Dielectric relaxation of high-k oxides
© Zhao et al.; licensee Springer. 2013
Received: 3 October 2013
Accepted: 18 October 2013
Published: 1 November 2013
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.
KeywordsFrequency dispersion High-k Grain size Dielectric relaxation
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 [1–4]. Extensive efforts have been focused on finding alternative gate dielectrics for future technologies to overcome leakage problems [5–7]. 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) [8–12]. Thicker equivalent oxide thickness, to reduce the leakage current of gate oxides, is obtained by introducing the high-k dielectric to real application [13–15].
There are a number of high-k dielectrics that have been actively pursued to replace SiO2. Among them are cerium oxide CeO2[16–23], cerium zirconate CeZrO4, gadolinium oxide Gd2O3[25–27], erbium oxide Er2O3[28, 29], neodymium oxide Nd2O3[30, 31], aluminum oxide Al2O3[32, 33], lanthanum aluminum oxide LaAlO3[34, 35], lanthanum oxide La2O3, yttrium oxide Y2O3, tantalum pentoxide Ta2O5, titanium dioxide TiO2, zirconium dioxide ZrO2[40, 41], lanthanum-doped zirconium oxide La x Zr1−xO2−δ[42, 43], hafnium oxide HfO2, HfO2-based oxides La2Hf2O7, Ce x Hf 1-x O 2 , hafnium silicate HfSi x O y , and rare-earth scandates LaScO3, GdScO3, DyScO3, and SmScO3. 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 [52–57]. 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.
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.
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
Parasitic effects in MOS devices included parasitic resistances and capacitances such as bulk series resistances, series contact, cables, and many other parasitic effects [64–67]. 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 , 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 , 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 . 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 . 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
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.
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.
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 . 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.
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.
Intrinsic frequency dispersion: physical mechanisms
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.
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.
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.
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.
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