Soft Optical Phonon Research Articles

Temperature Dependence of Channel Mobility in>tex<$hbox HfO_2$>/tex<-Gated NMOSFETs

The degradation mechanisms of effective electron channel mobility in HfO/sub 2/-gated nMOSFETs have been studied by analyzing experimental data at various temperatures from 120 to 320 K. The major finding is that, while significant Coulomb scattering plays an important role in causing the observed mobility degradation, it does not account for all of the degradation; rather, it requires an extra phonon scattering mechanism, beyond that arising from the phonons in the Si substrate, to explain our experimental results. This extra phonon scattering mechanism has been found to exhibit relatively weak temperature dependence, and is attributed to the soft optical phonons in the HfO/sub 2/ layer.

Soft optical phonon in Ba-doped Sr 2Nb 2O 7 ceramics

The Raman scattering technique was applied to examine the soft optical phonon of the Ba 0.32Sr 0.68Nb 2O 7 in the temperature range from 26 to 1100 °C. The line shape of Raman spectra can be well fitted by multidamped–harmonic oscillator model. Two soft optical phonons were observed at 43.1, 52.4 cm −1 at room temperature. Both modes show softening approaching their corresponding phase transition temperature. It is found that damping factor γ of the lowest soft optical mode increases, while frequency of this mode decreases rapidly with temperature. Near T c, the soft mode becomes over damped ( γ/ ω>1). The soft mode frequency related to the order parameter of this ferroelectric phase shows a non-classical behavior, and the critical exponent connected to the increase of the order parameters obtained as β=0.377. From the relation of soft mode frequency with temperature, the ferroelectric phase transition temperature T c was estimated to be 1058 °C.

Thickness and strain effects on electronic transport and Curie temperature in La_0.67Ca0.33MnO_3 films

La_0.67Ca_0.33Mn_O.3 films with thickness between 25 and 400nm were fabricated on (001)SrTiO_3 and (001)LaAlO_3 substrates, using pulsed laser deposition. The magnetization and resistivity ρ of the fil ms were studied as functions of thickness. The reduction of t causes the decrease of the Curie temperature T_C in addition to the increase of ρ of the films. Com pared with the compressive strain in the La_0.67Ca_0.33Mn_O.3/La AlO_3 films, the tensile strain in the La_0.67Ca_0.33Mn_O.3/SrTiO_3 films causes a faster reduction of T_C with t, and a larger value of ρ_０. The low_temperature ρ is found to follow well ρ=ρ_0+Bω_s/sin h^2(ω_s/2/k_BT)+CT^n， with ρ_０ being the residual resistivity. The second term arises fro m the scattering by a soft optical phonon mode, and the third term denotes the other possible transp ort mechanisms. B, ω_s(the frequency of a soft optical mode) and C are fitting parameters. At temperatures higher than T_C, ρ of all the films show activated conduction with ρ=DT×exp（E_a/k_BT）. Here, E_a is the activation energy. Based on the investigation of ρ_０, ω_s and E_a, the thickness and strain effect s in the films are discussed, separately. Further study shows that the variation of T_C is mai nly associated with E_a and ω_s, confirming the crucial role of the electron_phonon coupling in the strain effects on T_C.

Mobility Measurement and Degradation Mechanisms of MOSFETs Made With Ultrathin High-k Dielectrics

Accurate measurements and degradation mechanisms of the channel mobility for MOSFETs with HfO/sub 2/ as the gate dielectric have been systematically studied in this paper. The error in mobility extraction caused by a high density of interface traps for a MOSFET with high-k gate dielectric has been analyzed, and a new method to correct this error has been proposed. Other sources of error in mobility extraction, including channel resistance, gate leakage current, and contact resistance for a MOSFET with ultrathin high-k dielectric have also been investigated and reported in this paper. Based on the accurately measured channel mobility, we have analyzed the degradation mechanisms of channel mobility for a MOSFET with HfO/sub 2/ as the gate dielectric. The mobility degradation due to Coulomb scattering arising from interface trapped charges, and that due to remote soft optical phonon scattering are discussed.

Effective electron mobility in Si inversion layers in metal–oxide–semiconductor systems with a high-κ insulator: The role of remote phonon scattering

The high dielectric constant of insulators currently investigated as alternatives to SiO2 in metal–oxide–semiconductor structures is due to their large ionic polarizability. This is usually accompanied by the presence of soft optical phonons. We show that the long-range dipole field associated with the interface excitations resulting from these modes and from their coupling with surface plasmons, while small in the case of SiO2, for most high-κ materials causes a reduction of the effective electron mobility in the inversion layer of the Si substrate. We study the dispersion of the interfacial coupled phonon-plasmon modes, their electron-scattering strength, and their effect on the electron mobility for Si-gate structures employing films of SiO2, Al2O3, AlN, ZrO2, HfO2, and ZrSiO4 for “SiO2-equivalent” thicknesses ranging from 5 to 0.5 nm.

