1. Introduction
The miniaturization of electronic devices has led to the advancement of three-dimensional (3D) integration technologies, which are a fabrication method in which dices or wafers are stacked in the height direction and then interconnected perpendicularly and/or horizontally. These technologies support the following features: multifunction, smaller form factor, higher integration density, more advanced electrical characteristics and reliability, higher communication bandwidth, less communication power, less production cost, and effective thermal dissipation [
1]. However, this trend has also resulted in a new increased structural complexity of microelectronic devices. Also, new types of failures arising in service or fabrication process can occur. Consequently, fault isolation (FI) or failure analysis (FA) tasks for the identification of defects in the integrated circuits (ICs) become more complicated.
Because local exothermic faults, one of the major types of faults possible in microelectronic devices, may be caused by electrical short circuits, junction breakdowns, high resistive opens, or other kinds of internal faults [
2,
3], microscopic thermography methods can be a very useful tool for FI or FA. Several thermography techniques for microelectronic devices have been developed and utilized to analyze the thermal characteristics of them, such as photon emission microscopy (PEM) [
4], liquid crystal thermography (LCT) [
5], fluorescence micro-thermography (FMT) [
6], scanning thermal microscopy (SThM) [
7], steady-state infrared thermography (IRT) [
8], and thermo-reflectance microscopy (TRM) [
9]. However, these techniques are not applicable to locate the defects at interconnect levels in miniature multi-layered integrated architectures such as microelectronic devices, because they have some limitations in the depth estimation of heat sources which are buried in multi-layered opaque materials. To overcome this limitation, lock-in thermography (LIT) has been developed by incorporating a lock-in algorithm into the infrared thermal sensing technique [
10,
11,
12,
13,
14]. LIT enables the effective spatial and temperature resolutions to be improved through the dynamic and averaging nature of it. Therefore, it facilitates the detection of exothermic fault by providing enhanced position or depth information of fault [
15].
Since the seminal work on LIT by Busse et al. [
10], many research efforts have been devoted to the application of LIT to ICs, semiconductor packages, or semiconductor devices for FA [
2,
3,
12,
16,
17,
18,
19]. Breitenstein et al. [
12] investigated the shunting and leakage phenomena in electronic devices such as solar cells and metal oxide semiconductor (MOS) structures by developing dynamic precision contact thermography (DPCT), which is the first LIT technique enabling the detection of temperature of 100 μK with a spatial resolution of 30 μm. Rakotoniaina et al. [
2] improved the performance of LIT systems to include enhanced temperature and spatial resolution functions, and to non-contact methods, and used this system for detecting local shunts in solar cells and for localizing weak heat sources in ICs. These studies provided valuable data to establish LIT for application to semiconductor packages; however, it is restricted to detecting the 2D failure location only. More recently, Schmidt et al. [
3] experimentally showed that LIT can be used for 2D defect localization on decapsulated and fully packaged ICs and for 3D faults isolation in a stacked die device by calculating the phase shift. However, they used a heat source configuration that only passes the covering encapsulation material, such as a mold compound with low thermal diffusivity, to demonstrate the principle of 3D hotspot localization.
Because actual IC or semiconductor packages are stacked by dissimilar materials with different thermal properties, e.g., thermal diffusivity, the influence of these properties has to be considered when calculating the phase shift. Considering these facts, the phase shift for 3D defect localization on the effects of the thermal contact resistance between two different layers should be quantified by various heat source configurations [
18]. Kijkanjanapaiboon et al. [
19] investigated the accuracy of the interpretation of the LIT data based on semi-infinite models, which have a heat source located at the origin and homogeneous material with infinite dimensionality, by using an analytical solution and finite element (FE) analysis. They focused on analyzing the effects of using finite dimensionality, heat source configuration, the convective heat transfer coefficient, the thickness and thermal diffusivity of the material, and the lock-in frequency in a homogeneous and single material, by calculating the difference in the phase shift and the estimated depth of the error. They also investigated the effect of the shapes and locations of the heat source and the multiple materials, by calculating the phase shift only. Even though these studies addressed the problem relating to the use of multiple materials, they did not present an estimation of the depth of the actual defect within the multi-layered structures. Furthermore, their examination was based on a semi-infinite model only. Actually, to locate the depth using LIT, it is of considerable importance to understand the effect on the 3D defect localization by the system parameters and sample properties such as the sensitivity of the infrared camera, the optical properties of material such as transparency and emissivity, the thermal properties of the material such as thermal diffusivity, the sampling rate, and heat source configuration [
19,
20]. Therefore, the combination of experimental and numerical demonstrations for actual LIT applications is very important for the success of 3D defect localization in 3D IC or semiconductor packages.
