Pure-temperature Contributions Research Articles

Study on processing step uniformity tuning during FET fabrication and sensor wafer response as a function of chuck temperature adjustment

The effect of chuck temperature adjustment on critical dimension uniformity was studied for the shallow trench isolation etch process by introducing a temperature gradient in a multi-temperature-zone electrostatic chuck. It is shown that the initial radial critical dimension non-uniformity can be improved by a gradual temperature adjustment of the electrostatic chuck and results in the target specification values of uniformity, 3σ ≤ 1.5 nm, for a critical dimension of about 35 nm. Both temperature and RF sensor wafers were used to analyze the impact of an electrostatic chuck temperature gradient on process uniformity by utilizing their unique in situ spatial and temporal mapping capabilities. Thus, the across-wafer thermal sensitivity of the critical dimension was estimated for dense structures: a temperature change of 1 °C leads to a critical dimension change of ∼0.7 nm. The RF sensor wafer was also shown to have a clear response of RF current uniformity to the electrostatic chuck temperature gradient that suggests there could be other phenomena affecting critical dimension uniformity besides temperature itself. The pure temperature contribution to critical dimension change was found to be less than 0.3 nm/°C for the temperature range studied. Finally, a possible mechanism of critical dimension tuning is discussed and an assessment of each separate etch step’s sensitivity to the electrostatic chuck temperature gradient is performed.

Strongly intrinsic anharmonicity in the low-frequency Raman mode in nanocrystalline anatase TiO 2

Temperature dependence of Raman spectra was obtained to study the unusual hardening behavior of lowest-frequency Raman mode of nanocrystalline anatase TiO 2. A model was employed to analyze the frequency shifts of three Raman modes upon increasing temperature firstly. The pure-volume and pure-temperature contributions to the frequency shifts of three Raman modes have been calculated. The result indicated that the strongly intrinsic anharmonicity arising from optical-phonon couplings was the origin of hardening upon increasing temperature for the Raman mode frequencies.

Temperature-dependent Raman scattering spectra of ε-GaSe layered crystal

The temperature dependencies (15–300 K) of seven Raman-active mode frequencies and linewidths in layered gallium selenide have been measured in the frequency range from 10 to 320 cm −1. We observed softening and broadening of the optical phonon lines with increasing temperature. Comparison between the experimental data and theories of the shift and broadening of the intralayer phonon lines during heating of the crystal showed that the experimental dependencies can be explained by the contributions from thermal expansion, lattice anharmonicity and crystal disorder. The pure-temperature contribution (phonon–phonon coupling) is due to three-phonon processes. Moreover, it was established that the effect of crystal disorder on the linewidth broadening of TO mode is stronger than that of LO mode.

Temperature dependence of the first-order Raman scattering in GaS layered crystals

The temperature dependence (15–293 K) of the six Raman-active mode frequencies and linewitdhs in gallium sulfide has been measured in the frequency range from 15 to 380 cm −1. We observed softening and broadening of the optical phonon lines with increasing temperature. Comparison between the experimental data and theories of the shift and broadening of the interlayer and intralayer phonon lines during the heating of the crystal showed that the experimental dependencies can be explained by the contributions from thermal expansion and lattice anharmonicity. The pure-temperature contribution (phonon–phonon coupling) is due to three- and four-phonon processes.

Temperature dependence of the Raman-active phonon frequencies in indium sulfide

The temperature dependence of the Raman-active mode frequencies in indium sulfide was measured in the range from 10 to 300 K. The analysis of the temperature dependence of the A g intralayer optical modes show that Raman frequency shift results from the change of harmonic frequency with volume expansion and anharmonic coupling to phonons of other branches. The pure-temperature contribution (phonon–phonon coupling) is due to three- and four-phonon processes.

Anharmonic effects in light scattering due to optical phonons in CuGaS2.

The ternary compound CuGaS2 is a direct energy gap semiconductor ~Eg;2.50 eV at 300 K! that crystallizes in the tetragonal chalcopyrite (I 42d) structure and its isoelectronic cubic analog is ZnS. The temperature dependence ~10–300 K! of the Raman active phonons has been studied up to 18 GPa in a membrane diamond anvil cell, using helium gas as a pressure transmitting medium. These measurements allowed us to determine the temperature dependence of the mode Gruneisen parameters and to separate the isobaric temperature dependence of the optical modes into pure-volume and pure-temperature contributions. By this procedure, the cubic and quartic anharmonicities responsible for the pure-temperature contributions to the mode frequencies were determined. The mode Gruneisen parameters of the center-of-zone G5 1 mode ~which corresponds to the edge-of-zone TA in ZnS! is negative throughout the whole temperature range, reaching 21.12 at 77 K. At low temperatures, this provides a possible driving mechanism for the negative values of the thermal expansion coefficient in semiconductors. @S0163-1829~96!07428-0#

