Skip to main content

Dielectric relaxation of high-k oxides


Frequency dispersion of high-k dielectrics was observed and classified into two parts: extrinsic cause and intrinsic cause. Frequency dependence of dielectric constant (dielectric relaxation), that is the intrinsic frequency dispersion, could not be characterized before considering the effects of extrinsic frequency dispersion. Several mathematical models were discussed to describe the dielectric relaxation of high-k dielectrics. For the physical mechanism, dielectric relaxation was found to be related to the degree of polarization, which depended on the structure of the high-k material. It was attributed to the enhancement of the correlations among polar nanodomain. The effect of grain size for the high-k materials' structure mainly originated from higher surface stress in smaller grain due to its higher concentration of grain boundary.



As the thickness of SiO2 gate dielectric films used in complementary metal oxide semiconductor (CMOS) devices is reduced toward 1 nm, the gate leakage current level becomes unacceptable [14]. Extensive efforts have been focused on finding alternative gate dielectrics for future technologies to overcome leakage problems [57]. Oxide materials with large dielectric constants (so-called high-k dielectrics) have attracted much attention due to their potential use as gate dielectrics in metal-oxide-semiconductor field-effect transistor (MOSFETs) [812]. Thicker equivalent oxide thickness, to reduce the leakage current of gate oxides, is obtained by introducing the high-k dielectric to real application [1315].

There are a number of high-k dielectrics that have been actively pursued to replace SiO2. Among them are cerium oxide CeO2[1623], cerium zirconate CeZrO4[24], gadolinium oxide Gd2O3[2527], erbium oxide Er2O3[28, 29], neodymium oxide Nd2O3[30, 31], aluminum oxide Al2O3[32, 33], lanthanum aluminum oxide LaAlO3[34, 35], lanthanum oxide La2O3[36], yttrium oxide Y2O3[37], tantalum pentoxide Ta2O5[38], titanium dioxide TiO2[39], zirconium dioxide ZrO2[40, 41], lanthanum-doped zirconium oxide La x Zr1−xO2−δ[42, 43], hafnium oxide HfO2[44], HfO2-based oxides La2Hf2O7[45], Ce x Hf 1-x O 2 [46], hafnium silicate HfSi x O y [47], and rare-earth scandates LaScO3[48], GdScO3[49], DyScO3[50], and SmScO3[51]. Among them, HfO2, HfO2-based materials, ZrO2, and ZrO2-based materials are considered as the most promising candidates combining high dielectric permittivity and thermal stability with low leakage current due to a reasonably high barrier height that limits electron tunneling. CeO2 is also proposed to be a possible gate dielectric material, because CeO2 has high dielectric constant. CeO2 has successfully been added to HfO2 in order to stabilize the high-k cubic and tetragonal phases. Consequently, La x Zr1−xO2−δ, La2Hf2O7, Ce x Hf1−xO2, and CeO2 have received lots of attention for promising high-k gate dielectric materials for potential applications in sub-32-nm node CMOS devices.

Since dielectric relaxation and associated losses impaired MOSFET performance, the larger dielectric relaxation of most high-k dielectrics compared with SiO2 was a significant issue for their use [5257]. However, there is insufficient information about dielectric relaxation of high-k thin films, which prompts us to investigate the phenomenon and the underlying mechanism. In this paper, the dielectric relaxation of the high-k dielectric was reviewed. The extrinsic causes of frequency dispersion during C-V measurement were studied before validating dielectric relaxation. In order to describe dielectric relaxation, many mathematic models were proposed. After mathematical models were finalized for fitting experimental data, physical mechanisms of dielectric relaxation were under investigation. Dielectric relaxation behaviors observed in the high-k dielectrics were partly due to the level of stress in the crystalline grains, depending on the grain size, analogous to the behavior of ferroelectric ceramics. As surface stress changes, glasslike transition temperature varied considerably. Dielectric relaxation appears to be a common feature in ferroelectrics associated with non-negligible ionic conductivity.


Sample preparation

HfO2, ZrO2, and LaAlO3 thin films were deposited on n-type Si(100) substrates using liquid injection metal organic chemical vapor deposition (MOCVD) or atomic layer deposition (ALD), carried out on a modified Aixtron AIX 200FE AVD reactor (Herzogenrath, Germany) fitted with the “Trijet”™ liquid injector system. During the MOCVD experiments, oxygen was introduced at the inlet of the reactor. For the ALD experiments, the oxygen was replaced by water vapor, which was controlled by a pneumatic valve. The substrate was rotated throughout all experiments for good uniformity. Auger electron spectroscopy (AES) results suggested they are stoichiometric films. All the high-k dielectric layers considered were 16 nm in thickness.

La x Zr1−xO2−δ thin films were deposited onto n-type Si(100) wafers by the same modified Aixtron AIX 200FE AVD reactor liquid injection ALD at 300°C. Both Zr and La sources were Cp-based precursors ([(MeCp)2ZrMe(OMe)] and [(iPrCp)3La]). The La concentration was varied in different films. Particular attention has been given to the results from films with a La concentration of x = 0.09 (55 nm) and x = 0.35 (35 nm) but results are also included from films with a concentration of x = 0.22 (50 nm) and x = 0, i.e., un-doped ZrO2 (35 nm). Post deposition annealing was performed at 900°C in a pure N2 ambient for 15 min. To form MOS capacitors (Au/La x Zr1−xO2/IL/n-Si, where IL stands for interfacial layer), metal (Au) gate electrodes with an effective contact area of 4.9 × 10−4 cm2 were evaporated onto the samples. The backsides of the Si samples were cleaned with a buffered HF solution and subsequently a 200-nm-thick film of Al was deposited by thermal evaporation to form an ohmic back contact.

La2Hf2O7 thin films were deposited on n-type Si(100) substrates by the same liquid injection ALD at 300°C. Both Hf and La sources are Cp-based precursors ([(MeCp)2HfMe(OMe)] and [(iPrCp)3La]). The composition of the La-doped HfO2 thin films was estimated to be La2Hf2O7. Selected thin films were subjected to 900°C post-deposition annealing (PDA) in N2 for 15 min.

Amorphous Ce x Hf1−xO2 thin films (x = 0.1) were deposited on n-type Si(100) substrates using the same liquid injection ALD. The doping level was varied up to a concentration level of 63%, i.e., x = 0.63. The interfacial layer between high-k thin film and silicon substrate is approximately 1-nm native SiO2. Samples were then annealed at 900°C for 15 min in an N2 ambient to crystallize the thin films.