The objective of this study was to demonstrate the feasibility and superiority of LIT method for the 3D localization of an exothermic fault within multi-layered structures through experimental and numerical approaches. For this goal, an infrared microscopic imaging system was constructed, and two silicon wafer stacked heat source chips (SSHSCs) were fabricated. In addition, the 3D FE models of the SSHSCs were developed for the coupled electro-thermal simulation of them. The specific objectives of this study were to analyze phase shifts of transient thermal responses; secondly, to estimate the depth of heat source buried in test samples (SSHSCs) by using LIT experiments and FE simulations; and, to investigate the effects of the volumetric heat source configuration on the depth estimation by carrying out a FE simulation of through silicon via (TSV) mimicking models.
5. Results and Discussion
The lock-in technique was used to reconstruct the phase image of registered thermal sequences, and the resultant phase images were evaluated for different lock-in frequency and bias voltage.
Figure 6a,b show the representative phase images of the two SSHSCs for various lock-in frequencies with bias voltage of 4 V. The halo in
Figure 6 indicates the heat generation of the polysilicon resistor that exists at the bottom of the SSHSC; therefore, an exothermic fault, which was not clearly detected by conventional infrared imaging techniques such as passive infrared imaging and pulse thermography, was more clearly isolated by lock-in operation [
23,
24]. In addition, the contrast created by the halo in the phase image has increased for increasing lock-in frequency. Basically, because a lock-in operation of high frequency utilizes more periods during calculation, it naturally leads to the calculation of a high-contrast phase image with high frequency. This phenomenon was well verified by the phase images of
Figure 6, which are calculated for increasing lock-in frequencies.
An analysis of the thermal response obtained from the numerical simulation showed that the thermal diffusion mechanism in the multi-layered structure was clearly represented, and the phase shift was analyzed using lock-in method.
Figure 7 shows the numerical simulation results on the transient thermal responses for the two-layer and three-layer SSHSC for the whole range of lock-in frequencies with different bias voltages, by representing the continuous cycle. The temperature was measured at a point located on the surface at a vertical distance from the heat source (see
Figure 5a). For all cases, the amplitude of the periodical temperature (
) was raised with an increase in the bias voltage, whereas the size of
diminished with an increase in the lock-in frequency at the same voltage. A comparison of the two-layer SSHSC (thick) with the three-layer SSHSC (thin) under the same Joule heating conditions revealed that
was larger for the thin specimen than the thick one. From these results, we could suppose that
is basically related with the magnitude of the
(according to the electric power formula
), the heating time within one cycle is determined by the lock-in frequency, material thickness, and configuration.
For a detailed analysis, we enlarged the view of the final cycle in
Figure 7 of the thermal response profiles for all bias voltages with lock-in frequency of 1 and 5 Hz for the two-layer SSHSC and 2 and 10 Hz for the three-layer SSHSC, respectively, as shown in
Figure 8. As can be found by the marked orange and blue point indicating the peak temperature in a cycle, the locations within the time period were almost identical regardless of the fact that
depends on the magnitude of
and the lock-in frequency. In other words, even though the size of
was varied according to the aforementioned factors, only the material thickness and configuration can affect the phase shift. Consequently, these phenomena imply that the control of
with the aim of stably detecting the thermal signal by the infrared camera would be unaffected when obtaining the real phase shift of the multi-layered structure during experimental LIT operation.
Figure 9 presents the phase values that were estimated by both experiments and FE simulations for various lock-in frequencies and bias input voltages. The ideal phases were calculated by Equation (10) by considering both the actual depth of heat source buried in specimen and the physical configurations of each stacked material. The experimental phases were analyzed by employing the full width at half-maximum (FWHM) value of the respective phase image in
Figure 6. The phase average of the circular area, which was decided by the FWHM of its phase image, determined the experimental phase, and numerical phases were calculated based on the transient thermal response profiles as presented in
Figure 7. The phase shift results of numerical simulation shown in
Figure 9 are calculated for 4 V of the bias voltage because the phase shifts were the same for different bias input voltages. As shown in
Figure 9, the phase shifts of the experiment and numerical simulation simultaneously increased as the lock-in frequency increased.
In case of two-layer SSHSC (
Figure 9a), the averages of the experimental phase for the applied lock-in frequencies were estimated as 13.6, 21.2, 25.07, 27.7, and 33.62 degrees, respectively, and the percent deviation of each numerical phase for the corresponding lock-in frequency was evaluated as 7.11%, 9.35%, 5.68%, 9.83%, and 7.36%, respectively. The difference between the ideal phase and experimental phase average for the respective lock-in frequency was estimated as 0.9, 0.69, 0.05, 1.29, and 1.19 degrees, respectively, on the basis of the ideal phase. Furthermore, the difference between the ideal phase and numerical phase average for the respective lock-in frequency was estimated as 1.87, 1.29, 1.47, 1.43, and 1.28 degrees, respectively, on the basis of the ideal phase.