Pressure and temperature dependences of the raman-active phonons in CuGaS 2

The ternary compound, CuGaS 2 is a direct energy gap semiconductor ( E g ~ 2.50 eV at 300 K) that crystallizes in the tetragonal chalcopyrite ( I 4 ̄ 2d ) structure and its isoelectronic cubic analog is ZnS. The temperature dependence (10–300 K) of the Raman active phonons has been studied up to 18 GPa in a membrane diamond anvil cell, using helium gas as the pressure transmitting medium. These measurements allowed us to determine the temperature dependence of the mode Grüneisen parameters and to separate the isobaric temperature dependence of the optical modes into pure-volume and pure-temperature contributions. By this procedure, the cubic and quartic anharmonicities responsible for the pure-temperature contributions to the mode frequencies were determined. The mode Grüneisen parameters of the center-of-the-zone Γ 5 1 mode (which corresponds to the edge-of-the-zone TA in ZnS) is negative throughout the whole temperature range, reaching − 0.64 at 77 K. At low temperatures, this provides a possible driving mechanism for the negative values of the thermal expansion coefficient in semiconductors.

Temperature dependence of the Raman active phonons in CaWO 4, SrWO 4 and BaWO 4

The temperature dependence (10–300 K) of the Raman frequency shifts for three different tungstates CaWO 4, SrWO 4 and BaWO 4 are reported. The lowest frequency mode shows soft mode behaviour in the calcium compound and negligible change in the other two. The remaining external modes and the other internal modes behave quite normally, that is to say, small dω dT for the external (typically <10 −2 cm −1 K .) and larger dωdT for the internal (typically 10 −2 cm −1 K ) modes. By using av pressure data we calculate the pure volume and pure temperature contributions to the frequency changes and find that the compounds don't behave like normal molecular crystals. We surmise that the instability with respect to a change of phase causes the abnormality.

Piezo- and thermo-optic behavior of LiTaO3

The variation of the ordinary and extraordinary refractive indices of ferroelectric LiTaO3 with hydrostatic pressure to 14 kbars has been measured for three wavelengths in the visible region of the spectrum by an interferometric method. Both the indices are found to increase linearly with pressure. The polarization induced contribution to the observed piezo-optic behavior has been evaluated. The strain polarizability constant L is positive and large, and increases for shorter wavelengths. The pure temperature contribution to the index is calculated and found to be large. Corresponding results for isomorphic LiNbO3 are discussed in terms of the difference in covalency between the Ta-O and Nb-O bonds.

Raman spectra of TiO 2-II, TiO 2-III, SnO 2, and GeO 2 at high pressure

Raman spectra of the orthorhombic (II) and high pressure (III) phases of titanium dioxide at pressures to 372 kbar and effects of temperature and hydrostatic pressure on Raman spectra of the tetagonal cassiterite-like phases of TiO 2, GeO 2 and SnO 2 are described. At room temperature, the TiO 2 II–III transition is sluggish, and metastable coexistence was observed from 200 to 300 kbar. The Raman spectra of TiO 2-III imply that its primitive cell contains at least four formula units; however, the structure could not be established from the Raman spectra and available powder X-ray diffraction patterns. The temperature and pressure dependences of the spectrum of the tetragonal MO 2 phases together with bulk moduli and thermal expansion data were used to evaluate the pure-volume and pure-temperature contributions to the isobaric temperature dependence of the Raman frequencies. Large anharmonicities in TiO 2 are attributed to hybridization of the oxygen p states with the d states of the Ti ion. GeO 2, where p-electron bonding is involved, is much less Enharmonic.

Temperature Dependence of the Raman Spectrum in Anatase TiO2

The frequency and linewidth of the four Raman active modes in anatase have been investigated over the temperature range 20 to 1100 K. The temperature ( T ) dependence of the frequency of the 639 cm -1 mode showed typical behavior in normal ionic crystals, whereas the other modes at 399, 197 and 144 cm -1 did anomalous behavior. These T dependent results were combined with pressure dependent results, thermal expansion and compressibility data to evaluate the pure-volume and pure-temperature contributions to the T dependence of each frequency. The results indicate that the anomalous T dependence of the 399 cm -1 mode reflects the near cancellation of the cubic and quartic contributions to the frequency shift, and that of the modes at 197 and 144 cm -1 arises from strong quartic contributions. The T dependence of the linewidth is well explained qualitatively in terms of simple anharmonic effects involving three phonon processes.