Strong oxygen-isotope effect on the intrinsic resistivity in the ferromagnetic state of manganites

Oxygen-isotope effects on the intrinsic resistivity have been studied in high-quality epitaxial thin films of ${\mathrm{La}}_{0.75}{\mathrm{Ca}}_{0.25}{\mathrm{MnO}}_{3}$ and ${\mathrm{Nd}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_{3}.$ We found that the residual resistivity ${\ensuremath{\rho}}_{o}$ increases by about 15(3)% upon replacing ${}^{16}\mathrm{O}$ by ${}^{18}\mathrm{O}.$ Furthermore, the temperature dependent part of the resistivity at low temperatures consists of an ${\mathrm{AT}}^{4.5}$ term contributed from two-magnon scattering, and a $B{\ensuremath{\omega}}_{s}/{\mathrm{sinh}}^{2}(\ensuremath{\Elzxh}{\ensuremath{\omega}}_{s}{/2k}_{B}T)$ term which arises from scattering by a soft optical phonon mode. The absolute magnitudes of the coefficient A and the phonon energy $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{s}$ for both isotope samples are in quantitative agreement with theoretical predictions.

Soft-Mode Spectroscopy in Fe:KTa1-xNbxO3 Crystals

Fe-doped potassium tantalite niobate, Fe:KTa 1-x Nb x O 3 (Fe:KTN), crystallizes with x = 0.48 and a perovskite-type structure in tetragonal system with point group 4mm, conforming space group P4mm. The paraelectric-ferroelectric structural transition of the Fe:KTN is studied by Raman scattering investigations. A condensed soft lattice vibrational mode at the phase transition has been analyzed. It originates from the symmetric O2/O3-Nb/Ta-O3/O2 in-plane bending of the Nb/TaO 6 group. The soft optical phonon mode concerns the extraordinary transverse optical phonons propagating along the [110] direction. The Raman spectra measured reflect the crystal disorder. Curie temperature measured by two methods is within 353 and 3 56.5 K.

Electrical transport in the ferromagnetic state of manganites: small-polaron metallic conduction at low temperatures.

We report measurements of the resistivity in the ferromagnetic state of epitaxial thin films of La(1-x)Ca(x)MnO3 and the low-temperature specific heat of a polycrystalline La0.8Ca0.2MnO3. The resistivity below 100 K can be well fitted by rho-rho(0) = Eomega(s)/sinh (2)(hs/ 2k(B)T) with h(omega)(s)/k(B) approximately 80 K and E being a constant. Such behavior is consistent with small-polaron coherent motion which involves a relaxation due to a soft optical phonon mode that is strongly coupled to the carriers. The specific-heat data also suggest the existence of such a phonon mode. The present results thus provide evidence for small-polaron metallic conduction in the ferromagnetic state of manganites.

Phase transition and the soft lattice mode of a perovskite crystal studied by Raman scattering and thermal measurements

The paraelectric–ferroelectric structural transition of potassium lithium tantalite niobate has been studied by both Raman scattering and thermal measurements. A condensed soft lattice vibrational mode at the phase transition has been analyzed. It originates from the symmetric O2/O3–Nb/Ta–O3/O2 in-plane bending of the Nb/TaO6group. The soft optical phonon mode concerns the extraordinary transverse optical phonons propagating along the [110] direction. The thermal expansion experiments show a displacive phase transition and a big thermal contraction in thecdirection of the crystal, with an average linear expansion coefficient αc= −4.52 × 10−5K−1. The phase transition temperature and enthalpy are 358 K and 0.50 J/g, respectively. Curie temperature measured by four methods is within 353 and 360 K.

