Effects of the photogenerated excess carriers on the thermal and elastic properties of n-type silicon excited with a modulated light source: Theoretical analysis

Abstract

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.

Experimental photoacoustic observation of the photogenerated excess carrier influence on the thermoelastic response of n-type silicon

“…1). 23 More importantly, the modulated temperature component T s (l) at the non-illuminated back surface of a plasma-thin sample can be higher than the corresponding one T s (0) at its illuminated front surface, within a wide range of modulation frequencies. 23 In other words, the excess carriers of plasmathin samples can be used to remove the absorbed light energy from the illuminated surface and transfer it to the non-illuminated one, and, therefore, these materials could become efficient heat sinks.…”

“…[14][15][16][17][18] The experimental observation of these effects still remains a challenge due to the separate analysis of either the amplitude or phase of the PA signal in a relatively short range of modulation frequencies. [19][20][21][22][23] The simultaneous monitoring of both of these signals in a wide interval of modulation frequencies is thus desirable to observe the effects of photogenerated excess carriers.…”

“…In our recent theoretical studies of n-type silicon circular plates, 22,23 we noticed that the impact of photogenerated excess carriers on their PA response depends mostly on the semiconductor surface quality determined by the surface recombination speed s, the sample thickness l, and the carrier diffusion length L p ¼ ffiffiffiffiffiffiffi ffi D p τ p , with D p being the diffusion coefficient of the minority carriers with lifetime τ. Favorable conditions for the observation of this impact were found when the illuminated sample surface is passivated (s 1 !…”

Thermal properties study of silicon nanostructures by photoacoustic techniques

“…In the considered case, the source can be expressed as a thermoelastic force that depends on the temperature field in the layers: here I is the intensity of the absorbed radiation, is the optical absorption coefficient. It should be noted that the effect of electron-hole recombination was neglected in heat conduction equation, since the lifetime of carriers in porous silicon and silicon nanowires is small and the recombination processes are fast enough in comparison with period of heating 28,29 . It should be noted that the effects of thermal interface resistance could be neglected because the ratio of the nano-Si sample thickness relative to its thermal conductivity (~10 -5 m 2 K/W) was much higher for all series of samples than the typical thermal interface resistance value (~10 -7 m 2 K/W) [30][31][32] .…”

“…It should be noted that the effect of electron-hole recombination was neglected in heat conduction equation, since the lifetime of carriers in porous silicon and silicon nanowires is small and the recombination processes are fast enough in comparison with period of heating 28,29 .…”