Temperature and pressure dependences of the dielectric properties of PbF2and the alkaline-earth fluorides

The effects of temperature and hydrostatic pressure on the real (${\ensuremath{\epsilon}}^{\ensuremath{'}}$) and imaginary (${\ensuremath{\epsilon}}^{\ensuremath{'}\ensuremath{'}}$) parts of the static dielectric constant of single crystals of Pb${\mathrm{F}}_{2}$, Ba${\mathrm{F}}_{2}$, Sr${\mathrm{F}}_{2}$, and Ca${\mathrm{F}}_{2}$ were investigated. In all cases ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ decreases with increasing pressure. However, unlike the alkaline-earth fluorides and other normal ionic dielectrics where ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ increases slowly with increasing temperature, ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ of cubic Pb${\mathrm{F}}_{2}$ exhibits a relatively large decrease with increasing temperature and obeys a Curie-Weiss law over a substantial temperature range. It is suggested that this anomalous temperature dependence and the large value of ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ (\ensuremath{\sim}30) are associated with a soft longwavelength transverse optic phonon, i.e., a ferroelectric (FE) mode, although the crystal remains stable with respect to this mode down to the lowest temperatures. This is the first example of a soft FE mode in a crystal having the relatively simple cubic fluorite structure. The measured isobaric temperature dependence of ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ is separated into its pure-volume and pure-temperature contributions. For the alkaline-earth fluorides both contributions are positive and additive, whereas for cubic Pb${\mathrm{F}}_{2}$ the pure-temperature contribution is negative and dominates the measured ${\ensuremath{\epsilon}}^{\ensuremath{'}}(T)$ response. This is attributed to the dominance of quartic anharmonicities in this crystal---a circumstance similar to that in other soft-FE-mode crystals. The Szigeti effective charges were calculated and the validity of the Lyddane-Sachs-Teller relationship was tested for all crystals. The effects of the pressure-induced cubic ($\mathrm{Fm}3m\ensuremath{-}{O}_{h}^{5}$) to orthorhombic ($\mathrm{Pm}nb\ensuremath{-}{V}_{2h}^{16}$) phase transition on the dielectric properties of Pb${\mathrm{F}}_{2}$ and Ba${\mathrm{F}}_{2}$ were also investigated, and the possible lattice-dynamical origin of the transition is briefly discussed. In Pb${\mathrm{F}}_{2}$ the orthorhombic phase is recovered at ambient conditions after releasing the pressure, and the effects of temperature and pressure on the dielectric properties of this phase were investigated. Unlike cubic Pb${\mathrm{F}}_{2}$, the orthorhombic phase behaves as a normal ionic dielectric. At $T\ensuremath{\ge}300$\ifmmode^\circ\else\textdegree\fi{}K the dielectric loss in both phases of Pb${\mathrm{F}}_{2}$ becomes very large due to the high ionic conductivity of the material. The activation energies deduced from the loss data are in excellent agreement with those obtained from ionic conductivity measurements.

Raman scattering study of the effect of pressure and temperature on the order-disorder phase transition in ammonium chloride

The temperature and pressure dependence of the lattice and internal modes in NH4Cl have been measured. By keeping the temperature fixed, it has been possible to induce the phase transition by changing the external pressure. From the frequency and intensity measurements of several lattice modes as a function of temperature at various pressures, it was found that the character of the order-disorder phase transition in NH4Cl varies significantly at different points along the phase transition line in the P-T plane. An analysis of the Grüneisen parameter for the various lattice modes was presented. The isobaric temperature dependent frequencies of the lattice modes was discussed in terms of the pure-volume contributions. From the pure-temperature contribution, it was found that anharmonic interaction potential is the main mechanism responsible for the temperature dependence of the anomalous 93 cm−1 mode in NH4Cl.

Anharmonic Effects in KTaO3: Ferroelectric Mode, Thermal Expansion,and Compressibility

