frequencies, the normalized k value of the as-deposited sample is lower. Obviously, the worst-case situation occurs at 1 MHz when the normalized dielectric constant is 0.11. It means that the k value is only 10% of the highest k value measured below 100 Hz. The conclusion is made from the data that the frequency dispersion for the CeO2 samples has been alleviated after annealing. From the analysis of Figure 2, the grain size for annealed samples is larger than the as-deposited one. It is easy to make an inference that grain size affects dielectric relaxation. The smaller grain size has a more intense dielectric relaxation. These findings are in good agreement with the theoretical and experimental studies proposed by Yu et al. , which reported the effect of grain size on the ferroelectric relaxor behavior in CaCu3TiO12 (CCTO) ceramics. Since its unusual dielectric properties were discovered in 2000, an ABO3-type perovskite material, CCTO, in which Ca2+ and Cu2+ share the A site, has attracted extensive attention. Many mechanisms have been proposed to interpret the nature of its giant dielectric response, and the frequency dispersion of the CCTO samples is found to be dependent on grain size. Thus, it is considered to be the supporting evidence of the cerium oxides. The response for the normalized dielectric constant values of CCTO over different frequencies (100 Hz and 1, 10, and 100 kHz) is extracted and shown in the inset of Figure 5. In the inset, the CCTO ceramics have different grain sizes (small, medium, and large). Strong frequency dispersion for all the samples with different grain sizes is related to the frequency-dependent boardening and shift of glasslike transition temperature. It is associated with the slowing down of dipolar fluctuations within the polar nanodomains. The dielectric relaxation for the small grain size sample is the worst case. The dielectric constant of 100 kHz is only 10% of the value below 100 Hz, which is similar to the as-deposited 250°C CeO2 sample. The medium-grain-size CCTO sample is superior to the small-grain-size sample within the range of various frequencies. Moreover, the large-grain-size sample performs better than the medium-sized one. The effect of grain size mainly originates from higher surface stress in smaller grain due to its higher concentration of grain boundaries. To illustrate this point, surface stress in the grains is high, medium, and low for the small-, medium-, and large-grain-size CCTO samples, respectively. As surface stress increases, the glasslike transition temperature decreases considerably. This is attributed to the enhancement of the correlations among the polar nanodomains. Ultimately, both frequency dispersion and relaxation strength, as typical characteristic of relaxor ferroelectrics, will increase when grain sizes decrease.
Figure 6 shows the normalized dielectric constants for all the as-deposited CeO2 samples under the different deposition temperatures (150°C, 200°C, 250°C, 300°C, and 350°C). It is known from the XRD (Figure 1, inset) and Raman spectra (Figure 3) that grain size increases as the deposition temperature increases. The relationship between the grain size value and the deposition temperature is shown as follows: 6.13 nm for 150°C, 6.69 nm for 200°C, 8.83 nm for 250°C, 15.85 nm for 300°C, and 23.62 nm for 350°C. Large dielectric relaxation is observed for the sample of 6.13 nm (diamond symbol). The minimum k value at 1 MHz is one third of the maximum value at 100 Hz. When the deposition temperature increases, the dielectric relaxation is even worse for the sample of 6.69 nm (square symbol). The k value variation is more significant across all the frequency range. In addition, the most severe dielectric relaxation is measured for the sample of 8.83 nm (star symbol). The worst situation is that the k value calculated at 1 MHz is only 10% of the k value below 100 Hz. Also, from the preceding figure, the normalized dielectric constants are the smallest for all of the frequencies, which means that the dielectric constant makes the most significant value drop within the region of different frequencies for the sample of 8.83 nm. The sample of 15.85 nm (triangle symbol) has significant improvement on dielectric relaxation. The k value variation from 100 Hz to 1 MHz is narrowed accordingly. The sample of 23.62 nm (round symbol) shows a more stable frequency response. As a consequence, it is not always true for the inference we made earlier: the smaller grain size has a larger dielectric relaxation (the sample of 8.83 nm has the worst dielectric relaxation, but 8.83 nm is not the smallest grain size value among all the samples). Nevertheless, if a comparison is made between samples of 6.13 nm (the smallest) and 23.62 nm (the largest), the larger-grain-size sample is shown to have better dielectric relaxation performance. It is also