Theoretical model for optically excited two-layer elastic plate, which includes plasmaelastic, thermoelastic, and thermodiffusion mechanisms, is given in order to study the dependence of the photoacoustic (PA) elastic bending signal on the optical, thermal, and elastic properties of thin film—substrate system. Thin film-semiconductor sample (in our case Silicon) is modeled by simultaneous analysis of the plasma, thermal, and elastic wave equations. Multireflection effects in thin film are included in theoretical model and analyzed. Relations for the amplitude and phase of electronic and thermal elastic bending in the optically excited two-layer mechanically-supported circular plate are derived. Theoretical analysis of the thermodiffusion, plasmaelastic, and thermoelastic effects in a sample-gas-microphone photoacoustic detection configuration is given. Two normalization procedures of the photoacoustic elastic bending signal in function of the modulation frequency of the optical excitation are established. Given theoretical model can be used for various photoacoustic detection configurations, for example, in the study of optical, thermal, and elastic properties of the dielectric-semiconductor or metal-semiconductor structure, etc., Theoretical analysis shows that it is possible to develop new noncontact and nondestructive experimental method—PA elastic bending method for thin film study, with possibility to obtain the optical, thermal, and elastic parameters of the film thinner than 1 μm.
Methods for photoacoustic signal measurement, rectification, and analysis for 85 μm thin Si samples in the 20-20 000 Hz modulation frequency range are presented. Methods for frequency-dependent amplitude and phase signal rectification in the presence of coherent and incoherent noise as well as distortion due to microphone characteristics are presented. Signal correction is accomplished using inverse system response functions deduced by comparing real to ideal signals for a sample with well-known bulk parameters and dimensions. The system response is a piece-wise construction, each component being due to a particular effect of the measurement system. Heat transfer and elastic effects are modeled using standard Rosencweig-Gersho and elastic-bending theories. Thermal diffusion, thermoelastic, and plasmaelastic signal components are calculated and compared to measurements. The differences between theory and experiment are used to detect and correct signal distortion and to determine detector and sound-card characteristics. Corrected signal analysis is found to faithfully reflect known sample parameters.
The photogenerated excess carriers’ influence on the temperature distribution and thermoelastic photoacoustic signals of n-type silicon excited with a light source of modulated intensity is theoretically investigated for modulation frequencies ranging from 1 to 107 Hz. This is done by comparing the amplitude and the phase of the temperature and photoacoustic signals with and without the presence of excess carriers, giving special attention to the presence of characteristic peaks of the amplitude ratios and phase differences between the signals at the front and rear sample surfaces. It is shown that these peaks can be understood as the fingerprints of the excess carrier presence in the semiconductor. Furthermore, the strong dependence of the temperature distribution on the carrier recombination processes at the surfaces of thin samples is quantified and found to drastically change the thermoelastic component of the photoacoustic signal.
The aim of this work is the development of photoacoustic (PA) method for the measurement and determination of parametres of thin films (with a thickness of less than 1 μm). Experimental study of the optical, thermal, and elastic characteristics of the thin film on Si substrate by PA elastic bending method was given. Thin film–semiconductor (Si) sample is modeled by simultaneous analysis of the plasma, thermal, and elastic wave equations. Two normalization procedures of the PA elastic bending signal in function of the modulation frequency of the optical excitation were established. The experimental PA elastic bending signals were measured and analysed. Without loss of generality, the TiO2 thin film (with a thickness of 0.5 μm) on Si substrate (circular plate) was experimentaly studied. We have studied the PA elastic bending signals in order to obtain the values of optical, thermal, and elastic parameters of TiO2 film. The analysis shows that it is possible to develop noncontact and nondestructive experimental method—PA elastic bending method for thin film study, with possibility to obtain the optical, thermal, and elastic parameters of the film thinner than 1 μm.
Based on the experimental and theoretical signals of an open photoacoustic cell operating with modulation frequencies from 20 Hz to 20 kHz, a significant contribution of photogenerated excess carriers on the thermal and thermoelastic responses of an n-type silicon plate is observed for the very first time. This is achieved by comparing the measured amplitude and phase of the photoacoustic signal with their corresponding theoretical thermoelastic counterparts, for high enough modulation frequencies mainly. It is shown that the amplitude of the thermoelastic component of plasma-thin samples varies about two orders of magnitude with respect to the corresponding one of plasma-thick samples. Furthermore, we find a maximal temperature difference ΔT = − 35 nK between the illuminated and non-illuminated sample surfaces, which shows that thin silicon plates with excess carriers could be used as heat sinks.
The temperature distributions in the n-type silicon circular plate, excited by a frequency-modulated light source from one side, are investigated theoretically in the frequency domain. The influence of the photogenerated excess carrier density on the temperature distributions is considered with respect to the sample thickness, surface quality and carrier lifetime. The presence of the thermalization and non-radiative recombination processes are taken into account. The existence of the fast and slow heat sources in the sample is recognized. It is shown that the temperature distribution on sample surfaces is a sensitive function of an excess carrier density under a bulk and surface recombination. The most favorable values of surface velocities ratio and bulk lifetime are established, assigned for a simpler and more effective analysis of the carrier influence in semiconductors. The photothermal and photoacoustic transmission detection configuration is proposed as a most suitable experimental scheme for the investigation of the excess carrier influence on the silicon surface temperatures. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. ON171016]
International audienceThe open-cell photoacoustic signal measured in the transmission configuration for aluminum thin plates with thicknesses of 280 lm, 197 lm, and 112 lm is experimentally and theoretically analyzed, in the 20 Hz–7 kHz modulation frequency range. It is shown that the observed differences between the predictions of the standard thermoelastic model and the experiment data of both the amplitude and phase of the photoacoustic signal can be overcome by considering the aluminum samples coated with a thin layer of black paint as volume-absorber materials. This new approach provides a quite good agreement with the obtained experimental data, in the whole frequency range, and yields an effective absorption coefficient of (16 6 2) mm À1 , for a 280 lm-thick sample. The introduction of the finite absorption coefficient led to the correct ratio between the thermal diffusion and thermoelastic components of the photoacoustic signal. Furthermore, it is found that the " volume-absorber " approach accurately describes the behavior of the amplitude, but not that of the phase recorded for a 112 lm-thick sample, due to its relatively strong thermoelastic bending, which is not considered by this theory. Within the approximation of the small bending, the proposed " volume-absorber " model provides a reliable description of the photoacoustic signal for Al samples thicker than 112 lm, and extends the applicability of the classical " opaque " approach
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