tuning the distance between the transducer and the reflecting wall.
The transmission angle can be calculated using the Brekhvoskikh’s
method [30]. This method results in a theoretical transmission angle
of 29.9 for a Si wafer with a thickness around 775 lm and a
driving frequency of 928 kHz. The calculated angle corresponds
to the observed reflected power peak. Next, the anechoic material
is included at all the vertical walls of the cleaning tank and the re-
flected power peak disappears. As a result, a wave with a large
traveling component is obtained around the transmission angle
of the wafer.
The sound emission or cavitation noise spectrum at 450 mW/
cm2 for a wafer placed at the transmission angle is shown in
Fig. 3(a). This spectrum is corrected by subtracting the background
signal, recorded when no sound wave is applied. The cavitation
noise spectra are averaged over approx. 60 spectra, which are obtained
during one minute. This averaging is necessary since bubble
activity in bubble clouds varies over time. The sub and higher harmonics
in the sound emission spectrum are clearly visible. Fig. 3(b)
shows the sum of the intensity of the 3/2, 5/2 and 7/2 harmonic
peaks as function of the applied power density. Each data point
is the average of 6 measurements (each measurement is an average
of approx. 60 cavitation noise spectra) in order to reduce uncertainty.
The error bars represent the standard deviation of these 6
measurements. A clear increase in the acoustic emission of the
subharmonic intensity peaks as function of the power density
can be observed, which verifies the measurement technique.
Fig. 3(c) indicates the intensity variations for the sum of the 3/2,
5/2 and 7/2 harmonic peaks at 320 and 450 mW/cm2 forward
power for several angles of incidence (defined in Fig. 1). A measurement
at a lower power of 320 mW/cm2 is also included since
the intensity versus applied power curve shows a stronger variation
around 320 mW/cm2 compared to 450 mW/cm2 with a lower
signal to noise ratio. For both powers, the subharmonic peak intensity
shows no clear trend when the angle of incidence of the Si wafer
is varied. This can be caused by the fact that various phenomena
play a role. On the one hand, bubbles are attracted towards nodes
or antinodes in a standing wave field depending on their size, so
the local bubble density in a standing wave field is higher. This increases
the bubble bubble interaction and the bubble coalescence
rate. Other experiments with charged surfactants showed that
bubble bubble interaction and the increase in bubble coalescence
rate lower the harmonic maxima [19]. On the other hand, the maximum
acoustic field amplitude is higher for a standing wave
(sound reflection present) than when a traveling wave is applied.
A higher acoustic amplitude should increase the subharmonic
intensities. Both effects play at the same time, which makes the
subharmonic variation as function of the wafer angle difficult to
interpret.
On the other hand, cleaning tests performed as a function of the
angle of incidence do show a surprisingly clear trend. During the
first 2 min of the cleaning procedure, the wafer is scanned 1.5 cm
vertically upwards. Next, the wafer is moved 0.5 cm horizontally
and scanned 1.5 cm down again during the following 2 min (the total
duration of the cleaning procedure is 4 min). The wafer movement
is implemented to obtain a more uniform clean, by
averaging out to some extent the near-field pressure maxima created
by the large dimensions of the transducer. The pressure distribution
of the transducer has been measured and simulated before
[31]. The average PRE over the sonicated area is plotted in Fig. 4.
Each measurement was repeated 3 times, and the error bars show
the standard deviation of the average PRE. In contrast to the sound
emission measurements, the PRE experiment shows a peak around
the transmission angle of the wafer. Particle removal is maximized
when the traveling wave component is maximized, while particle
removal is completely absent at angles 620 and P40. The individual
cleaning maps are shown in Fig. 5. In order to compare
F