CeO2 thin films used the same liquid injection ALD for deposition. The precursor was a 0.05 M solution of [Ce(mmp)4] in toluene and a source of oxygen was deionized water. ALD procedures were run at substrate temperatures of 150, 200, 250, 300, and 350°C, respectively. The evaporator temperature was 100°C and reactor pressure was 1 mbar. CeO2 films were grown on n-Si (100) wafers. Argon carrier gas flow was performed with 100 cm3 · min−1. 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, which is important in order to achieve high reproducibility of film growth and precise control of film thickness by the number of deposition cycles. The thicknesses for the samples are within 56 nm to 98 nm. Post deposition annealing (PDA) was operated on the 250°C as-deposited samples in vacuum at 800°C for 15 min.

Material characterization

The physical properties of the high-k thin films were studied using X-ray diffraction (XRD) and cross-sectional transmission electron microscopy (XTEM). Electrical properties of the films were obtained by capacitance-voltage (C-V) and capacitance-frequency (C-f).

XRD were operated using a Rigaku Miniflex diffractometer (Beijing, China) 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.

Atomic force microscopy (AFM) was used to investigate variations in surface morphology of these films, and was carried out using a Digital Instruments Nanoscope III, in contact mode.

AES was used to determine the atomic composition of the thin films, which was carried out using a Varian scanning Auger spectrometer (Palo Alto, CA, USA). The atomic compositions are from the bulk of the thin film, free from surface contamination, and were obtained by combining AES with sequential argon ion bombardment until comparable compositions were obtained for consecutive data points.

XTEM was used to obtain the film thickness and information about the crystal grain size. A JEOL 3010 or a JEOL 2000FX (Akishima-shi, Japan) operated at 300 and 200 keV, respectively, was used.

C-V measurements were implemented using an Agilent E4980A precision LCR meter (Santa Clara, CA, USA). C-V measurements were performed in parallel mode, from strong inversion toward strong accumulation (and vice versa), at frequencies ranging from 20 Hz to 2 MHz. C-f measurements were carried out in a strong accumulation region.

Results and discussion

Extrinsic frequency dispersion

Frequency dispersion was categorized into two parts: extrinsic causes and intrinsic causes. The extrinsic causes of frequency dispersion during C-V measurement in high-k thin film (shown in Figure 1), which were studied before validating the effects of k-value dependence, were parasitic effect, lossy interfacial layer, and surface roughness [56]. Two further potential extrinsic causes: polysilicon depletion effect [5860] and quantum mechanical confinement [6163], for frequency dispersion were negligible if the thickness of the high-k thin film is high enough. Polysilicon depletion effects were not considered due to the implementation of metal gate. Existing causes of extrinsic frequency dispersion during C-V measurement in the high-k thin film were the parasitic effect (including back contact imperfection resistance R S and capacitance C S , cables resistance R S and capacitance C S , substrate series resistance R S , and depletion layer capacitance of silicon C D ) and the lossy interfacial layer effect (interfacial layer capacitance C i and conductance G i ). Surface roughness effect and polysilicon depletion effect were included, where high-k capacitance C h , high-k conductance G h , the lossy interfacial layer capacitance C i and conductance G i were given. The oxide capacitance C ox consisted of the high-k capacitance C h and the lossy interfacial layer capacitance C i .

Figure 1
figure 1

Causes of frequency dispersion during C-V measurement in the MOS capacitor with high- k dielectric [[56]].

Parasitic effects in MOS devices included parasitic resistances and capacitances such as bulk series resistances, series contact, cables, and many other parasitic effects [6467]. However, only two of them which had influential importance are listed as follows: (1) the series resistance R S of the quasi-neutral silicon bulk between the back contact and the depletion layer edge at the silicon surface underneath the gate; and (2) the imperfect contact of the back of the silicon wafer. Dispersion could be avoided by depositing an Al thin film at the back of the silicon substrate. The correction models were able to minimize the dispersion as well. Then, it has been demonstrated that once the parasitic components are taken into account, it was possible to determine the true capacitance values free from errors.

The existence of frequency dispersion in the LaAlO3 sample was discussed in the previous work [68], which was mainly due to the effect of the lossy interfacial layer between the high-k thin film and silicon substrate on the MOS capacitor. The frequency dispersion effect was significant even with the Al back contact and the bigger substrate area. In this case, C h (CET = 2.7 nm) was comparable with C i (approximately 1-nm native SiO2) and the frequency dispersion effect was attributed to losses in the interfacial layer capacitance, caused by interfacial dislocation and intrinsic differences in the bonding coordination across the chemically abrupt ZrO2/SiO2 interface. Relative thicker thickness of the high-k thin film than the interfacial layer significantly prevented frequency dispersion. Also, extracted C-V curves were reconstructed by a four-element circuit model for high-k stacks, adapted from a dual frequency technique [69], with the capacitance value reconstructed from the loss.

Frequency dispersion from the effect of surface roughness was best demonstrated in an ultra-thin SiO2 MOS device [70]. To investigate whether the unwanted frequency dispersion of the high-k materials (La x Zr1−xO2 δ) was caused by the surface roughness or not, the surface properties of the La x Zr1−xO2−δ thin films was studied using AFM [52]. The root mean square (RMS) roughness of the x = 0.35 thin film was 0.64 nm after annealing. However, no significant roughness was observed for the x = 0.09 thin film (RMS roughness of 0.3 nm). It means that the x = 0.35 thin film had more surface roughness than the x = 0.09 thin film. The annealed thin film with x = 0.09 had large frequency dispersion. However, the annealed thin film with x = 0.35 showed small frequency dispersion. By comparing these results from the C-V measurements, it has led to the conclusion that the surface roughness was not responsible for the observed frequency dispersion of the high-k dielectric thin films (La x Zr1−xO2−δ).

Intrinsic frequency dispersion: mathematic models

After careful considerations of the above extrinsic causes for frequency dispersion, high-k capacitance C h was determined. A is the area of the MOS capacitance and t h is the thickness of the high-k oxides. Via the equation below, dielectric constant (k) was able to be extracted from the high-k capacitance.

C h = Ak ϵ 0 t h

Frequency dispersion can now solely be associated with the frequency dependence of the k-value. The frequency dependence of the k value can be extracted as shown in Figure 2. The figure showed no frequency dependence of the k value in LaAlO3/SiO2, ZrO2/SiO2 and SiO2 stacks [56]. However, the frequency dependence of the k-value was observed in La x Zr 1–x O2/SiO2 stacks [52]. The zirconium thin film with a lanthanum (La) concentration of x = 0.09 showed a sharp decreased k-value and suffered from a severe dielectric relaxation. A k value of 39 was obtained at 100 Hz, but this value was reduced to a k value of 19 at 1 MHz. The 10% Ce-doped hafnium thin film [55] also had a k value change from 33 at 100 Hz to 21 at 1 MHz. In order to interpret intrinsic frequency dispersion, many dielectric relaxation models were proposed in terms with frequency dependence of k value.

