Study of surface and bulk acoustic phonon excitations in superlattices using picosecond ultrasonics

We have performed picosecond ultrasonic studies on the surface and bulk acoustic phonons in amorphous Mo/Si superlattices. Localized surface modes within the first, second, and sixth frequency gaps of the zone-folded phonons are observed. A selection rule derived from symmetry considerations provides new understanding of why certain modes are seen and not the others. The excitation strengths and detailed spectral features of these lines are studied, and the results are well explained by an elastic-continuum theory. It is found that the line shapes are significantly modified by the presence of bulk modes near the zone center.     

Variable charges at govalent bonds and phonon dispersion in silicon

A model of variable charges at covalent bonds is proposed to describe the effective atomic interaction in a crystal lattice. It is shown that, in the region of elastic deformations, it is sufficient to take account only of the linear term in the expansion of the charge with respect to the relative deformation of the bond. Expressions are obtained for the dynamic matrix on the basis of the pseudopotential model and the model of variable charges at the bonds. The results of calculating the phonon spectrum of silicon are in good agreement with experimental data and reflect the characteristic features of the spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 95–98, July, 1988.     

Density of phonon states in amorphous germanium and silicon

The density of phonon states in amorphous germanium and silicon is calculated by statistically averaging the crystalline phonon density of states according to the radial distribution function. A simple rigid ion model is used to calculate the density of phonon states at various lattice spacings. The appropriate model parameters are obtained from the pressure dependent elastic constants and the Raman frequency. The calculated results compare favorably to experimental data obtained by infrared and Raman scattering and the results of other theoretical calculations.     

A microscopic model for the phonon dispersion in silicon

In this paper the quasi-ion picture recently developed^1,2,6 is applied to the lattice dynamics of covalent materials using Si as an example. The phonon dispersion of Si is investigated along the main symmetry directions by modelling the electronic charge density of the quasi-ions. It is demonstrated that the phonon frequencies can be calculated reasonably well by describing this density in terms of a small set of Gauss-functions.     

Phonon pulse detection in germanium and silicon with a fluorescence contact-type phonon spectrometer

Laser pulse produced nonequilibrium acoustic phonons in Ge and Si single crystals have been detected at several phonon frequencies in the THz range by the fluorescence from an insulting YF₃:Tn³⁺ film on the sample surface.     

Evaluation of elastic properties of nanoporous silicon oxide thin films by picosecond laser ultrasonics

Picosecond laser ultrasonics uses femtosecond laser pulses for the generation and detection of acoustic pulses with a typical duration between few picoseconds and few hundreds of pico seconds. The shorter the duration of the acoustic pulse is, the more precisely could be made the measurements of the film thickness [C. Thomsen et al., Phys. Rev. B 34, 4129 (1986)] and the elastic modulus by pulse-echo method or through Brillouin scattering detection. In this short communication we report the results of the evaluation of the properties of nanoporous silicon oxide thin films which present potential low-k and thermal barrier properties and are also of great interest for the microelectronic industry to replace the traditional silicate glass films in order to decrease the resistance-capacitance transition delay in the VLSI circuits. Most of the studies that have been carried so far have treated the optical properties of such structures. We report the results of the evaluation of acoustic properties of nanoporous thin films.     

Generation and detection of incoherent phonons in picosecond ultrasonics

In picosecond ultrasonics experiments the absorption of a femtosecond laser pulse in a thin metallic transducer is used to generate very short acoustic pulses. These pulses are made of coherent longitudinal waves with a frequency spectrum that can reach 100-200 GHz. The laser pulse absorption gives rise to a heating of the film of a few Kelvin within a typical time of 1 ps. Later on, the heat goes in the substrate through an interface thermal resistance and is diffused by thermal conduction. At very low temperature and in pure crystals the thermal phonons emitted by the heated metallic film can propagate ballistically over large distances and produce a so-called heat pulse. We report on the experimental evidence of the coexistence of the coherent acoustic pulse and the incoherent heat pulse generated and detected by laser ultrasonics.     