Structural Instability Associated with the Tilting of CuO6Octahedra in La2-xSrxCuO4

Comprehensive inelastic neutron-scattering measurements were performed to study the soft optical phonons in La2-xSrxCuO4 at x=0.10, 0.12 and 0.18. We found at x=0.18 that the softening of Z-point phonon, suggesting incipient structural transition from the low-temperature orthorhombic (LTO) to low-temperature tetragonal (LTT) phase, breaks at Tc, which is consistent with the previous report by Lee et al. for the optimally doped x=0.15 sample. As for x=0.10 and 0.12, on the other hand, the softening continues even below Tc. It is thus clarified that the breaking of soft phonon is characteristic of La2-xSrxCuO4 in the optimally and overdoped regions. In the course of studying the soft phonons, we discovered that a central peak remains above the LTO to high-temperature tetragonal (HTT) phase transition at Ts1 and splits into incommensurate components along the (1 1 0)HTT direction at higher temperatures. This is a common feature for both x=0.12 and 0.18 and their temperature dependences of the splitting 2d can be scaled by using a renormalized temperature T/Ts1. In the high temperature limit, d saturates around d ~ 0.12 r.l.u., which value is close to the splitting of incommensurate magnetic signals. This implies that the incipient lattice modulation starts appearing at very high temperature. Details of this modulation and its relations with other properties are, however, not yet clarified.

Soft modes and phonon interactions in studied by means of neutron scattering

This paper presents an inelastic neutron scattering study of the proper ferroelectric and elastic neutron scattering results on the satellite diffraction pattern which characterizes the modulated phase. The temperature dependences of the satellite intensities and modulation wavevector are in fair agreement with results from previous x-ray experiments. Close to the incommensurate-to-ferroelectric transition temperature , an unexpected intensity overshoot is observed, similar to that seen in birefringence and dilatation experiments. The relationship between the lattice dynamics and the observed phase transition sequence is examined. The dispersion of the ferroelectric soft optic phonon (-polarization) and of the acoustic phonons is followed along the and -directions. In the ferroelectric phase, the TO mode shows a considerable softening as the incommensurate phase is approached from below. In the paraelectric and incommensurate phases, the response from the TO (-polarization) and TA ( strain) branches has been investigated via a series of constant-q scans in the -direction (approximately the modulation wavevector direction). The combined inelastic line-shapes, as observed in a number of non-equivalent Brillouin zones, could all be analysed in terms of a coupled-mode damped harmonic oscillator model. In addition, a diverging, resolution-limited, central peak is observed close to . It is suggested that the TO-TA coupling lies at the origin of the incommensurate instability. A phenomenological free energy is developed, in the continuum approximation, in which the TO-TA interaction is included via a pseudo-Lifshitz term of the type .

Brillouin Scattering from the Soft Optical Phonon in the Orthorhombic Form of a K 3Co 1-xFex(CN) 6 (x≤ 0.03) Crystal

The soft optical phonon in the two-layer orthorhombic form of a K3Co1-xFex(CN)6 (x≤0.03) single crystal has been reinvestigated using a (3+3)-pass tandem Fabry-Pérot interferometer around the structural phase transition temperature. The soft phonon response can be well described using the phonon-relaxator coupled model. The soft phonon frequency ω∞/2π obeys the |T-T c±|1/2 law except in the vicinity of T c=82.5 ±0.1 K; (ω∞/2π)2=1.20×103(T-82.1) (GHz2) for T>T c and 4.55×103(83.0-T) (GHz2) for T<T c. The soft phonon-relaxator coupling constant increases linearly above the T c as the temperature decreases and the slope becomes steeper below T c. The relaxation time is longer than 40 ps and independent of temperature above T c, but becomes one order of magnitude shorter below T c. The Fe3+ defects seem to be responsible for these unusual temperature dependences.

On the origin of the anomalies in the temperature dependences of thermal conduction in sn2p2s6-like crystals at the phase transitions

The temperature dependences of thermal conduction coefficient λ for the Sn2P2S6 and Sn2P2Se6 crystals have been studied in the vicinity of the structural phase transitions (PT) by means of a stationary longitudinal heat flux method. λ(T) behaviour in these crystals close to PT has been simulated numerically with allowance made for the inelastic and quasielastic scattering of heat-carrying phonons by the critical optical phonons and the contribution of the soft optical phonons to the heat transfer. It has been suggested that the anomalies in λ(T) at PT are specified primarily by the ratio of the heat capacity anomalies and the average group velocity anomalies.

Comparison of the soft polar phonon in hexagonal barium titanate and ATiO 3 perovskite compounds

A polar soft optic phonon recently found in hexagonal barium titanate has been studied in detail by hyper-Raman spectroscopy. The oscillator strength of this polar soft phonon, estimated from the observed hyper-Raman spectrum, is found to be 80% of the lattice part of the static dielectric constant along the c-axis. The existence of the polar soft phonon as well as its large oscillator strength are common to ATiO 3 perovskite compounds (A: Pb, Ba, Sr,...). We also find that an accidental coupling between this soft phonon and another optic phonon of different origin occurs below the hexagonal-to-orthorhombic-transition temperature T a.

