# Rapid 3D-Imaging of Semiconductor Chips Using THz Time-of-Flight Technique
## 3 Results and Discussion  
Figure 2a shows the THz TOF imaging result of a packaged chip with dimensions 12.0 mm \(\times\) 20.25 mm \(\times\) 1.0 mm. Figure 2b shows the time-integrated C-scan data (plotted as a function of the \(x\)- and \(y\)-axis), in which the THz envelope signal (obtained via the Hilbert transformation) was time-integrated each pixel. In other words, the envelope signal was achieved from the complex THz signal \(\widetilde{E}_{\rm{THz}}=\rm{Re}(\widetilde{E}_{\rm{THz}})+iH[\rm{Re}( \widetilde{E}_{\rm{THz}})]\), where \(H\) is the Hilbert transformation [30]. The scan range was 22 \(\times\) 22 mm\({}^{2}\), and the pixel size was 100 \(\times\) 100 pxl\({}^{2}\). The bright square in the lower middle region indicates the semiconducting chip embedded in the package, with a size of 5 mm \(\times\) 3 mm. As mentioned previously, THz imaging is a powerful tool for nondestructive mapping of objects such as semiconductor chips embedded in nonconductive envelopes. However, the THz-TDS system has rarely been used for semiconducting analysis, especially with imaging speeds higher than 100 Hz/pixel. Thus, THz-TDS allows us to address the depth profiling of the packaged devices displayed as B-scan results in Figure 2c,d. In other words, in Figure 2c, the THz signal was plotted as a function of the position x (along the horizontal dashed line in Figure 2b) and time-delay (T). Another B-scan image (Figure 2d) taken along the vertical dashed line in Figure 2b shows similar results, with the chip location clearly displayed. It should be noted that the THz reflection signal beneath the chip area is suppressed significantly as most of the signal is reflected by the chip. There are multiple approaches for analyzing image data according to the application. Figure 3 shows a series of C-scan images for different z locations for the sample shown in Figure 2. Figure 3a-c show THz reflection images at top, chip, and bottom surfaces appeared at T = 22.7 ps, 25.9 ps, and 29.5 ps, respectively. Considering the refractive index of the packaging material (n = 2.0), the TOF time differences reveal that the chip surface is located at 0.24 mm (\(\Delta\)T = 3.2 ps) beneath the package surface. Conversely, the bottom surface appeared at 0.5 mm (\(\Delta\)T = 6.8 ps). We note that THz reflection at the other side of the package surface (located at 1 mm beneath the top surface) is very weak as it appeared at T \(\sim\) 36 ps in Figure 2c,d. Consequently, the THz TOF data can then be reconstructed into 3D images, as shown in Figure 3d. Here, different colors were assigned for the structures  
Figure 1: (**a**) A schematic illustration of THz TOF imaging equipment. (**b**) Photograph of the experimental setup. (**c**) A representative THz waveform in the time-domain (A-scan) reflected from a packaged chip. located at different heights, with red indicating the position of the chip. In this regard, 3D imaging could potentially be very effective in locating defects, a task that is virtually impossible using 2D section images. A Fourier transformation of THz amplitudes recorded using TDS spectroscopy allowed for inspection of the sample at specific spectral ranges. Figure 4a shows the spectrum of the reflected signal when the THz beam and the chip share a position. The oscillatory pattern is due to interference between different layers. A series of C-scan images are shown in Figure 4b-d, for the frequencies of 0.4 THz, 0.7 THz, and 1.0 THz, respectively. The transverse resolution was improved dramatically as we employed the high-frequency components, although the signal strength decreases with increasing frequency (from 1.8 mm at 0.4 THz to 700 um at 1.0 THz.) Therefore, it is desirable to develop THz sources with higher frequency ranges to identify the defects with a better transverse and longitudinal resolution for practical application in the industry.