consistent with our previous experimental results . However, the trade-off for the 23.62-nm sample is that the dielectric constant is smaller than the 6.13-nm sample. Especially in terms of the dielectric constant, on 100 Hz, the dielectric constant for the 23.62-nm sample is only half of the value for the 6.13-nm sample. Moreover, in 1 MHz, the dielectric constant for the 23.62-nm sample is two thirds that of the value for the 6.13-nm sample. Thus, the 23.62-nm samples perform best at the expense of the dielectric constant. Similarly, the effect of grain size on dielectric relaxation is found on the Nd-doped Pb1-3x/2Nd x (Zr0.65Ti0.35)O3 composition (PNZT) , where x = 0.00, 0.01, 0.03, 0.05, 0.07, and 0.09, respectively. Lead-based perovskite ferroelectric ceramics are widely applied in multilayer capacitors, microelectromechanical systems, and integrated devices such as ferroelectric memories, infrared sensors, microactuators, etc. Moreover, lead zirconium titanate is one of the best lead-based materials that have been studied extensively recently. The PNZT samples were fabricated according to the A-site vacancy formula and were prepared by the traditional mixed-oxide solid-state reaction method. The grain size decreases as Nd doping (x) increases. The normalized dielectric constant vs. frequency is extracted and shown in the inset of Figure 6. Strong frequency dispersion is observed for all of the samples. It is clear that the deteriorative degree of dielectric relaxation increases from 12.1 nm, reaches the peak at 22.5 nm, and then declines. A comparison between the samples of 12.1 and 25 nm is made. Uniformly, the sample with the grain size of 25 nm is shown to perform superior on dielectric relaxation. The dielectric constant frequency response of the PNZT samples shares exactly the same response for the CeO2 samples (one dielectric relaxation peak within the frequency range). A possible reason  to the cited observation could be the broadened dielectric peak and the transition temperature shift. The dielectric constant shows phase transition as expected for normal ferroelectrics. The region around the dielectric peak is broadened, which is one of the most important characteristics of disordered perovskite structure with the diffuse phase transition. The transition temperature is found to shift forward to lower temperature with the grain size from 12.1 to 22.5 nm, while the transition temperature remains at the same position with further increasing grain size. Concerning the strong frequency dispersion, it is mainly attributed to the low-frequency space charge accumulation effect. Such strong frequency dispersion in dielectric constant appears to be a common feature in ferroelectrics associated with non-negligible ionic conductivity. Therefore, the reason for the dielectric relaxation of the PNZT samples could be the possible mechanism behind the frequency dependence of the k value of the CeO2 samples.
where Ea is the activation energy of ion transport over the entire temperature range, T is a characteristic temperature corresponding to the freezing temperature of the material within VFT approach, k is the Boltzmann constant, and A is approximately a constant. The origin of the VFT law is the increase of the range of elastic interaction between local relaxation events. The transition of glass-forming materials on lowering the temperature may appear conceptually simple, yet this phenomenon has turned out to be one of the most difficult and controversial problems in condensed matter physics, the problem of the glass transition. At high temperature, relaxation time τ follows an Arrhenius dependence. Upon lowering the temperature, τ almost universally deviates from an Arrhenius dependence and follows the VFT law. Through the VFT law, the activation energy Ea and the freezing temperature T can be obtained. Tau τ is probably determined by the as-deposited temperature. So, the related activation and freezing temperature could be calculated afterwards. The cause of distribution of the relaxation times has been associated with certain particular factors, e.g., the suggestion made by Kliem and Arlt  concerning the occurrence of protonic resonance and Cabeza et al.  concerning the porosity effect. Equally, dielectric relaxation of the PNZT samples can be modeled by the CD law as well. The inset of Figure 7 shows the relationship between the CD fitting parameters (beta and tau) and the grain size value likewise. The trend of beta rises from 12.1 nm, peaks at 22.5 nm with the beta value of 0.03, and then glides back downwards within the range of 22.5 to 25 nm. The beta value is therefore shown to represent the deteriorative degree of dielectric relaxation. In the same manner, the trend of tau decreases from 12.1 to 25 nm. The trend of beta and tau for the PNZT samples is similar to the trends observed for the CeO2 samples.