Figure 2
figure 2

Frequency dependence of k value extracted from C- f measurements in the MOS capacitors with high- k dielectrics [[52],[55],[56]].

In 1889, the Curie-von Schweidler (CS) law was firstly announced and developed later in 1907 [71, 72]. The general type of dielectric relaxation in time domain can be described by the CS law (the t−n behavior, 0 ≤ n ≤ 1).

dP t dt t n ,

where P(t) represented the polarization and the exponent n indicated the degree of dielectric relaxation. After a Fourier transform, the complex susceptibility CS relation is:

χ CS = A n 1 ,

where A and n were the relaxation parameters, ϵ was the high frequency limit of the permittivity, χ CS = [ϵ CS × (ω) − ϵ ]/(ϵ s  − ϵ ) was the dielectric susceptibility related to the CS law. The value of the exponent (n) indicated the degree of dielectric relaxation. The exponent values n was a weak dependence of the permittivity on frequency. An n − 1 value of zero would indicate that the dielectric permittivity was frequency independent. The majority of the model was based on the presence of compositional or structural inhomogeneities and body effects.

In 1929, Debye described a model for the response of electric dipoles in an alternating electric field [73]. In time domain, the response of the polarization is:

dP t dt = P t τ
P t = P 0 exp t τ

Unlike the CS law of power law, Debye law was an equation of exponential. As two main branches in the development of dielectric relaxation modeling, the CS and Debye are the origins along the evolution beyond doubt. The Debye model led to a description for the complex dielectric constant ϵ*. An empirical expression, which originated from the Debye law, was proposed by Kohlrausch, Williams, and Watts, which is a stretched exponential function, to be referred to later as the Kohlrausch-Williams-Watts (KWW) function widely used to describe the relaxation behavior of glass-forming liquids and other complex systems [7476]. The equivalent of the dielectric response function in time domain is

P t = P 0 exp t τ β KWW

After a Fourier transform, the Debye equation in the frequency domain and its real and imaginary parts are

ϵ * ω = ϵ + ϵ s ϵ 1 + iωτ
ϵ ' ω = ϵ + ϵ s ϵ 1 + ω 2 τ 2
ϵ ' ' ω ϵ s ϵ ωτ 1 + ω 2 τ 2

where τ was called the relaxation time which was a function of temperature and it was independent of the time angular frequency ω = 2πf. ϵ s was also defined as the zero-frequency limit of the real part, ϵ’, of the complex permittivity. ϵ was the dielectric constant at ultra-high frequency. Finally, ϵ’ was the k value.

The Debye theory assumed that the molecules were spherical in shape and dipoles were independent in their response to the alternating field with only one relaxation time. Generally, the Debye theory of dielectric relaxation was utilized for particular types of polar gases and dilute solutions of polar liquids and polar solids. However, the dipoles for a majority of materials were more likely to be interactive and dependent in their response to the alternating field. Therefore, very few materials completely agreed with the Debye equation which had only one relaxation time.

Since the Debye expression cannot properly predict the behavior of some liquids and solids such as chlorinated diphenyl at −25°C and cyclohexanone at −70°C, in 1941, Cole K.S. and Cole R.H. proposed an improved Debye equation, known as the Cole-Cole equation, to interpret data observed on various dielectrics [77]. The Cole-Cole equation can be represented by ϵ*(ω):

ϵ * ω = ϵ + ϵ s ϵ 1 + iωτ 1 α ,

where τ was the relaxation time and α was a constant for a given material, having a value 0 ≤ α ≤ 1. α = 0 for Debye relaxation. The real and imaginary parts of the Cole-Cole equation are

ϵ ' ω = ϵ + ϵ s ϵ 1 + ωτ 1 α sin 1 2 απ 1 + 2 ωτ 1 α sin 1 2 απ + ωτ 2 1 α
ϵ ' ' ω = ϵ s ϵ 1 + ωτ 1 α cos 1 2 απ 1 + 2 ωτ 1 α sin 1 2 απ + ωτ 2 1 α

Ten years later, in 1951, Davidson et al. proposed the following expression (Cole-Davidson equation) to interpret data observed on propylene glycol and glycerol [7881] based on the Debye expression:

ϵ * ω = ϵ + ϵ s ϵ 1 + iωτ β ,

where τ was the relaxation time and β was a constant for a given material. 0 ≤ β ≤ 1 which controlled the width of the distribution and β = 1 for Debye relaxation. The smaller the value of β, the larger the distribution of relaxation times. The real and imaginary parts of the Cole-Davidson equation are given by

ϵ ' ω = ϵ + ϵ s ϵ cos φ β cos βφ
ϵ ' ' ω = ϵ s ϵ cos φ β sin βφ
φ = tan 1 ωτ

Both the Cole-Cole and Cole-Davidson equations were empirical and could be considered to be the consequence of the existence of a distribution of relaxation times rather than that of the single relaxation time (Debye equation). After 15 years, in 1966, S. Havriliak and S. J. Negami reported the Havriliak-Negami (HN) equation which combined the Cole-Cole and Cole-Davidson equations for 21 polymers [8284]. The HN equation is

ϵ * ω = ϵ + ϵ s ϵ 1 + iωτ 1 α β

The real and imaginary parts of the HN equation are given by

ϵ ' ω = ϵ + ϵ s ϵ cos βΦ 1 + 2 ωτ 1 α sin πα 2 + ωτ 2 1 α β 2
ϵ ' ' ω = ϵ s ϵ sin βΦ 1 + 2 ωτ 1 α sin πα 2 + ωτ 2 1 α β 2
Φ = tan 1 ωτ 1 α cos 1 2 πα 1 + ωτ 1 α sin 1 2 πα

where α and β were the two adjustable fitting parameters. α was related to the width of the loss peak and β controlled the asymmetry of the loss peak. In this model, parameters α and β could both vary between 0 and 1. The Debye dielectric relaxation model with a single relaxation time from α = 0 and β = 1, the Cole-Cole model with symmetric distribution of relaxation times followed for β = 1 and 0 ≤ α ≤ 1, and the Cole-Davidson model with an asymmetric distribution of relaxation times follows for α = 0 and 0 ≤ β ≤ 1. The HN equation had two distribution parameters α and β but Cole-Cole and Cole-Davidson equations had only one. HN model in the frequency domain can accurately describe the dynamic mechanical behavior of polymers, including the height, width, position, and shape of the loss peak. The evolution map for Debye, Cole-Cole, Cole-Davidson, and HN model is shown in Figure 3.