In case of the three-layer SSHSC (
Figure 9b), the experimental phase averages were estimated as 10.63, 13.32, 15.99, 18.08, and 21.94, respectively, for the corresponding lock-in frequency, and the percent deviation with each numerical phase for the corresponding lock-in frequency was evaluated as 23.41%, 3.15%, 3.72%, 9.75%, and 4.59%, respectively. The difference between the ideal phase and experimental phase average for the respective lock-in frequency was estimated to be 1.31, 0.13, 0.16, 0.56, and 1.09 degrees, respectively, on the basis of the ideal phase. In addition, the difference between the ideal phase and numerical phase average for the respective lock-in frequency was estimated as 1.18, 0.29, 0.76, 1.2, and 2.1 degrees, respectively, on the basis of the ideal phase.
Following the relationship between the phase and depth described by Equation (10), the depth of the heat source buried within each SSHSC was estimated by the experimentally and numerically acquired phase shift results provided in
Table 2 at different lock-in frequencies. In the case of the two-layer SSHSC with an actual depth of 1342 μm, the depth for the experimental averages was estimated as 1258.63, 1387.28, 1339.52, 1282.08, and 1391.43 μm, respectively, and the depth for the numerical averages was calculated as 1169.11, 1257.51, 1263.38, 1408.12, and 1289.06 μm, respectively, for the applied lock-in frequencies. The difference between the actual depth and experimental depth average for the respective lock-in frequency was estimated as 83.37, 45.28, 2.48, 59.92, and 49.43 μm, respectively, which corresponds to 6.21%, 3.37%, 0.18%, 4.46%, and 3.68% on the basis of the actual depth. Further, the difference between the actual depth and numerical depth average for the respective lock-in frequency was estimated as 172.89, 84.49, 78.62, 66.12, and 52.94 μm, respectively, which corresponds to 12.88%, 6.3%, 5.86%, 4.93%, and 3.94% on the basis of the actual depth.
In case of the three-layer SSHSC with an actual depth of 170 μm, the depth for the experimental averages was estimated as 193.88, 171.70, 168.28, 164.87, and 178.88 μm and the depth for the numerical averages was calculated as 148.50, 166.29, 161.98, 180.96, and 187.09 μm, respectively, for the applied lock-in frequencies. The difference between the actual depth and experimental depth average for the respective lock-in frequency was estimated as 23.88, 1.70, 1.72, 5.13, and 8.88 μm, respectively, which corresponds to 14.05%, 1.01%, 1.01%, 3.02%, and 5.22% on the basis of the actual depth. Further, the difference between the actual depth and numerical depth average for the respective lock-in frequency was estimated as 21.50, 3.71, 8.02, 10.96, and 17.09 μm, respectively, which corresponds to 12.64%, 2.17%, 4.69%, 6.44%, and 10.05% on the basis of the actual depth.
In the depth estimation of the heat source in the two-layer SSHSC, deviations of 0.18% (2.48 μm) and 3.94% (52.94 μm) were the best values obtained for the experimental and numerical simulation comparison with the actual depth, respectively, and the deviations of 1.01% (1.70 μm) and 2.17% (3.71 μm) were the best for experimental and numerical simulation in comparison with the actual depth, respectively, in the application of three-layer SSHSC. These statistics summarized the results of both the experiments and the numerical simulation for the two different target specimens, and the feasibility of this experimental and numerical approach for depth estimation was well demonstrated.
The numerical simulation was additionally carried out to investigate the effects of the volumetric heat source configuration on the depth estimation, mimicking the 3D TSV integration package. The TSV volumetric heat source was assumed to be a cylindrical shape with a diameter of 30 µm and height of 50 µm, and was buried under adhesive, silicon, and copper layers with a total thickness of 140 µm, as shown in
Figure 10. The phase shift and depth with different lock-in frequencies were assessed by following the numerical approach used in this study, and are presented in
Figure 10 with the height of the buried TSV heat source. As expected, the values of the calculated phase shift increased with an increase in the lock-in frequency. However, the estimated depth at lock-in frequencies of 2 and 4 Hz fell short of the location of the TSV heat source, whereas this value at the higher frequencies of 6, 8, and 10 Hz of the lock-in frequency was within range of the TSV height. Similar to what we found in the results of the three-layer SSHSC (thin), the estimated depth at the lower lock-in frequency has a relatively larger error compared to that at the higher lock-in frequency. This trend coincided well with the results of Kijkanjanapaiboon et al. [
19], who determined that, when a specimen becomes thinner at a lower lock-in frequency, the difference in its phase shifts becomes significant.