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 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]

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 paper discusses the most common impacts of the measuring system on the amplitude and phase of the photoacoustic signals in the frequency domain using the opencell experimental setup. The highest signal distortions are detected at the ends of the observed modulation frequency range from 20 Hz to 20 kHz. The attenuation of the signal is observed at lower frequencies, caused by the electronic filtering of the microphone and sound card, with characteristic frequencies of 15 Hz and 25 Hz. At higher frequencies, the dominant signal distortions are caused by the microphone acoustic filtering, having characteristic frequencies around 9 kHz and 15 kHz. It has been found that the microphone incoherent noise, the so called flicker noise, is negligibly small in comparison to the signal and does not affect the signal shape. However, a coherent noise originating from the power modulation system of the light source significantly affects the shape of the signal in the range greater than 10 kHz. The effects of the coherent noise and measuring system influence are eliminated completely using the relevant signal correction procedure targeting the photoacoustic signal generated by the sample.

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A hybrid numerical method is proposed involving a successful combination of the equivalent electrodes and boundary element method. Electric field and electric potential distribution are determined by using both equivalent electrodes and equivalent charges. Green's function for potential of the charge per unit length, placed in free space, on the boundary of two dielectrics, is used. Magnetic-field distribution is determined by applying equivalent currents through magnetic vector potential and substitution of Ampere's microscopic currents with total currents. The accuracy of the developed method is highlighted with some simple numerical examples.

The hybrid boundary element method, based on the equivalent electrodes method and the boundary element method, is presented in this article. This method is applied on several examples for calculating the characteristic impedance of transmission lines. It should be emphasized that the combination of the equivalent electrodes method and a new variant of the boundary element method can be efficiently implemented in quasi-transverse electromagnetic analysis of transmission lines without loss of accuracy. All results for the characteristic impedance of the observed transmission lines are compared to corresponding ones obtained by the finite-element method.

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