Figure 3
figure 3

Evolution map for Debye, Cole-Cole, Cole-Davidson, and HN model.

A theoretical description of the slow relaxation in complex condensed systems is still a topic of active research despite the great effort made in recent years. There exist two alternative approaches to the interpretation of dielectric relaxation: the parallel and series models [54]. The parallel model represents the classical relaxation of a large assembly of individual relaxing entities such as dipoles, each of which relaxes with an exponential probability in time but has a different relaxation time. The total relaxation process corresponds to a summation over the available modes, given a frequency domain response function, which can be approximated by the HN relationship.

The alternative approach is the series model, which can be used to describe briefly the origins of the CS law. Consider a system divided into two interacting sub-systems. The first of these responds rapidly to a stimulus generating a change in the interaction which, in turn, causes a much slower response of the second sub-system. The state of the total system then corresponds to the excited first system together with the un-responded second system and can be considered as a transient or meta-stable state, which slowly decays as the second system responds.

In some complex condensed systems, neither the pure parallel nor the pure series approach is accepted and instead interpolates smoothly between these extremes. For the final fitting of the frequency domain response, the frequency dependence of complex permittivity ϵ*(ω) can be combined with the CS law and the modified Debye law (HN law) [52]:

ϵ * ω = ϵ + χ CS * ω + χ HN * ω i σ DC ω ϵ S
χ CS * ω = A n 1
χ HN * ω = ϵ s ϵ 1 + iωτ 1 α β

where ϵ was the high-frequency limit permittivity, ϵs is the permittivity of free space, σDC is the DC conductivity. The parameters in the equation are in the form of physical meanings (activation energy: EA):

τ = τ 0 exp E A , τ k T T τ
σ DC = σ 0 exp E A , σ k T T σ
α = α 0 exp E A , α k T T α
β = β 0 exp E A , β k T T β
n = n 0 exp E A , n k T T n

The HN law was a modified Debye equation via evolution. Thus, the CS and HN laws in the time domain represented the original power-law and exponential dependence, respectively. Most of dielectric relaxation data were able to be modeled by the final fitting law: the combined CS + HN laws.

Based on the discussion above, the dielectric relaxation results of La0.35Zr0.65O2 for the as-deposited and PDA samples (shown in Figure 4) have been modeled with the CS and/or HN relationships (see solid lines in Figure 4) [54]. The relaxation of the as-deposited film obeyed a combined CS + HN law. After the 900°C PDA, the relaxation behavior of the N2-annealed film was dominated by the CS law, whereas the air-annealed film was predominantly modeled by the HN relationship that was accompanied by a sharp drop in the k value.

Figure 4
figure 4

Dielectric relaxation results of as-deposited and annealed La 0.35 Zr 0.65 O 2 samples [[54]].

The frequency-dependent change in the real and imaginary permittivity of La2Hf2O7 dielectric for the as-deposited and PDA samples is shown in Figure 5[53]. Clearly, the PDA process improved the dielectric relaxation and reduced the dielectric loss. The dielectric relaxation of the PDA films was revealed to be dominated mainly by the CS law (n = 0.9945, see two dot lines in Figure 5) at f < 3 × 104 Hz. However, at f > 3 × 104 Hz, the HN law plays an important role (α = 0.08, β = 0.45, and τ = 1 × 10−8 s, see two solid lines in Figure 5). The dielectric loss reduces at f < 3 × 104 Hz because an increase of the interfacial layer thickness caused the reduction of the DC conductivity.

Figure 5
figure 5

Dielectric relaxation results in the real and imaginary permittivity of as-deposited and annealed La 2 Hf 2 O 7 samples [[53]].

Frequency dependence of the k value was extracted from C-f measurements observed in the La x Zr1−xO2−δ thin films (shown in Figure 6) [56]. Solid lines are from fitting results from the Cole-Davidson equation, while the dashed line is from the HN equation. The parameters α, β, and τ are from the Cole-Davidson or HN equation. The Cole-Cole and Cole-Davidson equation could fit the dielectric relaxation results of the La0.91Zr0.09O2, La0.22Zr0.78O2, La0.35Zr0.65O2, and La0.63Zr0.37O2 thin films. The La x Zr1−xO2−δ thin films can be also modeled by the HN equation more accurately than the Cole-Cole and Cole-Davidson equations.

Figure 6
figure 6

Dielectric relaxation results of as-deposited La x Zr 1 −x O 2− δ samples [[56]].

Intrinsic frequency dispersion: physical mechanisms

A dielectric material is a non-conducting substance whose bound charges are polarized under the influence of an externally applied electric field. The dielectric behavior must be specified with respect to the time or frequency domain. Different mechanisms show different dynamic behavior in time domain. In consequence, adsorption occurs at different windows in frequency domain. For the physical mechanism of the dielectric relaxation, Figure 7 is to describe the degree of polarization in a given material within frequency domain [85].

Figure 7
figure 7

Physical mechanisms of dielectric relaxation in real and imaginary parts [[85]].

The response of the dielectric relaxation in lower frequency range is firstly categorized into the interface polarization. In the region, surfaces, grain boundaries, inter-phase boundaries may be charged, i.e., they contain dipoles which may become oriented to some degree in an external field and thus contribute to the polarization of the material. It is orientation polarization as frequency increasing. Here, the material must have natural dipoles which can rotate freely. As the frequency increases further, dielectric relaxation is termed as ionic and electronic polarization. The mutual displacement of negative and positive sub-lattice in ionic crystals has happened. In this case a solid material must have some ionic character. Then, it is observed that there is displacement of electron shell against positive nucleus. Also, the region is called atomic polarization. In a summary, it is clear that the degree of polarization is related to the structure of the material. In consequence, dielectric behavior in electrostatic and alternating electric fields depends on static and dynamical properties of the structure.

XTEM was carried out on both x = 0.09 and x = 0.35 lanthanum-doped zirconium oxide samples. Images from the annealed samples are shown in Figure 8a,b [52]. These images show that equiaxed nanocrystallites of approximately 4-nm diameter form in the x = 0.09 sample, in contrast to a larger crystal of approximately 15-nm diameter for the x = 0.35 sample. This trend is also consistent with the average grain size estimated using a Scherrer analysis of the XRD data shown in Figure 8c [52], which gives similar values. In Figure 8d, for the x = 0.35 dielectric (open and closed circle symbols), annealing improves the dielectric relaxation and there is less of an effect on the k value, i.e., there is a small increase in the k value at some frequencies and there is a flatter frequency response compared to the as-deposited sample [52]. The film with a La content of x = 0.09 has a significant increase in the k value of the dielectric and also has a large dielectric relaxation. For the x = 0.09 as-deposited sample, the k values are lower and annealing (and hence crystallization into predominantly tetragonal or cubic phase) produces the higher k values. It is possible that the dielectric relaxation behavior observed is due to the level of stress in the crystalline grains, depending on the grain size, analogous to the behavior of ferroelectric ceramics.

