ABSTRACT
Shinoda et al. (1999) explained the effect of ultrasound generation by PSi, based on a theoretical analysis of thermal conduction phenomena (Holman 1963) in the PSi/air system. Later generalized theory of thermo-acoustic emission from nanocrystalline PSi was proposed by Hu et al. (2012) and Wang et al. (2014). One should note that the idea of a thermal sound generator (a “thermophone”) was offered 80 years ago by Arnold and Crandall (1917). In their proposal, the acoustic element was a simple self-supporting thin metal film. Experimental and theoretical studies have shown that the thermo-acoustic effect observed in PSi is presumably because of complete carrier depletion-both the thermal conductivity and the heat capacity per unit volume of PSi are extremely low in comparison to those of c-Si. Ultrasound is emitted from the still PSi device as illustrated in Figure 10.2 by an AC electrical input and subsequent fast heat transfer to air. According to Shinoda et al. (1999), the temperature change induces an acoustic pressure P(x, ω)
FIGURE 10.1 A schematic of the cross-sectional view of the fabricated nanocrystalline PSi (nc-PSi) device and experimental configuration for sound emission measurements. (From Migita T. et al., Jpn. J. Appl. Phys. 41, 2588, 2002. Copyright 2002: The Japan Society of Applied Physics. With permission.)
exp (jωt) through the alternating thermal expansion of the air. Using the fundamental equations of photoacoustic analysis (McDonald and Wetsel 1978), it was found that
(10.1) P x A j x C
q A C
P T
( , ) exp( ) ( ),ω κ α
ω γα
υ =
−
= ⋅ a
where α and C are the heat conductivity and the heat capacity per unit volume of the insulator, i.e., PSi, Pa is atmospheric pressure, Ta is room temperature, v is the sound velocity, γ
γ = =
C C
p 1 4. , k is
the wavenumber of free-space sound, α is the thermal conductivity of air, and Ca is the heat capac-
ity per constant unit volume of air. The assumptions in this analysis are as follows: κ ω α
(that is, the sound wavelength is much larger than thermal diffusion length), αC ≫ γαaCa (that is, the heat flow into the device is much larger than that into the air), and the PSi itself does not
FIGURE 10.2 Device operation. (a) The air/thin-Al-film PSi/c-Si structure and the coordinate configuration. (b) Current I introduced into the top electrode induces the surface temperature change T0 by Joule’s heat q, which produces acoustic pressure P. Following an induced Joule heating, the temperature at the device surface fluctuates with a frequency two times higher than the input frequency. Because of an effectively quenched thermal conductivity in the nc-PSi layer, the change in the surface temperature is instantly and directly transferred to the expansion and compression of air in the region in proximity to the front surface. It directly induces sound pressure, while both the bulk and the surface of the PSi layer remain mechanically stable. (Reprinted by permission from Macmillan Publishers Ltd. Shinoda H. et al., 400, 853, copyright 1999.)
FIGURE 10.3 Observed frequency characteristics of thermally induced nc-PSi ultrasonic emitter. The electrical power input was 1 W/cm2. A decrease in the sound pressure observed in the low frequencies is related to the situation in which the sound wavelength is larger than the device size. (Data extracted from Shinoda H. et al., Nature 400, 853, 1999; and Migita T. et al., Jpn. J. Appl. Phys. 41, 2588, 2002.)
vibrate. Too large a value of PSi layer thickness (d) causes a stationary temperature rise on the surface (which is useless for our purposes) and, in contrast, too small a d decreases the signal of the acoustic pressure amplitude itself. We note that the ratio |P(ω)|/|q(ω)| is constant, and independent of ω. This means that an ideal, flat frequency response is expected from this device. Following experiments (Asamura et al. 2002; Migita et al. 2002; Watabe et al. 2006a) and theoretical simulations, Hu et al. (2012) and Wang et al. (2014) confirmed this model. In particular, Figure 10.3 shows flat frequency response of PSi-based emitters.
