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Thermally induced ultrasonic emission from porous silicon

26 August 1999 Nature 400, 853 - 855 (1999)

Japanese summary (日本語要約)
工学：熱的に誘起される多孔質シリコンからの超音波放出

空気中で超音波を発生させる最も一般的な方法は、圧電素子や静電気によって固体を振動させ、それを空気の振動へと変換するものである。しかし、この方法で発生する超音波は周波数帯域が狭く、発生可能な音圧は通常10Pa程度以下に限られる。また、微小な素子を多数配列したアレイをつくることも困難であった。シリコン微細加工技術を利用した静電振動方式ではこれらの欠点が克服されつつあるが、駆動に高電圧を必要とすることと、振動膜が機械的に弱いことが実用化にあたっての難点となるだろう。今回、多孔質シリコンから空気への熱伝導により、機械的な振動系をまったく必要とせずに十分な強度の超音波を発生できた。我々の装置は最適化したものではないが、消費電力が1Wcm-2で0.1Paの音圧を実現した。また、少なくとも100kHzまで周波数特性は平坦であった。超音波の発生効率は今後かなり改善できると思われる。さらに、この材料は通常の電気回路との統合に適しているため、この装置から微細なアレイをつくるのは比較的簡単だろう。そうなれば、音響放出の波面全体にわたる制御が可能となる。

H. SHINODA, T. NAKAJIMA, K. UENO & N. KOSHIDA

Department of Electrical & Electronic Engineering, Tokyo University of Agriculture & Technology, 2-24-16 Nakamachi, Koganei, Tokyo 184-8588, Japan

The most common mechanism1 for generating ultrasound in air is via a piezoelectric transducer, whereby an electrical signal is converted directly into a mechanical vibration. But the acoustic pressure so generated is usually limited to less than 10 Pa, the frequency bandwidth of most piezoelectric ceramics is narrow, and it is difficult to assemble such transducers into a fine-scale phase array with no crosstalk2,3. An alternative strategy using micromachined electrostatic diaphragms is showing some promise4,5, but the high voltages required and the mechanical weakness of the diaphragms may prove problematic for applications. Here we show that simple heat conduction from porous silicon to air results in high-intensity ultrasound without the need for any mechanical vibrational system. Our non-optimized device generates an acoustic pressure of 0.1 Pa at a power consumption of 1 W cm-2, and exhibits a flat frequency response up to at least 100 kHz. We expect that substantial improvements in efficiency should be possible. Moreover, as this material lends itself to integration with conventional electronic circuitry, it should be relatively straightforward to develop finely structured phase arrays of these devices, which would give control over the wavefront of the acoustic emissions.

The idea of a thermal sound generator (a "thermophone") was proposed 80 years ago6, in which the acoustic element was a simple self-supporting, thin metal film. The photoacoustic effect in porous silicon has also been reported7,8, but was used to characterize the porous silicon itself from gas expansion in a closed space. One might think that ultrasound generation by heat exchange is not possible, as the thermal conduction is too slow. However, we report here that the experimental device shown in Fig. 1 operates as an efficient ultrasound emitter. It is composed of a patterned, thin aluminium film electrode (30 nm thick), a microporous silicon layer (10 µm thick), and a p-type crystalline silicon (c-Si) wafer. The porous silicon layer consists of many confined silicon nanocrystallites with three-dimensional nanopores9. In our experiment, the porous silicon layer (with porosity of 70%) was formed by a conventional anodization technique in a solution of 55% HF:ethanol = 1:1 at a temperature of 20 °C at a current density of 20 mA cm-2 for 8-40 min. The aluminium electrode was used to input a sinusoidal current into the porous silicon layer, the temperature of which was raised by Joule's heating. The emitted acoustic pressure was measured as a function of output frequency by a microphone type 4138, Brüel & Kjær, Denmark) placed at a position of 3.5 cm from the front surface.

Figure 1 Our device for producing thermally induced ultrasonic emission. High resolution image and legend (155k)
We now explain the device concept, based on a theoretical analysis of thermal conduction phenomena10 in the porous-silicon/air system as illustrated in Fig. 2a. Suppose that a thermal power density q(omega)exp(jomegat) (in units of W cm-2) with an angular frequency omega is provided at the surface of the porous silicon layer through a sufficiently thin metal film on it. When the thickness d of the porous silicon layer is such that


where alpha and C are respectively the thermal conductivity and heat capacity per unit volume of porous silicon, then the surface temperature change T0(omega)exp(jomegat) is given by


if the expansion of porous silicon and the heat flow into the air are neglected (see Fig. 2b). The temperature change induces an acoustic pressure P(x,omega)exp(jomegat) through the alternating thermal expansion of the air. Using the fundamental equations of photoacoustic analysis11, we find that


where PA is atmospheric pressure, TA is room temperature, v is the sound velocity, italic gamma = Cp/Cv = 1.4, k is the wavenumber of free-space sound, alphaa is the thermal conductivity of air, and Ca is the heat capacity per constant unit volume of air. The assumptions in this analysis are as follows: (that is, the sound wavelength is much larger than thermal diffusion length), alphaC italic gammaalphaaCa (that is, the heat flow into the device is much larger than that into the air), and the porous silicon itself does not vibrate. Too large a value of 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(omega)|/|q(omega)| is constant, and independent of omega. This means that an ideal, flat frequency response is expected from this device.