The ALD CeO2 samples were grown as crystalline thin films for a range of substrate temperatures within the ALD growth window of the Ce[mmp]4 precursor, with water as an oxidant. XRD and Raman spectra show an increase in grain size for increasing growth temperatures. From the C-V measurement of the samples, strong frequency dispersion is observed. In order to further investigate the dielectric relaxation, the normalized dielectric constant is utilized for the CeO2 samples of different grain sizes. The CeO2 samples have better dielectric relaxation behavior after annealing since the annealed samples have a larger grain size. Within the grain size range of the CeO2 samples (6.13 to 23.62 nm), the most serious frequency dependence of the k value is found in the sample of thickness 8.83 nm. A similar relationship between grain size and dielectric relaxation is also observed in CCTO and Nd-doped PNZT samples. The mechanism of grain size effects is attributed to the alignment enhancement of the polar nanodomains.
CZ is a PhD student in the University of Liverpool. CZZ is a professor in Xi'an Jiaotong-Liverpool University. MW is a research associate in the University of Liverpool. ST and PC are professors in the University of Liverpool. PK is a research fellow in the University of Liverpool.
This research was funded in part by the Engineering and Physical Science Research Council of UK under the grant EP/D068606/1, the National Natural and Science Foundation of China under grant no. 60976075, and the Suzhou Science and Technology Bureau of China under grant SYG201007.
- Aspinall HC, Bacsa J, Jones AC, Wrench JS, Black K, Chalker PR, King PJ, Marshall P, Werner M, Davies HO, Odedra R: Ce(IV) complexes with donor-functionalized alkoxide ligands: improved precursors for chemical vapor deposition of CeO2. Inorg Chem 2011, 50: 11644–11652. 10.1021/ic201593sView ArticleGoogle Scholar
- Phokha S, Pinitsoontorn S, Chirawatkul P, Poo-arporn Y, Maensiri S: Synthesis, characterization, and magnetic properties of monodisperse CeO2 nanospheres prepared by PVP-assisted hydrothermal method. Nanoscale Res Lett 2012, 7: 425. 10.1186/1556-276X-7-425View ArticleGoogle Scholar
- Fukuda H, Miura M, Sakuma S, Nomura S: Structural and electrical properties of crystalline CeO2 films formed by metaorganic decomposition. Jpn J Appl Phys 1998, 37: 4158–4159. 10.1143/JJAP.37.4158View ArticleGoogle Scholar
- Santha NI, Sebastian MT, Mohanan P, Alford NM, Sarma K, Pullar RC, Kamba S, Pashkin A, Samukhina P, Petzelt J: Effect of doping on the dielectric properties of cerium oxide in the microwave and far-infrared frequency range. J Am Ceram Soc 2004, 87: 1233–1237. 10.1111/j.1151-2916.2004.tb07717_33.xView ArticleGoogle Scholar
- Nishikawa Y, Fukushima N, Yasuda N, Nakayama K, Ikegawa S: Electrical properties of single crystalline CeO2 high-k gate dielectrics directly grown on Si (111). Jpn J Appl Phys 2002, 41: 2480–2483. 10.1143/JJAP.41.2480View ArticleGoogle Scholar
- Tanvir S, Qiao L: Surface tension of nano fluid-type fuels containing suspended nanomaterials. Nanoscale Res Lett 2012, 7: 226. 10.1186/1556-276X-7-226View ArticleGoogle Scholar
- Jacqueline S, Black WK, Aspinall HC, Jones AC, Bacsa J, Chalker PR, King PJ, Werner M, Davies HO, Heys PN: MOCVD and ALD of CeO2 thin films using a novel monomeric CeIV alkoxide precursor. Chem Vap Deposition 2009, 15: 259–261.Google Scholar
- Zhao C, Zhao CZ, Tao J, Werner M, Taylor S, Chalker PR: Dielectric relaxation of lanthanide-based ternary oxides: physical and mathematical models. J Nanomat 2012, 2012: 241470.Google Scholar