Figure 8
figure 8

XTEM (a,b), XRD (c), and k- f data (d) of annealed and as-deposited samples. (a) XTEM of annealed La0.09Zr0.91O2 sample. (b) XTEM of annealed La0.35Zr0.65O2 sample. (c) XRD of as-deposited La x Zr 1−x O2−δ. (d) k-f data of as-deposited and annealed La x Zr 1−x O2−δ[52].

An interesting correlation of CeO2 as high-k thin film between grain size and dielectric relaxation was further discussed afterwards [57]. Figure 9a,b shows XRD diffraction patterns for the as-deposited and annealed samples, respectively. PDA in vacuum at 800°C for 15 min causes an increase in the size of the crystalline grains. The grain size of the annealed sample (9.55 nm) is larger than the original sample (8.83 nm). In order to investigate the frequency dispersion for CeO2, normalized dielectric constant in Figure 9b is quantitatively utilized to characterize the dielectric constant variation. It is observed that the dielectric relaxation for the as-deposited sample (triangle symbol) is much serious than the annealed one (square symbol). The smaller the grain size, the more intense is the dielectric relaxation. These findings are in good agreement with the theoretical and experimental studies proposed by Yu et al. [86], which reported the effect of grain size on the ferroelectric relaxor behavior in CaCu3TiO12 (CCTO) ceramics (shown in inset of Figure 9b). The dielectric relaxation for the small grain size sample is the worst. The effect of grain size mainly originates from higher surface stress in smaller grain due to its higher concentration of grain boundary. Surface stress in grain is high, medium and low for the small, medium, and large grain size CCTO samples. As surface stress increases, the glasslike transition temperature decreases considerably. It is attributed to the enhancement of the correlations among polar nanodomains.

Figure 9
figure 9

XRD of (a) and normalized dielectric constants (b) for as-deposited and annealed CeO 2 samples. (b) Under different frequencies [57].

XRD diffraction patterns for the as-deposited CeO2 thin films at 150, 200, 250, 300, and 350°C, respectively, are shown in the inset of Figure 10a [57]. The grain size value is obtained in Figure 10a using the Scherrer formula based on the XRD data. There is a clear trend that the grain size increases with increasing deposition temperatures. In Figure 10b, large dielectric relaxation is observed for the sample of 6.13 nm (diamond symbol) [57]. When the deposition temperature increases, the dielectric relaxation is even worse for the sample of 6.69 nm (square symbol). In addition, the most severe dielectric relaxation is measured for the sample of 8.83 nm (star symbol). The sample of 15.85 nm (triangle symbol) has significant improvement on the dielectric relaxation and the sample of 23.62 nm (round symbol) shows more stable frequency response. Similarly, the effect of grain size on the dielectric relaxation is found on the Nd-doped Pb1−3x/ 2Nd x (Zr0.65Ti0.35)O3 composition (PNZT) [87], where x = 0.00, 0.01, 0.03, 0.05, 0.07, and 0.09, respectively. It is observed in the inset of Figure 10b that the deteriorative degree of dielectric relaxation increases from 12.1 nm, reaches the peak at 22.5 nm, and then declines. One possible reason for the observation above could be due to the broadened dielectric peak and the transition temperature shift. The transition temperature of PNZT samples 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. Such strong frequency dispersion in the dielectric constant appears to be a common feature in ferroelectrics associated with non-negligible ionic conductivity.

Figure 10
figure 10

Grain sizes (a) and normalized dielectric constants (b) for as-deposited CeO 2 samples. (a) With various deposition temperatures. (b) Under different frequencies [57].


In C-V measurements, frequency dispersion in high-k dielectrics is very common to be observed. Dielectric relaxation, that is the intrinsic frequency dispersion, could not be assessed before suppressing the effects of extrinsic frequency dispersion. The dielectric relaxation models in the time domain (such as the Debye law and the CS law) and in the frequency domain after the Fourier transform (such as the Cole-Cole equation, the Cole-Davidson equation, the HN equation) were comprehensively considered. The relationship between the grain size and dielectric relaxation is observed in lanthanum-doped zirconium oxide samples. The mechanisms of grain size effects for CeO2 are discussed accordingly. A similar relationship between the grain size and dielectric relaxation is also found in CCTO and Nd-doped PNZT samples. The mechanism is attributed to the alignment enhancement of the polar nanodomains.

Authors’ information

CZ is a PhD student in the University of Liverpool. CZZ is a professor in Xi'an Jiaotong-Liverpool University. MW is a scientist in Nanoco Technologies Ltd. ST and PC are professors in the University of Liverpool.


  1. Juan PC, Liu CH, Lin CL, Ju SC, Chen MG, Chang IYK, Lu JH: Electrical characterization and dielectric property of MIS capacitors using a high- k CeZrO4 ternary oxide as the gate dielectric. Jpn J Appl Phys 2009, 48(05DA02):1–5.

    Google Scholar 

  2. Dong GF, Qiu Y: Pentacene thin-film transistors with Ta2O5 as the gate dielectric. J Kor Phys Soc 2009, 54(1):493–497.

    Article  Google Scholar 

  3. Zhu XH, Zhu JM, Li AD, Liu ZG, Ming NB: Challenges in atomic-scale characterization of high- k dielectrics and metal gate electrodes for advanced CMOS gate stacks. J Mater Sci Technol 2009, 25(3):289–313.

    Google Scholar 

  4. International Technology Roadmap for Semiconductors [] []

  5. Rahmani M, Ahmadi MT, Abadi HKF, Saeidmanesh M, Akbari E, Ismail R: Analytical modeling of trilayer graphene nanoribbon Schottky-barrier FET for high-speed switching applications. Nanoscale Res Lett 2013, 8: 55. 10.1186/1556-276X-8-55

    Article  Google Scholar 

  6. Ding SJ, Chen HB, Cui XM, Chen S, Sun QQ, Zhou P, Lu HL, Zhang DW, Shen C: Atomic layer deposition of high-density Pt nanodots on Al2O3 film using (MeCp)Pt(Me)3 and O2 precursors for nonvolatile memory applications. Nanoscale Res Lett 2013, 8: 80. 10.1186/1556-276X-8-80

    Article  Google Scholar 

  7. Chalker PR, Werner M, Romani S, Potter RJ, Black K, Aspinall HC, Jones AC, Zhao CZ, Taylor S, Heys PN: Permittivity enhancement of hafnium dioxide high- k films by cerium doping. Appl Phys Lett 2008, 93: 182911. 10.1063/1.3023059