Characterization of Ta and TaN diffusion barriers beneath Cu layers using picosecond ultrasonics

In computer chips, aluminum is being replaced with copper in order to produce smaller, faster and more efficient electronic devices. The usage of copper allows higher current densities and thus higher packaging densities than aluminum. However, copper leads to new challenges and problems. It has different mechanical properties and a tendency to migrate into the surrounding dielectric and/or semiconducting layers. These diffusion processes can be prevented by so called diffusion barriers. A diffusion barrier is a very thin layer consisting of tantalum and tantalum nitride or titanium and titanium nitride, deposited between the copper and the substrate. A pump-probe setup is used to determine the mechanical properties of the barrier layers and of the copper layer. This short-pulse-laser-acoustic method is contact-free and non-destructive. Mechanical waves are excited and detected thermoelastically using laser pulses of 70 fs duration. Thin film measurements of buried diffusion layers are provided and compared with scanning electron microscopy (SEM), transmission electron microscopy (TEM), and Rutherford Backscattering Spectroscopy measurements (RBS). Results of a thermo-elasto-mechanical simulation are presented and a short overview of the simulation procedure is given. Current limits of the presented method are discussed and future directions of the on-going research project are presented.     

Effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in germanium crystals

A method has been proposed for approximating a phonon spectrum of cubic crystals, which has been obtained from data on inelastic neutron scattering for symmetric directions, over the entire Brillouin zone in the form appropriate for studying relaxation characteristics of phonon systems. The effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in anharmonic processes of scattering with the participation of three longitudinal phonons has been investigated for germanium crystals. It has been shown that the inclusion of the dispersion leads to a decrease in the anisotropy of ultrasonic absorption in the LLL relaxation mechanism and makes it possible to fit the results obtained from calculations of the ultrasonic absorption coefficients to the experimental data in the low-temperature range. The temperature dependence and anisotropy of the relaxation rate of longitudinal thermal phonons in germanium crystals have been determined from experimental data on ultrasonic absorption. The performed analysis has refined values of the relaxation parameters obtained from the interpretation of the data on thermal conductivity of germanium crystals with different isotopic compositions in the isotropic-medium model.     

Pressure tuning of picosecond pulse transmission in germanium

The nonlinear transmission of intense 1.06 μm picosecond pulses in germanium has been measured at several hydrostatic pressures up to 24 kbar. A considerable variation in the enhanced transparency is observed with the maximum deviation from Beer's law observed at 14 kbar. The overall behavior is shown to be consistent with a recently proposed theoretical model in which plasmon-assisted recombination plays a fundamental role in influencing nonlinear pulse transmission in semiconductors.     

Quadrupole interactions of fluorine at implantation sites in germanium and silicon

Implantations of F in crystalline Ge has been examined by the DPAD method. Two unique fluorine EFG sites are found. The results show a strong resemblance to similar data obtained earlier for Si, e.g., in either host an axial symmetric EFG oriented along the <111> crystal direction is observed, also the temperature dependences of site populations follow similar trends. A thorough comparison of the Ge and Si data is given.     

Individual and collective vibrational modes of nanostructures studied by picosecond ultrasonics

We report on picosecond ultrasonic measurements obtained on aluminum and platinum nanostructures with variable dot size and lateral periodicity which realized a 2D phononic crystal. Performing investigations at different resolution scales, we have identified individual modes of vibration depending on the dot size, and mode of vibration strongly correlated with the bi-dimensional organization. The platinum dots sputtered on an aluminum layer have shown a behavior of isolated oscillators without any coupling between neighbor elements in this phononic crystal. The frequency of such normal modes, extracted from time resolved measurements are in good agreement with 3D finite element simulations. In contrast, with aluminum dot systems where the coupling is more efficient we observe a complex spectrum of vibrational modes related to the band structure induced by the bi-dimensional patterning.     

Direct measurement of picosecond and sub-picosecond phonon lifetimes in α-quartz

Using coherent Raman probe scattering of picosecond laser pulses, excited optical phonons at 465 cm^-1, close to the center of the Brillouin zone are investigated. A 3-phonon decay channel is suggested which accounts for the observed large variation of the phonon lifetime from 3.4 ps to 0.8 ps in the temperature range 23 to 295 K.     

Calculations on two phonon bound states in diamond and germanium

A careful numerical calculation is reported searching for two phonon bound states in diamond and germanium. Using the experimental phonon dispersion in germanium and an improved force model for diamond we examined the two phonon Green function for a bound state pole, working in a formulation in which Rayleigh's theorems can be used. Our results are consistent with the possibility of a bound state in diamond and germanium.     

Three-body interaction and phonon dispersion relations in aluminium

Based on an ab initio cohesive energy calculation and a model of three-body interaction, the pair potential can be calculated using the Möbius inversion theorem in the theory of numbers. Then the atomic force constants and the phonon dispersion for A1 are evaluated both with and without three-body interaction. Compared with experiments, the results show that taking the three-body interaction into account considerably improves the dispersions. Contrary to previous work, the method for calculating the atomic force constants and phonon dispersions presented here is simple, with only two adjustable parameters.