The effects of temperature and pressure on the static dielectric constant and lattice parameter of KTa${\mathrm{O}}_{3}$ have been measured. Combined with literature data, the present results allow a determination of the pressure and temperature dependence of the soft-ferroelectric-mode frequency ${\ensuremath{\omega}}_{f}$ over a wide temperature range (0-500\ifmmode^\circ\else\textdegree\fi{}K). The isobaric anharmonic self-energy shift of ${\ensuremath{\omega}}_{f}$ is separated into its pure-volume (thermal-strain) and pure-temperature contributions. Though small, the thermal-strain contribution is not negligible, amounting to 7% of the measured frequency at 300\ifmmode^\circ\else\textdegree\fi{}K and 10% at 500\ifmmode^\circ\else\textdegree\fi{}K. It acts to reduce the influence of the pure-temperature anharmonicities. The soft-mode Gr\uneisen parameter ${\ensuremath{\gamma}}_{f}$ is very large at low temperatures (460 at 4\ifmmode^\circ\else\textdegree\fi{}K) and decreases rapidly with increasing temperature---unique properties of the soft mode. It is estimated that the strictly harmonic frequency ${\ensuremath{\omega}}_{0}$ of the soft mode is just barely imaginary, and thus all of the stabilization of ${\ensuremath{\omega}}_{f}$ at 0\ifmmode^\circ\else\textdegree\fi{}K (\ensuremath{\ge}21\ifmmode\pm\else\textpm\fi{}4 ${\mathrm{cm}}^{\ensuremath{-}1}$) is provided by zero-point anharmonicities. At high pressure, ${\ensuremath{\omega}}_{0}$ becomes real. Interpreted in terms of the perturbation and self-consistent phonon treatments, the high-temperature stabilization of ${\ensuremath{\omega}}_{f}$ is dominated by quartic anharmonicities, but the nonlinear high-temperature ${\ensuremath{\omega}}_{f}^{2}(T)$ response suggests the importance of higher-order anharmonicities.

Pressure and Temperature Dependences of the Raman-Active Phonons in SnO2

The temperature (10-500 \ifmmode^\circ\else\textdegree\fi{}K) and pressure (0-4 kbar) dependences of the four Raman-active phonons ${B}_{1g}$, ${E}_{g}$, ${A}_{1g}$, and ${B}_{2g}$ as well as thermal expansion (93-700 \ifmmode^\circ\else\textdegree\fi{}K) and isothermal compressibility (0-3 kbar) in Sn${\mathrm{O}}_{2}$ were measured. These measurements allowed us to determine the mode Gr\uneisen parameters for the Raman-active phonons and to separate the isobaric temperature dependence of each frequency into pure-volume and pure-temperature contributions. By this procedure the cubic and quartic anharmonicities responsible for the pure-temperature contributions to the mode frequencies were determined. The ${B}_{1g}$ mode in Sn${\mathrm{O}}_{2}$ exhibited anomalous temperature and pressure dependences in that $\ensuremath{\omega}({B}_{1g})$ increased with temperature and decreased with pressure. The remaining modes exhibited decreases in frequency with increasing temperature and increases in frequency with increasing pressure, characteristic of ionic crystals. The results are compared with the recent results on the isomorphic compound tetragonal Ti${\mathrm{O}}_{2}$.

Pressure and Temperature Dependence of the Static Dielectric Constants and Raman Spectra of TiO2(Rutile)

The effects of temperature [(4-500)\ifmmode^\circ\else\textdegree\fi{}K] and hydrostatic pressure (0-4 kbar) on the static dielectric constants ${\ensuremath{\epsilon}}_{a}$ and ${\ensuremath{\epsilon}}_{c}$ and on the frequencies of the four Raman-active phonons ${B}_{1g}$, ${E}_{g}$, ${A}_{1g}$, and ${B}_{2g}$ of single-crystal rutile were investigated. The temperature and pressure dependence of the frequency of the infrared-active soft ferroelectric (FE) mode ${A}_{2u}$ were deduced from the dielectric-constant data. The Gr\"uneisen parameter $\ensuremath{\gamma}$ of each of the modes was determined. Particularly important are the results that $\ensuremath{\gamma}({A}_{2u})$ is large and increases with decreasing temperature-unique properties of the FE mode-and that $\ensuremath{\gamma}({B}_{1g})$ is relatively large and negative. This latter result, which is in agreement with an earlier measurement, may be significant from the standpoint of a pressure-induced phase transition in rutile. The temperature and pressure results are combined with thermal expansion and compressibility data to evaluate the pure-volume and pure-temperature contributions to the isobaric temperature dependence of each of the frequencies and dielectric constants. The results yield some important conclusions about the lattice dynamics of rutile. The pure-temperature contribution arises from cubic and quartic anharmonicities. It plays a dominant role in determining the anharmonic self-energy shift of the FE mode and accounts for 20% of the mode energy at 300 \ifmmode^\circ\else\textdegree\fi{}K. The Szigeti effective ionic-charge ratio for rutile is found to be $\frac{{e}^{*}}{e}=0.64$ at 4 \ifmmode^\circ\else\textdegree\fi{}K and 0.62 at 296 \ifmmode^\circ\else\textdegree\fi{}K. These results are discussed briefly.