    Article  Google Scholar 

  8. Chen SH, Liao WS, Yang HC, Wang SJ, Liaw YG, Wang H, Gu HS, Wang MC: High-performance III-V MOSFET with nano-stacked high- k gate dielectric and 3D fin-shaped structure. Nanoscale Res Lett 2012, 7: 431. 10.1186/1556-276X-7-431

    Article  Google Scholar 

  9. Wang JC, Lin CT, Chen CH: Gadolinium oxide nanocrystal nonvolatile memory with HfO2/Al2O3 nanostructure tunneling layers. Nanoscale Res Lett 2012, 7: 177. 10.1186/1556-276X-7-177

    Article  Google Scholar 

  10. Shi L, Liu ZG: Characterization upon electrical hysteresis and thermal diffusion of TiAl3O x dielectric film. Nanoscale Res Lett 2011, 6: 557. 10.1186/1556-276X-6-557

    Article  Google Scholar 

  11. Khomenkova L, Sahu BS, Slaoui A, Gourbilleau F: Hf-based high- k materials for Si nanocrystal floating gate memories. Nanoscale Res Lett 2011, 6: 172. 10.1186/1556-276X-6-172

    Article  Google Scholar 

  12. Chen FH, Her JL, Shao YH, Matsuda YH, Pan TM: Structural and electrical characteristics of high- k Er2O3 and Er2TiO5 gate dielectrics for a-IGZO thin-film transistors. Nanoscale Res Lett 2013, 8: 18. 10.1186/1556-276X-8-18

    Article  Google Scholar 

  13. Dalapati G, Wong TS, Li Y, Chia C, Das A, Mahata C, Gao H, Chattopadhyay S, Kumar M, Seng H, Maiti C, Chi D: Characterization of epitaxial GaAs MOS capacitors using atomic layer-deposited TiO2/Al2O3 gate stack: study of Ge auto-doping and p-type Zn doping. Nanoscale Res Lett 2012, 7: 99. 10.1186/1556-276X-7-99

    Article  Google Scholar 

  14. An YT, Labbé C, Khomenkova L, Morales M, Portier X, Gourbilleau F: Microstructure and optical properties of Pr3+-doped hafnium silicate films. Nanoscale Res Lett 2013, 8: 43. 10.1186/1556-276X-8-43

    Article  Google Scholar 

  15. Zhou P, Ye L, Sun QQ, Wang PF, Jiang AQ, Ding SJ, Zhang DW: Effect of concurrent joule heat and charge trapping on RESET for NbAlO fabricated by atomic layer deposition. Nanoscale Res Lett 2013, 8: 91. 10.1186/1556-276X-8-91

    Article  Google Scholar 

  16. 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.2011.02.025

    Article  Google Scholar 

  17. 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/ic201593s

    Article  Google Scholar 

  18. 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-7-425

    Article  Google Scholar 

  19. 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.37.4158

    Article  Google Scholar 

  20. 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.x

    Article  Google Scholar 

  21. 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.41.2480

    Article  Google Scholar 

  22. 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 

  23. Tye L, ElMasry NA, Chikyow T, McLarty P, Bedair SM: Electrical characteristics of epitaxial CeO2 on Si(111). Appl Phys Lett 1994, 65: 3081. 10.1063/1.112467

    Article  Google Scholar 

  24. Gross MS, Ulla MA, Querini CA: Catalytic oxidation of diesel soot: new characterization and kinetic evidence related to the reaction mechanism on K/CeO2 catalyst. Appl Catal Gen 2009, 1(360):81–88.

    Article  Google Scholar 

  25. Pan TM, Liao CS, Hsu HH, Chen CL, Lee JD, Wang KT, Wang JC: Excellent frequency dispersion of thin gadolinium oxide high- k gate dielectrics. Appl Phys Lett 2005, 26(87):262908–262908.

    Article  Google Scholar 

  26. Koveshnikov S, Tsai WOI, Lee JC, Torkanov V, Yakimov M, Oktyabrsky S: Metal-oxide-semiconductor capacitors on GaAs with high- k gate oxide and amorphous silicon interface passivation layer. Appl Phys Lett 2006, 2(88):022106–022106.

    Article  Google Scholar 

  27. Robertson J, Falabretti B: Band offsets of high- k gate oxides on III-V semiconductors. J Appl Phys 2006, 1(100):014111–014111.

    Article  Google Scholar 

  28. Pan TM, Chen CL, Yeh WW, Hou SJ: Structural and electrical characteristics of thin erbium oxide gate dielectrics. Appl Phys Lett 2006, 22(89):22912–222912.

    Google Scholar 

  29. Liu CH, Pan TM, Shu WH, Huang KC: Electrochem Solid-State Lett. 2007, 8(10):G54-G57.

    Article  Google Scholar 

  30. Anthony J, Aspinall HC, Chalker PR, Potter RJ, Manning TD, Loo YF, O’Kane R, Gaskell JM, Smith LM: MOCVD and ALD of high- k dielectric oxides using alkoxide precursors. Chem Vap Depos 2006, 12: 83–98. 10.1002/cvde.200500023

    Article  Google Scholar 

  31. Laha A, Bugiel E, Osten HJ, Fissel A: Crystalline ternary rare earth oxide with capacitance equivalent thickness below 1 nm for high- k application. Appl Phys Lett 2006, 17(88):172107–172107.

    Article  Google Scholar 

  32. Souza D, Kiewra JPE, Sun Y, Callegari A, Sadana DK, Shahidi G, Webb DJ: Inversion mode n-channel GaAs field effect transistor with high- k /metal gate. Appl Phys Lett 2008, 15(92):153508–153508.

    Article  Google Scholar 

  33. Adamopoulos G, Thomas S, Bradley DD, McLachlan MA, Anthopoulos TD: Low-voltage ZnO thin-film transistors based on Y2O3 and Al2O3 high- k dielectrics deposited by spray pyrolysis in air. Appl Phys Lett 2011, 98: 123503. 10.1063/1.3568893

    Article  Google Scholar 

  34. Yan L, Lu HB, Tan GT, Chen F, Zhou YL, Yang GZ, Liu W, Chen ZH: High quality, high- k gate dielectric: amorphous LaAlO3 thin films grown on Si (100) without Si interfacial layer. Applied Physics A 2003, 5(77):721–724.