- King PJ, Werner M, Chalker PR, Jones AC, Aspinall HC, Basca J, Wrench JS, Black K, Davies HO, Heys PN: Effect of deposition temperature on the properties of CeO2 films grown by atomic layer deposition. Thin Solid Films 2011, 519: 4192–4195. 10.1016/j.tsf.2011.02.025View ArticleGoogle Scholar
- Yamamoto T, Momida H, Hamada T, Uda T, Ohno T: First-principles study of dielectric properties of cerium oxide. Thin Solid Films 2005, 486: 136–140. 10.1016/j.tsf.2004.11.240View ArticleGoogle Scholar
- Tye L, ElMasry NA, Chikyow T, McLarty P, Bedair SM: Electrical characteristics of epitaxial CeO2 on Si(111). Appl Phys Lett 1994, 65: 3081. 10.1063/1.112467View ArticleGoogle Scholar
- Xia T, Kovochich M, Liong M, Madler L, Gilbert B, Shi H, Yeh JI, Nel AE: Comparison of the mechanism of toxicity of zinc oxide and cerium oxide nanoparticles based on dissolution and oxidative stress properties. ACS Nano 2008, 2: 2121–2134. 10.1021/nn800511kView ArticleGoogle Scholar
- Zhao CZ, Taylor S, Werner M, Chalker PR, Murray RT, Gaskell JM, Jones AC: Dielectric relaxation of lanthanum doped zirconium oxide. J Appl Phys 2009, 105: 044102. 10.1063/1.3078038View ArticleGoogle Scholar
- Zhao CZ, Werner M, Taylor S, Chalker PR, Jones AC, Zhao C: Dielectric relaxation of La-doped zirconia caused by annealing ambient. Nanoscale Res Lett 2011, 6: 48.Google Scholar
- Scherrer P: Estimation of the size and internal structure of colloidal particles by means of Rontgen. Gott Nachr 1918, 2: 98–100.Google Scholar
- Choi HC, Jung YM, Kim SB: Size effects in the Raman spectra of TiO2 nanoparticles. Vibra Spectro 2005, 37: 33–38. 10.1016/j.vibspec.2004.05.006View ArticleGoogle Scholar
- Tao J, Zhao CZ, Zhao C, Taechakumput P, Werner M, Taylor S, Chalker PR: Extrinsic and intrinsic frequency dispersion of high- k materials in capacitance-voltage measurements. Materials 2012, 5: 1005–1032. 10.3390/ma5061005View ArticleGoogle Scholar
- Yu HT, Liu HX, Hao H, Guo LL, Jin CJ: Grain size dependence of relaxor behavior in CaCu3Ti4O12 ceramics. Appl Phys Lett 2007, 91: 222911. 10.1063/1.2820446View ArticleGoogle Scholar
- Mohiddon MA, Kumar A, Yadav KL: Effect of Nd doping on structural, dielectric and thermodynamic properties of PZT (65/35) ceramic. Physica B 2007, 395: 1–9. 10.1016/j.physb.2006.09.022View ArticleGoogle Scholar
- Dotson TC, Budzien J, McCoy JD, Adolf DB: Cole-Davidson dynamics of simple chain models. J Chem Phys 2009, 130: 024903. 10.1063/1.3050105View ArticleGoogle Scholar
- Davidson DW, Cole RH: Dielectric relaxation in glycerol, propylene glycol and n-propanol. J Chem Phys 1951, 19: 1484–1490. 10.1063/1.1748105View ArticleGoogle Scholar
- Davidson DW, Cole RH: Dielectric relaxation in glycerine. J Chem Phys 1950, 18: 1417.View ArticleGoogle Scholar
- Ngai KL, McKenna GB, McMillan PF, Martin S: Relaxation in glass forming liquids and amorphous solids. J Appl Phys 2000, 88: 3113–3157. 10.1063/1.1286035View ArticleGoogle Scholar
- Kliem H, Arlt G: A relation between dielectric distribution functions and structural properties of amorphous matter. CEIDP Annu Rep 1987, 56: 325.Google Scholar
- Cabeza M, Keddam M, Novoa XR, Sanchez I, Takenouti H: Impedance spectroscopy to characterize the pore structure during the hardening process of Portland cement paste. Electrochim Acta 2006, 51: 1831–1841. 10.1016/j.electacta.2005.02.125View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.