## 1 Introduction  
Flip chip technology, which uses the solder balls to achieve electrical and mechanical interconnection between the chip and the substrate, has been widely used in many fields of high-density microelectronic packaging due to its advantages of improving the speed of signal transmission and processing as well as reducing stray capacitance and parasitic inductance [1, 2]. With the development of solder balls in flip chip toward high density and ultra-fine spacing, the size effect and surface effect will be more obvious [3]. At the same time, due to the lead-free materials used in the package and the internal structure of the chip in the packaging process, it is inevitable that thermal stress deformation and stress concentration happen, resulting in internal defects of solder balls, such as voids, cracks, ball missing and so on [4, 5], as can be seen in Figure 1. For ensuring the high reliability of internal connection, effective methods for non-destructively detecting the defects of flip chip are needed. A variety of techniques including \(X\)-ray microscopy [6], laser ultrasound [7], active infrared thermal imaging [8], vibration analysis [9], and AMI (acoustic micro imaging) [10, 11, 12] have been proven to be available for detecting the defects of interconnections in flip chip. \(X\)-ray detection technology has been widely used in non-destructive detection of defects; however, this method requires expensive equipment, generates harmful radiation to the human body, and needs experienced operators. [PERSON] et al. [13] established a defect diagnosis system of flip chip based on active infrared detection technology, which can successfully distinguish the temperature difference between the ball missing and defect-free solder ball, and realized the defect of ball missing diagnosis and recognition. Active infrared thermal detection technology has a better effect on detecting flip chip with a larger solder ball size, but as the size of the solder ball of the flip chip further shrinks, the resolution of the infrared camera cannot meet the detection requirements. Compared with active infrared thermal imaging technology, AMI has the highest detection resolution up to the submicron level, which completely covers the detection range of the microsystem from the grain boundary, grain, and characteristic size to the whole microstructure [14; 15; 16]. AMI technology is one of the most widely used techniques in the non-destructive testing of materials [17]. High-frequency ultrasound for micro-defects diagnosis technology refers to acoustic micro imaging technology, which has been effectively applied to the detection of typical defects such as voids, cracks, and ball missing [18]. It uses the high-frequency ultrasound emitted by the high-frequency focusing probe. The ultrasound wave propagates into the detected sample through the acoustic lens and the coupling medium-deionized water. When the acoustic wave is reflected, scattered, and transmitted at different interfaces within the object, the echo signal is received again through the probe. We can detect the position and size of micro defects in the object by comparing and analyzing both the time domain and frequency domain of a single point and the whole process echo signal carried out through the signal processing system [19]. [PERSON] et al. [20] used the MP and CP4 ultrasonic probes of 230 MHz to scan the same flip chip and obtained two ultrasonic images of the chip, and the chip defects are detected by image processing in a complementary way. This method can be used for the detection of solder ball cracks, but the image acquisition time is long, and the image processing is complex, so it is not suitable for online defect detection. For the current ultrasonic detection system, due to the wave characteristics of acoustic waves, the focus is a circular region with a diameter close to the wavelength size. This phenomenon causes the problem of edge blurring of ultrasound image [21].