    Article  Google Scholar 

  35. Lu XB, Liu ZG, Zhang X, Huang R, Zhou HW, Wang XP, Nguyen BY: Investigation of high-quality ultra-thin LaAlO3 films as high- k gate dielectrics. J Phys D Appl Phys 2003, 36(23):3047. 10.1088/0022-3727/36/23/027

    Article  Google Scholar 

  36. Gougousi T, Kelly MJ, Terry DB, Parsons GN: Properties of La-silicate high- k dielectric films formed by oxidation of La on silicon. J Appl Phys 2003, 3(93):1691–1696.

    Article  Google Scholar 

  37. Mahata CM, Bera K, Das T, Mallik S, Hota MK, Majhi B, Verma S, Bose PK, Maiti CK: Charge trapping and reliability characteristics of sputtered Y2O3 high- k dielectrics on N- and S-passivated germanium. Semicond Sci Technol 2009, 8(24):085006.

    Article  Google Scholar 

  38. Pan TM, Lei TF, Chao TS, Chang KL, Hsieh KC: High quality ultrathin CoTiO3 high- k gate dielectrics. Electrochem Solid-State Lett 2000, 9(3):433–434.

    Google Scholar 

  39. Kim SK, Kim KM, Kwon OS, Lee SW, Jeon CB, Park WY, Hwang CS, Jeong J: Structurally and electrically uniform deposition of high- k TiO2 thin films on a Ru electrode in three-dimensional contact holes using atomic layer deposition. Electrochem Solid-State Lett 2005, 12(8):F59-F62.

    Article  Google Scholar 

  40. Abermann S, Pozzovivo G, Kuzmik J, Strasser G, Pogany D, Carlin JF, Grandjean N, Bertagnolli E: MOCVD of HfO2 and ZrO2 high- k gate dielectrics for InAlN/AlN/GaN MOS-HEMTs. Semicond Sci Technol 2007, 12(22):1272.

    Article  Google Scholar 

  41. Adamopoulos G, Thomas S, Wöbkenberg PH, Bradley DD, McLachlan MA, Anthopoulos TD: High-mobility low-voltage ZnO and Li-doped ZnO transistors based on ZrO2 high- k dielectric grown by spray pyrolysis in ambient air. Adv Mater 2011, 16(23):1894–1898.

    Article  Google Scholar 

  42. Gaskell JM, Jones AC, Aspinall HC, Taylor S, Taechakumput P, Chalker PR, Heys PN, Odedra R: Deposition of lanthanum zirconium oxide high- k films by liquid injection atomic layer deposition. Appl Phys Lett 2007, 11(91):112912–112912.

    Article  Google Scholar 

  43. Gaskell JM, Jones AC, Chalker PR, Werner M, Aspinall HC, Taylor S, Taechakumput P, Heys PN: Deposition of lanthanum zirconium oxide high- k films by liquid injection ALD and MOCVD. Chem Vap Depos 2007, 12(13):684–690.

    Article  Google Scholar 

  44. Gutowski M, Jaffe JE, Liu CL, Stoker M, Hegde RI, Rai RS, Tobin PJ: Thermodynamic stability of high-k dielectric metal oxides ZrO2 and HfO2 in contact with Si and SiO2. MRS Proceedings 2002., 716(1): doi: doi:

  45. Dimoulas A, Vellianitis G, Mavrou G, Apostolopoulos G, Travlos A, Wiemer C, Fanciulli M, Rittersma ZM: La2Hf2O7 high- k gate dielectric grown directly on Si (001) by molecular-beam epitaxy. Appl Phys Lett 2004, 15(85):3205–3207.

    Article  Google Scholar 

  46. Gang H, Deng B, Sun ZQ, Chen XS, Liu YM, Zhang LD: CVD-derived Hf-based high- k gate dielectrics. Crit Rev Solid State Mater Sci 2013, 4(38):235–261.

    Google Scholar 

  47. Watanabe H, Saitoh M, Ikarashi N, Tatsumi T: High-quality HfSixOy gate dielectrics fabricated by solid phase interface reaction between physical –vapor -deposited metal-Hf and SiO2 underlayer. Appl Phys Lett 2004, 3(85):449–451.

    Article  Google Scholar 

  48. Darbandy G, Ritzenthaler R, Lime F, Garduño I, Estrada M, Cerdeira A, Iñiguez B: Analytical modeling of direct tunneling current through gate stacks for the determination of suitable high- k dielectrics for nanoscale double-gate MOSFETs. Semicond Sci Technol 2011, 4(26):045002.

    Article  Google Scholar 

  49. Myllymäki P, Roeckerath M, Putkonen M, Lenk S, Schubert J, Niinistö L, Mantl S: Characterization and electrical properties of high- k GdScO3 thin films grown by atomic layer deposition. Applied Physics A 2007, 4(88):633–637.

    Article  Google Scholar 

  50. Chan KC, Lee PF, Li DF, Dai JY: Memory characteristics and the tunneling mechanism of Au nanocrystals embedded in a DyScO3 high- k gate dielectric layer. Semicond Sci Technol 2011, 2(26):025015.

    Article  Google Scholar 

  51. Milanov AP, Xu K, Cwik S, Parala H, de los Arcos T, Becker HW, Devi A: Sc2O3, Er2O3, and Y2O3 thin films by MOCVD from volatile guanidinate class of rare-earth precursors. Dalton Trans 2012, 45(41):13936–13947.

    Article  Google Scholar 

  52. 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. 10.1063/1.3078038

    Article  Google Scholar 

  53. Zhao CZ, Taylor S, Werner M, Chalker PR, Gaskell JM, Jones AC: Frequency dispersion and dielectric relaxation of La2Hf2O7. J Vac Sci Technol B 2009, 1(27):333.

    Article  Google Scholar 

  54. 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 

  55. Zhao C, Zhao CZ, Tao J, Werner M, Taylor S, Chalker PR: Dielectric relaxation of lanthanide-based ternary oxides: physical and mathematical models. J Nanomater 2012, 241470.

    Google Scholar 

  56. 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/ma5061005

    Article  Google Scholar 

  57. Zhao C, Zhao CZ, Werner M, Taylor S, Chalker PR, King P: Grain size dependence of dielectric relaxation in cerium oxide as high- k layer. Nanoscale Res Lett 2013, 8: 172. 10.1186/1556-276X-8-172

    Article  Google Scholar 

  58. Schuegraf KF, King CC, Hu C: Impact of polysilicon depeletion in thin oxide MOS device. In VLSI Technology, Seattle, WA; 2–4 June 1992. Piscataway: IEEE; 1996:86–90.

    Google Scholar 

  59. Lee SW, Liang C, Pan CS, Lin W, Mark JB: A study on the physical mechanism in the recovery of gate capacitance to COX in implant polysilicon MOS structure. IEEE Electron Device Lett 1992, 1(13):2–4.

