Jian‐chun Cheng

Thermoelastic response of pulsed photothermal deformation of thin plates

A theoretical investigation of the dynamic thermoelastic response of pulsed photothermal deformation (PTD) deflection detections for some Q‐switch laser pulses and finite thickness samples has been presented. The results show that signals can be characterized by a quasistatic process when the laser pulse rise time is on the order of 1 μs and the sample thickness is in submillimeter range (typically for semiconductor wafers). However, as the pulse rise time decreases or the sample thickness increases, the dynamic wave behavior gradually becomes apparent, and the quasistatic approximation gives only a contour curve of the dynamic time evolution. When the rise time decreases on the order of 10 ns or less for the same kind of the samples, the PTD deflection signal reflects a totally dynamic wave behavior.

Excitations of thermoelastic waves in plates by a pulsed laser

The method of the eigenfunction expansion, also known as the expansion in normal modes, is employed to study numerically the axisymmetric excitation of the thermoelastic waves in plates by a pulsed laser. This method gives a systematic treatment and allows one to investigate not only the quasistatic and dynamic thermoelastic responses of pulsed photothermal deformation on the time scale of 1 μs, but also the thermoelastic generation of longitudinal, transverse, and surface acoustic waves in thick materials, as well as the excitations of the Rayleigh-Lamb wave modes in thin plates. The formalism is particularly suitable for waveform analyses of the excitations of transient Lamb waves in thin plates because one needs only to calculate the contributions of several lower eigenmodes. The numerical technique provides a quantitative tool for the experimental determination of material properties, especially the mechanical and elastic properties of free-standing films and thicker sheet materials by thermoelastic detection.

Study of acoustic wave behavior in silicon-based one-dimensional phononic-crystal plates using harmony response analysis

We promote an efficient method named harmony response analysis (HRA) as a comparison with transient response analysis and supercell plane wave expansion (supercell PWE) to study the behavior of Lamb wave in silicon-based one-dimensional composite plates. To implement HRA for dealing with Lamb waves in phononic-crystal plates, the viscous-spring artificial boundaries are employed to eliminate the boundary reflection in maximum. With the calculation of displacement field, the propagations of elastic waves under different frequency loads (inside/outside the completed band gap) are investigated in details. The method is then applied in plates both with and without substrate. We further study the plates with quasiperiodicity (generalized Fibonacci systems and double-period system) and investigate the change in band gaps induced by the quasiperiodicity.

Three‐dimensional theory to study photothermal phenomena of semiconductors. I. Modulated optical reflectance

A thorough theoretical study of the modulated optical reflectance (MOR) response of semiconductor samples has been presented. The three‐dimensional plasma and thermal equations are solved analytically, and then numerical calculations are given for the high‐frequency MOR signal. The influences of the optical, thermal, and electronic parameters on the MOR signal are discussed in detail. The generation mechanisms of the MOR signal will be clarified. On the other hand, the mathematical analyses also provide a quantitative tool by which one can fit the theoretical curves to experimental data to determine several material parameters, such as the surface recombination velocity, the lifetime of photogenerated carriers, and thermal conductivity of the materials.

Three‐dimensional theory to study photothermal phenomena of semiconductors. II. Modulated photothermal deflection

The investigation is further extended to the modulated photothermal deflection (PTD). The three‐dimensional Navier–Stokes equation is solved analytically for a layered‐structure sample, and then numerical calculations are given. The influences of the optical, thermal, and electronic parameters on the PTD signal are discussed in detail. It is shown that the thermal lens and electronic‐strain effects make significant contributions to the PTD signal, but the thermoelastic effect is dominant. The potential applications of the PTD technique to microscopic imaging are discussed.

Mechanisms of laser-generated ultrasound in plates

A theoretical study on the thermoelastic generation mechanisms of the characteristic elastic waveforms excited axisymmetrically by a pulsed laser in plates is presented by employing the method of eigenfunction expansion. The method gives a systematic treatment and allows one to investigate not only the thermoelastic generation of longitudinal, transverse and surface acoustic waves in thick samples, but also the excitation of the Rayleigh-Lamb wave modes in thin materials. The three-dimensional theoretical modelling takes account of both the sub-surface thermoelastic source (due to thermal diffusion and optical penetration into the solid) and the surface source resulting from the thermoelastic mode conversion at the illuminated surface. The excitation of the transient Lamb waves is also studied thoroughly in thin isotropic materials, and the results indicate that the Lamb waves characterized by a spike (termed sheet waves) and the frequency-modulated oscillation signal in a very thin sample will approach the Rayleigh wave in nature as the thickness of sample increases. The numerical technique provides a quantitative tool for experimental determination of material properties.

Long wavelength propagation of elastic waves in three-dimensional periodic solid-solid media

We present an approach for efficient, accurate calculations of the elastic wave properties of three-dimensional periodic solid-solid media with cubic lattice structures based on the principle that the elastic wave should be uniform when averaged over length scales much larger than the size of the scatterers. Utilizing the fact that the media has the same pure mode properties as natural crystal with the corresponding lattice structure, we derive formulas for effective velocities propagating along and normal to the lattice axis, from which three independent effective elastic moduli are calculated, respectively. Effective velocities propagating along any directions can be calculated with this method, which captures the multiple scattering and the structure of the periodic medium. The results agree well with those calculated directly from the slope of the corresponding bands near the Γ point of the first Brillouin zone and are in good agreement with previous isotropic theory at high-symmetry directions.

Reconstruction theory of thermal conductivity depth profiles by the modulated photoreflectance technique

A reconstruction theory of thermal conductivity depth profiles from modulated photoreflectance data has been reported. This theory is based on the pulsed spectrum technique and a regularization method. The performance of this approach is illustrated by numerical simulations.

Theoretical studies of pulsed photothermal phenomena in semiconductors

This paper presents a thorough theoretical study of pulsed photothermal phenomena in semiconductors. The explicit expressions of the temporal distributions of plasma wave, thermal wave, and displacement field within a finite semiconductor sample, excited by an incidence of the pulsed laser, are derived analytically. We simulate numerically the time evolutions of the pulsed photothermal optical reflectance, the pulsed photothermal optical beam deflection (i.e., Mirage effect), and the pulsed photothermal displacement signals for different characterized parameters of semiconductor samples. The theoretical works are significant to provide a quantitative time‐ and space‐resolved study of dynamic deexcitation processes and characterization of parameters of semiconductor samples under normal experimental conditions by the pulsed photothermal techniques.

A new method of reconstruction of thermal conductivity-depth profiles from photoacoustic or photothermal measurements

A new method to reconstruct the continuously inhomogeneous thermal conductivity-depth profiles of solid samples from photoacoustic or photothermal measurements by employing a hybrid of a Newton-like iterative method and a regularization method is presented. Three different error functions are defined in order to seek the proper regularization parameters automatically. Generally, the photoacoustic or photothermal signal is proportional to the temperature variation of the samples surface, therefore the profiles reconstruction requires only measurements of the photoacoustic or photothermal signal over a sufficiently wide frequency range. The numerical experiments demonstrate that this algorithm is effective and stable for the reconstruction of profiles from the measured data with random noise.