Figure 2 Device operation. High resolution image and legend (42k)

We now evaluate the product alphaC, because it determines the efficiency of the operation as suggested by equation (3). Table 1 shows typical thermal data of porous silicon in comparison to that of c-Si (refs 12, 13). The data of SiO2 are also shown for reference. It is clear that the value of alphaC is 1/400 that of c-Si: this big difference in alphaC between porous silicon and c-Si would prevent heat transfer of an alternating component to the inside of the device, while a possible stationary d.c. component would be quickly removed into the highly thermally-conductive c-Si substrate.

The measured acoustic pressure amplitudes are plotted in Fig. 3 as a function of output frequency for a sinusoidal Joule's heating power of 1 W cm-2. A significantly high acoustic pressure is observed over a wide frequency range up to 100 kHz. The limit of upper measurement frequency at 100 kHz is simply due to the specification of our measurement system; and the condition of equation (1) is satisfied at frequencies above 5 kHz. As predicted by theory, sound intensity is independent of frequency in the high-frequency range where the wavelength is smaller than the device size, although some fluctuations caused by environmental reflection noise are seen. The value of the pressure also coincides with that calculated from equation (2) and the data in Table 1, as P (in Pa) = 0.07 times q (in W cm-2).

Figure 3 Experimental results. High resolution image and legend (5k)

To compare (in Pa) the efficiency of our device with that of conventional methods is not straightforward, as the output acoustic pressure of our device is proportional to the input power per unit area, while that of piezoelectric or electrostatic devices is proportional to the input voltage. For conventional devices, an average membrane displacement of 12.6 nm V-1 at 1.7 MHz has been reported5: this corresponds to 55 Pa V-1, which we take as the highest efficiency at present. A PZT bimorph transducer with impedance matching cone (EFRTUB50K5, Matsushita) generates 2 Pa V-1 at 40 kHz when it is measured at distance of 30 cm. In the survey by Manthey et al.,1 typical efficiencies of both piezoelectric and (non-MEMS) electrostatic types are given as 0.1-1 Pa V-1 at 200 kHz when measured at a distance of 1 m. (Here MEMS indicates micro-electrical-mechanical systems.) As the impedance of our experimental device was 5 Omega, a 1 cm2 device driven by a 5 V source gives a 0.4 Pa plane wave whose intensity is not much less than that of the conventional resonant device, though our device consumes more power. We note that the frequency range of our device is broad, unlike the resonant devices, and that its efficiency increases as the sound intensity increases. The thermo-acoustic coupling factor, which is defined as the square root of the ratio of the acoustic power output to the input electric power, is 0.03% at 1 W cm-2, while that of the conventional method reaches 10%. This low coupling factor is a present drawback of our non-optimized device. But the freedom to select its electrical impedance, and a high intensity free from the upper bound of conventional methods, are also advantages of our device, as are mechanical toughness, ideally flat frequency characteristics, and the potential to assemble a phased array of such devices with low crosstalk.

As a result of the scaling principle in thermal conduction phenomena, the use of dot electrode structures (in which the heat exchange is concentrated in small islands) should greatly improve the efficiency and output acoustic pressure of our devices. Moreover, such construction could prove useful in two-dimensional array fabrication because it provides a large wiring space. On the other hand, as suggested by the data in Table 1, the use of oxidized porous silicon would be a promising and practical approach to enhancing the efficiency.

Although we have not performed rigorous tests of its stability, this device is free from the often-quoted instability of porous silicon. The porous silicon layer is protected by the aluminium electrode from the atmosphere, and is not exposed to an intense electric field. (It is conceivable that oxidation might in fact upgrade the efficiency rather than degrade it.) We can confirm that this device worked well after three months at room temperature, humidity and pressure.

Particular attention has been paid to the visible luminescence of porous silicon14,15,16. It is closely related to an optical bandgap widening, induced by strong quantum confinement in silicon nanocrystallites with the same band dispersions as c-Si (ref. 17). But complete carrier depletion in nanocrystallites associated with strong confinement, on the other hand, leads to extremely low values of alpha and C. The ability to control these parameters over a wide range, and the process compatibility with ultra-large-scale-integration (ULSI) technology--including a large difference in the thermal properties between porous silicon and c-Si--suggests applications of porous silicon in acoustic integrated devices.

Received 18 January;accepted 13 July 1999.

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Acknowledgements. We thank the late M. Fuchigami for his contribution to the analysis and experiments, and S. Ando who motivated this research. This work was partly supported by the Japan Society for the Promotion of Science, and a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.

Correspondence and requests for materials should be addressed to H.S. (e-mail: shino@cc.tuat.ac.jp).
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