    Article  Google Scholar 

  60. Spinelli AS, Pacelli A, Lacaita AL: An improved formula for the determination of the polysilicon doping. IEEE Electron Device Lett 2001, 6(22):281–283.

    Article  Google Scholar 

  61. Pregaldiny F, Lallement C, Mathiot D: Accounting for quantum mechanical effects from accumulation to inversion, in a fully analytical surface potential-based MOSFET model. Solid State Electron 2004, 5(48):781–787.

    Article  Google Scholar 

  62. Sune J, Olivo P, Ricco B: Quantum-mechanical modeling of accumulation layers in MOS structure. IEEE Trans. Electron Devices 1992, 7(39):1732–1739.

    Article  Google Scholar 

  63. Pregaldiny F, Lallement C, van Langevelde R, Mathiot D: An advanced explicit surface potential model physically accounting for the quantization effects in deep-submicron. Solid State Electron 2004, 3(48):427–435.

    Article  Google Scholar 

  64. Wu WH, Tsui BY, Huang YP, Hsieh FC, Chen MC, Hou YT, Jin Y, Tao HJ, Chen SC, Liang MS: Two-frequency C-V correction using five-element circuit model for high -k gate dielectric and ultrathin oxide. IEEE Electron Device Lett 2006, 5(27):399–401.

    Article  Google Scholar 

  65. Lerner EJ: The end of the road for Moore's law. IBM J. Res. Develop 1999, 4: 6–11.

    Google Scholar 

  66. Ahmed K, Ibok E, Yeap GCF, Qi X, Ogle B, Wortman JJ, Hauser JR: Impact of tunnel currents and channel resistance on the characterization of channel inversion layer charge and polysilicon-gate depletion of sub-20-A gate oxide MOSFET’s. IEEE Trans. Electron Devices 1999, 8(46):1650–1655.

    Article  Google Scholar 

  67. Choi CH, Goo JS, Oh TY, Yu ZP, Dutton RW, Bayoumi A, Cao M, Voorde PV, Vook D, Diaz CH: MOS C-V characterization of ultrathin gate oxide thickness (1.3–1.8 nm). IEEE Electron Device Lett 1999, 6(20):292–294.

    Article  Google Scholar 

  68. Taechakumput P, Zhao CZ, Taylor S, Werner M, Pham N, Chalker PR, Murray RT, Gaskell JM, Aspinall HC, Jones AC: Origin of frequency of dispersion in high-k dielectrics. In Proceedings of 7th International Semiconductor Technology Conference ISTC2008. Pudong. Shanghai: ; 2008.

    Google Scholar 

  69. Yang KJ, Hu CM: MOS capacitance measurements for high-leakage thin dielectrics. IEEE Trans. Electron Devices 1999, 7(46):1500–1501.

    Article  Google Scholar 

  70. Hirose M, Hiroshima M, Yasaka T, Miyazaki S: Characterization of silicon surface microroughness and tunneling transport through ultrathin gate oxide. J Vac Sci Technol A 1994, 4(12):1864–1868.

    Article  Google Scholar 

  71. Curie JR: sur le pouvoir inducteur specifique et sur la conductibilite des corps cristallises. Ann Chim Phys 1889, 18: 203.

    Google Scholar 

  72. Von Schweidler E: Studien uber die anomalien im verhalten der dielektrika. Ann Phys 1907, 24: 711–770.

    Article  Google Scholar 

  73. Debye P: Polar Molecules. New York, NY, USA: Chemical Catalogue Company; 1929.

    Google Scholar 

  74. Williams G, Watts DC: Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function. Trans Faraday Soc 1969, 66: 80–85.

    Article  Google Scholar 

  75. Bokov AA, Ye ZG: Double freezing of dielectric response in relaxor Pb(Mg1/3Nb2/3)O3 crystals. Phys Rev B 2006, 13(74):132102.

    Article  Google Scholar 

  76. Ngai KL, Plazek DJ: A quantitative explanation of the difference in the temperature dependences of the viscoelastic softening and terminal dispersions of linear amorphous polymers. J Polym Sci Polym Phys 1986, 3(24):619–632.

    Article  Google Scholar 

  77. Cole KS, Cole RH: Dispersion and absorption in dielectrics. J Chem Phys 1941, 9: 341–351. 10.1063/1.1750906

    Article  Google Scholar 

  78. Davidson DW, Cole RH: Dielectric relaxation in glycerine. J Chem Phys 1950, 18: 1417.

    Article  Google Scholar 

  79. Davidson DW, Cole RH: Dielectric relaxation in glycerol, propylene glycol and n-propanol. J Chem Phys 1951, 19: 1484–1490. 10.1063/1.1748105

    Article  Google Scholar 

  80. Dotson TC, Budzien J, McCoy JD, Adolf DB: Cole-Davidson dynamics of simple chain models. J Chem Phys 2009, 130: 024903. 10.1063/1.3050105

    Article  Google Scholar 

  81. Ngai KL, McKenna GB, McMillan PF, Martin S: Relaxation in glassforming liquids and amorphous solids. J Appl Phys 2000, 88: 3113–3157. 10.1063/1.1286035

    Article  Google Scholar 

  82. Havriliak S, Negami S: A complex plane analysis of α-dispersions in some polymer systems. J Polym Sci Pt C 1966, 1(14):99–117.

    Google Scholar 

  83. Havriliak S, Negami S: A complex plane representation of dielectric mechanical relaxation processes in some polymers. Polymer 1967, 8: 161–210.

    Article  Google Scholar 

  84. Hartmann B, Lee GF, Lee JD: Loss factor height and width limits for polymer relaxations. J Acoust Soc Am 1994, 1(95):226–233.

    Article  Google Scholar 

  85. Schroeder T: Physics of dielectric and DRAM. Frankfurt, Germany: IHP Im Technologiepark; 2010.

    Google Scholar 

  86. 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. 10.1063/1.2820446

    Article  Google Scholar 

  87. 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.2006.09.022

    Article  Google Scholar 

Download references


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 the grant no. 60976075 and 11375146, the Suzhou Science and Technology Bureau of China under the grant SYG201007 and SYG201223, and the Jiangsu Provincial Science and Technology Supporting Program under the grant BK2012636.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Ce Zhou Zhao.

Additional information

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

CZ reviewed the data and drafted the manuscript. CZZ lead the experiments and supervised the project. MW prepared the samples and performed the characterization. ST and PC participated in the discussions. All authors read and approved the final manuscript.

Authors’ original submitted files for images

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Zhao, C., Zhao, C.Z., Werner, M. et al. Dielectric relaxation of high-k oxides. Nanoscale Res Lett 8, 456 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


  • Frequency dispersion
  • High-k
  • Grain size
  • Dielectric relaxation