August_EDFA_Digital

edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 22 NO. 3 30 cell. Therefore, to increase the receiver sensitivity, the I CMUT should be increased. The receive current signal I CMUT is given by the following equations. where d g is the gap height, d dt and d db are the thickness of the insulating layers on the topandbottomside of the gap, and ε r is the relative dielectric constant of the insulating layers, respectively. The sumof d g , d dt , and d db needs to be decreased to decrease d 0 . Figure 3 shows a fabricated CMUT receiving probe for through-transmission SAT. The CMUT cell array was con- nected to a pair of 2 m coaxial cables, as shown in Fig. 3a. The cable from the lower electrode was connected to the DC voltage source, and the cable fromthe upper electrode was connected to an IV converter. A transimpedance amplifier (TIA) with a feedback resistance of 10 kΩ was used in the IV converter. The CMUT cell array consisted of approximately 10,000 cells connected in parallel in a 2-mm-diameter circle (Fig. 3b). The fabricated CMUT cells were hexagons with side lengths of 10 µm (Fig. 3c). Cross-sectional SEM images of the fabricated CMUT cell are shown in Fig. 3d. The gap width was 20 µm. A gap of 30 nm in height between the upper and lower electrodes was formed, and insulating filmswith a thickness of 50 nm were formed above andbelow the gap as shown in Figs. 3e and f. The equivalent distance between electrodes in the vacuum was 55 nm ( d g = 30 nm, d dt = 50 nm, d bt = 50 nm), which was much smaller than the distance (from 100 to 200 nm) used in the conventional medical ultrasonic diag- nostic apparatus. The center frequency of the CMUT cell was designed to be 30 MHz. HIGH RESOLUTION IMAGING WITH THROUGH-TRANSMISSION METHOD USING CMUT RECEIVING PROBE A scanning acoustic tomography apparatus (FineSAT III Hitachi Power Solutions Co. Ltd.) was used in through- transmission imaging of the internal structure of a ball grid array (BGA) package with a thickness of 2.3 mm. [7] A focused 50-MHz piezoelectric probe was used as the transmitter. The transmitting probe was placed at a focal point 13 mm above the BGA package sample on a 2-mm- thick acrylic plate. The 30-MHz CMUT probe was used as the receiver. The CMUT receiving probe was placed 12 mm below the bottom surface of the acrylic plate. An unfocused 25-MHz piezoelectric probe was also used as a receiver for comparisonwith the CMUT receiving probe. A DC voltage of 80 V was applied to the CMUT receiving probe. Figure 4 shows through-transmission SAT images of the BGApackage takenwith the CMUT andpiezoelectric receiving probes. There is a delaminated area at the center of both images, and it is represented as a dark spot. The image taken with the CMUT receiving probe had a higher resolution than that with the piezoelectric one as shown (Eq 4) (Eq 5) (Eq 6) In Eq 4, Q CMUT is the charge induced in the electrodes, C ( t ) and V ( t ) are the capacitance and voltage at time t , and V dc is the DC voltage applied between the electrodes, respectively. In the reception of ultrasound, V ( t ) is a con- stant; therefore, dV ( t )/ dt is zero, and V ( t ) is V dc . In Eq 5, x is the displacement of the membrane in the reception of ultrasound, ε 0 is the dielectric constant of the vacuum, S is the overlapping area of the electrodes across the gap, and d 0 is the equivalent distance in the vacuum between the upper and lower electrodes, respectively. The derivative of capacitance with respect to time in Eq 4 can be expressed as that of the displacement of the membrane (Eq 5). In most cases, x ismuch smaller than d 0 ; therefore, I CMUT is re- written as the product of ε 0 S/d 0 , E , and dx / dt as shown in Eq 6, where ε 0 S/d 0 is the capacitance at V dc = 0V, dx / dt is the velocity of the membrane in the reception of ultra- sound, and E is the electric fieldbetween the electrodes. To increase the I CMUT , the product should be increased. As for the capacitance ε 0 S/d 0 , ε 0 is a constant, and S has anupper limit value depending on the CMUT cell size; therefore, d 0 is the parameter that can increase I CMUT . Electric field E has an upper limit value that can be applied to the insulating layers between electrodes; therefore, it cannot increase beyond that. The velocity of themembrane dx / dt is deter- mined by the sound pressure and the frequency of the received signal; therefore, it cannot be improved by the performance of the CMUT cell. Therefore, decreasing d 0 is the only way to increase I CMUT . The equivalent distance in the vacuum between the upper and lower electrodes ( d 0 ) is defined by (Eq 7)