The ferroelastic transition of betaine borate

The ferroelastic transition of betaine borate at about 142 K and the nonlinear temperature dependence of the corresponding critical elastic modulus are related to the softening of optical phonons. The transition has to be considered a ferroelastic one of the optic type, i.e. pseudoproper one, therefore. It is shown by Raman spectroscopic results that the transition is induced by a strong bilinear coupling between a homogeneous strain and at least two optic lattice modes which are of the same symmetry as the strain. Optic and dielectric, investigations support the second-order character of and the classical behaviour at this transition, which have been reported in the literature. Differences and similarities to the ferroelastic transition of betaine fumarate are discussed.

‘Soft optical phonons’ and the structure transition of bismuth titanate system doped with Nd and Sb

Raman scattering results for Bi 2− x Nd x Ti 4O 11 and Bi 2− x Sb x Ti 4O 11 systems show that the square of the frequency of the ‘soft’ phonon changes linearly with the Nd and Sb concentration for x⪕0.3 and x⪕0.4 respectively, and that the structure phase transition occuring at x = 0.3 and 0.4 may be associated with an instability of the ‘soft’ phonon. It is shown that changes in the short-range harmonic forces play an important role in the x dependence of the ‘oft’ phonon frequency. The phase transition pressure occurring in Bi 1.8.Nd 0.2Ti 4O 11 is 3.32 GPa.

Observation of a polar soft-phonon in hexagonal barium titanate

Abstract By a hyper-Raman spectroscopy, it is found that a polar soft optic phonon with A2u symmetry exists in the hexagonal BaTiO3 polymorphic to perovskite BaTiO3, independently of another non-polar E2u optic phonon responsible for a phase transition at Ta = 222 K. The frequency is monotonously soft from 670 K to Ta, and thereby a virtual characteristic temperature of ferroelectric instability is deduced as 40K. Further, the magnitude of the TO-LO splitting of the relevant mode is found to be very large as is the case for perovskite BaTiO3 and SrTiO3. The remarkable temperature dependence of the dielectric constant εc can be well accounted for from the lattice-dynamical point of view, including an anomalous bump at Ta. Implication of the present findings is discussed.

Effect of the uniaxial compression on the phase transitions in Sn2P2S6‐type ferroelectrics

AbstractThe effect of uniaxial compression on the temperature dependences of birefringence and dielectric constant is studied for the proper uniaxial ferroelectrics Sn2P2S6 and Sn2P2Se6. The influences of compression on the ferroelectric phase transition (PT) in Sn2P2S6 and on the PT which restricts the incommensurate (IC) phase in Sn2P2Se6 are compared. The observed variations of PT temperature and IC‐phase range with pressure agree with those calculated in an approximation which takes into account the presence of a tricritical point on the phase diagram of the crystals under study along with the Lifshits point. The variation of the ratio of the rates of PT temperature change for different uniaxial mechanical stresses on the replacement of sulphur by selenium as well as the weak sensitivity of the IC‐phase to compression along the structure modulation axis are found. It is suggested that these manifestations of the anisotropy are related to the special features of the linear interaction of soft optical and acoustic phonon branches.

Binggeli and Chelikowsky reply.

This is a response to a comment (Phys. Rev. Lett. 71, 2674 (1993)) on the authors' previous work titled Elastic Instability in Alpha- Quartz under Pressure (Phys. Rev. Lett. 69, 2220 (1992)). The initiation mechanism for amorphous transition in alpha-quartz under pressure being a soft optic phonon in the Brillouin zone boundary as suggested by the comment does not contradict the authors' early suggestion which is the transverse acoustic mode near the zone center. (AIP)

Femtosecond time-resolved spectroscopy of polarization dynamics in KNbO3

Femtosecond time-resolved impulsive stimulated scattering experiments were conducted on KNbO3 at temperatures spanning the orthorhombic phase. A heavily damped soft optic phonon mode associated with the displacive character of the transition and relaxational modes associated with order-disorder character were examined. Previous frequency-domain light scattering experiments had yielded conflicting results for the dynamics of the soft mode and the symmetry of the order-disorder motions. We find the relaxational motion to be of A1 symmetry and the soft mode to be the only low-frequency exictation of B2 symmetry. The soft mode is well described by a damped polariton model without any coupling to a relaxational mode. These results are consistent with a previously proposed eight-site model for the phase transitions.